POPULAR LECTURES ON 
 SCIENTIFIC SUBJECTS
 
 POPULAR LECTURES ON 
 SCIENTIFIC SUBJECTS 
 
 Bv SIR JOHN F. W. HERSCHEL, BART., K.H. 
 
 M.A. J D.C.L. ; F.R.S. L. AND E. ; HON. M.R.I. A. ; F.R.A.S. ; M.C.U.P.S. 
 
 MEMBER OF THE INSTITUTE OF FRANCE ; AND 
 
 CORRESPONDENT, ASSOCIATE, HONORARY OR ORDINARY MEMBER OF VARIOUS OTHER 
 ACADEMIES AND INSTITUTIONS 
 
 LONDON 
 DALDY, ISBISTER & CO. 
 
 56, LUDGATE HILL 
 1876
 
 SRLE 
 
 URL' 
 
 PREFACE. 
 
 HE three first lectures in the following 
 collection on Earthquakes and Vol- 
 canoes, on the Sun, and on Comets 
 were delivered by the Author to a vil- 
 lage audience, in the school-house of the parish 
 of Hawkhurst, in Kent, his place of residence. 
 They were subsequently printed as contributions 
 to the pages of that excellent and useful periodi- 
 cal, Good Words, in which they were followed 
 by those " On the Weather and Weather Pro- 
 phets," " On Celestial Measurings and Weigh- 
 ings," and " On Light," the latter assuming in its 
 progress the dimensions of a little elementary 
 
 1 C ^ ' 
 
 -*- v--- .- ^ ,
 
 PREFACE. 
 
 treatise, adapted for the perusal of non-mathe- 
 matical readers. On the completion of this, it was 
 suggested by the publisher of that work to collect 
 and reprint them together, a proposal the more 
 welcome, as it afforded an opportunity for bring- 
 ing together several other pieces of a somewhat 
 similar character, some of which, though not 
 properly characterized as " Lectures," it seemed 
 desirable to reproduce. More especially, it ap- 
 peared to the Author an imperative duty to let 
 no opportunity pass of recalling the attention of the 
 public to the great question of the proposed aban- 
 donment of our national system of weights and 
 measures, and adoption in its stead of the metri- 
 cal system of the French, with its unit, the metre, 
 in place of the English yard, which has been so 
 actively, and, in his opinion, so mischievously 
 urged on Parliament ; the agitation in favour of 
 which only sleeps for the present, in the view of 
 allowing the public mind to familiarize itself with 
 the idea under a Permissive Act, to be assuredly 
 brought forward again with renewed activity, and 
 under a more intense and prolonged pressure (to 
 be met by a more concentrated and determined 
 resistance), on no distant occasion.
 
 PREFACE. 
 
 No apology will be considered necessary for re- 
 producing the little piece " On the Absorption of 
 Light/' the thirteenth in order of this collection. 
 Though it does not pretend to anticipate any of 
 the later experimental researches, and the reason- 
 ings grounded on them for concluding the con- 
 version of motion into heat, electricity, and mag- 
 netism, it is, nevertheless, a step (though a small 
 one) in that direction, by showing that a state of 
 apparent rest in a material body is not incom- 
 patible with the internal propagation ad infinitum 
 within it of movement impressed on it from with- 
 out. It is very conceivable that the internal or 
 atomic organization of ponderable matter may be 
 such as to concentrate and localize, in its individual 
 molecular groups, the broken -up and dispersed 
 undulations caused by any external shock ; and so 
 preserve them from attaining that final state of 
 complete mutual counteraction which is there 
 contemplated. 
 
 Some slight alterations in the wording, and 
 additions (not in every instance unimportant) to 
 the matter of the several Essays here reproduced, 
 have been made ; as well as, here and there, some 
 numerical corrections. In particular, the last little
 
 xii PREFACE. 
 
 piece, "On the Estimation of Skill in Target- 
 Shooting," has for one of its objects the correction 
 of an error in one of the Author's former works, 
 while, at the same time, calling attention to a 
 subject generally, and even nationally, interest- 
 ing. 
 
 COLLINGWOOD, June 8. 1866.
 
 CONTENTS. 
 
 TOB.PACE, '. . 
 
 T. ABOUT VOLCANOS AND EARTHQUAKES, , f I 
 
 II. THE SUN, -. . . . t i 47 
 
 III. ON COMETS, i . . . . .91 
 
 IV. THE WEATHER AND WEATHER PROPHETS, . . 142 
 V. CELESTIAL MEASURINGS AND WEIGHINGS, . . 176 
 
 VI. ON LIGHT. PART I. REFLEXION REFRACTION 
 
 DISPERSION COLOUR ABSORPTION, . . 2ig 
 VII. ON LIGHT. PART II. THEORIES OF LIGHT INTER- 
 FERENCES DIFFRACTION, .... 268 
 
 VIII. ON LIGHT. PART III. DOUBL3 REFRACTION POL- 
 ARIZATION, ...... 340 
 
 IX. ON SENSORIAL VISION, .... 400 
 
 X. THE YARD, THE PENDULUM, AND THE METRE, . 419 
 
 XI. ON ATOMS. A DIALOGUE, . . 452 
 
 XII. ON THE ORIGIN OF FORCE, .... 460 
 
 XIII. ON THE ABSORPTION OF LIGHT BY COLOURED MEDIA, 
 VIEWED IN CONNEXION WITH THE UNDULATORY 
 
 THEORY, ...... 476 
 
 XIV. ONVriE ESTIMATION OF SKILL IN TARGET-SHOOTING, 495 
 b
 
 LECTURE L 
 
 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 PURPOSE in this Lecture to say something 
 about volcanos and earthquakes. It is a 
 subject I have thought a good deal about, 
 and seen a little of, for though I have 
 never been so fortunate as to have seen a volcano 
 in eruption, or to have been shaken out of my bed 
 by an earthquake, still I have climbed the cones of 
 Vesuvius and Etna, hammer in hand and barometer on 
 back, and have wandered over and geologized among, 
 I believe, nearly all the principal scenes of extinct vol- 
 canic activity in Europe, those of Spain excepted. 
 
 (2.) Every one knows that a volcano is a mountain 
 that vomits out fire, and smoke, and cinders, and melted 
 lava, and sulphur, and steam, and gases, and all kinds 
 of horrible things ; nay, even sometimes mud, and boil- 
 ing water, and fishes ; and everybody has heard or read 
 of the earth opening, and swallowing up man and beast, 
 
 A
 
 2 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 and houses and churches ; and closing on them with a 
 snap, and smashing them to pieces ; and then perhaps 
 opening again, and casting them out with a flood of 
 dirty water from some river or lake that had been 
 gulped down with them. Now, all this, and much 
 more, is literally true, and has happened over and over 
 again ; and when we nave imagined it all, we shall have 
 formed a tolerably correct notion of some at least of 
 these visitations. And perhaps some may have been 
 tempted to ask why and how it is that God has per- 
 mitted this fair earth to be visited with such destruction. 
 It can hardly be for the sins of men : for when these 
 things occur they involve alike the innocent and the 
 guilty; and besides, the volcano and the earthquake 
 were raging on this earth with as much, nay greater 
 violence, thousands and thousands of years before man 
 ever set his foot upon it. But perhaps, on the other 
 hand, it may have occurred to some to ask themselves 
 whether it is not just possible that these ugly affairs are 
 sent among us for some beneficent purpose; or at all 
 events that they may form part and parcel of some, great 
 scheme of providential arrangement which is at work for 
 good, and not for ill. A ship sometimes strikes on a 
 rock, and all on board perish ; a railway train runs into 
 another, or breaks down, and then wounds and contu- 
 sions are the order of the day ; but nobody doubts that 
 navigation and railway communication are great bless- 
 ings. None of the great natural provisions for produc- 
 ing good are exempt in their workings from producing 
 occasional mischief. Storms disperse and dilute pesti-
 
 ABOUT VOLCANOS AND EARTHQUAKES. 3 
 
 lential vapours, and lightnings decompose and destroy 
 them j but both the one and the other often annihilate 
 the works of man, and inflict upon him sudden death. 
 Well, then, I think I shall be able to show that the vol- 
 cano and the earthquake, dreadful as they are, as local 
 and temporary visitations, are in fact unavoidable (I had 
 almost said necessary) incidents in a vast system of 
 action to which we owe the very ground we stand upon, 
 the very land we inhabit, without which neither man, 
 beast, nor bird would have a place for their existence, and 
 the world would be the habitation of nothing but fishes. 
 (3.) Now, to make this clear, I must go a little out 
 of my way and say something about the first principles 
 of geology. Geology does not pretend to go back to 
 the creation of the world, or concern itself about its 
 primitive state, but it does concern itself with the 
 changes it sees going on in it now, and with the evi- 
 dence of a long series of such changes it can produce in 
 the most unmistakable features of the structure of our 
 rocks and soil, and the way in which they lie one on 
 the other. As to what we SEE going on. We see every- 
 where, and along every coast-line, the sea warring 
 against the land, and everywhere overcoming it j wearing 
 and eating it down, and battering it to pieces ; grinding 
 those pieces to powder ; carrying that powder away, and 
 spreading it out over its own bottom, by the continued 
 effect of the tides and currents. Look at our chalk 
 cliffs, which once, no doubt, extended across the Chan- 
 nel to the similar cliffs on the French coast. What 
 do we see 1 ? Precipices cut down to the sea-beach,
 
 4 ABOUT YOLCANOS AND EARTHQUAKES. 
 
 constantly hammered by the waves and constantly 
 crumbling : the beach itself made of the flints outstand- 
 ing after the softer chalk has been ground down and 
 washed away; themselves grinding one another under 
 the same ceaseless discipline ; first rounded into pebbles, 
 then worn into sand, and then carried out farther and 
 farther down the slope, to be replaced by fresh ones 
 from the same source. 
 
 (4.) Well: the same thing is going on everywhere, round 
 ei>ery coast of Europe, Asia, Africa, and America. Foot 
 by foot or inch by inch, month by month or century by 
 century, down everything MUST go. Time is as nothing 
 in geology. And what the sea is doing the rivers are 
 helping it to do. Look at the sand-banks at the mouth 
 of the Thames. What are they but the materials of our 
 island carried out to sea by the stream] The Ganges 
 carries away from the soil of India, and delivers into 
 the sea, twice as much solid substance weekly as is con- 
 tained in the great pyramid of Egypt. The Irawaddy 
 sweeps off from Burmah 62 cubic feet of earth in every 
 second of time on an average, and there are 86,400 sec- 
 onds in every day, and 365 days in every year; and so on 
 for the other rivers. What has become of all that great 
 bed of chalk which once covered all the weald of Kent, 
 and formed a continuous mass from Ramsgate and Dover 
 to Beechy Head, running inland to Madamscourt Hill and 
 Seven Oaks? All clean gone, and swept out into the 
 bosom of the Atlantic, and there forming other chalk- 
 beds. Now, geology assures us, on the most conclusive 
 and undeniable evidence, that ALL our present land, all
 
 ABOUT VOLCANOS AND EARTHQUAKES. 5 
 
 our continents and islands, have been formed in this way 
 out of the ruins of former ones. The old ones which 
 existed at the beginning of things have all perished, and 
 what we now stand upon has most assuredly been, at one 
 time or other, perhaps manv times, the bottom of the sea. 
 
 (5.) Well, then, there is power enough at work, and it 
 has been at work long enough, utterly to have cleared 
 away and spread over the bed of the sea all our present 
 existing continents and islands, had they been placed 
 where they are at the creation of the world ; and from 
 this it follows, as clear as demonstration can make it, 
 that without some process of renovation or restoration to 
 act in antagonism to this destructive work of old Nep- 
 tune, there would not now be remaining a foot of dry 
 land for living thing to stand upon. 
 
 (6.) Now, what is this process of restoration? Let 
 the volcano and the earthquake tell their tale. Let the 
 earthquake tell how, within the memory of man under 
 the eyesight of eye-witnesses, one of whom (Mrs Graham) 
 has described the fact the whole coast line of Chili, 
 for 100 miles about Valparaiso, with the mighty chain 
 of the Andes mountains to which the Alps shrink into 
 insignificance was hoisted at one blow (in a single 
 night, Nov. 19, A.D. 1822) from two to seven feet above 
 its former level, leaving the beach below the old low water- 
 mark high and dry; leaving the shell-fish sticking on 
 the rocks out of reach of water; leaving the seaweed 
 rotting in the air, or rather drying up to dust under 
 the burning sun of a coast where rain never falls. The 
 ancients had a fable of Titan hurled from heaven and
 
 6 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 buried under Etna, and by his struggles causing the 
 earthquakes that desolated Sicily. But here we have an 
 exhibition of Titanic forces on a far mightier scale. One 
 of the Andes upheaved on this occasion was the gigantic 
 mass of Aconcagua, which overlooks Valparaiso. To 
 bring home to the mind the conception of such an effort, 
 we must form a clear idea of what sort of mountain this 
 is. It is nearly 24,000 feet in height. Chimborazo, the 
 loftiest of the volcanic cones of the Andes, is lower by 
 2500 feet ; and yet Etna, with Vesuvius at the top of it, 
 and another Vesuvius piled on that, would little more than 
 surpass the midway height of the snow-covered portion of 
 that cone, which is one of the many chimneys by which 
 the hidden fires of the Andes find vent. On the occa- 
 sion I am speaking of, at least 10,000 square miles of 
 country were estimated as having been upheaved, and 
 the upheaval was not confined to the land, but extended 
 far away to sea, which was proved by the soundings off 
 Valparaiso, and along the coast, having been found con- 
 siderably shallower than they were before the shock. 
 
 (7.) Again, in the year 1819, in an earthquake in 
 India, in the district of Cutch, bordering on the Indus, 
 a tract of country more tnaii ity miles long and sixteen 
 broad was suddenly raised ten feet above its former 
 level. The raised portion still stands up above the un- 
 raised, like a long perpendicular wall, which is known by 
 the name of the" Ullah Bund," or "God's Wall" And 
 again, in 1538, in that convulsion which threw up the 
 Monte Nuovo (New Mountain), a cone of ashes 450 
 feet high, in a single night ; the whole coast of Pozzuoli,
 
 ABOUT VOLCANOS AND EARTHQUAKES. J 
 
 near Naples, was raised twenty feet above its former 
 level, and remains so permanently upheaved to this day. 
 And I could mention innumerable other instances of the 
 same kind.* 
 
 (8.) This, then, is the manner in which the earthquake 
 does its work ; and it is always at work. Somewhere or 
 other in the world, there is perhaps not a day, certainly 
 not a month, without an earthquake. In those districts 
 of South and Central America, where the great chain of 
 volcanic cones is situated Chimborazo, Cotopaxi, and 
 a long list with names unmentionable, or at least unpro- 
 nounceable the inhabitants no more think of counting 
 earthquake shocks than we do of counting showers of. 
 rain. Indeed, in some places along that coast, a shower 
 is a greater rarity. Even in our own island, near Perth, 
 a year seldom passes without a shock, happily, within 
 the records of history, never powerful enough to do any 
 mischief. 
 
 (9.) It is not everywhere that this process goes on by 
 fits and starts. For instance, the northern gulfs, and 
 borders of the Baltic Sea, are steadily shallowing: and 
 the whole mass of Scandinavia, including Norway, 
 Sweden, and Lapland, is rising o^t of the sea at the 
 average rate of about two feet per century. But as this 
 fact (which is perfectly well established by reference to 
 ancient high and low water-marks) is not so evidently 
 connected with the action of earthquakes, I shall not 
 further refer to it just now. All that I want to show is, 
 
 * Not that earthquakes always raise the soil ; there are plenty 
 of instances of subsidence, etc.
 
 8 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 that there is a great cycle of changes going on, in which 
 the earthquake and volcano act a very conspicuous part, 
 and that part a restorative and conservative one; in oppo- 
 sition to the steadily destructive and levelling action of 
 the ocean waters. 
 
 (10.) How this can happen ; what can be the origin of 
 such an enormous power thus occasionally exerting 
 itself, will no doubt seem very marvellous little short, 
 indeed, of miraculous intervention but the mystery, 
 after all, is not quite so great as at first it seems. We 
 are permitted to look a little way into these great secrets 
 of nature ; not far enough, indeed, to clear up every 
 difficulty, but- quite enough to penetrate us with admira- 
 tion of that wonderful system of counterbalances and 
 compensations ; that adjustment of causes and conse- 
 quences, by which, throughout all nature, evils are made 
 to work their own cure ; life to spring out of death ; and 
 renovation to tread in the steps and efface the vestiges 
 of decay. 
 
 (n.) The key to the whole affair is to be found in the 
 central heat of the earth. This is no scientific dream, 
 no theoretical notion, but a fact established by direct 
 evidence up to a certain point, and standing out from 
 plain facts as a matter of unavoidable conclusion, in a 
 hundred ways. 
 
 (12.) We all know that when we go into a cellar out of 
 a summer sun, it feels cool; but when we go into it out 
 of a wintry frost it is warm. The fact is, that a cellar, 
 or a well, or any pit of a moderate depth, has always, 
 day and night, summer and winter, the same degree of
 
 ABOUT VOLCANOS AND EARTHQUAKES. 9 
 
 warmth, the same temperature, as it is called : and that 
 always and everywhere is the same, or nearly the same, 
 as the average warmth of the climate of the place. 
 Forty or fifty feet deep in the ground, a thermometer 
 here, in this spot,* would always mark the same degree, 
 49 that is, or seventeen degrees above the freezing 
 point. Under the equator, at the same depth, it always 
 stands at 84, which is our hot summer heat, but which 
 there is the average heat of the whole year. And this is 
 so everywhere. Just at the surface, or a few inches 
 below it, the ground is warm in the daytime, cool at 
 night : at two or three feet deep the difference of day 
 and night is hardly perceptible, but that of summer and 
 winter is considerable. But at forty or fifty feet this 
 difference also disappears, and you find a perfectly fixed, 
 uniform degree of warmth, day and night ; summer and 
 winter ; year after year. 
 
 (13.) But when we go deeper, as, for instance, down 
 into mines or coal-pits, this one broad and general fact is 
 always observed, everywhere, in all countries, in all 
 latitudes, in all climates, wherever there are mines, or 
 deep subterranean caves, the deeper you go, the hotter 
 the earth is found to be. In one and the same mine, 
 each particular depth has its own particular degree of 
 heat, which never varies : but the lower always the hotter ; 
 and that not by a trifling, but what may well be called 
 an astonishingly rapid rate of increase, about a degree of 
 the thermometer additional warmth for every 90 feet of 
 additional depth, which is about 58 per mile ! so that, 
 * At Hawkhurst in Kent.
 
 IO ABOUT VOLCANOS AND EARTHQUAKES. 
 
 if we had a shaft sunk a mile deep, we should find in the 
 rock a heat of 105, which is much hotter than the 
 hottest summer day ever experienced in England. 
 
 (14.) It is not everywhere, however, that it is worth 
 while to sink a shaft to any great depth ; but borings for 
 water (in what are called Artesian wells) are often made 
 to enormous depths, and the water always comes up hot ; 
 and the deeper the boring, the hotter the water. There 
 is a very famous boring of this sort in Paris, at La 
 Crenelle. The water rises from a depth of 1794 feet, 
 and its temperature is 82 of our scale, which is almost 
 that of the equator. And, again, at Salzwerth, in Oeyn- 
 hausen, in Germany, in a boring for salt-springs 2144 
 feet deep, the salt water comes up with a still higher 
 heat, viz., 91. Then, again, we have natural hot-water 
 springs, which rise, it is true, from depths we have no 
 means of ascertaining ; but which, from the earliest 
 recorded times, have always maintained the .same heat. 
 At Bath, for instance, the hottest well is 117 Fahr. On 
 the Arkansas River, in the United States, is a spring of 
 1 80; which is scalding hot; and that out of the neigh- 
 bourhood of any volcano. 
 
 (15.) Now, only consider what sort of a conclusion 
 this lands us in. This globe of ours is 8000 miles in 
 diameter ; a mile deep on its surface is a mere scratch. 
 If a man had twenty greatcoats on, and I found under 
 the first a warmth of 60 above the external air, I should 
 expect to find 60 more under the second, and 60 more 
 under the third, and so on ; and, within all, no man, but 
 a mass of red-hot iron. Just so with the outside crust of
 
 ABOUT VOLCANOS AND EARTHQUAKES. II 
 
 the earth. Every mile thick is such a greatcoat, and at 
 20 miles depth, according to this rate, the ground must 
 be fully red-hot; and at no such very great depth beyond, 
 either the whole must be melted, or only the most in- 
 fusible and intractable kinds of material, such as our fire- 
 clays and flints, would present some degree of solidity. 
 
 (16.) In short, what the icefloes and icebergs are to 
 the polar seas, so we shall come to regard our continents 
 and mountain-ranges in relation to the ocean of melted 
 matter beneath, I do not mean to say there is no solid 
 central mass ; there may be one, or there may not, and, 
 upon the whole, I think it likely enough that there is 
 kept solid, in spite of the heat, by the enormous pres- 
 sure ; but that has nothing to do with my present argu- 
 ment. All that I contend for is this, Grant me a sea 
 of liquid fire, on which we are all floating, land and 
 sea; for the bottom of the sea, anyhow, will not come 
 nearly down to the lava level. The sea is probably 
 nowhere more than five or six miles deep, which is far 
 enough above that level to keep its bed from becoming 
 red-hot. 
 
 (17.) Well, now, the land is perpetually wearing down, 
 and the materials being carried out to sea. The coat 
 of heavier matter is thinning off towards the land, and 
 thickening over all the bed of the sea. What must 
 happen? If a ship float even on her keel, transfer 
 weight from the starboard to the larboard side, will she 
 continue to float even ? No, certainly. She will heel 
 over to larboard. Many a good ship has gone to the 
 bottom in this way. If the continents be lightened,
 
 12 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 they will rise ; if the bed of the sea receive additional 
 weight, it will sink. The bottom of the Pacific is sink- 
 ing, in point of fact. Not that the Pacific is becoming 
 deeper. This seems a paradox ; but it is easily explained. 
 The whole bed of the sea is in the act of being pressed 
 down by the laying on of new solid substance over its bottom. 
 The new bottom then is laid upon the old, and so the 
 actual bed of the ocean remains at or nearly at the same 
 distance from the surface water. But what becomes of 
 the islands ? They form part and parcel of the old 
 bottom ; and Dr Darwin has shown, by the most curious 
 and convincing proofs, that they are sinking, and have 
 been sinking for ages, and are only kept above water by 
 what, think you ? By the labours of the coral insects, 
 which always build up to the surface ! 
 
 (18.) It is impossible but that this increase of pressure 
 in some places and relief in others must be very un- 
 equal in their bearings. So that at some place or other 
 this solid floating crust must be brought into a state of 
 strain, and if there be a weaK or a soft part, a crack will 
 at last take place. When this happens, down goes the 
 land on the heavy side, and up on the light side. Now 
 this is exactly what took place in the earthquake which 
 raised the Ullah Bund in Cutch. I have told you of a 
 great crack drawn across the country, not far from the 
 coast line ; the inland country rose ten feet, but much of 
 the sea-coast, and probably a large tract in the bed of 
 the Indian Ocean, sank considerably below its former 
 level And just as you see when a crack takes place in 
 ice, the water oozes up ; so this kind of thing is always,
 
 ABOUT VOLCANOS AND EARTHQUAKES. 13 
 
 or almost always, followed by an upburst of the subter- 
 ranean fiery matter. The earthquake of Cutch was 
 terminated by the outbreak of a volcano at the town of 
 Bhooi, which it destroyed. 
 
 (19.) Now where, following out this idea, should we 
 naturally expect such cracks and outbreaks to happen ] 
 Why, of course, along those lines where the relief of 
 pressure on the land side is the greatest, and also its 
 increase on the sea side ; that is to say, along or in the 
 neighbourhood of the sea-coasts, where the destruction 
 of the land is going on with most activity. Well, now, 
 it is a remarkable fact in the history of volcanos, that 
 there is hardly an instance of an active volcano at any 
 considerable distance from the sea-coast. All the great 
 volcanic chain of the Andes is close to the western 
 coast line of America. Etna is close to the sea ; so is 
 Vesuvius ; Teneriffe is very near the African coast ; 
 Mount Erebus is on the edge of the great Antarctic 
 continent. Out of 225 volcanos which are known to 
 have been in actual eruption over the whole earth 
 within the last 150 years, I remember only a single 
 instance of one more than 320 miles from the sea, and 
 even that is on the edge of the Caspian, the largest of 
 all the inland seas I mean Mount Demawend in Persia. 
 
 (20.) Suppose from this, or from any other cause, a 
 crack to take place in the solid crust of the earth. Don't 
 imagine that the melted matter below will simply ooze 
 up quietly, as water does from under an ice-crack. No 
 such thing. There is an element in the case we have 
 not considered : steam and condensed gases. We aU
 
 14 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 know what happens when a crack takes place in a high- 
 pressure steam-boiler, with what violence the contents 
 escape, and what havoc takes place. Now there is no 
 doubt that among the minerals of the subterranean 
 world, there is water in abundance, and sulphur, and 
 many other vaporizable substances, all kept subdued 
 and repressed by the enormous pressure. Let this pres- 
 sure be relieved, and forth they rush, and the nearer 
 they approach the surface the more they expand, and 
 the greater is the explosive force they acquire ; till at 
 length, after more or fewer preparatory shocks, each 
 accompanied with progressive weakening of the over- 
 lying strata, the surface finally breaks up, and forth rushes 
 the imprisoned power, with all the awful violence of a 
 volcanic eruption.. 
 
 (21.) Certainly a volcano does seem to be a very bad 
 neighbour ; and yet it affords a compensation in the ex- 
 traordinary richness of the volcanic soil, and the fertil- 
 izing quality of the ashes thrown out. The flanks of 
 Somma (the exterior crater of Vesuvius) are covered 
 with vineyards producing wonderful wine, and whoever 
 has visited Naples, will not fail to be astonished at the 
 productiveness of the volcanized territory as contrasted 
 with the barrenness of the limestone rocks bordering on 
 it. There you will see the amazing sight (as an English 
 farmer would call it) of a triple crop growing at once 
 on the same soil ; a vineyard, an orchard, and a corn- 
 field all in one. A magnificent wheat crop, five or six 
 feet high, overhung with clustering grape-vines swinging 
 from one apple or pear tree to another in the most luxu-
 
 ABOUT VOLCANOS AND EARTHQUAKES. 15 
 
 riant festoons ! When I visited Somma, to see the 
 country where the celebrated wine, the Lacryma Christi, 
 is grown, it was the festival of the Madonna del Arco. 
 Her church was crowded to suffocation with a hot and 
 dusty assemblage of the peasantry. The fine impalpable 
 volcanic dust was everywhere; in your eyes, in your 
 mouth, begriming every pore ; and there I saw what I 
 shall never forget. Jammed among the crowd, I felt 
 something jostling my legs. Looking down, and the 
 crowd making way, I beheld a line of worshippers crawl- 
 ing on their hands and knees from the door of the 
 church to the altar, licking the dusty pavement all the 
 way with their tongues, positively applied to the ground 
 and no mistake. No trifling dose of Lacryma would be 
 required to wash down what they must have swallowed 
 on that journey, and I have no doubt it was administered 
 pretty copiously after the penance was over. 
 
 (22.) Now I come to consider the manner in which 
 an earthquake is propagated from place to place ; how it 
 travels, in short. It runs along the earth precisely in 
 the same manner, and according to the same mechanical 
 laws as a wave along the sea, or rather as the waves of 
 sound run along the air, but quicker. The earthquake 
 which destroyed Lisbon ran out from thence, as from a 
 centre, in all directions, at a rate averaging about twenty 
 miles per minute, as far as could be gathered from a 
 comparison of the times of its occurrence at different 
 places ; but there is little doubt that it must have been 
 retarded by having to traverse all sorts of ground, for a 
 blow or shock of any description is conveyed through the
 
 t6 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 substance on which it is delivered with the rapidity of 
 sound in that substance. Perhaps it may be new to many 
 who hear me to be told that sound is conveyed by water, 
 by stone, by iron, and indeed by everything, and at a dif- 
 ferent rate for each. In air it travels at the rate of about 
 1140 feet per second, or about 13 miles in a minute. In 
 water much faster, more than four times as fast (4700 
 feet). In iron ten times as fast (11,400 feet), or about 
 130 miles in a minute, so that a blow delivered endways 
 at one end of an iron rod, 130 miles long, would only 
 reach the other after the lapse of a minute, and a 
 pull at one end of an iron wire of that length, would 
 require a minute before it would be felt at the other. 
 But the substance of the earth through which the shock 
 is conveyed is not only far less elastic than iron, but it 
 does not form a coherent, connected body ; it is full of 
 interruptions, cracks, loose materials, and all these tend 
 to deaden and retard the shock : and putting together all 
 the accounts of all the earthquakes that have been ex- 
 actly observed, their rate of travel may be taken to vary 
 from as low as 12 or 13 miles a minute to 70 or 80 : 
 but perhaps the low velocities arise from oblique waves. 
 (23.) The way, then, that we may conceive an earth- 
 quake to travel is this, I shall take the case which is 
 most common, when the motion of the ground to-and- 
 fro is horizontal. How far each particular spot on the 
 surface of the ground is actually pushed from its place 
 there is no way of ascertaining, since all the surrounding 
 objects receive the same impulse almost at the same in- 
 stant of time, but there are many indications that it is
 
 ABOUT VOLCANOS AND EARTHQUAKES. 17 
 
 often several yards. In the earthquake of Cutch, which 
 I have mentioned, trees were seen to flog the ground 
 with their branches, which proves that their stems must 
 have been jerked suddenly away for some considerable 
 distance and as suddenly pushed back; and the same 
 conclusion follows from the sudden rise of the water of 
 lakes on the side where the shock reaches them, and its 
 fall on the opposite side ; the bed of the lake has been 
 jerked away for a certain distance from under the water 
 and pulled back. 
 
 (24.) Now, suppose a row of sixty persons, standing 
 a mile apart from each other, in a straight line, in the 
 direction in which the shock travels ; at a rate, we will 
 suppose, of sixty miles per minute : and let the ground 
 below the first get a sudden and violent shove, carrying 
 it a yard in the direction of the next. Since this shock 
 will not reach the next till after the lapse of one second 
 of time, it is clear that the space between the two will be 
 shortened by a yard, and the ground that is to say, not 
 the mere loose soil on the surface, but the whole mass of 
 solid rock below, down to an unknown depth com- 
 pressed, or driven into a smaller space. It is this com- 
 pression that carries the shock forwards. The elastic 
 force of the rocky matter, like a coiled spring acts both 
 ways ; it drives back the first man to his old place, and 
 shoves the second a yard nearer to the third ; and so on. 
 Instead of men place a row of tall buildings, or columns, 
 and they will tumble down in succession, the base flying 
 forwards, and leaving the tops behind to drop on the 
 soil on the side/aw* which the shock came. This is 
 
 a
 
 l8 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 just what was seen to happen in Messina in the great 
 Calabrian earthquake. As the shock ran along the 
 ground, the houses of the Faro were seen to topple 
 down in succession ; beginning at one end and running 
 on to the other, as if a succession of mines had been 
 sprung. In the earthquake in Cutch, a sentinel standing 
 at one end of a long straight line of wall, saw the wall 
 bow forward and recover itself; not all at once, but with 
 a swell like a wave running all along it with immense 
 rapidity. In this case it is evident that the earthquake 
 wave must have had its front oblique to the direction of 
 the wall (just as an obliquely-held ruler runs along the 
 edge of a page of paper while it advances, like a wave of 
 the sea, perpendicularly to its own length). 
 
 (25.) In reference to extinct volcanos, I may just 
 mention that any one who wishes to see some of the 
 finest specimens in Europe may do so by making a 
 couple of days' railway travel to Clermont, in the depart- 
 ment of the Puy de Dome in France. There he will 
 find a magnificent series of volcanic cones, fields of ashes, 
 streams of lavas, and basaltic terraces or platforms, 
 proving the volcanic action to have been continued for 
 countless ages before the present surface of the earth 
 was formed ; and all so clear that he who runs may read 
 their lesson- There can there be seen a configuration 
 of surface quite resembling what telescopes show in the 
 most volcanic districts of the moon. Let not my hearers 
 be startled : half the moon's face is covered with unmis- 
 takable craters of extinct volcanos. 
 
 (26.) Many of the lavas of Auvergne and the Puy de
 
 ABOUT VOLCANOS AND EARTHQUAKES. 19 
 
 Dome are basaltic; that is, consisting of columns placec 
 close together ; and some of the cones are quite com- 
 plete, and covered with loose ashes and cinders, just as 
 Vesuvius is at this hour. 
 
 (27.) In the study of these vast and awful phenomena 
 we are brought in contact with those immense and rude 
 powers of nature which seem to convey to the imagina- 
 tion the impress of brute force and lawless violence ; bu 1 
 it is not so. Such an idea is not more derogatory to the 
 wisdom and benevolence that prevails throughout all the 
 scheme of creation than it is in itself erroneous. In 
 their wildest paroxysms the rage of the volcano and the 
 earthquake is subject to great and immutable laws : 
 they feel the bridle and obey it. The volcano bellows 
 forth its pent-up overplus of energy, and sinks into long 
 and tranquil repose. The earthquake rolls away, ami 
 industry, that balm which nature knows how to shed 
 over every wound, effaces its traces, and festoons its 
 ruins with flowers. There is mighty and rough work to 
 be accomplished, and it cannot be done by gentle means. 
 It seems, no doubt, terrible, awful, perhaps harsh, that 
 twenty or thirty thousand lives should be swept away in 
 a moment by a sudden and unforeseen calamity ; but we 
 must remember that sooner or later every one of those 
 lives must be called for, and it is by no means the most 
 sudden end that is the most afflictive. It is well too that 
 we should contemplate occasionally, if it were only to 
 teach us humility and submission, the immense energies 
 which are everywhere at work in maintaining the system 
 of nature we see going on so smoothly and tranquilly
 
 20 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 \ 
 
 around us, and of which these furious outbreaks, after all, 
 are but minute, and for the moment unbalanced sur- 
 pluses in the great account. The energy requisite to 
 overthrow a mountain is as a drop in the ocean com- 
 pared with that which holds it in its place, and makes it 
 a mountain. Chemistry tells us that the forces con- 
 stantly in action to maintain a single grain of water in 
 its habitual state ; when only partially and sparingly let 
 loose in the form of electricity, would manifest them- 
 selves as a powerful flash of lightning.* And we learn 
 from optical science that in even the smallest element of 
 every material body, nay, even in what we call empty 
 space, there are forces in perpetual action to which even 
 such energies sink into insignificance. Yet, amid all 
 this, nature holds her even course : the flowers blossom ; 
 animals enjoy their brief span of existence; and man has 
 leisure and opportunity to contemplate and adore, secure 
 of the watchful care which provides for his well-being 
 at every instant that he is permitted to remain on earth. 
 
 ON THE HISTORY OF EARTHQUAKES AND VOLCANOS. 
 
 (28.) The first great earthquake of which any very 
 distinct knowledge has reached us is that which occurred 
 in the year 63 after our Saviour, which produced great 
 destruction in the neighbourhood of Vesuvius, and 
 shattered the cities of Pompeii and Herculaneum upon 
 the Bay of Naples, though it did not destroy them. 
 This earthquake is chiefly remarkable as having been 
 * Faraday : " Experimental Researches in Electricity," 853.
 
 ABOUT VOLCANOS AND EARTHQUAKES. 21 
 
 the forerunner and the warning (if that warning could 
 have been understood) of the first eruption of Vesuvius 
 on record, which followed sixteen years afterwards in 
 the year 79. Before that time none of the ancients had 
 any notion of its being a volcano, though Pompeii itself 
 is paved with its lava. The crater was probably filled, 
 or at least the bottom occupied, by a lake ; and we 
 read of it as the stronghold of the rebel chief Spartacus, 
 who, when lured there by the Roman army, escaped 
 with his followers by clambering up the steep sides by 
 the help of the wild vines that festooned them. The 
 ground since the first earthquake in 63 had often been 
 shaken by slight shocks, when at length, in August 79, 
 they became more numerous and violent, and, on the 
 night preceding the eruption, so tremendous as to 
 threaten everything with destruction. A morning oi 
 comparative repose succeeded, and the terrified inhab- 
 itants of those devoted towns no doubt breathed more 
 freely, and hoped the worst was over ; when, about one 
 o'clock in the afternoon, the Elder Pliny, who was 
 stationed in command of the Roman fleet at Misenum in 
 full view of Vesuvius, beheld a huge black cloud ascend- 
 ing from the mountain, which, " rising slowly always 
 higher," at last spread out aloft like the head of one of 
 those picturesque flat-topped pines which lorm such an 
 ornament of the Italian landscape. The meaning of 
 such a phenomenon was to Pliny and to every one a 
 mystery. We know now too well what it imports, and 
 they were not long left in doubt From that cloud 
 descended stones, ashes, and pumice ; and the cloud
 
 22 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 itself lowered down upon the surrounding country, 
 involving land and sea in profound darkness, pierced by 
 flashes of fire more vivid than lightning. These, with 
 the volumes of ashes that began to encumber the soil, 
 and which covered the sea with floating pumice-stone ; 
 the constant heaving of the ground ; and the sudden 
 recoil of the sea, form a picture which is wonderfully 
 well described by the Younger Pliny. His uncle, ani- 
 mated by an eager desire to know what was going on, 
 and to afford aid to the inhabitants of the towns, made 
 sail for the nearest point of the coast and landed ; but 
 was instantly .enveloped in the dense sulphureous vapour 
 that swept down from the mountain, and perished 
 miserably. 
 
 (29.) It does not seem that any lava flowed on that 
 occasion. Pompeii was buried under the ashes ; Her- 
 culaneum by a torrent of mud, probably the contents of 
 the crater, ejected at the first explosion. This was most 
 fortunate. We owe to it the preservation of some of 
 the most wonderful remains of antiquity. For it is not 
 yet much more than a century ago that, in digging a 
 well at Portici near Naples, the Theatre of Herculaneum 
 was discovered, some sixty feet under ground, then 
 houses, baths, statues, and, most interesting of all, a 
 library, full of books ; and those books still legible, and 
 among them the writings of some ancient authors which 
 had never before been met with, but which have now 
 been read, copied, and published, while hundreds and 
 hundreds, I am sorry to say, still remain unopened. 
 Pompeii was not buried so deep ; the walls of some of
 
 ABOUT VOLCANOS AND EARTHQUAKES. 23 
 
 the buildings appeared among the modern vineyards ; 
 and led to excavations, which were easy, the ashes being 
 light and loose. And there you now may walk through 
 the streets, enter the houses, and find the skeletons of 
 their inmates, some in the very act of trying to escape. 
 Nothing can be more strange and striking. 
 
 (30.) Since that time Vesuvius has been frequently 
 but very irregularly in eruption. The next after Pom- 
 peii was in the year 202, under Severus: and in 472 
 occurred an eruption so tremendous that all Europe was 
 covered by the ashes, and even Constantinople thrown 
 into alarm. This may seem to savour of the marvellous ; 
 but before I have done, I hope to show that it is 
 not beyond what we know of the power of existing 
 volcanos. 
 
 (31.) I shall not, of course, occupy attention with a 
 history of Vesuvius, but pass at once to the eruption of 
 1779, one of the most interesting on record, from the 
 excellent account given of it by Sir William Hamilton, 
 who was then resident at Naples as our Minister, and 
 watched it throughout with the eye of an artist as well 
 as the scrutiny of a philosopher. 
 
 (32.) In 1767, there had been a considerable erup- 
 tion, during which Pliny's account of the great pine-like, 
 flat-topped, spreading mass of smoke had been superbly 
 exemplified ; extending over the Island of Capri, which 
 is twenty-eight miles from Vesuvius. The showers of 
 ashes, the lava currents, the lightnings, thunderings, and 
 earthquakes were very dreadful ; but they were at ones 
 brought to a close when the mob insisted that the head
 
 24 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 of St Januarius should be brought out and shown to the 
 mountain ; and when this was done, all the uproar 
 ceased on the instant, and Vesuvius became as quiet 
 as a lamb ! 
 
 (33.) He did not continue so, however, and it would 
 have been well for Naples if the good Saint's head could 
 have been permanently fixed in some conspicuous place 
 in sight of the hill for from that time till the year 1779 
 it never was quiet. In the spring of that year it begin 
 to pour out lava ; and on one occasion, when Sir Wil- 
 liam Hamilton approached too near, the running stream 
 was on the point of surrounding him ; and the sulphure- 
 ous vapour cut off his retreat, so that his only mode of 
 escape was to walk across the lava, which, to his aston- 
 ishment, and, no doubt, to his great joy, he found 
 accompanied with no difficulty, and with no more incon- 
 venience than what proceeded from the radiation of heat 
 on his legs and feet from the scoria? and cinders with 
 which the external crust of the lava was loaded ; and 
 which in great measure intercepted and confined the 
 glowing heat of the ignited mass below. 
 
 (34.) In such cases, and when cooled down to a 
 certain point, the motion of the lava-stream is slow and 
 creeping; rather rolling over itself than flowing like a 
 river ; the top becoming the bottom, owing to the tough- 
 ness of the half-congealed crust. When it issues, how- 
 ever, from any accessible vent, it is described as perfectly 
 liquid, of an intense white heat, and spouting or welling 
 forth with extreme rapidity. So Sir Humphry Davy 
 described it m an eruption at which he was present/
 
 ABOUT VOLCANOS AND EARTHQUAKES. 25 
 
 and so Sir William Hamilton, in the eruption we are 
 now concerned with, saw it " bubbling up violently" 
 from one of its fountains on the slope of the volcano, 
 " with a hissing and crackling noise, like that of an arti- 
 ficial firework ; and forming, by the continual splashing 
 up of the vitrified matter, a sort of dome or arch over 
 the crevice from which it issued," which was all, inter- 
 nally, " red-hot like a heated oven." 
 
 (35.) However, as time went on, this quiet mode of 
 getting rid of its contents would no longer suffice, and 
 the usual symptoms of more violent action rumbling 
 noises and explosions within the mountain ; puffs of 
 smoke from its crater, and jets of red-hot stones and 
 ashes continued till the end of July, when they in- 
 creased to such a degree as to exhibit at night the most 
 beautiful firework imaginable. The eruption came to 
 its climax from the 5th to the loth of August, on the 
 former of which days, after the ejection of an enormous 
 volume of white clouds, piled like bales of the whitest 
 cotton, in a mass exceeding four times the height and 
 size of the mountain itself; the lava began to overflow 
 the rim of the crater, and stream in torrents down the 
 steep slope of the cone. This was continued till the 
 8th, when the great mass of the lava would seem to have 
 been evacuated, and no longer repressing by its weight 
 the free discharge of the imprisoned gases, allowed 
 what remained to be ejected in fountains of fire, carried 
 up to an immense height in the air. The description of 
 one of these I must give in the picturesque and vivid 
 words of Sir William Hamilton himself. " About nine
 
 26 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 o'clock," he says, on Sunday the 8th of August, " there 
 was a loud report, which shook the houses at Portici 
 and its neighbourhood to such a degree, as to alarm the 
 inhabitants and drive them out into the streets. Many 
 windows were broken, and as I have since seen, walls 
 cracked by the concussion of the air from that explosion. 
 .... In one instant a fountain of liquid transparent 
 fire began to rise, and gradually increasing, arrived 
 at so amazing a height, as to strike every one who 
 beheld it with the most awful astonishment. I shall 
 scarcely be credited when I assure you that, to 
 the best of my judgment, the height of this stupen- 
 dous column of fire could not be less than three 
 times that of Vesuvius itself; which, you know, rises 
 perpendicularly near 3700 feet above the level of 
 the sea." (The height by my own measurement in 
 1824 is 3920 feet). "Puffs of smoke, as black as can 
 possibly be imagined, succeeded one another hastily, 
 and accompanied the red-hot, transparent, and liquid 
 lava, interrupting its splendid brightness here and there 
 by patches of the darkest hue. Within these puffs of 
 smoke, at the very moment of their emission from the 
 crater, I could perceive a bright but pale electrical fire 
 playing about in zigzag lines. The liquid lava, mixed 
 with scoriae and stones, after having mounted, I verily 
 believe at least 10,000 feet, falling perpendicularly on 
 Vesuvius, covered its whole cone, part of that of Somma, 
 and the valley between them. The falling matter being 
 nearly as vivid and inflamed as that which was continu- 
 ally issuing fresh from the crater, formed with it one
 
 ABOUT VOLCANOS AND EARTHQUAKES. 2? 
 
 complete body of fire, which could not be less than two 
 miles and a half in breadth, and of the extraordinary 
 height above mentioned ; casting a heat to the distance 
 of at least six miles around it. The brushwood of the 
 mountain of Somma was soon in a flame, which, being 
 of a different tint from the deep red of the matter thrown 
 out from the volcano, and from the silvery blue of the 
 electrical fire, still added to the contrast of this most 
 extraordinary scene. After the column of fire had con- 
 tinued in full force for nearly half an hour, the erup- 
 tion ceased at once, and Vesuvius remained sullen and 
 silent. ' 
 
 (36.) The lightnings here described arose evidently in 
 part from the chemical activity of gaseous decomposi- 
 tions going forward, in part to the friction of steam, and 
 in part from the still more intense friction of the dust, 
 stones, and ashes encountering one another in the air, in 
 analogy to the electric manifestations which accompany 
 the dust storms in India. 
 
 (37.) To give an idea of the state of the inhabitants 
 of the country when an explosion is going on, I will make 
 one other extract : " The mountain of Somma, at the 
 foot of which Ottaiano is situated, hides Vesuvius from 
 its sight : so that till the eruption became considerable 
 it was not visible to them. On Sunday night, when the 
 noise increased, and the fire began to appear above the 
 mountain of Somma, many of the inhabitants of the town 
 flew to the churches ; and others were preparing to quit 
 the town, when a sudden violent report was heard, soon 
 after which they found themselves involved in a thick
 
 8 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 cloud of smoke and minute ashes ; a horrid clashing 
 noise was heard in the air ; and presently fell a deluge 
 of stones and large scoriae, some of which scoriae were 
 of the diameter of seven or eight feet, and must have 
 weighed more than one hundred pounds before they 
 were broken by their falls, as some of the fragments 
 of them which I picked up in the streets still weighed 
 upwards of sixty pounds. When these large vitrified 
 masses either struck against each other in the air or fell 
 on the ground they broke in many pieces, and covered a 
 large space around them with vivid sparks of fire, which 
 communicated their heat to everything that was combus- 
 tible. In an instant the town and country about it was 
 on fire in many parts ; for in the vineyards there were 
 several straw-huts, which had been erected for the watch- 
 men of the grapes, all of which were burnt. A great 
 magazine of wood in the heart of the town was all in a 
 blaze : and had there been much wind, the flames must 
 have spread universally, and all the inhabitants would 
 have infallibly been burnt in their houses, for it was im- 
 possible for them to stir out. Some who attempted it 
 with pillows, tables, chairs, tops of wine casks, etc., on 
 their heads, were either knocked down or driven back to 
 their close quarters, under arches and in the cellars of the 
 houses. Many were wounded, but only two persons 
 have died of the wounds they received from this dread- 
 ful volcanic shower. To add to the horror of the scene, 
 incessant volcanic lightning was writhing about the black 
 cloiri that surrounded them, and the sulphureous smell and 
 heat would scarcely allow them to draw their breath."
 
 ABOUT VOLCANOS AND EARTHQUAKES. 2<) 
 
 (38.) The next volcano I shall introduce is ^Etna, the 
 grandest of all our European volcanos. I ascended it in 
 1824, and found its height by a very careful barometric 
 measurement to be 10,772 feet above the sea, which, by 
 the way, agrees within some eight or ten feet with 
 Admiral Smyth's measurement. 
 
 (39.) The scenery of ^Etna is on the grandest scale. 
 Ascending from Catania you skirt the stream of lava 
 which destroyed a large part of that city in 1669, and 
 which ran into the sea, forming a jetty or breakwater 
 that now gives Catania what it never had before, the 
 advantage of a harbour. There it lies as hard, rugged, 
 barren, and fresh-looking as if it had flowed but yester- 
 day. In many places it is full of huge caverns ; great 
 air-bubbles, into which one may ride on horseback (at 
 least large enough) and which communicate, in a suc- 
 cession of horrible vaults, where one might wander and 
 lose one's self without hope of escape. Higher up, near 
 Nicolosi, is the spot from which that lava flowed. It is 
 marked by two volcanic cones, each of them a consider- 
 able mountain, called the Monti Rossi, rising 300 feet 
 above the slope of the hill, and which were thrown up 
 on that occasion. Indeed, one of the most remarkable 
 features of ^Etna is that of its flanks bristling over with 
 innumerable smaller volcanos. For the height is so 
 great that the lava now scarcely ever rises to the tcp ot 
 the crater; for before that, its immense weight breaks 
 through at the sides. In one of the eruptions that hap- 
 pened in the early part of this century, I forget the date, 
 but I think it was in 1819, and which was described to
 
 3O ABOUT VOLCANOS AND EARTHQUAKES. 
 
 me on the spot by an eye-witness the Old Man of the 
 Mountain, Mario Gemellaro the side of JEtna. was 
 rent by a great fissure or crack, beginning near the top, 
 and throwing out jets of lava from openings fourteen or 
 fifteen in number all the way down, so as to form a row 
 of fiery fountains rising from different levels, and all 
 ascending nearly to the same height : thereby proving 
 them all to have originated in the great internal cistern 
 as it were, the crater being filled up to the top level. 
 
 (40.) From the summit of ^Etna extends a view of 
 extraordinary magnificence. The whole of Sicily lies at 
 your feet, and far beyond it are seen a string of lesser 
 volcanos; the Lipari Islands, between Sicily and the 
 Italian coast; one of which, Stromboli, is always in 
 eruption, unceasingly throwing up ashes, smoke, and 
 liquid fire. 
 
 (41.) But I must not linger on the summit of ytna. 
 We will now take a flight thence, all across Europe, to 
 Iceland a wonderful land of frost and fire. It is full of 
 volcanos, one of which, HECLA, has been twenty-two 
 times ,in eruption within the last 800 years. Besides 
 Hecla, there are five others, from which in the same 
 period twenty eruptions have burst forth, making about 
 one every twenty years. The most formidable of these 
 was that which happened in 1783, a year also memor- 
 able as that of the terrible earthquake in Calabria. In 
 May of that year, a bluish fog was observed over the 
 mountain called Skaptar Jokul, and the neighbourhood 
 was shaken by earthquakes. After a while a great pillar 
 of smoke was observed to ascend from it, which dark-
 
 ABOUT VOLCANOS AND EARTHQUAKES. 31 
 
 ened the whole surrounding district, and which descended 
 in a whirlwind of ashes. On the loth of May, innumer- 
 able fountains of fire were seen shooting up through the 
 ice and snow which covered the mountain ; and the 
 principal river, called the Skapta, after rolling down a 
 flood of foul and poisonous water, disappeared. Two 
 days after, a torrent of lava poured down into the bed 
 which the river had deserted. The river had run 
 in a ravine, 600 feet deep and 200 broad. This 
 the lava entirely filled; and not only so, but it over- 
 flowed the surrounding country, and ran into a great 
 lake, from which it instantly expelled the water in an ex- 
 plosion of steam. When' the lake was fairly filled, the 
 lava again overflowed and divided into two streams, one 
 of which covered some ancient lava fields ; the other re- 
 entered the bed of the Skapta lower down ; and pre- 
 sented the astounding sight of a cataract of liquid fire 
 pouring over what was formerly the waterfall of Stapafoss. 
 This was the greatest eruption on record in Europe. It 
 lasted in its violence till the end of August, and closed 
 with a violent earthquake; but for nearly the whole 
 year a canopy of cinder-laden cloud hung over the 
 island ; the Faroe Islands, nay, even Shetland and the 
 Orkneys, were deluged with the ashes ; and volcanic 
 dust and a preternatural smoke, which obscured the sun, 
 covered all Europe as far as the Alps, over which it could 
 not rise. It has been surmised that the great Fire- 
 ball of August 18, 1783, which traversed all England 
 and the Continent, from the North Sea to Rome, by far 
 the greatest ever known (for it was more than half a
 
 32 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 mile in diameter), was somehow connected with the 
 electric excitement of the upper atmosphere produced 
 by this enormous discharge of smoke and ashes. The 
 destruction of life in Iceland was frightful : 9000 men, 
 11,000 cattle, 28,000 horses, and 190,000 sheep per- 
 ished; mostly by suffocation. The lava ejected has 
 been computed to have amounted in volume to more 
 than twenty cubic miles. 
 
 (42.) We shall now proceed to still more remote re- 
 gions, and describe, in as few words as may be, two im- 
 mense eruptions, one in Mexico, in the year 1759 ; the 
 other in the island of Sumbawa in the Eastern Archi- 
 pelago, in 1815. 
 
 (43.) I ought to mention, by way of preliminary, that 
 almost the whole line of coast of South and Central 
 America, from Mexico southwards as far as Valparaiso 
 that is to say, nearly the whole chain of the Andes is 
 one mass of volcanos. In Mexico and Central America 
 there are two and twenty, and in Quito, Peru, and Chili, 
 six and twenty more, in activity ; and nearly as many 
 more extinct ones, any one of which may at any moment 
 break out afresh. This does not prevent the country 
 from being inhabited, fertile, and well cultivated. Well : 
 in a district of Mexico celebrated for the growth of the 
 finest cotton, between two streams called Cuitimba and 
 San Pedro, which furnished water for irrigation, lay the 
 farm and homestead of Don Pedro de Jurullo, one of 
 the richest and most fertile properties in that country. 
 He was a thriving man, and lived in comfort as a large 
 proprietor, little expecting the mischief that was to be-
 
 ABOUT VOLCANOS AND EARTHQUAKES. 33 
 
 fall him. In June 1759, however, a subterranean noise 
 was heard in this peaceful region. Hollow sounds of the 
 most alarming nature were succeeded by frequent earth- 
 quakes, succeeding one another for fifty or sixty days ; but 
 they died away, and in the beginning of September every- 
 thing seemed to have returned to its usual state of tran- 
 quillity. Suddenly, on the night of the 28th of Septem- 
 ber, the horrible noises recommenced. All the inhabit- 
 ants fled in terror; and the whole tract of ground, from 
 three to four square miles in extent, rose up in the form 
 of a bladder to a height of upwards of 500 feet ! Flames 
 broke forth over a surface of more than half a square 
 league, and through a thick cloud of ashes illuminated 
 by this ghastly light, the refugees, who had ascended a 
 mountain at some distance, could see the ground as if 
 softened by the heat, and swelling and sinking like an 
 agitated sea. Vast rents opened in the earth, into which 
 the two rivers I mentioned precipitated themselves, but so 
 far from quenching the fires, only seemed to make them 
 more furious. Finally, the whole plain became covered 
 with an immense torrent of boiling mud, out of which 
 sprang thousands of little volcanic cones called Hornitos, 
 or ovens. But the most astonishing part of the whole 
 was the opening of a chasm vomiting out fire, and red- 
 hot stones, and ashes, which accumulated so as to form 
 " a range of six large mountain masses, one of which is 
 upwards of 1600 feet in height above the old level, and 
 which is now known as the volcano of Jorullo. It is 
 continually burning ; and for a whole year continued to 
 throw up an immense quantity of ashes, lava, and frag- 
 
 c
 
 34 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 ments of rock. The roofs of houses at the town or vil- 
 lage of Queretaro, upwards of 140 miles distant, were 
 covered with the ashes. The two rivers have again 
 appeared, issuing at some distance from among the 
 hornitos, but no longer as sources of wealth and fertility, 
 for they are scalding hot, or at least were so when Baron 
 Humboldt visited them several years after the event 
 The ground even then retained a violent heat, and the 
 hornitos were pouring forth columns of steam twenty 
 or thirty feet high, with a rumbling noise like that of 
 a steam-boiler. 
 
 (44.) The Island of Sumbawa is one of that curious 
 line of islands which links on Australia to the south- 
 eastern corner of Asia. It forms, with one or two 
 smaller volcanic islands, a prolongation of Java, at that 
 time, in 1815, a British possession, and under the go- 
 vernment of Sir Stamford Raffles, to whom we owe the 
 account of the eruption, and who took a great deal 
 of pains to ascertain all the particulars. Java itself, I 
 should observe, is one rookery of volcanos, and so are 
 all the adjoining islands in that long crescent-shaped 
 line I refer to. 
 
 (45.) On the Island of Sumbawa is the volcano of 
 Tomboro, which broke out into eruption on the 5th of 
 April in that year; and I can hardly do better than 
 quote the account of it in Sir Stamford Raffles' own 
 words : 
 
 (46.) "Almost every one," says this writer, "is ac- 
 quainted with the intermitting convulsions of Etna and 
 Vesuvius as they appear in the descriptions of the poet,
 
 ABOUT VOLCANOS AND EARTHQUAKES. 35 
 
 and the authentic accounts of the naturalist; but the 
 most extraordinary of them can bear no comparison, in 
 point of duration and force, with that of Mount Tomboro 
 in the Island of Sumbawa ! This eruption extended per- 
 ceptible evidences of its existence over the whole of the 
 Molucca Islands, over Java, a considerable portion of 
 the Celebes, Sumatra, and Borneo, to a circumference of 
 1000 statute miles from its centre" (i.e., to 1000 miles' 
 distance}, " by tremulous motions and the report of explo- 
 sions. In a short time the whole mountain near the 
 Sang'ir appeared like a body of liquid fire, extending it- 
 self in every direction. The fire and columns of flame 
 continued to rage with unabated fury, until the darkness, 
 caused by the quantity of falling matter, obscured it at 
 about eight P.M. Stones at this time fell very thick at 
 Sang'ir, some of them as large as two fists, but generally 
 not larger than walnuts. Between nine and ten P.M., 
 ashes began to fall, and soon after a violent whirlwind 
 ensued, which blew down nearly every house of Sang'ir, 
 carrying the roofs and light parts away with it. In the 
 port of Sang'ir, adjoining Sumbawa, its effects were 
 much more violent, tearing up by the roots the largest 
 trees, and carrying them into the air, together with 
 men, horses, cattle, and whatsoever came within its 
 influence. This will account for the immense number 
 of floating trees seen at sea. The sea rose nearly 
 twelve feet higher than it had ever been known 
 to do before, and completely spoiled the only small 
 spots of rice land in Sang'ir, sweeping away houses and 
 everything within its reach. The whirlwind lasted about
 
 36 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 an hour. No explosions were heard till the whirlwind 
 had ceased at about eleven P.M. From midnight till the 
 evening of the nth, they continued without intermis- 
 sion ; after that time their violence moderated, and they 
 were heard only at intervals ; but the explosions did not 
 cease entirely until the i5th of July. Of all the villages 
 round Tomboro, Tempo, containing about forty inhabit- 
 ants, is the only one remaining. In Pekate' no vestige 
 of a house is left ; twenty-six of the people, who were at 
 Sumbawa at the time, are the whole of the population 
 who have escaped. From the best inquiries, there were 
 certainly not fewer than 1 2,000 individuals in Tomboro 
 and Pekate' at the time of the eruption, of whom five or 
 six survive. The trees and herbage of every description, 
 along the whole of the north and west of the peninsula, 
 have been completely destroyed, with the exception of a 
 high point of land near the spot where the village of 
 Tomboro stood. At Sang'ir, it is added, the famine 
 occasioned by this event was so extreme, that one of 
 the rajah's own daughters died of starvation." 
 
 (47.) I have seen it computed that the quantity of 
 ashes and lava vomited forth in this awful eruption 
 would have formed three mountains the size of Mont 
 Blanc, the highest of the Alps ; and if spread over the 
 surface of Germany, would have covered the whole of 
 it two feet deep ! The ashes did actually cover the 
 whole island of Tombock, more than 100 miles distant, 
 to that depth, and 44,000 persons there perished by 
 starvation, from the total destruction of all vegetation. 
 
 (48.) The mountain Kirauiah in the island of Owyhee,
 
 ABOUT VOLCANOS AND EARTHQUAKES. 37 
 
 one of the Sandwich Isles, exhibits the remarkable 
 phenomenon of a lake of molten and very liquid lava 
 always filling the bottom of the crater, and always in a 
 state of terrific ebullition : rolling to and fro its fiery 
 surge and flaming billows yet with this it is content, 
 for it would seem that at least for a long time past there 
 has been no violent outbreak so as to make what is 
 generally understood by a volcanic eruption. Volcanic 
 eruptions are almost always preceded by earthquakes, by 
 which the beds of rock, that overlie and keep down the 
 struggling powers beneath, are dislocated and cracked, 
 till at last they give way, and the strain is immediately 
 relieved. It is chiefly when this does not happen, when 
 the force below is sufficient to heave up and shake the 
 earth, but not to burst open the crust, and give vent to 
 the lava and gases, that the most destructive effects are 
 produced. The great earthquake of November i, 1755, 
 which destroyed Lisbon, was an instance of this kind, 
 and was one of the greatest, if not the very greatest on 
 record j for the concussion extended over all Spain and 
 Portugal indeed, over all Europe, and even into Scot- 
 land over North Africa, where in one town in Morocco 
 8000 or 10,000 people perished. Nay, its effects 
 extended even across the Atlantic to Madeira, where it 
 was very violent ; and to the West Indies. The most 
 striking feature about this earthquake was its extreme 
 suddenness. All was going on quite as usual in Lisbon 
 the morning of that memorable day ; the weather fine 
 and clear ; and nothing whatever to give the population 
 of that great capital the least suspicion of mischief. All
 
 38 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 at once, at twenty minutes before ten A.M., a noise was 
 heard like the rumbling of carriages under ground ; it 
 increased rapidly and became a succession of deafening 
 explosions like the loudest cannon. Then a shock, 
 which, as described by one writing from the spot, 
 seemed to last but the tenth part of a minute ; and down 
 came tumbling palaces, churches, theatres, and every 
 large public edifice, and about a third or a fourth part of 
 the dwelling-houses. More shocks followed in rapid 
 succession, and in six minutes from the commencement 
 60,000 persons were crushed in the ruins ! Here are 
 the simple but expressive words of one J. Latham, who 
 writes to his uncle in London. " I was on the river 
 with one of my customers going to a village three miles 
 off. Presently the boat made a noise as if on the shore 
 or landing, though then in the middle of the water. I 
 asked my companion if he knew what was the matter. 
 He stared at me, and looking at Lisbon, we saw the 
 houses falling, which made him say, ' God bless us, it is 
 an earthquake ! ' About four or five minutes after, the 
 boat made a noise as before; and we saw the houses 
 tumble down on both sides of the river." They then 
 landed and made for a hill ; whence they beheld the sea 
 (which had at first receded and laid a great tract dry) 
 come rolling in, in a vast mountain wave fifty or sixty 
 feet high, on the land, and sweeping all before it. Three 
 thousand people had taken refuge on a new stone quay 
 or jetty just completed at great expense. In an instant 
 it was turned topsy-turvy; and the whole quay, and 
 every person on it, with all the vessels moored to it,
 
 ABOUT VOLCANOS AND EARTHQUAKES. 39 
 
 disappeared, and not a vestige of them ever appeared 
 again. Where that quay stood, was afterwards found a 
 depth of 100 fathoms (600 feet) water. It happened to 
 be a religious festival, and most of the population were 
 assembled in the churches, which fell and crushed them. 
 That no horror might be wanting, fires broke out in 
 innumerable houses where the wood-work had fallen on 
 the fires ; and much that the earthquake had spared was 
 destroyed by fire. And then too broke forth that worst 
 of all scourges, a lawless ruffian-like mob, who plundered, 
 burned, and murdered in the midst of all that desolation 
 and horror. The huge wave I have spoken of swept the 
 whole coast of Spain and Portugal Its swell and fall 
 was ten or twelve feet at Madeira. It swept quite 
 across the Atlantic, and broke on the shores of the West 
 Indies. Every lake and firth in England and Scotland 
 was dashed for a moment out of its bed, the water not 
 partaking of the sudden shove given to the land, just as 
 when you splash a flat saucerful of water, the water 
 dashes over on the side from which the shock is given. 
 
 (49.) One of the most curious incidents in this earth- 
 quake was its effect on ships far out at sea, which would 
 lead us to suppose that the immediate impulse was in 
 the nature of a violent blow or thrust upwards, under the 
 bed of the ocean. Thus it is recorded that this upward 
 shock was so sudden and violent on a ship, at that time 
 forty leagues from Cape St Vincent, that the sailors on 
 deck were tossed up into the air to a height of eighteen 
 inches. So also, on another occasion in 1796, a British 
 ship eleven miles from land near the Philippine Islands
 
 4O ABOUT VOLCANOS AND EARTHQUAKES. 
 
 was struck upwards from below with such force as to un- 
 ship and split up the main-mast. 
 
 (50.) Evidences of a similar sudden and upward ex- 
 plosive action are of frequent occurrence among the 
 extinct volcanos of Auvergne and the Vivarais, where in 
 many instances the perforation of the granitic beds which 
 form the basis or substratum of the whole country ap- 
 pears to have been effected at a single blow, accom- 
 panied with little evidence of disturbance of the sur- 
 rounding rocks much in the same way as a bullet will 
 pass through a pane of glass without starring or shatter- 
 ing it. In such cases it would seem as if water in a 
 liquid state had suddenly been let in through a fissure 
 upon a most intensely heated and molten mass beneath, 
 producing a violent but local explosion, so instantaneous 
 as to break its way through the overlying rocks, without 
 allowing time for them to bend or crumple, and so dis- 
 place the surrounding masses. 
 
 (51.) The same kind of upward bounding movement 
 took place at Riobamba in Quito in the great earth- 
 quake of February 4, 1797, which was connected with 
 an eruption of the volcano of Tunguragua. That earth- 
 quake extended in its greatest intensity over an oval 
 space of 1 20 miles from south to north, and 60 from 
 east to west, within which space every town and village 
 was levelled with the ground ; but the total extent of 
 surface shaken was upwards of 500 miles in one direc- 
 tion (from Puna to Popayan), and 400 in the other. 
 Quero, Riobamba, and several other towns, were buried 
 under fallen mountains, and in a very few minutes
 
 ABOUT VOLCANOS AND EARTHQUAKES. 4! 
 
 30,000 persons were destroyed. At Riobamba, how- 
 ever, after the earthquake, a great number of corpses 
 were found to have been tossed across a river, and 
 scattered over the slope of a hill on the other side. 
 
 (52.) The frequency of these South American earth- 
 quakes is not more extraordinary than the duration of 
 the shocks. Humboldt relates that on one occasion, 
 when travelling on mule-back with his companion 
 Bonpland, they were obliged to dismount in a dense 
 forest, and throw themselves on the ground : the earth 
 being shaken uninterruptedly for upwards of a quarter 
 of an hour with such violence that they could not keep 
 their legs. 
 
 (53.) One of the most circumstantially described earth- 
 quakes on record is that which happened in Calabria 
 on the 5th of February 1783 ; I should say began then, 
 for it may be said to have lasted four years. In the 
 year 1783, for instance, 949 shocks took place, of which 
 501 were great ones, and in 1784, 151 shocks were felt, 
 98 of which were violent. The centre of action seemed 
 to be under the towns of Monteleone and Oppido. In 
 a circle twenty-two miles in radius round Oppido every 
 town and village was destroyed within two minutes by 
 the first shock, and within one of seventy miles' radius 
 all were seriously shaken and much damage done. 
 The whole of Calabria was affected, and even across 
 the sea Messina was shaken, and a great part ot 
 Sicily. 
 
 (54.) There is no end of the capricious and out-of-the- 
 way accidents and movements recorded in this Calabrian
 
 42 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 earthquake. The ground undulated like a ship at sea. 
 People became actually sea-sick, and to give an idea of 
 the undulation (just as it happens at sea), the scud of 
 the clouds before the wind seemed to be fitfully arrested 
 during the pitching movement when it took place in the 
 same direction, and to redouble its speed in the reverse 
 movement. At Oppido many houses were swallowed 
 up bodily. Loose objects were tossed up several yards 
 into the air. The flagstones in some places were found 
 after a severe shock all turned bottom upwards. Great 
 fissures opened in the earth, and at Terra Nova a mass 
 of rock 200 feet high and 400 in diameter travelled four 
 miles down a ravine. All landmarks were removed, and 
 the land itself, in some instances, with trees and hedges 
 growing on it, carried bodily away and set down in 
 another place. Altogether about 40,000 people perished 
 by the earthquakes, and some 20,000 more of the epide- 
 mic diseases produced by want and the effluvia of the 
 dead bodies. 
 
 (55.) Volcanos occasionally break forth at the bottom 
 of the sea, and, when this is the case, the result is usually 
 the production of a new island. This, in many cases, 
 disappears soon after its formation, being composed of 
 loose and incoherent materials, which easily yield to the 
 destructive power of the waves. Such was the case with 
 the Island of Sabrina, thrown up, in 1811, off St 
 Michaels, in the Azores, which disappeared almost as 
 soon as formed, and in that of Pantellaria, on the 
 Sicilian coast, which resisted longer, but was gradually 
 washed into a shoal, and at length has, we believe, com-
 
 ABOUT VOLCANOS AND EARTHQUAKES. 43 
 
 pletely disappeared.* In numerous other instances, the 
 cones of cinders and scoriae, once raised, have become 
 compacted and bound together by the effusion of lava, 
 hardening into solid stone, and thus, becoming habitual 
 volcanic vents, they continue to increase in height and 
 diameter, and assume the importance of permanent vol- 
 canic islands. Such has been, doubtless, the history of 
 those numerous insular volcanos which dot the ocean 
 in so many parts of the world, such as Teneriffe, the 
 Azores, Ascension, St Helena, Tristan d'Acunha, etc. 
 In some cases the process has been witnessed from its 
 commencement, as in that of two islands which arose in 
 the Aleutian group, connecting Kamtschatka with North 
 America, the one in 1796, the other in 1814, and which 
 both attained the elevation of 3000 feet 
 
 (56.) Besides these evident instances of eruptive action, 
 there is every reason to believe that enormous floods of 
 lava have been, at various remote periods in the earth's 
 history, poured forth at the bottom of seas so deep as to 
 repress, by the mere weight of water, all outbreak of 
 steam, gas, or ashes ; and reposing perhaps for ages in a 
 liquid state, protected from the cooling action of the 
 water on their upper surface by a thick crust of con- 
 gealed stony matter, to have assumed a perfect level; and, 
 at length, by slow cooling, taken on that peculiar colum- 
 nar structure which we see produced in miniature in 
 
 * Such an event is at this moment in progress (March 1 866), 
 close to the island of Santorini, in the bay of Thera, in the Greek 
 Archipelago : itself, with the adjacent Kaimeni Islands, products ol 
 the same kind.
 
 44 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 starch by the contraction or shrinkage, and consequent 
 splitting, of the material in drying ; and resulting in those 
 picturesque and singular landscape-features called basaltic 
 colonnades : when brought up to day by sudden or 
 gradual upheaval, and broken into cliffs and terraces by 
 the action of waves, torrents, or weather. Those grand 
 specimens of such colonnades which Britain possesses 
 in the Giant's Causeway of Antrim, and the cave of 
 Fingal in Staffa, for instance, are no doubt extreme out- 
 standing portions of such a vast submarine lava-flood 
 which at some inconceivably remote epoch occupied the 
 whole intermediate space ; affording the same kind of 
 evidence of a former connexion of the coasts of Scotland 
 and Ireland as do the opposing chalk cliffs of Dover and 
 Boulogne of the ancient connexion of France with 
 Britain. Here and there a small basaltic island, such 
 as that of Rathlin, remains to attest this former conti- 
 nuity, and to recall to the contemplative mind that sub- 
 lime antagonism between sudden violence and persever- 
 ing effort, which the study of geology impresses in every 
 form of repetition. 
 
 (57.) There exists a very general impression that earth- 
 quakes are preceded and ushered in by some kind of 
 preternatural, and, as it were, expectant calm in the 
 elements j as if to make the confusion and desolation 
 they create the more impressive. The records of such 
 visitations which we possess, however striking some par- 
 ticular cases of this kind may appear, by no means bear 
 out this as a general fact, or go to indicate any particular 
 phase of weather as preferentially accompanying their
 
 ABOUT VOLCANOS AND EARTHQUAKES. 45 
 
 occurrence. This does not prevent, however, certain 
 conjunctures of atmospheric or other circumstances from 
 exercising a determining influence on the times of their 
 occurrence. According to the view we have taken of 
 their origin (viz., the displacement of pressure, resulting 
 in a state of strain in the strata at certain points, gradu- 
 ally increasing to the maximum they can bear without 
 disruption), it is the last ounce which breaks the camel's 
 back. Great barometrical fluctuation, accumulating at- 
 mospheric pressure for a time over the sea, and reliev- 
 ing it over the land ; an unusually high tide, aided by 
 long-continued and powerful winds, heaping up the 
 water ; nay, even the tidal action of the sun and moon 
 on the solid portion of the earth's crust, all these 
 causes, for the moment combining, may very well suffice 
 to determine the instant of fracture, when the balance 
 between the opposing forces is on the eve of subversion. 
 The last-mentioned cause may need a few words of ex- 
 planation. The action of the sun and moon, though it 
 cannot produce a tide in the solid crust of the earth, 
 tends to do so, and, were it fluid, -would produce it. It 
 therefore, in point of fact, does bring the solid portions 
 of the earth's surface into a state alternately of strain and 
 compression. The effective part of their force, in the 
 present case, is not that which aids to lift or to press the 
 superficial matter (for that, acting alike on the continents 
 and on the bed of the sea, would have no influence), but 
 that which tends to produce lateral displacement; or 
 what geometers call the tangential force. This of neces- 
 sity brings the whole ring of the earth's surface, which
 
 46 ABOUT VOLCANOS AND EARTHQUAKES. 
 
 at any instant has the acting luminary on its horizon, into 
 a state of strain ; and the whole area over which it is 
 nearly vertical, into one of compression. We leave this 
 point to be further followed out, but we cannot forbear 
 remarking, that the great volcanic chains of the world 
 have, in point of fact, a direction which this cause of dis- 
 ruption would tend rather to favour than to contravene.
 
 LECTURE It 
 
 THE SUN. 
 
 j|HE subject I have chosen for this Lecture is 
 perhaps an ambitious one ; for it is no less 
 than an attempt to convey to my hearers 
 some faint impression of the vastness and 
 grandeur of the most magnificent object in nature 
 of that glorious body which occupies the centre of our 
 planetary system, and on which not only our own globe, 
 but all the other planets, many of them of far greater 
 magnitude and possibly too of greater importance in 
 the scale of being than our own ; depend in the most 
 immediate manner for the fulfilment of those conditions 
 without which animated existence and organic life are 
 impossible THE SUN. There is a poem of Byron's 
 entitled " Darkness," which begins thus : 
 
 " I had a dream which was not all a dream, 
 The bright sun was extinguish'd, and the earth 
 Did wander darkling in th' eternal space 
 Rayless and pathless,"
 
 48 THE SUN. 
 
 and so on : describing, or trying to describe, the horrors 
 of that desolation which would ensue. They are as- 
 sembled and piled on one another in this powerful 
 poem with the hand of a master of the horrible ; and 
 in the end everybody goes mad, fights with everybody 
 else, and dies of starvation. 
 
 (2.) But there would not be time for fighting or star- 
 vation. In three days from the extinction of the sun 
 there would, in all probability, not be a vestige of ani- 
 mal or vegetable life on the globe ; unless it were among 
 deep-sea fishes and the subterranean inhabitants of the 
 great limestone caves. The first forty-eight hours would 
 suffice to precipitate every atom of moisture from the 
 air in deluges of rain and piles of snow, and from that 
 moment would set in a universal frost such as Siberia 
 or the highest peak of the Himalayas never felt a tem- 
 perature of between two and three hundred degrees 
 below the zero of our thermometers. This is no fanciful 
 guess-work. Professor Tyndall has quite recently shown 
 that it is entirely to the moisture existing in the air 
 that our atmosphere owes its power of confining, and 
 cherishing as it were the heat which is always endea- 
 vouring to radiate away from the earth's surface into 
 space. Pure ai* is perfectly transparent to terrestrial 
 heat so that but for the moisture present in the atmo- 
 sphere, every night would place the earth's surface as it 
 were in contact with that intense cold which we are 
 certain exists in empty space : a degree of cold which 
 from several different and quite independent lines of in- 
 quiry we are sure is not less than 230 degrees of Fah
 
 THE SUN. 49 
 
 renheit's thermometer below the zero of that scale. No 
 animal or vegetable could resist such a frost for an horn, 
 any more than it could live for an hour in boiling water. 
 Such a frost exists, no doubt, over the dark half of the 
 moon, which has no atmosphere, neither air nor vapour, 
 and in all probability quite as violent an extreme of heat, 
 a boiling temperature at least, over the bright half; so 
 that we may pretty well make up our minds as to that 
 half of the moon at least which we see, being uninhabited; 
 while on the other hand, if it would not lead too far 
 away from our immediate subject, I think it might be 
 shown on admissible principles, that Venus and Mer- 
 cury, in spite of their nearness to the sun, and possibly 
 also Jupiter and Saturn, in spite of their remoteness, 
 may have climates in which animal and vegetable life 
 such as we see them here, might be maintained. 
 
 (3.) But it is with the sun itself that we are now con- 
 cerned. What I am going to say about the sun will 
 consist of a series of statements so enormous in all 
 their proportions, that I dare say, before I have done, 
 some of my hearers will almost think me mad, or in- 
 tending to palm on them a string of rhodomontades, 
 like some of the mythical stories of the Hindus. And 
 yet there is nothing more certain in modern science 
 than the truth of some of the most extravagant of these 
 statements ; and, wild as they may seem to those who 
 for the first time hear them, they appear not only not 
 extravagant, but actually dwarfed into littleness by the 
 still vaster revelations of that science respecting the scale 
 of the visible universe ; in every part of which when we 
 
 D
 
 50 THE SUN. 
 
 come to measure in figures either the magnitude or 
 the minuteness of its mechanisms, we find our arith- 
 metic almost breaking down in the attempt, and num- 
 bers of ten or twenty places of figures, as it were tossed 
 about like dust, and turning up on every occasion. 
 
 (4.) To come then to our subject. The first and 
 most important office the sun has to perform in our 
 system is to keep it together, to keep its members from 
 parting company, from seceding, and running off into 
 outer darkness, out of the reach of the genial influence 
 of his beams. Were the sun simply extinguished, the 
 planets would all continue to circulate round it as they 
 do at present, only in cold and darkness; but were it 
 annihilated, each would from that moment set forth 
 on a journey into infinite space in the direction in 
 which it happened then to be moving ; and wander 
 on, centuries after centuries, lost in that awful abyss 
 which separates us from the stars, and without making 
 any sensible approach even to the nearest of them in 
 many hundreds or even thousands of years. The power 
 by which the sun is enabled to perform this office to 
 gather the planets round its hearth and to keep them 
 there is the same in kind (though very different in 
 intensity) with that which when a stone is thrown up 
 into the air draws it down again to the earth. As to 
 the manner in which this is effected by the weight of 
 the stone, or its tendency to fall straight down, acting 
 to turn or draw it out of its right-lined course oblique 
 to the surface, and oblige it to move in a curve, with 
 the explanation of that we have here nothing to do.
 
 THE SUN. 51 
 
 That belongs to mechanics, and we must take it for 
 granted. But in order to understand how it is possible 
 to pass from this familiar case that we see every day 
 before our eyes, to that of a vast globe like the earth 
 revolving in an orbit about the sun, it will be neces- 
 sary to enlarge the scale of our ideas of magnitude 
 We must try to conceive a similar degree of command 
 and control exercised over such a mass as our globe, 
 and over the much greater masses of the remote planets, 
 by the sun as a central body; hardly moved from its 
 place, while as it were swinging all the others round 
 it. And for this purpose it is necessary to possess 
 some distinct conception of what sort of a body the 
 sun really is of its size of its distance from us of 
 its weight or mass and of the proportion it bears to 
 the other bodies, the earth included, which circulate 
 round it. 
 
 (5.) It is strange what crude ideas people in general 
 have about the size of very distant objects. I was read- 
 ing only the other day a letter to the Times giving an ac- 
 count of a magnificent meteor. The writer described it as 
 round, about ttie size of a cricket-ball, and apparently about 
 100 yards off. Many persons spoke of the tail of the 
 great comet of 1858 as being several yards long, without 
 at all seeming aware of the absurdity of such a way of 
 talking. The sun or the moon may be covered by a three- 
 penny piece held at arm's length : but it takes a house, 
 or a church, or a great tree to cover it on a near horizon, 
 and a hill or a mountain on a distant one; so that it 
 must be at least as large as any of these objects. Among
 
 52 THE SUN. 
 
 the ancient Greek philosophers there was a lively dispute 
 as to the real size of the sun. One maintained that it 
 was " precisely as large as it looks to be," a thoroughly 
 Greek way of getting out of a difficulty. All the best 
 thinkers among them, however, clearly saw that it must 
 be a very large body. One of them (Anaxagoras) went 
 the length of saying that it might be as large as all Greece, 
 for which he got laughed at. But he was outbid by 
 Anaximander, who said it was twenty-eight times as large 
 the earth. What would Anaximander or the scoffer of 
 Anaxagoras have said, could he have known what we now 
 know, that, seen from the same distance as the sun, the 
 territory of Greece would have been absolutely invisible; 
 and that even the whole earth, if laid upon it, would not 
 cover more than one thirteen-thousandth part of its ap- 
 parent surface, less in proportion, that is to say, than a 
 single letter in the broad expanse of type which meets 
 the reader's eye when a closely-printed volume with a 
 large page and small type lies open before him.* 
 
 (6.) My object in this notice is not to put before my 
 audience, except in one single instance, any connected 
 chain of reasoning and deduction ; or to show how, from 
 the principles of abstract science combined with observa- 
 tion, the results I have to state have been obtained. 
 This would lead me a great deal too far, and would re- 
 quire not one but a whole series of such lectures. What I 
 
 * The original type and page of "Good Words" were here re- 
 ferred to, in which this lecture first appeared in print : each page of 
 which contains about 6000 letters. The pages which now lie open 
 before the eye of the reader contain, together, only about 2600.
 
 THE SUN. 53 
 
 aim at is to convey to their minds, as matters of fact, 
 what those results are in the case of the sun, and to en- 
 able them to form a conception of it as a reality. Still it 
 is reasonable for any one to ask how it is possible to 
 prove such a statement, for instance, as that just made : 
 and as the kind of process by which our conclusions as 
 to the size and mass of the sun are arrived at may be 
 put in a few words, it will not be amiss to give a sketch 
 of it. 
 
 (7.) The first step towards ascertaining the real size of 
 the sun is to determine its distance. Now, the simplest 
 way to find the distance of an object which cannot be 
 got at, is to measure what is called a base line from the 
 two ends of which it can be seen at one and the same 
 moment, and then to measure with proper instruments 
 the angles at the base of the triangle formed by the dis- 
 tant object and the two ends of the base. Geography 
 and surveying in modern times have arrived at such per- 
 fection, that we know the size and form of the earth we 
 stand upon to an extreme nicety. It is a globe a little 
 flattened in the direction of the poles, the longer dia- 
 meter, that across the equator, being 7925 miles and five 
 furlongs, and the shorter, or polar axis, 7899 miles and 
 one furlong ; and in these measures it is pretty certain 
 that there is not an error of a quarter of a mile. And 
 knowing this, it is possible to calculate with quite as much 
 exactness as if it could be measured, the distance in a 
 straight line between any two places whose geographical 
 positions on the earth's surface are known. Now there 
 are two astronomical observatories very remote from one
 
 54 THE SUN. 
 
 another ; the one in the northern hemisphere, the other 
 in the southern, viz., at Hammerfest in Norway, and at 
 the Cape of Good Hope, both very nearly on the same 
 meridian, so that the sun, or the moon, or any other 
 heavenly body attains its greatest altitude above the hori- 
 zon of each (or as astronomers express it, passes the 
 meridian of each) very nearly at the same time. Suppos- 
 ing then that this, its meridian altitude, is carefully ob- 
 served at each of these two stations on the same day ; it 
 is easy to find, by computation, the angles included be- 
 tween each of the two lines of direction in which it was 
 seen from the two places, and their common line of 
 junction; so that taking this latter line for the base of a 
 triangle, of which the two sides are the distances of the 
 object from either place, those two sides can thence be 
 calculated by the very same process of computation which 
 is employed in geographical surveying to find the distance 
 of a signal from observations at the ends of a measured 
 base. Now, the distance between Hammerfest and the 
 Cape in a straight line is nearly 6300 miles, and owing 
 to the situations of the two places in latitude, the triangle 
 in question is always what a land surveyor would call a 
 favourable one for calculation : so that, with so long a base, 
 we may reasonably expect to arrive at a considerably 
 exact knowledge of its sides, after which a little addi 
 tional calculation will readily enable us to conclude the 
 distance of the object observed from the earth's centre. 
 
 (8.) When the moon is the object observed, this ex- 
 pectation is found to be justified. The triangle in ques- 
 tion, though a long one, is not extravagantly so. Its
 
 THE SUN. 55 
 
 sides are found to be, each about thirty-eight times the 
 length of the base, and the resulting distance of the moon 
 from the earth's centre about thirty diameters of the 
 latter, or more exactly sixty times and a quarter its 
 radius, that is to say, 238,100 (say 240,000) miles, 
 which is rather under a quarter of a million so that, 
 speaking roughly, we may consider the moon's orbit 
 round the earth as a circle about half a million of miles 
 across. In the case of the sun, however, it is otherwise. 
 The sides of our triangle are here what may be called 
 extravagantly out of proportion to its base : and the 
 result of the calculation is found to assign to the sun a 
 distance very little short of four hundred times that 
 already found for the moon being in effect no less than 
 23,984 (in round numbers 24,000) radii, or 12,000 
 diameters of the earth, or in miles 94,880,700 or about 
 95,000,000.* 
 
 (9.) When so vast a disproportion exists between the 
 distance of an object and the base employed to measure 
 it, a very trifling error in the measured angles produces a 
 great one in the result. Happily, however, there exists 
 another and a very much more precise method, though 
 far more refined in principle, by which this most import- 
 ant element can be determined j viz., by observations of 
 the planet Venus, at the time of its " transit " (or visible 
 passage) across the sun's disc. It would lead us too far 
 aside from our purpose to explain this, however, at 
 
 * These numbers and all the subsequent statements in miles are 
 too large by about I mile in 31. See Lecture III. oa Cometa 
 9-
 
 56 THE SUN. 
 
 length. The necessary observations were made at the 
 time of the last " transit" in 1769, and will no doubt be 
 repeated on the next occasion of the same kind, in 1874.* 
 
 (10.) From the distance of the sun so obtained, and 
 from its apparent size (or, as astronomers call it, its 
 angular diameter), measured very nicely by delicate 
 instruments called micrometers, the real diameter of the 
 sun has been calculated at 882,000 miles, which I sup- 
 pose may be taken as exact to a few odd thousands. 
 
 (n.) Now, only let us pause a little, and consider 
 among what sort of magnitudes we are landed. It runs 
 glibly over the tongue to talk of a distance of 95,000,000 
 of miles, and a globe of 880,000 miles in diameter, but 
 such numbers hardly convey any distinct notion to 
 the mind. Let us see what kind of conception we can 
 get of them in other ways. And first then, as to the 
 distance. By railway, at an average rate of 40 miles an 
 hour one might travel round the world in 26 days and 
 nights. At the same rate it would take 270 years and 
 more to get to the sun. The ball of an Armstrong 100- 
 pounder leaves the gun with a speed of about 400 yards 
 per second. Well, at the same rate of transit it would 
 be more than thirteen years and a quarter in its journey 
 to reach the sun ; and the sound of the explosion (sup- 
 posing it conveyed through the interval with the same 
 speed that sound travels in our air), would not arrive 
 till half a year later. The velocity of sound, or ot any 
 
 * The distance above stated is that which results from this more 
 precise mode of procedure. See this explained in Lecture V., 
 17-
 
 THE SUN. 57 
 
 other impulse conveyed along a steel bar, is about six- 
 teen times greater than in air. Now, suppose the sun 
 and the earth connected by a steel bar. A blow struck 
 at one end of the bar, or a pull applied to it, would not 
 be delivered would not begin to be felt at the sun till 
 after a lapse of 313 days. Even light, the speed ^of 
 which is such that it would travel round the globe in less 
 time than any bird takes to make a single stroke of his 
 wing, requires seven minutes and a half to reach us from 
 the sun. 
 
 (12.) The illustration of the distance of the sun which 
 I have just mentioned, by supposing it connected with 
 the earth by a steel bar, will serve to give us some notion 
 of the wonderful connexion which that mystery of mys- 
 teries, gravitation, establishes between them. The sun 
 draws or pulls the earth towards it. We know of no 
 material way of communicating a pull to a distant object 
 more immediate, more intimate, than grappling it with 
 bonds of steel; and how such a bond would suffice we 
 have just seen. But the///// on the earth which the sun 
 makes is instantaneous, or at all events incomparably 
 more rapid in its transmission across the interval than 
 any solid connexion would produce, and even demon- 
 strably far more rapid than the propagation of light 
 itself* 
 
 (13.) Let me now try to convey some sort of palpable 
 
 notion of the size of the sun itself. On a circle six feet 
 
 in diameter, representing a section of it through the 
 
 centre, a similar section of the earth would be about 
 
 * See note at the end of this lecture.
 
 58 THE SUN. 
 
 represented by a fourpenny-piece, and a distance of a 
 thousand miles by a line of less than one-twelfth of an 
 inch in length. A circle concentric with it, representing 
 on the same scale the size of the moon's orbit about the 
 earth, would have for its diameter only thirty-nine inches 
 and a quarter, or very little more than half the sun's. 
 Imagine, now, if you can, a globe concentric with this 
 earth on which we stand ; large enough not only to fill 
 the whole orbit of the moon, but to project beyond it on 
 all sides into space almost as far again on the outside ! 
 A spangle, representing the moon, placed on the circum- 
 ference of its orbit so represented, would require to be 
 only a sixth part of an inch in diameter. 
 
 (14.) It is nothing to have the size of a giant without 
 the strength of one. The sun retains the planets in their 
 several orbits by a powerful mechanical force, precisely 
 as the hand of a slinger retains the stone which he whirls 
 round till the proper moment comes for letting it go. 
 The stone pulls at the string one way, the controlling 
 hand at the centre of its circle the other. Were the 
 string too weak, it would break, and the stone, prema- 
 turely released, would fly off in a tangential direction. If a 
 mechanist were told the weight of the stone (say a pound), 
 the length of the string (say a yard, including the motion 
 of the hand), and the number of turns made by the stone 
 in a certain time (say sixty in a minute, or one in a 
 second), he would be able to tell precisely what ought to 
 be the strength of the string so zsjust not to break; that 
 is to say, what weight it ought at least to be able to lift 
 without breaking. In the case I have mentioned, it
 
 THE SUN. 59 
 
 ought to be capable of sustaining 3 Ib. 10 oz. 386 grs. 
 If it be weaker it will break. And this is the force or 
 effort which the hand must steadily exert, to draw the 
 stone in towards itself, out of the direction in which it 
 would naturally proceed if let go ; and to keep it revolv- 
 ing in a circle at that distance. 
 
 (15.) Now, what the string does to the stone in the 
 sling, that, in the case of the sun retaining the earth in 
 its orbit, is done that same office is performed that 
 effort (in some mysterious way which the human mind is 
 utterly incapable of comprehending) is exerted that 
 pull communicated ; in an instant of time, and so far as 
 we can discover, without any material tie; by the force 
 of gravitation. We know the time the earth takes to 
 revolve about the sun. It is a year ; of so many days, 
 hours, minutes and seconds ; and we know its distance 
 95,000,000 of miles, which may easily be turned into 
 yards. Well, now, suppose a stone or a lump of lead of 
 a ton weight to be tied to the sun by a string, and slung 
 round it in such a circle and in such a time. Then, 
 on the very same principles, and by the same rules of 
 arithmetic, one may calculate the amount of pull, or 
 tension of the string, and it will be found to come out 
 i Ib. 6 oz. 51 grs. 
 
 (16.) We all know what sort of lifting power what 
 amount of muscular force it takes to sustain a pound 
 weight. Multiply this by 2240 and you have the mus- 
 cular effort necessary to sustain a ton. It would require 
 three or four strong horses straining with all their might. 
 Well, now, it is one of the peculiarities of this mysterious
 
 6o THE SUN. 
 
 power of gravitation, that its intensity the energy of its 
 pull is less and less as the distance of the thing pulled 
 is greater : and that in a higher proportion. At double 
 the distance, the force of the pull is not halved, but 
 quartered : at triple, it is not a third part, but a ninth. 
 There are mountains in the world five miles high ; that 
 is to say, whose summits are five miles farther from the 
 centre of the earth than the sea-level. If a ton of lead 
 were carried up to the top of such a mountain, though 
 it would still balance another ton, or 2240 weights of a 
 pound each on the scales, then and there ; yet it would 
 not require so great an effort, such an exertion of mus- 
 cular force, to raise and sustain it by five pounds and a 
 half. Now, fancy it removed to a height of 94,900,000 
 miles from the earth's surface, and estimating by the 
 same rule its apparent weight, you will find, if you make 
 the calculation, that it would not require more effort to sus- 
 tain it from falling, than would suffice to lift one thirty- 
 seventh part of a grain from the surface of the earth. 
 
 (17.) This, then, one thirty-seventh part of a grain, is 
 the force which the earth, placed where the sun is, would 
 exert on our lump of lead. But we have seen that to 
 retain such a lump in such an orbit requires a pull of i 
 Ib. 6 oz. 51 grs. Of course, then, the earth, so placed, 
 would be quite inadequate to retain it from flying off. 
 To do this would require as many earths to pull it as 
 there are thirty-seventh parts of a grain in i Ib. 6 oz. 
 5 1 grs. : that is to say, by an easy sum in arithmetic, 
 356,929; or in round numbers, 360,000. Now. this is 
 equivalent to saying, that to do the work which the sun
 
 THE SUN. 6l 
 
 does upon each individual ton of matter which the earth 
 consists of, it must pull it as if (mind I say as if) it were 
 made up of 360,000 earths. And this is what is meant 
 by saying, that the mass or quantity of gravitating 
 matter constituting the sun is 360,000 times as great as 
 the mass or quantity of such matter in the earth. 
 
 (18.) Thus, now, you see, we have weighed as well as 
 measured the sun, arid the comparison of the two results 
 leads to a very remarkable conclusion. In point of size, 
 the globe of the sun, being in diameter no times that of 
 the earth, occupies in bulk the cube of that number, or 
 1,331,000 times the amount of space. The disproportion 
 in bulk, then, is much greater than the disproportion in 
 weight, very nearly four times greater : so that you see, 
 comparatively speaking, and of course on an average of 
 its whole mass, the sun consists of much lighter materials 
 than the earth. And in this respect it agrees with all the 
 four great exterior planets, Jupiter, Saturn, Uranus, and 
 Neptune ; while all the others Mercury, Venus, and 
 Mars agree much more nearly with the earth, and seem 
 to form a quite distinct and separate family. 
 
 (19.) From this calculation of the mass of the sun, and 
 from its diameter, we are enabled to calculate the pres- 
 sure which any heavy body placed on its surface would 
 exercise upon it, or what power it would require to lift 
 it off. It is very nearly thirty times the power required 
 to lift the same mass here on earth. A pound of lead, 
 for instance, transported to the sun's surface, could not 
 be raised from it by an effort short of what would lift 
 thirty pounds here. A man could no more stand
 
 62 THE SUN. 
 
 upright there, than he could here on earth with twenty- 
 nine men on his shoulders. He would be squeezed as 
 flat as a pancake by his own weight. 
 
 (20.) Giant Size and Giant Strength are ugly qualities 
 without beneficence. But the sun is the almoner of the 
 Almighty, the delegated dispenser to us of light and 
 warmth, as well as the centre of attraction ; and as such, 
 the immediate source of all our comforts, and indeed 
 of the very possibility of our existence on earth. Even 
 the very coals which we burn, owe their origin to the 
 sun's influence, being all of vegetable materials, the re- 
 mains of vast forests which have been buried and pre- 
 served in that form for the use of man, millions of ages 
 before he was placed on the earth ; and which, but for 
 the solar light and heat, would have had no existence.* 
 Indeed, the theory of heat which is now gaining ground 
 would almost go to prove that it is the actual identical 
 heat which the sun put into the coal, while in the form 
 of living vegetation, that comes out again when it is 
 burnt as coal in our grates and furnaces ; so that, after 
 all, Swift's idea of extracting sunbeams out of cucumbers, 
 which he attributes to his Laputan philosophers, may 
 not be so very absurd, f 
 
 * See the treatise on Astronomy, by the author of this paper, in 
 "Lardner's Cabinet Cyclopaedia," published in 1833. Stevenson 
 (the celebrated engineer) has more recently drawn attention to this 
 fact. 
 
 T Not more so at least than some of his other Laputan speculations ; 
 such as calcining ice into gunpowder : or moving vast locomotive 
 masses by magnetism, both which feats have, in a somewhat altered 
 form of expiession, been accomplished (as in the explosion of potas- 
 sium when laid on ice, and the movement of a ship by electro-mag-
 
 THE SUN. 63 
 
 (21.) But how shall I attempt to convey to you any 
 conception of the scale on which the great work of 
 warming and lighting is carried on in the sun ? It is 
 not by large words that it can be done. All "word- 
 painting" must break down, and it is only by bringing 
 before you the consideration of great facts in the sim- 
 plest language, that there is any chance of doing it. In 
 the very outset here is the greatest fact of all the enor- 
 mous waste, or what appears to us to be waste the ex- 
 cessive, exorbitant prodigality of diffusion of the sun's 
 light and heat. No doubt it is a great thing to light 
 and warm the whole surface of our globe. Then look at 
 such globes as Jupiter and Saturn and the others. This, 
 as you will soon see, is something astounding ; but then 
 look what a trifling space they occupy in the whole 
 sphere of diffusion around the sun. Conceive that little 
 globe of the earth, such as we have described it in com- 
 parison with our six feet sphere, removed 12,000 of its 
 own diameters, that is to say, 210 yards from the centre 
 of such a sphere (for that would be the relative size of 
 its orbit) ! why, it would be an invisible point, and would 
 require a strong telescope to be seen at all as a thing 
 having size and shape. It occupies only the 75,oooth 
 part of the circumference of the circle which it describes 
 about the sun. So that 75,000 of such earths at that 
 distance, and in that circle placed side by side, would 
 
 netism) ; or than his plan for writing books by the concourse of acci- 
 dental letters, and selection of such combinations as form syllables, 
 words, sentences, &c., which has a close parallel in the learned 
 theories of the production of the existing races of animals by natural 
 selection.
 
 64 THE SUN. 
 
 all be equally well wanned and lighted, and, then, that 
 is only in one plane ! But there is the whole sphere of 
 space above and below, unoccupied ; at any single point 
 of which if an earth were placed at the same distance, 
 it would receive the same amount of light and heat. 
 Take all the planets together, great and small ; the light 
 and heat they receive is only one 227 millionth part of 
 the whole quantity thrown out by the sun. All the rest 
 escapes into free space, and is lost among the stars ; or 
 Iocs there some other work that we know nothing about. 
 Of the small fraction thus utilized in our system, the 
 earth takes for its share only one loth part, or less than 
 one 2000 millionth part of the whole supply. 
 
 (22.) Now, then, bearing in mind this huge preliminary 
 fact to start with, let us see what amount of heat the 
 earth does receive from the sun. The earth is a globe ; 
 and therefore, taken on an average, it is constantly re- 
 ceiving as much, both of light and heat, as a flat circle 
 8000 miles in diameter, held perpendicularly to receive 
 it. Now, that section is 50,000,000 square miles, so that 
 there falls at every instant on the whole earth 50,000,000 
 times as much heat as falls on a square mile of the hottest 
 desert under the equator at noonday with a vertical sun 
 and with not a cloud in the sky and in fact nearly a 
 third more ; for more than a quarter of the sun's heat is 
 absorbed in the air in the clearest weather, and never 
 reaches the ground. Now, we all know that in those 
 countries it is much hotter than we like to keep our 
 rooms by fires. I have seen the thermometer four inches 
 deep in the sand in South Africa rise to 159 Fahrenheit
 
 THE SUN. 6$ 
 
 and I have cooked a beef-steak and boiled eggs hard 
 by simple exposure to the sun in a box covered with a 
 pane of window-glass, and placed in another box so 
 covered. 
 
 (23.) From a series of experiments I made there, I 
 ascertained that the direct heat of the sun, received on a 
 a surface capable of absorbing and retaining it, is com- 
 petent to melt an inch in thickness of ice in 2 i3 m , and 
 from this I was enabled to calculate how much ice would 
 be melted per hour by the heat actually thrown on a 
 square mile exposed at noon under the equator, and the 
 result is 58,360,000 lb., or in round numbers, 26,000 
 tons, and this vast mass, has to be multiplied 50 million- 
 fold to give the effect produced on a diametral section of 
 our globe. 
 
 (24.) And, now, let us endeavour to form some kind of 
 estimate of the temperature; that is to say, the degree or 
 intensity of the heat at the actual surface of the sun. By 
 a calculation, with which I will not trouble you, it turns 
 out to be more than 90,000 times greater than the in- 
 tensity of sunshine here on our globe at noon and under 
 the equator a far greater heat than can be produced in 
 the focus of any burning-glass ; though some have been 
 made powerful enough to melt, not only silver and gold, 
 but even platina, and, indeed, all metals which resist the 
 greatest heats that can be raised in furnaces. 
 
 (25.) Perhaps the best way to convey some sort of 
 conception of it, will be to state the result of certain ex- 
 periments and calculations recently published ; which is 
 this that the heat thrown out FROM EVERY SQUARE YARD 
 
 E
 
 66 THE SUN. 
 
 of the sun's surface is equal to that which would be pro- 
 duced by burning on that square yard six tons of coal 
 per hour, and keeping up constantly to that rate of con- 
 sumption which, if used to the greatest advantage, would 
 keep a 63,000 horse steam-engine at work. And this, 
 mind, on each individual square yard of that enormous 
 surface which is 12,000 times that of the whole surface 
 of the earth ! 
 
 (26.) Let me say something now of the light of the sun. 
 The means we have of measuring the intensity of light 
 are not nearly so exact as in the case of heat but this at 
 least we know that the most intense lights we can pro- 
 duce artificially, are as nothing compared surface for sur- 
 face with the sun. The most brilliant and beautiful light 
 which can be artificially produced is that of a ball of 
 quicklime kept violently hot by a flame of mixed ignited 
 oxygen and hydrogen gases playing on its surface. Such 
 a ball, if brought near enough to appear of the same size 
 as the sun does, can no more be looked at without hurt 
 than the sun but if it be held between the eye and the 
 sun, and both so enfeebled by a dark glass as to allow of 
 their being looked at together it appears as a black 
 spot on the sun or as the black outline of the moon in 
 an eclipse, seen thrown upon it. It has been ascertained 
 by experiments which I cannot now describe, that the 
 brightness, the intrinsic splendour, of the surface of such 
 a lime-ball is only one i46th part of that of the sun's 
 surface. That is to say, that the sun gives out as much 
 light as 146 balls of quicklime each the size of the sun, and 
 each heated over all its surface in the way I have de-
 
 THE SUN. 67 
 
 scribed, which is the most intense heat we can raise, and 
 in which platina melts like lead. 
 
 (27.) On the benefits which the sun's light confers on 
 us it cannot be necessary to say much ; only one thing, 
 I think, may not be known to all who may read these 
 pages, viz., that it is not only by enabling us to see that 
 it is useful, but that it is quite as necessary as its heat 
 to the life and well-being both of plants and animals. 
 Animals, indeed, may live some time in complete dark- 
 ness, but they grow unhealthy; lose strength and pine 
 away; while plants very quickly lose their green colour; 
 turn white or pale yellow; lose all their peculiar scent and 
 flavour; refuse to flower; and at last rot and die off. 
 What I have now to say about the light of the sun is of 
 quite a different nature. 
 
 (28.) The sun's light, as we all know, is purely white. 
 If the sun sometimes looks yellow or red, it is because it is 
 seen through vapours, or smoke, or a London fog of smoke 
 and vapour mixed. It has been seen blue ;* but when 
 high up, in a clear sky, it is quite white. The whiteness 
 of snow, of a white cloud, of white paper, is the whiteness 
 of the sun's light which falls upon them. Whatever re- 
 flects the rays of the sun without choice or preference, appears 
 white. Whatever does not do so appears coloured ; and 
 if it does not reflect them at all black. Now I must 
 explain what I mean by saying " without choice cr pre- 
 
 * This has been denied by Arago. But I have a description of 
 the phoc-nomenon by an eye-witness, accompanied with a coloured 
 drawing, which leaves no doubt on my mind of the reality of the fact. 
 It was after a hurricane at Barbadoes.
 
 68 THE SUN. 
 
 ference." Every ray of light which comes from the sun is 
 not a simple but a compound thing. Here, again, I must 
 explain. The air we breathe is not a simple but a com- 
 pound thing. It is separable at least into four distinct 
 things, as different from one another as any four things 
 you can name. Well, then, so of a ray or beam of the 
 sun ; it may be separated, split, subdivided, not into four, 
 but into many hundreds, nay, thousands, of perfectly dis- 
 tinct rays or things, or rather of three distinct sorts or 
 species of rays ; of which one sort affects the eyes as 
 light ; one the sense of feeling and the thermometer as 
 heat ; and one the chemical composition of everything 
 it falls upon ; and which produces all the effects of photo- 
 graphy. Each of these three classes (and I believe there 
 are several more, indeed I have proved the existence of 
 one more) consists of absolutely innumerable species or 
 sorts ; every one of which is separated from every other 
 by a boundary line, as sharp and as distinct as that which 
 separates Kent and Sussex on a map. A ray of light is 
 a world in miniature, and if I were to set down all that 
 experiment has revealed to us of its nature and constitu- 
 tion, it would take more volumes than there are pages 
 in the manuscript of this lecture. 
 
 (29.) When the sun's light is allowed to pass through 
 a small hole in a dark place, the course of the ray or 
 sunbeam may be traced through the air (by reason of the 
 small fine dust that is always floating in it), as a straight 
 line or thread of light of the same apparent size, or very 
 nearly so, from the hole to the opposite wall. But if in 
 the course of such a beam, be held at any point the edge
 
 THE SUN. 69 
 
 of a clear angular polished piece of glass called a prism, 
 the course of the beam from that place will be seen to 
 be bent aside in a direction towards the thicker part ol 
 the glass and not only so bent or refracted, but spread 
 out to a certain degree, so that the beam in its furthei 
 progress grows continually broader, the light being dis- 
 persed, into a flat fan-shaped plane : and if this be re- 
 ceived on white paper ; instead of a single white spot 
 which the unbroken beam would have formed on it, 
 appears a coloured streak ; the colours being of exceed- 
 ing vividness and brilliancy, and following one another 
 in a certain fixed order graduating from a pure crimson 
 red at the end least remote from the original direction 
 (or least deviated], through orange, yellow, green, and 
 blue, to a faint and rather rosy violet. This beautiful 
 phenomenon the Prismatic Spectrum, as it is called 
 strikes every one who sees it for the first time in a high 
 degree of purity, with wonder and delight ; as I once 
 had the gratification of witnessing in the case of that 
 eminent artist the late Sir David Wilkie, who, strange to 
 say, had never seen a " Spectrum" till I had the pleasure 
 of showing him one ; and whose exclamations, though a 
 man habitually of few words, I shall not easily forget. I 
 shall not attempt to give any account of the theory of 
 this prismatic dispersion of the sunbeam ; but an illustra- 
 tion of it may be found in a very familiar and primitive 
 operation the winnowing of wheat. Suppose I had a 
 sieve full of mixed grains and other things shot, for 
 instance ; wheat grains ; sand ; chaff ; feathers ; and 
 that I flung them all out across a side wind, and noticed
 
 7O THE SUN. 
 
 where they fell The shot would fall in one place, the 
 wheat in another, the sand in another, the chaff in 
 another, and the feathers anywhere nowhere ; but none 
 of them in the straight direction in which they were 
 originally tossed. All would be deviated ; and if you 
 marked the places of each sort, you would find them all 
 arranged in a certain order that of their relative light- 
 ness in a line on the ground, oblique to the line of their 
 projection. You would have separated and assorted 
 them, and formed a spectrum, so to speak, on the 
 ground; or a picture of what had taken place in the 
 process ; which would in effect have been the perfor- 
 mance of a mechanical analysis of the contents of your 
 basket. 
 
 (30.) Bearing always in mind that it is an illustration 
 of a series of facts, not a theoretical explanation of a 
 natural process, which is here intended ; I will now pro- 
 ceed to observe that the analogy of this case to that of 
 the prismatic analysis of a sunbeam may be pursued still 
 further. If the original contents of the basket had been 
 all of one material, such as sand, consisting of a mixture 
 of particles of every gradation of coarseness and fineness ; 
 from small pebbles down to impalpable dust ; the trace 
 upon the ground, the sand spectrum, however long, 
 would be uninterrupted : the coarsest particles lying at 
 one end ; the finest at the other ; and every intermediate 
 size in every intermediate place. On the other hand, in 
 the case first supposed, and supposing the shot to differ 
 inter se in respect of size within certain limits ; the wheat 
 grains again within certain other ; the sand within other ;
 
 THE SUN. 
 
 and so on ; they would be found after projection all in- 
 deed lying in a line, but that line an interrupted one 
 consisting first of shot occupying a certain length ; then 
 an interval; then wheaten grains to a certain extent 
 another interval then sand, chaff, and so on. Now this 
 is by no means an inapt though a coarse representation 
 of the constitution of the Prismatic Spectrum. When it 
 is formed by an extremely pure prism, and with certain 
 precautions (which need not here be detailed) to ensure 
 the perfect purity of its colours, it is found to be discon- 
 tinuous : that is to say, not a simple streak like a riband 
 of paper coloured from end to end by tints graduating 
 insensibly from red to violet, but like such a riband 
 marked, across its breadth, by perfectly black lines of 
 exceeding delicacy, yet some wider some narrower than 
 others ; and where these lines are, the paper is not illu- 
 minated at all. Into these spaces (for narrow as they 
 are, they have each a certain breadth) none of the light 
 dispersed by the prism falls. These lines, be it also 
 observed, are not occasional or accidental, but perma- 
 nent ; and belong to the sun's light as such. They 
 divide the spectrum into compartments as the boundary 
 lines between counties on a map divide the soil into 
 regions ; and each individual of these compartments 
 differs in other qualities besides colour from its neigh- 
 bours on either side ; much as contiguous regions of a 
 country differ in soil and cultivation as well as in climate. 
 It is as if our assorted grains were distinguished not 
 only by being coloured according to their respective 
 sizes, but each particular size and weight distinguished
 
 72 THE SUN. 
 
 also by differences in the material of which they con- 
 sisted. 
 
 (31.) Every observer who has examined the spectrum 
 with more care than the last, has added to the number 
 of these lines. Dr Wollaston first noticed two or three 
 of the most conspicuous. Fraunhofer registered and 
 fixed the places of some thirty or forty more ; and later 
 observers have mapped down with all the precision of a 
 geographical survey, not less than two thousand of them. 
 The knowledge of them, and the precise measurement of 
 their distances from one another, has proved most valu- 
 able in a great many lines of scientific enquiry, and most 
 particularly in Optics and Chemistry ; and, quite recently, 
 has been the means of revealing facts respecting the con- 
 stitution of the sun itself, which one would have supposed 
 it impossible for man ever to have become acquainted 
 with. One word more on these lines for we must hus- 
 band time, as there remains a great deal more ground 
 to go over. I have said that they are not occasional, but 
 belong to the sun's light as such. But they may be con- 
 sidered as in some sort accidental as regards the sun for 
 the light of each of the stars when thrown into a spec- 
 trum, is found to have a different system of these " fixed 
 lines." And what is more, the light of every flame has 
 its peculiar lines, which indicate the nature of the burn- 
 ing substance. And in this way there seems to arise a 
 possibility that by studying these lines carefully, as ex 
 hibited by terrestrial flames and other sources of artificial 
 light, we may come to a knowlege of what the sun and 
 stars are made of. This is what men of science are now
 
 THE SUN 73 
 
 very busily occupied about, and it seems to have been 
 rendered at least highly probable I do not say that it 
 has been proved that a great many of the chemical 
 elements of this our earth exist in the sun such as, for 
 instance, iron, soda, magnesia, and some others. We 
 cannot here state the extraordinary facts on which this 
 conclusion rests. But the conclusion itself is not so ab- 
 solutely strange and startling as it may at first appear. 
 The analysis of meteorolites, which there can be no doubt 
 have come to the earth from very remote regions of the 
 Planetary spaces, has, up to the present time, exhibited 
 no new chemical element so that a community of 
 nature, at least as regards material constitution, between 
 our earth and the rest of the bodies of our system, is at 
 all events no unexpected, as it is, in itself, no unreason- 
 able conclusion. 
 
 (32.) Not that it is meant, by anything above said, to 
 imply that the light of the sun is that of any flame, in the 
 usual sense of the word. A late celebrated French phil- 
 osopher, M. Arago, indeed, considered that he had 
 proved it to be so by certain optical tests. But in the 
 first place his proof is vitiated by an enormous oversight ; 
 and the thing, besides, is a physical impossibility. The 
 light and heat of the sun cannot possibly arise from the 
 burning of fuel, so as to give out what we call flame. If 
 it be the sun's substance that burns (I mean consumes), 
 where is the oxygen to come from 1 and what is to become 
 of the ashes, and other products of combustion ? Even 
 supposing the oxygen supplied from the material, as in 
 the cases of gunpowder, Bengal light, or gun cotton, still
 
 74 THE SUN. 
 
 the chemical products have to be disposed of. In the 
 case of gun cotton, it has been calculated that, if the sun 
 were made of it so condensed as only to burn on the 
 surface, it would burn out, at the rate of the sun's ex- 
 penditure of light and heat, in eight thousand years. Any- 
 how fire, kept up by fuel and air, is out of the question. 
 There remain only three possible sources of them, so far 
 as we can perceive electricity, friction, and vital action. 
 The first of these was suggested by the late Sir William 
 Herschel in 1801; the second, at least as a possibility, 
 though without indicating any mode by which the neces- 
 sary friction could arise, by myself, in a work* published 
 in 1833. The theory at present current of it is founded 
 on what may not unfairly be considered a further develop- 
 ment of this idea, the friction being supposed to arise 
 from meteoric matter circulating round the sun, and 
 gradually subsiding into it, and either tearing up its sur- 
 face, or ploughing into its atmosphere. But on this we 
 cannot dilate, as nothing has been hitherto said about 
 the appearance of the sun in telescopes, and the strange 
 phgenomena its surface, so examined, exhibits. 
 
 (33.) One of the earliest applications of the telescope 
 was to turn it on the sun. And the first fruits of this 
 application (which originated about the same time in 
 the year 1611, with Harriot in England, Galileo in Italy, 
 and Fabricius and Scheiner in Germany), was the dis- 
 
 * "Lardner's Cabinet Cyclopaedia," Astronomy, s. 337, p. 212. 
 Aristotle was earlier in making this suggestion : but such random 
 guesses as those of the ancients can hardly merit the name of scien- 
 tific suppestions.
 
 THE SUN. 75 
 
 covery of black spots on its surface, which, when watched 
 from day to day, were found to change their situation on 
 its disc, in a certain regular manner; coming in, or 
 making their first appearance on the eastern edge or 
 border of the disc : i.e., on the left-hand side of the sun 
 when seen at noonday; and going off, or disappearing 
 at the west, or on the right-hand side. It very soon 
 became evident that, whatever these spots might be, they 
 adhered to the body of the sun, and that their apparent 
 motions could only be accounted for by a real motion of 
 rotation of the sun on an axis nearly, but not quite, per- 
 pendicular to the ecliptic. By following out this indica- 
 tion by careful observation and calculation, it has become 
 known that the sun does so rotate; that the time 
 occupied in a single rotation is very nearly 25 days 7 
 hours 48 minutes ; that the axis of rotation is about 7 
 inclined to a line perpendicular to the ecliptic, its direc- 
 tion in space being that of a line pointing nearly to the 
 star r (tau), in the constellation of the Dragon ; in con- 
 sequence of which on and about the nth of June, the 
 spots appear to pass across the sun in straight lines, from 
 the apparent northern to the apparent southern hemi- 
 sphere of the sun, and the reverse on and about the i2th 
 of December, while at intervening times, their course 
 across the sun is a flattened elliptical or oval curve ; a 
 necessary consequence of their real motion being in a 
 circle much inclined to the line of sight. Their ellipses 
 are most open on the i ith of March, and the i3th of Sep- 
 tember; on the former of which days we get the best view of 
 the south pole of the sun, and on the latter of the north,
 
 76 THE SUN. 
 
 (34.) But here comes the strange part of their history. 
 These spots are not permanent marks on the sun's 
 surface. They come and go. They begin as small dim 
 specks ; grow to be great blotches ; and then dwindle 
 away. Sometimes they are large enough to be seen 
 without a telescope, when the sun is near setting or just 
 risen, so as to have its dazzling splendour mitigated by 
 the vapours of the horizon, and admit of being looked 
 at steadily. Many instances of such appearances are 
 recorded, some very remarkable ones, long before the 
 invention of the telescope. Two were so seen by my 
 son, Mr A. Herschel, in London, in November, 1861, 
 who sent me a drawing of them, which I found verified 
 on comparison with a drawing taken from the telescope 
 on the same day, by a very assiduous observer in my im- 
 mediate neighbourhood. 
 
 (35.) Ever since the first discovery of the solar spots, 
 they have been watched with great interest, and it has 
 been ascertained that they do not make their appearance 
 indiscriminately upon every part of the globe of the 
 sun. At or near either of its poles they never appear ; 
 and very rarely indeed on its equator, or on any part of 
 its body beyond the 4oth degree of latitude understand- 
 ing that term on the sun in the same acceptation which 
 geographers attach to it on our own globe. They 
 mainly frequent two zones or belts parallel to its equator ; 
 bearing very nearly the same relation to that great circle 
 of its sphere which the regions on our own globe in 
 which tne trade winds prevail, bear to the equatorial 
 region of the earth extending, that is to say, to some
 
 THE SUN. 77 
 
 25 or 3O 3 of north, and not quite so far, or in such 
 abundance in south latitude; with a comparatively spot- 
 less intermediate belt, of five or six degrees broad be- 
 tween them, answering to our region of equatorial calms. 
 The resemblance is so striking as most strongly to suggest 
 some analogy in the causes of the two phaenomena and 
 it has been suggested that as our trade winds originate in 
 a greater influx of heat from without, on and near the 
 equator, than at the poles, combined with the earth's 
 rotation on its axis : so the maculiferous belts of the sun 
 may owe their origin to a less * equatorial efflux of heat, 
 combined with the axial rotation of that luminary.t 
 There is another extremely remarkable feature in the 
 appearance and disappearance of these spots. I have 
 said that they are not permanent. Sometimes, indeed, 
 but rarely, one and the same spot lasts long enough, after 
 disappearing at the western edge of the sun, to come 
 round again and reappear at the eastern ; and it has 
 happened that a spot has lasted long enough to reappear 
 four or five times ; but for the most part this is not the 
 case. But as regards the number of spots which appear 
 on the sun at different times, there is the greatest pos- 
 sible difference. Sometimes it is quite spotless ; al 
 others the spots swarm upon it : and as many as fifty 01 
 sixty spots or groups, large and small, have been seen at 
 once, arranged in two belts. 
 
 (36.) Now, it has lately been ascertained by a careful 
 
 * Misprinted grea'er in the original lecture as it appeared in 
 Good Words. 
 
 t " Results of Astronomical Observations at the Cape of Good 
 Hope," by the author, p. 434.
 
 78 THE SUN. 
 
 comparison of all the recorded observations of the spots, 
 that the periods of their scarcity and abundance succeed 
 one another at regular intervals of a trifle more than five 
 years and a half: so that in eleven years and one-tenth, 
 or nine times in a century, the sun passes through all its 
 states of purity and spottiness. Thus, for instance, in 
 the present century, the years 1800, 1811, 1822, 1833, 
 1844, 1855-6 were years in which the sun exhibited few 
 or no spots, while in the years 1805, 1816, 1827, 1838, 
 1849, 1860, the spots have been remarkably abundant 
 and large. Several attempts have been made to connect 
 this with periodical variations in the weather, with hot 
 and cold years wet and dry ones years of good and 
 bad harvests, etc. ; but though I believe there is some 
 such connexion, it is so overlaid and, as it were, masked 
 by the multitude of causes which act to produce what 
 we call the prevalent weather of a season, that nothing 
 satisfactory has been made out. But there are two classes 
 of phenomena or facts which occur here on earth which 
 certainly do stand in very singular accordance with the 
 appearance and disappearance of the sun's spots. The 
 first is that splendid and beautiful appearance in the sky 
 which we call the Aurora or Northern lights ; and which, 
 by comparison of the recorded displays, have been ascer- 
 tained to be much more frequent in the years when the 
 spots are abundant, and extremely rare in those years 
 when the sun is free from spots. The other is a class of 
 facts not so obvious to common observation, but of very 
 great importance to us ; because it is connected with the 
 history and theory of the mariner's compass, and with
 
 THE SUN. 79 
 
 the magnetism of the earth ; which we all know to be 
 the cause of the compass needle pointing to the north. 
 This is only a rough way of speaking. It does not 
 point to the north, but very considerably to the west of 
 north, and that, not always alike. Three centuries ago 
 it pointed nearly as much east as now west of north. 
 From year to year the change is very perceptible ; and, 
 what is more, at every hour of the day there is a small 
 but perfectly distinct movement to and fro, eastward and 
 westward, of its average direction. But besides this, the 
 compass needle is subject to irregular, sudden, and ca- 
 pricious variations jerking, as it were, aside, and oscil- 
 lating backwards and forwards without any visible cause 
 of disturbance. And, what is still more strange ; these 
 disturbances and jerks sometimes go on for many hours 
 and even days, and often at the same instants of time, 
 over very large regions of the globe ; and in some 
 remarkable instances, over the whole earth the same 
 jerks and jumps occurring at the same moments of time 
 (allowance made for the difference of longitude). These 
 occurrences are called magnetic storms, and they invari- 
 ably accompany great displays of the Aurora ; and are 
 very much more frequent when the sun is most spotted, 
 and rarely or never witnessed in the years of few spots. 
 
 (37.) The last four years* have been remarkable for 
 spots, and there occurred on the ist September 1859, an 
 appearance on the sun which may be considered an 
 epoch, if not in the sun's history, at least in our know- 
 
 * This lecture was delivered about the end of 1 86 1.
 
 8o THE SUN. 
 
 ledge of it. On that day great spots were exhibited ; 
 and two observers, far apart and unknown to each other, 
 were viewing them with powerful telescopes ; when sud- 
 denly, at the same moment of time, both saw a strikingly 
 brilliant luminous appearance, like a cloud of light far 
 brighter than the general surface of the sun, break out 
 in the immediate neighbourhood of one of the spots, 
 and sweep across and beside it. It occupied about five 
 minutes in its passage, and in that time travelled over a 
 space on the sun's surface which could not be estimated 
 at less than 35,000 miles. 
 
 (38.) A magnetic storm was in progress at the time. 
 From the 28th of August to the 4th of September many 
 indications showed the earth to have been in a perfect 
 convulsion of electro-magnetism. When one of the 
 observers I have mentioned had registered his observa- 
 tion ; he bethought himself of sending to Kew, where 
 there are self-registering magnetic instruments always at 
 work, recording by photography at every instant of the 
 twenty-four hours the positions of three magnetic needles 
 differently arranged. On examining the record for that 
 day, it was found that at that very moment of time (as if 
 the influence had arrived with the light) all three had 
 made a strongly marked jerk from their former positions. 
 By degrees, accounts began to pour in of great Auroras 
 seen on the nights of those days ; not only in these lati- 
 tudes, but at Rome ; in the West Indies ; on the tropics 
 within 1 8 of the equator (where they hardly ever ap- 
 pear), nay, what is still more striking, in South America 
 and in Australia ; where, at Melbourne, on the night of
 
 THE SUN. 8l 
 
 the zd of September the greatest Aurora ever seen there 
 made its appearance. These Auroras were accompanied 
 with unusually great electro-magnetic disturbances in 
 every part of the world. In many places the telegraphic 
 wires struck work. They had too many private messages 
 of their own to convey. At Washington and Philadel- 
 phia, in America, the telegraph signal-men received 
 severe electric shocks. At a station in Norway the 
 telegraphic apparatus was set fire to ; and at Boston, in 
 North America, a flame of fire followed the pen of Bain's 
 electric telegraph, which, as my hearers perhaps know, 
 writes down the message upon chemically prepared 
 paper. 
 
 (39.) I must now proceed to tell you what the tele- 
 scope has revealed to us as to the nature and magnitude 
 of these spots. And here again, the closer we look, the 
 more the wonder increases. The spots were at first 
 supposed to be clouds of black smoke floating over the 
 great fieiy furnace beneath, then great lumps of fresh 
 coal laid on ; then comets fallen in to feed the fire ; then 
 tops of mountains standing up above a great surging 
 ocean of melted matter. They are none of all these 
 things ; they are not clouds floating above the light, nor 
 protuberances sticking up above the general surface ; 
 they are regions in which, by the action of some most 
 violent cause, the bright, luminous clouds, or what at all 
 events we may provisionally call clouds, which float in 
 the sun's atmosphere, are for a time cleared off; and 
 through the irregular vacuities thus created, allow us to 
 see perhaps thousands or tens of thousands of miles 
 
 F
 
 82 THE SUN. 
 
 below them, first, a layer of what we may consider real 
 clouds, which appear comparatively dark, as if they were 
 not self-luminous, but were seen only by the reflected 
 light of the upper layer of bright ones ; secondly, through 
 other openings in this first layer, a second still darker 
 layer, independent of the first, and probably still thou- 
 sands of miles below that, and reached by some but 
 very little light from above ; and thirdly, through 
 again other openings, what at present we must consider 
 to be the body of the sun itself at some vast and im- 
 measurable depth still lower and emitting so little 
 light in comparison as to appear quite black, though that 
 does not prevent its being in as vivid a state of fiery 
 glare as a white-hot iron ; when we remember what has 
 been said of the lime light appearing black against the 
 light of the sun's surface. And it is a fact, that when 
 Venus, and Mercury pass across the sun, and are seen 
 as round spots on it, they do really appear . sensibly 
 blacker than the blackest parts of the spots. 
 
 (40.) The sun then has an atmosphere, and in that 
 atmosphere float at least three layers of something, that, 
 for want of a better word, we must call clouds. The 
 two nearest the body are not luminous. They cannot 
 possibly be clouds of watery vapour, such as we have in 
 our air, for water in a non-transparent state could not 
 exist at that heat; but they may be what perhaps we 
 might call smokes, that is to say, clouds in which the 
 metals or their oxides and the earths exist in the same 
 intermediate form that water does in our clouds. The 
 third or upper layer of luminous clouds ; or, as it is called,
 
 THE SUN. 83 
 
 " the photosphere," is a sort of thing that three or four 
 years ago we might be said to know nothing at all about ; 
 I mean as to its nature and constitution; but within 
 that time a most wonderful discovery has been made by 
 Mr Nasmyth. According to his observations, made 
 with a very fine telescope of his own making, the bright 
 surface of the sun consists of separate, insulated, indi- 
 vidual objects or things, all nearly or exactly of one cer- 
 tain definite size and shape, which is more like that of 
 a willow leaf, as he describes them, than anything else. 
 These leaves or scales are not arranged in any order 
 (as those on a butterfly's wing are), but lie crossing one 
 another in all directions, like what are called spills in 
 the game of spillikins ; except at the borders of a spot, 
 where they point for the most part inwards towards the 
 middle of the spot, presenting much the sort of appear- 
 ance that the small leaves of some water-plants or sea- 
 weeds do at the edge of a deep hole of clear water. The 
 exceedingly definite shape of these objects ; their exact 
 similarity one to another ; and the way in which they lie 
 across and athwart each other (except where they form a 
 sort of bridge across a spot, in which case they seem to 
 affect a common direction, that, namely, of the bridge 
 itself), all these characters seem quite repugnant to 
 the notion of their being of a vaporous, a cloudy, or a 
 fluid nature. Nothing remains but to consider them as 
 separate and independent sheets, flakes, or scales, having 
 some sort of solidity. And these flakes, be they what 
 they may, and whatever may be said about the dashing 
 of meteoric stones into the sun's atmosphere, etc., are
 
 84 THE SUN. 
 
 evidently the immediate sources of the solar light and heat, 
 by whatever mechanism or whatever processes they may 
 be enabled to develop and, as it were, elaborate these 
 elements from the bosom of the non-luminous fluid in 
 which they appear to float. Looked at in this point of 
 view, we cannot refuse to regard them as organisms of 
 some peculiar and amazing kind ; and though it would 
 be too daring to speak of such organization as partaking 
 of the nature of life, yet we do know that vital action is 
 competent to develop both heat, light, and electricity. 
 These wonderful objects have been seen by others 
 as well as by Mr Nasmyth, so that there is no room to 
 doubt of their reality. To be seen at all, however, even 
 with the highest magnifying powers our telescopes will 
 bear when applied to the sun, they can hardly be less 
 than a thousand miles in length, and two or three 
 hundred in breadth. 
 
 (41.) Next as to the actual size of the spots them- 
 selves : the distance of the sun is so vast, that a single 
 second of angular measure on its surface as seen from 
 the earth corresponds to 460 miles ; and since, to pre- 
 sent a distinguishable form, so as to allow of a certainty, 
 for instance, that it is round or square, in the best tele- 
 scopes, an object must present a surface of at least a 
 second in diameter, it follows that to be seen at all so as 
 to make out its shape, a spot must cover an area of not 
 less than two hundred thousand square miles. Now, 
 spots of not very irregular, and what may be called a com- 
 pact form, of two minutes in extent, covering, that is to 
 gay, an area of between seven and eight hundred millions
 
 THE SUN. 85 
 
 of square miles, are by no means uncommon. One spot 
 which I measured in the year 1837 occupied no less than 
 three thousand seven hundred and eighty millions, taking 
 in all the irregularities of its form ; and the black space 
 or "' umbra " in the middle of one, which was very nearly 
 round, would have allowed the earth to drop through 
 it, leaving a thousand miles clear of contact on every 
 side : and many instances of much larger spots than 
 these are on record. What are we to think, then, of the 
 awful scale of hurricane and turmoil and fiery tempest 
 which can in a few days totally change the form of such 
 a region, break it up into distinct parts open up great 
 abysses in one part, such as that I have just described, 
 and fill up others beside them ? As to the forms of the 
 spots, they are so conspicuously irregular as to defy de- 
 scription. 
 
 (42.) But we must proceed, for there are more won- 
 ders yet to relate. Far beyond the photosphere, or 
 brilliant surface of the sun, extends what perhaps may 
 be considered as its true atmosphere. This can only 
 be seen at all in the rare opportunities afforded by total 
 eclipses of the sun. Everybody knows that an eclipse of 
 the sun is caused by the moon coming between it and 
 us. Now, by an odd coincidence, it so happens that 
 the sun being 400 times farther off than the moon, is 
 also ALMOST exactly, but a trifle less than 400 times as 
 large in diameter; so that when the centre of the moon 
 comes exactly in the line with the centre of the sun it 
 appears to cover it, and a very little more, so as to pro- 
 ject on all sides a very little beyond it Now, as the
 
 86 THE SUN. 
 
 moon is opaque (or not transparent), it completely stops 
 all the light from every part of the bright disc of the sun, 
 so long as the total eclipse continues, which is sometimes 
 as much as two or three minutes ; and then are witnessed, 
 what at no other time can be seen, viz., certain wonder- 
 ful appearances of rose-coloured masses of light project- 
 ing, as it were, from the dark edge of the moon, for the 
 most part like knobs, or cones, or long ranged ridges 
 of what would seem to be mountains, rising from it ; but 
 sometimes like clouds or flaring flag-shaped masses of 
 red light, some of which have been seen quite detatched 
 from all connexion with the moon's border. That they 
 belong to the sun, however, and not the moon, is evident 
 from the fact that the moon in its progress over the sun's 
 face gradually hides those to which it is approaching, and 
 discloses those which belong to that side of the sun 
 which the moon is going to leave ; for I should mention 
 that they are seen irregularly placed all round the edge 
 of the sun. 
 
 (43.) Now, what are these singular lights? Flames 
 they certainly are not; clouds of some sort it is ex- 
 tremely probable that they are, of most excessively thin 
 and filmy vapour, floating in a transparent atmosphere 
 which must for that purpose extend to a very consider- 
 able height above the luminous surface of the sun. We 
 are all familiar with the beautiful appearance of those 
 thin vapoury clouds which appear in our own atmosphere 
 at sunset. But these solar clouds must be almost infi- 
 nitely thinner and more unsubstantial, since even in that 
 intense illumination they are only seen when the sun
 
 THE SUN. 87 
 
 itself is hidden ; and when it is remembered that the 
 head of the comet of 1843 was seen at noon-day within 
 two or three degrees of the sun by the naked eye. 
 
 (44.) Then, again, as to the magnitude of these cloudy 
 masses, it must be enormous. Some of them have pro- 
 jected or stood out from the edge of the sun to a distance 
 calculated at no less than forty or fifty thousand miles. 
 They have now been observed in three great eclipses, 
 that of 1842, 1851, and 1859; on which last occasion 
 they were photographed in Spain by Mr De la Rue, 
 under such circumstances as left no possibility of doubt- 
 ing their belonging to the sun. I dwell upon this, be- 
 cause there is another luminous appearance seen about 
 the moon in total eclipses of the sun, which can only be 
 referred to vapours of excessive tenuity, existing at an 
 immense height in our own atmosphere ; and which sur- 
 rounds the disc of the moon like a glory, or corona, as it 
 is called. By the accounts of all who have witnessed 
 a total eclipse of the sun, it is one of the most awful 
 natural phenomena. An earthquake has " rolled unheed- 
 edly away" during a battle, but an eclipse has on more 
 than one occasion either stopped tne combat or so para- 
 lyzed one of the parties with terror, as to give the others 
 who were prepared for it an easy victory: and I may as 
 well add that two very remarkable battles in ancient 
 history, the one on the a8th May, B.C. 585, the other the 
 i gth May, B.C. 557, which were in progress during total 
 eclipses, have had the years and days of their occurrence 
 thereby fixed by calculation with a certainty which be- 
 longs to no other epochs in ancient chronology.
 
 88 THE SUN. 
 
 (45.) There is only one more point which my limits 
 will allow me to touch upon. I will go back to my origi- 
 nal metaphor. Our giant may be a huge giant and a 
 strong giant, and a good-natured giant, but if he be a 
 sluggard he is no giant worth the name. We have seen 
 that he is a little slow to turn on his axis and roll himself 
 round in his nest. But take him in his relation to the 
 outer world, he is lively enough ; he "rejoices as a giant 
 to run his course ;" and vindicates his credit as a swift 
 runner with a vengeance ! Hitherto I have only spoken 
 of the sun as a sun, the centre of our system ; and, as 
 such, regarded by us as immovable. Even in this 
 capacity he is not quite fixed. If he pulls the planets, 
 they pull him and each other ; but such family struggles 
 affect him but little. They amuse them, and set them 
 dancing rather oddly ; but don't disturb him. As all the 
 gods in the ancient mythology hung dangling from and 
 tugging at the golden chain which linked them to the 
 throne of Jove ; but without power to draw him from his 
 seat : so if all the planets were in one straight line, and 
 exerting their joint attractions, the sun, leaning a little 
 back as it were to resist their force, would not be dis- 
 placed by a space equal to his own radius ; and the fixed 
 centre, or, as an engineer would call it, the centre of 
 gravity of our system, would still lie within the sun's 
 globe. 
 
 (46.) But the sun has another and, so far as we can 
 judge, a much vaster part in creation to perform than to 
 sit still as the quiet patriarch of a domestic circle. 
 He is up and active as a member of a community like
 
 THE SUN. 89 
 
 himself. The sun is not only a sun, he is a STAR also, 
 and that but a small one in comparison with individual 
 stars (one of which, Sirius, would make two or three 
 hundred of him); and among these glorious compeers he 
 moves on a path which is just beginning to become 
 known to us ; though in what orbit, or for what purpose, 
 will never be given to man to know. Yet we do know 
 almost to a nicety the direction in which that path is 
 leading ; and the rate of his travel (though this is less 
 exactly determined). Still this rate, at the very lowest 
 estimate, cannot be taken under four or five hundred 
 thousand miles a day; and yet this speed, vast as it is, 
 in the 2000 years which separate us from the observations 
 of Hipparchus (who made the first catalogue of the stars), 
 would not suffice to carry it (and of course our system 
 along with it) over one sixtieth part of the distance which 
 now separates it from the very nearest of the stars. 
 When we travel through a diversified country, we become 
 aware of our change of situation by the different group- 
 ing and presentation of the objects around us. But 
 though travelling at this amazing rate through space, 
 successive generations of mankind witness no change in 
 the order and arrangement of the stars ; and Hipparchus, 
 were he to come once more among us, would recognize 
 the old familiar forms of his constellations; and, without 
 better means of observation than he then possessed, 
 would be unable to detect, with certainty, any change in 
 their appearance; though we, who are better provided 
 in that respect, are enabled to do so. 
 
 (47.) Such, then, is the scale of things with which we
 
 9O THE SUN. 
 
 become familiar when we contemplate the sun. In what 
 has been said, it will be perceived that I have been more 
 anxious to dwell upon facts than theories, and rather to 
 supply the imaginations of my audience with materials for 
 forming a just conception of the stupendous magnificence 
 of this member of God's creation, than to puzzle them 
 with physical and mathematical reasonings and argu- 
 ments. 
 
 NOTE ON 12. The effect of any supposed small loss of time in 
 the transmission of the sun's attractive force on the earth across the in- 
 tervening space, may be very easily made intelligible without going 
 through any abstruse calculation. The pull exerted on the earth 
 would be delivered there, not in the direction of the line joining the 
 sun and earth at the instant of its arrival, but of that which did join 
 them when it left the sun. Its action on the earth would therefore 
 be oblique to their actual line of junction, or to what is called the 
 radius vector of the orbit tending, not towards the sun, but towards 
 a point somewhat in advance of it (i.e., lying from it in the direc- 
 tion in space of the region towards which the earth is moving). 
 This force then being resolved in radial and tangential directions 
 would produce, in the former, a force directed to the sun differing 
 by a mere infinitesimal from its direct gravity and in the latter, one 
 always accelerating the earth in its orbit, and which, however minute, 
 must of necessity result in a continually progressive increa.se of the 
 major axis, and therefore of the length of the year. Supposing the 
 transmission of gravity to be performed with the speed only of light 
 the inclination of the line of pull to the radius vector would be 
 2o"'25 (the exact value of the coefficient of aberration), and the 
 accelerating tangential force thence resulting would amount to 
 I-ioi88th part of the sun's direct attraction, a force whose effects 
 would become evident in a very few years to say nothing of the 
 centuries elapsed since the first determination of the length of the 
 year.
 
 LECTURE III. 
 
 ON COMETS. 
 
 ]HE subject of comets, about which I now pro- 
 pose to say something, is one that has of late 
 naturally drawn to it a good deal of inquiry 
 and general interest, by reason of the un- 
 usually magnificent spectacles of this description whicn 
 have within the last few years been exhibited to us.* In 
 itself it is perhaps not one of the best adapted for 
 popular discussion and familiar explanation of this 
 nature, because there are so many things in the history of 
 comets unexplained, and so many wild and extravagant 
 notions in consequence floating about in the minds of 
 even well-informed persons, that the whole subject has 
 rather, in the public mind, that kind of dreamy inde- 
 finite interest that attaches to signs and wonders than 
 any distinct, positive, practical bearing. The fact is, 
 that, though much is certainly known about comets, there 
 * This lecture was delivered on February 14, 1859.
 
 92 ON COMETS. 
 
 is a great deal more about which our theories are quite 
 at fault; and, in short, that it is a subject rather cal- 
 culated to show us the extent of our ignorance than to 
 make us vain of our knowledge, and to cause us to ex- 
 claim with Hamlet, " There are more things in heaven 
 and earth, Horatio, than are dreamt of in our philo- 
 sophy." This ; the sublimity of the spectacle they 
 afford ; and the universal interest they inspire, make the 
 appearance of a great comet an occasion for the ima- 
 ginations of men to break loose from all restraint of 
 reason, and luxuriate in the strangest conceptions. I 
 have received letters about the comets of the last few 
 years, enough to make one's hair stand on end at the 
 absurdity of the theories they propose, and at the 
 ignorance of the commonest laws of optics, of motion, of 
 heat, and of general physics they betray in their writers. 
 This is always the case whenever a great comet appears, 
 only that in the later instances one feature of the general 
 commotion of mind they inspire has been wanting. 
 Thanks to the prevalence of juster notions of the con- 
 stitution of the universe, and of the relation in which 
 man stands to its Author; countries calling them- 
 selves civilized appear not to have been disgraced by 
 any of those panic terrors, or thought it necessary to 
 propitiate Heaven by any of those superstitious ex- 
 travagances, about which we read on several former 
 occasions. Even at Naples, which seems to be almost 
 the lowest point of Europe in the scale of intellec- 
 tual and social progress, I have not heard that it was 
 thought necessary to liquefy the blood of St Januarius,
 
 ON COMETS. 93 
 
 or to cany his bones about the streets on account of 
 any of these later great comets. 
 
 (2.) When we look through nature and observe the 
 manifest indications of design which every point of it ex- 
 hibits, it would be very presumptuous in us to assert that 
 comets are of no use, and serve no purpose in our system. 
 Hitherto, however, no one has been able to assign any 
 single point in which we should be a bit better or worse 
 off, materially speaking, if there were no such thing as 
 a comet. Persons, even thinking persons, have busied 
 themselves with conjectures: such as that they may serve 
 for fuel for the sun (into which, however, they never 
 fall), or that they may cause warm summers which 
 is a mere fancy or that they may give rise to epidemics, 
 or potato-blights, and so forth. But I need hardly say 
 this is all wild talking, as my readers will be better 
 able to judge when I shall have stated a few things which 
 are known for certain about them. But there is a use, 
 and a very important one, of a purely intellectual kind, 
 which they have amply fulfilled ; and who shall say that 
 it has not been designed that such should be the case 1 
 They have afforded some of the sublimest and most 
 satisfactory verifications of our astronomical theories 
 they have furnished us with a proof amounting to 
 demonstration of the existence of a repulsive force* 
 directed (under certain circumstances, and acting on 
 certain forms of matter) from the sun as well as of that 
 
 * See on this subject my " Results of Astronomical Observations 
 at the Cape of Good Hope," p. 407, et sey., where the existence of 
 such a re^ul -ivc force is clearly demonstrated.
 
 94 ON COMETS. 
 
 great and general attractive force which keeps the planets 
 in their orbits and they have actually informed us of 
 the weight of one of the planets which could not have 
 been determined with any exactness if a comet had not 
 on one occasion passed very near to it. 
 
 (3.) The ancients believed comets to be much of the 
 same nature as meteors or shooting stars either in the 
 earth's atmosphere not far above the clouds ; or, at all 
 events, much lower than the moon or else as a species 
 of vapours or exhalations raised up from the earth by 
 the sun's heat, or by some other unknown cause; but 
 they never for a moment dreamed of their forming part 
 and parcel of that vast system of planetary bodies cir- 
 culating about the sun, of which in fact they had hardly 
 any distinct notions. In ancient history, however, 
 several very remarkable comets stand recorded. One 
 is mentioned by the Greek philosopher Aristotle in 371 
 B.C., with a tail extending over a third part of the sky. 
 Many great comets are recorded at even more ancient 
 dates in the Chinese annals : for that strange people kept 
 an official record of all the remarkable stars, meteors, 
 and other celestial appearances, for more than a thou- 
 sand years before the Christian era, and what is stranger 
 still, that record has been handed down to us and seems 
 dependable. A great comet was seen close to the sun 
 62 years before Christ, during a total eclipse and one 
 which appeared in the year 43 B.C., soon after the 
 murder of Julius Caesar at Rome, was seen by all the 
 assembled people in full daylight. Such a thing, though 
 very uncommon, is by no means singular it has hap-
 
 ON COMETS. 95 
 
 pened several times, and in one case quite recently; for 
 the great comet of 1843 was seen at noonday quite close 
 to the sun both in Nova Scotia and at Madrid, and be- 
 fore sunset at the Cape of Good Hope.* Of course it 
 is only the brightest part, or the head of a comet that 
 can ever be so seen. The faint light of the tail has no 
 chance of contending against broad daylight. 
 
 (4.) Before the invention of telescopes the appearance 
 of a comet was a rare occurrence, because only a small 
 proportion of them can ever be seen by the naked eye, 
 and of them again only a small portion are considerable 
 enough to attract much attention but since that dis- 
 covery it has been ascertained that they are very numer- 
 ous hardly a year passes without one ; and very often 
 two, three, and in one year, 1846, no less than eight were 
 observed. Taking only two a year on an average as 
 visible if looked for in a telescope, and considering that 
 at least as many must occur in such situations that we 
 could not expect to see them in the 6000 years of re- 
 corded history there must have been between twenty and 
 thirty thousand comets, great and small. A great comet, 
 however, hardly occurs on an average oftener than once 
 in fifteen or twenty years, or even yet more rarely; 
 
 * At Halifax, in the first mentioned colony, my informant saw a 
 number of persons natives of the place hale and sturdy men, 
 gathered in a group and gazing full on the sun, which, when he at- 
 tempted to do, dazzled and almost blinded him. He was compelled 
 to desist, and inquire what they were looking at, and how they 
 could do so without being blinded. "Blinded !" was the reply 
 " Lord bless you, it does not hurt us; what, can't you see it that 
 thing up by the sun?"
 
 96 ON COMETS. 
 
 though, as sometimes happens in matters of pure acci- 
 dent and in the run of chances, it is not very unfrequent 
 (and we have lately seen it remarkably exemplified) for 
 two or even three very great comets to follow each other 
 in rapid succession. Thus the great comet of 1680 was 
 followed in 1682 by two other very conspicuous ones, of 
 which we shall have more to say presently. 
 
 (5.) When a comet is first discovered in a telescope it is 
 for the most part seen only as a small, faint, round, or oval 
 patch of foggy, or, as it is called, nebulous light, somewhat 
 brighter in the middle. By degrees it grows larger and 
 brighter, and at the same time more oval, and at length 
 begins to throw out a " tail" that is to say a streak of light 
 extending always in a direction/TWtf the sun, or in the con- 
 tinuation of a line supposed to be drawn from the place of 
 the sun below the horizon to the head of the comet above 
 it. As time goes on, night after night the tail grows 
 longer and brighter, the "head" or nebulous mass from 
 which the tail seems to spring also increases, and within 
 it begins to be seen what is called a "nucleus" or kernel, 
 a sort of rounded, misty lump of light dying off rapidly 
 into a haziness called the " coma " or hair. Within this, 
 but often a good deal out of the centre, there is seen 
 with a good telescope and a high magnifying power a 
 very small spark or pellet of light which may or may not 
 be the solid body of the comet, and which is the real 
 nucleus. What in an indifferent telescope looks like a 
 rather large puffy ball, more or less oval, is certainly not 
 a solid substance. All the while the comet is getting 
 every evening nearer and nearer to the place of the sun,
 
 ON COMETS. 97 
 
 and is therefore seen for a shorter time after sunset or 
 before sunrise, as the case may be (for quite as many 
 comets are seen in the morning before sunrise as in the 
 evening after sunset). At last it approaches so near the 
 sun as to rise or set very nearly at the same time, and so 
 ceases to be seen except it should be so very bright and 
 so great a comet as to be visible in presence of the sun. 
 (6.) When this has taken place, however, the comet is 
 by no means to be considered as dead and buried. After 
 a time it reappears, having passed by the sun, or perhaps 
 before or behind it, and got so far away on the other side 
 as to rise before the sun or set after him. If it first 
 appeared after sunset in the west, it will now reappear in 
 the east before sunrise. And what is very remarkable, 
 its shape and size are usually totally different after its 
 reappearance from what they were before its disappeai- 
 ance. Some, indeed, never reappear at all. The path 
 they pursue carries them into situations where they could 
 not be seen by the same spectators who saw them before. 
 Others like those which appeared in 1858 and 1861, 
 without altogether disappearing as if swallowed up by the 
 sun after attaining a certain maximum or climax of 
 splendour and size die away, and at the same time move 
 southward, and are seen, as that of 1858 was (on the 
 nth of October for the first time), in the southern hemi- 
 sphere, the faded remnants of a brighter and more glori- 
 ous existence of which we here witnessed the grandest 
 display. And on the other hand we here receive as it 
 were many comets from the southern sky, whose greatest 
 display the inhabitants of the southern parts of the earth
 
 98 ON COMETS. 
 
 only have witnessed. It also very often happens that a 
 comet, which before its disappearance in the sun's rays 
 was but a feeble and insignificant object, reappears mag- 
 nified and glorified, throwing out an immense tail and 
 exhibiting every symptom of violent excitement, as if set 
 on fire by a near approach to the source of light and heat. 
 Such was the case with the great comet of 1680 and 
 that of 1843, both of which, as I shall presently take 
 occasion to explain, really did approach extremely near 
 to the body of the sun, and must have undergone a very 
 violent heat Other comets, furnished with beautiful and 
 conspicuous tails before their immersion in the sun's 
 rays, at their reappearance are seen stripped of that ap- 
 pendage, and altogether so very different that, but for a 
 knowledge of their courses, it would be quite impossible 
 to identify them as the same bodies. This was the case 
 with the beautiful comet of 1835-6, one of the most re- 
 markable comets in history. Some, on the other hand, 
 which have escaped notice altogether in their approach 
 to the sun burst upon us at once in the plenitude of their 
 splendour, quite unexpectedly, as did that of the year 
 1861. 
 
 (7.) I come now to speak of the paths described by 
 comets in the sky among the stars (which I need hardly ob- 
 serve keep always the same relative situations one among 
 the other, and stand as landmarks, among which comets, 
 planets, the moon and the sun pursue, or seem to us to 
 pursue, their destined courses). Now we all know that the 
 sun, moon, and planets, keep to certain high roads, like 
 beaten tracks in the sky, from which they never deviate
 
 ON COMETS. 99 
 
 beyond definite and narrow limits assignable by calcula- 
 tion. With comets it is far otherwise. They are wild 
 wanderers, and care nothing for beaten tracks. A comet 
 is just as likely to appear in any one region of the starry 
 heavens as in any other. They are no respecters of 
 boundaries. The first time a comet is seen, no one can 
 tell where it may next day be. The next observation 
 still leaves a great uncertainty as to its future course. 
 The third nails it. After three good observations, care- 
 fully made, of its place, we can thence foretell where it 
 will go. Meanwhile, such is the variety of which their 
 paths are susceptible, that for a very long time theii 
 movements were considered to be altogether capricious 
 and unaccountable creatures of chance governed by 
 no laws. Now the case is different. Most persons will 
 remember that the comet of 1858 passed on the 5th of 
 October of that year close to a very brilliant star, Arc- 
 turus, which shone through its tail at a very little distance 
 from its root or outspring from the head. Well ! within 
 a very short time from the first appearance of that comet, 
 while yet it was but a faint object, it was known to cal- 
 culating persons that it wo uld pass over Arcturus the 
 day the hour nay, almost the minute when the nucleus 
 of the comet would be closest to the star were predicted 
 and the prediction was exactly verified. How this 
 could happen I must now proceed to explain ; but before 
 I do so, I must premise that my hearers are not to be 
 startled if I use some words that are not familiar to many 
 of them, and ask for a little more of their attention than 
 if I were merely telling some amusing story. What I am
 
 ON COMETS. 
 
 going to say will be already well known to a portion of 
 them, but will be quite new to many, and I will try to 
 put it in such a way as shall not only be clearly intel- 
 ligible, but shall stick by them, and become part and parcel 
 of their minds and thoughts henceforward and I am 
 mistaken if many of this class of hearers (provided they 
 will give me the attention the thing requires) do not rise 
 from the perusal of this brief statement with much larger 
 and higher conceptions of the magnificent system we 
 belong to than they commenced it with. 
 
 (8.) The sun, as we all know, or may have heard, stands 
 immovable, or nearly immovable, in the centre of our 
 system, and all the planets, including the earth, circulate 
 or revolve round it, each in its own time and at its own 
 proper distance. These distances, for each planet, stand 
 to each other in relations of proportional magnitude, 
 which have become, by a long course of astronomical 
 observation and calculations, known to us with extreme 
 exactness, so that if the exact distance of any one of the 
 planets from the sun, or the exact interval between any 
 two of their orbits, can anyhow be ascertained in miles, 
 yards, or feet, the dimensions of all the rest in similar 
 units of measure may thence be derived. Supposing, 
 for instance, we knew exactly the interval between the 
 orbits of the earth and Mars, then if we would know the 
 respective distances of the several planets in their order 
 from the sun, it would only be necessary to multiply 
 that interval, in the case of Mercury, by the decimal 
 fraction 07392; in that of Venus by i'38i2; of the 
 Earth by 1-9095; of Mars by 2*9095; of Jupiter by
 
 ON COMETS. IOI 
 
 9-9349 j of Saturn by 18-2146 ; of Uranus by 36*6293 ; 
 and of Neptune, the most distant of the known planets, 
 
 by 57-3551-* 
 
 Now the interval between the earth's orbit and that 
 of Mars (or the distance between that planet and the 
 earth when they approach nearest) has quite recently 
 been ascertained by a concerted system of observation, 
 made during the past year, in which the astronomers in 
 all the principal observatories of the globe have borne a 
 part, and of which the final result has only within these 
 few weeks become known. From these observations, so 
 far as they have as yet been communicated and reduced, f 
 it has been concluded that the interval in question is 
 6071 diameters of the earth, and as we know to a great 
 nicety, by actual measurement of the earth's circum- 
 ference, that its diameter is 7912^ miles, we are enabled 
 at once to reduce the distance so obtained into miles 
 (which gives 48,036,200 miles), and thence, as above in- 
 dicated, to derive the earth's distance from the sun, 
 which comes out 91,718,000, or about 92 millions of 
 miles; and in the same way we may obtain the numerical 
 dimensions in miles of the orbits of all the other planets, 
 as also the sun's actual diameter, which appears to be 
 852,600 miles. 
 
 (9.) Such of our readers as may take the trouble to com- 
 pare the distances and dimensions here set down with 
 
 * We consider in this and what follows, the orbits as circles, which 
 is quite sufficient for purposes of illustration. 
 
 t Some time will probably elapse before our whole series can be 
 collected and finally reduced.
 
 IO2 ON COMETS. 
 
 those stated in my paper on the sun in the last lecture, 
 will not fail to observe that they are materially smaller 
 by one thirtieth part of their respective amounts. The 
 numbers there stated are in accordance with the state of 
 our knowledge accepted at the time when that lecture 
 was delivered, which rested for its basis on observa- 
 tions made upon Venus at the time of her transit across 
 the sun's disc in the year 1769 observations by which 
 the nearest distance of the orbits of Venus and the earth 
 was concluded in terms of the earth's diameter, on the 
 same general principle, though by a somewhat more re- 
 fined and circuitous process, as that from which the 
 least distance of Mars has just now been derived. As 
 the circumstances of this earlier determination (delicacy 
 of instruments and means of observation alone excepted) 
 were much more favourable to exactness, astronomers 
 would have hesitated in accepting the more recent con- 
 clusion in preference to the former, were it not for the 
 support and corroboration it derives from another deter- 
 mination, also quite recent (though somewhat prior in 
 point of date), depending on a direct measurement of 
 the velocity of light by a peculiarly ingenious and delicate 
 process invented and executed by M. Foucault To ex- 
 plain the nature of this process here would lead me too 
 far away from the immediate object of this discourse, from 
 which, indeed, the whole of what is above said on the 
 distance of the sun and planets would be justly con- 
 sidered as a digression were it not in some sort obliga- 
 tory on every one to account for a departure from 
 numerical statements once made. Suffice it therefore
 
 ON COMETS. 103 
 
 to say that the velocity of light so concluded was found 
 to be somewhat less (and that by about one 3oth part) 
 of that which had been hitherto received (192,000 miles 
 per second) and which was concluded from the observed 
 fact of its traversing the diameter of the earth's orbit in 
 i6 m - 26 sec - of time, and very considerably less than that 
 before obtained by M. Fizeau, with a less perfect appa- 
 ratus, and a less delicate and refined system of procedure. 
 Now it will not fail to be remarked, that the time (i6 m - 
 26 sec -) remaining unaltered, and the velocity diminished 
 by one 3oth, the distance traversed (the diameter of the 
 orbit) in that time will also be diminished by the same 
 aliquot fraction, so that there is a coincidence between 
 the two corrections of the sun's distance, which, coming 
 simultaneously, from such very different sources r cannot 
 but lead to their acceptance, at least provisionally, and 
 until the recurrence of that grand phaenomenon, the 
 transit of Venus, which will take place in the year 1874, 
 shall put an end to all uncertainty on the subject of the 
 true numerical dimensions of our system. 
 
 (10.) Bearing now these dimensions in mind, let us 
 construct in imagination a figure consisting of concentric 
 circles, to represent the orbits of the planets. Taking 
 the largest, that of Neptune, as 30 feet in diameter, then 
 will that of Uranus measure a little more than 19 feet 
 across, of Saturn somewhere less than 10, of Jupiter rather 
 more than 5, of Mars about 18 inches, and of the earth a 
 foot, while the enormous body of the sun will stand repre- 
 sented in the centre of all by a pellet of very little more 
 than one-ninth of an inch in diameter the orbits of
 
 IO4 ON COMETS. 
 
 Mercury and Venus by circles of 4^ and 9 inches respec- 
 tively that of the moon above the earth by one isth of 
 an inch, and the globe of the earth itself by a dot barely 
 the thousandth part of an inch in size. 
 
 (i i.) Strictly speaking, the orbits are not circles they 
 are slightly oval, or, as it is called, elliptic in form, and 
 the sun does not occupy their common centre, but what 
 is called the focus of each ; that is to say, one of the two 
 pins round which an ellipse may be described by carry- 
 ing a pencil round them confined by a looped string 
 encircling them both. The planetary orbits, moreover, 
 all lie nearly in one plane, or very slightly inclined to 
 that in which the earth performs its annual revolution, 
 which is called the plane of the ecliptic the angle at 
 which the plane of each orbit meets and cuts this, being 
 called its inclination to the ecliptic. They all circulate 
 the same way round the sun, and the farther they are 
 from the sun the slower they move so that while the 
 earth goes round it in 365 days, Mercury occupies only 
 88 in its revolution, while Neptune requires no less than 
 1 68 years to complete one of his circuits. 
 
 (12.) When we come to the comets, however, we find a 
 very different state of things. A comet, it is true, moves 
 round the sun as his centre of motion : not, however, in 
 a circle, or any approach to a circle, but (with a very 
 few, and those highly remarkable exceptions) in an im- 
 mensely elongated, or, as it is termed, a very eccentric 
 ellipse. In consequence, the nearest distances to which 
 they approach the sun bear almost universally an exceed- 
 ingly small proportion to those they attain when most
 
 ON COMETS. 105 
 
 remote, that is to say, at the two extremities of their 
 elliptic orbits, or what are termed their perihelion and 
 aphelion. By far the great majority approach it at their 
 perihelion near enough to arrive within the earth's orbit 
 very many within that of Venus, or even of Mercury 
 and not a few attain an extreme proximity to the 
 actual surface of the sun, while on the other hand only 
 four or five among the vast number of recorded comets 
 (those of 1747, 1826, 1835, 1847) have failed to arrive 
 within twice the earth's distance, or within the orbits of 
 those small planets called asteroids ; and one only has 
 had a perihelion distance exceeding four times the earth's 
 distance (that of 1729), still falling short of the orbit of 
 Jupiter. Probably, however, a comet, which should 
 always remain outside of the latter planet's orbit, would 
 have no chance of ever being seen by us. As to the 
 extreme distances to which they recede from the sun, it 
 is only in comparatively few instances that it can be even 
 estimated their ellipses being in general so elongated 
 as to be undistinguishable from that extreme and limit- 
 ing form which is called a parabola, which never returns 
 into itself at all. The form of this curve is that which a 
 stone thrown into the air describes, or which a jet of 
 water thrown up obliquely by a smooth round pipe 
 assumes in the air, being very much curved or bent 
 about the point which is called the vertex, and less and 
 less so in the ascending and descending branches. 
 
 (13.) Comets, we have said, are wild wanderers, and 
 despise beaten tracks. No way confined, as the planets 
 are, to move in planes nearly coincident with the ecliptic,
 
 106 ON COMETS. 
 
 they cut across it at every possible angle, and, as nearly 
 as can be ascertained (with exception of one small class 
 of comets), quite indifferently as to the degree of their 
 inclination, or to the direction of the longer axes or long- 
 est dimensions of their orbits in space ; so that there is 
 no region of space, however situated either in direction 
 or distance from the sun, which a comet may not visit. 
 Neither do they conform to that other universal planet- 
 ary rule of circulation round the sun in one direction. 
 Retrograde comets, or those whose motion is opposite to 
 that of the planets, are as common as direct ones, or 
 those which conform to the planetary rule. Here again, 
 however, there is a small class in which a tendency to 
 conformity is exhibited, co-extensive with that above 
 noticed, which affects a certain proximity to the ecliptic. 
 But of this we shall have occasion to speak more at 
 large. 
 
 (14.) It is only when all the particulars which determine 
 geometrically the situation and the form of the orbit of 
 a comet, its nearest distance from the sun, and the 
 direction in which it is moving, or what are called the 
 elements of its orbit, that it can be ascertained whether 
 it has ever been seen before, and whether we are to 
 expect ever to see it again ; and that its future course, 
 while it remains invisible, can be predicted with cer- 
 tainty. These elements are technically called 
 
 1. Tho, perihelion distance, or nearest approach to the 
 
 sun. 
 
 2. The eccentricity of its ellipse, or whether the orbit 
 
 be sensibly a parabola.
 
 ON COMETS. IO7 
 
 3. The inclination of its plane to the ecliptic. 
 
 4. The longitude of its node, or the direction of the 
 
 line in which its plane intersects the ecliptic, 
 which is called the line of its nodes. 
 
 5. The longitude of its perihelion, or, which comes to 
 
 the same thing, the angle which the axis of the 
 orbit makes with the line of nodes. 
 
 6. The exact moment when the comet passed through 
 
 \\.s perihelion, or was nearest to the sun. 
 
 7. The direction of its motion (direct or retro- 
 
 grade). 
 
 (15.) It is natural to ask how all these particulars ever 
 can be known ; and to this the answer is By the same 
 system of observation and calculation combined, by which 
 we have come to know the form and dimensions of the 
 orbits of the planets, their times of revolution round the 
 sun, and their situation in space. 
 
 (16.) I believe it was Tycho Brahe, a celebrated Danish 
 astronomer, who first rose to the conception that comets 
 are beyond the moon, and not mere exhalations. The 
 appearance of a great comet in 1577 set him thinking 
 about it, and he was led by his observations and reason- 
 ings on them to a certain knowledge of the fact of its 
 being much more remote than our own satellite ; and he 
 was therefore led to conjecture that the motions of 
 comets had reference rather to the sun as their centre 
 than the earth. The elliptic form of the planetary orbits 
 was not then known, and Tycho accordingly supposed 
 that comets moved about the sun in perfect circles. 
 Borelli, a Neapolitan mathematician, suggested the idea
 
 IO8 ON COMETS. 
 
 of a long ellipse or parabola as the possible form of a 
 cornet's orbit ; and Dorfel, a German astronomer in 
 1 68 1, upon a careful consideration of all the observa- 
 tions of the great comet of 1680, came to the positive 
 conclusion that that comet did really move in a parabolic 
 orbit with the sun in its focus. This was an immense 
 step ; but neither Dorfel nor any one else could at that 
 time give any account of the reason why this should be 
 the case, or in what manner the comet was made to con- 
 form its sweep through space in so singular a way to the 
 sun. 
 
 (17.) The wonderful discoveries of Sir Isaac Newton 
 made all this clear. He first showed that the sun controls 
 the movements of these wanderers by the very same force 
 acting according to the very same law which retains the 
 planets in their paths that marvellous law of gravita- 
 tion the same power which draws a stone thrown from 
 the hand back to the earth (in a parabolic curve) 
 which keeps the moon from flying off, and holds her to 
 us as a companion which keeps the planets in their 
 circles, or rather ellipses, about the sun and which we 
 now know holds together several of the stars in couples, 
 circulating one about the other. 
 
 (18.) The great comet of 1680, which occurred while 
 Newton was brooding over these grand ideas which 
 broke upon the world like the dawn of a new day in his 
 " Principia," afforded him a beautiful occasion to test 
 the truth of his gravitation theory by the most extreme 
 case which could be proposed. The planets were tame 
 and gentle things to deal with. A little tightening of
 
 ON COMETS. log 
 
 the rein here and a little relaxation there, as they ca- 
 reered round and round, would suffice perhaps to keep 
 them regular, and guide them in their graceful and 
 smooth evolutions. But here we had a stranger from 
 afar from out beyond the extremest limits of our sys- 
 tem dashing in, scorning all their conventions, cutting 
 across all their orbits, and rushing like some wild infu- 
 riated thing close up to the central sun, and steering 
 short round it in a sharp and violent curve with a speed 
 (for such it was) of 1,200,000 miles an hour at the 
 turning point, and then going off as if curbed by the 
 guidance of a firm and steady leading rein, held by a 
 powerful hand, in a path exactly similar to that of its 
 arrival, with perfect regularity and beautiful precision ; 
 in conformity to a rule which required not the smallest 
 alteration in its wording to make it applicable to such 
 a case. If anything could carry conviction to men's 
 minds of the truth of a theory, it was this. And it did 
 so. I believe that Newton's explanation of the motions 
 of comets, so exemplified, was that which stamped his 
 discoveries in the minds of men with the impress of 
 reality beyond all other things. 
 
 (19.) This comet was perhaps the most magnificent ever 
 seen. It appeared from November 1680 to March 1681. 
 In its approach to the sun it was not very bright, but 
 began to throw out a tail when about as far from the sun 
 as the earth. It passed its perihelion on December 8 
 and when nearest was only one-sixth part of the sun's 
 diameter from his surface one fifty-fourth part of an inch 
 on the conventional scale of our imaginary figure, and at
 
 110 ON COMETS. 
 
 that moment had the astonishing speed I have just men- 
 tioned. Now observe one thing. The distance from the 
 sun's centre was about one i6oth part of our distance 
 from it. All the heat we enjoy on this earth comes from 
 the sun. Imagine the heat we should have to endure if 
 the sun were to approach us or we the sun to Trrth part 
 of its present distance. It would not be merely as if 
 1 60 suns were shining on us all at once, but 160 times 
 1 60, according to a rule which is well known to all 
 who are conversant with such matters. Now that is 
 25,600. Only imagine a glare 25,600 times fiercer than 
 that of an equatorial sunshine at noonday with the sun 
 vertical. And again, only conceive a light 25,600 times 
 more glaring than the glare of such a noonday! In such 
 a heat there is no solid substance we know of which 
 would not run like water boil and be converted into 
 smoke or vapour. No wonder it gave evidence of vio- 
 lent excitement coming from the cold region outside 
 the planetary system, torpid and icebound ; already when 
 arrived even in our temperate region it began to show 
 signs of internal activity the head had begun to develop 
 and the tail to elongate till the comet was for a time lost 
 sight of. No human eye beheld the wondrous spectacle 
 it must have offered on the 8th December. Only four 
 days afterwards, however, it was seen : and its tail, whose 
 direction was reversed and which (observe) could not 
 possibly be the same tail it had before (for it is not to 
 be conceived as a stick brandished round, or a flaming 
 sword, but fresh matter continually streaming forth), its 
 tail I say had already lengthened to an extent of about
 
 ON COMETS. 
 
 90 millions of miles, so that it must have been shot out 
 with immense force in a direction from the sun, a force 
 far greater than that with which the sun acted on and con- 
 trolled the head of the comet itself, which, as the reader 
 will have observed, took from November 10 to December 8, 
 or 28 days, to fall to the sun from the same distance, and 
 that with all the velocity it had on November 10 to start 
 with. 
 
 (20.) All this is very mysterious. We shall never perhaps 
 quite understand it, but the mystery will be at all events 
 a little diminished when we shall have described some of 
 the things which are seen to be going on in the heads 
 of comets under the excitement of the sun's action, and 
 when calming and quieting down afterwards. At pre- 
 oent, however, we must get on with another part of our 
 subject. 
 
 (21.) Only two years after this appeared another bril- 
 liant comet, and our countryman, Edmund Halley, fol- 
 lowing Newton's example and employing his system of 
 calculation, computed its orbit, assuming (which simpli- 
 fies the calculation very much) that orbit to be a para- 
 bola. He found its path to be very different from that 
 of Newton's comet. Instead of nearly grazing the sur- 
 face of the sun, its nearest approach to it was about 55 
 millions of miles, or about half-way between the orbits of 
 Mercury and Venus. The plane of its motion, too, was 
 much less inclined to that of the planets' orbit or the 
 ecliptic viz., about 17!, and its motion was not direct, 
 as Newton's was, but retrograde. 
 
 (22.) Halley was encouraged by the good agreement of
 
 ON COMETS. 
 
 his calculations with the observed places of this comet 
 to collect observations of former comets, and endea- 
 vour to make out their paths, or, as we now express 
 it, to determine the elements of their orbits. With in- 
 credible labour he calculated the orbits of twenty-four 
 remarkable comets, and among them he found two 
 whose " elements " agreed in a remarkable manner with 
 those of his first comet both great comets, viz., one 
 observed by Appian in 1531, and one by Kepler in 
 1607, and he noticed also this fact, this remarkable ap- 
 proximate coincidence from 1531 to 1607 is 76 years, 
 and from 1607 to 1682 75 years. This led him to sus- 
 pect that all three were one and the same comet, return- 
 ing periodically; and guided by this idea he was led to 
 examine the records of history for comets of earlier date. 
 Among them, three turned up in the years 1305, 1380, 
 1456 and when all these years are arranged in a series, 
 you see that the intervals are alternately 75 and 76 
 years. This confirmed him in his impression of its peri- 
 odical return ; and emboldened him to predict its return 
 about the end of 1758 or beginning of 1759. You will 
 observe that he allowed more than an average length of 
 the period (77 years) for the fulfilment of his prediction. 
 He had a reason for this. He ascertained that in com- 
 ing back it would pass near the planet Jupiter, which is 
 a large and massive planet, and Newton's discoveries had 
 already taught him to contemplate the possibility of some 
 disturbance of its motion from the attraction of such a 
 body, and even enabled him to perceive that it would 
 act to retard the return or prolong the period. Such
 
 ON COMETS. 
 
 disturbances do really exist, and have often very con- 
 siderable effects on the return of comets. This very 
 comet, in the table of its returns set down in the note 
 below,* offers some striking examples. There occurs, for 
 instance, 1378 A.D. and not 1380 set down for one of the 
 epochs of its appearance, with 78 years interval between 
 that and 1456. The fact is that Halley was mistaken in 
 supposing either the comet of 1305 or that of 1380 to be 
 the same with that in question. That comet really ap- 
 nearedin 1378, but that fact Halley had no means of know- 
 ing. It has very lately come to light on searching the 
 Chinese annals. And the same annals have informed us 
 of no less than six other still more ancient appearances 
 of this selfsame comet, the earliest in the nth year be- 
 fore our Saviour. And this, it must be allowed, greatly 
 tends to increase our confidence in those venerable re- 
 cords of Chinese history. All this apparent irregu- 
 larity is owing to the action mainly of Jupiter, which is 
 a general disturber of comets, and gives a vast deal of 
 trouble to calculators, as I shall soon explain; and 
 Saturn is not without a finger in the pie. 
 
 (23.) This prediction of Halley's, as the time for its 
 accomplishment drew near, created a great sensation all 
 the astronomers furbished up their telescopes, and all 
 the mathematicians set to work to calculate. The 
 mutual actions of the planets in that long interval had 
 been well studied, and it was clearly ascertained that 
 
 * A.D. 451, July 3 ; 760, June II ; 1378, Nov. 8 ; 1456, Tune 8 : 
 1531, Aug. 24; 1607, Oct. 26; 1682, Sept 14; 1759, March 12 ; 
 1835, Nov. 15. 
 
 U
 
 114 ON COMETS. 
 
 Halley was right in his conjecture about Jupiter, and 
 that in fact the return of the comet would be delayed by 
 the attraction of that planet 518 days, and by that of 
 Saturn 100 more, and that it would make its next closest 
 approach to the sun within a month one way or another 
 of the i3th of April 1759. 
 
 (24.) All the astronomers of Europe were looking out 
 for it, eager to seize it on its first coming within the range 
 of human vision. They were all disappointed of their 
 prize. It was carried off by a Saxon farmer of the name 
 of Palitzch, an astronomer of Nature's own creating, 
 who was always watching the heavens, without tele- 
 scopes, without knowledge, simply from the profound 
 interest their aspect inspired him with. He it was who 
 first caught sight of it, on the i3th December 1758. It 
 was taken up by others and regularly observed. It 
 passed its perihelion on the i3th of March, just within 
 the limit of possible uncertainty the mathematicians had 
 allowed for their calculations. 
 
 (25.) This was certainly a very great and signal triumph. 
 It was repeated, with every circumstance that could 
 make it decisive or give it notoriety, in the year 1835, 
 the epoch of the next appearance of " Halley's Comet." 
 The calculation of the planetary perturbations (as the 
 disturbances they cause in each other's motions are 
 called) had then been brought to great perfection. The 
 passage through the perihelion was predicted by M. 
 Pontecoulant to take place on the i2th November, 
 and by Rosenberger between the nth and i6th. In 
 point of fact, it happened on the isth. And this time,
 
 ON COMETS. 115 
 
 too, the astronomers were not beaten by the farmers. 
 Their telescopes were from day to day pointed right on 
 the spot where it would be sure to appear which was 
 advertised all over the world in the almanacs; and it 
 was caught at the earliest possible moment, and pursued 
 till it faded away into a dim mist. 
 
 (26.) When lost to European astronomers (for, like 
 those of 1858 and 1861, it ran southwards), Mr Maclear 
 and myself received it in the southern hemisphere ; and 
 it was fortunate we did so; for, extraordinary as were the 
 appearances it presented on its approach to the sun, they 
 were if possible surpassed by those it exhibited after- 
 wards ; and the whole series of its phaenomena has given 
 us more insight into the interior (Economy of a comet and 
 the forces developed in it by the sun's action, than any- 
 thing before or since. 
 
 (27.) When first it was seen, it presented the usual aspect 
 of a round misty spot, and by degrees threw out a tail, 
 which was never very long or brilliant, and which to the 
 naked eye or in a low-magnifying telescope appeared 
 like a narrow, straight streak of light, terminating in a 
 bright head; which in a telescope of small po\ver ap- 
 peared capped with a kind of crescent; but in one of 
 great power exhibited the appearance of jets, as it were, 
 of flame, or rather of luminous smoke, like a gas fan- 
 light. These varied from day to day, as if wavering 
 backwards and forwards, and as if they were thrown out 
 of particular parts of the internal nucleus or kernel, 
 which shifted round, or to and fro, by their recoil, like a 
 squib not held fast. The bright smoke of these jets, how-
 
 Il6 ON COMETS. 
 
 ever, never seemed to be able to get far out towards the 
 sun, but always to be driven back and forced into the 
 tail, as if by the action of a violent wind setting against 
 them, always from the sun, so as to make it clear that 
 this tail is neither more nor less than the accumulation 
 of this sort of luminous vapour darted off in the first 
 instance TOWARDS the sun, as if it were something raised 
 up, and, as it were, exploded by the sun's heat, out of 
 the kernel, and then immediately and forcibly turned 
 back and repelled from the sun. 
 
 (28.) As this comet approached the sun, its tail, far 
 from increasing, diminished ; and between the middle of 
 November and the 2ist of January, strange to say, both 
 head (that is coma) and tail were altogether destroyed, 
 or at least rendered invisible. On the 2 ist of January 
 the comet was actually seen like a small star without any 
 tail or any haziness, and was only known not to be a star 
 by being exactly in its calculated place, and by its not 
 being there next night After that its head seemed to 
 form again round this star, and grew rapidly and visibly 
 from night to night, putting on appearances which could 
 not be clearly apprehended without elaborate figures. 
 This growth of the comet was so very rapid, that in the 
 interval of 1 7 days from the time I first saw it as a round 
 body its real bulk had increased to 74 times the size it 
 then had and at the same rate it continued to swell 
 out, not, however, preserving a round form, but growing 
 longer in proportion to its breadth as if it intended to 
 develop a new tail. But this it never did the dilatation 
 or swelling out continued, and at one time it had exactly
 
 ON COMETS. 117 
 
 the appearance of a ground glass lamp the light always 
 becoming fainter and fainter, till it at last seemed to pass 
 away from view from mere faintness. All this while, 
 however, there was a sort of smaller and much brighter 
 interior comet visible, with a tail-like appendage, which 
 seemed to be as it were a conducting channel by which 
 the matter of the newly-forming head was gradually re- 
 treating back into the centre. 
 
 (29.) The discovery of the periodical return of Halley's 
 comets forms an epoch in the history of their bodies. 
 Since that time a great many more have been ascer- 
 tained to return at regular intervals. I will mention some 
 of the most remarkable cases of this kind. 
 
 (30.) In 1770 a comet appeared which proved rebellious 
 to the then adopted system of calculation, which set out 
 with assuming the orbit to be a parabola. It very soon 
 appeared, by the calculations of M. Lexell, that the real 
 orbit was an ellipse, and that not a very eccentric one. 
 In fact, all the observations were perfectly consistent with 
 an ellipse nearly coincident with the plane of the earth's 
 orbit, of such dimensions as that the extreme excursion 
 from the sun would carry it over a little beyond the 
 orbit of Jupiter, and its nearest approach would bring it 
 within that of Venus the time of its revolution being 
 5^ years. Here was quite a new fact. All other comets 
 then known had run out to limits far beyond our system 
 since even Halley's, with its period of 76 years at its 
 greatest distance from the sun, passed very far beyond 
 the orbit of Saturn, the most distant planet then known, 
 and in fact beyond the two since discovered, Uranus and
 
 Il8 ON COMETS. 
 
 Neptune. But here we seemed to have quite a sort of 
 tame comet keeping within bounds, and within call. Of 
 course its return was watched for with eagerness, but 
 alas ! it never made its appearance again. At its next 
 return in 1776 this was well accounted for, as owing to 
 the relative situations of the earth, sun, and comet, it 
 could not have been visible; but at the next, in 1781, 
 the earth was favourably situated, since 5^ years would 
 place the sun in the opposite part of its orbit ; but 1 1 
 years in the same, and the calculators for a time were 
 puzzled. The solution of the enigma was a very strange 
 one. The poor comet had got bewildered. It had 
 plunged headlong into the immediate sphere of Jupiter's 
 attraction had intruded, an uninvited guest, into his 
 family circle actually nearer to him than his fourth 
 satellite, and into a situation where Jupiter's attraction 
 for it was two hundred times that of the sun. Of course 
 its course was for a time commanded entirely by this 
 new centre of motion, and the comet was completely 
 diverted from its former orbit. 
 
 (31.) So far all was clear enough. But people began 
 to ask how, with so short a period, and being a tolerably 
 large comet, it had never been seen before ] Here again 
 Lexell called Jupiter to the rescue. As he had taken 
 away, so it turned out he had given. Jupiter, it will be 
 borne in mind, comes round to the same point of his 
 orbit in ii years and 10 months; two of the comet's re- 
 volutions would occupy n years and 3 months, so that 
 tracing back the comet two revolutions in its ellipse, and 
 Jupiter rather less than one in his circle from the place
 
 ON COMETS. 119 
 
 of their final rencontre, which took place in 1779, it is 
 clear they could not have been far asunder in 1767, 3 
 years before it became visible j and in fact, on executing 
 the calculations necessary, it was clearly proved that 
 before 1767 this unhappy comet had been revolving in 
 a totally different orbit of much greater dimensions, and 
 was actually siezed upon then and there by Jupiter, 
 flung as it were inwards and then after making two 
 visits to the sun, again seized on, and thrown off into 
 space, into an orbit of 20 years' period, where perhaps 
 it may be quietly circulating to this day. Jupiter, in 
 fact, is a regular stumbling-block in the way of comets. 
 
 (32.) This is a strange history but it proved a very 
 instructive one. The comet passed, as I have said, 
 through the system of Jupiter's satellites. Now the 
 motions of these bodies have been studied with a degree 
 of care and precision quite remarkable by reason of their 
 furnishing one of the means for ascertaining the longi- 
 tudes of places. And if the comet had been a heavy 
 massive body, its attraction must have produced some 
 sensible disturbance in their motions. But no, not a 
 trace of anything of the kind was detected. One and 
 all of them pursued their courses with the very same 
 precision and regularity as if nothing had happened. 
 The conclusion is irresistible. That comet at least had 
 no sensible weight or mass it was a mere bunch of 
 vapours. 
 
 (33.) Another very remarkable periodical comet is that 
 of Encke, which makes its circuit about the sun m 1200 
 days, or about 3 years and 4 months, in the same
 
 ON COMETS. 
 
 direction as the planets. It is but a small one, being 
 seldom visible without a telescope. Its orbit was first 
 computed on its appearance in 1795 (when it was dis- 
 covered by Miss C. Herschel), and again in 1805 and 
 1819. Upon this last occasion M. Encke, an eminent 
 computist, found that its motion could not be explained 
 without supposing it to move in an ellipse of the last 
 period I have mentioned and on searching back into 
 the records of comets he found those two I have just 
 named, which agreed perfectly, and proved to have been 
 really the same. 
 
 (34.) Since that time it has been re-observed on every 
 subsequent revolution in '22, '25, '29, '32, '35, '38, '42, 
 '45, '48, '5 1, '55, and is always announced in the almanacs 
 as a regular member of our system. Its nearest approach 
 to the sun brings it just within the orbit of Mercury, and 
 on one occasion that planet happened to be so very near 
 it on its arrival, that it produced a pretty considerable 
 disturbance of the comet. But here, too, as in the case 
 of Lexell's comet, not the smallest perceptible effect was 
 produced by the comet on the planet; and thus two 
 valuable pieces of information were gained. First; As- 
 tronomers were enabled to estimate the mass or weight 
 of that small planet better than by any other means ; and 
 secondly; It was proved that this comet also has no per- 
 ceptible weight and is also a mere puff of vapour, or 
 something as unsubstantial 
 
 (35.) There is another strange fact which this comet 
 has revealed. Its successive revolutions are each a little 
 shorter than the last a small fraction of a day, it is true,
 
 ON COMETS. 121 
 
 but still unquestionably made out. This has been held to 
 prove that the comet is by very slow degrees approaching 
 the sun, and will at last fall into it as if it moved in a 
 space not quite empty, and were in some very slight 
 degree resisted in its motion. I cannot quite reconcile 
 myself to this opinion, and I think I have perceived 
 another explanation of the fact, which I have given else- 
 where ; but to state this would lead me too far, and I 
 must now go on to relate one of the strangest and most 
 uncouth facts of this strange cometic history. 
 
 (36.) On the 27th February 1826, Professor Biela, an 
 Austrian astronomer of Josephstadt, discovered a small 
 comet. When its motions were carefully studied it was 
 found by M. Clausen, another of those indefatigable 
 German computists, that it revolved in an elliptic orbit 
 in a period of 6 years and 8 months. On looking back 
 into the list of comets, it proved to be identical with 
 comets that had been observed in 1772, 1805, and 
 perhaps in 1818. Its return was accordingly predicted, 
 and the prediction verified with the most striking exact- 
 ness. And this went on regularly till its appearance 
 (also predicted) in 1846. In that year it was observed 
 as usual, and all seemed to be going on quietly and com- 
 fortably, when behold ! suddenly on the i3th of January 
 it split into two distinct comets! each with a head and 
 coma and a little nucleus of its own. There is some 
 little contradiction about the exact date. Lieutenant 
 Maury, of the United States Observatory of Washington, 
 reported officially on the i$th having seen it double on the 
 , but Professor Wichmann, who saw it double on the
 
 ON COMETS. 
 
 , avers that he had a good view of it on the 
 and remarked nothing particular in its appearance. Be 
 that as it may, the comet from a single became a double 
 one. What domestic troubles caused the secession it is 
 impossible to conjecture, but the two receded farther 
 and farther from each other up to a certain moderate 
 distance, with some degree of mutual communication and 
 a very odd interchange of light one day one head being 
 brighter and another the other till they seem to have 
 agreed finally to part company. The oddest part of the 
 story, however, is yet to come. The year 1852 brought 
 round the time for their reappearance, and behold ! there 
 they both were, at about the same distance from each 
 other, and both visible in one telescope. 
 
 (37.) The orbit of this comet very nearly indeed inter- 
 sects that of the earth on the place which the earth oc- 
 cupies on the 3oth of November. If ever the earth is to 
 be swallowed up by a comet, or to swallow up one, it will 
 be on or about that day of the year. In the year 1832 
 we missed it by a month. The head of the comet en- 
 veloped that point of our orbit, but this happened on the 
 2Qth of October, so that we escaped that time. Had a 
 meeting taken place, from what we know of comets, it is 
 most probable that no harm would have happened, and 
 that nobody would have known anything about it.* 
 
 * It would appear that we are happily relieved from the dread of 
 such a collision. It is now (Feb. 1866) over duel Its orbit has 
 been recomputed and an ephemeris calculated. Astronomers have 
 been eagerly looking out for its reappearance for the last two 
 months, when, according to all former experience, it ought to have
 
 ON COMETS. 123 
 
 (38.) The number of comets whose periodical return 
 has been calculated is pretty considerable. Altogether 
 about 36 ; and of these there are 5 which revolve in 
 periods of from 70 to 80 years, and several of the rest in 
 short periods from 3 to 7 years ; and it is a very remark- 
 able feature in their history that all the comets of short 
 period, and three out of the five of those of the larger 
 ones specified, revolve in the same direction round the 
 sun as the planets, and have their orbits inclined at no 
 very large angles to the ecliptic. 
 
 (39.) Of comets not periodical, I have already men- 
 tioned that most remarkable one of 1680, but several 
 others deserve special notice. That of 1744 was a truly 
 wonderful object. It is described, and has been depicted, 
 with six tails spread out like an immense fan extending 
 30 from the head which is fully the extent of the tail of 
 the comet of 1858; and the appearance of its head when 
 viewed through a telescope exhibited the same sort of 
 jets of luminous smoke, the same curved envelopes and 
 arches as I have already described, showing the same 
 kind of excitement by the sun's heat, and the same 
 action driving the vapour back into the tail. 
 
 (40.) The comet of 1843 was still more remarkable. 
 Many of my hearers, I dare say, remember its immense 
 
 been conspicuously visible but without success! giving rise to the 
 strangest theories. At all events it seems to have fairly disappeared, 
 and that without any such excuse as in the case of Lexell's, the pre- 
 ponderant attraction of some great planet. Can it have come into 
 contact or exceedingly close approach to some asteroid as yet undis- 
 covered ; or, peradventure, plunged into and got bewildered among 
 the ring of meteorolites, which astronomers more than suspect ?
 
 124 ON COMETS. 
 
 tail, which stretched half-way across the sky after sunset 
 in March of that year. But its head, as we here saw it, 
 was not worthy such a tail Farther south, however, it 
 was seen in great splendour. I possess a picture by Mr 
 Piazzi Smythe, Astronomer-Royal of Edinburgh, of its 
 appearance at the Cape of Good Hope, which represents 
 it with an immensely long, brilliant, but very slender and 
 forked tail. Of all the comets on record, that approached 
 nearest the sun indeed, it was at first supposed that it 
 had actually grazed the sun's surface, but it proved to 
 have just missed by an interval of not more than 80,000 
 miles about a third of the distance of the moon from 
 the earth, which (in such a matter) is a very close shave 
 indeed to get clear off. There seems very considerable 
 reason to believe that this comet has figured as a great 
 comet on many occasions in history, and especially in 
 the year 1668, when just such a comet, with the same 
 remarkable peculiarity, of a comparatively feeble head 
 and an immense train, was seen at the same season of 
 the year, and in the very same situation among the stars. 
 Thirty-five years has been assigned with considerable 
 probability as its period of return, but it cannot be re- 
 garded as quite certain. (It will of course be understood 
 that the return of a great comet to the neighbourhood of 
 the sun by no means implies that it should be a con- 
 spicuous one, as seen from the earth. The phase of its 
 greatest development may be, and is, indeed, more likely 
 than not to be, ill-timed, as regards the relative situations 
 of the earth and sun, for its exhibition as a great celes- 
 tial phenomenon.)
 
 ON COMETS. 125 
 
 (41.) Another great comet which has assumed a sort of 
 historical and political importance is that which ap- 
 peared in A.D. 1556. According to the account of 
 Gemma, it would not seem to have been a very large 
 one, as he assigns to it a tail of only four degrees long. 
 Its head, however, equalled Jupiter in brightness, and in 
 size was estimated at about one-third or one-half of the 
 diameter of the moon. It appeared about the end of 
 February, and on the i6th of March is described by 
 Ripamonte as a really terrific object. Terrific indeed 
 it might well have been to the mind of a prince prepared 
 by the most abject superstition to receive its appearance 
 as a warning of approaching death, and as specially sent, 
 whether in anger or in mercy, to detach his thoughts 
 from earthly things, and fix them on his eternal inter- 
 ests. Such was its effect on the Emperor Charles V., 
 whose abdication of the imperial throne is distinctly 
 ascribed by many historians to this cause, and whose 
 words on the occasion of his first beholding it have 
 even been recorded 
 
 "His ergo indiciis me meafata vacant!" 
 
 the language and the metrical form of which exclamation 
 afford no ground for disputing its authenticity, when the 
 habits and education of those times are fairly considered. 
 This comet has been supposed to be periodical, and to 
 return in 291 years, on the ground of the prior appear- 
 ance of great comets in the years 975 and 1264 (at in- 
 tervals, that is, of 289 and 292 years respectively), and 
 the general agreement of their orbits, so far as could be
 
 126 ON COMETS. 
 
 made out from the imperfect records we possess of their 
 courses, with that of the comet in question. The next 
 return, on this supposition, would have fallen about the 
 year 1846 or 1847. It did not, however, appear at that 
 epoch, nor in any subsequent year up to the present 
 time, although, from some very elaborate calculations by 
 Mr Hind and Professor Bomme (too elaborate, it would 
 appear, to have been bestowed on the imperfect records 
 we possess of its previous history) it should have been 
 delayed by planetary perturbations for several years be- 
 yond that date, and even so late as to the year 1858 
 or 1860. 
 
 (42 ) Accordingly, when the three great comets, whose 
 arrival in and since the year 1858 has so surprised and 
 delighted the astronomical world, made their successive 
 appearances, there were few persons at all acquainted 
 with cometary history whose first impression was not 
 that of the return of " Hind's Comet," as it had grown 
 to be called, from the eminent calculator and mathe- 
 matician who had bestowed so much pains on it. This, 
 however, it is needless to observe, was not the case. 
 Neither of them had ever been seen before, nor can 
 either of them ever be expected to appear again, unless 
 to a posterity which may look back on our record of 
 them as we do on those ancient Chinese annals already 
 spoken of. Of these, by far the most magnificent 
 in point of mere display, as well as the most inter- 
 esting, when contemplated in a physical point of view, 
 was that of 1858 (the fifth of that year), or Donati's 
 comet, as it is now called, from the astronomer of that
 
 ON COMETS. 127 
 
 name, who first observed it at Florence on the 2d of 
 June, at which time it appeared only as a round misty 
 patch or "nebula." This was about a month after it 
 had passed from the southern to the northern side of 
 the plane of the earth's orbit : and that of the comet 
 being very highly inclined (63) to the ecliptic ; its peri- 
 helion lying also on the north side of that plane ; its 
 motion being retrograde, and the earth accordingly ad- 
 vancing to meet it ; all these favourable circumstances 
 concurring, it so happened that our nearest proximity to 
 it occurred only six days after its "perihelion passage" 
 or time of nearest approach to the sun, which took place 
 on the 2 Qth of September, and in a situation with respect 
 to the sun every way advantageous to obtaining a good 
 view of it Accordingly, with the exception of the comet 
 of Halley in 1835, no comet on record has been watched 
 with such assiduity, or been more thoroughly scrutinized. 
 A resume of all the observations of it has been recently 
 published by Professor Bond, forming the third volume 
 of the " Annals of the Observatory of Harvard College, 
 in the United States," in which its appearance in every 
 stage of its progress is represented in a series of engrav- 
 ings, which in point of exquisite finish and beauty of 
 delineation leave far behind everything hitherto done in 
 that department of astronomy. 
 
 (43.) It was not till the i4th of August, or 73 days after 
 its first discovery, that it began to throw out a tail, and 
 to become a conspicuous object. Very soon after this, 
 its first appearance ; a slight but perceptible curvature 
 was perceived in the tail, which, on the i6th of Sep-
 
 128 ON COMETS. 
 
 tember, had become unmistakable, and continued to 
 increase in amount as the latter extended in apparent 
 dimension, till it assumed at length that superb aigrette- 
 like form, like a tall plume wafted by the breeze, which 
 has never probably formed so conspicuous a feature in 
 any previous comet. To a certain extent, it is a common 
 enough feature in the tails of comets, and is usually re- 
 garded as conveying the idea of their moving in a 
 resisting medium ; in a space, that is to say, not quite 
 empty, as smoke is left behind a moving torch. But 
 this is a very gross and inadequate conception of the 
 peculiarity in question. The resistance of the " ether," 
 such as the phenomena of Encke's comet already 
 noticed, may be supposed to indicate, is far too infin- 
 itesmally small to be competent to produce any per- 
 ceptible deviation from straightness. Nor is it at all 
 necessary to resort to any such explanation of the fact. 
 Such an appearance would naturally arise from a combi- 
 nation of the motion the matter of the tail had (in 
 participation with that of the nucleus) with the impulse 
 given it by the sun each particle of it describing, from 
 the moment of quitting the head, an orbit quite different 
 from that of the latter; being necessarily, under the 
 influence of the repulsive force directed from the sun, a 
 curve of the form called by geometers an hyperbola, 
 nearly approaching to a straight line, and having its con- 
 vexity turned towards the sun : the visible form of the 
 tail (be it observed) being, not the perspective view of 
 such an orbit, but that of the portion of space contain- 
 ing, for the time being, all those particles, each descrih-
 
 ON COMETS. 129 
 
 ing its own independent orbit, and each reflecting to the 
 eye its quota of the solar light.* 
 
 (44.) A very striking feature in Professor Bond's en- 
 gravings, which he describes as frequently and certainly 
 observed in America, and which did not pass wholly 
 unnoticed in Europe, consists in the appearance of one, 
 and on some nights two, excessively faint, narrow, and 
 perfectly straight rays of light, or " secondary tails," start- 
 ing off from the main tail on its preceding or anterior 
 side (that towards which the comet was advancing, and 
 which side was always the brightest, sharpest, and best 
 denned) in the direction of tangents to its curvature 
 at points very near the head, and extending on some 
 nights (on the 4th, 5th, and 6th of October) to a much 
 greater length than the primary or more luminous tail. 
 These appearances were presented from the 28th Sep- 
 tember to the nth of October with more or less dis- 
 tinctness. They are peculiarly instructive, as they clearly 
 indicate an analysis of the cometic matter by the sun 's repul- 
 sive action the matter of the secondary tails being 
 evidentlv darted off with incomparably greater velocity 
 (indicating an incomparably greater intensity of repulsive 
 energy) than that which went to form the primary one. 
 The primary tail also presented another feature, fre- 
 quently, indeed almost always, observed in comets, viz., 
 
 * Some anomalous appearances in the early development of the 
 tail in this comet, which was slightly curved, even when the earth 
 was in the plane of the orbit, can by no means be regarded as 
 fatal to this explanation of the general phenomenon, as they might 
 have originated in a lateral direction of projection of the caudal 
 matter from the nucleus in ipso tnotus initio, 
 
 I
 
 I3O ON COMETS. 
 
 its separation, behind the head, into two main streams 
 with comparative darkness between them. This would 
 be a natural and necessary optical consequence of the 
 tail consisting of a hollow, conical envelope, streaming 
 off on all sides around from the head, and presenting to 
 the eye therefore a much greater thickness of luminous 
 matter at its edges than at its middle. But in this comet 
 the separation, when viewed through powerful telescopes, 
 was singularly sharp ; and appeared as a clear, narrow, 
 straight cut, or dark chink, originating close to the nucleus 
 (as, indeed, on that explanation of the fact it ought). 
 And this brings me to treat of the appearances presented 
 by the head and nucleus under the inspection of power- 
 ful telescopes. 
 
 (45.) All considerable comets which have been ex- 
 amined with anything like what would in these days be re- 
 garded as & powerful telescope, have presented the appear- 
 ance of a nucleus of more or less definable and condensed 
 light, sometimes having a much brighter and almost 
 stellar point in or near its centre, and at some distance, 
 in the direction of the sun, a capping of light sometimes 
 quite separated, as if some transparent atmosphere 
 sustained it more frequently connected by those fan- 
 like jets of " flame," such as we have mentioned in the 
 case of Halley's comet, and putting on the aspect of a 
 "sector," or fan, opening out into a widening arc, and 
 bounded internally by two crescents springing from the 
 nucleus. Donati's comet exhibited this feature in per- 
 fection ; not, however, without striking variations and 
 individual peculiarities. There was the same appearance
 
 ON COMETS. 131 
 
 with low magnifying powers of an envelope surrounding 
 a nucleus in the general way above described, but the 
 connexion was singularly varied, as if several jets of 
 luminous (or illuminated) matter had been issuing from 
 various parts of the nucleus, giving rise, by their more or 
 less oblique presentation to the eye, to exceedingly 
 varied appearances sometimes like the spokes of a 
 wheel or the radial sticks of a fan, sometimes blotted 
 by patches of irregular light, and sometimes interrupted 
 by equally irregular blots of darkness. From the 24th 
 September to the loth October, however, there were 
 seen to form no less than three distinct caps or envelopes 
 in front of the nucleus, each separated from that below 
 it by a more or less distinct comparatively dark inter- 
 val. These Professor Bond appears to consider as hav- 
 ing been thrown off in intermittent succession, as if the 
 forces of ejection had been temporarily exhausted, and 
 again and again resumed a phase of activity; the peculiar 
 action by which the matter of the envelopes was ulti- 
 mately driven into the tail (or, as we conceive ifc an 
 analysis of that matter performed by solar action, the 
 levitating portion of it being hurried off the gravitating 
 remaining behind in the form of a transparent, gaseous, 
 non-reflective medium), taking place, not on the surface 
 of the nucleus, but at successively higher levels. Mean- 
 while, and especially from the yth to the loth of October, 
 that is to say, when the full effect of the perihelion action 
 had been endured, the nucleus and its adjacent sector 
 offered every appearance of most violent, and, so to 
 speak, angry excitement, evidenced by the complicated
 
 ON COMETS. 
 
 structure and convolutions of the jets issuing from it 
 From this time, to its final disappearance, the violence 
 of action gradually calmed down, while the comet it- 
 self went southwards, and at length vanished from our 
 horizon. 
 
 (46.) An idea of the actual dimensions of this comet 
 may be formed from the measurements taken by Professor 
 Bond on ihe 2d October, which, combined with the dis- 
 tance of the comets from the earth at that date afford 
 the following results, viz. : 
 
 Miles. 
 
 Diameter of the bright internal pellet or nucleus, . 1,600 
 
 Distance from its centre to the summit of the 
 
 first envelope, .... 7, 500 
 
 Distance to that of the second envelope, . . 13,200 
 
 Breadth of the brightest part of the tail where it 
 seemed (to the naked eye) to issue from the 
 comet, ..... 90,000 
 
 to which it may be added that the actual length of the 
 tail, when at its greatest development, could not have 
 been less than 30 millions of miles, and those of the 
 faint streaks or secondary tails 34 or 35 millions. 
 
 (47.) The comet of 1861, which burst suddenly on us in 
 its full splendour on the 3oth of June in that year (though 
 it had been seen for seven weeks before in the southern 
 hemisphere), was considered by those who saw it at its 
 first appearance to surpass in brightness even that of 
 1858, and was remarkable for the extreme breadth and 
 diffusion of its tail when first seen, arising from the cir- 
 cumstance of the earth having been then situated nearly 
 in its prolongation. Indeed, it is not impossible that on 
 hat day we actually traversed some portion of it, our
 
 'ON COMETS. 133 
 
 distance from the head being then only about 13,000,000 
 miles, and more than one observer having noticed and 
 been much struck with an unusual and general brightness, 
 like an auroral light not confined to the neighbourhood 
 of the comet, but spreading over the whole sky. The 
 most remarkable peculiarity of this comet, however, con- 
 sisted in the enormous length which one side of its tail 
 attained between the 2d and the 4th of July, extending 
 in a perfectly straight but feeble ray from near the star 
 Alpha in the Great Bear, to and beyond that designated 
 by the same letter in Ophiuchus, or over 75 degrees in 
 angular measure, contrasting strikingly with the stunted 
 development and bushy aspect of the opposite branch. 
 Its head, when viewed with good telescopes, exhibited 
 the same general phenomena of luminous jets and 
 crescent-like emanations as its predecessor, but much 
 less complex and varied. Owing to the great inclination 
 of its orbit, this comet, coming to us from the southern 
 side of the ecliptic, soared high above it on the northern 
 side and remained long and conspicuously visible as a 
 cricumpolar object, the whole of its diurnal course being 
 above our horizon. Not so its successor of 1862, whose 
 orbit being but slightly inclined to our own, its motion 
 retrograde (or meeting the earth), its perihelion distance 
 almost exactly equal to our distance from the sun, and 
 its passage through the perihelion occurring at a time 
 when the earth was not very remote from that point, it 
 passed us closely and swiftly, swelling into importance, 
 and dying away with unusual rapidity. The phenomena 
 exhibited by its nucleus and head were on this account
 
 134 ON COMETS. 
 
 peculiarly interesting and instructive, it being only on 
 very rare occasions that a comet can be closely inspected 
 at the very crisis of its fate, so as to witness the actual 
 effect of the sun's rays on it. In this instance, the pour- 
 ing forth of the cometic matter from the singularly bright 
 and highly condensed, almost planetary nucleus, took 
 place in a single compact stream, which after attaining a 
 short distance, equal to rather less than a diameter of 
 the nucleus itself, was so suddenly broken up and dis- 
 persed as to give, on the first inspection, the impression 
 of a double nucleus. The direction of this jet varied 
 considerably from day to day, but always declined more 
 or less in one direction from the exact direction from the 
 sun. So far as I am aware, the formation of an envelope 
 disjoined from the head was not witnessed in this comet. 
 (48.) And now, I daresay, all my hearers are ready to 
 ask After all what is the tail of a comet ? Is it material 
 substance in the first place 1 To this I answer unhesi- 
 tatingly, Yes ! Donati's comet has given a decisive proof 
 on that point There is a criterion by which, when it is 
 observed, it can be positively asserted that the light by 
 which anything is seen has been reflected from a ma- 
 terial substance. The light reflected, when it exhibits 
 that peculiar property in which this criterion consists is 
 said to be polarized. The direct light of the sun or that 
 of a candle is not polarized, but when reflected at a par- 
 ticular angle on any surface but a metallic one, it is, and 
 if it is polarized, we may be sure that it is not direct 
 light thrown out by the object seen, but borrowed or in- 
 direct light No matter at present what this polarization
 
 ON COMETS. 135 
 
 is, all I wish to convey is, that there is a simple enough 
 experiment which everybody who understands optics 
 knows how to make, which if the result be of a certain kind, 
 the reflection of the light is demonstrated (the con- 
 verse, be it observed, does not hold good) in an instant, 
 by merely looking through a small instrument contrived 
 on purpose. Now, Mr Airy, the present astronomer- 
 royal, a person who is not only an excellent astronomer, 
 but who stands very high as an authority on this especial 
 branch of optics, applied this test to the light of the 
 comet's tail on the 27th September, and found it polar- 
 ized. The (ail then shone by reflected light, and there 
 was also another particular indication or character of the 
 polarization impressed, which the same trial afforded, and 
 which enabled him to say positively that the light had 
 been reflected from some source of light agreeing in 
 situation with the sun. 
 
 (49.) The tail of the comet then was material substance.* 
 But now, only conceive what must be the thinness, the 
 almost spiritual lightness of a vapour or fog, which, oc- 
 cupying such an enormous space, would not extinguish 
 
 * I applied the same test to the comet of 1862. There are various 
 modes of making the trial. Mine was by looking at the comet 
 through an achromatized doubly refracting prism, and turning the 
 prism round in its own plane. I could perceive no alternate maxima 
 and minima of brightness in the images. But in this case it is the 
 positive result which is conclusive. Everything depends in the first 
 instance on the relative situations of the objects and the eye. And, 
 moreover, the light of the comet of 1862 was far inferior to that of 
 Donati's, rendering the experiment pro tanto more delicate and it 
 is very possible that to septuagenarian eyes, indications of partial 
 polarization might escape observation.
 
 136 ON COMETS. 
 
 the stars shining through it. Arcturus was noway dimmed 
 when it shone through the very middle of the brightest 
 part of the tail of that comet. But I have already stated 
 that that part measured 90,000 miles, and as this part of 
 the tail was no doubt round, as thick as broad, the star's 
 light must have shone through 90,000 miles of this mist. 
 Now, every one must have noticed that the steam puff of 
 a railway carriage completely obscures the sun, much 
 more a star. You cannot see the sun through it. Well, 
 then : there must have been less substance in the line of 
 90,000 miles of tail between the eye and star than in the 
 line of a few yards of steam smoke penetrated by the 
 eye in the other case. 
 
 (50.) If you look at a filmy cloud at sunset, though not 
 thick enough to hide a star, you see it bright with vivid 
 golden light by reflection from the sun. How much 
 more then if it were much nearer to the sun, and much 
 more strongly illuminated. Such a cloud is penetrated 
 with light through its whole thickness and reflects it 
 equally from its interior and exterior. Just so in the 
 almost infinitely more thin texture of a comet even in 
 the densest part of the head it cannot be compared to 
 the lightest cloud so far as substance goes. In Biela's 
 comet very minute stars have been seen by myself 
 through a part of the head at least 50,000 miles in thick- 
 ness, which a fog a few yards thick would have extin- 
 guished. A solid body of a round shape would exhibit 
 phases like the moon, and would appear sometimes as a 
 half moon, sometimes as a crescent, and sometimes as a 
 full moon but the heads of comets show no such appear-
 
 ON COMETS. 137 
 
 ances. Of course I do not mean to deny that that very 
 minute brilliant point which some are said to have ex- 
 hibited, may not be a solid body but it must be a very 
 small one perhaps not a tenth or a hundredth part the 
 size of the moon ; and, indeed, if there be not some little 
 solid mass, it seems impossible to conceive how the ob- 
 servations of a loose bundle of smoke, rolling and career- 
 ing about, could ever be represented by any calculation. 
 Certain it is, that what appears to be the central point of 
 a comet, is that point (and no other is) which conforms 
 rigorously to the laws of solar gravitation, and moves 
 strictly in a parabolic or elliptic orbit. 
 
 (51.) There is a very curious feature common to all the 
 comets which have little or no tail, and which circulate 
 about the sun in short periods ; such as that of Encke, 
 in which it has been especially observed. As they ap- 
 proach the sun, so far from dilating in size, they con 
 tract, I mean in their real bulk, orat least their visible 
 bulk, and on receding from the sun they grow again to 
 their former size. The only possible explanation of 
 this is, that a portion of their substance is evaporated by 
 the heat that is to say, converted from the state of fog 
 or cloud into that of invisible transparent vapour. Per- 
 haps I ought to explain what is the difference. Take 
 the case of a light cloud in a clear sky when the sun 
 shines on it. If you watch it attentively, you will very 
 often see it grow thinner and thinner, and at last dis- 
 appear altogether. It has been converted from mist to 
 invisible vapour. The material substance, the watery 
 particles are there, but they have passed into another
 
 138 ON COMETS. 
 
 form of existence, in which, like the air itself, they are 
 invisible. As the comet then gets heated a portion is 
 actually vaporized and the vapour condenses as it 
 cools again. The whole substance of the comet of 
 Halley, as you have heard, was so evaporated in 1835-6, 
 all but what I suppose must have been really its solid 
 body ; that star which I have already mentioned, which 
 was seen on the 22d January 1836 : and all that curious 
 process that went on afterwards, no doubt was that of the 
 re-condensation of the evaporated matter, and its gradual 
 re-absorption into and close around the body. 
 
 (52.) There is still one point in the history of comets 
 which I have not touched upon, or but slightly. Compa- 
 ratively only a few of the great number of comets which 
 have been observed, and of which the orbits have been 
 calculated, have been seen more than once the great 
 majority once seen, seem lost for ever. What becomes 
 of them, is a very natural question. The answer to this 
 is, that the time of the periodical return of a comet 
 depends entirely on the distance to which it may run out 
 from the sun. Now we know of nothing to interfere 
 with or disturb the motion of a comet, once clear of the 
 planetary system, between the farthest planet and the 
 nearest fixed star ; and that interval is so immense that 
 the imagination is lost in attempting to conceive it. The 
 farthest planet we know of is only 30 times the distance 
 of the earth from the sun. Halley's comet in its ellip- 
 tic orbit of 75 years, goes only a little beyond that, or to 
 about 36 times the earth's distance. Donati's comet, if 
 the computists are right, will return in 2100 years, and
 
 ON COMETS. 139 
 
 will have gone out to a distance 238 times the earth's 
 distance from the sun, or nearly 80 times the distance of 
 the planet Neptune. But this is still hardly the thou- 
 sandth part of the distance to the very nearest fixed star 
 and supposing the elliptical orbit of a comet should be 
 so long as to carry it out only half-way to the nearest 
 star its return to the sun would require upwards of u 
 millions of years from its last appearance. Few of those 
 who saw the last-mentioned comet pass over Arcturus, 
 had any idea of the enormous distance at which the star 
 really was behind the comet : and Arcturus is by no 
 means the nearest star. 
 
 (53.) I think, from what I have said, you will perceive 
 that there is in the history of comets matter enough both 
 to encourage inquiry and to check presumption. Looking 
 to the amount of our positive knowledge of them know- 
 ledge acquired by centuries of observation, and by the 
 conspiring efforts within the last two centuries of the 
 profoundest thought and the most persevering labour of 
 which man is capable, we may reasonably enough con- 
 gratulate ourselves on what has been done, and while we 
 can afford to look back with an indulgent smile on the 
 unfledged and somewhat puerile attempts of the ancient 
 mind to penetrate their secret, we may as reasonably 
 look forward to the revelations they will afford, as time 
 rolls on, of facts and laws of which at present we have no 
 idea. This may, and ought to inspire confidence of the 
 powers of man to penetrate always deeper and deeper 
 into the secrets of nature. But, on the other hand, here, 
 as on every other occasion, we find that the last and
 
 140 ON COMETS. 
 
 greatest discoveries only land us on the confines of a 
 wider and more wonderfully diversified view of the uni- 
 verse ; and have now, as we always shall have, to ac- 
 knowledge ourselves baffled and bowed down by the 
 infinite which surrounds us on every side. 
 
 (54.) Beyond all doubt, the widest and most interesting 
 prospect of future discovery which their study holds out 
 to us, is that distinction between gravitating and levitating 
 matter, that positive and unrefutable demonstration of 
 the existence in nature of a repulsive force, co-extensive 
 with but enormously more powerful than the attractive 
 force we call gravity, which the phenomena of their tails 
 afford. This force cannot possibly be of the nature of 
 electric or magnetic forces.* These forces are especially 
 polar in their action between particle and particle a 
 magnet, or an electrified particle, of indefinitely minute 
 dimensions so minute as the discrete particles which go 
 to form a comet's tail, could by no possibility be either 
 attracted or repelled, as such, by a body, however power- 
 fully magnetized or electrified, placed at the distance of 
 the sun. It might have a direction given to its magnetic 
 or electric axis, but its centre of gravity would not be 
 
 * This and much of what follows may seem inconsistent with 
 what is said in my "Results of Ast. Obs., &c., at the Cape of 
 Good Hope," p. 409, and note thereon. To a certain extent it 
 is so, and to that extent it is a recommendation, but I am here 
 speaking only of that portion of the matter of the comet whose 
 chemical union may be considered as completely overcome, and 
 whose levitating or negative constituent is fairly driven off, never 
 to return. That which may be conceived to remain behind may 
 conform under the circumstances of the case to the dynamical 
 relations there indicated.
 
 ON COMETS. 141 
 
 affected one way or the other. The attraction on one 
 of its sides would precisely equal the repulsion on the 
 other. The separation of one portion of the matter of 
 a comet from the other by the action of the sun, which 
 we see, unmistakably, operated at and near the peri- 
 helion passage (a separation which the late Sir William 
 Herschel certainly had in mind, though perhaps some- 
 what indistinctly, when he spoke of a comet visiting our 
 system for the first time as consisting of "unperiheli- 
 oned " matter in contradistinction to those which he con- 
 sidered to have lost their tails by the effect of repeated 
 appulses, and to consist mainly of perihelioned matter) 
 this separation I can only conceive, as I have ven- 
 tured to express it above, as an analysis of the mate- 
 rials : analogous to that analysis or rather disunion by 
 the action of heat which St Clair Deville has lately shown 
 to take place between the constituents of water at high 
 temperatures. In this latter case the chemical affinity is so 
 weakened that the mere difference of difficulty in travers- 
 ing an earthenware tube suffices to set them free of one 
 another. How much more so, then, were the one con- 
 stituent of a chemical compound subject to a powerful 
 repulsion from a centre which should attract the other, 
 and with it by far the larger mass of the total comet. 
 Might not, under such circumstances, the mere ordinary 
 action of the sun's heat sufficiently weaken their bond of 
 union : and might not the residual mass, losing at every 
 return to the perihelion more and more of its levitating 
 constituents, at length settle down into a quiet, sober, 
 unexcitable denizen of our system ?
 
 LECTURE IV. 
 
 THE WEATHER, AND WEATHER PROPHETS. 
 " Varium et mutabile semper." 
 
 [HERE is an ugly look about the sky, and 
 the wind is getting up, and Fiizro/s storm- 
 signals were hoisted yesterday evening and 
 are up now. We shall have a gale. I am 
 afraid we must put off our boating for to-day anyhow," 
 
 said my friend A to his wife the other day ; " there 
 
 may be nothing in it ; but we should look very silly to 
 come home half-drowned in the face of a warning." 
 
 (2.) And it was well the lady took the advice. It was 
 but a pleasure party after all. But the fishermen to 
 whom the loss of a day was a serious matter, put off. 
 Not that they altogether pooh-pooh 1 d the inverted cone 
 and drum : but they reckoned on twenty-fours' law at 
 least, and suffered for their miscalculation. One boat 
 came on shore in fragments, several suffered damage, 
 and all agreed it would have been wiser to have stayed 
 at home.
 
 THE WEATHER, AND WEATHER PROPHETS. 143 
 
 (3.) An occurrence like this took place at one of our 
 southern watering-places not far from hence, a few days 
 ago ; and the gale which followed was one of the pre- 
 cursors of that far more fearful one which has just (appa- 
 rently) blown itself out ;* part and parcel, no doubt, of 
 that great periodical phaenomenon whose recurrence 
 under the name of " the November atmospheric wave," 
 is beginning to be recognized as one of the features of 
 our European weather table a vast and considerably 
 well-defined atmospherical disturbance ; peculiar, it 
 would seem, to this portion of the globe, though origin- 
 ating, as we shall see reason to believe, in the opposite 
 hemisphere ; and of which the gale of the Royal Charter 
 (October 25, 1859) ; the great Crimean hurricane of 
 disastrous memory (November 14, 1855) ; and the still 
 more awful storm of December 8, (N.S.) 1703, the 
 greatest which has ever swept this island, may be 
 considered as shadowing out the beginning, middle, and 
 end. 
 
 (4.) The actual barometric fluctuation to which the 
 epithet has been affixed by Mr Birt, who first drew 
 attention to one of its most peculiar features, is, how- 
 ever, confined to narrower limits of time ; and refers to 
 one great billow or mountainous breaker (so to speak) of 
 air, which sweeps in November across the whole North 
 Atlantic and the European continent from N.W. to S.E. ; 
 preceded and followed by sudden and violent subor- 
 
 * This was written on the morning of the 3d of November 1863, 
 after a night of most terrific storm.
 
 144 THE WEATHER, AND WEATHER PROPHETS. 
 
 dinate fluctuations, embracing in their whole extent and 
 in different years the longer period referred to.* 
 
 (5.) Meteorology, so far as prediction of the weather 
 is concerned (which most persons consider, very erron- 
 eously, to be its only practical object), may be regarded 
 as a science still in its infancy ; though if such be the 
 case, to judge from the voluminous nature of its records, 
 and the multitude of books which have been written 
 on it, its maturity, if ever attained, would promise to be 
 gigantic indeed ; were it not that the progress of all 
 real science is towards compression and condensation, 
 and its whole aim to supersede the endless detail of 
 individual cases by the announcement of easily remem- 
 bered and readily applicable laws. Most of the indica- 
 tions of the " weatherwise," from Aratus down to Foster, 
 have hitherto been little more than what, in the language 
 of Mr Mill, would be called " simple connotations." 
 The condor is circling in the sky : therefore a lion is 
 devouring a horse below. The sheep turn their tails to 
 the south-west: therefore there will be a gale of wind 
 from that quarter. The " Rainbow in the morning," 
 &c. The " Evening red and the morning gray," &c., 
 &c. All such connotations have their value in an abso- 
 lute ignorance of causes and modes of action : but it is 
 only by the study of these that we learn what to connote. 
 And there is no doubt, that since, after an immense 
 
 * This is the direction of the progress of the wave. That of the 
 wind during the gales which accompany it is at right angles to that 
 direction, or from S.W. to N.E. : in analogy (?) to the transverse 
 rotation of the ethenal molecules in the piopagaiion of a circularly 
 polarized ray of light.
 
 THE WEATHER, AND WEATHER PROPHETS. 145 
 
 amount of persevering labour bestowed on daily and 
 hourly records of the weather, an insight (and no incon- 
 siderable one) has been gained into the causes which 
 determine it, and the sequence of phenomena which 
 exhibit them in action ; a style of connotation has com- 
 menced, which is already bearing practical fruit, in the 
 form of telegraphic warnings of approaching bad weather, 
 of positive value and interest. There can be no better 
 proof of this, than in the fact that the example set by 
 our own Admiralty in the establishment of a system of 
 coast weather signals, has already been followed to a 
 certain extent in Holland, and is in course of being so 
 in France. Nations are perhaps not overready in fol- 
 lowing up the improvements of their neighbours ; but 
 at all events, they are remarkably slow in adopting each 
 other's practical blunders. 
 
 (6.) The indications of the coming weather which 
 experience has shown to be in any degree dependable, 
 have been embodied by Admiral Fitzroy in a sort of 
 code of instructions or " forecasts," which have been 
 so very extensively circulated by his praiseworthy zeal, 
 aided by the powerful means at his disposal, that we do 
 not consider it necessary to recapitulate them. They 
 rely mainly on the indications of the barometer and 
 thermometer, together with the observation of the direc- 
 tion and force of the wind at the time and place, and of 
 its immediately previous course ; all these particulars 
 being regarded not per se, but as in connexion with 
 eacn other; their indications not being absolute, but 
 relative : so that a nse in the barometer, coupled in one 
 
 K.
 
 146 THE WEATHER, AND WEATHER PROPHETS. 
 
 case with a rise, and in another with a fall in the ther- 
 mometer, may indicate, under given, or, as the case may 
 be, differing circumstances of wind ; widely different or 
 even opposite features in the character of the approach- 
 ing weather. It is to be borne in mind, however, most 
 carefully, that all such indications are to be received as 
 valid (pro tanto) only for a very brief interval in advance ; 
 and that the " weather-prophet" who ventures his pre- 
 dictions on the great scale, is altogether to be distrusted. 
 A lucky hit may be made : nay, some rude approach to 
 the perception of " a cycle of seasons" may possibly be 
 attainable. But no person in his senses would alter his 
 plans of conduct for six months in advance in the most 
 trifling particular, on the faith of any special prediction 
 of a warm or a cold, a wet or a dry, a calm or a stormy 
 summer or winter. Of all the minor or simply connotative 
 indications of the coming weather (as distinct from 
 those which connect themselves with our knowledge of 
 causes), the only one in which we place the slightest 
 reliance is that the appearance of " anvil-shaped clouds" 
 is very likely to be speedily followed by a gale of wind. 
 (7.) The moon is often appealed to as a great indi- 
 cator of the weather, and especially its changes as taken 
 in conjunction with some existing state of wind or sky. 
 As an attracting body causing an " aerial tide," it has 
 of course an effect, but one utterly insignificant as a 
 meteorological cause ; and the only effect distinctly 
 connected with its position with regard to the sun which 
 can be reckoned upon with any degree of certainty, is its 
 tendency to clear the sky of cloud, and to prodmv not
 
 THE WEATHER, AND WEATHER PROPHETS. 147 
 
 only a seiene, but a calm night, when so near the full ai 
 to appear round to the eye a tendency of which we 
 have assured ourselves by long continued and registered 
 observation. This, however, is more than a " simple 
 connotation." The effect in question, so far as the 
 clearance of the sky is concerned, is traceable to a dis- 
 tinct physical cause, the warmth radiated from its highly 
 heated surface ; though why the effect should not continue 
 for several nights after the full, remains problematic 
 
 (8.) Lunar prognostics about the weather may be 
 classed under three several heads, viz., ist, Simple 
 connotations of the appearance of halos, coronas, lunar 
 rainbows, and " a watery" moon, as prognostics of wet. 
 No doubt they do indicate the presence of vapour, pass- 
 ing into cloud, in the higher regions of the air (in that of 
 the rainbow, actual rain not far away), and so may be 
 put on a par with the indications which may sometimes 
 be gathered from the behaviour of birds, especially such 
 as fly high, and make long excursions, and which may 
 convey to us some notion of their cogitations as to the 
 coming weather ; which are perhaps more likely to be 
 right than our own, as founded on a wider range of per- 
 ception. 2d, Purely arbitrary laws or rules founded on 
 the hour of the day or night at which the changes of the 
 moon take place. There is (or was a few years ago, foi 
 we believe the race is dying out) hardly a small farmei 
 or farm-labourer who had not some faith in certain " wea- 
 ther-tables" in the " Farmer's Almanac." ascribed (we 
 need hardly say falsely) to the late Sir W. Herschel, and 
 which went on this principle. Others, again, pressed
 
 148 THE WEATHER, AND WEATHER PROPHETS. 
 
 into the service the great and recondite names of APO- 
 GEE and PERIGEE ; and professed to determine the char- 
 acter of the lunation from her proximity at new or full to 
 these mysterious points of her orbit. Both the one and 
 other rule utterly break down when brought to the tests 
 of long-continued and registered experience. Others, 
 again, drew their prognostic for the whole lunation from 
 the character of the weather during the first quarter. 
 Such was the rule said to have been implicitly adhered 
 to by the late Marshal Bugeaud in the planning of any 
 military expedition whose success was likely to be any 
 way dependent on weather : 
 
 *' Primus, secundus, tertius, nullus, 
 Quartus, aliquis, 
 Quintus, sextus, qualis ; 
 Tota Luna talis." 
 
 (9.) 3dly. A more ambitious form of lunar prediction 
 was that of the late eminent meteorologist (for such, this 
 one crotchet excepted, he certainly was), Luke Howard ; 
 who took great account of the moon's declination as 
 influencing the averages of rainfall, and of the height of 
 the barometer. Still more so was his weather-cycle of 
 nineteen years, the period of the circulation of the nodes 
 of the moon's orbit ; in the course of which the absolute 
 maximum of north declination occurs when the ascending 
 node is in the spring equinox, and the moon 90 in 
 advance of the node in her orbit, and that of south in 
 the reversed circumstances the intermediate situations 
 of the node corresponding to the absolute minima of each. 
 These situations, according to the declination theory,
 
 THE WEATHER, AND WEATHER PROPHETS. 149 
 
 ought to bring round a periodical increase and diminu- 
 tion in the average rainfalls and barometric heights. 
 Like the others, however, when compared on any ex- 
 tended scale with recorded facts, this results in no 
 establishment of any positive conclusion. 
 
 (10.) A small monthly depression in the average tem- 
 perature arising from the nocturnal radiation consequent 
 on the cloudless state of the sky about the full moon, 
 would seem almost a necessary consequence of that 
 phenomenon. 
 
 (n.) The causes by which that " various and mutable 
 thing" which we call THE WEATHER are produced are in 
 themselves few and simple enough ; but the physical 
 laws which determine their actions are numerous and 
 complex ; and the results, in consequence, so mutually 
 interwoven, and the momentary conditions of their ac- 
 tion so dependent on the state of things induced by 
 their previous agency, that it is no wonder it should 
 be next to impossible to trace each specific cause (act- 
 ing as it has done through all past time) direct to its 
 present effect. Yet from this very complexity results 
 that sort of regulated casualty that apparently acci- 
 dental, yet limited departure and excursion on either 
 side from a monotonous medium that exceeding variety 
 of climate, which renders our globe a fit habitation for 
 such innumerable diversities of incompatible life and 
 that general equilibrium in each which secures to every 
 species, and to each individual of them all, its due share 
 in the distribution of heat, moisture, and wholesome 
 air : considerations, these, which are not lost on those
 
 I$O THE WEATHER, AND WEATHER PROPHETS. 
 
 who believe that they can trace in nature the operation 
 of motive and design as distinct from a mere necessity 
 arising out of the nature of things and the so-called 
 conservation of vis viva. 
 
 (12.) Let us take our globe as we find it revolving on 
 its axis in twenty-four hours ; and carried round the sun 
 in an orbit oblique to its equator in a year ; which is 
 divided into two somewhat unequal halves (if such an 
 expression may be pardoned) from equinox to equinox 
 by its unequal angular motion in a slightly elliptic orbit ; 
 thus giving rise to unequal summers and winters in the 
 two hemispheres : its surface very unequally divided 
 between land and sea the land mainly congregated 
 upon one half of it, and that half principally belonging 
 to the northern hemisphere ; and so distributed as effect- 
 ually to bar all free circulation of the ocean in the direc- 
 tion of the diurnal rotation (or round the equator), and 
 allow but a restricted one in that at right angles to it (or 
 across the poles) : thus compelling whatever circulation 
 does exist, to take place within three great basins or 
 semi-land-locked areas, and a vast southern expanse into 
 which all the three open ; and within each of which 
 a system of circulation is kept up by the action of the 
 winds ; its course being determined partly by the sinuosi- 
 ties of their shores, partly by the inequalities of their 
 bottoms, and partly by the rotation of the earth itself 
 
 (13.) We have, besides, to consider the globe as en 
 tirely and deeply covered by an atmosphere of mixed 
 gases highly elastic, very dilatable by heat, and of 
 extreme mobility : expanding itself in virtue of its elas-
 
 THE WEATHER, AND WEATHER PROPHETS. !$! 
 
 ticity out into space, far above the tops of the highest 
 mountains ; yet, in virtue of its compressibility, so con- 
 densed (comparatively) in its lower strata as that one- 
 third of its total ponderable mass lies within a mile of 
 altitude above the sea-level nearly one-half within two, 
 and nearly two-thirds within five miles ; within which 
 latter limit the whole would be contained, were it every- 
 where of the same density as on the surface : so that 
 only about one-third of its total mass is free to range, 
 unimpeded by the crests of the highest Himalaya ; and 
 not much more than two-fifths can entirely clear the 
 range of the Andes without pressure d tergo. In conse- 
 quence, when driven in the state of WIND over these or 
 other mountain ranges, it is thrown up into vast ripples 
 or waves, which are propagated thenceforward onwards 
 over indefinite areas of land or sea, and become no 
 doubt the origin of a great part of those casual fluctua- 
 tions of the barometer which give so much trouble to 
 meteorologists. 
 
 (14.) This aerial ocean is not of the same temperature 
 throughout, even in the same climate and over the same 
 tract of country. It is everywhere warmer near the 
 ground, colder aloft and at very great heights a most 
 intense cold always prevails ; more intense than that of 
 our severest winters. Hence the snow which covers the 
 summits of lofty mountains even in the hottest climates. 
 This relation between the temperatures existing below 
 and aloft is not subverted by any amount of mutual 
 admixture of the strata, such as internal movements or 
 ascending currents would produce. On the contrary,
 
 152 THE WEATHER, AND WEATHER PROPHETS. 
 
 paradoxical as it may appear, such ascensional move- 
 ments are the primary cause of this state of things ; in 
 consequence of the habitudes of air with respect to heat 
 when compressed or expanded, according to a mode of 
 action well understood by meteorologists, which we need 
 not stop here to explain, as the reader will readily collect 
 it for himself from what follows. 
 
 (15.) As the air aloft is colder than below, so also is 
 it drier. Every one considers that he knows the dis- 
 tinction between damp and dry air ; but many are not 
 aware that all air contains some moisture, in the form of 
 transparent invisible vapour ; or that in summer and 
 winter on two days, both which would in common par- 
 lance be pronounced dry ones, there is more than twice 
 as much moisture present in an equal bulk of air in the 
 summer, as in the winter day. Tn this state of invisible 
 vapour which water is always assuming (throwing itself 
 off in that form from its surface whenever exposed, and 
 the more copiously the warmer it is), the air is its general 
 recipient and distributor. The mechanism by which it 
 is enabled to do so on the great scale is exceedingly 
 curious. We shall endeavour to exhibit it, as it were in 
 action not so much with a view to affording a coup-d'<zil 
 of the whole of meteorology, as with that of rendering 
 in some degree more intelligible than at present it seems 
 to be, that great phenomenon of the November storms, 
 with the mention of which we began this lecture, which 
 has never been satisfactorily explained. 
 
 (16.) Looking at our globe as revolving under the 
 warming influence of the sun, whose rays at noon fall on
 
 THE WEATHER, AND WEATHER PROPHETS. 153 
 
 it with little obliquity in tropical regions, while their 
 incidence on those near the poles is always very oblique, 
 and during the half of each year null ; it is obvious that 
 its surface must be very unequally warmed. The cook, 
 to use a homely illustration, knows full well that, how- 
 ever good her fire, the two ends of her joint will be 
 under-roasted when the middle is done brown ; unless 
 she apply a couple of concave reflectors on her spit to 
 throw some of the lateral heat upon them. As a matter 
 of fact, no one needs to be told that it is so ; and that 
 the intertropical regions of the globe are very hot, and 
 the polar, habitually very cold. The average annual 
 temperature at the equator is about 84 Fahr., while in 
 the colder regions near the North Pole it is as low as 
 5 Fahr., or 27 below freezing. The difference would 
 be much greater were there no sea, or even were the 
 whole surface initially moist soil. Whatever that initial 
 moisture, it would soon dry 0^"from the warmer portions, 
 to settle down in snow or hoar frost on the colder ; after 
 which the dried portions would grow hotter and hotter. 
 Every one knows what a cooling power there is in the 
 evaporation of water. So long as a vestige of moisture 
 were present, the temperature of the soil could never, at 
 at all events exceed, however it might fall short of, that 
 of boiling water : but when once completely dried off, 
 there would no longer be a limit to the possible increase 
 of temperature , since there would then be no circulation 
 or return of moisture to the part once dried. How this 
 circulation is kept up under the existing circumstances 
 is what we must now explain : and first of all how it
 
 154 THE WEATHER, AND WEATHER PROPHETS. 
 
 happens that in the course of ages the whole ocean has 
 not been transferred by this sort of distillatory process 
 from the tropics to the poles ; leaving the former dry, 
 and piling the latter with mountainous accumulations of 
 ice. Were the Polar regions of the globe occupied 
 by land instead of by sea, there is every reason to be- 
 lieve that such would be the case. As it is, the contrary 
 arrangement prevails, and the Polar snows fall upon 
 these seas or upon their frozen surfaces, and form float- 
 ing masses of ice, which are partly broken up and drifted 
 away, and partly melted in situ by currents of water per- 
 petually streaming in against and beneath them from 
 warmer regions, and thus become restored to the general 
 ocean. 
 
 (17.) But what, it will be asked of course, produces 
 these warm currents ? And how is the water of which 
 that snow consists, and all the rain which falls and feeds 
 the rivers that restore it to the sea, raised into the air, 
 and distributed over the world, and thrown down again 
 indiscriminately over all its surface? Common sense 
 assures us that all the rain, &<x, which falls from the 
 skies must have originated in the sea, and must (if the 
 present state of things is to endure) find its way back to 
 it. But how is it done 1 And, in the first place, where 
 are we to look for the motive power? To this the 
 answer presents itself at once. In the sun's heat. Any 
 of our readers who will take the trouble to refer to Lect. 
 II., 23, will find that the amount of solar heat which 
 actually reaches the surface of our globe would suffice to 
 melt an inch in thickness of ice in two hours thirteen
 
 THE WEATHER, AND WEATHER PROPHETS. I$5 
 
 minutes on a surface perpendicularly exposed to it ; and 
 from this he will have no difficulty in calculating the 
 depth of water over the whole area of the globe, land 
 and sea, per annum, which it would suffice to convert 
 into vapour if wholly expended in so doing. This he 
 will find to amount, as nearly as may be, to nine feet.* 
 Meteorologists, collecting the registers of "rainfall" in 
 all regions of the globe, and comparing and calculating 
 on their indications, have come to the conclusion that 
 taking one region with another, the quantity of water 
 actually precipitated from the air per annum, in the 
 forms of rain, hail, snow, and dew, would suffice to 
 cover the whole of its surface to a depth of five feet 
 Remains the equivalent of four feet, expended in warming 
 the soil ; which is partly radiated away, and partly com- 
 municated to the air, thus going to maintain the average 
 temperature, according to its climatic distribution. And 
 as solely expended on this last-mentioned object, we 
 have to reckon fully one-third of the sun's total radia- 
 tion, or one-half of that already accounted for, which is 
 absorbed by the air, or rather by the moisture in it, 
 before reaching the eauh. The joint effect of these 
 two portions is, as we have seen, to maintain the air in 
 
 * We will make the calculation for him. An inch of ice melted 
 in 2 hours 1 3 minutes over a great circle of the globe perpendicu- 
 larly exposed to the sun, corresponds to a quarter of an inch in 
 that time over the whole surface (which is four great circles), or, 
 per annum, to 98775 inches ; or to nine-tenths of this, or 890 inches 
 of water raised 135 Fahr. in temperature; or (taking the initial 
 temperature of the water evaporated on an average at 60 Fahr.) to 
 108 inches or 9 feet heated 1112 to convert it into steam.
 
 156 THE WEATHER, AND WEATHER PROPHETS. 
 
 the equatorial region of the earth habitually hotter by 
 about 80 Fahr. on an average of all seasons and hours, 
 than the Polar, 
 
 (18.) Hot air under equal barometric pressure is 
 lighter than cold. The equatorial portion of the atmo- 
 sphere, then, in comparison with the polar, is dilated 
 upwards ; the only direction in which the lateral pressure 
 it experiences will permit it to dilate. Hence, the ex- 
 ternal form of the atmosphere, and of each of its upper 
 strata, instead of conforming in exact parallelism to the 
 spherical* form of the globe on which it reposes, as the 
 laws of equilibrium would require ; are unduly elevated, 
 and bulged out, equatorially, into elliptic forms, a state 
 of things inconsistent with repose. The prominent 
 portion rests, in fact, either way, on a slope, and being 
 unsupported laterally, flows down on either side that is, 
 from the equator towards the poles. In so doing, how- 
 ever, it deserts its place, and ceases to contribute by its 
 weight to the total pressure on the equatorial region ; 
 while at the same time it goes to add to the weight in- 
 cumbent on the polar. Thus the hydrostatic equilibrium 
 of pressure is subverted, and air is pressed inwards to- 
 wards the equator from the poles below, to make good 
 the efflux aloft. A circulation is established in each 
 hemisphere by inferior currents of air running in on both 
 sides towards the equator and superior ones setting out- 
 wards, all around the globe, from the equator towards 
 the poles. Both these, were the earth at rest, would 
 
 * We neglect the spheroidal form of the earth, which in meteor- 
 ology is never worth considering.
 
 THE WEATHER, AND WEATHER PROPHETS. 157 
 
 follow the directions of meridians, but are converted by 
 its rotation on its axis and the gradual diminution of the 
 rotatory velocity in advancing from the equator to the 
 poles, into relatively oblique currents. The upper or out- 
 ward follow precisely the reverse direction to the lower 
 or inward, and being drawn downwards, and are ultimately 
 brought down to the sea level, in their approach towards 
 the poles to supply the void which would otherwise be 
 left by the withdrawal of air below.* They thus become 
 surface winds, prevalent in the regions beyond the tropics 
 from about 30 of latitude either way. 
 
 (19.) In the view thus taken of the great and per- 
 manent system of winds known as the " trades" and 
 " anti-trades," it will be observed that we have been 
 careful to regard them as resulting not so much from the 
 immediate (and diurnally intermittent) action of the sun, 
 as in a certain established gradation of climatic tem- 
 perature, the result of its action on the whole earth's 
 surface continued through successive ages. Were the 
 sun extinguished, the system of the trade winds would 
 continue to subsist, though with diminishing intensity, 
 so long as the equator continued in any degree warmer 
 than the poles. 
 
 (20.) By the action of the trade winds which occupy 
 
 * Those of our readers who are not already familiar with the 
 nature of this transformation, and who would wish to follow it out 
 more closely, are referred (as well as for every other matter of detail 
 in similar cases, precluded by our limits) to the article Meteorology, 
 in the " Encyclopaedia Britannica," or to the same article pub- 
 lished separately by (A. & C. Black, Edinburgh) the editors of 
 that worK.
 
 158 THE WEATHER, AND WEATHER PROPHETS. 
 
 the intertropical region, and a little more, and which, 
 though differing as to north and south, conspire in their 
 general easterly character, the surface of the equatorial 
 ocean is driven westward, and directed full against the 
 two great barriers (the west coasts of America and Asia), 
 and divided northward and southward into streams or 
 currents which in their progress, after issuing from 
 tropical latitudes, receive a direction, by reason of the 
 rotation of the earth, corresponding to that of the anti- 
 trade winds. These also, beginning about the same 
 latitudes to descend to the sea level and strike on the 
 ocean, aid their further progress, and carry them, or 
 portions of them, far northward and southward : .nto the 
 Polar Seas, there to perform the work above assigned to 
 them of melting the ice, and so keeping up the total 
 amount of the ocean-water ; besides mitigating, to a 
 great extent, the severity of the cold on the coasts in 
 high latitudes on which they strike ; of which we have a 
 familiar example in the warming influence of the cele- 
 brated Gulf-stream. 
 
 (21.) The steady and equalized agency by which the 
 great system of the permanent winds and oceanic cur- 
 rents is kept up, which we have just described, contrasts 
 itself strongly with the violent and, as it may almost in 
 comparison be called, impulsive action of the sun on 
 and around the point of the globe over which, for the 
 moment, it happens to be vertical ; and which corre- 
 sponds to that portion of the solar energy which is 
 directly employed in producing evaporation. The nature 
 of this process we have now to explain.
 
 THE WEATHER, AND WEATHER PROPHETS. 159 
 
 (22.) When water is converted into invisible vapour, 
 it occupies between sixteen and seventeen hundred 
 times its original volume, and becomes much lighter 
 than air as light, indeed, as the ordinary coal gas with 
 which balloons are filled, so that if enclosed in a similar 
 envelope it would rise in the air like a balloon. Being 
 free, however, it mixes with the air, and that not merely 
 by a simple chance-medley confusion, but by a peculiar 
 self-diffusive energy arising from its inherent elasticity; 
 by which the particles of every one species of gas or 
 vapour struggle to interpenetrate, and needle, as it were, 
 their way among those of every other. These latter oppose 
 to them no elastic pressure, out that simple resistance to 
 jostling which an inert body of any other kind might do, 
 which feathers, for instance, might oppose to air, in- 
 troduced and struggling to diffuse itself among them. 
 Of course they will be pushed from their places in the 
 struggle, both laterally and vertically, and thus arises 
 over the whole region in which the vapour is in course 
 of production, a pressure on the air both outwards and 
 upwards. The former, however, cannot be effective in 
 removing air bodily to any great distance horizontally, 
 for the simple reason that to do so it would have to 
 shove aside the whole surrounding aerial atmosphere, and 
 to crowd it upon that which is beyond : while there is 
 room in a vertical direction for an indefinite removal, 
 and the upward pressure is also aided by the lightness of 
 the up-struggling vapour, which therefore rises rapidly 
 not without dragging up with it a great deal of air. The 
 consequence is to establish, immediately under the sun,
 
 l6o THE WEATHER, AND WEATHER PROPHETS. 
 
 at whatever part of the globe it happens to be vertical, 
 and at which there is a supply of moisture, and for 
 a very large space around it; what may be likened 
 to a vast up-surging fountain of air and vapour throw- 
 ing itself up with an impetus ; breaking up and bulg- 
 ing outwards the immediately incumbent aerial strata 
 very far above their natural levels ; and introducing 
 at the same time into the air a great quantity of va- 
 pour, as well as withdrawing, by direct transfer, from the 
 lower atmosphere, a great deal of air; which of course 
 has to be supplied by in-draft along the surface of the 
 earth. 
 
 (23.) The process now described, is in a great many 
 of its features similar to that gentler one previously 
 stated : and as it always takes place at some point 
 or other of the intertropical region, it conspires with 
 and locally exaggerates its result so far as the transfer 
 and circulation of air and the production of winds is 
 concerned. As regards the vapour, a large portion is 
 very speedily deprived of its elasticity and ascensional 
 power, and reduced to the state of visible cloud, col- 
 lecting and descending in rain. This is a consequence 
 partly of its arrival in a colder region, but mainly of the 
 property which all gases and all vapours alike possess, 
 of absorbing and rendering latent a large quantity of 
 heat as they expand in volume, and so becoming, ipso 
 facto, colder. Both the air and the vapour do so expand 
 as they rise, by reason of the diminution of pressure they 
 experience. The air indeed retains its elastic state as 
 air, however cold it may become ; and therefore merely
 
 THE WEATHER, AND WEATHER PROPHETS. l6l 
 
 takes its place in its new situation as very cold air, with- 
 out further tendency to rise. But the vapour so chilled 
 loses its vaporous state, and condenses in the manner 
 above stated ; leaving only so much uncondensed as can 
 remain -vaporous under that temperature and pressure. This 
 is the origin of those continual and violent tropical rains 
 which always accompany the vertical sun, and its near 
 neighbourhood, and of which we feel the influence, 
 though slightly, in our wet Julys. The vapour being 
 thus arrested in its upward progress, the whole of the 
 evaporatory process we have just described, however 
 tumultuous in its origin, is confined to what may be con- 
 sidered comparatively the lower strata of the atmosphere. 
 But these become in this manner saturated with moist- 
 ure ; and when carried into the general circulation, con* 
 vey it either as cloud or as invisible vapour to the 
 farthest regions of the earth. 
 
 (24.) Besides the evaporation produced by the direct 
 action of the sun, a vast amount of moisture is taken up 
 by the air immediately from the sea and land over which 
 it passes in its indraft towards the Equator as a trade- 
 wind. Coming from a colder region to a warmer, and 
 acquiring heat as it advances, its capacity for receiving 
 and retaining moisture in an invisible state is continually 
 increasing; and hence, even during the absence of the 
 sun in the night hours, it is constantly absorbing moist- 
 ure ; which : t carries along with it, and delivers, as 
 a contribution of its own collecting, into the general 
 ascending mass, to be handed over in the returning 
 upper current into the circulation. Hence it arises that
 
 162 THE WEATHER, AND WEATHER PE.OPHET3. 
 
 the regions of the earth habitually swept by the trade- 
 winds abound in sandy deserts and arid wastes. When, 
 however, in the progress of that circulation, it descends 
 again to the earth, and becomes a surface-wind (assum- 
 ing the character of an " anti-trade "), it finds itself in 
 precisely reversed circumstances. It is now travelling 
 from a warmer to a colder region. Saturated with 
 moisture in the warmer, and parting with the heat 
 which alone enabled it to retain it, its vapour condenses. 
 Clouds already formed thicken, and descend in rain, 
 and fresh ones are continually forming, to fall in snow 
 at a further stage of its progress ; till all the superfluous 
 moisture is thus successively drained off, and it is pre- 
 pared to re-assume, while starting on a fresh circuit, the 
 character of a drying wind. 
 
 (25.) We have here the origin of that generally ob- 
 served difference of character between our two most 
 prevalent winds the S.W. and the N.E. The former is 
 our " anti-trade," that which from our geographical posi- 
 tion we are chiefly entitled to expect, and which, in 
 point of fact, is of far the most frequent occurrence. 
 Its prevailing characters are warmth, moisture, cloud 
 and rain, as well as persistence and strength. In the 
 former of these characters it is strongly reinforced by the 
 circumstance of its accompanying across the Atlantic the 
 Gulf-stream, which, in fact, it helps to drift upon oui 
 western coasts, and which, retaining a considerable 
 amount of the equatorial heat, sends up along its whole 
 course a copious supply of vapour, in addition to that 
 with which the air above it is already loaded : and this
 
 THE WEATHER, AND WEATHER PROPHETS. l6j 
 
 it is which gives to our west coasts, and to that of Ire- 
 land, their moist and rainy climate double, and more 
 than double, the amount of rain falling annually on the 
 coasts exposed to its full influence, as compared with 
 the eastern coast ; which it does not reach until drained 
 of its excess of humidity. 
 
 (26.) The characters of our North-east winds (for 
 such as are in common parlance called Easterly winds 
 are almost always such) are the reverse of these in every 
 particular. They are cold, dry, and hence often spoken 
 of as cutting, from their parching effect on the skin ; and, 
 as a natural consequence, for the most part accompanied 
 with a clear sky. They are seldom of very long continu- 
 ance, and may be regarded rather as casual winds, except 
 in the spring ; when the advance of the sun to the north 
 of the equator begins to call into action a northern 
 indraft to push to the northward the limit of the north- 
 east trades, and to unsettle by its intrusion the line of 
 demarcation between the wind-zones which its long continu- 
 ance in extreme south latitude, near the winter solstice, had 
 allowed to take up, and rest in, its extreme southernmost 
 position. To this opposition of characters we may add, 
 that the South-west wind is generally accompanied with 
 a lower, and that of the North-east with a higher than 
 average barometric pressure ; a connexion partially, but 
 not entirely, accounted for by the lightness of warm and 
 moist air as compared with cold and dry ; and which is 
 the origin of those indications of the weather (fair, 
 settled fair, rain, much rain, &c., 6^.) which we find 
 inscribed opposite to the divisions of the scale of inches
 
 164 THE WEATHER, AND WEATHER PROPHETS. 
 
 in our ordinary barometers. When the North-east wind 
 brings snow, as it very frequently does, it is not by the 
 precipitation of its own moisture ; but by its intrusion as a 
 cold wind into a warmer atmosphere charged with mois- 
 ture, and ready to deposit it under any cooling influence. 
 
 (27.) Complementary to the phenomenon just men- 
 tioned of a tendency to North-easterly wind in the 
 spring, i.e., to the production of a lull or temporary 
 intermittence in the regular South-west current, and the 
 substitution for it of its opposite ; may be considered that 
 aggravation of its intensity which takes place subsequent 
 to the autumnal equinox ; exaggerated, however, and 
 thrown later into the season, viz., into November, by the 
 conspiring action of several distinct causes, which we 
 will now proceed to explain. 
 
 (28.) As the sun in its annual course traverses the 
 northern and southern halves of the ecliptic, it creates 
 summer in the one hemisphere, simultaneously with 
 winter in the other ; and the balance of aerial expansion 
 and aqueous evaporation is alternately struck in favour 
 of each. As a necessary consequence, a large amount 
 both of air and of aqueous vapour carrying air along 
 with it, is alternately driven over from one hemispheie 
 to the other. The only course which the elements so 
 transferred can pursue, is by passing in the higher 
 regions of the atmosphere across that medial line where 
 the two superior out-flowing currents separate on their 
 courses towards either pole in other words, by joining 
 with, and reinforcing the " anti-trade" current on that 
 side of the equator towards which they are propelled.
 
 THE WEATHER, AND WEATHER PROPHETS. 165 
 
 Now this cause of reinforcement cannot begin to be felt 
 until the sun, having passed the equinoctial, has ad- 
 vanced considerably towards the other solstice. In the 
 case of the northern anti-trade, the effect in question is 
 rendered still more sensible by the great preponderance 
 of sea in the southern hemisphere as compared with the 
 northern ; and the much greater quantity of vapour 
 raised by the summer sun on that side of the equator. 
 And besides all this, it will be remembered that all the 
 air which had been dragged across the equator into the 
 southern hemisphere by transferred vapour during the 
 continuance of our northern summer, and there as it 
 were imprisoned, is now released; and returns, neces- 
 sarily by the same course, and contributes to reinforce 
 the northern anti-trades. 
 
 (29.) There is a special cause, too, arising from the 
 geographical position of Britain and north-west Europe, 
 in relation to the South American continent, which is 
 probably not uninfluential in producing or aggravating 
 this disturbance. If we trace on a map the course of 
 the wind which reaches our island from the south-west, 
 we shall find that it has its origin on the coast of Guiana, 
 between the fiftieth and sixtieth degrees of west longi- 
 tude. This also is nearly about the point where the 
 medial line between the north and south trades, in its 
 average position, intersects the South American coast. 
 Here the South American continent is comparatively 
 narrow, but south of this it expands in longitude, and 
 between the fifth and fifteenth degrees of south latitude 
 has an average breadth of between 30 and 40.
 
 l66 THE WEATHER, AND WEATHER PROPHETS. 
 
 (30.) In the view we have taken of the production of 
 the trades, the immediate verticality of the sun acts as a 
 disturbing force. In its passage from solstice to solstice 
 it causes an annual fluctuation or oscillation to and fro 
 of this medial line, and of the northern and southern 
 limits of the wind-zones ; which, where those limits cross 
 the ocean, is but of moderate amount, because the 
 medium temperature of the intertropical seas varies but 
 little with the seasons. But where they cross extensive 
 tracts of land, their oscillations to and fro may become 
 very considerable, owing to the high temperature which 
 the land is capable of acquiring. Now in this case, so 
 soon as the autumnal equinox is passed, the vertical sun 
 enters on the full breadth of this vast continental tract ; 
 and commences throwing up torrents of vapour and in- 
 tensely heated air, the latter being far in excess of what 
 it would be over an equal area of sea ; while at the same 
 time, owing to the sun's then rapid motion in declina- 
 tion, the limits of the wind-zones retreat southward, and 
 their regularity is disturbed and broken ; which cannot 
 but give rise to great temporary confusion and disturb- 
 ance in the winds themselves. As to the " atmospheric 
 wave" which recurs periodically at this season, it results 
 most probably from the operation of the more general of 
 the causes above mentioned, by which a large amount of 
 extraneous air and vapour is thrown into the atmosphere 
 of the North Pacific; causing the south-west wind of that 
 ocean to sweep with increased force up the western 
 slope of that vast range of lofty mountains which fringes 
 the Norm American continent; and to be thrown up
 
 THE WEATHER, AND WEATHER PROPHETS. 167 
 
 along the whole length of that range into a broad swell, 
 propagated onwards as a wave across America and the 
 North Atlantic into Europe. No merely local action, 
 and no casual conjunction of circumstances, can be con- 
 sidered competent to produce so extensive and so 
 regularly recurring an effect. A mere inspection of 
 Admiral Fitzroy's interesting compendium of the state of 
 the barometer, &c., &c., over the area occupied by our 
 island and the neighbouring continental coasts, as re- 
 corded from day to day in the Times, will suffice to 
 satisfy any one of its occurrence in former years, and to 
 show that its character has been (so far at least, Nov. 
 21) fully maintained in the present (1864). 
 
 (31.) If we are ever to make any material progress in 
 the prediction of the weather beyond " forecasts" of a 
 few hours, or it may be a whole day in advance, it can 
 only be by the continued study of such of its phases as 
 recur periodically, or of such as manifest a periodicity of 
 event, as distinct from that of times and seasons, with a 
 view to connecting them with their efficient physical 
 causes. Of this latter description we have an example 
 of one, and of its successful reduction under the domain 
 of philosophical reasoning, in the law of the rota- 
 tion of the winds. That the winds in their changes, 
 in a general way, " follow the sun," i.e., have a ten- 
 dency to veer in the same direction round the com- 
 pass card with the sun's apparent diurnal course in 
 the heavens (from east round by south, west, and 
 north in the northern hemisphere, and reversely in the 
 southern), in continual succession back to the original
 
 l68 THE WEATHER, AND WEATHER PROPHETS. 
 
 point has been surmised from very early times ; but 
 until lately, rather as a matter of occasional remark, 
 agreeing on the whole with the general impressions of 
 casual observers, than as a meteorological law of uni- 
 versal applicability. As such, however, it has now taken 
 its place among ascertained facts ; verified by the regis- 
 tered movements of the wind- vane at every station where 
 continuous observation is made ; and connected by the 
 researches of M. Dove with that great fact which under- 
 lies so many other phsenomena the rotation of the 
 earth on its axis.* Nothing apparently can be more 
 capricious than the shifting and veering of a weather- 
 cock on a gusty day, and to any one who watches its 
 leaps to and fro for a few hours, it may well be a matter 
 of surprise to be told that with anything like a fair expo- 
 sure, the preponderance of its movement is sure to be in 
 one direction if not in a week or two, at all events on 
 the long average, and in a great majority of cases before 
 the expiration of a month. Thus it appears from the 
 record kept at the Observatory at Greenwich, in which 
 every change of the wind's direction is noted by a piece 
 of mechanism attached to the vane and traced on a 
 table by a pencil that in the thirteen years elapsed 
 from the beginning of 1849 to the end of 1861, the vane 
 made 166 complete revolutions more in the direction 
 
 * For the reasoning by which this connexion is made, and for 
 the mode in which any casual advance and retreat of a body of air 
 over an extensive but limited tract of country is transformed by 
 this cause into a relative gyration, the reader is referred to the 
 Works already cited in a former note.
 
 THE WEATHER, AND WEATHER PROPHETS. 169 
 
 above indicated than in the opposite, on a comparison 
 of the sums of all its angular movements either way or 
 on an average, nearly thirteen revolutions per annum. 
 In all this interval, two years only, 1853 and 1860, gave 
 a contrary result, and that only to the total amount of 
 two revolutions in excess the wrong way in each. And 
 of these the year 1860 was in many points an abnormal 
 one in respect of stormy weather. Nothing can convey 
 a better idea of the disappointment to which all meteor- 
 ological predictions, even though founded on just prin- 
 ciples, and supported by extensive inductions, are liable, 
 than this example. Still there remains a decided balance 
 of probabilities in favour of a change of wind occurring in 
 this rather than in a contrary direction on any specified 
 occasion. A continuous circuit round the horizon in 
 the contrary direction would certainly be in a high de- 
 gree improbable. 
 
 (32.) On the other hand we have an instance of the 
 failure of a distinctly periodical cause (as to all appear- 
 ance it would seem fairly entitled to be considered 
 a priori), to exhibit itself in any cognizable periodical 
 effect on the seasons, in that curious recurrence of a 
 spotted state of the sun's surface which takes place every 
 eleven years (see Lecture II., 36). Looking to the sun 
 as the great source of all meteorological action, it might 
 most reasonably be expected that such indications of an 
 activity of some sort going on in its very photosphere 
 in the actual visible laboratory 01 its light and heat 
 would correspond to some difference in its supply of 
 both ; which, recurring periodically at stated intervals,
 
 170 THE WEATHER, AND WEATHER PROPHETS. 
 
 must, one would think, manifest itself in some effect 01 
 other on our weather and climates. Such, however, 
 does not yet appear to be the case. The most obvious 
 consequence would seem to be a periodical return of 
 hot and cold years, which, however, the average regis- 
 tered temperatures of successive years in different places 
 have not borne out. Yet, after all, it is possible that 
 meteorologists may here have been on a wrong scent, 
 and that increased emission of heat from the sun may 
 make itself felt, not so much in any material increase 
 of the average annual temperature, as in an increased 
 generation of vapour from the ocean ; in a much more 
 copious and immediate rainfall in the equatorial regions 
 of the globe, and in a sensible increase of it over the 
 whole earth's surface : but especially in a more cloudy 
 state of the general atmosphere, consequent on the intro- 
 duction of a larger amount of vapour into it ; and in an 
 increased tendency to atmospheric disturbance and bar- 
 ometric fluctuation. No one who has watched with dis- 
 appointment the rapid upcast of cloud on a calm morn- 
 ing commencing with unclouded sunshine, which blots 
 the prospect of a glorious summer day, and who has 
 seen the same change take place day after day, often for 
 weeks in succession, can have failed to be struck by that 
 self-induced interposition of a veil between the sun and 
 the earth's surface which mitigates the ardour of his 
 beams and tempers them to the requirements of animal 
 and vegetable life. The increased heat, or by far the 
 greater part of it, may be expended in re-evaporating the 
 upper surface of this very cloud, and, by so doing, simply
 
 THE WEATHER, AND WEATHER PROPHETS. 17! 
 
 extending the limits of the vaporous atmosphere and 
 maintaining the higher regions of the air in a state 
 of increased humidity. And this is the way in which 
 we conceive it possible the planets Venus and Mercury 
 (as we have before hinted in our Lecture on the Sun, 
 but without further explanation) may be maintained at a 
 degree of superficial temperature not incompatible with 
 even terrestrial forms of life. Their climate, to be sure, 
 would have little to recommend it to our tastes ; as 
 it would probably afford small relief from a perpetual 
 succession of cloudy days and rainy nights. 
 
 (33.) Is it in any degree within the power of man to 
 alter the weather? A strange question, it may seem at 
 first sight to propose ! but by no means so absurd a one 
 as it may appear. The total amount of annual rainfall 
 over any district, is an element of its weather and its 
 climate of the last importance ; and when we look over 
 the registers of rainfalls which are now so assiduously 
 kept in almost every part of England and other civilized 
 countries, it is impossible not to be struck by its very 
 great local diversity ; even in neighbouring places, whose 
 general similarity of situation as regards wind-exposure 
 and surface configuration would seem to preclude any 
 material difference on an average of years in their re- 
 ception of rain ; if really indifferent in its choice whete 
 to fall. There is evidently something distinct from mere 
 local situation which determines this element of climate ; 
 and we must look for it in the nature of the surface of 
 the districts, and its relations to heat and moisture 
 relations which the operations of man on the soil itself,
 
 172 THE WEATHER, AND WEATHER PROPHETS. 
 
 and his selection of the kind of vegetation with which it 
 shall be habitually clothed, place to a great extent 
 within his power. It is chiefly in his clearance or allow- 
 ance of arborescent vegetation, and in his artificial 
 drainage of the soil over extensive districts for agricul- 
 tural purposes, that his influence on these relations is 
 perceptible. The total rainfall, and (which is perhaps 
 as regards weather and climate of even more import- 
 ance) the frequency of showers on an extensive well- 
 wooded tract, or one entirely covered by forests, ought, 
 on every theoretical view of the causes which determine 
 rain, to be greater than on the same tract denuded of 
 trees. The foliage of trees defends the soil beneath and 
 around them from the sun's direct rays, and disperses 
 their heat in the air, to be carried away by winds, and 
 thus prevents the ground from becoming heated in the 
 summer ; while, on the other hand, a heated surface-soil 
 reacts by its radiation on the clouds as they pass over it, 
 and thus prevents many a refreshing shower, which they 
 would otherwise deposit, or disperses them altogether. 
 So again of drainage : by carrying away rapidly the 
 surface-water down to the rivulet, and so hurrying it 
 away to the ocean, it not only cuts off a great deal of 
 the supply of local evaporation, which is a mateiial 
 element in the amount of rainfall, but by causing the 
 suiface to dry more rapidly under the sun's influence, 
 it allows it also to become more heated ; and so to con- 
 spire with the action of the denudation of trees to prevent 
 rain. Evidence is not wanting to corroborate this d 
 priori view of *he matter. The rainfall over large regions
 
 THE WEATHER, AND WEATHER PROPHETS. 173 
 
 of North America is said to be gradually diminishing, 
 and the climate otherwise altering, in consequence of the 
 clearance of the forests ; while, on the other hand, under 
 the beneficent influence of a largely increased cultivation 
 of the palm in Egypt, rain is annually becoming more 
 frequent. Lakes are cited in what was formerly Spanish 
 America whose water supply (derived of rourse from at- 
 mospheric sources) had been so largely diminished, owing 
 to the denudation of the country under the Spanish re- 
 gime, as to contract their area, and leave large tracts of 
 their shores dry ; which, now that the vegetation is again 
 restored, are once more covered by their waters. Even 
 in our own southern counties complaints are beginning 
 to be heard of a diminution of water supply, partly, it is 
 said, owing to gradually decreasing rainfall from the 
 universal clearance of timber,* though chiefly perhaps 
 attributable to robbing the springs of their supply by 
 draining a practice beneficial no doubt to agricul- 
 ture, if used with caution and in moderation, but 
 of which the conseauences^ if carried to excess, may ere 
 long be very severely felt, in rendering large tracts of 
 
 * On the other hand, forests, owing to the immense evaporation 
 from their foliage which must be supplied from the soil beneath, 
 have a direct tendency to drain that soil upwards, and so throw its 
 moisture into the air. This has been well pointed out and strongly 
 insisted on by M. le Marechal Vaillant, in " Les Mondes," T. 8, 
 p. 674. As a matter of fact, it seems pretty distinctly proved by 
 the collection of data laboriously accumulated by Mr Symonds 
 that the annual average rainfall is decreasing over the whole of the 
 British Isles, and more especially along a line running nearly S.W. 
 N.E. from Cornwall to the Wash. (Symond's Report of British 
 Association, 1865.)
 
 174 THE WEATHER, AND WEATHER PROPHETS. 
 
 country uninhabitable in summer from mere want of 
 water. 
 
 (34.) To return to our prognostics. We would 
 strongly recommend any of our readers whose occupa- 
 tions lead them to attend to the " signs of the weather," 
 and who, from hearing a particular weather adage often 
 repeated, and from noticing themselves a few remarkable 
 instances of its verification, have " begun to put faith in 
 it," to commence keeping a note-book, and to set down 
 without bias all the instances which occur to them of 
 the recognized antecedent, and the occurrence or non- 
 occurrence of the expected consequent, not omitting 
 also to set down the cases in which it is left undecided ; 
 and after so collecting a considerable number of in- 
 stances (not less than a hundred), proceed to form his 
 judgment on a fair comparison of the favourable, the 
 unfavourable, and the undecided cases : remembering 
 always that the absence of a majority one way or the 
 other would be in itself an improbability, and that, 
 therefore, to have any weight, the majority should 
 be a very decided one, and that not only in itself, 
 but in reference to the neutral instances. We are 
 all involuntarily much more strongly impressed by the 
 fulfilment than by the failure of a prediction, and it 
 is only when thus placing ourselves face to face with 
 fact and experience, that we can fully divest ourselves of 
 this bias. Any one before whose eyes these pages may 
 pass, for instance, who may feel disposed to give our 
 dictum respecting the clearance of :he sky under the in- 
 fluence of the full moon (we will not say through a hun
 
 THE WEATHER, AND WEATHER PROPHETS. I7j 
 
 dred lunations, but throughout the year 1864) a fair trial 
 of the kind, should record the state of the sky as to cloud 
 on three successive nights of each lunation that on 
 which the full moon occurs, and those immediately pre- 
 ceding and succeeding it, from an hour before the rise 
 of the moon, and thence hourly to as late an hour of the 
 night as his usual habits will allo^ noting the strength 
 and direction of the wind, and accompanying his memo- 
 randa in every instance with a note of the day and hour 
 at wlu'ch the observation it refers to was made.
 
 LECTURE V. 
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 
 " Omnia in numero, pondere, et mensura." 
 
 |HERE are epochs in the history of every great 
 operation, and in the course of every under- 
 taking, to which the co-operations of succes- 
 sive generations of men have contributed 
 (especially such as have received their increments at 
 various and remote periods of history) ; when it becomes 
 desirable to pause for a while, and, as it were, to take 
 stock ; to review the progress made and estimate the 
 amount of work done : not so much for complacency, as 
 for the purpose of forming a judgment of the efficiency 
 of the methods resorted to, to do it ; and to lead us to 
 inquire how they may yet be improved, if such improve- 
 ment be possible ; to accelerate the furtherance of the 
 object ; or to ensure the ultimate perfection of its attain- 
 ment. In scientific, no less than in material or social 
 undertakings, such pauses and resumes are eminently 
 useful ; and are sometimes forced on our consideration
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 177 
 
 by a conjuncture of circumstances, which almost of ne- 
 cessity obliges us to take a coup-(T ceil Q{ the whole subject, 
 and make up our minds, not only as to the validity of 
 what is done, but of the manner in which it has been 
 done ; the methods employed ; the direction in which 
 we are henceforth to proceed, and the probability ot 
 further progress. 
 
 (2.) The subject to which this lecture is devoted 
 affords an instance of a conjuncture of this kind. We 
 have already had occasion incidentally, in Lect. III. 
 9, to call attention to the change which it has 
 been found necessary to make (at present of a pro- 
 visional rather than a definitive character) in our esti- 
 mate of the distance of the sun a change, implying 
 of course the necessity of a proportionate alteration in 
 all those statements of the dimensions of our system, 
 such as the diameters of the planetary orbits ; of the sun 
 and the planets themselves ; and the distances of their 
 satellites from the primary, and even the estimate of the 
 masses of all these bodies and the dimensions of the 
 cometary orbits : all those elements, in short, which 
 assume directly or indirectly the mean distance of the 
 sun as their unit of scale. There is reason to believe, 
 too, that the distance of the moon (our knowledge of 
 which does not assume that of the sun as known) has 
 been somewhat misestimated, and that an alteration 
 (though not nearly to so great a proportional extent), 
 bringing our nearest celestial neighbour into somewhat 
 closer proximity than heretofore supposed, is required. 
 
 (3.) The dimensions and figure of the earth itself too
 
 178 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 as concluded from the immense series of great Trigono- 
 metrical Surveys carried on now during nearly two 
 centuries, have quite recently, and in two distinct and 
 independent quarters,* undergone a fresh, and most 
 searching and elaborate inquiry. And the conclusion 
 from both is, that our knowledge on this point is not 
 likely to be improved in any material degree by any 
 further operations of the kind ; at least until the time, 
 probably yet far distant, when the Australian Continent 
 shall have become easily and conveniently traversable 
 from North to South, and when the wastes of Patagonia 
 and Terra del Fuego shall afford to future geodesists the 
 opportunity of winning a hard-earned distinction. Till 
 then (and most probably then also), we must rest satisfied 
 with the conclusions arrived at, conclusions, be it ob- 
 served, which have disclosed a numerical relation of 
 singular simplicity between our British unit of measure 
 and the length of the earth's polar axis. 
 
 (4.) Moreover, in ignorance probably of this last-men- 
 tioned fact, and therefore with too gratuitous a contempt 
 for our national and time-honoured standards, and too 
 hasty a preference for the apparently more scientifically, 
 and certainly more symmetrically, constructed system of 
 our continental neighbours, an agitation is and has for 
 some time been going on, headed by persons of con- 
 siderable influence, and strongly, no doubt, though we 
 think unduly, impressed with the advantage of the 
 change; with the object of abolishing in toto our British 
 
 * By Gen. de Schubeit (Mem. Imp. Acad. Petersburg, 1859), 
 and Capt. A. R. Clarke, R.E. (Mem. R.A.S., ;86o).
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 179 
 
 system of weights and measures, and introducing in its 
 stead the French metrical system. A bill was intro- 
 duced in the session of 1863 into Parliament with this 
 avowed object : and though withdrawn, after passing the 
 second reading, has been reintroduced in the present 
 (1864), and reached the same stage, with every prospect 
 of being passed.* It is true that the change immediately 
 proposed is permissive, not compulsory: but there can 
 be no doubt that the attempt, if successful, will be fol- 
 lowed up at no distant period by the introduction of a 
 compulsoiy measure ; one whose effect on the habits, 
 feelings, and interests of nine hundred and ninety-nine 
 out of a thousand persons in the whole community, this 
 is not the proper place to dilate upon. 
 
 (5.) As civilization extends, wants and desires of a 
 higher order than material gratifications arise; and 
 among them that of extending knowledge for the sake of 
 knowing; the craving after a larger grasp, a clearer in- 
 sight, a more complete conception in all its relations of 
 the wondrous universe of which we form a part. Such 
 desires, when accompanied with the means of their grati- 
 fication, are included by the author of a recent work of 
 much interest on the subject of wealth (under the some- 
 what inappropriate title of Plutologyf ), among those 
 
 * It has passed, and is now the law of the land. So far there is 
 no actual harm done, beyond unsettling opinions and creating un- 
 easiness ; but we trust the common sense of the nation will repudiate 
 any attempt to carry out to its designed completion a measure so 
 thoroughly retrograde. 
 
 f By Professor Hearn, of Melbourne University, Australia. The 
 title ought to have been A phnology. Aphnos, or Aphenos (a^yoj.
 
 l8o CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 sources of positive enjoyment which are not less real 
 because they are intellectual, or less valuable because 
 they cannot be appropriated or bartered in exchange : 
 but which yet cannot be attained by mere intellectual 
 aspiration or effort ; but require for their production and 
 dissemination appliances and means of a refined charac- 
 ter, and combinations of a recondite kind ; such as only 
 an advanced stage of material as well as intellectual pro- 
 gress can furnish. Such a piece of intellectual wealth is 
 the solution of that great enigma (such, at least, in all 
 former time) of the distance of the stars, a problem 
 which has yielded, at length, to the delicacy and refine- 
 ment of astronomical observation, during the lapse of 
 the last thirty years ; combined with and acting through 
 the marvels of mechanical skill and workmanship which 
 are now obtainable. That distance is now no longer 
 the hazy and absolutely indefinite matter of conjecture 
 jdiich it was (to go no farther back) in the time of New- 
 ton, or even in the middle of the last century. Of some, 
 at least, of them it can be said with every reasonable 
 assurance of probability, that their distance is known 
 within an eighth or a ninth part of the truth, one way or 
 the other ; and of several, that we can arrange them in 
 order of distance, nearer and more remote, with little or 
 no presumption of mistake. A stepping-stone is thus laid 
 for another upward struggle towards the infinite to the 
 nebulae, the remotest objects of which we have any know- 
 
 o<pf cos, Gr. ), expresses wealth in its largest sense of general abund, 
 ance and well-being. Ploutos (wXoirroj, Plutus), riches, in the more 
 restricted sense of the precious metals, or, at the utmost, of exchange- 
 able value.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. l8l 
 
 ledge : though the stride is here too vast, as it may seem, 
 for the limited faculties of man ever to take. Nor can 
 it be said that man is dwarfed and humiliated by such 
 attempts : that they teach him nothing but his own in- 
 significance, and so are the reverse of ennobling. The 
 greatness of nature is not synonymous with the littleness 
 of man. That only is little which cannot rise to great 
 conceptions. 
 
 (6.) Enough, perhaps, has been said to justify an 
 attempt to lay before our readers the actual state of our 
 positive knowledge of these subjects ; of the methods by 
 which it has been attained ; and of the history of their 
 development; and to give them a distinct conception 
 of the several links which connect the British standard 
 inch with the distances of the fixed stars, and of the sort 
 of intermediate units we have to deal with in the inquiry. 
 It fortunately happens that we shall not need for our pur- 
 pose any resort to abstruse considerations, or have occasion 
 for any illustrations which are not of the simplest kind. 
 
 (7.) In every country having the slightest pretensions 
 to civilization there is preserved, with more or less care, 
 some rod, bar, ruler, or other standard, the material in- 
 corporation of the national idea of the most ordinary 
 unit of length ; and its representative, when it is required 
 to test the correctness of one in vulgar use, or to multiply 
 and disseminate copies of itself for purposes of ordinary 
 mensuration. Thus, among the Jews, we find (Exodus 
 xxx. 2) the cubit* identified as equal to either of the 
 
 * This cubit is presumed to be identical with the Egyptian cubit, 
 still preserved, of the Nilometer.
 
 f82 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 sides, or to half the height of the altar of incense. And 
 the same is true of similar representatives of the most 
 commonly received units of weight and measure of 
 capacity. What the original type might be, which such 
 standard professed to represent, matters little. The 
 inhabitants of a nation might agree to use for their unit 
 of length the foot of one of their ancient heroes, or the 
 hundredth part of the height of their principal church, 
 or the hundred thousandth part of the extreme breadth 
 of their country from sea to sea. But as these objects 
 could never be appealed to for the settlement of any 
 practical dispute between man and man, or to convict 
 the user of any fraudulent measure, a material and pro- 
 ducible object must exist in some safe custody, carefully 
 preserved, or safe in its received sanctity, from damage ; 
 and authoritatively declared, and generally believed to 
 be, rigorously equal in length to its prototype; and to 
 have been, at some period, however remote, ascertained 
 to be so by some appropriate process of comparison ; or, 
 at all events, by the exact copying of some former and 
 lost standard so compared. And from the moment of 
 such authoritative declaration, the length of this material 
 representative necessarily becomes the real and legal 
 unit of length. The hero may turn out, on a close and 
 irreverent scrutiny of history, to have been a purely 
 mythical personage; the church may have been con- 
 sumed by fire ; the breadth of the land diminished by the 
 encroachments of the sea : but so long as the standard 
 remains uninjured by rough usage, and secured from loss 
 by a sufficient multiplication of authentic copies, its
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 183 
 
 practical utility is unimpaired by such mishaps ; and 
 should it be really damaged or lost, public opinion readily 
 transfers the same reverence to its legitimate successor. 
 
 (S.) The history of our existing " Imperial" standard 
 is not quite so simple. It is the successor of one 
 destroyed by fire in 1834: not, however, being copied 
 or even having been immediately compared with its pre- 
 decessor ; but recovered by the evidence of an assem- 
 blage of other standards which had, at various times, been 
 compared with that and with each other. And that 
 again had been derived, not by direct copying and exact 
 equalizing with its predecessor the then "reputed Ex- 
 chequer Standard," but by a somewhat similar process, 
 from all the best evidence that could be procured of a 
 former state of things. The ultimate prototype is either 
 to be referred to the age of Henry I., who is said " to 
 have settled the yard by the length of his own arm," or 
 to the more ancient foot of twelve inches, "each the 
 length of three barleycorns from the middle of the ear, 
 laid end to end." The point is not of the slightest im- 
 portance, now that we are assured from the number and 
 exactness of the copies taken j their wide distribution ; 
 and the precautions taken to ensure their preservation ; 
 that it is scarcely in the power of accident to deprive us 
 of a perfectly " legitimate " successor in the sense in 
 which we have above used the term. 
 
 (9.) To measure lengths of many miles (to say nothing 
 of the breadth of a country or of a kingdom), by the 
 simple repetition and laying end to end of yard measures 
 (supposed exactly equal), would not only be intolerably
 
 184 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 tedious but impracticable, except on a carefully-levelled 
 plain free from all obstructions. Nevertheless, when the 
 object is to measure any large tract of country, or to con- 
 struct a chart of a territory by what is called a " Trigono- 
 metrical Survey" it is indispensable to lay down and 
 measure, no matter at what cost of time and labour, 
 some one such very long line, as a ''base line;" and to 
 mark its two extremities in some very distinct and per- 
 manent manner: so that their linear distance (a large 
 multiple of the original standard unit) shall not only be 
 exactly known, but shall be capable of being appealed 
 to for all future time, or at least till the whole work is 
 completed, as a new and larger unit, "the length of the 
 base" to which all other distances in the survey are tem- 
 porarily referred. These, being subsequently reduced 
 by calculation to multiples and fractions of the original 
 unit, all the dimensions of the territory become finally 
 known in yards, feet, and inches. For the purpose of 
 measuring such a base, the ground must be cleared and 
 reduced to perfect horizontality (or any slight inclina- 
 tion exactly taken account of), and the intended base 
 line allineated by placing a telescope a little beyond one 
 of its proposed extremities, so as to command them 
 both, and as it were to fore-shorten its whole length into 
 one point, the intersection of two wires in its focus. 
 Anything seen in the telescope to the right or left of 
 this point, or above or below it, is out of the line. 
 
 (10.) Whenever lengths are to be added by the re- 
 petition of one and the same unit, there is always a pos- 
 sibility of error arising from imperfect juxta-positions.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 185 
 
 And the oftener the unit is repeated (when it once be- 
 comes wearisome), the greater is the difficulty of keeping 
 up the necessary attention, and the greater therefore the 
 amount of error to be feared in each case. To diminish 
 this source of accumulating error (besides the saving of 
 time), it is desirable to diminish the number and increase 
 the nicety of these juxtapositions. Hence the utility and 
 convenience of creating an intermediate unit or set of 
 such units or " Base-measuring bars," and of devising 
 some means of juxtaposing or laying them end to end, 
 without the derangement of one by the small shock 
 arising from the contact (however delicately performed) 
 of its successor. These bars should not be so long as to 
 prevent their being conveniently manageable, yet long 
 enough to diminish greatly the requisite number of their 
 repetitions. The bars now actually used for this pur- 
 pose are miracles of ingenious contrivance and delicate 
 workmanship. They are self-compensating for changes of 
 temperature; that is to say, the two fine dots which mark 
 the two extremities of the measure remain exactly at the 
 same distance from each other whatever be the tempera- 
 ture of the bars, which are compound ones of two differ- 
 ently expansible metals combined on a principle devised 
 by the late Lieutenant Drummond. And their repetition 
 is performed, not by driving the end of one against the 
 other, or by laying dot against dot, but by focussing a 
 detached microscope on the more advanced dot, remov- 
 ing the bar and bringing the other dot under the micro- 
 scope to occupy the exact position in the centre of its 
 field (marked by a cross wire) which its predecessor
 
 186 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 did* Thus the bar has been moved forward by its exact 
 length in the air, as it were, without touching anything. 
 Arrived at the end of the base, a dot is made and ad- 
 justed under the terminal microscope on a gold or 
 platina plate let into a solid block of stone already pre- 
 pared the starting point having been a similar one 
 similarly fixed at the other end. 
 
 (n.) The base measured, the " Trianguiation" com' 
 mences. This is founded on the universally known fact 
 that when two angles of a triangle are known, a know- 
 ledge of the length of the side between them leads by 
 exact rules of calculation to that of the other two ; ac- 
 cordingly, at the two extremities of the base, and cen- 
 trally over the dots which mark them, are placed deli- 
 cately divided instruments called theodolites, competent 
 to the measurement of angles to an extreme nicety. The 
 telescopes of these being pointed so as to look down the 
 throats of each other, it is clear that both must be 
 directed along the base line, and if then turned on some 
 one object at a distance considerably greater from either 
 than they are from each other, that object becomes the 
 summit of a triangle, the inclinations of whose sides to 
 the base is measured. Its distance from either end of 
 the base then can be calculated. Thenceforward either 
 of those sides becomes available as a new and longer 
 base. And thus the survey may go on, throwing out 
 
 * In actual practice the procedure is a little more complex, but 
 the principle is the same ; and it is only intended here to convey to 
 the uninitiated a general notion of the sort of niceties which have 
 to be attended to.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 187 
 
 new triangles on all sides, of larger and larger dimen- 
 sions ; till the whole surface of a kingdom or a continent 
 becomes covered with a network of them, all whose 
 angular points are precisely determined. The strides 
 so taken, moderate at first, become gigantic at last : 
 steeples, towers, obelisks, mountain cairns, and snowy 
 peaks, becoming in turn the stepping-stones for further 
 progress ; the distances being only limited by the range 
 of distinct visibility of objects through the haze of the 
 atmosphere. Even this is extended by artificial means 
 by Bengal lights at night and by the use of the " helio- 
 trope," a contrivance of the celebrated Gauss for reflect- 
 a strong sunbeam from station to station ; by the use of 
 which, stations 90 or 100 miles distant have been brought 
 into direct connexion. 
 
 (12.) If the earth's surface were a plane such a process 
 might be continued ad infinittim. The general roundness 
 of the earth, however, has been recognized as a fact from 
 very early ages ; and indeed it is scarcely possible for 
 any thinking person, with ever so slight an acquaintance 
 with^he most elementary geometry, not to be aware of 
 it It was not, however, till about some three centuries 
 before our era, that something like just notions of its 
 actual size were entertained : unless we admit (an opinion 
 which has found strenuous defenders) that this important 
 datum was already exactly known to the ancient Egyp- 
 tians 1800 years previously;* a fact, if true, all memory 
 
 * The height of the great pyramid from base to apex is (was) con- 
 tained exactly 270,000 times in the circumference of some one diame- 
 trical section of the earth.
 
 l88 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 of which had perished in the lapse of that interval. The 
 Chaldean astronomers at the later epoch above men- 
 tioned are reported to have arrived at an estimate not 
 very remote from the truth. But the first estimate which 
 has been handed down to us, accompanied with a state- 
 ment of the process by which it was arrived at, is that of 
 Eratosthenes (B.C. 250) ; who, measuring the shadow 
 cast by a vertical rod on the day of the summer solstice 
 at Alexandria, and coupling it with the fact reported to 
 him, that at Syene in Upper Egypt on the same day, 
 the bottom of a well received the full sunshine, con 
 eluded a difference of latitude between the two places, 
 equal to one 5oth part of the circumference of a meridian. 
 Hence, imagining the two places to lie pretty nearly 
 north and south of one another, he concluded the cir- 
 cumference of the earth to be fifty times the distance 
 from Alexandria to Syene, which on the most probable 
 interpretation of his estimate of that distance in the 
 itinerary measures of the time, affords an approximation 
 to what we now know to be the truth, by no means con- 
 temptible ; falling within about a sixth part of the real 
 circumference, and if the deviation of the mutual direc 
 tion of the places from the true meridian be allowed for, 
 within much less. 
 
 (13.) Thus we see that with very coarse and rude 
 means of observation and measurement, it is not difficult 
 to arrive at what may be termed a respectable estimate 
 (as contrasted with a mere guess) of the size of our own 
 globe ; which is our first step outwards into those distant 
 regions which will next engage our attention. We need
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 189 
 
 not, therefore, dwell on a multitude of intermediate 
 attempts between that epoch and the year 1669, when 
 Picard, under the auspices of the then newly constituted 
 French Academy of Sciences, took up the subject in a 
 truly scientific manner, and with means and appliances 
 of a higher order. They all turned, of course, as every 
 such estimate must do, on the more or less precise 
 measurement of the length of a degree or a certain number 
 of degrees of latitude on the earth's surface. But the step 
 which this measure of Picard inaugurated, is distinguished 
 by the abandonment of the old methods of ascertaining 
 such length (viz. by simply measuring it as an itinerary 
 distance by rods, or measuring chains, or by rolling 
 wheels self-registering their own revolutions) ; and sub- 
 stituting for it the infinitely more precise one, which con- 
 sists in the very careful measurement of a base line; the 
 extension from it, northward and southward, of a series 
 of triangles, as above described; the ascertaining, by 
 accurate astronomical observations, the latitudes of the 
 extreme points ; and the taking account of the deviation 
 from the true meridian of their mutual direction, by a 
 systematic process of calculation, grounded also on the 
 astronomical determination of their bearings. From 
 that to the present time, this process (in which consists 
 "geodesy" as distinct from mere mensuration and survey- 
 ing) has been generally adopted ; with continual improve- 
 ment of the instruments used ; increasing accuracy in all 
 the requisite astronomical observations ; and the adop- 
 tion of a more and more perfect and refined system of 
 computation for the " reduction " of the observations and
 
 IQO CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 calculation of the sides of the triangles, considered as lying 
 not on a plane, but on a spherical surf ace, and ultimately 
 (as we shall see) on a spheroidal one. It is not our 
 object to dwell on these details, or to describe more 
 minutely any one of the many operations of the kind 
 which have been carried out or are still in progress in 
 France, England, America, Prussia, Austria, Italy (but 
 more especially and on the vastest scale in the Russian 
 and in our own Indian Empire), and in the southern 
 hemisphere at the Cape of Good Hope. We are only 
 concerned here with the final conclusions arrived at, and 
 with the reasons on which they rest, and these are : 
 
 ist. The length of a degree of the meridian, in what- 
 ever region of the earth it is measured, is very nearly the 
 same, nowhere varying from a general average by more 
 than about one 2ooth part of its amount. And from 
 this it follows that the figure of the earth approaches 
 exceedingly near to that of an exact sphere. For the 
 length of such a degree is a measure of the curvature of 
 the surface, it being evident that were any one to travel 
 southward till the meridian altitude of a star was 
 increased by one degree, he must have arrived at a 
 place where the surface on which he stands is just 
 one degree inclined to that at his starting point : so that 
 in walking on he is at that moment pursuing a course 
 deviating by one degree from the direction of his outset. 
 Now this deviation from a straight course is our idea of 
 curvature. The curvature of each geographical meridian 
 then is very nearly the same everywhere. In other 
 words, the earth is very nearly a sphere. The average
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 19! 
 
 length of a degree of its circumference is 364,578 Eng- 
 lish feet ; or very nearly as many thousand feet as there 
 are clays in a year. 
 
 2d. Though nearly, the degrees are not precisely 
 equal. In all geographical longitudes the degrees of lati- 
 tude are found to increase in length in going from the 
 equator towards the poles. An increase in the length of 
 a degree indicates a less amount of curvature. The 
 earth's surface is therefore less curved, or less convex 
 that is, flatter as we approach its poles on all sides 
 from the equator. Its form then is elliptical, or oblate, 
 and its polar diameter somewhat shorter than its equato- 
 rial. From the most recent calculations (those of Cap- 
 tain Clarke, founded on a general assemblage of all the 
 measured arcs) it results that the difference of these two 
 diameters is one 2Q2d part of the former. 
 
 3d. That the length of its polar diameter is 41,707,796 
 British imperial standard feet, which is within a single 
 furlong of 500,500,000 such inches. 
 
 (14.) Hence it follows, that if we were to increase all 
 our imperial standard measures, each by one precise thou- 
 sandth part * and designate the measures so increased by 
 the epithet geometrical instead of imperial, a geometrical 
 inch would be the exact 5oo,ooo,oooth part ; a rod of 
 fifty such inches the exact io,ooo,oooth part of the 
 earth's polar axis ; and one of twenty-five such (which 
 might be called A GEOMETRICAL CUBIT) the io,ooo,oooth 
 
 * I have before me for ordinary use two foot rules, both bought 
 at respectable shops, and not the worst for wear, which differ by 
 more than this amount.
 
 1Q2 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 part of its polar semi-axis : that is to say, if we disregard 
 so insignificant an error as a furlong upon 8000 miles, 
 or one part in 64,000. 
 
 (15.) It follows, moreover (as may be verified by any 
 one who will make the calculation), that if we consent 
 to disregard so trifling an error as one part in 8000 ; one 
 cubic geometrical foot of distilled water at our standard 
 temperature weighs exactly 1000 of our actual imperial 
 ounces, and is exactly filled by 100 of our actual impe- 
 rial half-pints.* 
 
 (16.) Having thus exhibited the connexion between 
 our ordinary measures of len^ h, weight, and capacity, 
 and the dimensions of the globe we inhabit (a connexion 
 of singular felicity, when we consider the simplicity of 
 the numerical relations), we are prepared to take a fur- 
 ther step, and, by using the diameter of the earth itself 
 as a base-line, carry on the same principle of triangu- 
 lation into our solar and planetary system. In this, the 
 natural unit that to which astronomers have agreed 
 with one accord to refer all its dimensions is the mean 
 or average distance of the earth from the sun, or the 
 semi-axis of the ellipse which it describes about that 
 luminary. 
 
 (17.) The way in which a knowledge of this distance 
 is obtained being very fully described in our Lectures on 
 "The Sun" and on " Comets," f it is unnecessary to re- 
 
 * The deviation of the actual French litre and gramme from 
 their true theoretical values, is more than three times as great, be 
 ing one part in 2730. 
 
 t A very unfortunate erratum exists in one of the numbers in p.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 193 
 
 peat the explanations there given. The use which may 
 be made of Venus as a stepping-stone on the way 
 towards the great centre of our system, however, is 
 there rather alluded to than explained ; so that a few 
 words on this subject will not be out of place here. 
 The interval between Venus and the earth when near 
 est, is not more than one-fourth of the sun's distance, 
 and its angular displacement when seen from opposite 
 extremities of a diameter of our globe, therefore, four 
 times as great as the sun's. Venus, however, is invisible 
 in this situation, except on those very rare occasions 
 (occurring at intervals alternating between eight years 
 and upwards of a century) on which it passes between 
 us and the sun, and is seen as a round black spot on its 
 disc. In this state of things the face of the sun itself 
 serves as a screen on which the planet is seen projected ; 
 and its circular outline serves as a celestial line of refer- 
 ence, across which the planet is seen to " transit," as it 
 would across wires fixed in the focus of a telescope ; or 
 rather as it would across the circular outline of what 
 astronomers call a " ring micrometer." The sun itself is 
 thus transformed for the time into an astronomical in- 
 strument of that description, freed by nature from all 
 the sources of fluctuation and instability which affect our 
 instruments. And the whole observation is reduced to 
 determining the precise moments of time at which the 
 foremost and hindmost borders of the planet cross this 
 
 479, col. I, line 52, of this last-mentioned Lecture as printed ori- 
 ginally in "Good Words" For 16,071, read 6,071. All the other 
 numbers are right, as they there stand. 
 
 N
 
 194 CELESTIAL MEASUR1NGS AND WEIGHINGS. 
 
 ring (which they do in a very leisurely manner), leaving 
 the apparent displacement of the planet on the sun's disc 
 to subsequent calculation, on a comparison of reports 
 from all the points of observation selected. One-fourth 
 of the advantage arising from its proximity, it is true, is 
 lost, by the sun itself sharing to that extent in the dis- 
 placement of the planet; but enough remains to give 
 this a superiority over every other method of measuring 
 the sun's distance. 
 
 (18.) Taking as the general conclusion for that dis- 
 tance which we must at present rest in, that assigned in 
 our article last cited, viz., 91,718,000 imperial (or 
 91,626,282 geometrical) miles, we find it equivalent to 
 23,222 polar semi-diameters of the earth, or ten million 
 times that number of GEOMETRICAL CUBITS of twenty-five 
 geometrical inches each. 
 
 (19.) Our next step is to the fixed stars, within whose 
 sphere modern science has at length made good a foot- 
 ing, secure, though somewhat unsteady for the present 
 In conformity with the same principle of procedure, we 
 here rest for our base of operations on our last and 
 greatest accessible measured length, viz., the diameter of 
 the earth's annual orbit, a base line of 183,000,000 miles, 
 which, as the orbit is very nearly circular, presents itself 
 (in some situation or other across it) perpendicularly to 
 a line joining the sun and any selected star, so as to be 
 seen unforeshortened from the star. As the earth at 
 half-yearly intervals passes alternately from one to the 
 other extremity of such a diameter, the visual line by
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 195 
 
 which the star is seen will undergo a semi-annual dis- 
 placement to and fro to the amount of the apparent (an- 
 gular) breadth of the orbit as it would be seen by a spec- 
 tator in the star. And this, in its equivalent form of 
 annual displacement, is the angle astronomers have to 
 measure for the purpose in question. One would natu- 
 rally suppose that so enormous a magnitude would be 
 something conspicuous from any distance short of the 
 fabulous; and that here at least we should have some- 
 thing to deal with palpable to very moderate means of 
 observation. Pent up and " chafing within the narrow- 
 limit of the world" the astronomer in his measurement 
 of the sun's distance might complain, in the words which 
 the poet puts into the mouth of the great conqueror of 
 antiquity, of restricted elbow-room. Using the world 
 itself as a means of transport, and thus enabled to com- 
 mence anew on so vast a scale, he might expect to find 
 "ample room and verge enough" for his operations. 
 Quite the contrary ! The earth itself seen from the sun 
 would appear as large as the globe of Saturn at its medium 
 distance does to us a very conspicuous object in a 
 moderately good telescope. A globe large enough to 
 fill the earth's orbit round the sun would appear to a 
 spectator placed in the nearest fixed star, hardly larger 
 than the third satellite of Jupiter, as seen from the earth ; 
 which requires a very good telescope to be perceived to 
 have any size at all. 
 
 (20.) Two methods only have been devised by which 
 this annual or parallactic displacement (as it is technically
 
 196 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 called by astronomers)* can be ascertained. The first 
 consists in determining the exact situation which its 
 direction in space holds at all times of the year in rela- 
 tion to some plane, and to some line in that plane \vhich 
 we have reason to consider as fixed ; or at all events of 
 whose movements (exceedingly small in amount) we can 
 render an exact account. Such a plane is that in which 
 the earth revolves round the sun, or the ecliptic, and such 
 a line that of the equinoxes, and the astronomical process 
 employed is that by which the two elements technically 
 called the longitude and latitude of the star are determined. 
 This is in effect the process by which all celestial charts 
 are constructed and catalogues of stars made. Only for 
 this purpose the observations require to be made with 
 the very best instruments ; with the minutest attention to 
 everything which can affect their precision ; and with the 
 most rigorous application of an innumerable host of "cor- 
 rections" some large, some small, but of which the 
 smallest, neglected or erroneously applied, would be 
 quite sufficient to overlay and conceal from view the 
 minute quantity we are in search of. To give some idea 
 of the delicacies which have to be attended to in this in- 
 quiry, it will suffice to mention that the stability not only 
 of the instruments used and the masonry which supports 
 them, but of the very rock itself on which it is founded, 
 is found to be subject to annual fluctuations capable of 
 seriously affecting the result. So that it is only when 
 after a series of observations continued for several years 
 
 What is technically called parallax t is only the half of the total 
 annual apoarent displacement
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 197 
 
 it is found that one star appears to be subject to a regu- 
 larly recurring annual displacement, such as that which 
 *Jie earths orbital motion might cause, and others in its 
 near neighbourhood show no signs of it, we can accept 
 the double conclusion that the one is and the others are 
 not at a measurable distance. 
 
 (21.) As the ancients had no knowledge of the earth's 
 motion, so they could have had no conception of this 
 annual displacement of the stars or of their " parallax." 
 Tycho Brahe who rejected the Copernican system, might 
 perhaps have been led to do so from his not having been 
 able to perceive any such displacement of the pole star, 
 which, from the rudeness of his means of observation, he 
 could not possibly have done. Much more lately, in the 
 latter years of the i7th and beginning of the i8th cen- 
 turies, the attention of many eminent astronomers was 
 drawn, in consequence of the improvements then intro- 
 duced in the construction of astronomical instrumems, 
 to a regularly recurring annual displacement of certain 
 stars observed by them to a very considerable amount, 
 which was at first supposed to be parallax, but which 
 proved to be what is now called " aberration," and to be 
 common to all the stars ; and when this was recognized 
 finally by Bradley as a result of the motion of light, the 
 idea of a measurable "parallax" was abandoned in de- 
 spair; to be revived again by Dr Brinkley in 1810 ; who 
 from his observations with a very fine circle in the Royal 
 Observatory of Dublin thought he had detected a paral- 
 lax of i" in the bright star Lyra (corresponding to an 
 annual displacement of 2"). This however proved to be
 
 198 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 illusory; and it was not till the year 1839 that Mr Hen- 
 derson, having returned from filling the situation of As- 
 tronomer Royal at the Cape of Good Hope, and discuss- 
 ing a series of observations made there with a large 
 " mural circle " of the bright star a Centauri, was enabled 
 to announce as a positive fact the existence of a measur- 
 able parallax for that star : a result since fully confirmed 
 with a very trifling correction by the observations of his 
 successor, Sir T. Maclean 
 
 (22.) The parallax thus assigned to a Centauri is so 
 very nearly a whole second in amount (o"'98) that we 
 may speak of it as such. It corresponds to a distance 
 from the sun of. 206, 265 times that of the sun from the 
 earth, which, as we have already seen, is itself 23,222 
 polar semi-axes of the latter, thus making a total of 
 4,789,880,000 such semi-axes (or 10,000,000 times 
 that number of geometrical cubits), equivalent to 
 18,918,000,000,000 (nearly nineteen billions) of British 
 statute miles. Its near neighbour # of the same con- 
 stellation and other stars adjacent exhibit no such 
 annual displacement, and are therefore beyond the 
 reach of our measurement. Such, then, is the length 
 of the sounding-line with which we have first touched 
 bottom in the attempt to fathom the great abyss of the 
 sidereal heavens. At such a distance, the vast globe 
 filling the earth's orbit, above spoken of, would be 
 covered from sight by a human hair held at twenty-five 
 feet from the eye.* 
 
 (23.) The other mode in which this great question 
 * Supposing the pupil reduced to a point.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 199 
 
 has been approached is to select for inquiry bright stars, 
 which have in their immediate vicinity, so near as to be 
 seen with them at the same time in the same telescope, 
 two or three other very much smaller ones ; and without 
 troubling ourselves to determine their absolute places in 
 the heavens (so throwing overboard the enormous diffi- 
 culties which, as we have seen, that determination to a 
 sufficient precision presents), confine ourselves to what 
 may be called a microscopic examination and mapping 
 down of the relative distances and situations of these 
 stars inter se. Repeating this at all seasons of the year, 
 we are enabled to ascertain whether the large star main- 
 tains steadily the same invariable position among the 
 smaller ones ; or is affected by any movements of which 
 they do not partake. There is a general prima facie 
 probability that the brighter stars are nearer than very 
 faint ones : and, near objects being more displaced than 
 distant ones by the spectator's change of place; the 
 large star in the case supposed would appear, by the 
 effect of parallax, to move to and fro among the smaller 
 ones; or rather to describe annually a minute ellipsis 
 among them, the exact counterpart, equal in size and 
 similar in the situation of its longer and shorter dia- 
 meters, to that into which the earth's orbit itself would 
 be seen projected by the effect of perspective from the 
 star. Now no casual movement, or one arising from 
 any other physical cause, could be mistaken for such a 
 motion as this. For, not to mention the completion of 
 the revolution in an exact year, the two diameters of 
 the ellipse ought to stand to each other in a certain defi-
 
 ZOO CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 nite and calculable proportion known beforehand ; and, 
 moreover, the longer ought to be situated in a parallel of 
 latitude, and the shorter in a circle of longitude passing 
 through the star. 
 
 (24.) There is a star, the 6ist of Flamsteed's list, of 
 those in the Constellation Cygnus a star far, however, 
 from conspicuous for its brightness; being only of the 
 fifth magnitude ; but which, for a reason presently to be 
 mentioned, was suspected to be nearer than the gener- 
 ality of the stars. This star was subjected by the late 
 Professor Bessel to the examination above described 
 between the years 1834 and 1838, and the result of his 
 examination (made public by a singular coincidence a 
 few days before the announcement of Professor Hender- 
 son's discovery) was such as to leave no doubt of the 
 reality of its parallax, to the amount (as slightly cor- 
 rected by a further continuance of his observations) of 
 o"'35. Later astronomers,* going over the same ground, 
 with more perfect instruments and improved practice in 
 this very delicate process of observation, have found 
 a somewhat larger result stated by one at o"'S7, and 
 by another at o"'5i so that we may take it at o" - 54, 
 corresponding to somewhat less than twice the distance 
 of Centauri; or to 374,320 solar distances, which 
 light would require about eight years and four months 
 to travel over. 
 
 (25.) It cannot be supposed that results like these 
 would be accepted without undergoing the most severe 
 scrutiny and receiving confirmation from further and 
 * Messrs Auwers and O. Struve.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 2OI 
 
 continued observation. They have received it, and 
 (with exception of those subsequent corrections in the 
 numerical values which we have noticed and included 
 in the above statement) they remain intact, and rar.k 
 among the well-established facts of astronomy. More- 
 over, numerous other stars have been subjected to ex- 
 amination, some by one, some by the other method 
 And the result is not a little surprising. Up to the pre- 
 sent time, out of all the stars examined, only a very few 
 exhibit any distinctly measurable amount of parallax. 
 The list hitherto accumulated consists only of about ten 
 or at most a dozen. Of these a Centauri, in the south- 
 ern hemisphere, is the nearest. It is a fine star of the 
 first magnitude, the third or fourth in brightness of all 
 the sidereal host. This is our next neighbour. On the 
 other hand, Sirius, the brightest of all the stars, and 
 Lyra (next to Sirius, one of the four most conspicuous 
 stars in our hemisphere) stand low in the order of prox- 
 imity. This, of course, only proves that among the 
 stars there exists a very wide range of absolute bright- 
 ness, but by no means invalidates the strong a priori 
 reasons for admitting distance as a very important ele- 
 ment in determining their relative apparent brightness. 
 
 (26.) But how, it will be asked, came such a seem- 
 ingly insignificant object as this No. 61 to be selected 
 for examination at all, to the exclusion or postponement 
 of so many more conspicuous 1 We reply, by reason of 
 its large apparent proper motion. None of the stars we 
 see maintains quite the same relative situation among its 
 compeers. It would be strange if it did. Unless nailed
 
 202 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 to the celestial vault and carried round with it, such a 
 thing is not to be supposed. In the total absence then 
 of any information as to the velocity or direction of the 
 real motions, we can only presume that such as appear 
 to move fastest are nearest. The fact may be otherwise, 
 but such at least is the prima facie presumption. Now, 
 while the stars in general exhibit an annual apparent 
 proper motion averaging less than a second per annum, 
 these two 61 Cygni and a Centauri, are carried annually 
 from their places, by movements apparently rectilineal 
 of 5"'3 and 3'"6 respectively : motions which would carry 
 them away from their places through a space equal to 
 the moon's apparent diameter in 339 and 499 years re- 
 spectively. In point of fact, we find that they are nearer, 
 so that a part at least of their great apparent motions is 
 owing to proximity. 
 
 (27.) Such a uniformly progressive change of place 
 complicates apparently, but not really, the microscopic 
 process we have described. Being accurately known by 
 long continued observation, both in amount and direc- 
 tion ; its effect in displacing the star among its neigh- 
 bours is easily taken account of and allowed for. The 
 combination of these two motions, the one real and 
 rectilinear, and the other apparent and elliptic, will be 
 readily understood from the accompanying diagram, 
 where ab, be, cd represent the former continued for 
 three years; e,f, g, the ellipses described in those years 
 in virtue of the latter in the direction of the arrows ; and 
 h i k the sort of undulating line apparently described in 
 virtue of them both going on together.
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 2OJ 
 
 (28.) But, besides this, the two stars in question are 
 remarkable in another way. They are both conspicuous 
 DOUBLE STARS, and have been long watched with especial 
 
 o 
 
 / y 
 
 Fig. i. 
 
 interest by reason of the two individuals of which each 
 respectively consists standing to each other in the rela- 
 tion of sun and planet, or planet and satellite. Not only 
 do they keep close company with each other in their 
 journey through space by a common proper motion ; but 
 while so journeying together they revolve about each 
 other or about their common centre of gravity in regular 
 elliptic orbits, under the influence of that very same law 
 of gravitation which retains the planets in their circula- 
 tion round the sun. They are, therefore, at the same 
 distance from us, and therefore both equally and simi- 
 larly apparently displaced by parallax; so that each of 
 them, microscopically watched, appeais to describe the 
 same minute annual parallactic ellipse above spoken of. 
 This must not be confounded with the elliptic orbit the 
 two stars describe about each other. That is on a far 
 larger scale, and requires many years for its completion.
 
 2O4 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 It is to the dimensions of these and similar orbits de- 
 scribed by others of those wonderful bodies, the double 
 stars, about each other, that we have now to turn our 
 attention : thus opening another chapter in the history 
 
 Fig a. 
 
 of sidereal mensuration. The mode in which these two 
 elliptic movements, the larger real, and the smaller ap- 
 parent or parallactic, are combined together or super- 
 posed, and the sort of undulating line apparently de- 
 scribed by either star in consequence, will easily be 
 understood by a glance at Fig. 2. 
 
 (29.) Assiduous observation, aided by a powerful and 
 not very complicated system of calculation, has enabled 
 astronomers to assign in a great many instances with 
 considerable precision the true forms of these orbits as 
 distinguished from those in which, by the effect of per- 
 spective (owing to their oblique presentation to our 
 sight), they appear; to state the amount of that obliquity;
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 20$ 
 
 the situation in space of the planes in which they revolve ; 
 and the number of years required to complete their re- 
 volutions. Among them occurs every variety of form 
 (always elliptic), from the nearly circular one of the 
 planetary, to the long ellipsis of the cometary orbits : 
 every variety of oblique presentation, from a plane pass- 
 ing nearly or quite edgeways through the eye of the 
 spectator to one nearly perpendicular to the visual line ; 
 and every length of period, from thirty years up to many 
 centuries. The only element about which in the great 
 majority of cases we are left in complete uncertainty, is 
 the actual size of the orbit, which cannot become known 
 till the distance of the star is ascertained. For our pre- 
 sent purpose then we must confine our attention to those 
 of which at present the distance is known. The two 
 just spoken of present a striking contrast. The revolu- 
 tion of the two stars of a Centauri is performed in about 
 seventy-eight years. Their orbit is a very elongated 
 ellipse, decidedly cometary in its character ; and its pre- 
 sentation to our sight so nearly edgeways, that the two 
 stars at present almost occult or cover one another; 
 though when at their greatest distance from each other, 
 they would appear, if viewed perpendicularly, nearly 
 thirty seconds apart. The other requires about 514 
 years for a complete revolution. Its orbit is nearly 
 circular, and its presentation to our view nearly perpen- 
 dicular: so that we see the distance between the two 
 stars unforeshortened ; and so seen it measures almost 
 exactly sixteen seconds, or a little less than the average 
 apparent diameter of the globe of Saturn. Now we have
 
 O6 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 already seen that in the former case the distance between 
 the earth and sun would appear under an angle of i" and 
 in the latter o" - 54, whence it is easy to conclude that the 
 mean distances of the stars from each other, or the semi- 
 axes of their orbits, are, in the former case about 15, and 
 in the latter about 29! times that distance. The former 
 orbit would be contained between those of Saturn and 
 Uranus : the latter is about the size of that of Neptune. 
 
 (30.) In such orbits, then, gyrating round each other 
 not in the subordinate relation of sun and planet, but 
 as compeers in dignity and on the equal footing of regal 
 splendour ; communicating to each other we know not 
 what benefits, and bound on we know not what errand, 
 are these wonderful sidereal couples journeying onward 
 through space at the respective rates of 920,000 and 
 2,500,000 miles per diem at the very least : for such 
 would be their proper motions were we sure that they are 
 not foreshortened by oblique presentation to our line of 
 sight ! 
 
 (31.) An interesting, and what to many of our read- 
 ers will probably appear a very unexpected, conclusion 
 follows from this determination of the distance of these 
 stars, conjoined with the knowledge so obtained of the 
 periodic times of their orbital motion. It enables us to 
 weigh them; that is. to state in numbers the proportion 
 which the total ponderable mass or amount of gravitating 
 matter of the two stars of either couple bears to that of 
 the sun, and therefore as a necessary consequence to that 
 of our own globe, and ultimately (if we choose to lux- 
 uriate in the long array of figures in which such a calcu-
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 207 
 
 lation would land us) to our British standard ounce, of 
 which this our globe is equivalent to about 210 quad- 
 rillions* 
 
 (32.) It is an elementary proposition in physical 
 astronomy that the time in which two masses so con- 
 nected into a system by their mutual attraction, revolve 
 about each other in elliptic orbits, depends only on the 
 sum of their masses or weights, and on the length of the 
 elliptic relative orbit, and not at all on its breadth, and is 
 therefore the same as if the orbit were circular, i.e., as 
 if the two masses were retained constantly at the same dis- 
 tance from each other, viz., that which we have called their 
 mean distance; and which mean distances, as we have seen 
 in the cases before us, are respectively in round numbers 
 fifteen and thirty times that of the sun from the earth. 
 
 (33.) It is an equally elementary conclusion from the 
 theory of gravitation, and was long since demonstrated 
 by Newton, that, so far as the time of revolution is con- 
 cerned, it is unimportant in what proportions the sum of 
 the masses or the entire ponderable matter of the system 
 is distributed between the two, the distance being un- 
 altered. That time, therefore, would remain unaltered, 
 
 * Adopting that nomenclature which calls I followed by 6 ciphers 
 a million, by 12 a billion, by 18 a trillion, and by 24 a quadrillion. 
 For the weight of our globe in tons (5852 trillions), see Herschtl's 
 " Physical Geography," 2d edit. sect. 5. The elastic forces with 
 which Mr Bailey, in his repetitions of the celebrated " Cavendish 
 Experiment " (from which this estimate of the weight of our globe 
 is concluded) compared that weight, varied from less than one 
 29,oooth part of a grain in some experiments to one 25Ooth in 
 others ! The result, however, being corroborated in various ways, 
 is received without hesitation.
 
 208 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 if all the ponderable matter but a single pound were col- 
 lected in one of them, and that pound circulated about 
 it as the earth does about the sun. Here, then, we have 
 the case stated over again, with only the difference of 
 times and distances, which, in our Lecture on " The 
 Sun," already referred to, 16, 17, served us to show how 
 we might arrive at a knowledge of the sun's mass, and tc 
 calculate that mass. Substitute in the reasoning there 
 explained for one year 78 or 514 years, and for the sun's 
 distance respectively fifteen and thirty times that distance ; 
 and the result, in place of the mass of the sun, will fur- 
 nish us with the total or joint masses of the two stars in 
 the one or the other of these two sidereal combinations or 
 "binary systems" respectively. We shall not trouble 
 our readers with the calculation : suffice it to state the 
 result, viz., that the joint mass in question in the former 
 pair (that in the Centaur), is about |^, a little more 
 than half that of the sun, or equal to 198,000 earths ; 
 and in the latter (in the Swan), about fo of the sun, 
 equivalent to 36,000 earths. 
 
 (34.) Beyond the distances of these two remarkable 
 sidereal combinations, our grasp becomes less and less 
 assured as we push forward into space. Remarkably 
 enough, Sirius and Arcturus, the two brightest stars 
 visible in our hemisphere, stand barely within the limits 
 of any estimation approaching to certainty, the former 
 being between six and seven, the latter about eight, 
 times the distance of our nearest neighbour in the Cen- 
 taur. At the distance thus assigned to Sirius, our sun (if 
 any faith can be placed in photometry) would appear as
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 209 
 
 a star hardly of the sixth magnitude invisible, therefore, 
 or but barely discernible to the ordinary unassisted eye ; 
 and it would require four hundred such suns concentred 
 into one to send us the light which that superb star 
 actually does; supposing none lost or extinguished in 
 traversing so enormous a distance : a journey which it 
 would take more than twenty years to accomplish ! We 
 speak here only of the proportion between the lights of 
 the two bodies ; but this can give no indication of that 
 between either their magnitudes or their weights or 
 masses, since the intrinsic splendour of the surface of the 
 one may, for anything we can tell, exceed that of the 
 other in any proportion. As to the proportion between 
 the masses, however, a very unexpected prospect of be- 
 ing able to ascertain it ere many years shall have 
 elapsed ; and even of forming something like a rude 
 estimate of it already, has quite recently opened to us : 
 the history of which may serve to show what persevering 
 industry will accomplish in apparently the most hopeless 
 lines of inquiry. 
 
 (35.) Sirius, as the most conspicuous of the stars, has 
 been watched by all astronomers with the utmost assi- 
 duity as the principal of the great landmarks of their 
 science ; the chief of their list of " fundamental stars ;" 
 those to which every observer of necessity resorts to test 
 the stability of his instruments ; the rates of his clocks ; 
 and every condition which gives precision to his obser- 
 vations. It has long been known, like most and prob- 
 ably all the othei stars, not to be absolutely fixed in the 
 heavens; but subject to what we have above described 
 
 o
 
 2IO CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 as a "proper motion," or slow progressive movement 
 proper to itself as an individual : smaller indeed than 
 those already specified in its apparent amount, but by 
 no means inconsiderable, being sufficient to displace it 
 by about two minutes in angle or one-fifteenth part of 
 the apparent diameter of the moon per century : corre- 
 sponding at the distance of the star to no less an amount 
 of actual linear travel than 1,900,000 miles per diem. 
 This movement, in the absence of all apparent reason to 
 the contrary, was of course presumed to be uniform and 
 rectilineal } but as instruments improved, as observations 
 became more exact, and their calculation more scrupu- 
 lous and refined, this became at first doubtful, and at 
 length demonstrably incorrect Not to dwell on the 
 steps of the proof, it became apparent that the visible 
 path of the star, mapped down from year to year and 
 from century to century, is not a straight line, but is 
 affected by a small and regularly recurring undulation, 
 alternately carrying it to a small distance above and 
 below the medial line, similar to those represented in 
 Fig. i : the performance of one complete undulation 
 occupying about 49^ years, and the excursions to and 
 fro on either side of the medial line being about one- 
 sixtieth part of the linear distance passed over in the 
 same interval. 
 
 (36.) It was impossible to ascribe this phenomenon 
 (as in the case of our star in the Swan) to parallax. 
 Were this its origin, the undulations (as above explained) 
 would be annual, instead of extending over a period of 
 nearly fifty years ; and moreover that Cause of apparent
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 211 
 
 motion was taken account of in the investigation, in a 
 manner we need not here explain. The only other, and 
 in the then state of knowledge a very obvious, way of 
 accounting for it, was to ascribe these anomalous move- 
 ments to the attraction of an unseen companion ; in other 
 words, to consider Sirius as in reality a " double star ;" 
 its companion being either a non-luminous body, and in 
 the nature rather of a planet than an associated sun ; or, 
 if luminous, so feebly so as to be lost in the rays of Sirius 
 itself, which, in powerful telescopes, is of dazzling bright- 
 ness. Accordingly, Professor Peters, to whom we owe 
 this interesting investigation, proceeded (by steps which 
 we could not possibly make clear to our readers, and 
 which indeed only experts in mathematical calculation 
 can follow) to compute the relative orbit of the pair on 
 the theory of gravitation, and thence to ascertain, not 
 their mutual distance from each other (for that neces- 
 sarily then remained uncertain) but that of Sirius itself 
 from their common centre of gravity. For this he found 
 an apparent angular measure, of 2 ri< 4, corresponding to 
 about 16^ times the distance of the earth from the sun; 
 and calculating on his final result, the observed anoma- 
 lous deviations from uniform rectilinear motion were 
 found to be satisfactorily accounted for. 
 
 (37.) It is now time, however, to mention what, to 
 render our explanation more simple, we have hitherto 
 kept out of view, viz., that all the foregoing calculations 
 were directed only to that part of the " proper motion" 
 of Sirius which carries it in the direction of a parallel to 
 the earth's equator, or, as it is technically called, " in
 
 212 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 right ascension." If that movement were coincident in 
 direction with such a parallel, there would remain no- 
 thing further to explain. But such is not the case. It 
 is oblique ; and may therefore be regarded as composed 
 of two movements, the one along that parallel (in right 
 ascension), the other perpendicular to it, or, as it is 
 technically called, " in declination." Now these move- 
 ments admit of a distinct and separate examination, and 
 it is clear that, if both do not agree in indicating the 
 same kind of undulation and the same identical period, 
 the explanation so afforded of what may be called one 
 half of the phenomenon is at variance with that of the 
 other. Mr Peters left this other half untouched ; but 
 very recently that also has been examined by an Ameri- 
 can computist, Mr Safford, on the same principles ; and 
 the result is that the orbital motion, which accounts for 
 the one set of movements, gives at the same time a suffi- 
 ciently satisfactory explanation of the other. 
 
 (38.) Here, then, we are furnished with another ex- 
 ample like that afforded by the grand discovery of the 
 planet Neptune by the calculations of Adams and Lever 
 rier. The existence of a celestial body not seen and not 
 before known to exist, has been revealed to us and its 
 orbit computed, by the simple" application of mathema- 
 tical calculation grounded upon observed irregularities 
 in the movements of one already well known. 
 
 (39.) The parallel of the cases promises to be still 
 closer. Neptune, as is well known, was immediately 
 sought and found in the place assigned to it by the cal- 
 culation. In January 1862, Mr Alvan Clark, an eminent
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 213 
 
 optician of New York, turning on Sirius a fine telescope 
 of his own construction, noticed extremely near to it a 
 minute star which had eluded all former observation. 
 This may be the body in question. There is even some 
 reason to suppose it is. Its apparent situation is stated 
 to be at least not such as to be incompatible with such 
 a connexion. Its real existence has been verified, and its 
 apparent distance from Sirius measured, and found to be 
 about seven seconds ; corresponding (if seen unfore- 
 shortened) to about forty-seven times the distance of 
 the sun from the earth. 
 
 (40.) Another beautiful specimen of these binary side- 
 real systems is presented by the star No. 70 in Flam- 
 steed's list of those in the constellation Ophiuchus, and 
 therefore cited as 70 Ophiuchi. The ellipse described 
 by the stars of this pair (the one a star of the fourth, the 
 other of the sixth, magnitude) has been determined with 
 much care and every probability of considerable pre- 
 cision. The period of their mutual circulation may be 
 stated at about ninety-six years, and the semiaxis of their 
 mutual ellipse in angular measure at 4 //- 8. Of this ele- 
 gant couple the parallax has been ascertained by M. 
 Kriiger, from observations made in 1858 and 1859, at 
 o"'i6. And from these data he concludes in the very 
 same way : First, their distance from our own system 
 (1,272,000 semi-diameters of the earth's orbit) ; sec- 
 ondly, the mean distance of the stars from each other 
 (30^ such semi-diameters, so that here also their relative 
 orbit is nearly equal to that of Neptune) ; and, thirdly, 
 the total mass (equivalent to 3^ times that of the sun).
 
 214 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 (41.) Shall we spread our wings for a farther flight to 
 the region of the nebulae ? For such an excursion we are 
 hardly yet prepared. Our present reach extends, as we 
 have seen, only to a very few of our nearest neighbours 
 among the stars ; a class of bodies which we have every 
 reason to believe form with our own sun a system to us 
 a universe but which, removed to the distance of the 
 nebulae, would appear perhaps as one of them. More- 
 over, it is not wings, but a resting-place for the sole of 
 our foot that we want. If we knew in what orbit the sun 
 itself is moving (for that it moves is certain, and with no 
 trifling speed), and if human observations were to endure 
 till it had completed half a circuit in that vast orbit then 
 indeed we should have established a new base line from 
 whose extremities the parallax of the nearest nebula 
 might become sensible. Failing this, we must rest con- 
 tent with such probable indications as we can glean from 
 other sources. 
 
 (42.) There is one which can hardly fail to strike any 
 one who does not reject altogether from his philosophy 
 the consideration of design and purpose in the construc- 
 tion of the frame of nature. In their orbits round the 
 sun, the earth and other planets carry round with them 
 satellites retained in their orbits by gravitation to their 
 primaries. These orbits, though very sensibly disturbed 
 by the sun's attraction, are yet in no case so much so as 
 to hazard in the smallest degree the stability of these 
 miniature planetary systems, or in the lapse of even in- 
 definite ages to produce any very material change in 
 their relations to their primaries or to each other. The
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 21$ 
 
 enormous distance which separates the sun from the 
 nearest fixed star affords a still more complete guarantee 
 against the possibility of any disturbance of the plane- 
 tary movements by their attraction, and may not un- 
 naturally be considered as so intended. A continuance 
 of the same system of precaution (if we may venture on 
 the use of such a word) against external influence, into 
 the mutual relations of sidereal systems might therefore 
 lead us to expect that the intervals between them would 
 at least bear some very large proportion to the extent of 
 each. That there exist instances of nebulae which appear 
 to be bound together by a kind of companionship similar 
 to that of the double stars, does not in the least invalidate 
 this as a general conclusion. Here, however, figures 
 avail us nothing. Nor can it be necessary, after what 
 has been already said, to stimulate our imaginations to 
 any further effort to grasp and comprehend distances 
 and magnitudes inconceivable by man. Suffice it that 
 in the dim glimpse thus caught of an immensity of mate- 
 rial existence stretching outward by steps continually 
 more and more gigantic, we carry with us not a mere 
 general impression, but a well-founded conviction 
 grounded on an induction from observed facts of mea- 
 surement and computation, that the same mechanical 
 laws at least ; the same relation between matter, force, 
 and motion as those we see in action around us, prevail 
 in the uttermost regions of space ; and regulate, there as 
 here, the evolutions of the systems disseminated through 
 it. In the endless variety of combination exhibited 
 among the double stars too (to say nothing of a multi-
 
 2l6 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 tude of other phenomena, less clearly intelligible, which 
 the sidereal heavens present, and to which our subject 
 has not led us to refer), we trace the same inexhaustible 
 fecundity of design realized and embodied in the same 
 unity of workmanship which in this our planetary system 
 we find luxuriating in so surprising a variety of forms, 
 magnitudes, and mutual relations among its primaries, 
 satellites, rings, comets, and asteroids. 
 
 (43.) Is the material universe finite or infinite ? The 
 question is as old as Aristotle ; and the answer, though 
 unanswerable, never yet convinced mortal man. A 
 material universe must consist of material objects, each 
 individual of which, being a really existing thing, must 
 possess that attribute of all real existing things, place. 
 Every two objects then, be they where they will at any 
 certain moment of time, mark two definite places, and the 
 distance between them, or the straight line joining 
 them, has two definite terminations. It is not therefore 
 infinite in length, but finite, i.e., terminated. Now an 
 assemblage of objects, every two of which are distant 
 from each other by a finite interval, cannot be infinite in 
 extent The speculation is unprofitable enough in 
 itself, and the difficulty it involves turns on the mental 
 substitution of a positive and conceivable notion of " the 
 infinite " for the purely negative and utterly inconceivable 
 one which it carries with it into all matters where the 
 term is employed in its logical sense. Our only reason 
 for at all alluding to it is, that to us, practically speak- 
 ing, the material universe must be regarded as infinite : 
 seeing that we can perceive no reason which can place
 
 CELESTIAL MEASURINGS AND WEIGHINGS. 217 
 
 any bounds to the further extension of that principle of 
 systematic subordination which we have already traced 
 to a certain extent; and which combines in its fullest 
 conception a unity of plan and singleness of result with 
 an unlimited multiplicity of subordinated individuals, 
 groups, systems, and families of systems. Thus it by no 
 means follows that all those objects which stand classed 
 under the general designation of " nebulae " or " clusters 
 of stars," and of which the number already known 
 amounts to upwards of five thousand, are objects (looked 
 upon from this point of view) of the same order. Among 
 those dim and mysterious existences, which only a prac- 
 tised eye, aided by a powerful telescope, can pronounce 
 to be something different from minute stars, may, for any- 
 thing we can prove to the contrary, be included systems 
 of a higher order than that which comprehends all our 
 nebulae (properly such) reduced by immensity of distance 
 to the very last limit of visibility. And this conception, 
 we may remark, affofds something like a reasonable 
 answer to those who have assumed an imperfect trans- 
 parency of the celestial spaces, on the ground that, but 
 for some such cause, the whole celestial vault ought to 
 blaze with solar splendour, seeing that in no direction of 
 the visual ray, if continued far enough, would it fail to 
 meet with a star. Such would no doubt be the case 
 were all space occupied by stars disseminated through it 
 uniformly, i.e., so that the same number of stars should 
 in every region be comprised in the same space. But no 
 such consequence would follow were the law of sidereal 
 distribution such as we have been here describing : a
 
 2l8 CELESTIAL MEASURINGS AND WEIGHINGS. 
 
 position, however, with whose demonstration (founded 
 on the very elementary properties of a decreasing geomet- 
 rical progression) we shall not trouble our readers. 
 
 (44.) Such a speculation as this just mentioned may 
 possibly appear irrelevant. But it must be remembered 
 that it is LIGHT, and the free communication of it from the 
 remotest regions of the universe, which alone can give, and 
 does fully give us, the assurance of a uniform and all- 
 pervading energy a mechanism almost beyond concep- 
 tion complex, minute, and powerful, by which that 
 influence, or rather that movement, is propagated. 
 Our evidence of the existence of gravitation fails us 
 beyond the region of the double stars, or leaves us at 
 best only a presumption amounting to moral conviction 
 in its favour. But the argument for a unity of design 
 and action afforded by light stands unweakened by dis' 
 tance, and is co-extensive with the universe itself
 
 LECTURE VL 
 ON LIGHT, 
 
 PART I. REFLEXION REFRACTION DISPERSION- 
 COLOUR ABSORPTION. 
 
 j N a conversation held some years ago by the 
 author of these pages with his lamented 
 friend, Dr Hawtrey, Head-Master and late 
 Provost of Eton College, on the subject of 
 Etymology, I happened to remark that the syllable Ur 
 or Or must have had some very remote origin, having 
 found its way into many languages, conveying the sense 
 of something absolute, solemn, definite, fundamental, or 
 of unknown antiquity, as in the German words Ur-alt 
 (primeval), Ur-satz (a fundamental proposition), Ur-theil 
 (a solemn judgment) in the Latin Oriri (to arise), 
 Origo (the origin), Aurora (the dawn) in the Greek 
 *Oos (a boundary, a mountain, the extreme limit of 
 our vision, whence our horizon), 'Ogau (to see), 'Oe&b( 
 (straight, just, right), "Owoi (an oath or solemn sanction), 
 r na/ (the seasons, the great natural divisions of time), 
 &c. "You are right," was his reply, "it is the oldest of
 
 22O ON LIGHT. 
 
 all words; the first word ever recorded to have been 
 pronounced. It is the Hebrew for LIGHT (liN AOR)." 
 
 (2.) Assuredly there is something in the phaenomena 
 of Light ; in its universality ; in the high office it per- 
 forms in creation; in the very hypotheses which have 
 been advanced as to its nature ; which powerfully sug- 
 gests the idea of the fundamental, the primeval, the ante- 
 cedent and superior in point of rank and conception to 
 all other products or results of creative power in the 
 physical world. " It is LIGHT," as we took occasion to 
 observe at the conclusion of the last lecture (not with- 
 out reference to this very consideration), " and the free 
 communication of it from the remotest regions of the 
 universe, which alone can give, and does fully give us, 
 the assurance of a uniform and all-pervading energy 
 a MECHANISM almost beyond conception complex, mi- 
 nute, and powerful, by which that influence, or rather 
 that movement, is propagated. Our evidence of the 
 existence of gravitation fails us beyond the region of the 
 double stars, or leaves us at best only a presumption 
 amounting to moral conviction in its favour. But the 
 argument for a unity of design and action afforded by 
 light stands unweakened by distance, and is co-extensive 
 with the universe itself." * 
 
 (3.) What we propose in the following lecture is to 
 make intelligible, in as simple language and form as the 
 nature of the subject will admit, the grounds of this 
 assertion. In some of its features it is too complex 
 and abstruse to be thoroughly followed out by any one 
 * "Celestial Measurings and Weighings," p. 218.
 
 ON LIGHT. 221 
 
 not familiar with some of the most intricate departments 
 of mathematical science. In explaining such features 
 (when unavoidable), without prejudice to the strictness 
 of mathematical reasoning adducible and held to be 
 conclusive and satisfactory by those who have mastered 
 it, we must have recourse to analogies more or less close 
 with processes we see going on in nature ; and which, 
 whether perfectly understood or not in their modus oper- 
 andi, we, at all events, perceive to consist in a sequence 
 of events, comprehensible in themselves and arising 
 naturally and familiarly one out of another. There are 
 many phsenomena of polarized light which admit of be- 
 ing so, as it were, shadowed forth to the mind of a 
 beginner as analogous to things familiar enough. In 
 such cases, though the analogy may be imperfect, or 
 even altogether incompetent to stand for an explana- 
 tion, the phaenomenon is sometimes so neatly conveyed 
 to the intellect, that by generalizing to the extreme all 
 the terms used in describing the one, it is very conceiv- 
 able that the cardinal feature of the other that which 
 dominates its whole explanation may be included. 
 Even if not so, the object is so far answered, that the 
 student remains possessed of a mental picture which 
 will not allow him to forget its prototype. And it is 
 not a compendium of Optics, or an essay on Vision, or 
 an account of telescopes, microscopes, or other optical 
 instruments, that he has here to expect. Nothing of the 
 kind could by possibility be comprised within such limits 
 as a contributor to a work of this kind must necessarily 
 observe. Suffice it to convey to his apprehension some
 
 222 ON LIGHT. 
 
 idea of at least the general nature of the mechanism by 
 which it seems now agreed, with hardly a dissentient 
 voice, that the peculiar communication between distant 
 objects which we call light is effected ; and by which, or 
 by some mechanism of a nature still more recondite, and 
 at present perhaps beyond our conception of possibility, 
 it must be so. 
 
 (4.) That we see, is proof of a communication of some 
 sort between the eye and the thing seen. That we can- 
 not see in the dark, is proof that such communication is 
 not the mere act of the eye. And that one object is 
 capable of impressing a photographic picture of itself on 
 another, is proof that the eye, though essential to seeing, 
 has nothing whatever to do with the process by which 
 such communication is performed. And furthermore, 
 the immense variety and extent of the chemical agencies 
 of light as displayed in its action both on organic and 
 on inorganic matter, revealed to us by the late discov- 
 eries in photography, assign to it a rank among natural 
 agents of the highest and most universal character ; and 
 have even rendered it exceedingly probable, if they have 
 not actually demonstrated, that vision itself is nothing 
 but the mental perception of a chemical change wrought 
 by its action on the material tissue of the retina of the 
 eye. 
 
 (5.) At all events, it is not by any sympathy, or abso- 
 lute direct relation between the eye and the object, that 
 the latter is seen. The intermediate space, and indeed 
 all space, is concerned in the process. An object is not 
 seen unless it be in a certain state, which we call " lumin-
 
 ON LIGHT. 223 
 
 'cms:" a state either natural to it, as in the flame of 
 a candle or the sun ; or induced, by being placed in pre- 
 sence of another luminous object, as when a sheet of 
 white paper is laid in the sun or before a candle. Nor 
 is it then seen if a screen of metal or any of the class of 
 substances called "opake" be interposed anywhere in 
 the direct straight line of communication ; while on the 
 other hand, when so hidden from direct vision, it may 
 be rendered visible "by reflexion" from a polished sur- 
 face held at a fitting angle, anywhere out of that direct 
 line, provided only such surface be not similarly screened 
 either from the object or from the eye. Thus we learn 
 two things : First, that the line of uninterrupted lumin- 
 ous communication is a straight one; and, secondly, that 
 any point whatever in a sphere of indefinite radius sur- 
 rounding a luminous object (in other words, in infinite 
 space) may become included in the line of indirect or 
 deflected luminous communication between any two 
 places. The agency, whatever its nature, is there and 
 ready, requiring only a fitting arrangement of material 
 and tangible substances to make it available. 
 
 (6.) Light, though the cause of vision, is itself invis- 
 ible. A sunbeam, indeed, is said to be seen when it 
 traverses a dark room through a hole in the shutter or 
 when in a partially clouded sky luminous bands or rays 
 are observed as if darted through openings in the clouds, 
 diverging from the place (unseen) of the sun as the 
 vanishing point of their parallel lines seen in perspective. 
 But the thing seen in such cases is not the light, but the 
 innumerable particles of floating dust or smoky vapour
 
 224 ON LIGHT. 
 
 which catch and reflect a small portion of it, as when in 
 a thick fog the bull's-eye of a Ian thorn seems to throw 
 out a broad diverging luminous cone, consisting in 
 reality of the whole illuminated portion of the fog. The 
 moon is seen in virtue of the sun's light thrown upon it. 
 Where the moon is not we see nothing, though we are 
 very sure that when in the course of its revolution it 
 shall arrive in the place we are looking at, we shall see 
 it, and that if our eyes could be transferred to the moon's 
 place, wherever it may be in the firmament (if not 
 eclipsed), we should from it see the sun. There then, 
 at all times, is the light of the sun, but not visible as a 
 thing. It exists as an agency. What is true of the sun 
 is no doubt equally so of a star ; so that when we look 
 out on a dark night, though we are sure that all space is 
 continually being crossed in every direction by the lines 
 of its communication, along all which it is active; and in 
 particular, that all the dark space immediately around 
 us (outside of the earth's shadow) is, so to speak, flooded 
 with the sun's light, we yet peiceive only darkness, 
 except where our line of vision encounters a star. 
 
 (7.) What then is LIGHT ] or, in other words, what is 
 the nature of that communication by which not only 
 information is conveyed to our intellectual and per- 
 ceptive being ; but chemical and various other changes 
 are operated even on inorganic matter by processes 
 originating as it would seem in sources situate in the 
 most distant regions of space (for, be it observed, it has 
 been clearly proved that the light of the stars does pro- 
 duce photographic effects powerful enough to imprint
 
 ON LIGHT. 225 
 
 their images permanently on surfaces duly prepared to 
 receive them). Is there any physical mode of convey- 
 ance by which, reasoning from what we see in cases 
 which we are able to analyze, we can imagine either a 
 material agent to be bodily transported, or a movement 
 propagated, or an influence wafted, from place to place, 
 so as to render a rational and consistent account of the 
 phenomena of light, or so at least as, generalized, and 
 (so to speak) sublimated in modes not inconsistent with 
 the known properties of matter, to do so ? 
 
 (8.) One feature is common to all ordinary physical 
 modes of communication. The transmission from place 
 to place, be it of what it may of a letter by post, a 
 gunshot, a sound, a wave, a tremor, or a shock even Oi 
 an earthquake occupies time. It has a velocity : some- 
 times a very great, but anyhow a measurable one. Is 
 this the case with light 1 The answer, from all ordinary 
 experience, would be in the negative. But this is only 
 because the velocity in question is so great that the 
 longest distances to which we can send a flash of light 
 and receive it back again by reflexion is traversed in an 
 interval of time too short to be perceived as an interval, 
 so that the reflexion appears to be simultaneous with the 
 direct flash. It is otherwise when we bring to bear on 
 the question the ingenious combinations and delicate 
 appliances of modern science. The telescope enables 
 us to become eye-witnesses in the way of astronomical 
 observation of events which take place at distances m 
 space almost inconceivably greater than any we can 
 measure here on earth ; at times calculable beforehand, 
 
 p
 
 226 ON LIGHT. 
 
 And in the way of experiment, the contrivances of 
 clock-work enable us to register the subdivisions of what 
 we call " an instant" into hundreds, nay, thousands, of 
 equal and exactly measurable portions applying, so to 
 speak, a microscope to time, and estimating, by unde- 
 niable calculation, portions of it utterly eluding all our 
 powers of perception. The question has been asked in 
 both these modes, by astronomical observation and 
 by direct physical experiment, and the answer, from 
 each, has been affirmative ; and from both agreeing, 
 in a manner which may well be considered wonder- 
 ful 
 
 (9.) The planet Jupiter is attended by four satellites 
 which revolve round it in orbits very nearly circular, 
 and whose dimensions, forms, and situations with respect 
 to that of the planet itself are now perfectly well known. 
 The periodical times of their respective revolutions are 
 also ascertained with extreme precision, and all the par- 
 ticulars of their motions have been investigated with 
 extraordinary care and perseverance. The three interior 
 of them are so near the planet and the planes of their 
 orbits so little inclined to that in which it revolves 
 round the sun, that they pass through its shadow, and 
 therefore undergo eclipse, at every revolution. These 
 eclipses have been assiduously observed ever since the 
 discovery of the satellites, and their times of occurrence 
 registered. As they afford a means of determining the 
 longitudes of places, the prediction beforehand of the 
 exact times of their occurrence becomes an object of 
 great importance : and it is evident enough that, all the
 
 ON LIGHT. 227 
 
 particulars of their motions being known (as well as of 
 that of the planet itself, and therefore of the size and 
 situation of its shadow), there would be no difficulty in 
 making such prediction (starting from the time of some 
 one observed eclipse of each as an epoch) ; provided 
 always each eclipse were seen at the identical moment when 
 it actually happened. Moreover, on that supposition, the 
 times recorded of all the subsequent eclipses ought to 
 agree with the times so predicted. This, however, proved 
 not to be the case. The observed times were some- 
 times earlier, sometimes later than the predicted ; not, 
 however, capriciously, but according to a regular law of 
 increase and decrease in the amount of discordance, the 
 difference either way increasing to a maximum, then 
 diminishing, vanishing, and passing over to a maximum 
 the other way, and the total amount of fluctuation to 
 and fro being about i6 m 27 s . Soon after this discrep- 
 ancy between the predicted and observed times of 
 eclipse was noticed, it was suggested that such a dis- 
 agreement would necessarily arise if the transmission of 
 light were not instantaneous. This suggestion was con- 
 verted into a certainty by Roemer, a Danish astronomer, 
 who ascertained that they always happened earlier than 
 their calculated time when the earth in the course of its 
 annual revolution approached nearest to Jupiter, and 
 later when receding farthest : so that in effect the ex- 
 treme difference of the errors or total extent of fluctua- 
 tion the i6 m 27 s in question is no other than the 
 time taken by light to travel over the diameter of the 
 earth's orbit, that being the extreme difference of the
 
 28 ON LIGHT. 
 
 distances of the two planets at different points of their 
 respective revolutions. At present, in our almanacs a 
 due allowance of time for the transmission of light at 
 this rate, assuming a uniform velocity, is made in the 
 calculation of these eclipses; and the discrepancy in 
 question between the observed and predicted times has 
 ceased to exist. 
 
 (10.) Taking the diameter of the earth's orbit, as con- 
 cluded from the sun's observed parallax,* at 24,000 
 diameters of the earth itself, and the latter diameter 
 at 7925! miles, t this gives a velocity of 192,700 miles 
 per second. 
 
 (n.) So vast a speed seemed at first incredible; to 
 some indeed even more so than an instantaneous com- 
 munication. The one might be conceived as the result 
 of some sort of spiritual communication : the other 
 seemed, in those days, to transcend all imaginable limits 
 of mere physical agency. But it soon received a very 
 unexpected confirmation from Dr Bradley's discovery of 
 the ABERRATION of light : to conceive which, let any 
 one imagine a long tube held perpendicularly, at perfect 
 rest, while a falling body (a drop, suppose of a shower of 
 rain), descending also perpendicularly, should pass down 
 its axis. If it entered at the centre of its upper orifice, 
 it would issue at that of the lower ; and, judging from 
 this indication alone, and knowing the tube to be exactly 
 vertical, a spectator would truly conclude from it that 
 the descent of the drop was so also. Supposing him and 
 
 * See p. 196. note. 
 
 t This is the equatorial diameter.
 
 ON LIGHT. 229 
 
 the tube, however, to be carried along uniformly in any 
 direction by a movement unperceived by himself, the 
 hinder part of it would advance to meet the falling drop ; 
 which would, if the movement in advance were suffi- 
 ciently rapid, cause it to strike against it ; or if not, to 
 emerge at the lower end so far behind the centre as that 
 movement had carried the tube during the time of its 
 passage from end to end. And this deviation would 
 obviously bear the same proportion to the length of the 
 tube that the velocity of the falling drop bore to that of 
 the tube's advance. Judging, then, from this indication 
 alone, if unaware of his own motion ; he would conclude 
 the fall of the drop to be inclined backward from the 
 perpendicular by a certain angle but if, suspecting it, 
 he should reverse his movement, and travel with equal 
 speed the contrary way, he would find an equal devia- 
 tion in the contrary direction, and would thus arrive at 
 the certainty that it was to the motion of himself and the 
 tube, and not to any real obliquity in the fall of the 
 drop, that this apparent deviation was owing. And by 
 measuring its angular amount (which would be easy by 
 the help of the marks left by two drops in the opposite 
 circumstances on a screen at the lower end of the tube, 
 and comparing it with the length of the latter), this angle, 
 which might be called the Aberration (from perpendicu- 
 larity) of the apparent line of fall, would inform him of 
 the proportion his own velocity bore to that of the drop 
 in its passage, and, the former being known, would enable 
 him to estimate the latter. 
 
 (12.) All this is a parapnrase of the astronomical phae-
 
 *30 ON LIGHT. 
 
 nomenon in question. The rain-drop is the light ; the 
 tube, a telescope ; the screen at its lower end, a mi- 
 crometer; and the two opposite directions of the 
 observer's motion, the two tangents at opposite sides of 
 the earth's orbit at right angles to the situation of a star 
 as viewed from either. And the angle in question is 
 what astronomers call their " Constant of Aberration " 
 a very minute one indeed, but perfectly well measurable 
 amounting to about a third of a minute (2o"'45), from 
 which it results that the velocity of light is about ten 
 thousand (more exactly 10,089) times that of the earth 
 in its orbit, which we know to be very nearly 19 miles 
 (18-923) per second, which gives 190,860 miles per 
 second for the velocity of light 
 
 (13.) Two different experimental processes for measure- 
 ing this velocity have been devised and executed the 
 one by M. Fizeau, of the Parisian Academy of Sciences ; 
 the other by M. Leon Foucault, recently and most de- 
 servedly elected into the same illustrious body ; the 
 inventor of that elegant instrument, the Gyroscope. 
 Both depend on the principle that the impression left on 
 the eye by any luminous object persists for a sensible, 
 though very minute, time (about the tenth of a second); 
 so that an object presented to the sight by successive 
 glimpses only, following each other more frequently than 
 ten times in a second, is seen continuously. If only 
 just so frequent, a fluttering is perceived ; but this 
 diminishes as the rapidity of presentation is increased : 
 and when much more frequent, distinct and perfectly 
 uninterrupted vision is produced. In M. Fizeau's ex
 
 ON LIGHT. 231 
 
 periment (which is the simplest in its conception and 
 explanation), these glimpses are obtained by looking 
 tfirough an opening in a screen corresponding exactly 
 in size and shape to one of the intervals between the 
 teeth of a metallic wheel which is made to revolve before 
 the opening, so that as the teeth pass in succession, they 
 intercept the light so long as they cover it ; but allow it 
 to pass when, in place of a tooth, an interval is presented 
 be r ore the eye. Imagine such a wheel, screen, and 
 opening, the wheel being at rest in the last-described 
 sitiation ; and through another such an opening in the 
 sane screen, corresponding exactly in size, shape, and 
 sitiation to another of the intervals between the teeth, 
 let i sunbeam be directed outwards, in a direction par- 
 alld to the axis of the wheel, by a highly-polished 
 reflector, so as to strike upon another such reflector so 
 placed at some considerable and measured distance from 
 the wheel, that the light shall be reflected back again by 
 this second mirror. By slightly inclining and properly 
 ad. usting this it may be made to return, not to the orifice 
 frcm which it issued, but to the other behind which the 
 eye of the observer is placed. In this state of things, 
 wien all is at rest, he will see the reflected light ; but if 
 the wheel be turned slowly round, a tooth will come be- 
 fore the first reflector in place of an opening, and inter- 
 cept the light then another opening, another tooth, and 
 so on, producing successive glimpses of light separated 
 by dark intervals. 
 
 (14.) If the motion of the wheel be gradually accele- 
 rated, so that more than ten teeth pass before the orifice
 
 2\2 ON LIGHT. 
 
 in a second of time, these glimpses run together into 
 continuous vision ; and if considerably more numerous 
 (suppose fifty or sixty per second), the light is perceived 
 steadily as if the wheel were at perfect rest only, hov- 
 ever (if the intervals between the teeth be exactly equal 
 to the breadths of the latter), of half the brilliancy, see- 
 ing that only half the quantity of light will have entered 
 the eye in the same time. The motion of the wheel 
 still continuing to be accelerated, however, when it las 
 attained a certain very great rapidity the light is gradu- 
 ally perceived to grow feebler and at length altogether 
 disappears. This happens when the velocity of rotation 
 is such as to bring a tooth of the wheel precisel) to 
 cover the whole of the orifice in the screen into wlich 
 the returning beam should be delivered at the very 
 moment of its arrival, so closing it up altogether ; that 
 is to say, when the rotation is just so rapid as to carry 
 each tooth over its own breadth during the time talen 
 by the light to go and return. When this happeis, 
 suppose the acceleration of the wheel to cease, and its 
 motion to be maintained uniform. Then by counting 
 the turns made per minute by the driving-handle of the 
 train of wheel-work, or otherwise registering its speed ; 
 and knowing (from the construction of the train) how 
 many turns of the wheel correspond to one of the driver, 
 as also how many teeth it carries, the exact duration cf 
 this interval, no matter how minute, can be exactly 
 computed, so that the time and the space run over by 
 the light in that time both become known. 
 
 (15.) If the rotation be now still further accelerated,
 
 ON LIGHT. 233 
 
 the light begins to reappear, and gradually increases to 
 its former brightness, in which state of things the ob- 
 structing tooth has been carried, in that same interval of 
 time, quite clear of the opening, and the next notch 
 brought exactly opposite to it. With yet increased 
 speed, the light again vanishes, again reappears, and so 
 on alternately, as the second, third, or fourth tooth or 
 notch is successively brought before the opening ; and 
 on comparing the velocities of rotation corresponding, 
 they are found to increase in arithmetical progression ; 
 which obviously ought to be the case. In M. Fizeau's 
 experiments,* the distance between the reflector and the 
 revolving wheel was about 8600 metres, thus giving for 
 the whole distance travelled over by the light going and 
 returning 17,200 metres, or about io| miles; and for 
 the time occupied in its journey, hardly more than the 
 1 8,oooth part of a second. A velocity of 196,000 miles 
 per second was assigned by him as their final result, 
 exceeding by about one-sixtieth part that resulting from 
 the astronomical observations. 
 
 (16.) The experiments of M. Foucault, however, 
 leave no doubt that this last result is too great. In 
 these experiments, instead of measuring these minute 
 intervals of time by the rotation of a toothed wheel, a 
 revolving reflector was employed in pursuance of an 
 idea suggested by Mr Wheatstone, and applied by him 
 
 * The actual details of this experiment, as executed by M. 
 Fizeau, were somewhat more complicated. Telescopes were used, 
 &c. For clearness of explanation, we have reduced the whole 
 process to its simplest form of expression.
 
 234 ON LIGHT. 
 
 to measure the velocity of electricity. Without figures, 
 and without much more verbal detail than would be 
 compatible with our limits, it would be impossible to 
 give a clear conception of the conduct of this delicate 
 and refined experiment. Suffice it to state, as its ulti- 
 mate result, a velocity of 185,172 miles per second.* 
 As there are other and independent reasons for believ- 
 ing that the sun's distance has been over-rated by about 
 one-thirtieth in our estimate of 12,000 diameters of the 
 earth, and that, in consequence, the velocity of light 
 deduced from the phenomenon of aberration ought to 
 be diminished in the same proportion (which would 
 reduce it to 186,300 miles per second), we are autho- 
 rized to conclude that in estimating this velocity at 
 186,000 miles we are within a thousand miles of the 
 truth. 
 
 (17.) The form of experiment proposed and executed 
 by M. Foucault has this great advantage over the other 
 that it can be carried out within much smaller limits 
 of distance. A few yards of travel suffices for the deter- 
 mination of this enormous speed. And this makes it 
 possible to compare the velocity of light in its passage 
 through air and water, and other transparent liquids 
 with this remarkable result, that the rate is found to be 
 slower in the denser medium ; a result of the utmost 
 importance, as we shall presently see, as a crucial fact in 
 deciding between the claims of the two great rival 
 theories of light to be received as valid. 
 
 * 298 millions of metres. See Comptes Rendus de /' Institut, 
 Sept. 22, 1860.
 
 ON LIGHT. 235 
 
 (18.) Before we can give any intelligible account of 
 these theories, however, it is necessary to enter a little 
 more particularly into the modes by which a ray of light 
 may be deflected from its rectilinear path, and the laws 
 of such deflection. By this expression we understand 
 nothing more than that the line of communication between 
 the illuminating and illuminated object is, in some way 
 or other rendered circuitous. It is so natural to speak of 
 light as a thing, and of its line of communication as the 
 path along which that thing, be it what it may, travels, 
 that we are apt to forget that (except on one hypothesis 
 as to its nature, viz., that it is, actually, a material sub- 
 stance, bodily transported from place to place) this form of 
 expression is purely metaphorical, and that by a ray 
 nothing more is meant than the mathematical line, be it 
 straight or bent, between two points, standing to each 
 other in the relations of illuminat/;^ and illuminate/ 
 along which the communication is kept up the test 
 being, that an opake body being placed anywhere in 
 that line, the illumination ceases. Such a circuitous 
 line of communication may be established, independent 
 of and in addition to the direct rectilinear one, by plac- 
 ing anywhere in space any material object whatever, 
 provided there be no opake body interposed between 
 it and either of the two points ; and this in two different 
 modes. In the one the whole path of the ray, both be- 
 fore and after its deflection, is outside of the deflecting 
 body. In this case the light is said to be ''reflected:" if 
 at a smooth and polished surface, regularly, if at a rough 
 one, irregularly; in which case the light is said to be
 
 836 ON LIGHT. 
 
 "scattered" In the other mode the path of the ray, 
 subsequent to the point where it first encounters the 
 deflecting body, is wholly or partly within it, and the 
 light is said to be " refracted," or " transmitted." 
 
 (19.) The first law observed in every case, whether of 
 direct or circuitous illumination, is gathered from ordi- 
 nary and universal experience. The illuminating and 
 illuminated points are mutually interchangeable. By 
 whatever path, however circuitous, light is conveyed from 
 A to B, by the same it can be conveyed from B to A. 
 This condition alone suffices to determine the path, and 
 to fix the situation of the point at which its flexure takes 
 place by reflexion, when the light is " incident " on any 
 polished surface, whether plane or curved. That point 
 (p) must be so situated on the surface, that the two lines 
 joining it and the illuminating and illuminated points (A, 
 B) shall there make equal angles with the surface, the 
 three points (A, B, p) all lying in one plane with a perpen- 
 dicular to the surface. For, ist, except the angles were 
 equal, the two directions (PB, PA) would not be similarly 
 related to the surface at the point of incidence ; so that 
 in reversing the path of the ray, the physical condition 
 which determined the obliquity of the incident ray to the 
 surface in proceeding from A to B, to be greater or less 
 than that of the reflected, would have to be reversed in 
 the passage of light from B to A. And similarly, if the 
 reflected ray lay in a plane to the right or left of that in 
 which the perpendicular and the incident one were con- 
 tained, the physical condition which determined it to 
 deviate to the one side or to the other of that plane, would
 
 ON LIGHT. 237 
 
 in like manner have to be reversed on interchanging the 
 illuminating and illuminated points. On neither suppo- 
 sition could the same intrinsic law of communication 
 carry the ray from A through p, to B, and from B, through 
 P, to A. This, then, is the law of regular reflexion, com- 
 monly expressed by saying that the angle of incidence in 
 equal to that of reflexion and lies in the same plane with it. 
 (20.) If the reflecting surface be a plane, there will be 
 only one point in it which fulfils these conditions. Thus 
 a perfectly polished flat surface of silver, free from 
 scratches, or that of still water, sends no light to the eye 
 from a candle, and is in fact invisible, except at this one 
 point so determined whence the light is reflected to the 
 eye, and in the direction of which from the eye the re- 
 flected candle is seen. With curved surfaces, as well 
 as with those we designate as "rough" or " unpolished," 
 the case is different In all surfaces of this last-men- 
 tioned description the microscope reveals to us such irre- 
 gularities, such innumerable and abruptly broken facets, 
 protuberances and hollows, as to satisfy us that in every, 
 the most minute, visible portion of such a surface, places 
 must occur in which the condition of equal inclination of 
 the two lines in question to the actual surface, as it exists 
 in those places, is satisfied so that a ray there reflected 
 may reach an eye however situated. By such rays, and 
 by others which have entered into the substance of the 
 object and been there internally reflected or otherwise 
 bent, in a manner presently to be explained, all surfaces 
 not self-luminous become -visible as objects^ being seen by 
 rays " scattered " from them in every possible direction.
 
 238 ON LIGHT. 
 
 (21.) It is to this power of "scattering" the incident 
 light in all directions, then, that surfaces owe their visi- 
 bility, and that by its aid we are enabled to trace the 
 course of a ray of light itself as if it were a visible thing. 
 Thus a sunbeam passing through a small hole and re- 
 ceived on smoke is seen, and on a white screen moved 
 rapidly to and fro behind it, appears as a straight lumin- 
 ous line or beam, by the momentary persistence of the 
 sensation caused in the eye at every successive point of 
 its motion ; and so, after reflexion or refraction, may its 
 subsequent course be rendered matter of ocular inspec- 
 tion. A pleasing and elegant experiment is to hold a 
 common reading-glass (or even a spectacle-glass) in the 
 sun, and to move rapidly to and fro behind it a white 
 paper, when the course of the refracted light, converging 
 from all parts of the glass to the " focus," will be seen in 
 the air as a solid luminous cone, having the glass for 
 its base and the focus for its apex. 
 
 (22.) The reflexion of light, whether "regular" or 
 " scattered," is, except under very peculiar circumstances 
 to be presently noticed, only partial; so that the re- 
 flected image of an object is seen fainter and less 
 luminous than the object itself directly viewed. This is 
 perceptible in an ordinary looking-glass ; yet more so 
 when the reflecting surface is still water, or unsilvered 
 glass. The most reflective substances are the white 
 metals such as silver, speculum-metal, steel, or quick- 
 silver : transparent or semi-transparent bodies being 
 much inferior in respect of this quality. If the substance 
 on which the light falls be of the kind called opake, the
 
 ON LIGHT. 239 
 
 reflected is the only portion which can be rendered sen- 
 sible to sight or otherwise traced. But if transparent, a 
 very remarkable phasnomenon occurs. The incident ray 
 is, as it were, split or subdivided at the point where it 
 meets the surface of the body ; one portion pursuing its 
 subsequent course outside of it, as a reflected ray, in the 
 manner above described ; the other within it, undergo- 
 ing what is called " refraction" being bent aside from its 
 former direction at its point of entry, after which it pur- 
 sues a straight course within the substance or " medium." 
 (23.) If the "refracting medium" be a liquid, a glass, 
 a jelly, or any substance in which no indications of 
 inequality of internal texture can be discovered no 
 signs of lamination or " grain" shown by a greater- ten- 
 dency to split or " cleave" in one direction more than 
 another, this intromitted portion is single. The whole of 
 the refracted light pursues its course from the point of 
 its entry as one ray. The same is also the case when 
 the refracting medium belongs to the class of bodies 
 called " crystallized," or which present a definite " cleav- 
 age ;" provided the " primitive form" of their crystals 
 be either a cuoe, a regular octohedron, or a rhomboidal 
 dodecahedron, such as rock-salt, alum, or garnet. In 
 all other transparent crystals the intromitted portion of 
 the light divides itself from the moment of its entry into 
 two distinct rays, pursuing different courses, and present- 
 ing the phenomenon known under the name of " double 
 refraction," such substances being called " doubly- 
 refractive media," of which the substance called Iceland 
 Spar, or crystallized carbonate of lime, offers a beautiful
 
 4O ON LIGHT. 
 
 example. And here we may pause for a moment to 
 observe that at this point we already find ourselves in- 
 troduced to an assemblage of relations between light and 
 material objects, which divide x the whole universe of such 
 objects, infinite as they are in variety, into classes, char- 
 acterized by their habitudes with respect to light in its 
 reflexion from and passage through them. The import- 
 ance of this remark will grow upon us as we advance 
 further into the subject, and come to perceive that the 
 classification of bodies according to their " optical pro- 
 perties" stands in direct connexion with their most 
 intimate peculiarities of mechanical structure and chemi- 
 cal constitution ; and brings us, so to speak, into con- 
 tact with all those more recondite properties and reac- 
 tions of the ultimate particles of bodies which constitute 
 the domain of molecular physics. 
 
 (24.) Confining ourselves now to the case where the 
 refraction is single, the rule which determines the course 
 of the refracted ray is as follows. Suppose at the " point 
 of incidence" (i.e., where the ray first enters the medium) 
 a line be drawn perpendicular to the surface. Then, 
 first, the refracted ray will lie in the same plane which 
 contains both the incident ray and this perpendicular ; 
 and, secondly, the ray will be so bent at that point that 
 the exterior and interior portions shall make with the 
 perpendicular, not equal angles as would be the case 
 were there no flexure, but angles so related that their 
 sines (not the angles) shall bear to each other a certain 
 invariable proportion, whatever be the angles them- 
 selves, or whatever be the obliquity of the incident ray
 
 ON LIGHT. 
 
 241 
 
 to the surface. As it is quite essential to the under- 
 standing of what follows that this, " the law of ordinary 
 refraction," should be clearly apprehended, we will illus- 
 trate it by a figure. Let A c B be a section of the surface 
 
 by the plane in which the ray D c, incident at c, and 
 p c Q the line perpendicular to the surface at c, both lie, 
 and c E the refracted ray. Taking c for a centre, with 
 any radius, c M, describe a circle cutting the incident 
 and refracted rays in M and N, from which points draw 
 M R, N s perpendicular to p c Q. Then will these two 
 lines be to each other, in one and the same invariable 
 proportion, whatever be the inclination of the original 
 ray D c to the surface, or to the perpendicular c P. 
 This latter inclination is what is understood by the 
 "angle of incidence" and the corresponding inclination 
 (to the perpendicular Q c P) of the refracted ray, by " the 
 angle of refraction"
 
 242 ON LIGHT. 
 
 (25.) It is evident from what we said in the last para- 
 graph, that according to the greater or less disproportion 
 between the lines M R, N s, on the diagram there given, 
 or the sines of the two angles of incidence and refraction, 
 the greater or less will be the amount of bending (or 
 angle of deviation, as it is called) of the ray at its point of 
 transmission, for one and the same degree of obliquity 
 as also that for one and the same medium, the deviation 
 increases with the angle of incidence (though not propor- 
 tionally to *t) being nil when the ray enters perpendi- 
 cularly, and a maximum when just grazing the surface. 
 If in any case M R be greater than N s, or the " ratio of the 
 sines" be one of "greater inequality," the bending will be 
 towards the perpendicular ; if less, or if that ratio be one 
 " of less inequality," from it; as indicated by the course 
 of the dotted ray in the figure. If the former be the case 
 in any instance, as in that where a ray passes out of air 
 into water, the latter will happen in the reverse case, as 
 where it passes out of water into air : that is to say, in 
 optical language, " out of a denser medium into a rarer." 
 This follows, from the general fact that the illuminating 
 and illuminated points are convertible, or that a ray can 
 always return by the path of its arrival, so that the re- 
 fraction of a ray out of any medium into air is per- 
 formed according to the same rule of the sines, only 
 reversing the terms of the proportion ; or in other words, 
 regarding what was the angle of incidence in the one 
 case as that of refraction in the other and vice versa. 
 Numerically expressed, this reversal of the terms of a 
 proportion, or ratio, is equivalent to inverting the numer-
 
 ON LIGHT. 243 
 
 ator and denominator of the fraction expressing it, so 
 that, for instance, in the passage of light out of water 
 into air, the "law of the sines" is expressed in the same 
 general terms, but the " refractive index" (by which is 
 meant the number expressing the proportion in question) 
 has to be changed into its numerical reciprocal. In the 
 case supposed, when light passes out of air into water, 
 the proportion of the sines is that of 1336 to 1000, or 
 almost exactly 4 to 3; and the "refractive index" is 
 accordingly expressed by the fraction A, or the almost 
 exactly equivalent decimal i'336. In the reversed case, 
 then, when the transmission is out of water into air, it 
 will be 1=075, or mor e precisely 0749. 
 
 (26.) As a matter of experiment, it is found that be- 
 tween transparent media, or substances capable of being 
 traversed by light, there exists a very wide diversity in 
 this ratio of the sines of the two angles in question, or 
 in the numerical values of the "refractive indices." 
 Thus when light passes out of air into the less refractive 
 species of plate-glass, the index instead of is | or i -5 ; 
 into sulphur (which in its crystalline form is transparent), 
 2 - o; and into diamond, or the mineral called octohe- 
 drite, 2*5. In fact, each particular transparent sub- 
 stance, solid, liquid, or gaseous, has its own peculiar, and, 
 so to speak, characteristic index of refraction, which is 
 found to stand in relation to its physical habitudes in 
 many other respects, especially with its chemical com- 
 position, and its state of aggregation and density. 
 
 (27.) Even common air, in respect of a vacuum, has 
 its refractive index viz., i -0003 the effect of which is
 
 244 ON LIGHT. 
 
 perceived in the phenomenon of astronomical refraction, 
 by which the sun or moon is rendered visible when 
 actually sunk below the level of the true horizon. 
 
 (28.) From what is above stated, it is easy to see that 
 when a ray is transmitted through a sheet or plate of any 
 substance (as a window-glass) with parallel surfaces, its 
 course after emergence will be parallel to its original 
 direction, so that though displaced laterally, its direction 
 in space is unchanged, which is the reason we see objects 
 in their proper directions through a window. If the sur- 
 face at which it emerges be not parallel to that through 
 which it enters, this exact restoration of the original 
 direction will not take place ; and as we judge of the 
 situation of an object only by the direction in which its 
 light ultimately enters the eye, anything seen through a 
 transparent substance whose surfaces are so inclined, 
 will appear shifted in angular position. Any transparent 
 substance so formed of polished plane surfaces inclined 
 to each other, is called in optics "afrism;" and the 
 angle at which the two planes in question meet, or 
 would meet if extended, its "refractive angle." If such 
 a prism of glass, for instance be held before the eye 
 with its refractive angle vertical, and to the left, an 
 object seen through it will appear deviated or shifted to 
 the left of its true situation, the ray (as a slight consi- 
 deration will show) being bent towards the thicker 
 pan oi the prism. And thus by a very simple calcula- 
 tion, with which we shall not trouble our readers, from 
 the angular amount of deviation caused by a prism of 
 any medium whose refracting angle is measured, ran
 
 ON LIGHT. 
 
 245 
 
 the " refractive index " of that medium be ascer- 
 tained. 
 
 Fig. a. 
 
 (29.) When refraction takes place out of any one trans- 
 parent medium into any other in close and perfect con- 
 tact with it such contact as exists, for instance, be- 
 tween a fluid and a solid that it wets, or between two 
 fluids of different specific gravities, which do not mix, 
 resting the one on the other experiment shows that, so 
 far as the mere direction of the refracted ray is concerned, 
 it is the same as if the two media were separated by an 
 exceedingly thin film of air. In that case, the same per- 
 pendicular being common to both surfaces at the point 
 of contact, the angle of refraction out of the first medium 
 is the same with that of incidence on the second. And 
 from this it results that the proportion of the sine of in- 
 ternal incidence on the surface of the first to that of
 
 246 ON LIGHT. 
 
 internal refraction at that of the second, or the " relative 
 index of refraction," is constant for the same media, and 
 is equal to the quotient of their respective absolute re- 
 fractive indices. Thus, if the first medium be water, 
 and the second be plate-glass, whose respective absolute 
 indices are | and I, the relative index, or that out of 
 water into glass, will be \ divided by f or !=ri25. 
 
 (30.) A very curious result follows from what has been 
 said, viz., that though light can pass out of a rarer 
 medium into a denser, whatever be the obliquity ot 
 incidence, even when the. incident ray but just as it 
 were grazes the surface, yet the converse is not the case. 
 For every denser medium, there is a limit of obliquity, 
 beyond which transmission into a rarer cannot take 
 place. The ray is wholly reflected without undergoing 
 any diminution of brightness whatever; observing the 
 same law of equality between the angles of incidence 
 and reflexion, as in the case of ordinary reflexion on a 
 mirror. The brightness of the reflexion, however, far 
 surpasses anything that can be obtained from the most 
 brilliant looking-glass or metallic mirror, being equal to 
 that of the object directly seen. The effect is very 
 striking, and is easily seen by immersing a small rod 
 obliquely in a glass tumbler of water, and viewing the 
 under surface of the water from below upwards at a 
 moderate obliquity. The reflexion of the rod is seen 
 without the smallest diminution of brightness. It is 
 thus that fishes see the bottom of their pond redupli- 
 cated by internal reflexion on the distant parts of its 
 surface. The rationale is simple enough. If two angles
 
 ON LIGHT. 247 
 
 always have their sines in a fixed proportion, the greater 
 may increase up to a right angle, but the less cannot ; 
 since the contrary would require the sine of the greater 
 to exceed the radius of the circle. 
 
 (31.) Within this limit, when the angle of incidence 
 is such as to admit of the transmission of the ray, the 
 reflexion is less than total. The incident beam is sub- 
 divided ; a part only is transmitted, the rest undergoes 
 reflexion. The total amount of incident light is divided 
 between them, but very unequally, and the more so the 
 less the difference between the refractive indices of the 
 media ; or, in optical language, between their " refrac- 
 tive densities." Thus, when light passes at a perpen- 
 dicular incidence out of air into water, only 2 per cent, 
 of the whole incident beam is reflected; when into plate- 
 glass, about 4 per cent., but when out of water into such 
 glass, the amount of reflected light is less than per 
 cent. At oblique incidences, the reflexion is more 
 copious, increasing in intensity as the obliquity in- 
 creases, until the incident light but just grazes the 
 surface. 
 
 (32.) The laws of reflexion and refraction being known, 
 it is the part of geometry to follow them out in the 
 several cases where light is incident on plane, spherical, 
 or any other curved surfaces, reflecting or refracting, 
 and thus to deduce the various theorems and proposi- 
 tions which the practical optician has need of for the 
 construction of his mirrors, lenses, prisms, telescopes, 
 and microscopes. All these, as beside our present pur- 
 pose, we pretermit, confining ourselves entirely to the
 
 248 ON LIGHT. 
 
 physical properties of light, and the theories which have 
 been advanced for their explanation. This need not 
 prevent us, however, from appealing to the effects pro- 
 duced by such instruments, especially such as are in 
 most common use, and as can hardly be other than 
 familiar to most of our readers, such as magnifying 
 glasses (or lenses), telescopes, &c. It requires no 
 knowledge of geometry, for instance, or any acquaint- 
 ance with its application to theoretical optics, to enable 
 any one to form a perfectly just conception of the mode 
 in which the eye enables him to see, when his attention 
 is called to a photographic picture, and he sees it im- 
 pressed on its ground by the rays of light collected and 
 brought to a focus by that assemblage of convex and 
 concave lenses in a camera obscura which the photo- 
 grapher uses for the purpose. The dissection of an 
 eye shows it to be such an assemblage, and the picture 
 it produces may be actually seen at the back of the 
 eye of an animal recently killed, by removing the 
 opake leathery coat which envelopes it, and disclosing 
 the retina. How the nerves of that tissue, indeed, con- 
 vey to the mind the perception of colour and form, is, 
 and will probably ever remain, a mystery; but is no 
 more so in the case of vision than of any other of the 
 senses ; from which vision differs only in its transcendent 
 refinement and the elaborate structure of that most 
 wonderful of all optical instruments by which form, as 
 well as colour and brightness, is brought within its range. 
 The latter qualities are probably perceived by animals 
 unprovided with eyes, such as ft&proteus angttinus, which
 
 ON LIGHT. 240 
 
 inhabits dark caves, and whose delicate skin is evidently 
 and painfully affected by the light ; but to convey the 
 perception of form, a picture must be produced, and in 
 its own peculiar manner. 
 
 (33.) We are now prepared to understand the mode 
 in which colour originates. This, to the ancients, was 
 always a mystery. The light of the sun, and of ordinary 
 daylight, which is only that of the sun dispersed and 
 reflected backwards and forwards among the clouds, is 
 white, or nearly so. Nevertheless, when we look through 
 a red glass, or view a green leaf, it conveys to the mind 
 the perception of those colours. How is this 1 If it be 
 by light only that we see, and if that light convey to us 
 absolutely none of the material elements of the bodies 
 from which we receive it, how comes it that it excites in 
 us such various and perfectly distinct sensations ? The 
 light itself must have either acquired or parted with 
 something in its passage through or reflexion from the 
 coloured body. Supposing, for instance, light to be a 
 substance ; it may have taken up some excessively 
 minute portion of the object and introduced it to the 
 direct contact of our nerves. In that case the sense of 
 colour would be assimilated to those of taste or smell. 
 Or it may have undergone analysis, and colour would 
 then arise from a deficiency of something existing in the 
 sun's light, and the relative redundancy of some other 
 portion. In this view, light would be regarded, not as a 
 simple, but a compound substance, or a mixture of so 
 many simple ones as would suffice to explain all the 
 observed differences of tint On the other hand, if light
 
 2$0 ON LIGHT. 
 
 be a movement, or an influence, we must admit in that 
 movement or influence a similar capacity for analysis or 
 composition, or else have recourse to some unknown 
 modification of the one or the other, leaving the phae- 
 nomenon as unexplained as before. There may, for 
 instance, be a great variety of such movements, all 
 luminiferous, but not all alike ; and some may be de- 
 stroyed, or some exaggerated, in the act of reflexion or 
 transmission. 
 
 (34.) The key to this mystery, up to a certain point, 
 was furnished by Newton, in his analysis of white light 
 by prismatic refraction. A full account of the manner 
 in which that analysis is performed, of the phenomena 
 it presents, and of the nature and subdivisions of the 
 " Prismatic spectrum," is given in our lecture on " The 
 Sun," 29, to which, to avoid repetition, we refer our 
 readers. Let us, however, consider what kind of general 
 theoretical interpretation we are entitled to put on this 
 analysis. Now, the first and most obvious conclusion is, 
 that the phaenomenon we have to deal with, is not what 
 in the accuracy of modern scientific language is under- 
 stood by the term " analysis." It is the separation and 
 redistribution (according to degrees of a certain quality 
 common to all its elements viz., that of REFRANGI- 
 BILITY) of a mixture, rather than the <#alysis of a true 
 compound. The simile by which we there illustrated it 
 is so far exact A glacier moraine might be redistributed 
 by tidal action over the floor of the Ocean ; the great 
 blocks left in situ, or little moved the smaller forming 
 shingle, gravel beds, sandstones, or incoherent muddy
 
 ON LIGHT. 251 
 
 deposits, with every possible intermediate gradation of 
 size. But if in all this series any particular size were 
 found entirely and universally deficient, throughout the 
 whole series of formations traceable to that source, we 
 should conclude, not that a mass of that size is an im- 
 possibility in rerum natura, but that owing to some un- 
 known cause in the nature of a previous sifting, every 
 pebble or grain of that size had been already separated, 
 or otherwise arrested in limine, and might expect else- 
 where to find it in the case of some other series of 
 geological formations. So it is with the sun's light. 
 Certain definite and marked degrees of refrangibility are 
 wanting in its spectrum, indicated by the dark lines 
 which cross it But if absent in solar light, they exist in 
 the light of flames, and of other luminous sources, which 
 in their turn are again deficient in other degrees which 
 yet abound in the solar rays. Refrangibility, then, 
 taken as a property of light generally, is a quality sus- 
 ceptible of indefinite gradation, from the one extreme of 
 the spectrum to the other. 
 
 (35.) If we limit our consideration to some one 
 medium glass, for instance we find each particular 
 degree of refrangibility associated, first, with a deter- 
 minate and invariable index of refraction, which de- 
 termines its place in the spectrum by determining the 
 amount of deflexion it shall undergo in passing through 
 the prism ; and, secondly, with an equally determinate 
 and invariable tint in the scale of " prismatic colour," 
 the red corresponding to the least and the violet to the 
 greatest refractive index. The truth of these proposi-
 
 52 ON LIGHT. 
 
 tions is easily tested on any one ray of the spectrum 
 insulated from the rest by intercepting all the others. 
 The ray so insulated, whatever its tint, is no longer 
 separated or " dispersed" by subsequent refraction into 
 a new spectrum. It preserves its tint unaltered, and 
 conforms to the " rule of the sines" in its flexure, as if 
 no other colour or refrangibility existed. Hence we 
 might be led to conclude, as Newton himself did, that 
 between these two qualities refrangibility and colour 
 an absolute and invariable connexion exists. This, 
 however, is not the case. The propositions in question 
 cannot be generalized. When different media are 
 examined, we find that not only does the same colour 
 correspond to different degrees of refrangibility, or to 
 different absolute values of the refractive index in each, 
 but that the same change of colour does not correspond 
 in different media to the same proportionate change of 
 the refractive index ; and that, in short, taking the 
 " scale of colour" in all its gradations, from red, through 
 orange, yellow, green, blue, and indigo, to the least per- 
 ceptible violet, and that feeble tint beyond the violet 
 which can hardly be called a colour, but which is most 
 nearly expressed by the term lavender, as a guide, each 
 particular medium distributes these rays through its 
 spectrum, though always in the same order of succes- 
 sion, yet in other respects according to a law peculiar to 
 itself: thus indicating both a total amount of dispersion 
 and a scale of 'action dependent on the physical proper- 
 ties of the medium, and in some sort as it were personal 
 to each. This power which a transparent medium has
 
 ON LIGHT. 253 
 
 of separating the differently-coloured rays and spreading 
 them over an angular space greater or less in proportion 
 to the total deviation of some one ray, taken as a stand- 
 ard, from its former course, is called in optics the " dis- 
 persive power" of the medium. It differs very widely in 
 different media, and in consequence, the lengths of the 
 spectra which they produce, corresponding to one and 
 the same mean or average refraction, differ accordingly. 
 Thus, for example, the total lengths of the spectra pro- 
 duced by prisms of fluorspar, water, diamond, flint glass, 
 and oil of cassia (the mean refractions being the same), 
 are to each other in the proportions of the numbers 22, 
 35> 3 8 > 48, and 139. 
 
 (36.) This quality of dispersion stands in very dis- 
 tinct relation to the chemical constitution of the refract- 
 ing medium. Thus it is found that all the compounds 
 of lead, whether in liquid solution, natural or artificial 
 crystals, or glasses into which that metal enters largely, 
 possess very high dispersive powers; while those into 
 which strontia enters exhibit remarkably low ones. It 
 is on this property of lead that the formation of highly 
 dispersive glasses, to imitate the brilliant colours of gems, 
 and to give the vivid prismatic colours of the pendants 
 of chandeliers by candle-light, depends, as well as that far 
 more important application which, by the combination 
 of two glasses of different dispersive powers, the one con- 
 taining lead, the other none, enables the optician to 
 effect refraction without producing colour, and so to con- 
 struct that admirable instrument, the achromatic telescope. 
 
 (37.) Not only are the total lengths of the spectra pro-
 
 254 ON LIGHT. 
 
 duced by different media different foi the same mean 
 amount of refraction, but within those lengths the dis- 
 tribution of the several colours differs, the spaces occu- 
 pied by the several tints differing very considerably in 
 proportion to each other and to the whole. Thus, in 
 the spectrum formed by flint-glass, and most other of 
 the highly dispersive media, the green is situated nearer 
 to the red than to the violet end of the spectrum, while 
 in that formed by muriatic ("hydrochloric") acid the 
 reverse is the case. 
 
 (38.) By the reunion of all the coloured prismatic 
 rays (which may be effected by an equal and contrary 
 refraction of the whole spectrum through a prism of the 
 same material reversely placed), white light is repro- 
 duced. And hence we conclude that colour is not a 
 superinduced but an inherent quality of the luminous rays. 
 Again, if we exclude from this reunion any portion of 
 the spectrum, the reconstituted beam is coloured : and if 
 the rays so excluded be not extinguished, but diverted 
 aside, and themselves collected and reunited into 
 another and separate beam (which may easily be 
 effected, with a little management, by one skilled in ex- 
 perimental optics), this will also be coloured, but with a 
 tint complementary to that of the first. Between the 
 tints so arising is always found to prevail that beautiful 
 and, so to speak, harmonious contrast which is so effec- 
 tive in the ornamental arts, where one colour is said to 
 set-off another, or show it to the greatest advantage. 
 Thus, crimson or pink is complementary to green, 
 scarlet or orange to blue, yellow to purple, &c. The
 
 ON LIGHT. 255 
 
 relation to each other of these complementary colours 
 is curiously and strikingly illustrated by the spontaneous 
 production within the eye itself of the tint complement- 
 ary to any vivid colour, which takes place when, after 
 gazing steadfastly on an area so coloured, on a white 
 ground, and strongly illuminated, the gaze is suddenly 
 transferred to a uniformly white surface. There is seen 
 on it, though only for a few moments, a picture or opti- 
 cal image of an area similar in form and size, but tinted 
 with the complementary hue, which fades quickly away. 
 This curious and beautiful experiment, which requires no 
 apparatus to exhibit, and which any one may try in a 
 moment, is exceedingly illustrative of the mode in which 
 the sensation of colour is produced. It proves that, in 
 the nervous tissue which receives and feels the picture 
 within the eye, there are nerves individually and exclu- 
 sively sensitive to each of the coloured rays, or at all 
 events to each of those primary colours (if such there 
 be) by whose mixture all colours are compounded. 
 When white light falls on a portion of the retina wholly 
 or partially deadened or fatigued by the excitement of 
 the nerves appropriate to one set of rays, the sensibility 
 of the others being left unexhausted ; that other portion 
 will be for a time proportionably more sensitive to the 
 remaining rays : so that under the stimulus of white light 
 an undue preponderance is temporarily given to their 
 influence, and the sensation of the complementary tint 
 is conveyed to the mind. This is only one of innumer- 
 able instances of the wonderful adaptation of that most 
 astonishing orean to the performance of its office of con-
 
 256 ON LIGHT. 
 
 veying to us information not only of the forms and situa- 
 tions of objects, but of all that multitude of their physical 
 properties which stand in relation to colour, both those 
 which ordinary experience teaches and which science 
 reveals. 
 
 (39.) Lastly, by thus reuniting into one beam rays 
 going to form distant portions of the spectrum, and ex- 
 cluding the rest, we find that it is possible to produce a 
 compound beam which shall excite directly in the eye, 
 or illuminate a screen with any one of the innumerable 
 varieties of tint which we observe in nature ; and what 
 is especially remarkable, the same tint, or one undis- 
 tinguishable from it to ordinary eyes, is producible by 
 very different combinations of the prismatic rays ; while 
 yet there exist individuals, and these not unfrequent, 
 who are perfectly capable of discriminating (in many 
 cases) between such compound tints, and who even 
 declare them to be widely different. To such cases of 
 what is called, though improperly, "colour-blindness," 
 we shall presently have occasion to recur. 
 
 (40.) The consideration of these facts has given rise 
 to a speculation which, if not demonstrable, has at least 
 a high degree of plausibility, and which, at all events, 
 has never yet been disproved, viz., that there is no 
 real connexion between COLOUR and REFRANGIBILITY, 
 but that there exist three inherently distinct species of 
 light, each competent per se to excite the sensation of 
 one of three PRIMARY COLOURS, by whose mixture all 
 compound tints are produced, white consisting of their 
 totality, and black being the exponent of their entire
 
 ON LIGHT. 257 
 
 absence. That, moreover, each of them has a spectrum 
 of its own, over the whole length of which it is dis- 
 tributed according to its own peculiar law of intensity, 
 and from whose superposition on the same ground re- 
 sults the prismatic spectrum, coloured as we see it. 
 The annexed figure will convey a better conception oi 
 
 9 
 
 Fijr. 3- 
 
 this than any lengthened description, where A B repre- 
 sents the length of the total spectrum wherewith each 
 of the three is co-extensive, and where the curved lines 
 marked R, G, B, severally express, by the height to 
 which they rise on any one point in A B, the intensity 
 in its own spectrum of each of the primary colours ; 
 while the dotted curve, whose ordinate or height cor- 
 responding to any point is the sum of those of the 
 other curves, will of course express the joint intensity 
 or degree of illumination in the visible spectrum. 
 
 (41.) In this view of the subject, the prismatic 
 colours, with the exception of the extreme red, are all 
 more or less mixed tints, and this agrees well with its 
 general aspect, in which the red and indigo-blue are 
 the only full and pure tints, the green being by no 
 means a saturated or full green, and the violet having 
 a strong dash of purplish-red in it 
 
 R
 
 258 ON LIGHT. 
 
 (42.) The three primary colours assumed in the 
 above figure are red, green, and blue, each in its highest 
 degree of purity and undilution, for it will be readily 
 apprehended that while the admixture of any one, in 
 however small a proportion, will produce a rich though 
 a mixed tint, that of both the others tends to dilution. 
 The only three colours which answer all the experi- 
 mental conditions, are these three. This may seem 
 contrary to the experience of the artist, who from his 
 habitual practice in mixing the colours he uses (all of 
 them without exception compound tints), would name 
 yellow, in place of green, as the intermediate primary. 
 The reason is obvious. In all the yellows which he 
 uses there is a large admixture of red with green, and 
 in all his blues more or less green. When mixed, then, 
 there is sure to be a preponderance of green, while the 
 red goes to neutralize a portion of the other two, and 
 so to dilute the outstanding green. On the other hand, 
 the direct mixture of the prismatic yellow and blue, in 
 whatever proportions, can no-how be made to produce green, 
 as Professor Maxwell's, M. Helmholz's, and my own 
 experiments* have distinctly proved ; while that of the 
 prismatic green and red does produce yellow. This 
 will be better understood when we come to speak of 
 the absorption of coloured light 
 
 (43.) Since at each point of a compound spectrum 
 so constituted, all the three primary elements, in what- 
 ever proportion mixed, have one and the same degree 
 of refrangibility, it is evident that the compound tint 
 See " Notices of the Royal Society," vol. x. p. 52.
 
 ON LIGHT. 259 
 
 arising from their mixture cannot be separated by any 
 subsequent refraction into its components. 
 
 (44.) In persons who are what is called " colour- 
 blind," the eye is sensible to all the rays of the prismatic 
 spectrum as light, though even in that respect the red 
 rays appear comparatively deficient in power to stimulate 
 the nerves of vision, so that all colours, into which a 
 large proportional admixture of primary red enters, are 
 described by them as sombre tints. But besides this 
 two of the primary coloured rays, the red and the green, 
 appear to excite in their nerves sensations of colour 
 nearly or exactly similar. Their vision is therefore, in 
 fact, dichromic; all their compound colours are resolv- 
 able into two elements only instead of three. Red 
 they do not distinguish from green. The scarlet coat 
 of the soldier and the turf on which he is exercised 
 the ripe cherries and the green leaves among which 
 they hang are to them undistinguishable by colour, 
 though from constantly hearing them so spoken of, 
 they habitually speak of the fruit as red and the leaves 
 as green. Their sensation of blue is probably the same 
 as in normal vision ; though whether that excited by 
 their other colour, be such as a normal-eyed person 
 would call red, yellow, green, or something quite 
 different from either, we have no means of ascertain- 
 ing, nor can they give us any information. The face 
 of nature must appear, however, to them far inferior 
 in splendour and variety to that which we behold 
 and if there be, as is asserted, here and there an in- 
 dividual totally destitute of the sensation of difference
 
 260 ON LIGHT. 
 
 of colour, it must present to his eyes what we should 
 be disposed to call a hideous monotony light and 
 shade only revealing the forms of objects as in an en- 
 graving. Yet what we never knew we never miss. 
 There may, and not improbably do, exist beings in 
 other spheres, if not here on earth, whose vision is 
 sensitive to those rays of the spectrum which extend 
 far beyond the violet or its lavender prolongation, and 
 which we know at present only by their powerful 
 photographic activity, and by their agency in producing 
 that singular species of phosphorescence in certain 
 media to which Professor Stokes has given the name 
 of Fluorescence. By these properties, the solar spec- 
 trum is proved to be prolonged far beyond its visible 
 limits at its most refracted extremity; as it is by other 
 invisible rays OF HEAT, which have been traced up to 
 nearly an equal distance beyond the extreme red in 
 the opposite direction.* All, however, whether of heat 
 or chemical influence, conform each for itself, and ac- 
 cording to its own special " refractive index," to the 
 same general law of the sines, as well as to every other 
 of those singular and complicated relations of the 
 luminous rays, we shall hereafter have to describe ; 
 and both the one and the other extending into and 
 thinning out as it were in the luminous region, just 
 as we have described the spectra of the primary colours 
 into those of each other. Such, and so wondrously 
 complex a compound is a sunbeam ! 
 
 * See my paper in the Phil. Trans. R. S. 1842, "On the Action 
 of the Solar Rays on Vegetable Colours."
 
 ON LIGHT. 26l 
 
 (45.) The analysis into its prismatic elements of the 
 colour of any natural object, is readily performed by 
 examining through the refracting angle of a prism of 
 perfectly colourless glass a rectilinear band or strip of 
 the colour to be analysed, so narrow as to have scarcely 
 any apparent breadth, and to appear as little more than 
 a coloured line. Placing this on a perfectly black 
 ground, parallel to the refracting edge of the prism, and 
 illuminating it as strongly as possible, it will be seen 
 dilated into a spectrum, or broad riband of colour, ex- 
 hibiting of course those coloured rays only which belong 
 to the composition of the tint examined. An exceed- 
 ingly convenient arrangement for this purpose is to 
 fasten across one end of a hollow square tube of metal 
 or pasteboard blackened within, of about an inch square 
 and twelve or fourteen inches long, a metal plate having 
 in it a very narrow slit parallel to one side, quite straight, 
 and very cleanly and sharply cut. At the other end 
 within the tube is to be fixed a small prism of highly 
 dispersive colourless flint glass, having its refracting 
 angle parallel to the slit, and so placed that when the 
 tube is directed to the sky, or rather to a white cloud, 
 the slit shall be seen dilated into a clear and distinct 
 prismatic spectrum. In this of course all the prismatic 
 colours will be seen in their due order. But if, instead 
 of this, any coloured object as the leaf of a flower, for 
 instance, or a coloured paper, strongly illuminated by 
 direct sunshine (if necessary, concentred on it by a lens, 
 so, however, as not to scorch the object by the heat of 
 its focus), be placed so near to the slit as completely to
 
 262 ON LIGHT. 
 
 occupy its whole area and suffer no ray to enter it which 
 does not come from some part of the coloured surface ; 
 the spectrum will be seen deficient in all those rays 
 which the object does not reflect, and which belong to 
 its complementary colour. The use of this little instru- 
 ment, at once simple, portable, and inexpensive, will be 
 found to afford an inexhaustible source of amusement 
 and interest. To the florist, on a bright sunny morning, 
 the analysis of the tints of flowers and leaves, or the 
 hues of a butterfly's wing, and of every variety of coloured 
 object; to the water-colour painter, the study of the 
 prismatic composition of his (so fancied) simple washes 
 of colour and the effects of their mixture and super- 
 position ; to the oil painter, that of the various bril- 
 liantly coloured powders which mixed with oil form the 
 material of his artistic creations, are all replete with 
 interest and instruction. 
 
 (46.) If instead of a reflected colour we would exa- 
 mine a transmitted one, as in the case of a coloured 
 glass, or some natural transparent coloured product, if 
 in the form of a plate or lamina, it may be laid over the 
 slit, and when directed to any bright white light (as that 
 of a white cloud), its spectrum will be exhibited if a 
 coloured flame, the slit may be placed close to it, but if 
 a liquid, it will be preferable to make it its own prism 
 by enclosing it in a hollow prism formed of plates of 
 glass cemented together, when the differences arising 
 from difference of the thickness of the medium traversed 
 by the refracted rays will be more easily studied. 
 
 (47.) The colours of transparent media such as
 
 ON LIGHT. 363 
 
 coloured glasses, crystals, resins, and liquids depend 
 upon the greater or less facility with which the several 
 coloured rays are transmitted through their substance. 
 There is no medium known, not even air or the purest 
 water, which allows all the coloured rays to pass through 
 it with equal facility. Independent of the partial re- 
 flexion which takes place at the surfaces of entry and 
 emergence, a portion greater or less according to the 
 nature of the medium, is always stifled, or as it is called 
 in optical language, " absorbed '.-" and this absorptive 
 action is exerted unequally on the differently refrangible 
 rays ; so that when a beam of white light is incident on 
 any such medium, it will be found at its emergence 
 deficient in some one or more of the elements of colour, 
 and will therefore have a tint complementary to that of 
 the absorbed portion. Supposing, as is most probable 
 in itself, and agrees with the general tenor of the facts, 
 that an equal per-centage of the light of any specified 
 colour which arrives at any depth within the medium is 
 absorbed in traversing an equal additional thickness of 
 it, the intensity of the coloured ray so circumstanced 
 would diminish in geometrical, as the thickness traversed 
 increases in arithmetical progression. The more absorb- 
 able any prismatic colour, then, the more quickly will it 
 become so much reduced in proportion to the rest as to 
 exercise no perceptible colorific action on the eye. And 
 thus it is found that in looking through different thick- 
 nesses of one and the same coloured glass or liquid, the 
 tint does not merely become deeper and fuller, but 
 changes its character. Thus a solution of sap-green, or
 
 264 ON LIGHT. 
 
 of muriate of chromium, in small thicknesses is green 
 in great ones red ; tincture of violets, and that species of 
 rich blue glass which is coloured with cobalt, in like 
 manner are red when we look through a great thickness, 
 but beautifully blue when thin ; and so in a multitude of 
 other cases. Those who paint in water colours are well 
 aware of what importance it is to effect the tint they aim 
 at by a single wash of their colour. A second applica- 
 tion of the very same liquid, after allowing the first to 
 dry, does not simply heighten the colour, but changes the 
 tint, a circumstance which those who practise that fas- 
 cinating art will do well to bear in mind. 
 
 (48.) When white light is transmitted successively 
 through two or more coloured media whose scales of 
 absorption differ materially, the residual beam, or that 
 which struggles through after passing their successive 
 ordeal, will consist of those rays only whose transmis- 
 sion is favoured by all the media. Hence it will follow, 
 first, that the final tint, or that of the beam ultimately 
 emergent, will most probably be very different not only 
 from that exhibited by either of them separately, but 
 from that which might be expected to arise from a union 
 or blending of their tints, and which would arise were we 
 to unite together distinct luminous beams having those 
 tints; and, secondly, that all such successive transmis- 
 sions tend to produce sombre tints, and ultimately 
 complete blackness ; inasmuch as each successive trans- 
 mission destroys (or absorbs) a greater or less proportion 
 of the total illuminating power of the original beam. 
 Thus when colour is produced on white paper by the
 
 ON LIGHT. 265 
 
 laying on of successive washes of different transparent 
 colours, the tendency is to produce, first, a tint very 
 remote from that expected to result from their union ; and 
 secondly, becoming more and more muddy and sombre, 
 the greater the number of such heterogeneous layers of 
 colour. Hence the maxim in water-colour painting, to 
 secure brilliancy by using only a single wash of colour, 
 if possible, to produce the required effect The painter 
 should never forget that his notion of colour (as com- 
 pared with that of the photologist) is a negative one. 
 He operates solely by the destruction of light, and his 
 aim should always be to destroy as little as possible. 
 His direct action (unknown to himself) is upon the tint 
 complementary to that which he aims at producing. 
 
 (49.) Each particular coloured medium has its own 
 peculiar and specific scale of absorptive action, differing 
 inter se in the most singular and capricious manner. In 
 many, indeed in most cases, the spectrum viewed through 
 such a thickness as to give a strong colour to common 
 daylight, in place of being seen as a continuous band of 
 graduating colour, is broken up into distinct coloured 
 spaces, more or less intense, and more or less well- 
 defined, separated by dark intervals. This is particularly 
 the case with coloured gases or vapours. Thus the red 
 vapour of nitrous gas, especially when its absorptive 
 action is intensified by heat, breaks up the spectrum 
 into a succession of narrow spaces, alternately dark and 
 bright, from one end to the other. 
 
 (50.) When coloured flames are examined with such a 
 " spectroscope" as above described, the phenomena are
 
 266 ON LIGHT. 
 
 no less varied, and in the highest degree characteristic. 
 The presence in the flame of each particular chemical 
 element determines the presence in its light of some one 
 or more coloured rays of definite refrangibility and colour, 
 producing often in its spectrum the appearance of a 
 definite line of coloured light out of all proportion 
 brighter than the rest. Thus the presence of soda in 
 any flaming body is characterized by a narrow and 
 exceedingly vivid line of yellow light. So completely 
 characteristic are these lines of the chemical elements to 
 which they bear relation, that no less than four new 
 metals, Thallium, Rubidium, Caesium, and Indium owe 
 their first discovery to the observation of definite spectral 
 lines of their appropriate colour, produced by their 
 presence in quantities too minute to be rendered sen- 
 sible in any other manner.* 
 
 (51.) It is impossible in the compass of a lecture like 
 the present, to do more than notice with extreme brevity 
 these remarkable classes of phenomena, and that only 
 as bearing upon the general object we have in view. 
 They prove in the most convincing manner the close 
 and intimate relation in which LIGHT stands to MATTER. 
 It enters into the interior of the hardest and least pene- 
 trable bodies, and thereout brings us information of an 
 
 *"In reference to what is now called " Spectrum Analysis," in a 
 chemical point of view, I may be here allowed to call attention to a 
 passage in my "Treatise on Light," published in 1827 (Encyc. 
 Metrop., vol. iv.): "The colours thus communicated by the dif- 
 ferent bases to flame, afford in many cases a ready and neat way ot 
 detecting extremely minute quantities of them." -Article, " Light,"
 
 ON LIGHT. 267 
 
 almost infinite variety of particulars as to their intimate 
 nature and constitution (and, as we shall see further on, 
 of their internal structure, and the mechanism by which 
 they are held together as bodies), which by no other 
 means we can obtain : information which at present we 
 are only imperfectly able to interpret, but whose import, 
 from year to year, and almost from week to week, is 
 becoming better understood. Its language in this 
 respect bears no distant similitude to that of a series 
 of ancient inscriptions in some unknown tongue and 
 character. A single sentence once developed by some 
 happy and unmistakable concurrence of evidence, affords 
 a clue to others, which in their turn become the step- 
 ping-stones of further progress. By the one are revealed 
 the histories of ages long buried in oblivion, and of the 
 phases of human thought and action under circumstances 
 bearing little analogy to anything we now see around us : 
 by the other we are admitted a step nearer to the per- 
 ception of the intimate working of those powers which 
 maintain the material universe as it stands, and the laws 
 they observe.
 
 LECTURE VIL 
 ON LIGHT. 
 
 PART II. THEORIES OF LIGHT INTERFERENCES 
 
 DIFFRACTION. 
 
 [WO theories only, entitled to any consideration 
 as rational and intelligible explanations of 
 the phenomena of Light, have been ad- 
 vanced the one proposed by Sir Isaac 
 Newton, commonly known as the "Corpuscular/' the 
 other by Christian Huyghens, as the " Undulatory" 
 theory. According to the former, light consists in 
 " Corpuscules," or excessively minute material particles 
 darted out in all directions from the luminous body, 
 in virtue of some violent repulsive power, or other en- 
 ergetic form of internal action, acting under such cir- 
 cumstances, and under such laws, as to give them all the 
 same initial velocity which they retain unchanged in their 
 progress through space, as well as their initial direction 
 according to the general laws of motion (to all which 
 they implicitly conform), until they meet with some mate- 
 rial body by whose action their course is changed. Afl
 
 ON LIGHT. 269 
 
 this, and all subsequent changes of direction and velo- 
 city, are held, on this theory, to be effected by attractive 
 or repulsive powers resident in the bodies on which the 
 light-corpuscules fall (or, which comes to the same thing, 
 in the corpuscules themselves), and from which they are 
 either reflected, if the repulsive powers be too strong to 
 permit their penetration; or in which they are refracted, 
 if they are able to enter and make their way among the 
 particles of the refracting body. Colour, according to 
 this theory, is accounted for by specific diversity among 
 the luminous particles ; and difference of refrangibility, 
 by differences in the intrinsic energy of the acting forces 
 as determined by the specific nature of the molecules, 
 or, which comes to the same, by a difference of propor- 
 tion between their moving force and their inertia. This 
 is one of the many weak points of the theory. It runs 
 counter to the only analogy which the observation 
 of nature furnishes. It is as if the sun should be sup- 
 posed to attract a planet of lead and one of cork with 
 different accelerating forces; or as if, here on earth, a 
 lump of platina and a lump of iron should be supposed 
 to acquire different velocities in falling through the same 
 space. It runs counter, too, to the original assumption, 
 that when first emitted from a luminous body, in their 
 passage through empty space, all the coloured particles 
 move with equal velocities, and have therefore been 
 equally accelerated by the emitting forces. That they do 
 so, we know from astronomical observation. The Aber- 
 ration of all the coloured rays is the same. Were it not 
 so, every star seen through a highly magnifying telescope
 
 VJO ON LIGHT. 
 
 ought to appear as drawn out into a short, coloured 
 spectrum in a certain definite direction. Light requires 
 forty-two minutes to reach the earth from Jupiter at its 
 mean distance. Supposing the rays of one end of the 
 spectrum the violet, for instance to travel faster than 
 those at the other (the red), a satellite undergoing 
 eclipse by immersion in the shadow of the planet ought 
 to change colour before extinction, from white to red 
 the last-emitted red rays lagging behind the violet on 
 their journey to the earth ; while at its reappearance a 
 blue colour ought to be first perceptible. 
 
 (53.) Among the stars are many which vary periodi- 
 cally in brightness, and some of them undergo complete 
 extinction. As light takes several years to travel from 
 the stars, the difference in the times of arrival for any 
 sensible difference of velocity would amount to many 
 days, and would be quite sufficient to tinge the disap- 
 pearing and reappearing star with the hues belonging to 
 opposite ends of the spectrum. No such thing, how- 
 ever, is observed. Most of them retain their whiteness; 
 and though some do assume a deep-red colour when un- 
 dergoing extinction, or when at their minimum of splen- 
 dour, it is not changed to blue at their reappearance, or 
 on their commencing augmentation of brightness. 
 
 (54.) The reflexion and refraction of light are, as we 
 have stated, accounted for on this theory by supposing 
 the particles of all material bodies, besides the attractive 
 force of gravitation, to be endowed with other forces, 
 both attractive and repulsive the latter extending to a 
 greater distance than the former, so as to constitute an
 
 ON LIGHT. 271 
 
 attractive and a repulsive sphere one within the other 
 the particles of light being repelled while passing through 
 the outer or repulsive sphere, and attracted when arrived 
 within the internal or attractive one. These forces are 
 supposed immensely energetic, and to decrease with such 
 excessive rapidity as to be absolutely insensible at any, 
 the very smallest, distance appretiable to our senses. In 
 virtue of this repulsive force, the surface of any mate- 
 rial body may be conceived as coated (metaphorically 
 speaking) with a film of repulsive power, off which, as 
 from an elastic cushion, the luminous particles may be 
 imagined to rebound : in which case, according to the 
 known laws of elastic rebound, the angle of reflexion 
 (perfect elasticity being supposed) would be equal to 
 that of incidence, and the velocities before and after re- 
 flexion equal. 
 
 (55.) Reflexion, then, is easily and readily explained 
 on this theory. In fact, it is explained too well. For it 
 will be at once asked, how, on such suppositions, there 
 can be such a thing as partial reflexion. Since all the 
 luminous particles of a ray arrive at (suppose) a plane 
 surface in the same direction and with the same velocity; 
 whatever happens to one, the repulsive force being the 
 same, must happen to all. This is another weak point of 
 the corpuscular theory; and to escape from the difficulty 
 so created, it becomes necessary to supplement the 
 original hypothesis of luminous particles with another, 
 converting those particles into mechanisms of a peculiar 
 nature, of which the simplest conception that can be 
 formed is to suppose them as it were minute magnets
 
 272 ON LIGHT. 
 
 having attractive and repulsive poles, and during their 
 progress through space revolving round their own centres 
 about axes not coincident with the direction of their 
 motion. Under such circumstances it is clear that some 
 might arrive at the reflecting surface with the attractive 
 pole foremost others with the repulsive. The former 
 would be attracted, and escape the reflective action ; the 
 latter repelled, and therefore subjected to it. Or, with- 
 out making any supposition as to the sort of mechanism 
 by which such a result might be attained, we might con- 
 tent ourselves with assuming, as Newton (the framer of 
 this hypothesis) did, that the particles of light, through- 
 out their whole progress through space, pass periodically 
 through a succession of alternating physical states or, 
 as he called them, " fits " " of easy reflexion and easy 
 transmission :" the only objection to such a form of 
 statement being, that it conveys no clear physical con- 
 ception to the mind. 
 
 (56.) The particles so escaping reflexion are conceived 
 to have penetrated within the limit of the repulsive, and 
 to have entered that of the attractive forces, while yet at 
 some inconceivably minute distance outside of the actual 
 surface of the medium. Their movement of approach 
 therefore to the surface is accelerated by the attractive 
 force whose resultant direction is perpendicular to the 
 surface, and when they have arrived within the medium 
 so far that all further action ceases (by the counteraction 
 of equal and opposite forces on all sides) each of them 
 will have undergone the total amount of acceleration 
 due to the attractive force in the direction of thatforce^
 
 ON LIGHT. 273 
 
 i.e., at right angles to the surface. Its velocity esti- 
 mated in this direction will therefore be greater within 
 the medium than without while that parallel to the 
 surface remains unchanged : the force in that direction 
 being nil. The direction of the motion therefore will 
 be more highly inclined to the surface within the medium 
 than without, in the same manner and for the very same 
 reason, that the path of a projectile shot obliquely down- 
 wards from the top of a hill makes a greater angle with 
 the horizon when it reaches the ground than it did in the 
 commencement of its descent. And the conclusion, on 
 strict dynamical principles, is the same in both cases. 
 Supposing the initial velocity of projection the same, the 
 sines of the angles made by the direction of the motion 
 with the vertical or perpendicular to the surface, at the 
 beginning, and at the end of the descent (i.e., in the case 
 of light, those of the angles of incidence and refraction), 
 will be to each other in an invariable proportion, the 
 total height of the descent being the same. Thus we see 
 that the law of refraction is satisfactorily accounted for, 
 on the corpuscular hypothesis ; and that, on that theory, 
 the velocity is greater in the interior of a refracting 
 medium than in empty space; and the more so, the 
 greater the refractive power. 
 
 (57.) Let us now see in what sort of conclusion we are 
 landed as to the intensity of the forces we have pressed 
 into our service. To consider only the reflective force, 
 we have this to guide us that, supposing the incidence 
 perpendicular, and the light therefore reflected back by 
 the path of its arrival, that force must have been suffici- 
 
 s
 
 274 ON LIGHT. 
 
 ently great to destroy the whole velocity of the luminous 
 particle, and to generate an equal one in the opposite 
 direction, in the time occupied by the particle in travers- 
 ing forwards and backwards the thickness of our stratum 
 of reflecting force. Now the velocity of light, as we have 
 seen, is 186,000 miles per second. To destroy and re- 
 produce this velocity in a projectile shot directly upwards, 
 by the force of gravity on the earth, supposed uniform or 
 undiminished by distance, would require its action to be 
 continued for 706 days, or very nearly two years, while 
 the same effect has to be produced by the reflecting force 
 (also supposed uniform), in that inappretiable instant of 
 time in which the act of reflection is performed a time 
 which would be extravagantly overrated at the billionth* 
 part of a second. After this we need hardly trouble our 
 readers with any estimation of the intensity of the re- 
 fracting forces. The sturdiest philosophy may fairly 
 be staggered at such a postulate as the foundation of a 
 physical theory. 
 
 (58.) According to the "undulatory theory" light con- 
 sists in an undulatory or vibratory movement propagated 
 through an elastic medium "pervading all space, not even 
 excepting what is occupied, or seems to be occupied, by 
 what we call material bodies that is, such as have weight, 
 and which, to us, constitute the visible and tangible uni- 
 verse of things. It therefore resembles sound, which is 
 not a travelling entity, but a propagated motion in the air, 
 analogous to the tremulous movement which runs from 
 
 * A billion is a million times a million. The French milliard it 
 a thousand millions.
 
 ON LIGHT. 275 
 
 end to end of a stretched cord, or to the waves which ap- 
 pear to travel along the surface of water ; though in reality 
 such a wave is only an advancing form, the real move- 
 ment of the watery particles being vertically up and down. 
 Colour in this view of the subject is analogous to tone, or 
 pitch, in music (if it be supposed to depend solely on re- 
 frangibility). As the frequency of the vibrations which 
 reach the ear from a sounding-string determines the pitch 
 of the musical note it yields, so the frequency of the un- 
 dulations of this elastic medium or luminiferous " ether" 
 as it is called, determines to the nerves of the eye the 
 colour of the light. Or in that view of colour which 
 considers all but three primary hues composite, it must 
 on this theory be assimilated to a difference analogous to 
 quality in a musical tone as, for instance, between the 
 sounds of a violin, a flute, and a trumpet, only much 
 more decided and strongly characterized. 
 
 (59.) As sound spreads through the air with equal rapid- 
 ity in all directions, and may be considered as propagated 
 from its origin as a spherical shell continually enlarging, 
 so in this theory must light be regarded as the move- 
 ment of a WAVE in the ether, running out spherically in 
 all directions from the luminous point, whose situation 
 with respect to the eye, or to any other point on which 
 the wave may strike, is judged of as the centre of the 
 sphere i.e., as lying in a line perpendicular to its sur- 
 face. A ray of light then, in this theory, is a purely 
 imaginary line from such point, perpendicular to the 
 general surface, or front of the wave, and has no other 
 meaning. The wave, not the ray, is the primary object
 
 276 ON LIGHT. 
 
 of contemplation. If the point where the luminous ex- 
 citement originates be near, the -perpendiculars from it 
 to the wave-surface diverge conically ; but if so far re- 
 mote that the portion of that surface at the eye may be 
 regarded as sensibly plane, they are to all sense parallel, 
 as in the case of light emanating from the stars or the 
 sun. 
 
 (60.) The reflection of light in this theory is in exact 
 analogy with that of any other undulatory movement 
 We cannot see the waves of sound, but those on smooth 
 water are easily followed and their reflexion made matter 
 of ocular inspection. Drop a small pebble into still 
 water, and a wave will be seen to spread out in an en- 
 larging ring. Let this be done near the perpendicular 
 and smooth side of any large tank or pond, or near a 
 board held vertically in the water, and the ring will be 
 seen on reaching the board to be reflected, and will 
 thence spread back over the surface, still enlarging, as 
 the segment of another ring whose centre might be sup- 
 posed as far on the land side of the reflecting surface as 
 the place where the pebble was dropped was in reality 
 on the water side. If several pebbles be dropped in 
 succession, or a regular up-and-down movement given 
 to the water at that point, a continued series of circular 
 waves will be generated and reflected, the reflected 
 waves running out and intersecting the direct exactly as 
 if they originated in two distinct centres. What in water 
 is seen to be a reflected wave, in air we recognize as an 
 echo. And in the fact that a sound, though partially re- 
 flected as such from a window, a board partition, or a
 
 ON LIGHT. 
 
 wall, is heard, though with diminished intensity, on the 
 other side, we have the analogue to the partial reflexion 
 of a beam of light at a transparent surface ; and on the 
 other hand, in the deadening of sound in passing through 
 woolly or puffy substances, while it is transmitted with 
 exceeding sharpness and distinctness through compact 
 solids or through water, we have the parallel to the 
 absorption of light in some media, and its copious trans- 
 mission through others. 
 
 (61.) The explanation of refraction on the undulatory 
 theory is exceedingly simple. Suppose a plane wave to 
 sweep obliquely along the surface B E of a medium 
 capable of propagating within it the luminiferous undu- 
 lation, and let it be supposed at equal intervals of time 
 
 Fie. 4- 
 
 (successive seconds, for instance) to assume successive 
 positions B b, c c, D d, EC, arriving in succession at 
 equidistant points B c D E of the surface. So soon as
 
 278 ON LIGHT. 
 
 any point in the surface is struck by the wave it will be 
 set in undulatory motion and propagate from it a move- 
 ment which will run out spherically from that point in 
 all directions with such (uniform) velocity as belongs 
 to the luminous undulation in the medium. When, there- 
 fore, the wave has reached the position E e, E will just 
 have begun to move ; the internal wave propagated from 
 D will have travelled during one second, from c two, 
 from B three seconds, and the motion, in virtue of 
 these, respectively, will have extended to the surfaces of 
 spheres about those points as centres, having radii in 
 the proportions i, 2, 3, so that a plane passing through 
 E, which touches one of them, will touch them all, and 
 the same is true for all points intermediate between 
 these. Such a plane will define the limit up to which the 
 movement has reached within the medium when the ex- 
 terior wave has the position E e, and will, therefore, be 
 the front of a plane wave advancing within it. If the 
 velocity of the undulation within the medium be the 
 same as without, DO, c N, B M, the radii of our spheres 
 will be equal to E H, E G, E F, the spaces run over in 
 one, two, three seconds outside, and the touching plane 
 E o N M will evidently be a continuation of the exterior 
 plane wave e E. In this case, then, there is no refrac- 
 tion, the direction of the interior ray B M being the same 
 as A B, perpendicular to the exterior wave. But suppose 
 the velocity within the medium less than that without. 
 In that case the radii of our spheres D R, c Q, B p, will 
 be less than D o, c N, B M, and in a constant proportion. 
 The plane E P touching them all then, or the front of
 
 ON LIGHT. 279 
 
 the interior wave will be inclined at a less angle B E p to 
 the surface than B E M, or its equal E B F, and the sines 
 of these angles to a common radius E B are evidently in 
 the proportion to each other of P B to B M, or of the velo- 
 city of light in the medium to the velocity out of it. Now, 
 as the ray is perpendicular to the wave, the inclination of 
 the latter to the surface is the same as that of the former 
 to the perpendicular, and thus these angles are respec- 
 tively identical with those of refraction and incidence. 
 
 (62.) To such of our readers as may find a difficulty in 
 following out this reasoning, the following familiar illus- 
 tration will convey a full conception of its principle. 
 Imagine a line of soldiers in march across a tract of 
 country divided by a straight boundary line into two 
 regions, the one smooth, level, and well adapted for 
 marching, the other difficult, rough, and in which from 
 its nature the same progress cannot be made in the same 
 time. Suppose, moreover, their line of front oblique to 
 the line of demarcation between the two regions, so that 
 the men shall arrive at it in succession, and not simul- 
 taneously. Each man, then, from the moment he has 
 stepped across this line, will find himself unable to make 
 the same progress as before. He will be therefore un- 
 able to keep line with that part of the troop which is 
 still on the better ground, but must of necessity lag be- 
 hind ; and that, by the greater space, the longer he 
 travels. Since each man on his reaching the line of di- 
 vision experiences the same difficulty: if they will not 
 break line and straggle, but persist in still marching in 
 line and keeping up their connexion, it will follow of
 
 8o ON LIGHT. 
 
 necessity that the front of their line must to a certain ex- 
 tent fall back and make an obtuse angle at its point of 
 junction with that of the unimpeded line. Thus, in our 
 figure, B E will represent the line of division between the 
 two regions, B b the advancing front of the troop when 
 the first man arrives at that line, E e that of the portion 
 still on the good ground after some time elapsed, and 
 EP that of the other portion who have been unable to 
 keep up to the same rate of march. And as the neces- 
 sity of keeping step and not crossing each other's line 
 of march will oblige each man to step out right in front 
 (i.e., at right angles to the new frontage), the progress, 
 B P, made by the first man after crossing the line, will be 
 perpendicular to E P, and will be to what he would have 
 made (B M) had it not been for the retardation, in the 
 proportion of his new to his former velocity of march. 
 
 (63.) Thus then we see that when light passes (in this 
 theory) out of what is called a rarer medium into a 
 denser, or when the angle of refraction is less than that 
 of incidence, the velocity of propagation of the undulatory 
 movement is diminished, while on the corpuscular doctrine 
 it is increased, and vice versa. Thus, too, we see that on 
 the undulatory hypothesis the connexion between refran- 
 gibility and velocity within the refracting medium is im- 
 mediate and absolute, and consequently that it being cer- 
 tain, as we have shown, that light of all refrangibilities 
 travels equally fast in what we call empty space (i.e., 
 through the ether alone), it follows with equal certainty 
 that in material media the more refrangible rays are pro- 
 pagated slower than the less so ; and all, more slowly than
 
 ON LIGHT. 28l 
 
 in free space. In other words, this amounts to suppos- 
 ing the elastic force of the ether either to be enfeebled 
 in the interior of material bodies, or else that the move- 
 ments of its particles are in some way or other clogged or 
 burthened by some sort of connexion with or adhesion 
 to the material molecules among which they are dissem- 
 inated, and that more for the more refrangible rays than 
 for the less so. 
 
 (64.) Until lately this difference of velocity between 
 the differently refrangible rays had always been consi- 
 dered an insuperable obstacle to the admission of the 
 undulatory hypothesis. All sounds of whatever pitch (it 
 was contended) travel equally fast in one and the same 
 elastic medium. The profounder researches of later 
 mathematicians, however, have shown that this conclu- 
 sion is not absolute, and that on certain suppositions 
 which are not altogether inadmissible in respect of the 
 vibrations of light, the difference is not contradictory to 
 strict dynamical laws. 
 
 (65.) As we have attempted to form an estimate of the 
 intensity of the forces required to account for observed 
 facts on the corpuscular hypothesis, let us now attempt 
 a parallel estimate on the undulatory. And here the 
 way is equally open and obvious. Starting with the ob- 
 served facts, that sound travels in air at the rate of 1090 
 feet per second, while light is propagated through the 
 ether 186,000 miles in the same time (that is to say, 
 901,000 times as fast), we are enabled to say how many 
 fold the elastic force of the air, or its resistance to com- 
 pression, would require to be increased in proportion to
 
 282 ON LIGHT. 
 
 the inertia of its molecules, to give rise to an equally rapid 
 transmission of a wave through it. For it results from 
 the theory of sound that in media of different elasticities 
 (so understood), but similarly constituted in other re- 
 spects, these forces are to each other as the squares of 
 the velocities with which the waves travel : so that the 
 elastic force of the air would require to be increased in 
 the proportion of the square of 901,000 (i.e., 811,801 
 millions) to i, to produce an equal velocity. Even this 
 enormous number must be still further increased, since 
 the velocity of sound is augmented by a peculiarity in 
 the constitution of air which we should hardly be justified 
 in attributing to the luminiferous ether, in virtue of 
 which its elasticity is increased by heat given out in the 
 act of its compression, and without which the velocity of 
 sound would be only 916 feet per second instead of 
 1090. Thus the number above arrived at has to be 
 further increased in the proportion of the square of 1090 
 to that of 916, which brings it to 1,148,000,000,000. 
 Let us suppose now that an amount of our etherial 
 medium equal in quantity of matter to that which is con- 
 tained in a cubic inch of air (which weigh* about one- 
 third of a grain) were enclosed in a cube of an inch in the 
 side. The bursting power of air so enclosed we know to 
 be 15 Ibs. on each side of the cube. That of the impri- 
 soned ether then would be 15 times the above immense 
 number (or upwards of 17 billions) of pounds. Do what 
 we will adopt what hypotheses we please there is no 
 escape, in dealing with the phsenomena of light, from 
 these gigantic numbers ; or Irom the conception of enor-
 
 ON LIGHT. 283 
 
 tnous physical force in perpetual exertion at every point, 
 through all the immensity of space. 
 
 (66.) As this is the conclusion we are landed in (for 
 the evidence for the truth of the undulatory doctrine, or 
 something equivalent to it, accumulating, as we shall see, 
 in all quarters, and in the most unexpected manner re- 
 ceiving confirmation from facts utterly uncontemplated 
 by its originator, obliges us to look on this result as some- 
 thing more than a scientific rhodomontade) we shall 
 endeavour to present it to the conception of our readers 
 in a point of view which may enable them to realize it 
 more distinctly. All who know the nature of a baro- 
 meter are aware that the column of mercury 30 inches 
 in height sustained in its tube, is the equivalent of the 
 pressure of the aerial ocean which covers us, on its sec- 
 tional area ; and is just sufficient to counterbalance the 
 pressure, on an equal area, of an atmosphere five miles 
 in height of air everywhere of the same density as at the 
 surface of the earth. This height (five miles) is what is 
 termed in Barometry, " the height of a homogeneous 
 atmosphere," and affords a measure of what may be 
 called the intrinsic elasticity of the air, of an exceedingly 
 convenient nature ; and which is received as a kind of 
 natural unit, in Meteorology and Pneumatics. Substi- 
 tuting now light for sound, and for air the luminiferous 
 ether, we should have for the corresponding height of 
 our homogeneous atmosphere (gravity being supposed 
 uniform) five and a half billions of miles, or about one- 
 third of the distance to the nearest fixed star! The 
 measure thus afforded of intrinsic elastic power is of the
 
 284 ON LIGHT. 
 
 same kind as that afforded of the intrinsic tensile strength 
 of a wire or thread of any material by the statement of 
 how much in length of itself it can bear without break- 
 ing. It frees us from the necessity of any mental refer- 
 ence to the actual weight or specific gravity of the 
 material, which in this case is the more necessary, as, 
 though we suppose the ethereal molecules to possess 
 inertia, we cannot suppose them affected by the force of 
 gravitation. 
 
 (67.) There is yet another theory of light which might 
 be proposed, in which, still retaining the idea of an 
 ethereal medium, its constitution should be conceived 
 as an indefinite number of regularly arranged equidistant 
 points (mathematical localities) absolutely fixed and im- 
 movable in space, upon which, as on central pivots, the 
 molecules of the ether, supposed polar in their constitu- 
 tion, like little magnets (but each with three pairs of poles, 
 at the extremities of three axes at right angles to each 
 other), should be capable of oscillating freely, as a com- 
 pass-needle on its centre, but in all directions. Any one 
 who will be at the trouble of arranging half a dozen 
 small magnetic bars on pivots in the linear arrangement 
 of the annexed figure, will at once perceive how any 
 
 M "M M K ' V M - 
 
 F"ig-5- 
 
 vibratory movement given to one, at any point of the 
 chain, will run on, wave-fashion, both ways through its 
 whole length. And he will not fail to notice that the
 
 ON LIGHT. 385 
 
 bodily movement of each vibrating element will be 
 transverse to the direction of the propagated wave a con- 
 dition which, as we shall hereafter see, is essential to be 
 fulfilled in the luminous undulations. As this hypo- 
 thesis, however, has hitherto received no discussion, and 
 is here suggested only as one not unworthy of consider- 
 ation, however strange its postulates, we shall not dwell 
 on it ; remarking only that every phsenomenon of light 
 points strongly to the conception of a solid rather than 
 a fluid constitution of the luminiferous ether, in this 
 sense, that none of its elementary molecules are to be sup- 
 posed capable of interchanging places, or of bodily transfer 
 to any measurable distance from their own special and 
 assigned localities in the universe. The constitution 
 above suggested would merely superadd to this abstract 
 idea of a solid structure, the further conception of polar 
 forces bearing some general analogy to those which may 
 possibly subsist among the gross particles of a tesseral 
 crystal 
 
 (68.) This would go to realize (in however unexpected 
 a form), the ancient idea of a crystalline orb. And it 
 deserves notice that under no conception but that of a 
 solid can an elastic and expansible medium be self-con- 
 tained* If free to expand in all directions, it would 
 require a bounding envelope of sufficient strength to 
 resist its outward pressure. And to evade this by sup- 
 posing it infinite in extent, is to solve a difficulty by 
 words without ideas to take refuge from it in the 
 
 From a liquid the extreme particles would be constantly flying 
 off in vapour and dissipating themselves in space.
 
 *86 ON LIGHT. 
 
 simple negation of that which constitutes the difficulty. 
 On the other hand, such a "crystalline orb" or "firma- 
 ment" of solid matter conceived as a hollow shell of 
 sufficient strength to sustain the internal tension, and 
 filled with a medium attractively, and not repulsively 
 elastic, might realize (without supposing a solid struc- 
 ture in the contained ether) the condition of transverse 
 vibration ; by establishing, if so facto, lines of tension in 
 every possible direction, along which undulations might 
 be conveyed, like waves along a stretched cord, thus- 
 furnishing a fourth hypothesis, which, to those fond of 
 such speculations may afford matter, sui generis, for con- 
 sideration. 
 
 (69.) Interference of the rays of light. There is hardly 
 a more beautiful or a more instructive object in nature 
 than a large well-blown soap-bubble. Whether we con- 
 sider the perfect regularity of its form, illustrating, as it 
 does, in its exact equilibration the - great mechanical 
 laws to which the sun and planets owe their spherical 
 figure demonstrating, by its resistance to disruption by 
 blasts of wind which distort it, and by its ready and 
 complete resumption of its normal shape on their cessa- 
 tion, the powerful tensile force which holds it together ; 
 and proving, by the instantaneous collection of its filmy 
 tissue into water-globules, in the act of bursting, the 
 immense intrinsic energy of that force as compared with 
 gravitation to the mechanician it is fraught with matter 
 of the highest interest To the photologist, on the other 
 hand, the vivid colours which glitter on its surface afford 
 at once the simplest and most elegant optical illustra-
 
 ON LIGHT. 287 
 
 tion of the " law of interference " of the rays of light : a 
 law .we shall now proceed to explain, taking for our 
 first exemplification of it this very phenomenon. 
 
 (70.) If a soap-bubble be blown in a clean circular 
 saucer with a very smooth, even rim, well moistened 
 with the soapy liquid,* and care be taken in the blowing 
 that it be single, quite free from any small adhering 
 bubbles, and somewhat more than hemispherical ; so 
 that, while it touches and springs from the rim all round, 
 it shall somewhat overhang the saucer : and if in this 
 state it be placed under a clear glass hemisphere or 
 other transparent cover to defend it from gusts of air 
 and prevent its drying too quickly ; the colours, which 
 in the act of blowing wander irregularly over its surface, 
 will be observed to arrange themselves into regular 
 circles surrounding the highest point or vertex of the 
 sphere. If the bubble be a thick one (/.<?., not blown to 
 near the bursting point), only faint, or perhaps no colours 
 at all will at first appear, but will gradually come on 
 growing more full and vivid, and that, not by any par- 
 
 * M. Plateau gives the following recipe for such a liquid, i. 
 Dissolve one part, by weight, of Marseilles soap, cut into thin slices 
 in forty parts of distilled water, and filter. Call the filtered liquid 
 A. 2. Mix two parts, by measure, of pure glycerine with one part 
 of the solution A, in a temperature of 66 Fahr., and after shaking 
 them together long and violently, leave them at rest for some days. 
 - A clear liquid will settle, with a turbid one above. The lower is 
 to be sucked out from beneath the upper with a siphon, taking the 
 utmost care not to carry down any of the latter to mix with the 
 clear fluid. A bubble blown with this will last several hours even 
 in the open air. Or, the mixed liquid, after standing twenty-four 
 hours, may be filtered,
 
 288 ON LIGHT. 
 
 ticular colour assuming a greater richness and depth of 
 tint, but, by the gradual withdrawal of the faint tints 
 from the vertex, while fresh, and more and more in- 
 tense hues appear at that point, and open out into cir- 
 cular rings surrounding it ; giving place as they enlarge 
 to others still more brilliant, until at length a very bright 
 white spot makes its appearance, quickly succeeded by 
 a perfectly black one. Soon after the appearance of 
 this the bubble bursts. During the whole process it has 
 been growing gradually thinner by the slow descent of 
 its liquid substance on all sides from the vertex, till at 
 length the cohesion of the film at that point gives way 
 under the general tension of the surface. The annular 
 arrangement of the colours, and the coincidence of their 
 common centre with this, the thinnest point of the film, 
 evidently go to connect their tints with the thicknesses 
 of that film at their points of manifestation, and to indi- 
 cate that a certain tint is developed at a certain thickness, 
 and at no other. This, we shall presently see, is really 
 the case. 
 
 (7 1.) The order of the colours and the sequence of the 
 tints is in all cases one and the same, provided the series 
 be complete, i.e., provided time has been given for the 
 black central spot to form. Thus the first series, or 
 order, contained within the first ring consists of black, 
 very pale blue, brilliant white, very pale yellow, orange, 
 red ; tJie second of dark purple, blue, imperfect yellow- 
 green, bright yellow, crimson ; the third of purple, blue, 
 grass green, fine yellow, pink, crimson ; the fourth of 
 bluish-green, pale pink inclining to yellow, red ; the
 
 ON LIGHT. 289 
 
 fifth pale bluish-green, white, pink. After these the 
 colours grow paler and paler, alternately bluish-green 
 and pink, and can hardly be traced beyond the seventh 
 order. 
 
 (72.) None of these tints are pure prismatic colours. 
 To see them to the best advantage the bubble with its 
 glass shade should be placed out of direct sunshine, 
 where only dispersed light, such as that of a cloudy sky, 
 shall fall on it. Or, the illumination of the rings may be 
 effected by a thin semi-transparent paper, or a groxmd- 
 glass screen interposed between them and the incident 
 light. And if, instead of illuminating this with the direct 
 light of the sky, the coloured rays of a spectrum, formed 
 by passing a sunbeam through a glass prism, be thrown 
 upon it, the composite nature of their tints will be at 
 once apparent. If all the rays but those at the red end 
 of the spectrum be excluded from the illuminating beam, 
 the rings will appear wholly red, separated by black 
 intervals, and much more numerous. And if, now, the 
 colour of the illuminating light be changed, so as to pass 
 in succession through the whole prismatic scale of tints 
 orange, yellow, green, &c., from the red to the violet 
 the colour of the rings will undergo a corresponding 
 change, the dividing intervals preserving their blackness, 
 bit their number still continuing greater than in white 
 light. But, besides this, a very remarkable phenomenon 
 will be observed. The rings contract rapidly in diametet 
 as the colour of the illumination changes, being a maxi- 
 mum foi a red and a minimum for a violet illumination ; 
 and if, by a slight movement given to the prism, the 
 
 I
 
 29O ON LIGHT. 
 
 spectrum be made to traverse to and fro on the illumin- 
 ating screen, the rings will appear to open and close in 
 an exceedingly beautiful manner, undergoing at the same 
 time a corresponding change of colour. 
 
 (73.) The composite nature of the rings, as seen in 
 white light, is now abundantly clear. White light is a mix- 
 ture of all the prismatic rays, and the set of rings seen in 
 such light is of course a mixture of the several individual 
 sets (concentric, but differing by a regular gradation of size), 
 of all the several coloured elements of which white light 
 consists. Imagine a painter who could " dip in the 
 rainbow" and lay on, one after another, on the same 
 paper and with the same centre, such a series of rings 
 gradually decreasing in diameter, and each set tinted 
 with the pure prismatic hue which corresponds to its 
 size, from the extreme red to the extreme violet, in their 
 proper degrees of intensity ; he would produce just 
 such a series. If the diameters for all colours were 
 alike, the compound rings would evidently be white and 
 infinite in number, separated by black intervals. If they 
 differed only a little starting from a common origin 
 the first ring would be nearly white, but exhibiting a 
 bluish border inwards and a reddish outwards, growing 
 more and more " pronounced," and broken into inter- 
 mediate tints in those beyond ; but if considerable, the 
 rings of different orders for different colours would soon 
 mingle with and confuse each other's tints, creating the 
 sensation of uniform whiteness : thus accounting for the 
 comparative paucity of the mixed series.
 
 ON LIGHT. 29! 
 
 (74.) In order, then, clearly to understand the nature 
 of this phenomenon, it must be divested of this source 
 of complexity, and studied in reference to light of one 
 single colour or refrangibility or, as it is called, " homo- 
 geneous" light, pure red or yellow, for instance. But be- 
 fore proceeding further, something more must be said of 
 the whole class of phenomena referable to this head. 
 And first, these colours are not dependent in any way 
 on any colorific quality of the liquid of which the 
 bubbles consist. Any sufficiently thin film, of any kind, 
 suffices to produce them. They are seen in the oily 
 scum on the surface of a stagnant pool. They are seen 
 on the brilliant scales of old glass in stable windows, or 
 on the wings of gaudy-coloured insects, or even on 
 polished steel. Bubbles may be blown of a variety of 
 liquids nay, even of glass. However highly coloured, 
 their intrinsic colour disappears when reduced to such 
 extreme tenuity as is requisite for the purpose in ques- 
 tion. But all exhibit tJu same hues in the same invariable 
 order. Nay, more it requires no medium at all to pro- 
 duce them, but only an interval between two surfaces. 
 They are seen in the crack of a thick piece of glass 
 which does not extend quite through its whole substance. 
 They are seen when a piece of mica is partially split and 
 one of the laminae lifted up, following as a series of 
 coloured lines the limit of the commencing fissure. 
 It may be said that though no solid or liquid medium is 
 here present, there is air between the divided surfaces. 
 But under the exhausted receiver of an air-pump, there
 
 2Q2 ON LIGHT. 
 
 is no diminution of the colours, or alteration of their 
 forms. It is to the interval between the surfaces that we 
 have to look for their origin. 
 
 (75.) Here, then, we have LIGHT brought face to face 
 with SPACE, and no escape! What happens at or be- 
 tween these surfaces? How is it that while a single 
 surface reflects a dispersed beam of light indifferently 
 over its whole extent, this indifference is destroyed by 
 placing another reflecting surface behind it ; and the 
 reflexion (at least the effective reflexion as regards the 
 spectator) rendered impossible when the second surface 
 is at a certain distance, or at certain distances, from the 
 first; while if placed at intermediate distances, it is 
 either not at all affected, or only to a certain extent 
 enfeebled 1 and that, when there is nothing, or at least 
 nothing realizable to any of our methods of observation, 
 between them? This is the problem before us, reduced 
 to its simplest terms, a problem which the corpuscular 
 theory of light resolves imperfectly and unsatisfactorily, 
 and the undulatory fully and without reserve. 
 
 (76.) When instead of using the prismatic spectrum 
 (of which it is next to impossible to insulate from the 
 rest a ray of perfectly definite refrangibility) to illuminate 
 the film, we employ artificial light (such as that of a 
 spirit lamp with a salted wick, which may be considered 
 as almost perfectly homogeneous), the rings are seen 
 with extraordinary sharpness; their central spot and' their 
 divisions having the blackness of ink, and absolutely in- 
 numerable ; being traceable with a magnifier when too 
 close to be otherwise distinguishable, apparently without
 
 ON LIGHT. 293 
 
 limit. Thus disembarrassed of the complexity of over- 
 lapping rings of several colours, the phaenomenon now is 
 studied to greater advantage, and its explanation on 
 either theory is more readily intelligible. That afforded 
 by the corpuscular theory (supplemented by the New- 
 tonian hypothesis of the fits of easy reflexion and trans- 
 mission) is very simple and obvious. These "fits" or 
 phases, it will be remembered, are supposed periodically 
 recurrent i.e., succeed one another, or rather are re- 
 peated over and over again, in the same order and in- 
 tensity, at equal intervals of time. The same phase then 
 will recur to the corpuscules, at equidistant points of 
 space in their progress through any uniform medium (in 
 which the velocity of light is constant). Where the 
 thickness of the film is nil, or so very minute as to bear 
 no comparison to the distance which separates two of 
 the equidistant points, it is obvious that having passed 
 one surface they will still be in a state to pass through 
 another, and will therefore not be reflected, so that in 
 that case the reflected illumination of the first surface 
 will receive no augmentation from light reflected at the 
 second. The same is true if the thickness of the film be 
 exactly that of two such equidistant points, or its double, 
 triple, &c., for in those cases the corpuscule will arrive at 
 the second surface in the same state and with the same 
 dispositions as to reflexion or transmission as at the first ; 
 and therefore, having penetrated the first, will also pene- 
 trate the second. On the other hand, for thicknesses of 
 the film exactly intermediate between these, the cor- 
 puscule on arrival at the second surface will be exactly
 
 2Q4 ON LIGHT. 
 
 in the opposite state or disposition. Having been trans- 
 mitted then at the first, it will be reflected at the second, 
 and, having in its passage back through another equal 
 thickness reassumed its original state in which it first en- 
 tered, it will there be transmitted, and so will reinforce by 
 its light the general reflected illumination of that surface. 
 Since the per-centage of the total light reflected at any 
 transparent medium is but trifling, the light so sent back 
 from the second surface will be nearly equal to that re- 
 flected from the first. Thus for these exactly interme- 
 diate thicknesses, the joint-reflected illumination is very 
 nearly doubled, and between these and the former series 
 of thicknesses will increase and diminish alternately and 
 gradually. 
 
 (77.) Suppose now in the case of our soap-bubble 
 the thickness of the film to increase uniformly outwards 
 from its vertex (where it is nearly nit). Then it is evi- 
 dent that when exposed to dispersed light it will appear 
 divided into equivalent circular zones alternately bright, 
 and comparatively dark, the centre being also dark. And 
 here we have a representation of our observed rings, with, 
 however, this remarkable and most important difference, 
 viz. : that the central spot and the dark divisions, on this 
 explanation, ought not to appear absolutely black, but 
 half bright, when compared with the brightest portions 
 between them. In point of fact, some exceedingly slight 
 reflexion is perceivable in the dark centre, but instead 
 of half, it cannot be estimated at the fiftieth part of the 
 illumination of the bright ring which immediately ad- 
 joins it
 
 ON LIGHT. 
 
 295 
 
 (78.) As the thickness of a soap-bubble cannot be sub- 
 jected to direct measurement, it is impracticable, in its 
 case, to verify what must be considered the fundamental 
 principle of this explanation viz., the regular increase, 
 in arithmetical progression, of the thicknesses at which the 
 several successive black or bright rings appear. But of 
 this we may satisfy ourselves, by adopting a different 
 mode of producing and viewing them. When a spectacle- 
 glass or any other convex glass lens of long focus is laid 
 
 down upon a plane glass before an open window (both 
 being scrupulously clean and well polished), and a slight 
 pressure applied, the same dark spot, surrounded by the 
 same series of coloured rings, is seen, their centre being 
 at the point of contact of the glasses, where of course 
 their distance is nil. If the focal length of the leas be
 
 296 ON LIGHT. 
 
 not very large, they will require a magnifier to be well 
 seen, their diameters being in that case very small ; but 
 with a lens of 20 or 30 feet focal length it is consider- 
 able, and the rings may be seen, and their diameters 
 measured, with ease. Now it is found that these diame- 
 ters, for the first, second, third, &c., dark rings in order 
 (reckoned from the centre), are not in the proportion of 
 the numbers i, 2, 3, &c., but of the numbers i, i'4i4, 
 1732, 2-000, &c., which are their exact square roots, 
 giving to their system the appearance represented in the 
 preceding diagram ; and this is exactly the progression of 
 distances from the point of contact measured on the 
 surface of the plane glass which correspond to the 
 series of perpendicular distances between it and the convex 
 spherical surf ace of the upper glass in the proportion of the 
 arithmetical series, as may be seen in Fig. 7. 
 
 (79.) So far, then, the Newtonian hypothesis affords a 
 satisfactory account of the facts ; in all, that is, but that 
 one particular already adverted to. This, however, must 
 be considered as conclusive against it ; while, on a con- 
 sideration of the whole case, there remains outstanding 
 this strange fact that at certain distances between two 
 partially reflecting surfaces, forming a regular arithmetical 
 progression from nil upwards, the portion of a beam of 
 light reflected from the second, after passing back 
 through the first, so far from augmenting the first reflected 
 light, annihilates it, and furnishes us with an instance 
 (which is, as we shall see hereafter, not the only one) of 
 the combination of lights creating darkness ! 
 
 (80.) The question now arises, Will the undulatory
 
 ON LIGHT. 
 
 theory help us in this difficulty, while at the same time 
 rendering an equally satisfactory account of the other 
 facts ? To this we are enabled to reply in the affirma- 
 tive. Two equal sounds we know, under certain circum- 
 stances, can produce silence, as when the two strings 
 which, in a pianoforte, go to produce, when exactly in 
 unison, a uniform and liquid note ; if very slightly out 
 of tune, produce what are called beats, or a succession 
 more or less rapid (accordingly as the strings are more 
 or less discordant) of sound and silence. The same 
 tide-wave arriving at the same spots in the sea by two 
 courses of different lengths, results in producing no rise 
 and fall of the water at all, if the difference of path be 
 such that the high water of one portion shall reach 
 
 "x 
 
 
 
 
 O-< 
 
 
 2. 
 
 246 
 
 
 
 / 
 
 
 
 ^ 
 
 
 
 
 
 2 . 000 
 
 
 
 /" 
 
 
 
 
 
 ^> 
 
 
 
 1 
 
 7-3 a 
 
 
 ' 
 
 
 
 
 
 
 
 ^s^ 
 
 
 
 1 . 41 
 
 1 
 
 ^^^ 
 
 
 
 
 
 
 
 
 
 ""^-^^ ~ 
 
 1. 000 
 
 ^. *' 
 
 
 
 
 
 
 
 
 
 
 r ' ' 
 
 . "~~ 
 
 
 
 
 
 
 
 Fig. 7. 
 
 the place at the same moment with the low water of 
 the other. This is the case at a point in the North 
 Sea, midway between Lowestoft and the coast of Hol- 
 land, in lat. 52 27' N., long. 3 14' E. Its position was 
 pointed out by Dr Whewell from theory, and the fact 
 verified by Captain Hewett, R.N. 
 
 (8 1.) This latter exemplification contains the essential 
 principle of the explanation in question, in nearly its 
 simplest state. If two waves, or rather two regular series 
 of equal waves all exactly like one another, and all
 
 298 
 
 ON LIGHT. 
 
 having set out initially from one common origin, reach the 
 same point by two different channels or lines of com- 
 
 munication differing just so much in length that the
 
 ON LIGHT. 299 
 
 crests of the one series shall reach it at the same identi- 
 cal moment with the crests of the other ; the two series of 
 crests conspiring and being superposed on each other 
 will produce crests of double the height of either singly : 
 while, on the other hand, if the difference of channels be 
 such that the crests of the first series shall reach it simul- 
 taneously with the troughs (or lowest depressions) of the 
 second ; the one will destroy the other, and there will be 
 neither elevation nor depression at their joint point of 
 arrival. In the former case, supposing the two channels 
 thenceforward to unite into one (as in the annexed figures, 
 which require no explanation further than that the series 
 of cross lines represent the crests of the waves), the two 
 series when they reunite in a channel c D, as in Fig. 8, the 
 exact size of the initial one, A B, will form a joint series 
 exactly similar to that in A B, which will run on in that 
 channel thenceforward ; but in the latter, as in Fig. 9, there 
 will be produced no waves at all, and the water in c D 
 will (except just close to the point of junction, where 
 some kind of eddy will be formed) remain undisturbed. 
 
 (82.) Accepting the term "wave" in its most general 
 sense, in whatever way we suppose it propagated, whether 
 by alternate up-and-down movements of the successive 
 particles, as in water-waves by transverse lateral ones, 
 as in a stretched cord wagged horizontally or by direct 
 to-and-fro vibration, as in the air-waves, in which sound 
 consists or in any more complex manner, the same 
 considerations evidently apply. If two sets of exactly 
 equal and similar waves can by any previous arrange- 
 ment be made to arrive simultaneously '.at the "entrance"
 
 30O ON LIGHT. 
 
 of one and the same "channel" (using these terms also 
 in their most general sense) along which each set, separ- 
 ately, might be freely propagated i.e., so that the fore- 
 most crest of the first set shall strike the mouth of the 
 channel at the same moment with that of the other they 
 will combine and run on along the channel as a single 
 set or series of waves of double the height or intensity. 
 In this case they are said to arrive "in the same phase" 
 (a term borrowed from the phases of the moon which 
 passes periodically through the states of full and new, 
 increase and wane). The same will be the case if the 
 foremost crest of the series be so timed (by the previous 
 arrangements) as to reach the mouth of the channel 
 simultaneously with the second, third, or fourth crest of 
 the other, in which case the one set is said to be in 
 arrear or advance of the other (as the case may be) by 
 one, two, or more entire "undulations." On the other 
 hand, if the foremost crest of the one set be so timed as to 
 arrive simultaneously with the first, second, third, &c., 
 trough of the other up to the time of its arrival indeed 
 the one, two, or three foremost waves which are not con- 
 tradicted will run forward ; but, from the moment when 
 the others begin to arrive, they will cease to be followed 
 up by any more. In this case the one set is in advance 
 or arrear of the other by exactly one, or three, or five, 
 &c., semi-undulations, and the series are said to be in 
 opposite phases. In the intermediate " phases " it is easy 
 to see that a combined set of waves will be pro- 
 duced, but intermediate in height, intensity, or (as 
 it is called) "amplitude" between these two extremes
 
 ON LIGHT. 
 
 301 
 
 viz., nil on the one hand, and reduplication on the 
 other. 
 
 (83.) The vibrations by which light and musical sounds 
 (to which light is analogous) are conveyed are so exceed- 
 ingly minute, and the shock conveyed by each separately 
 to our nerves, in consequence, so small, that it requires 
 a continued series of them to impress our senses. The 
 first few vibrations therefore which run on " uninterfered 
 with " produce no sensation, and are as if they existed 
 not. And thus we see how it may happen, that in the 
 case of a complete opposition of phase two equal musical 
 sounds may produce silence, and two equal rays of light 
 complete and continued darkness ; that a perfect coinci- 
 dence of phase has the effect of doubling the sensation ; 
 and the intermediate states, a greater or less intensity as 
 the case may be, short of that limit 
 
 (84.) Let us now proceed to apply our principle (that 
 of "superposed and INTERFERING VIBRATIONS") to the 
 matter in hand. Suppose a series of equal and equidis- 
 tant light-waves (such as a ray of homogeneous light is 
 in this theory always understood to mean) to fall perpen- 
 dicularly upon a plate of any transparent medium. A 
 certain very small per-centage of it will be reflected back 
 by the first surface that is to say, a series of similar 
 undulations, but of much less intensity or " amplitude," 
 will be propagated back from the point of incidence. 
 The remainder of the total movement thus subdivided 
 will pass on, and, arriving at the second surface, again a 
 very nearly equal series (the per-centage being the same, 
 and the total incident light having suffered very little
 
 302 ON LIGHT. 
 
 diminution) will be returned, and, passing back through 
 the first surface (with only the same trifling per-centage of 
 loss), will, on emerging, be superposed on the first reflected 
 series, with which it will be coincident in direction. If 
 then the thickness of the plate be such that in passing 
 to the hinder surface, back again, and out at the first, the 
 second series shall have lost upon the first precisely one, 
 three, five, or any odd number of jm/-undulations, it 
 will begin to emerge in the exact opposite " phase " ot 
 its period to that of the undulation of the first reflected 
 series which starts from the same point at the same in- 
 stant Here, then, we have the case contemplated above 
 of two series of equal waves entering the same " chan- 
 nel" in opposite phases. They will therefore destroy 
 each other, or the intensity of the joint ray will be nil. 
 The contrary will happen if the thickness be such as to 
 produce a retardation of two, four, or any even number 
 of semi-undulations. In that case the two reflected rays 
 will conspire and produce a joint one of double inten- 
 sity: and of intermediate in the various cases of inter- 
 mediate retardation. 
 
 (85.) Thus we see that the degree of brightness of the 
 reflected light depends on the thickness of the reflecting 
 film, and that for a certain series of thicknesses in arith- 
 metical progression^ the joint reflection is nil; for another 
 series exactly intermediate, it attains a maximum "of inten- 
 sity; and between these limits, all gradations of illumina- 
 tion will arise according to the intermediate thicknesses 
 supposed to exist This is so far in general accordance with 
 the phaenomena described : but before applying it to the
 
 ON LIGHT. 303 
 
 case of our coloured rings, it must be mentioned that in 
 reckoning the number of undulations or semi-undulations 
 by which the second reflected ray actually is in arrear of 
 the first on emergence, we have to consider the different 
 modes in which the reflexion of a wave is accomplished 
 at the surface of a medium denser or rarer than that in 
 which it moves and is reflected. To present this clearly, 
 we will take the most familiar illustration that of the 
 propagation of motion by the collision of elastic balls. 
 Imagine a great number of equal ivory balls (supposed 
 perfectly elastic) in contact, but connected only by an elastic 
 string passing centrally through each and along the com- 
 mon axis of all ; and pinned or fastened to each at its centre 
 so that the separation of any two shall stretch only that 
 part of the string between their centres. Suppose now 
 that a shock is given to the extreme ball at one end in 
 the direction of the common axis, by another similar and 
 equal detached ball driven against it. By the received 
 laws of elastic collision it will give up its whole motion to 
 that which it first strikes, and be itself reduced to rest 
 In like manner the motion so communicated to the first 
 will be handed on undiminished to the second ; itself rest- 
 ing and therefore remaining in contact with the striking 
 ball, and so on. Thus what may be termed a " wave of 
 compression," will run along the series till it reaches the 
 ball at the other end. This, having none in front to 
 communicate its motion to, will start off; and, were it 
 free, would quit the series. But this it cannot do, by 
 reason of the elastic thread ; which however it will stretch 
 in its effort to do so, and be ultimately brought back
 
 ;04 ON LIGHT. 
 
 by its pull. But in so doing the same pull will also be 
 communicated to the ball behind it, drawing it forward, 
 and so in succession to those yet behind; and in this 
 manner, a wave of extension will run back along the 
 series. If the tension of the string be very violent (sup- 
 pose equal to the repulsive elasticity of the balls), this 
 wave will run back with the same -velocity as the other. 
 Here we have then a case of the reflexion of a wave, 
 where, in the very instant of reflexion, its character is 
 changed ipso facto from that of a wave of compression 
 to one of extension in other words, it starts backwards 
 in the opposite phase to that of its arrival ; or, again in 
 other words, a semi-undulation is lost or gained (for it 
 matters not which) in the act of reflexion, 
 
 (86.) This is the extreme case of reflexion from a 
 denser medium on a rarer for here there is absolutely 
 nothing to carry on the motion beyond the terminal 
 ball. Such a case never occurs in nature as regards 
 light ; since even what we call a vacuum is filled with 
 the luminiferous ether. To assimilate it to such as do 
 occur, suppose a second series of smaller balls, similarly 
 connected with each other, but not with the first set, and 
 brought end to end with it, with just room between for 
 one intermediate free ball of the smaller size to play 
 backwards and forwards as a go-between ; and let this, 
 in the first instance, be placed in contact with the last 
 ball of the first set When the movement reaches it, it 
 will be driven off, and immediately striking the end ball 
 of the second set, will propagate along // a wave of com- 
 pression, coming itself to rest. In so doing it will carry
 
 ON LIGHT. 305 
 
 off some, but not all of the motion of the terminal ball of 
 the first set This will still continue to advance after 
 the blow, but to a less extent, and with less momentum 
 than in the former case, and, just as in that case, will 
 propagate backward a wave, though a feebler one, of 
 extension. Starting, then, from the same place at the 
 same moment, the two waves the reflected portion (or 
 echo) and that which runs forward in the second set of 
 balls, set out each in its own direction in opposite 
 phases. 
 
 (87.) The intensity of the reflected wave or echo will 
 be feebler the nearer the balls of the two sets approach 
 to equality (or the less the difference of density in the two 
 media). If they are exactly equal, the go-between ball 
 will carry off all the motion of the ball which strikes it 
 or there will be no reflected wave, no echo. And this 
 agrees with fact. At the common surface of two trans- 
 parent media of equal refractive power, however they 
 may differ in other respects, there is no reflexion. But 
 suppose the second set of balls, as also the single inter- 
 mediate one, larger than the first. In that case (still 
 according to the laws of elastic collision) the last ball 
 of the first set not only will not advance after the shock, 
 but will be driven back, and the wave which it will pro- 
 pagate backwards will no longer be one of extension, 
 but of compression. This being also the case with that 
 propagated onwards in the second series, in this case 
 both will start on their respective courses from the point 
 of reflexion in the same phase. 
 
 (88.) In the uiidulatory theory of light the "denser" 
 
 u
 
 3O6 ON LIGHT. 
 
 medium corresponds to the series of larger balls in this 
 illustration. This ought to be so, for the velocity is less 
 in the denser medium as it is in the larger of two balls 
 after their collision ; and because, as already remarked, 
 the ether in such media must be either denser in propor- 
 tion to its elastic force, or somehow encumbered by 
 their material atoms. And hence we finally conclude 
 that in the act of the reflexion of light on the surface of 
 a rarer medium, the phase of the undv'ation changes, 
 and a semi-undulation is lost (or gained- it matters not 
 which) : but not so when the light is reflected from a 
 denser medium. 
 
 (89.) To return now to the case of a thin pellucid 
 film. If its thickness, i.e., the interval separating its 
 two surfaces, be any number of ^^/-undulations; double 
 that number, i.e., an exact number of entire waves, will 
 have been lost by the wave reflected from the second 
 surface at its re-emergence from the first, by reason of 
 its greater length of path ; and thus were no part of an 
 undulation lost or gained in the act of reflexion, it would 
 start thence in exact harmony with the first reflected ray. 
 But the second reflexion being made at the surface of a 
 rarer medium, an additional semi-undulation will have 
 been lost, so that the two reflected rays will really start 
 from the first surface in complete discordance, and destroy 
 each other. The same is the case if the thickness be 
 nil, or so excessively minute as to be much less than the 
 length of a wave, as at the vertex of a soap-bubble when 
 just about to burst. Here also will the same mutual 
 destruction of the reflected waves take place. And thus
 
 ON LIGHT. 307 
 
 we have explained the complete or very nearly com- 
 plete darkness of the central spot, and of a series of 
 rings corresponding to thickness of i, 2, 3, or more 
 semi- wave lengths. At the intermediate thicknesses 
 (*>., of i, 3, 5, &c., ^z/tfrfcr-wave-lengths) the exact re- 
 verse will happen the reflected rays will start together 
 in harmony and appear as a ray of double intensity, 
 thus explaining the intermediate bright rings. 
 
 (90.) In the case of the rings produced between two 
 glasses of the same material, the intermediate film being 
 air, it is the reflexion from its first surface, not its second, 
 that is effected from a rarer medium ; so that it is at this 
 surface that the additional j<?w/-undulation is gained by 
 the first reflected ray. In all other respects the reason- 
 ing is the same in both cases, and the explanation 
 equally complete in both. 
 
 (91.) It will be perceived that we have not been 
 sparing of words in this explanation. The epigram- 
 matic style is ill-suited to clearness in the exposition 
 of a principle which it is essential to seize with perfect 
 distinctness, and in seizing which considerable difficulty 
 is commonly experienced. If any doubt or misgiving, 
 however, should still linger on the mind as to the appli- 
 cability of the analogy by which the loss of half an un- 
 dulation necessitated by the blackness of the central 
 spot has been explained, a simple but striking expert 
 ment will suffice to dissipate it. Let a set of rings be 
 lormed by interposing, between two glasses of very dif- 
 feient refractive densities, a film of liquid intermediate 
 in that respect as, for instance, oil of sassafras be-
 
 308 ON LIGHT. 
 
 tween a lens of light crown, and a plate of heavy flint- 
 glass. In this case the reflexions from the two surfaces 
 are performed either both from a denser medium upon a 
 rarer, or both from a rarer on a denser according as one 
 or the other glass is uppermost. In the former case 
 two semi-(or one entire) undulation will be gained or 
 lost between the reflected rays at emergence, in addition 
 to the entire ones lost between the glasses : in the latter 
 none. At the central spot, then, the two reflected rays 
 will start on their backward course in exact harmony, 
 and the spot will be white, not black ; and a similar re- 
 versal of character will of course pervade the whole 
 series of rings. This result, predicted by theory, has 
 been found confirmed by experiment 
 
 (92.) It was a favourite idea of Newton that the 
 colours of all natural bodies are in fact the colours of 
 thin pellucid particles of such sizes and thicknesses 
 as to reflect those tints which, in the scale of tints of the 
 coloured rings above described, most nearly correspond 
 to them. This idea we know now to be untenable, if 
 for no other reason than that we are sure the ultimate 
 particles or indivisible atoms of bodies (if any such there 
 be), are at all events many hundreds, thousands, or 
 millions of times smaller than even a single wave-length 
 of any homogeneous ray of light. It will, of course, be 
 asked how we know these wave-lengths. And this we 
 must now explain : in doing which we shall have to de- 
 velop the most astounding facts in the way of numerical 
 statement which physical science has yet revealed. 
 
 (93.) In a series of equal waves running along still
 
 ON LIGHT. 309 
 
 water, the " wave-length," or " length of an entire undu- 
 lation," is the linear distance between two consecutive 
 crests or two consecutive troughs. This is its sim- 
 plest conception, and it will suffice for our immediate 
 purpose. The waves being equal and similar will all run 
 on with the same velocity, which may be ascertained by 
 noticing how long any one takes to run over a measured 
 distance on the surface, or the distance run over in a 
 determinable time, suppose a second. And if at the 
 same time we note the number of waves whose crests 
 pass a fixed point (a float, for instance) in the surface, in 
 a second of time the interval between two consecutive 
 crests will of course become known. And vice versa, if 
 this interval be known, and the velocity of the waves ; 
 the number of undulations passing the float per second 
 is easily calculated. Now this number is necessarily 
 identical with that of the periodically reciprocating move- 
 ments or vibrations of the first mover (whatever it be) by 
 which the waves are originally excited. This continu- 
 ing the same, the same number of waves will pass the 
 float in the same time, whatever be their velocity of pro- 
 pagation. Of these three things the velocity of propa- 
 gation, the number of alternating movements, waves, or 
 pulses per second, and the linear interval between two 
 consecutive ones any two being given, the third is 
 easily calculated. For example, a string sounding a 
 certain note C in the musical scale makes 256 complete 
 oscillations to and fro, per second. As each of these 
 sends forward an air-wave consisting of a semi-wave of 
 (ompression by which the particles of air advance, and
 
 310 ON LIGHT. 
 
 another of expansion by which they return to their places, 
 these waves, 256 in number, being all comprised in, and 
 exactly filling the distance (1090 feet) run over by sound 
 in that time, each entire wave will occupy 4^254 ft. 
 And, vice versd, if we knew this & priori to be the wave- 
 length, we should rightly conclude 256 to be the num- 
 ber of complete vibrations or pulses per second. 
 
 (94.) Mechanical processes enable us to grind and 
 polish a glass surface into the segment of a sphere of 
 any required radius as well as to a plane almost mathe- 
 matically true. Suppose such a glass surface worked, 
 we will say, to a sphere of 100 feet radius, to be laid 
 (convexity downwards) on a truly plane glass. The 
 coloured rings will be formed, as above described, about 
 a central dark spot ; and if illuminated, instead of 
 ordinary daylight, by the prismatic rays, in succession, 
 a series of simply bright and dark rings of the several 
 colours in their order will be formed, whose diameters in 
 different series will correspond to their respective tints. 
 Under these circumstances the linear measurement of 
 these diameters may be performed with ease and with 
 great precision. Now these diameters are the chords of 
 arcs of a circle on a radius of 100 feet represented in fig. 
 7, by the horizontal lines, the versed sines of whose halves 
 corresponding (represented by the perpendicular lines) are 
 the distances between the glasses at those points, or the 
 thicknesses of the interposed film of air, and are easily 
 calculated when the radius and the chords are known. 
 On executing the measurements it is found that these 
 distances, reckoning outwards and commencing with the
 
 ON LIGHT. 311 
 
 centre, do actually follow the law of arithmetical pro- 
 gression (as on the above theory they should do), being 
 in the proportions of the numbers o, i, 2, 3, etc. 
 
 (95.) By measuring then the diameter of (say) the 
 tenth dark ring (for the sake of greater precision), cal 
 culating the corresponding interval, or versed sine, and 
 taking one-tenth of the result, we shall get the interval 
 corresponding to the first dark ring for any particular 
 coloured light and this, by what has been above shown, 
 is the half of a wave-length for such light. Proceeding 
 thus, Newton found for what he considered the most 
 luminous yellow rays, one 89,oooth part of an inch for 
 the interval in question, which gives for the length of an 
 entire undulation of such rays, one 44,5001,11 of an inch. 
 This comes exceedingly near to the result which later 
 experimenters have obtained for that purely homogene- 
 ous yellow light emitted by a salted spirit-lamp, which is 
 one 43,197^ of an inch. For the extreme red and ex- 
 treme violet rays, (as well as their limits can be fixed,) the 
 corresponding wave-lengths are respectively one 33,866th, 
 and one 70,5 5 5th of an inch. 
 
 (96.) These, it will be observed, are the lengths of 
 the undulations in air. In water, glass, or other media, 
 they are smaller, in the inverse proportion of the refrac- 
 tive index of the medium ; for in such media the velo- 
 city of light, as we have seen, is less in that propor- 
 tion ; and the number of undulations pet second re- 
 maining the same, while the space occupied by them is 
 less, their individual extent must of course be less in 
 the same proportion. This, too, is in accordance with
 
 312 ON LIGHT. 
 
 experiment. If water, oil, or any other liquid be intro- 
 duced between the glasses, the rings are observed to 
 shrink in diameter, and the more so (and to the exact 
 extent required by theory) the greater the refractive 
 power of the liquid. 
 
 (97.) If the sensation of colour be, in analogy to that 
 of tone or musical pitch, dependent on the frequency of 
 the vibrational movements conveyed to our nerves of 
 sensation, it becomes highly interesting to ascertain their 
 degree of frequency, in order to establish the relation be- 
 tween the two senses of hearing and seeing in that re- 
 spect The ear, we know, can discriminate tones only 
 between certain limits, comprising about nine octaves, 
 the lowest sound audible as a note making about 16, 
 and the highest about 8200 vibrations per second. 
 Taking the velocity of light (as above) at 186,000 miles* 
 per second, and reckoning 33,866 wave-breadths to the 
 inch for the extreme red, 43,197 for the soda-yellow, 
 and 70,555 for the extreme violet, we find for the im- 
 pulses on the retina per second which produce these 
 sensations of colour, respectively, the following enormous 
 numbers : 
 
 Extreme red, . . , 3 99, 101,000, 000,000 
 
 Soda-yellow, -,' 509,069,000,000,000 
 Extreme violet, . . . 831,479,000,000,000 
 
 These extremes are nearly in the proportion of 2 to i, 
 so that the whole range of visual sensation on this view 
 of the subject is comprised in about one octave. If the 
 
 Roughly, 1000 million feet
 
 ON LIGHT. 313 
 
 ear could appretiate vibrations of this degree of fre- 
 quency, the sensation corresponding to the middle ray 
 of the spectrum would be that of a note about forty- 
 two octaves above the middle C of a pianoforte. 
 
 (98.) In each of these inconceivably minute intervals 
 of time (compared to which a single second is a sort of 
 eternity), a process has been gone through by every molecule 
 of the ether concerned in the propagation of the ray: a pro- 
 cess as strictly definite, as exactly regulated, as the 
 movement of a drop of the ocean in its conveyance of 
 the tide-wave. Taking up its motion from the particle 
 immediately behind it (whose movement it exactly 
 imitates), and transmitting it on to that immediately 
 before, it starts from rest, not suddenly, with a jerk, but 
 (under the strict control of those elastic forces already 
 mentioned), increasing gradually in speed to a maxi- 
 mum then, as gradually, relaxing, coming to a momen- 
 tary rest, and retreating to its original position by the 
 same series of measured gradations in reverse order, to 
 be ready in its place for the reception of the next im- 
 pulse. Nor does it seem possible to avoid the conclu- 
 sion, if we trace up the movement to its commencement 
 to the source of the light the material particle in 
 whose combustion or incandescence it originates that 
 such is the actual vibratory movement of that particle 
 itself. And thus we are brought into the presence of 
 the working of that mechanism by which flame and in- 
 candescence (" <p\<>y UK w erj/j.a vvgos the brilliant miracle 
 of fire," as the Greek poet* not inaptly terms it) are pro-
 
 3F4 ON LIGHT. 
 
 duced. In the disruption of one chemical combination, 
 and the constitution of another, a movement of mutual 
 approach, more or less direct, is communicated to the 
 uniting molecules, which, under the influence of enor- 
 mous coercive powers, is converted into a series of 
 tremulous, vibratory, or circulating movements com- 
 municated from them to the luminiferous ether, and so 
 dispersed through space. Incandescence without com- 
 bustion (as in a piece of red-hot iron) must be looked 
 upon, from this point of view, as a result of the con- 
 tinuance of this vibratory movement after the primary 
 exciting cause has ceased, and of its gradual decay by 
 communication to the surrounding ether ; as a musical 
 string continues to sound after the blow which set it in 
 motion, till gradually brought to rest by the surround- 
 ing air. 
 
 (99.) This may perhaps appear a digression from our 
 subject. But it will be recollected that our object in 
 these lectures is not to produce a treatise on optics, 
 but to fix attention on the immensity of the forces 
 in action, and the minuteness and delicacy of the me- 
 chanism which they animate in the most ordinary opera- 
 tions of Nature, and which the phenomena of light have 
 been the means of revealing to us. We have no means, 
 indeed, of measuring the actual intensity of the " coercive 
 forces" so called into action in the excitement of a lumi- 
 nous vibration, but that we are fully justified in applying 
 to them the epithet " enormous," the following consider- 
 ation will suffice to show. Whatever be the extreme 
 distance of excursion to which a vibrating molecule is
 
 ON LIGHT. 315 
 
 carried from its point of repose, or its medium situation, 
 in the act of vibration; the acting or coercive force 
 must suffice to bring it back from that distance in one 
 fourth part of that inconceivably minute fraction of a 
 second by which, as above shown, the period of a com- 
 plete vibration is expressed. Taking the case, then, of 
 any particular ray (as for instance that between the 
 green and blue rays of the spectrum, corresponding 
 to a wave-length of one 5o,oooth of an inch, and to a 
 period of one 589 billionth of a second), if we assume 
 the extent of excursion, we can very readily calculate the 
 intensity of the force (as compared with that of gravi- 
 tation) which, acting uniformly during that time, would 
 urge it through that space. Let us suppose then, that the 
 nerves of the retina are so constituted as to be sensibly 
 affected by a vibratory movement of no greater extent 
 or amplitude than one trillionth* part of an inch either 
 way; and the calculation executed, we shall find that 
 a force exceeding that of gravity in the proportion of 
 nearly thirty thousand millions to one must be called 
 into action to keep up such a movement. Our choice 
 lies between two immensities, we had almost said be- 
 tween two infinities. If we would bring the force within 
 the limits of human comprehension, we must in the 
 same proportion exaggerate the delicacy of our nervous 
 mechanism, and vice versa.\ 
 
 * A trillion is a million of billions = IO 1S , or 1,000,000,000, 
 000,000,000. 
 
 t The hypothesis of a uniform action of the coercive force in the 
 text is only assumed for the convenience of such of my readers
 
 36 ON LIGHT. 
 
 (too.) Connected with the colours of thin plates are 
 several distinct classes of optical phsenomena, in which 
 colours of the same kind, and explicable on the same 
 principle, arise in the reflexion and transmission of light 
 through or between pellucid plates of considerable thick- 
 ness, or through spherical drops of water, examples of 
 which are to be observed in the pink and green fringes 
 which are often seen bordering the interior of a rainbow, 
 and in those similarly coloured fringes (of exceedingly 
 rare occurrence) which sometimes run, like a bordering 
 ribband, just within the contour of a thin white cloud 
 in the near neighbourhood of the sun. Upon this class 
 of phsenomena, however, we shall not dwell further than 
 to observe that they prove the law of the periodical re- 
 currence of similar phases at equal intervals, not to be 
 confined to very minute distances in the immediate 
 neighbourhood of reflecting or refracting surfaces, but to 
 extend over the whole course of a ray of light as, on 
 the undulatory theory, it necessarily must do. We now, 
 
 whose knowledge of dynamics is limited by this very elementary 
 application. Properly speaking, we ought to assume the coer- 
 cive force to vary in the direct ratio of the distance; on which 
 supposition only will large and small vibrations be executed in 
 equal times. Calculating on this (the correct) principle, and taking 
 the extreme excursion (as in the text) at one-trillionth of an inch, 
 the ratio of the coercive force to gravity at that distance will be 
 found as 35,465 ,000,000 to I. On the other hand, as a strange 
 contrast to the immensity of such a force, we shall find the maxi- 
 mum velocity it will have generated on the arrival of the molecule 
 at the medial point of its vibration not to exceed i-ayoth part of an 
 inch per second!
 
 ON LIGHT. 317 
 
 therefore, proceed to the next branch of our general 
 subject, that of the Diffraction of Light 
 
 (101.) DIFFRACTION. The optical phenomena which 
 refer themselves to this head are many and various. 
 They are not, for the most part, very obvious, but are 
 exceedingly curious and interesting in their details, and 
 some of them, under careful arrangement and with good 
 optical appliances, very brilliant. Familiar examples 
 offer themselves in the twinkling of the stars and the 
 changes of colour they exhibit during the different 
 phases of their scintillations : in the vivid radiating 
 streaks of light which seem to stream outwards from any 
 small and dazzlingly brilliant point of light (as for instance 
 the reflection of the sun on a small polished globe, as a 
 thermometer ball) : in the colours exhibited when a 
 bright point is seen reflected on or refracted through a 
 surface regularly striated or scratched across with fine 
 equidistant lines, as beautifully exhibited in the so-called 
 " Barton's buttons " (from the name of the ingenious and 
 skilful amateur mechanist who first executed them) ; 
 brass or steel buttons delicately cross-lined by engine 
 work : in the lateral images of a candle seen reflected 
 on polished mother-of pearl : and in the coloured halos 
 often seen to surround the flame of a candle in certain 
 states of the eye and their artificial imitations in a mode 
 presently to be described. Less obvious to common 
 observation, and requiring particular arrangement, in- 
 strumental or otherwise, to see them distinctly, are the 
 phaenomena (referable to the head of diffraction) of the 
 rings and other appendages seen to surround the images
 
 3*8 ON LIGHT. 
 
 of stars when viewed through telescopes of great magni- 
 fying power, and with apertures either of the usual 
 circular form, or of forms otherwise varied for this ex- 
 press purpose. And though last in our order of enumer 
 ation, by far the most important and instructive as 
 elucidatory of the principle of explanation, applicable to 
 all the phaenomena of this class ; the coloured fringes 
 seen to follow the outlines of shadows when thrown by 
 a light emanating from an extremely small but intensely 
 luminous point. With these, therefore, we shall begin. 
 
 (102.) It was objected to the undulatory theory of 
 light by Newton himself, that sound, to which that 
 theory assimilates it, spreads from an aperture through 
 which it is transmitted, or round the edge of an inter- 
 cepting screen of any kind, equally in all directions ; and 
 thus, were the analogy exact, there could be no shadows. 
 The objection is founded partly on an imperfect state- 
 ment of the fact, and partly on omitting to allow for pos- 
 sible differences in the natures of the conveying media, 
 and in the modes of vibratory motion conveyed. Every 
 one is familiar with the sudden outbreak of sound from 
 a railway train heard at a great distance when it emerges 
 from a cutting, or turns the corner of a wall or of a hill. 
 Sound is propagated through water with greater sharp- 
 ness, velocity, and distinctness, than through air. But 
 an obstacle interposed under water, as a -projecting pier, 
 or a rock, cuts off the rays of sound, as appears from 
 direct experiment, with much greater defmiteness than 
 in air, and casts, so to speak, an evident acoustic shadow. 
 Nor will it appear at all surprising that an effect of this
 
 ON LIGHT. 3ig 
 
 kind should, in the case of light, be carried still farther 
 when we consider that the aerial impulses by which 
 sound is propagated, take place in the direction of the 
 sound-ray, so that in passing (for instance) through an 
 aperture in a screen, a quantity of air is pushed bodily 
 through it, and issuing on the other side, causes an in- 
 crease of local density due to the actual introduction of 
 additional air at a given spot, which of course tends to 
 expand laterally as well as to push forward, and is not re- 
 strained from so doing by the lateral pressure of the 
 rest of the wave, which is suppressed. Light, as we have 
 already intimated, is propagated through an elastic 
 medium more in analogy with a solid than a fluid, 
 (which Newton's objection implies,) and by vibrational 
 movements not in the direction of the ray, but trans- 
 verse to it, so that in its passage through an aperture, 
 or beside the edge of an obstacle, this cause of lateral 
 spreading, at least, is absent; whatever other this 
 peculiar mode of propagation may call into action. 
 Lastly, however, the phenomena of diffraction with 
 which we are now concerned rely for their explanation 
 on this very principle that shadows are not strictly 
 definite, and that there really is a certain, and not very 
 small amount of lateral spreading of the light into the 
 space occupied by what may be called the geometrical 
 shadow. 
 
 (103.) If a room be darkened and the sun allowed to 
 shine into it only through a very small aperture, as a 
 pin-hole, the rays which emanate from different points 
 of its apparent disc, passing straight through and cross-
 
 32O ON LIGHT. 
 
 ing at the hole, will depict on a white screen held at a 
 distance of several feet from the hole a circular image or 
 inverted picture of the sun, which may be considered as 
 the circular base of a cone of rays having the pin-hole 
 for its vertex. In this case, the illumination of the 
 screen, if placed at a great distance, is feeble, and, if 
 near, the circular patch of light inconveniently small. 
 But if instead of a pin-hole, be substituted a convex 
 glass lens of short focus, the whole of the sun-light re 
 ceived on it will be concentrated in the very small 
 image of the sun formed in its focus, and, diverging 
 thence will spread out into a much wider cone of light, 
 and form a much larger circular and brilliantly illumin- 
 ated area on the screen, affording every facility for the 
 examination of the shadows of objects thrown upon it ; 
 with the additional convenience that by a reflector out- 
 side of the window, the illuminating sunbeam may be 
 thrown horizontally, at whatever time of day the experi- 
 ment is made. 
 
 (104.) The condition essential to the distinct exhibition 
 of all phenomena of this class that of a very brilliant 
 light emanating from a very small point being thus 
 secured, let an opake body of any form be placed 
 between the point and the screen, so as to cast a shadow 
 on it It would naturally be expected under such cir- 
 cumstances that the termination of the shadow on aU 
 sides should be a clear and sharply-marked outline, 
 separating a uniformly bright space on the outside irorn 
 a uniformly dark one within, and free from that external 
 gradation from light to darkness which constitutes what
 
 ON LIGHT. 521 
 
 is called the penumbra in ordinary shadows, which arises 
 from the angular diameter of the sun.* Quite otherwise. 
 A shadow indeed is formed, but instead of a sharp and 
 sudden transition from darkness to light, it terminates in 
 three coloured fringes, following its contour, the inner 
 being the broadest and more distinctly coloured, the 
 outer extremely faint and feebly tinted. The order of 
 the. colours, reckoning from the first dark fringe, is, 
 generally speaking, analogous to that of the colours ot 
 thin plates proceeding outwards from the dark centre 
 rings, only degrading more rapidly, viz., blue within, and 
 yellow and red without. And that the tints originate in 
 the same way from the superposition of a series of dark 
 and bright fringes of the different prismatic colours, of 
 different breadths, is shown (as in the colours of thin 
 plates) by throwing on the lens in succession the several 
 coloured prismatic rays, when the fringes are seen in each 
 colour much more numerously and sharply defined, 
 being broadest in red light and narrowest in violet. 
 
 (105.) If the object casting the shadow be long and 
 very narrow, as a hair or a strip of card not more than a 
 3oth of an inch broad, the phaenomena are still more 
 curious and complex. Besides the exterior coloured 
 fringes already described, others are seen within the 
 shad.iUy running parallel to its length, similarly disposed 
 along both its edges, and blending in the middle into a 
 
 * The diffracted fringes may be seen very well on the borders of 
 shadows cast by the light of Venus when at its greatest brightness, 
 on a white surface, in a room with a single window, and under 
 favourable circumstances as to twilight. 
 
 X
 
 322 ON LIGHT. 
 
 central line devoid of colour. That these fringes origi- 
 nate in the mutual interference of rays which have passed 
 beside both the edges of the object and entered the 
 shadow, is proved by intercepting the light on one side 
 only, leaving that on the other to pass freely. All the 
 interior fringes and the central streak disappear, leaving 
 only the exterior ones on the illuminated side outstanding. 
 The shadow (which is now formed under the same cir- 
 cumstances as in the former case) must, it is clear, be 
 still receiving one-half the total quantity of light which 
 it did before ; and if its edge be narrowly examined, it 
 will be seen not to terminate in any sharply-defined line 
 cutting it off from the fringes, but to graduate off insen- 
 sibly; and hence arises a very singular phenomenon. 
 If the light be readmitted on both sides, and the breadth 
 of the shadow, or what under such circumstances must be 
 accepted as such, be measured, it is found to be much 
 broader than it ought to be were it limited by sTaight 
 lines drawn from the illuminating point through the edges 
 of the object And, what is still more remarkable, if its 
 breadth be measured on a screen, successively placed at 
 different distances from the object, its increase of 
 breadth is found not to be in the simple proportion of 
 its increased distance ; as it would were the aerial shadow 
 (or the space shaded by the object) bounded by straight 
 lines ; but as if by curves starting from its edges, and 
 having their convexities towards the light. And, finally, 
 if the object and the screen, preserving the same distance 
 between t/iem, be moved gradually nearer and nearer to 
 the illuminating point, the fringes, both interior and ex-
 
 ON LIGHT. 323 
 
 terior, are observed to dilate in breadth, according to a 
 certain law which it is not necessary here to state, but 
 whose agreement with the result of calculation affords a 
 very satisfactory verification of the theory adopted foi 
 the explanation of the whole series of these phenomena 
 on the undulatory hypothesis : while, on the other hand, 
 it is very obvious that no such dilatation could possibly 
 take place were the fringes produced by any kind ot 
 action on the rays in their passage by or near to the 
 edges of the object, in the nature of attractive or repul- 
 sive forces originating in the material substance of which 
 it consists, and deflecting them from their rectilinear 
 paths; inasmuch as such action could neither be increased 
 nor diminished, or in any way modified, by the greater 
 or less distance traversed by the rays before their arrival 
 within its sphere. 
 
 (106.) The appearances exhibited when the light is 
 transmitted through a narrow rectangular slit, are even 
 more curious. In this case a bright image of the open- 
 ing is thrown on the screen, but instead of being an 
 evenly illuminated narrow band, bounded on either side 
 by uniform darkness, it is bordered both externally and 
 internally by parallel fringes. The external ones are 
 bright and highly coloured, and vary in breadth, but not 
 materially in brightness, as the screen is withdrawn from 
 the slit ; but the interior fringes undergo singular changes 
 as the distance increases. At near distances they are 
 narrow and close, and leave a medial space of uniform 
 light , uut as the distance increases they enlarge in 
 breadth, and close in on the illuminated space, so that
 
 324 N LIGHT. 
 
 at a certain distance a medial dark line makes its appear- 
 ance which, if the distance be still further increased, 
 changes to a bright one, and so on alternately till after a 
 certain distance is attained the alternations cease. If 
 the screen be stopped at the last position in which the 
 medial line is dark, and there fixed, and an opake strip, 
 exactly half the breadth of the slit, be held medially 
 along its whole length, so as to divide the slit and reduce 
 it to two parallel ones, each one quarter of the original 
 breadth (by which, of course, the total light traversing the 
 aperture will be reduced to half its amount), instead of 
 darkening still more the medial dark fringe on the screen, 
 as would naturally be expected on throwing a shadow up- 
 on it, the very reverse happens : the dark fringe in ques- 
 tion disappears altogether, and is replaced by a bright one. 
 (107.) If the shape of the body which casts the shadow 
 *>e angular, having salient and re-entering angles; the 
 fringes where they surround the re-entering angles cross 
 and pursue their courses up to the shadows of the sides 
 respectively opposite to them ; but those which surround 
 salient ones curve round them, preserving their continuity. 
 At an angle of the latter kind too, crested or plume- 
 shaped interior fringes are seen "Grimaldi's crested 
 fringes," as they are called, from the name of Father 
 Grimaldi of Bologna, who first described (in 1665) these 
 curious appearances. If a re-entering angle, however, be 
 very acute, the external fringes which border its sides on 
 approaching the angular point curve outwards, cross one 
 mother, and run out both ways into the shadow in ele- 
 gant curves of a hyperbolic form. Nothing can be ima-
 
 ON LIGHT. 325 
 
 gined more singular and bizarre than the appearance of 
 shadows cast on a screen in this manner by a variety of 
 minute objects of different shapes, needles, feathers, 
 lace-work, locks of hair, &c. ; and as their observation, 
 as we have shown, is exceedingly simple and easy, we 
 earnestly recommend them to the attention of our 
 readers a bit of looking glass, or, still better, a polished 
 metallic reflector, a hole in a window shutter, a lens of 
 an inch focus, a screen of white paper, and a sunny day, 
 being all the requisites. 
 
 (108.) When the image of a small circular aperture (as 
 a pin hole) is thrown on the screen, it is seen as a small 
 round disc, highly coloured, the colours varying as the 
 screen is approached from a distance to the hole pre- 
 senting in regular succession the tints of the reflected 
 colours of thin plates described in a former part of this 
 article, beginning with the first white : or, if the illumin- 
 ation be effected by homogenous light, alternate grada- 
 tions of light from brightness down to total obscurity, 
 and thence through an alternate succession of light and 
 darkness. Around the central spot, too, coloured rings 
 are formed, the tints of which vary in dependence on 
 those of the centre. When the light is transmitted 
 through two holes side by side, and very near together, 
 besides the rings belonging to each, a set of intersectional 
 coloured streaks is formed, straight if the holes be equal, 
 hyperbolically curved if unequal. With three holes form- 
 ing an equilateral triangle, or with a still greater number 
 arranged with perfect regularity (as in machine-stamped 
 paper in patterns), an endless variety of elegant and
 
 3^6 ON LIGHT. 
 
 pleasing appearances will be witnessed. To see them to 
 the greatest advantage, a magnifying glass should be 
 used, placing the eye in the place of the screen, and looking 
 through the glass at the fringes and images of tlie holes as if 
 they were real objects in itsfuus. 
 
 (109.) When the system of apertures examined con- 
 sists of a great multitude of exceedingly narrow parallel 
 slits, precisely equal and equidistant, they constitute 
 what is called a " diffractive grating," and present very 
 curious, and in some cases brilliant, phaenomena, which 
 are best viewed by placing the eye close behind the grat- 
 ing. The luminous point (which appears colourless) is 
 then seen accompanied laterally and on either side by a 
 succession of highly coloured spectra, arranged in a line 
 passing through it, and with their lengths directed along 
 that line ; their colours, unlike those of the fringes 
 (which are composite) are the pure unmingled hues of 
 the prismatic spectrum : even more vivid (if the grating 
 be delicately executed) than the best spectrum which 
 can be formed by refracting a sunbeam through a prism; 
 and exceedingly remarkable in another respect, viz., that 
 the proportional lengths of the coloured spaces in each, 
 instead of depending, as in the case of the spectrum 
 formed by a prism, on the nature of the particular 
 medium of which the prism consists, is independent of 
 any such consideration, and determined solely by the 
 proportion between the wave-lengths corresponding to 
 the colours of the rays. They are, therefore, what may 
 be called normal spectra. So pure and undiluted indeed 
 are their tints, that by the aid of a magnifying telescope
 
 ON LIGHT. 327 
 
 the "fixed lines," so often above referred to, may be 
 seen in them, and thus the wave-lengths, corresponding 
 to the most conspicuous of these lines, ascertained with 
 great precision. The violet ends of all the spectra are 
 nearest to the central point, and the more distant spectra 
 longer than the nearer, so that at length they overlap 
 and confuse one another by the intermingling of the red 
 end of one with the violet of that next in order. 
 
 (no.) If the apertures of which the grating consists 
 be formed by removing with a graver portions of an 
 opake varnish covering a glass surface, spectra exactly 
 similar are seen accompanying the image of the lumin- 
 ous point reflected on the anterior surface of the glass 
 from the polished portions laid bare. The same is 
 observed, and with far more brilliancy, when a highly 
 polished surface of metal is furrowed in equidistant par- 
 allel grooves by a graver or diamond point (which de- 
 stroys the polish of those lines), and if the metal be 
 hardened steel, the furrows so formed are transferable 
 by violent pressure to the polished surface of a softer 
 metal, which then in its turn exhibits similar appear- 
 ances, and thus are produced the "buttons" above 
 spoken of. Mother-of-pearl, too, which consists of ex- 
 ceedingly thin layers of calcareous matter superposed, 
 and agglutinated or otherwise held together ; when, 
 ground and polished, has these layers, which lie very 
 little oblique to the general surface, torn up at their 
 edges, where they crop out ; which remain rough and un- 
 polished, however brilliantly polished the general surface. 
 The polished surface, therefore, is lined all over with
 
 328 ON LIGHT. 
 
 almost exactly .equidistant, exceedingly minute, non- 
 reflective grooves, and when, if held close to the eye, a 
 candle is seen in it reflected, its image is accompanied 
 with two lateral and very vivid spectra of similar origin, 
 and an impression of the surface taken on black seal- 
 ing-wax presents the same phenomenon. 
 
 (in.) When, as occasionally happens, the eyes are 
 sufTased with a nebulous film (due to the presence in the 
 lacrymatory secretion of extremely minute globular par- 
 ticles of equal size), the image of a candle in a dark 
 room some feet distant is seen surrounded with two or 
 three broad circular halos of rainbow colours alternately 
 ruddy and green. Similar halos are formed round the 
 candle when viewed through t\vo pieces of clear glass 
 between which has been placed a little oil mixed with 
 the delicate powder of the common puff-ball or lycoper- 
 don> reduced to a thin even film by pressure and gently 
 rubbing them together. In this case they are much 
 more vivid and beautiful, the tints being those of the 
 colours of thin plates beginning from the centre, only 
 more dilute, so that it is difficult to discern more than 
 a feeble indication of the fourth ring. Their diameters, 
 however, unlike those of the coloured rings figured in 
 Fig. 6, increase in arithmetical progression, or nearly so ; 
 that of the first or smallest, reckoned to the minimum 
 of illumination, being 21 36' or thereabouts. They owe 
 their origin to the exceeding minuteness, uniformity of 
 size and sphericity (or at least circularity) of outline (if 
 flat discs) of the spores of this fungus. 
 
 (112.) The explanation of these and of other nhseno-
 
 ON LIGHT. 329 
 
 mena referable to the head of diffraction, turns on two 
 considerations, one of which may be regarded as a 
 theoretical postulate (founded, however, on the analogy 
 of sound), viz., that if a portion of a luminous wave be 
 intercepted, the non-intercepted undulation spreads 
 laterally into the dark space beyond, diminishing, how- 
 ever, in intensity as the lateral deviation of the ray (or 
 perpendicular to the wave) from its original rectilinear 
 course increases : the other, a natural consequence of 
 the mode in which a wave is propagated, viz., that every 
 point in the surface of the non-intercepted portion may be 
 regarded as the origin of a new wave spreading out spheri- 
 cally in all directions from that point as a centre; only with 
 this proviso, that all such secondary waves start, each from 
 its own origin, at the same precise instant of time and 
 in the same precise phase of its undulation. And this, be- 
 
 Fig. 10. 
 
 cause all belong to one wave surface, and are therefore 
 necessarily coincident in time and identical in phase. 
 
 (113.) To show how this last consideration affects the 
 question of diffraction, let us suppose a point p on a
 
 330 ON LIGHT. 
 
 screen illuminated by light emanating from a single 
 bright point O (Fig. 10), from which is propagated a series 
 of equidistant spherical waves corresponding to light of 
 any one refrangibility, and therefore distant from each 
 other by one entire undulation of such light (say, to fix 
 our ideas, a 5o,oooth of an inch). If o P be joined, inter- 
 secting the surface of any one such wave, at a given 
 distance, o A from o in A ; PA will be the shortest line 
 that can be drawn from P to that surface. Suppose, 
 now, we take on either side of A a series of points B, b ; 
 C, c ; D, d, &c., progressively more distant (by pairs) 
 from P than A is, by i, 2, 3, &c., hundred-thousandths 
 of an inch, or semi-undulations of the light under con- 
 sideration ; and let the whole figure be conceived as 
 turned round on o P as an axis. Then these points will 
 mark off on the spherical surface of the wave, a central 
 circular area (call it the area A), and a series of con- 
 centric rings or rather zones of the waves (call them in 
 succession B, c, D, &c.), surrounding it, like those repre- 
 sented in Fig. 7, from every point in each one of which 
 the light sent to P will reach it in more or less discord- 
 ance of phase, with that which reaches it from the next 
 in succession. Thus if all the vibrations propagated 
 from the central circle (A) arrive at P in a phase of com- 
 pression, all these simultaneously reaching it from the 
 zone (B) will arrive in a phase of expansion, all from 
 (c) again in one of compression, and so on alternately. 
 Now if the distance A P of P from the wave be anything 
 considerable, suppose a few feet or even incnes, it 
 will be enormously great in proportion to one semi-
 
 ON LIGHT. 331 
 
 undulation or ioo,oooth of an inch, the length by which 
 the distances p A, P B, &c., differ from each other, and 
 in that case it is very easy to show by geometry, that the 
 successive areas (A), (B), (c), &c., are almost exactly 
 equal. Were these areas rigorously equal, and were 
 moreover the vibrations (propagated as they are from 
 them to P more and more obliquely with respect to the 
 general surface of the wave at their points of emanation) 
 all of equal intensity, it would follow therefore that the 
 totality of the movement propagated to P from (A) would 
 be precisely opposed and destroyed by that from (B), 
 that from (c) by that from (D), and so on; so that an 
 ethereal molecule at P would in effect be agitated by no 
 preponderating movement, one way or another, and 
 there would be no illumination on the screen at P. In- 
 asmuch, however, as the vibrations diminish in intensity 
 as they are propagated more obliquely, and as the areas 
 (A), (B), (c), (D), &c., are; though very nearly, yet not 
 rigorously equal, this mutual destruction in the case of 
 each consecutive pair is only partial, and the point P 
 will be agitated by the sum of all these outstanding 
 excesses (taken in pairs) from the centre outwards; 
 which, though excessively small individually, in virtue of 
 their immense number make up a finite sum. And as 
 the same is true for each point of the screen (if spherical, 
 and therefore everywhere equidistant from o), the whole 
 of its surface will be equally illuminated : if plane, very 
 nearly so, in all the region around P. 
 
 (114.) A very singular consequence follows from this 
 reasoning, and one admirably calculated to test its
 
 332 ON LIGHT. 
 
 validity, and the soundness of the theory it relies on, by 
 experiment. There can be no better presumptive 
 evidence of the truth of a physical theory than its 
 enabling us to predict, antecedent to trial, a result in 
 direct contradiction to what mankind in general would 
 consider as the obvious conclusion of common sense 
 founded on all ordinary experience. This is the case in 
 the present instance. Since the total illumination of one 
 point P on the screen is only that due to the undula- 
 tions which remain outstanding after the mutual destruc- 
 tion of by far the greater proportion of those propagated 
 from the zones (A), (c), (E), &c., (the odd zones, reckon- 
 ing (A) as No. 1), by those emanating from the even 
 ones (B), (D), (F), &c., it follows that if all the even zones 
 could be entirely suppressed or rendered ineffective, the 
 illumination at P wou'd be prodigiously increased, and 
 that even the obliteration of a few of them would pro- 
 duce a very material augmentation of brightness at that 
 point. In other words, that by stopping out a large pro- 
 portion of the luminous rays passing through a circular 
 aperture from a bright illuminating point, the illumina- 
 tion of the central point of the image of such aperture 
 thrown on a screen at a certain distance behind it, may 
 be made to exceed by many times what it would be were 
 the whole aperture left open. This strangely paradoxical 
 result is stated by M. Billet* to have been experiment- 
 
 * Billet, Trait'e (Toptique Physique, 1858, ii. 55, by far the 
 fullest resume of that subject hitherto published ; only too little ex- 
 planatory, and sadly deficient in facility of reference. It deserves a 
 goodjudex.
 
 ON LIGHT. 333 
 
 ally verified by M. Fresnel (to whom its suggestion is 
 due), and more recently by M. Billet himself, who by 
 merely interposing (concentrically) between the luminous 
 point and the centre of the screen, a small opake an- 
 nulus exactly corresponding to the calculated dimensions 
 (for red rays and using red light) of the first even ring (B) 
 obtained an illumination at p estimated at five times 
 that when no obstacle was interposed. 
 
 (115.) By way of showing the kind of explanation 
 these principles afford of some of the simplest and 
 easiest cases of diffraction (for their calculation is for the 
 most part very complicated in its details, though simple 
 enough in its principles) ; let us suppose first the case of 
 a screen illuminated by a minute radiant point o through 
 a small circular aperture, and consider only the illumina- 
 tion of the central point of projection on the screen, or 
 of P in our figure. Suppose p to approach the screen 
 from a very great distance so great that the difference of 
 its distance from the centre and either edge of the aperture 
 shall be less than a semi-undulation of the light con- 
 sidered (say ioo,oooth of an inch). Then the undula- 
 tions from every part of the aperture will reach P in 
 phases more or less accordant with each other, and P 
 will therefore be more or less illuminated : and, P still 
 approaching, its illumination will increase till it attains 
 such a distance that the difference in question exactly 
 equals a semi-undulation. In this case the portion of 
 the wave transmitted corresponds precisely to the whole 
 of the central circle (A) of our system of wave-zones 
 above discussed, and we have here the greatest possible
 
 334 ON LIGHT. 
 
 amount of concordant and no discordant rays, and the 
 illumination will be a maximum. But if P approach 
 nearer, the difference in question will be greater than a 
 semi-undulation, and the portion of an aperture near the 
 edges will send rays to P more or less in discordance with 
 those from the centre, and these will destroy a por- 
 tion of P'S illumination. P approaching this will go on 
 till the difference amounts to an entire undulation 
 (i-5o,oooth); that is to say, till the aperture extends (as 
 respects the new situation of P) over the whole of the two 
 first zones (A) and (B), of which the second (B) destroys 
 almost the whole of the light from (A) (being equal in 
 area, and differing very little in obliquity). Here then 
 the illumination at P will be nil or very small. P still 
 approaching, the third zone (c) (which sends vibrations 
 in unison with (A) ) will begin to be included within the 
 limits of the aperture, and the illumination will again in- 
 crease to another maximum, viz., when the three, (A), 
 (B), (c), are just included ; thence again it will diminish 
 to a degree of obscuration not quite so complete as be- 
 fore ; and so on. Thus as the screen approaches the 
 aperture, its central point, after attaining a maximum ot 
 illumination, will suffer a succession of eclipses or obscur- 
 ations gradually less and less complete, with intermediate 
 recoveries, just as we have seen above, is really the case. 
 When the light is not homogeneous, the different coloured 
 rays having different wave-lengths, the obscurations of 
 one colour will not correspond to those of the others, 
 and thus will arise a succession of colours at the central 
 point of the screen, agreeing with those there described.
 
 ON LIGHT. 335 
 
 (116.) Take now the case of the exterior fringes, when 
 the shadow of a broad straight-edged body, as a ruler, is 
 thrown on a fixed screen at a considerable distance be- 
 hind it. Suppose P first placed exactly at the edge of 
 the geometrical shadow. In that case, the view of ex- 
 actly half of each of the concentric wave-zones (A), (B), 
 (c), &c., will be intercepted, and P will therefore receive 
 from the remaining halves just half the amount of lumin- 
 iferous agitation it received when opposed to the whole 
 wave, viz., half the amount of concordant and half of 
 discordant undulation. . Its intensity of illumination will 
 therefore be one-fourth of that when the ruler is altogether 
 removed.* Now, suppose the ruler withdrawn gradually, 
 and laterally, so as to disclose to the view of P succes- 
 sively, ist, the whole of the central zone (A) of the wave 
 surface ; 2dly, the whole of the two first zones (A), (B) ; 
 3dly, the three first, (A), (B), (c), and so on. It is very 
 evident then, on merely casting our eyes on Fig. 6, (p. 
 295), and imagining a line drawn through the common 
 centre of all the circles to be removed parallel to itself, 
 step by step, so as to become in succession a tangent to 
 the ist, ad, 3d, &c., circles; that in the first step of its 
 removal it will disclose to P all the remaining half of the 
 central area (A), which sends to it undulations concordant 
 with those by which P is already illuminated, but less 
 
 * The effect on the retina is estimated, not by the simple momen- 
 tum or -velocity of the impulse communicated by the vibration, but 
 by the "vis viva," "energy," or "work done," which is proportion- 
 ate to the square of the velocity of movement. In this the undulatory 
 doctrine of light agrees with the theory of sound.
 
 336 ON LIGHT. 
 
 than half of the second (discordant), still less of the third, 
 &c., so that on the whole there will be a preponderance 
 of the concordant undulations so introduced, and p will 
 be more strongly illuminated than before. When re- 
 moved one step farther however, since the newly intro- 
 duced half of (B) the second zone almost exactly coun- 
 teracts that of (A), the effect of the change will have its 
 character decided by the proportional magnitudes of the 
 segments of (c), (D), &c., disclosed, among which the 
 preponderance is evidently in favour of (c), that is, of 
 discordant undulation, so that by this removal of the 
 shading obstacle the illumination of P will be diminished; 
 and so on alternately. Now at each stage of these re- 
 movals of the shading body, the edge of the geometrical 
 shadow retreats farther and farther from p, or (which is 
 the same thing) p is successively farther and farther out- 
 side of the edge of the shadow, becoming alternately 
 more and less illuminated than at the actual edge. 
 Here then we see the origin of the bright and dark ex- 
 ternal fringes exhibited in homogeneous light ; and there- 
 fore by the very same reasoning, of the coloured ones 
 produced by the successive overlapping of those formed 
 by several coloured rays to each of which corresponds a 
 different breadth of fringe ; that for the red being broad- 
 est and for the violet narrowest 
 
 (117.) The twinkling or scintillation of tlie stars partakes 
 so far of the nature of a phenomenon of diffraction, as 
 that it depends for its origin on the mutual interference 
 of discordant rays arriving at one instant, but by different 
 routes, on the same point of the retina of the eye ; and
 
 ON LIGHT. 337 
 
 which, therefore, do not interfere with or enfeeble one 
 another in any part of their previous course. The image 
 of a star on the retina is formed by the union in a focal 
 point of the whole bundle or pencil of parallel rays con- 
 tained within a cylindrical space or column, having the 
 circular opening of the pupil for a base or section, con- 
 tinued through the whole atmosphere, however far it may 
 extend. Now the air, though a very feebly refracting 
 medium, has still a certain amount of refractive power, 
 and that a variable one, depending on its density, tem- 
 perature, and moisture ; and corresponding to the 
 degree of this power is the velocity with which it is tra- 
 versed by the luminous undulations. Now; however 
 the density, temperature, and moisture of the lo'*ei and 
 upper regions of the air may differ; if throughout the 
 whole extent of this column it were perfectly uniform in 
 these respects, at every point of each cross section of it 
 (however it might differ in different sections) all the rays 
 traversing its length from the star to the eye would have 
 their undulations equally retarded by the aerial medium : 
 and therefore all the rays belonging to any one wave 
 setting out at the same instant of time from the star 
 would reach the focal point on tne retina at the same 
 moment ; such being the condition which determines the 
 focal point of a lens. But if the air in one side of the 
 column should for any considerable distance along it be 
 slightly different in these respects from that in the other, 
 the undulations transmitted along that side would be 
 differently retarded from those along the other, and would 
 not arrive on the retina at the same instant The one 
 
 Y
 
 338 ON LIGHT. 
 
 portion, then, on its arrival would meet there, not the 
 other portion of the same wave to which it originally be- 
 longed, but one in advance or in arrear of that by either 
 a whole, a half, or any part of an undulation, or any 
 number of such, according to the extent of the difference 
 in the quality of the aerial contents of the column. Sup- 
 pose, for instance, the Hght from tne two halves of the 
 column to differ in their time of arrival by i, 3, 5, or any 
 odd number of semi-undulations of the most luminous 
 or the yellow rays; these then would interfere and totally 
 extinguish each other, and the apparent light of the star 
 would undergo a great obscuration, assuming at the same 
 time a hue complementary to yellow ; i.e., dark purple : 
 and so for other rays. Now the constitution of the air 
 is so irregular such a perpetual mixture of masses of it, 
 differing in temperature and moisture, is continually go- 
 ing on under the influence of wind-currents, that such 
 differences as above supposed must be almost con- 
 stantly in progress, even within the narrow space of a 
 column no wider than the pupil of the eye, much more 
 in that corresponding to the aperture of a small telescope. 
 The scintillations, with their accompanying changes of 
 colour, are beautifully seen through an opera -glass 
 (not binocular), especially if somewhat out of focus, in 
 which case the colours and the darkness are seen, as it 
 were, to run over the circular disc into which the image 
 is dilated in a very singular and capricious manner. If 
 a small circular motion be given to the glass, so as to 
 make the image of the star (when in focus) describe a 
 circle, this will be seen as a luminous circle (as when a
 
 ON T-IGHT. 339 
 
 burning stick is whirled round, forming a ring of light), 
 and in the circle so formed spaces highly coloured 
 red, blue, or green, as well as dark and bright will 
 be seen, corresponding to the state of the image at the 
 instant it occupied those spaces, forming an easy, pleas- 
 ing, and very interesting experiment. 
 
 (118.) An effect, the precise parallel to the scintillation 
 of the stars, might be produced, affecting the ear instead 
 of the eye, by sounding together two strings, at first ex- 
 actly in unison, and then very slightly increasing and 
 diminishing alternately the tension of one of them, thus 
 producing a succession of beats, not regular as in the 
 case of two strings permanently differing by a minute 
 interval of pitch, but capricious in their succession.
 
 LECTURE VJIL 
 ON LIGHT. 
 
 PART III. DOUBLE REFRACTION POLARIZATION. 
 
 JN that most wonderful work, the Optics of 
 Sir I. Newton, among the queries annexed 
 at the end, occurs this very singular one : 
 " Have not the rays of light different sides, 
 endued with different original properties?"* The con- 
 ception intended to be conveyed, as further illustrated 
 by Newton himself, embodies that abstract notion of 
 polarity which Dr Whewell in his " Philosophy of Induc- 
 tive Science," expresses by " opposite qualities in oppo- 
 site directions," or, as we should prefer to say, for this 
 purpose, " different qualities in different directions," with 
 reference (that is) to surrounding space and the objects 
 therein situated. The same form of the general concep- 
 tion, as regards light, which Newton employed to desig- 
 nate the very same peculiarity in its habitudes, was 
 adopted by Malus in his first announcement of the rc- 
 
 * "Optics," Book iii., Query 26. 4th Edition.
 
 ON LIGHT. 341 
 
 markable discovery which introduced the term POLARIZ- 
 ATION into optical language. " We find," says he, " that 
 light acquires properties which are relative only to the 
 sides of the ray which are the same for the north and 
 south sides of the ray" (i.e., of a vertical ray), "using the 
 points of the compass for description's sake only, and 
 which are different when we go from the north and south 
 to the east and west sides of the ray." The polarization 
 of light has in fact been an integral part of the science of 
 optics (wanting only a name to designate it) ever since 
 this suggestion of Newton, who derived it from the con- 
 templation of one of what Bacon calls " instantise luci- 
 ferae," luminiferous instances ; exhibiting the property or 
 " nature searched after " " in an eminent maner," or in 
 its clearest or most manifest form ; and who described 
 with the utmost clearness and precision the phenomenon 
 in which its manifestation consisted in the special case 
 before him.* We shall, therefore, approach the subject 
 from Newton's point of view, choosing for our illustration 
 the very phaenomenon which led him to the singular 
 conclusion embodied in his query. 
 
 * The same phaenomenon is described, and with no less clear- 
 ness and precision, by Huyghens, in his admirable work, "Traite* 
 de la lumiere," published in 1690, fourteen years before the Optics 
 of Newton and from that epoch, or from 1678, when that treatise 
 was communicated to the French Academy, must date the discovery 
 of the polarization of light as a fact. Huyghens, moreover, correctly 
 attributed it to a peculiarity impressed on the vibrations of the 
 ethereal medium. But the picturesque phrase of Newton embodies 
 the idea in a form easily apprehended, while it seems to have floated 
 rather vaguely before the mind of his great predecessor, not so much 
 as a general attribute, but us a specialty limited to the case in 
 question.
 
 34* ON LIGHT. 
 
 (120.) As we have already stated when speaking of re- 
 fraction generally, a ray of light incident on any trans- 
 parent crystal (certain specified classes of crystals ex- 
 cepted) is subdivided by refraction into two distinct rays, 
 pursuing different paths within the crystal, and of course 
 emerging from it at different points, and so, of necessity, 
 reappearing, not as a single, but as two distinct and 
 separate rays, each pursuing its subsequent course inde- 
 pendent of the other through space. Of these, when 
 traced, one is found to have been refracted in the rlane 
 of its incidence on the transmitting surface, and accord- 
 ing to the ordinary simple " law of the sines " already 
 explained. It is therefore said to be ordinarily refracted, 
 and it is called the ordinary ray. The other, except in 
 special cases, deviates after refraction from the plane of 
 its incidence, more or less according to the situation of 
 that plane with respect to the faces of the crystal: and, 
 moreover, in respect of the amount of its flexure, does 
 not conform to the simple law of the sines, but to a rule 
 much more complex in its expression, called the law of 
 extraordinary refraction; this ray being designated as the 
 extraordinary ray. Such is the case if the original, inci- 
 dent ray be one directly emitted from the sun, a candle, 
 or any self-lumin us body. But if in place of such a ray, 
 we employ either of the two rays so separated as above 
 described, for transmission through a second crystal of 
 the same kind, the result will be very different. If it fall 
 upon such second crystal in the same manner, according 
 to the same angles and with the same relative situation 
 as to its plane of incidence with the sides of the crystal,
 
 ON LIGHT. 343 
 
 as in the case of the original incident ray, it will not be 
 further subdivided, but refracted singly: if an ordinary 
 ray, ordinarily; and if extraordinary t extraordinarily. Its 
 refraction will also be single, if the second crystal be 
 turned round on the ray as an axis exactly through a right 
 angle; but in this case the second refraction, if an ordi- 
 nary ray have been used, will be extraordinay, and via 
 versa. In every intermediate situation of the second 
 crystal, it will be subdivided into two, the one ordinarily, 
 the other extraordinarily refracted, but the two fractions 
 will be found to differ in relative intensity : generally 
 speaking, the more according as the conversion of the 
 second crystal has been through a less angle from its 
 first position, and they are equal when the angle of con- 
 version is 45, 135, 225, or 315, i.e., exactly half-way 
 between the rectangular positions of the crystal. 
 
 (121.) All these particulars are easily and elegantly 
 exhibited by means of two crystals of the mineral called 
 Iceland spar (crystallized carbonate of lime), a mineral 
 of perfect and colourless transparency, which, if frac- 
 tured, will always separate itself 
 along its three " planes of cleav- 
 age" (which in this mineral are 
 singularly distinct and palpable) 
 into forms whose type is the ob- 
 tuse rhomboid (whose six faces, 
 all equal and similar rhombs of Fi s- " 
 
 101 32' and 78 28', are united three and three, by 
 their obtuse angles, at the opposite extremities of a 
 line called the axis of the rhomboid, the shortest that
 
 344 ON LIGHT. 
 
 can be drawn across it, and to which it is symmetrical, 
 as shown in the preceding figure). 
 
 (122.) If such a rhomboid be laid down on an ink- 
 spot on white paper, or, still better, on a small pinhole 
 in a plate of metal, and held up to the light, the ink-spot, 
 or the dot of light, will appear through it doubled : the 
 two images being separated, in the direc- 
 tion of the shorter diagonal of the face 
 through which they are seen, by an inter- 
 lg ' 1X val of about one-ninth part of the thick- 
 ness seen through. Thus, if over the first rhomboid 
 another of equal thickness be laid conformably (i.e., so 
 that all the faces of the second shall be parallel to the 
 corresponding ones of the first), the only effect will be 
 that the apparent separation of the two images will be 
 doubled, just as if a single crystal of double thickness 
 had been used. But if from this position the upper 
 crystal be turned slowly round in its own plane upon 
 the lower, kept firm ; two other images will make their 
 appearance between the former, at first very faint and 
 almost close together, but, as the rotation of the upper 
 crystal continues, gaining strength (while the others grow 
 fainter) and opening out from each other in a direction 
 transverse to the line of junction of the first. When the 
 angle of rotation attains 45, four images are seen of 
 equal intensity, after which the two first grow fainter, 
 and at 90 vanish, the whole of their light having 
 passed into the other two and so on alternately. When 
 the upper rhomboid has made an exact semi-revolution 
 on the other, the image is single, and contains the whole
 
 ON LIGHT. 345 
 
 of the incident light In this case, the ordinary ray has 
 been refracted ordinarily, and preserves its situation; 
 the extraordinary extraordinarily, but its displacement 
 by the second refraction being exactly equal and oppo- 
 site (in consequence of the now reversed position of the 
 refracting rhomb) to that by the first, it is brought to 
 coincidence with the other, and the two united form one 
 image. 
 
 (123.) The opposite sides of a rhomboid being par- 
 allel, both the ordinary and extraordinary rays after 
 transmission emerge parallel to the incident ray, by a 
 necessary consequence of that general law of retro-ver- 
 sion, in virtue of which a ray of light, whatever path it 
 may have pursued from one point to another, can always 
 retrace that path; the opposite faces being symmetri- 
 cally situated with respect to the axis. And the same 
 is true for a parallel plate of this or any other crystallized 
 substance artificially cut and polished, whatever be the 
 position which such plate may have held in the interior 
 of the crystal from which it is cut. Now it is found, by 
 cutting from rhombs of Iceland spar parallel plates in 
 various directions, that there is one through which a ray 
 of ordinary light can be transmitted perpendicularly 
 without being divided into two. This is the case when 
 the faces of the plate are at right angles to the line above 
 designated as the axis of the rhomboid. And generally 
 that a ray which within the crystal pursues a path par- 
 allel to this axis, will emerge from it single, whatever be 
 the situation of the surface of emergence. The axis, 
 then, is a line of no double rejraction, and in the case of
 
 ON LIGHT. 
 
 the substance in question (or of any crystallized body 
 whose primitive form is the acute or obtuse rhomboid, 
 the regular hexagonal prism, and some others, compris- 
 ing all those primitive forms which can be described as 
 symmetrical to one line and to one only) it is the only direc- 
 tion endued with this property. And on the other hand, 
 the amount of the double refraction or the angular sepa- 
 ration of the two rays into which the incident ray is 
 divided, is greatest when they lie in a plane perpendi- 
 cular to this axis. On account of these properties, the 
 line in question is sometimes called the optic axis of the 
 crystal. 
 
 (124.) If a crystal of Iceland spar, or any similar 
 body, be cut into the form of a prism, in such a manner 
 as to have its refracting edge parallel to its optic axis, 
 neither of the two refracted rays will emerge parallel to 
 the incident one, or to each other. They will diverge, 
 including an angle between them, greater as the refract- 
 ing angle of the prism is greater, exactly as if the medium 
 had two different refractive indices. And in this parti- 
 cular case both refractions follow the ordinary " law of 
 the sines," and there is no deviation of either ray from 
 the plane of incidence. And what is extremely remark- 
 able, not only the refractive indices, but the dispersive 
 powers of the two refractions differ, in some cases widely, 
 so as to give two spectra (when a sunbeam is refracted) 
 of very different lengths. In the case of Iceland spar, 
 the respective refractive indices for the ordinary and 
 extraordinary ray are 1-654 and i'483. It is inconse- 
 quence of this grea 4 - difference that the two images of a
 
 ON LIGHT. 347 
 
 point, seen through a rhomboid of the mineral, appear 
 unequally raised above their natural level ; that seen by 
 the ordinarily refracted rays, appearing nearer the eye 
 than the other. 
 
 (125.) By the employment of such a prism as here 
 described, it is easy to insulate either the ordinary or 
 extraordinary refracted ray, and examine it separately. 
 Suppose, for instance, the latter to be stopped by a 
 screen, and the former only allowed to reach the eye. 
 If before doing so it be made to pass through a second 
 such prism, whose refracting edge is parallel to that of 
 the first, it will be refracted singly and ordinarily : if the 
 edge be held perpendicularly to that of the other, then, 
 singly but extraordinarily. In every intermediate posi- 
 tion the image will be doubled, more of the light passing 
 into the extraordinary image, and less into the ordinary, 
 according as the angle at which the edges cross is in- 
 creased from o to 90; and at 45 of inclination the 
 light is equally divided between the two. This, it is 
 obvious, could not be if the ray were indifferently dis- 
 posed with respect to surrounding space. There sub- 
 sists in it a difference of properties depending on situa- 
 tion a difference analogous to that between a square 
 rod and a round one. It has acquired sides in its pas- 
 sage through the crystal, which it preserves in its subse- 
 quent course through space till it meets some body whose 
 action on it may bring their existence into ocular evi- 
 dence. It would seem almost as if light consisted of 
 particles having polarity, like magnets ; and that in its 
 passage through a doubly refracting substance these
 
 348 ON LIGHT. 
 
 came to be arranged, half with their poles in one direc- 
 tion (as regards the sides of the crystal), and half in a 
 direction at right angles to the former. And this is the 
 vray in which Newton conceived it, as he himself dis- 
 tinctly states (Opt., Query 21); and as it necessarily must 
 be conceived if the corpuscular theory were to be 
 adopted How it is explained on the undulatory hypo- 
 thesis, we shall presently see. 
 
 (126.) It was while gazing one evening in 1808, through 
 such a prism of Iceland spar as we have just described, 
 from his study in the Rue d'Enfer at the windows of the 
 Luxembourg Palace in Paris, that M. Malus, at that time 
 engaged in studying the law of extraordinary refraction in 
 this body, happened to notice that the reflexion of the sun 
 on a window of the palace disappeared from one of its 
 images, in a certain position of the prism, and from the 
 other when held at right angles to that position ; while in 
 the intermediate situations, the glare was visible in both 
 images, unequally divided, however, between them, ex- 
 cept when held in a situation exactly intermediate, or at 
 45 from its first position : in a word, that the light re- 
 flected from the window had acquired precisely the pecu- 
 liarity which would have been impressed on it by pre- 
 vious transmission through a similar prism. To this 
 peculiarity he gave the name of POLARIZATION, and light 
 so affected has ever since been said to be POLARIZED. 
 
 (127.) Total and partial polarization of light by reflexion. 
 The angle at which a ray of light must be incident on 
 glass that the reflected ray may acquire this property is 
 56 45' from the perpendicular, or at an inclination of
 
 ON LIGHT. 340 
 
 33 15' to the surface, and in this case the polarization is 
 complete, or the whole of the reflected light has acquired 
 the property in question.* If at any other obliquity ; it 
 is only partially polarized, or a portion only of the re- 
 flected light has acquired it. How this portion is to be 
 distinguished and separated from the unpolarized portion, 
 we shall presently explain. Suffice it here to observe 
 that this latter portion bears a greater proportion to the 
 whole reflected beam, as the angle of incidence deviates 
 more from that above specified (which is called the/0/- 
 arizing angle). The plane in which reflexion has been 
 made is called the plane of polarization ; and two rays 
 which have undergone reflection at the polarizing angle 
 in planes perpendicular to each other, are said to be 
 oppositely polarized, 
 
 (128.) The angle of incidence 56 45' has this pecu- 
 liarity that if we consider the directions subsequently 
 pursued by the two portions into which a ray so incident 
 on glass is divided, the one pursuing its course by re- 
 flexion in the air, the other by refraction within the glass, 
 these two directions include a right angle as in the figure 
 overleaf, where A c is the incident, C B the reflected, 
 and c D the refracted rays, at the surface of a glass P Q, 
 When the angle A c P or B c Q is 33 15' Q c D is 56 45', 
 and D c B is a right angle. The law of polarization so 
 announced, as Sir David Brewster has shown, is general, 
 
 * In point of fact the differently coloured rays are not all polar- 
 ized at exactly the same angle, so that this is rigorously exact only 
 for homogeneous light But ihe difference is so trifling that it is 
 purpose/ y here kept out of view.
 
 35 ON LIGHT. 
 
 and extends to all media, whatever their refractive 
 powers. Thus, for water, the polarizing angle is 53 n', 
 and for diamond 68 6' numbers concluded from this 
 simple rule (equivalent to the geometrical property above 
 
 D 
 Fig- 
 
 stated) that the index of refraction is in a}l cases the tangent 
 of the polarizing angle. 
 
 (129.) If a ray of light so polarized by reflexion be 
 received on such a prism as is above described, held 
 with its refracting edge (i.e., the optic axis of the crystal) 
 at right angles to the plane of reflexion, or parallel to 
 the reflecting surface, it will entirely pass into the ordi- 
 nary, or most refracted image ; vice versa if the prism be 
 turned round 90, -so as to have its edge parallel to the 
 plane of reflexion (i.e., of polarization), wholly into the 
 extraordinary. The same interchange will of course 
 take place if the prism be held immovable, and the re- 
 flecting glass turned round, so as to change the plane of 
 reflexion, and thus we perceive that rays oppositely polar- 
 ized are distinguished by the characters of passing entirely 
 into the one and entirely into the other of the two images, 
 when so refracted. A beam of light partially polarized 
 may be regarded as a mixture of two portions, the one 
 wholly polarized, the other wholly unpolarized ; and a
 
 ON LIGHT. 351 
 
 beam of unpolarizcd light may, conversely, always be re- 
 garded as a mixture of two equal rays oppositely polar- 
 ized, in any two planes at right angles to each other. 
 
 (130.) If a ray reflected from any medium at the 
 polarizing angle (and therefore wholly polarized) be 
 received on a second surface of the same medium at 
 the same angle of incidence, and in a plane coincident 
 with that of the first reflexion, it undergoes partial re- 
 flexion just as an unpolarized ray would do, and both 
 the reflected and refracted portions retain their polariza- 
 tion. But if the plane of the second incidence be at 
 right angles to that of the first, no portion of the light is 
 reflected, but the whole passes into the refracted ray, re- 
 taining its polarization, just in the same manner as, 
 had it been incident on our doubly refracting prism held 
 with its edge at right angles to its plane of polarization, 
 it would have wholly passed into the extraordinary ray. 
 Vice versa, if the ray extraordinarily refracted by such 
 a prism be received on a glass plate at the polarizing 
 angle of incidence, no reflexion will take place if the 
 edge of the prism be parallel to the plate. Hence we 
 are entitled to conclude that it is the very same property 
 which is impressed on light in both cases, and that a 
 ray polarized by reflexion differs in no respect from one 
 which has received this property by passing through a 
 doubly refracting crystal. 
 
 (131.) A ray partially polarized by reflexion at a 
 greater or less incidence than that at which it would 
 have been completely so, may be wholly polarized, or 
 nearly so, by repeated reflexions at the same angle.
 
 3$2 ON LIGHT. 
 
 This, which might be concluded a priori 'by considering 
 that the un polarized portion differs in no respect from 
 ordinary light, and is therefore susceptible of so receiv- 
 ing partial polarization, while the polarized portion re- 
 tains its polarization unchanged by reflexion, is verified 
 by experiment 
 
 (132.) If a ray partially polarized in any plane be 
 received on the doubly refracting prism already men- 
 tioned, with its edge perpendicular to the plane of 
 polarization, the polarized portion will pass wholly into 
 the ordinary image, while the unpolarized will be equally 
 divided between the two. Thus the two images will be 
 unequally bright By turning round such a prism, then, 
 till a position is found at which the contrast between 
 the two images is most striking, this plane will be dis- 
 covered, and the difference of their illuminations is the 
 measure of the quantity of polarized light in the beam. 
 
 (133.) Polarization of light by refraction. When light 
 is incident on glass or any uncrystallized transparent 
 body at the polarizing angle, the reflected portion (a 
 small per-centage, not more than one-twelfth of the whole 
 light) is wholly polarized in the plane of incidence, as 
 already stated. The refracted beam (by far the larger 
 portion), when examined in the mode just described, is 
 found to be partially polarized in a plane at right angles 
 to that of incidence, and the amount of polarized light 
 which it contains to be precisely equal to that in the 
 reflected beam. Thus we see that when light falls upon 
 such a surface, the greater portion passes unchanged, 
 while the other is divided into two equal portions oppo*
 
 ON LIGHT. 353 
 
 sitely polarized, the one being reflected, the other trans- 
 mitted, and intermingled with the unpolarized part. 
 
 (134.) If a parallel plate of glass be used for this ex- 
 periment, the same process is repeated at the hinder 
 surface. An equal per-centage of the unpolarized por- 
 tion is similarly divided between the reflected and 
 transmitted rays, oppositely polarized, and as the trans- 
 mitted polarized portion is, ipso facto, guaranteed from 
 subsequent reflection at the polarizing angle, the total 
 amount of polarized light in each of the two beams is 
 nearly doubled. If behind this a second parallel glass 
 plate be applied, the same process is again repeated on 
 the remaining unpolarized portion, and so, by multiply- 
 ing the plates, the whole incident beam is ultimately 
 divided equally into a reflected and a refracted beam 
 completely polarized in opposite planes. Such at least 
 would be the case were the plates perfectly transparent 
 and infinite in number ; but as these conditions cannot 
 be fully realized, the transmitted beam is never com- 
 pletely polarized, though enough so to afford 'a very 
 convenient mode of viewing many optical phaenomena. 
 On the other hand, if the plates be truly plane and their 
 surfaces exactly parallel, the reflected beam is wholly 
 polarized, and as its intensity is nearly half that of the 
 incident light, this affords an excellent mode of procur- 
 ing a polarized beam available for purposes of experi- 
 ment. A frame containing six or eight squares of good 
 window glass laid one on the other, and backed by a 
 sheet of black velvet, is one of the most convenient and 
 useful of optical instruments, and will be frequently
 
 J54 ON LIGHT. 
 
 referred to in what follows as a " polarizing frame," a 
 similar series set transparently being termed a " polariz- 
 ing pile." 
 
 (135.) Other modes of polarization. There are certain 
 doubly refractive crystals, more or less coloured, which 
 possess the singular property of absorbing or stifling in 
 their passage through them, unequally, the two oppositely 
 polarized rays into which they divide the incident light. 
 Two bodies especially have been noticed in an eminent 
 degree endowed with this property the one a mineral 
 occurring more or less frequently among the rocks of 
 igneous origin, called the tourmaline, the other an arti- 
 ficial chemical compound, the iodo-sulphate of quinine. 
 The former crystallizes for the most part in long prisms of 
 many sides, terminated by faces, three of which belong 
 to the primitive form, an obtuse rhomboid, whose axis is 
 that of the prism itself. In consequence, like all crys- 
 tals of this class, it is doubly refractive, and if artifi- 
 cially cut and polished into a doubly refracting prism, 
 having its refracting edge parallel to that of the rhom- 
 boid, an object viewed transversely through it will 
 appear double ; provided the eye be held quite close to 
 the refracting edge ; but if ever so little removed, so as 
 to look through a greater thickness of the substance, one 
 of the images will be observed to diminish rapidly in 
 intensity ; and at a certain, usually very moderate, thick- 
 ness to disappear altogether, as if extinguished by a 
 deeper colour or a higher degree of opacity in the 
 medium, the other remaining undiminished. The unex- 
 tinguished ray is, of course, completely polarized, and
 
 ON LIGHT. 355 
 
 that in the plane of the section of the prism at right 
 angles to the edge. If. instead of cutting the crystal 
 into such a prism, it be formed into a flat plate, with its 
 faces parallel to the axis of the rhomboid ; such plate 
 will in like manner extinguish one of the pencils into 
 which a ray incident perpendicularly on it is divided, 
 allowing the other to pass ; and the pencil so transmitted 
 js completely polarized in a plane perpendicular to the 
 axis of the plate. This property of a tourmaline plate 
 renders it invaluable as an optical instrument, affording 
 the readiest and most convenient means of procuring a 
 polarized beam of light for the examination of crystals 
 and other purposes. Its only drawback is, that this 
 mineral is most commonly coloured with a strong tint of 
 blue or green, which affects the colour of the trans- 
 mitted light. Some specimens, however, while equally 
 effective in destroying one of the refracted pencils, are 
 yet but slightly tinged with colour as respects the other, 
 which is therefore transmitted fully polarized, but with 
 only a slight tinge of brownish yellow. The other 
 substance, of late much resorted to for the same pur- 
 pose, the iodo-sulphate of quinine, crystallizes in very 
 thin scales like mica, of a purplish-brown hue, which in 
 like manner polarize completely one half the incident 
 light, which passes freely through them ; the other half 
 being extinguished. This curious property was dis- 
 covered by Mr Herapath, who first formed the com- 
 pound in question. 
 
 (136.) When two parallel plates of tourmaline cut 
 from the same crystal in the mode above described, or
 
 356 ON LIGHT. 
 
 two laminae of Mr Herapath's quinine salt, are laid one 
 on the other conformably (or with their axes parallel), 
 the light polarized by one passes freely through the other; 
 but if the one be turned round on its own plane, on the 
 other, the intensity of the transmittted beam gradually 
 diminishes, until the axes cross at right angles, in which 
 position the combination is quite opake. A similar 
 gradual diminution of light, up to complete extinction, 
 takes place when a ray polarized by reflexion from glass, 
 or in any other manner, is received on such a plate, made 
 to rotate in its own plane. The effects are just what 
 might be expected to happen if a flight of 'flattened arrows 
 were discharged at a grating of parallel wires. Those 
 only whose planes were parallel to the wires would be 
 able to pass, and having passed one such grating, would 
 penetrate any number of others placed conformably be- 
 hirid it, but not if placed transversely. This is a simile, 
 not an explanation, but it conveys, though coarsely, to 
 the mind a conception of the distinction between polar- 
 ized and unpolarized light, not to be despised as an aid 
 to the imagination. 
 
 (137.) If a "polarizing frame" of glass plates, such as 
 above described, be laid down before an open window, 
 and, the eye being held near it so as to embrace a large 
 illuminated area or " field of view," a tourmaline plate be 
 looked through, and turned slowly round, in its own plane 
 before the eye ; a position will be found in which the 
 appearance of a dark cloud comes over the frame, extend- 
 ing over a very considerable visual angle ; the central 
 portion being completely obscure; and the darkness shad-
 
 ON LIGHT. 357 
 
 ing off at the borders by insensible though rapid degrees. 
 Within this " polarized field," a vast variety of brilliant 
 and beautiful optical phenomena, hereafter to be de- 
 scribed, are very conveniently and elegantly exhibited. 
 One effect is very striking. If instead of a black velvet 
 backing, the glasses be laid on any bright surface, the 
 printed page of a book, for instance this, which, with- 
 out the interposition of the tourmaline, cannot be dis- 
 cerned for the glare of light reflected from the glasses, 
 becomes distinctly visible, and may be read with facility 
 when that glare is taken off in the manner described. 
 So, too, by looking through a tourmaline plate held trans- 
 versely, on the surface of a pond, at the polarizing angle ; 
 the reflected light from the surface being destroyed, the 
 objects at the bottom, the fishes, &c., are distinctly seen, 
 though completely invisible to a bystander. So, too, by 
 polarizing alternately in a vertical and a horizontal plane, 
 the light of one or more lamps, night signals may be 
 made, and a message transmitted, visible and interpretabk 
 as signals, to a distant spectator provided with a tourma- 
 line plate, while a bystander not so provided, though he 
 see the lamps, will have no suspicion that any such com- 
 munication is in progress.* 
 
 (138.) Polarization of the sky light. The light of a clear 
 and perfectly cloudless blue sky is partially polarized in a 
 plane passing through the sun, the eye, and the point of 
 the sky examined. At each point in that great circle of 
 
 * I mention this to prevent a patent being hereafter taken out 
 "for secret communication at a distance by means of polarized 
 light"
 
 358 ON LIGHT. 
 
 the celestial concave, which is 90 remote from the sun's 
 place, the amount of polarized light which it sends to 
 the eye bears a very considerable proportion to the total 
 illumination, amounting to nearly a fourth of the whole. 
 At every other inclination of the visual ray to the direct 
 sunbeam, the proportion is less, and in the neighbour- 
 hood of the sun, or of the point on the horizon directly 
 opposed to it very small. When examined in a mode 
 hereafter to be described, by the intervention of a tour- 
 maline plate, and a crystallized lamina, this gives rise to 
 a series of exceedingly beautiful and brilliant phenomena, 
 productive of the greatest astonishment to those who 
 learn for the first time by their exhibition, that totally 
 different, and even opposite qualities, characterize dif- 
 ferent portions of an illuminated surface apparently so 
 perfectly uniform and homogeneous. This effect is sup- 
 posed to originate in the reflexion of the solar rays on 
 the particles of the air itself, an explanation encumbered 
 with many difficulties, but the best (indeed the only one) 
 that has yet been offered. 
 
 (139.) Polarization interpreted on the undulatory theory. 
 According to any conception we can form of an elastic 
 medium, its particles must be conceived free to move 
 (within certain limits greater or less according to the 
 coercive forces which may restrain them) in every direc- 
 tion from their positions of rest, or equilibrium. It by 
 no means follows, however, that the nerves of the retina 
 are equally susceptible of excitement by vibrations of the 
 luminiferous ether (in which they may be conceived im- 
 mersed) in all diiections. In the case of sound, the
 
 ON LIGHT. 359 
 
 tympanum of the ear which receives the impulse of the 
 aerial medium, would appear to vibrate like the parch- 
 ment of a drum, by the direct impact of its waves per- 
 pendicular to its surface. It is, therefore, sensible to 
 such of the movements of the vibrating medium only as 
 are in the direction of the sound-ray, and not at all to 
 transverse vibrations. But if we conceive the nervous 
 filaments of the retina as minute elastic fibres, standing 
 forth at right angles to its plane, like the bristles of a 
 brush (the reader will pardon the apparent coarseness ot 
 the illustration, which is only intended as an illustration 
 of what may be, and no doubt is, a process of trans- 
 cendent delicacy), immersed in the ether; it is evident 
 that movements of the latter parallel to their direction 
 would not, but that those transverse to it would tend to 
 throw them into vibration, just as ears of corn would be 
 little or not at all agitated by a straight and slender 
 rod moved up and down between the stalks, or to and 
 fro in the direction of its own length, but violently by 
 a transverse horizontal motion of the rod. 
 
 (140.) Whatever be, at any instant, the motion of an 
 ethereal molecule, it may always be resolved into two, 
 one in the direction of the ray in the act of propagation, 
 and the other in a direction transverse to it, in the plane 
 of the wave surface. If the sensation of light be sup- 
 posed to be produced by the former resolved portion, 
 no account can be given of the phenomenon of polar- 
 ization ; such movement being equally related to sur- 
 rounding space in all directions outward from the raj- 
 as an axis. The contrary is obviously the case with
 
 ?6o ON LIGHT. 
 
 the other resolved portion. Suppose one end of a long 
 horizontal cord fastened to a wall, the other held in the 
 \iand, and tightly strained. If a small vibratory motion 
 oross-wise to the cord be given to the hand in a hori- 
 zontal plane, an undulation confined to that plane, will 
 run along the cord ; if in a vertical one, then will the 
 undulation be wholly performed in a vertical plane. If 
 the propagation of a wave along a stretched cord be 
 assimilated to that of a ray of light, the former of 
 these cases will convey the idea of a ray polarized in 
 a horizontal, the latter in a vertical plane. If the 
 movement of the hand (always transverse to the cord) 
 be not confined to any particular plane, but take place 
 sometimes in one, sometimes in another, at all sorts 
 of inclinations to the horizon the undulation which 
 runs along the cord in this case will convey the idea of 
 an unpolarized ray. (According to Sir David Brewster, 
 however, a partially polarized ray would, in this manner 
 of viewing it, be assimilated to the case when the vibra- 
 tory movement should neither be strictly confined to one 
 plane, nor altogether irregular, but confined in its devia- 
 tions from it to some angular limit less than a right angle.) 
 (141.) There is nothing to lead us to believe that the 
 vibratory motions of the particles of material bodies, 
 especially those in the state of gases in the act of com- 
 bustion, in virtue of which they are luminous, are ne- 
 cessarily confined to any particular plane. Many thou- 
 sands, or even millions, of vibrations in one plane may 
 be succeeded by as many in any other, according to the 
 direction and frequency of the shocks which five rise to
 
 ON LIGHT. 36l 
 
 them within an interval of time inappretiably short, and 
 without prejudice to the continuous perception of the 
 vibratory movement communicated to the ether as light. 
 The act of polarization consists then in the subsequent 
 arrangement, at some definite point in the line of progress 
 of the ray, of all these vibratory movements, into parallel- 
 ism with each other, or into a single plane from which 
 they have afterwards no tendency (per se) to deviate. 
 As the particles of crystallized bodies must be con- 
 ceived to be arranged in definite lines and planes, it 
 is easily conceivable that, whether among them, or in 
 conjunction with them, the ethereal molecules may 
 be confined in their vibrations to two particular 
 planes determined by the internal constitution of 
 the crystal and the incidence of the light ; that a 
 vibratory movement propagated into a body so con- 
 stituted should ipso facto resolve itself into two such 
 movements in these two planes (according to the general 
 mechanical principle of the composition and resolution 
 of motion) ; that it should be so propagated during its 
 progress through the crystal ; and that at its emergence 
 into free space, each vibration should thenceforward sub- 
 sist separately, there being nothing to change it. Again, 
 it is no less conceivable that in these vibrations the 
 molecules of the ether moving in one plane may be 
 differently impeded by, or stand in a different connexion 
 with those of the medium, from those moving in the 
 other, and that, in consequence, their propagation of 
 the movement may be effected with a different velocity, 
 and thus give rise to a difference of refractive power,
 
 362 ON LIGHT. 
 
 which, as we have seen, depends on the proportion of 
 velocity of the light in and out of a medium. In the 
 case of one set of vibrations, again, the propagation of 
 the medium may be equally impeded or influenced in 
 all directions of the ray in which case a wave starting 
 from any point in the surface would run out spherically 
 within the crystal, while in that of the other the amount 
 of obstruction might vary with the direction of the ray, 
 and thus give rise to a wave running out with different 
 velocities in different directions from its centre of propaga- 
 tion, and therefore not spherically. 
 
 (142.) To this conclusion, but without passing through 
 the intermediate considerations which have led us up to 
 it, Huyghens (who certainly had formed no conception 
 of transverse vibrations) appears to have jumped, by one 
 of the happiest divinations on record in the history of 
 science, viz., that in the double refraction of Iceland 
 spar, while the ordinary ray is propagated in a spherical, 
 that of the extraordinary spreads from its point of origin 
 at the surface of the crystal in an elliptical wave, the 
 form being that of an oblate spheroid of revolution, 
 having its polar axis parallel to the axis of the rhom- 
 boid, and bearing to its equatorial diameter a definite 
 numerical proportion, viz., that of eight to nine (very 
 nearly). Making this assumption, and laying it down 
 as a principle (capable of demonstration), that the 
 direction of a ray of light in such a mode of propaga- 
 tion is not that of a perpendicular to the surface of the 
 wave at any point, but that of a line drawn from the 
 centre of the wave to its point of contact with a plane,
 
 ON LIGHT. 363 
 
 touching at the same time all the wave su r faces in pro- 
 gress, at the same time, through the crystal, which have 
 originated in one and the same plane wave sweeping 
 over its external surface (just as in the explanation of 
 ordinary refraction given in our first part, in the case of 
 spherical waves, in which case the latter line is perpen- 
 dicular to the wave surface) ; he was enabled to explain 
 every particular of the double refraction in Iceland spar, 
 so far as the direction of the extraordinary ray is con- 
 cerned, including its deviation from the plane of the 
 angle of incidence, and its non-conformity with the 
 ordinary law of the sines except in special cases. The 
 results of his reasoning have been compared with experi- 
 ment, with extreme care, by M. Malus, as already men- 
 tioned, and found exactly in accordance with fact. We 
 cannot, of course, in an essay like the present, give any 
 account of the special conclusions, or of the mathe- 
 matical reasoning on which they are founded; which 
 involve more geometry than the generality of our 
 readers are likely to possess. But we can put into a 
 very few words, and we think make readily intelligible, 
 the main feature of the reasoning, that which determines 
 the deviation of the extraordinary ray from perpendi- 
 cularity to the wave surface, and from the plane of in- 
 cidence. 
 
 (143.) Let A B c D represent a plane wave descending 
 perpendicularly upon the upper surface E H (supposed 
 horizontal) of a crystal of Iceland spar, of which E H M I 
 is the principal section, or that cutting through both the 
 obtuse angles of the rhomboid, and in which its axis lies.
 
 364 
 
 ON LIGHT. 
 
 The light then which this wave conveys will be incident 
 perpendicularly on the surface E H, or in the direction of 
 the lines B F, c G, and these lines continued to K and L, 
 on the lower surface, would be the course of the rays B F, 
 c G, supposing them to undergo the ordinary refrac- 
 tion. Considering now the extraordinary; suppose the 
 portions E F, G H of the surface screened, and only the 
 portion F G of the wave allowed to enter. This on strik- 
 ing the surface, will excite at every point over its whole 
 extent a luminiferous vibration, which will be propagated 
 
 \ 
 
 Fig. 14. 
 
 within the crystal in a spheroidal wave, having its shorter 
 axis parallel to that of the crystal : and all these spheroids 
 being equal and similar, the plane which touches them all, 
 and which is, in effect, the extraordinarily refracted plane 
 wave within the crystal, will advance parallel to the sur- 
 face E H. Suppose it arrived at the other surface I M, 
 and let N o be the points of contact of that surface with 
 the spheroidal elementary waves whose centres are F and 
 G at that moment. Then will N o be that portion of the
 
 ON LIGHT. 365 
 
 posterior surface which will first be struck by the refracted 
 wave. The portions beyond on either side, I N and o M, 
 will subsequently receive the divergent undulations, which 
 (as we have already explained) give rise to diffracted 
 fringes bordering the shadows of the screens E F, G H. 
 Thus we see that the space between N and o, and not 
 that between K and L, will receive the full illumination 
 from the aperture F G, which has therefore been propa- 
 gated obliquely in the direction of the lines F N, GO, and 
 not of the perpendiculars F K, G L.* 
 
 (144.) The deviation of the refracted ray from the plane 
 of incidence, and from that of ordinary refraction, will 
 be readily understood when it is borne in mind that 
 whether at a perpendicular or an oblique incidence, a 
 plane exterior wave is transformed by the extraordinary, 
 as well as the ordinary refraction, into a plane interior 
 one, and that the plane of incidence of a ray is perpen- 
 dicular to both these planes. It cannot therefore con- 
 tain the extraordinary refracted ray (which is a radius of 
 the spheroid) without containing at the same time a 
 normal to the elliptic surface of propagation at its point 
 of contact with the interior plane wave, that is to say, 
 unless it contain also the axis of the spheroid. In other 
 words, the extraordinary ray will always deviate from the 
 plane of incidence, unless in the case when that plane 
 coincides with some one of the meridians of the spheroid 
 in question. 
 
 (145.) Since there is no double refraction in the direc- 
 tion of the axis of the rhomboid, it follows that in that 
 This is Huyghens's explaiiation, and the correct one.
 
 366 ON LIGHT. 
 
 direction the velocities of propagation of the ordinary 
 and extraordinary rays within the crystal are the same, 
 and that therefore, supposing the two corresponding un- 
 dulations propagated from the same point in its surface 
 to run out internally, the one in the form of a spherical, 
 the other of a spheroidal shell, these shells will have a 
 common axis, viz. : the shorter axis of the spheroid, 
 which will therefore wholly include the sphere, being in 
 contact with it at the poles of the spheroid. Cceteris 
 paribus, too, it is equally obvious that, when we come to 
 consider different sorts of crystals possessing the pro- 
 perty of double refraction, the intensity of this quality, 
 or the amount of angular separation of the two refracted 
 rays at the same incidence, will be determined by the 
 greater or less amount of ellipticity of the spheroid .n 
 question. Should this ellipticity be nil, the spheroid will 
 coincide over its whole extent with the sphere, and there 
 will be no double refraction This is the case with all crys- 
 tallized bodies, whether mineral or artificial salts, whose 
 primitive form is the cube. In some cases (compara- 
 tively rare ones), of which quartz or common rock crystal 
 is an example, the spheroid is of the kind called prolate, 
 or one formed by the revolution of an ellipse round its 
 longest diameter, and is therefore wholly contained within 
 the sphere. In these, then, the velocity of the extraordi- 
 nary ray within the crystal is less than that of the ordi- 
 nary ; and the latter ray, which is the more refracted of 
 the two in Iceland spar, is in such crystals the less so. 
 On comparing different crystals, however, it is not found 
 (which perhaps might have been expected) that the el-
 
 ON LIGHT. 367 
 
 lipticity of the spheroid in question is determined solely, 
 or even principally, by the degree of obtuseness of the 
 rhomboidal form of the crystal. It appears to be regu- 
 lated far more by the chemical and other physical quali- 
 ties of the material. 
 
 (146.) Of the interference of polarized rays. The assimi- 
 lation of a ray of light to a series of equidistant waves 
 running along a stretched string, will afford a very clear 
 conception of the interference of polarized rays. Sup- 
 pose a vibratory movement in a horizontal plane to be 
 communicated to one end of such a string, and to propa- 
 gate along it such a series of waves, which will therefore 
 all be confined to the same horizontal plane. If then a 
 simultaneous movement, exactly equal and similar, and 
 in the same plane, were communicated to a point in the 
 string exactly half a wave breadth in advance of the point 
 where the first series originated ; each point in its length 
 anywhere in advance of both these origins of movement 
 would be always solicited by two equal and opposite im- 
 pulses, the one of which, would contradict the other, and 
 in consequence it would remain at rest, and the two 
 series of waves would destroy one another. If the origin 
 of the two vibratory movements were distant from each 
 other by a whole wave breadth, they would conspire to 
 produce a double extent of vibratory excursion all along 
 the string. All this is merely recapitulatory of what was 
 stated, in Lecture VII., when explaining the general 
 nature of the interference of rays. But it is evident that 
 these conclusions only follow if the interfering vibratory 
 movements are performed in the same plane. Supposing
 
 368 ON LIGHT. 
 
 them performed in planes at right angles to each other, 
 no such mutual destruction or reinforcement of move- 
 ment can take place. Two movements at right angles 
 to each other, communicated at the same instant to the 
 same material molecule, combine, in virtue of the me- 
 chanical principle of the composition of motions, to pro- 
 duce a movement intermediate in direction ; and can in 
 no case destroy each other. 
 
 (147.) It follows from this, that if such be really the 
 nature of the luminous vibrations and such the true ex- 
 planation of the phenomenon of polarization interfer- 
 ence can only take place between rays polarized in the 
 same plane such complete interference at least as shall 
 result in the extinction of both, in the manner above de- 
 scribed. This conclusion is, happily, capable of being 
 brought to the test of experiment, and the result is found 
 to be in exact accordance with the d priori reasoning. 
 The experiment is simple and direct. Let two small 
 holes, or, better, parallel slits very near each other in a 
 thin opake screen, be placed between the eye and a 
 very minute and brilliant point of light; and viewed 
 through a lens, as described in a former paragraph; so 
 as to see the diffractive fringes. Now over the holes or 
 slits let two plates of tourmaline of precisely equal thick- 
 ness and in every respect similar be applied (to secure 
 which conditions, the two halves of a single plate worked 
 to exact parallelism and cut across, may be used). Then 
 if the axes of these plates be parallel, in which case the 
 light passing through both the apertures will be similarly 
 polarized, the fringes will continue to be seen. If one
 
 ON LIGHT. 369 
 
 of them be slowly turned round in its own plane till its 
 axis comes to be situate at right angles to that of the 
 other, they will gradually decrease in intensity and at 
 length disappear altogether when this rectangularity is 
 precisely attained. In the first case, then, the rays have 
 interfered in the last, not : while in the intermediate 
 states a partial interference takes place, the more com- 
 plete the nearer the axes are to parallelism. How this 
 is operated we shall now proceed to explain. 
 
 (148.) Circular and elliptic polarization. If we regard 
 the vibratory movement of any single particle of an elas- 
 tic medium in its most general mode of conception, we 
 shall find that it may always be considered as capable of 
 resolution into three rectilinear vibrations in three planes 
 at right angles to each other, each going on as if the 
 others had no existence : and its place in space at any 
 instant will be had by estimating its distance on one side 
 or the other of its neutral or central position (those of 
 perfect equilibrium and rest), reckoned along each of the 
 three lines in which these planes intersect (which, after 
 the manner of geometers, may be considered as three 
 rectangular axes, or co-ordinate lines), which it would 
 have attained at that instant in virtue of each separately, 
 and independent of the others. This is nothing more ^ 
 than the enunciation of one of the simplest of mechanical 
 laws, that of the composition and resolution of motions. 
 But the theory of movements propagated through elastic 
 media (a theory far too elevated and intricate to admit 
 of any explanation in these pages, and whose results the 
 reader must take for granted) further teaches us that a 
 
 2 A
 
 3?O ON LIGHT. 
 
 vibratory movement once set up and steadily maintained, 
 according to a regular law of periodicity in any one 
 molecule of such a fluid will, sooner or later (according 
 to its distance and situation), reach every other, which 
 from that moment will be agitated by a vibratory move- 
 ment precisely similar in its phases (though of inferior 
 extent in its excursions) to the original movement, and 
 performed in the same period of time. It matters not 
 whether the medium be or be not equally elastic in all 
 directions. This will affect the rate of progress of a wave 
 through it in different directions, and by consequence 
 the form of the wave, and the length of time that has to 
 elapse before the molecule in question begins its vibra- 
 tory movement ; but once set up in any molecule, that 
 movement will be maintained, so long as it is, so to 
 speak, fed from behind so long as successive waves 
 continue to pass through it. In the theory of light, the 
 eye being insensible to vibratory movements in the di- 
 rection of the ray, we have only to consider those com- 
 ponents of the motion which lie in a plane at right 
 angles to that direction, and which, for the present, we 
 will suppose to be that of the paper before us. 
 
 (149.) Let us consider, then, the kind of motion which 
 an ethereal molecule will assume, under the influence ot 
 two such vibratory movements simultaneously affecting 
 it, in directions transverse or otherwise inclined to each 
 other, but both directions lying in one common plane, 
 that of the paper, or of the wave-surface ; each of which 
 will therefore represent the vibratory movement proper 
 to a ray polarized in a plane at right angles to our paper,
 
 ON LIGHT. 371 
 
 and intersecting it in its line of direction. And first, for 
 simplicity, let us suppose the two vibrations of equal in- 
 tensity (i.e., in both which the molecular excursions on 
 either side of the point of rest are equal), and that their 
 directions form a right angle with each other. Let A B 
 and a b, fig. 15, represent two such lines of vibratory 
 movement, c, c, their central points, or the positions of 
 rest of the molecules when undisturbed, and c A, c B ; 
 ca, c b ; their extreme excursions to and fro. The times 
 of vibration being equal (which is an indispensable 
 condition for the union into one of two distinct luminous 
 rays : as a red ray, for instance, cannot interfere with a 
 violet one), let each be supposed divided into the same 
 number of equal parts (say 360). Then supposing the 
 molecules to set out at the same instant from c and c, 
 they will arrive at A a, respectively in 90 such units of 
 time, will have returned again to c c, in 180; have 
 reached B, b, in 270, and again returned to C and c, in 
 360. In so doing, however, their motions are not uni- 
 form, but most rapid when traversing the central points, 
 and gradually retarded as they recede from these : so 
 that in equal intervals of time the spaces traversed along 
 the lines C A, c a, will be unequal. Then let the whole 
 time (90) of describing c A, be divided into five equal 
 times of 1 8 each, and suppose that at the end of 
 the ist, 2d, 3d, 4th, and 5th of these, the molecule has 
 arrived at the points i, 2, 3, 4, 5. It is demonstrable, 
 then, that the several distances C i, C 2, C 3, C 4, C 5, 
 of these points from c will be to each other in the pro- 
 portion of the Sines of 18, 36, 54, 72, and of 90"
 
 372 
 
 ON LIGHT. 
 
 or radius; and the same is true of c i, c 2, c 3, c 4, 
 
 '5- 
 
 (150.) This premised, we are now in a condition to 
 trace the movement of a molecule affected at once by 
 both these causes of displacement. Let it be O. Then 
 at the expiration of the first interval of 18 units of time 
 it will in virture of the vibration parallel to C A, be 
 carried to a distance equal to C i in a direction O P 
 parallel to that line, and will be found so far from the 
 
 \ 
 
 xxxxxx 
 
 5 + * 
 
 He. 13. 
 
 line O / parallel to c a. And in virtue of the other 
 vibration similarly it will be found at the same time at
 
 ON LIGHT. 373 
 
 the distances i (=C i) from O P, or in the direction O/ 
 parallel to c a. In virtue of both movements, then, it 
 will be found at x, the extremity of the diagonal of the 
 square O x at that moment. And similarly at the end 
 of the 2d, 3d, &c., interval, it will be found at the ex- 
 tremities of the diagonals of the squares next in succes- 
 sion, and as these all lie in one line, o E, 45 inclined 
 both to O P and O /, it appears that in this case the 
 resultant vibration will be rectilinear, and will be per- 
 formed along the diagonal E G of the square E F G H ; 
 and thus it appears that the superposition of two rays of 
 equal intensity, polarized in opposite (i.e., rectangular) 
 planes, results in the production of a ray polarized in a 
 plane 45 inclined to each of the former. Moreover, 
 the square of the diagonal being double that of either 
 side of a square, and the intensity of a ray being mea- 
 sured by the square of the vibrational excursion of its 
 ethereal molecules, the intensity of the compound ray 
 will be double that of the components, or, equal to their 
 sum. And, vice versa, any polarized ray may be con- 
 sidered as equivalent to two rays, each of half its in- 
 tensity, polarized in planes 45 inclined on one side, 
 and on the other of its plane of polarization. It need 
 hardly be observed that if the molecule in starting from 
 O be moving in the direction C A, in virtue of the one 
 vibration, and of c b in virtue of the other, that is, if 
 it be commencing its first semi-vibration in the one 
 direction, and its second in the other, or again in other 
 words, if the vibrations differ in phase by an exact semi- 
 undulation ; all the same reasoning will apply, with this
 
 374 ON LIGHT. 
 
 only difference : viz., that the resultant rectilinear vibra- 
 tion will be performed along the other diagonal, H F, of 
 the same square. 
 
 (151.) It appears, then, that a change of phase in the 
 vibrations of one of the component rays, of half an un- 
 dulation, exactly reverses the polarization of the com- 
 pound ray, and causes its vibration to be performed 
 along the diagonal H F instead of G E. Let us now 
 examine by what sort of gradations the one of these 
 movements passes into the other, when the phase of one 
 of the vibrations C c is changed gradually. Suppose, 
 for instance, the vibration a b (so, for brevity, we will 
 designate it) to be in advance of the vibration A B by 
 one-twentieth part of a complete undulation, so that at 
 the moment when c starts from c in the direction c A, 
 c shall have already got to i in the direction c a. Then 
 at that moment our molecule O will not be at O but at y. 
 After the lapse of one-twentieth more of a period, C will 
 have got to I in the direction C A, and c to 2 in the 
 direction c #, and O, actuated by both movements, will 
 have arrived at z, having of course described in the in- 
 terval a line y z, connecting these two extremities of the 
 diagonal of the rectangle xyz. And exactly in the same 
 way, at the expiration of the next twentieth of a period, 
 it will be found in u, the extremity of the diagonal of 
 the next rectangle and thus tracing its course step by 
 step through the whole twenty, which constitute a 
 period, we shall see that it will have described a narrow 
 ellipse, having m n for its shorter axis, and E G for ///* 
 direction of its longer, and touching the four sides of the
 
 ON LIGHT. 375 
 
 square E F G H. If the initial difference of phase be 
 two, three, or four twentieths of the period, it will be 
 seen, by following out the movement in the same way, 
 that more and more open ellipses will come to be 
 described as represented in the figure ; and that, when 
 this difference amounts to five twentieths or a quarter 
 undulation, the movement will be circular in the direc- 
 tion / p q Q, or of the arrow marked thus -j-. The 
 difference of phases still continuing to increase, this 
 will again degenerate into an ellipse by a continued 
 elongation in the direction H F, and contraction in 
 the direction E G, till it passes at length, after another 
 quarter-undulation of phase-difference, into the straight 
 line H F. The circulation in all, however, being in the 
 same direction, or +. On the other hand, if instead of 
 supposing the vibration a b to be initially in advance of 
 A B by one-twentieth, we suppose it to be so much in 
 arrear, we shall have the same ellipse n E m described 
 as in the former case, but in the opposite direction, that 
 of the arrow marked , as will be easily seen by going 
 through the successive steps of our reasoning: and so 
 for all the rest ; so that in the case of a circular revolu- 
 tion, the direction of the rotation will be one way or the 
 other, according as the vibration a c is a quarter-undu- 
 lation in advance or in arrear, in respect of phase, of A c. 
 (152.) This, then, is what is meant by circular and 
 elliptic polarization. It is easy to extend the reasoning 
 above stated to cases in which the component vibrations 
 are of unequal intensity (or extent of excursion), and 
 make other than a right-angle with each other's direc-
 
 3?6 ON LIGHT. 
 
 tions. We have only to suppose our lines A B, b a, and 
 their parallels p Q, / q, inclined to each other at the 
 angle in question, and of unequal length ; to divide them 
 similarly (i.e., in the same proportion) in the points i, 2, 
 3, 4, 5 and we shall obtain a set of ellipses, none of 
 which, however, can in either of the cases have its axes 
 equal, or pass into a circle, for this plain reason that 
 no circle can touch internally all the four sides of any 
 parallelogram except a rhomb. 
 
 (153.) Conversely, a ray circularly polarized may be 
 considered as compounded of, and may (by suppressing 
 either of them and letting the other pass, through a 
 tourmaline plate) be resolved into two equal rays, each 
 of half its intensity, polarized at right-angles to each 
 other, and differing in phase by a quarter-undulation. 
 If one of them be in advance of the other by that phase- 
 difference, the rotation will be in one direction if in 
 arrear, in the other. Elliptic polarization, on the other 
 hand, when it exists, may be recognized by the possi- 
 bility of resolving the ray so polarized into two op- 
 positely polarized, and either of unequal intensity, or, if 
 equal, differing in phase otherwise than by a quarter- 
 undulation. 
 
 (154.) Finally, a ray polarized in any one plane may 
 be regarded as equivalent to two equal rays, circularly 
 polarized in opposite directions of rotation, and having 
 a common zero-point. 
 
 (155.) A ray of ordinary light may be considered as a 
 confused assemblage of rays, polarized indifferently in 
 all sorts of planes. It is, therefore, a mixed phaenome-
 
 ON LIGHT. 377 
 
 non ; and to study it in its simplicity, we must in idea 
 break it up into its component elements, and examine 
 their phaenomena per se. Now it results, from a series 
 of experiments too extensive and refined to be here de- 
 tailed, and from reasonings upon them which the gene- 
 rality of our readers could hardly be expected to follow, 
 that when a ray, polarized in any plane, undergoes re- 
 flexion in a different plane, the reflected portion comes 
 off in all cases more or less elliptically polarized that 
 is to say, that it consists of, or can be resolved into, two 
 rays, the one polarized in the plane of incidence, the 
 other in a plane at right angles to it that both these 
 portions have undergone a change of phase at the mo- 
 ment of reflexion, but not the same for both, so that 
 arriving at the surface in the same phase, they quit it in 
 different, and therefore constitute by their superposition 
 an elliptically polarized ray. The amount of ellipticity 
 varies, for each reflecting medium (according to the 
 nature of its material) with the angle of incidence at 
 which the reflexion takes place, and also with the inclina- 
 tion of the plane of incidence to that of the primitive 
 polarization of the incident ray. If the reflexion take 
 place on ordinary transparent media of not very high 
 refractive power, as glass, or water, and at the polariz- 
 ing angle, the degree of ellipticity is so slight that the 
 vibration may be considered as rectilinear, and the re- 
 flected ray as completely polarized in the plane of 
 incidence. As the refractive power of the surface in- 
 creases, the ellipticity impressed is greater, and in some 
 substances, of very high refractive power, such as dia-
 
 378 ON LIGHT. 
 
 mond, and all those bodies which possess what is called 
 the adamantive lustre (a consequence of such high refrac- 
 tive power) it is considerable. From such bodies accord- 
 ingly it is not possible, at any angle of incidence to obtain 
 a reflected ray completely polarized in one plane. And 
 when we come to reflexion from polished metals,* the 
 ellipticity becomes very considerable. In consequence, 
 only a very imperfect polarization of the reflected light 
 in the plane of incidence can be obtained by reflexion 
 from any metalic surface at any angle. 
 
 (156.) In all the above enumerated cases, the degree 
 of ellipticity increases with the reflective poiver of the 
 medium of which the reflecting surface is constituted ; 
 which itself stands in intimate connexion with the mag- 
 nitude of the refractive index. It might naturally, there- 
 fore, be expected to attain its maximum possible amount, 
 or that the ellipse should become a circle in the case 
 of total reflexion. This can only take place, however, 
 when the reflexion is made on the internal surface of a 
 transparent medium. This accordingly happens in the 
 case of a beautiful experiment of M. Fresnel, who found 
 that a parallelepiped of glass, t A B c D, fig. 15, being 
 cut and polished, having the acute angles at A and D, 
 
 * All metals, even the densest, are in some slight degree trans- 
 parent, and all have enormously large refractive indices. The 
 transparency of gold is perceptible in gold leaf, which transmits a 
 green light. That of silver is perceptible in the thin films deposited 
 on glass in Liebig's process for silvering mirrors the transmitted 
 light being bluish. 
 
 t The glass used was that known in France as " Verre de St. 
 Gobain. "
 
 ON LIGHT. 
 
 379 
 
 each 54 37', and a ray P Q, polarized in a plane 45 
 inclined to the plane of the section A B c D intromitted 
 perpendicularly at the face A B, so as to be reflected inter- 
 nally at Q on the side A c, (in which case, the reflexion 
 being at an angle of incidence 54 37' was total) ; and 
 
 Fig. i& 
 
 again at R, at the same angle, on the opposite side D B, 
 it emerged from the face D c, along the line R s, circu- 
 larly polarized. In this case, the plane of reflexion 
 making an angle of 45, with that of original polariza- 
 tion, the reflected ray will consist of two equal rays, 
 oppositely polarized j and of these the one in each act of 
 reflection has lost, in the other gained, an exact i6th of 
 an undulation, making an 8th difference at each reflexion, 
 or a quarter after both ; so as to emerge under all the 
 conditions of circular polarization. In consequence, 
 when analysed at its emergence by a tourmaline plate, 
 it is found to undergo no change of brightness on turning 
 the plate in its own plane, whereas the original ray, P Q,
 
 380 ON LIGHT. 
 
 would have been wholly extinguished at each quarter 
 revolution. 
 
 (157.) Another mode of communicating circular polariz- 
 ation to a ray, is to transmit it at a perpendicular in- 
 cidence through a parallel plate of any perfectly colour- 
 less and transparent doubly refracting crystal, of such 
 thickness, that in the passage through it of the two 
 waves, parallel to its surfaces, into which the incident 
 wave (supposed plane) is divided, (the one conveyed by 
 ordinary refraction, the other by extraordinary, and there- 
 fore travelling with different velocities in the crystal,) 
 the one shall have gained or lost, after emergence, 
 exactly a quarter of an undulation on the other. For as 
 the corresponding rays emerge of equal intensity, and 
 oppositely polarized, they here also fulfil all the con- 
 ditions of circular polarization. If the thickness of the 
 plate be such, that the difference of phases is more or 
 less than an exact quarter (or any number of quarters) 
 of an undulation, the compound ray will be elliptically 
 polarized, and the degree of ellipticity will be determined 
 by the thickness of the plate. 
 
 (158.) It may be asked, in what does a ray so circu- 
 larly polarized differ from an ordinary unpolarized ray, 
 seeing that the latter may always be regarded as com- 
 pounded of two ordinary rays of half the intensity oppo- 
 sitely polarized? We reply, in this: viz., that if again 
 transmitted through another such glass parallelepiped, 
 similarly situated, the difference of phase will be doubled. 
 The emergent ray then will consist of two equal rays 
 oppositely polarized (and therefore not interfering), dif-
 
 ON LIGHT. 381 
 
 faring in phase by half an undulation, and which there- 
 fore (by what we have before shown) compound a single 
 ray polarized in a plane half-way intermediate, or 45 
 inclined to the original plane of polarization ; whereas a 
 ray of ordinary light so transmitted would show no signs 
 of polarization in any one plane more than in any other. 
 (159.) The most remarkable cases of circular polar- 
 ization, however, are those which occur when a ray is 
 transmitted along the optic axis of a crystal of quartz, 
 and some few other crystals, as also through certain 
 liquids. The phaenomena so exhibited cannot be ex- 
 plained, or even described, however, till we shall have 
 said something 
 
 OF THE COLOURS EXHIBITED BY CRYSTALLIZED PLATES 
 ON EXPOSURE TO POLARIZED LIGHT. 
 
 (160.) Uniaxal crystals. If a plate cut from a crystal 
 of Iceland spar, so as to have its faces perpendicular to 
 the axis of the primitive rhomboid, be placed close to 
 or very near the eye ; and before it a tourmaline plate 
 having its axis vertical, so as to polarize all the light in- 
 cident upon it in vertical planes passing through the 
 eye ; and if any brightly illuminated white surface, such 
 as a white cloud, or a sheet of paper laid in the sun- 
 shine, be viewed through it : or if, instead of a tourma- 
 line plate, a "polarizing frame" of glass plates, such as 
 above described, be laid horizontally, and the reflexion 
 of a clouded sky be in like manner viewed through the 
 crystal ; in the " polarized field " so obtained nothing
 
 382 ON LIGHT. 
 
 especially is seen which would lead to a suspicion that 
 the crystal were other than an ordinary piece of glass. 
 But if, in this state of things, between the crystal and 
 the eye, be placed another tourmaline plate, having its 
 axis horizontal, a magnificent set of coloured rings will be 
 seen ; the exact counterpart of the reflected rings described 
 by Newton (only infinitely more vivid and brilliant), in 
 every respect but these : First, that they are all divided 
 into four quadrants of coloured light by a dark cross 
 passing through their common centre, and having its 
 arms vertical and horizontal; and, secondly, that the 
 rings themselves are of unequal brightness in different 
 parts of their circumference, being most luminous at the 
 middle points of the quadrants into which the cross 
 divides them, and fading away very gradually on either 
 side of these points, till they cease to be traceable and 
 are lost in the darkness of the cross. On the other 
 hand, if the tourmaline plate between the eye and the 
 crystal (which we shall call the " analyzing plate" or the 
 " analyzer," for a reason which will presently appear) be 
 placed with its axis vertical, a series of rings will also be 
 seen : but they are, now, the complementary series 
 those seen by transmission in the Newtonian experi- 
 ment; and the cross, instead of black, is now white. 
 Lastly, if the analyzing plate be placed obliquely, both 
 sets of rings will be partially, and, as it were, confusedly, 
 exhibited ; the one dislocating the other, in consequence 
 of the brighter annuli of the one set abutting upon the 
 obscurer of the other, the reds on the greens, the purples 
 on the yellows, &c. : the preponderance in light, distinct-
 
 ON LIGHT. 383 
 
 ness, and extent, falling to the share of that set which 
 the position of the analyzer most favours. 
 
 (161.) It is manifest that these colours originate in 
 the interference of two series of undulations propagated 
 with different velocities within the crystal, and which 
 therefore must necessarily belong the one to the 
 ordinary, the other to the extraordinary, pencils into 
 which the incident light is divided, which, as before 
 shown, travel with different velocities within its sub- 
 stance. These pencils, however, during their progress 
 through it, are proceeding in different directions (by 
 reason of the double refraction of the medium) and are 
 oppositely polarized so that, while within the crystal, 
 they cannot interfere. Their interference, then, must be 
 accomplished after their emergence, when their direc- 
 tions have been again reduced to parallelism, and they 
 have been (wholly or partially) brought to a common 
 plane of polarization by the action of the second tour- 
 maline. Let us, therefore, examine how this is brought 
 about. And first, along the vertical arm of the black 
 cross, the whole of the incident light being polarized in 
 the plane of a vertical section of the crystal containing 
 its axis, will pass into the ordinary pencil, and none into 
 the extraordinary so that there will be nothing to in- 
 terfere with it : and emerging wholly polarized in that 
 plane, will be wholly stopped by the analyzing tourma- 
 line the result being darkness. But if this tourmaline 
 be turned 90 round in its own plane, it will be wholly 
 transmitted, and the arm of the cross in question will be 
 white. As regards the horizontal arm of the cross, in
 
 384 ON LIGHT. 
 
 like manner, the visual ray throughout its whole extent 
 is inclined to the axis in a plane at right angles to that 
 of the primitive polarization. The light, therefore, in- 
 cident in this plane through the first tourmaline will 
 pass wholly into the extraordinary pencil, and will there- 
 fore emerge polarized in a plane at right angles to the 
 (now) horizontal section of the crystal containing its axis 
 in which its direction lies, i.e., again, in a vertical plane, 
 and will be stopped, for the same reason, by the second 
 tourmaline ; so that this arm of the cross also will be 
 black in the horizontal, and white in the vertical, posi- 
 tion of the analyzer. Let us now consider a ray inci- 
 dent in a plane 45 inclined to the vertical, or in a plane 
 intermediate between the arms of the cross (the axis of 
 the crystal being in all cases supposed held horizontally). 
 The incident ray then will fall on the crystal in a sec- 
 tion through its axis 45 inclined to that of its primitive 
 polarization, and will therefore be equally divided be- 
 tween the ordinary and extraordinary pencils. These 
 portions will emerge parallel, and of equal intensity, 
 though differing in phase by such a number of undula- 
 tions, and parts of an undulation, as the latter, by 
 reason of its greater velocity, has gained on the former. 
 In this state they are both incident on the second tour- 
 maline, having its axis 45 inclined to both their planes 
 of polarization, which therefore will subdivide each of 
 them into two equal portions oppositely polarized, sup- 
 pressing or absorbing one, and allowing the other to pass, 
 and the transmitted portions, being of equal intensity, 
 similarly polarized (viz., both in the plane of the axis of
 
 OH LIGHT. 385 
 
 the analyzing plate), and differing in phase, will inter- 
 fere and give rise to the phoenomena of coloration in the 
 manner already sufficiently explained. It remains now 
 to account for the colours being arranged in regular 
 succession in rings round the centre of the black cross 
 (which corresponds to the axis of the crystal). Now the 
 colour developed, or the order of the tint, in the series of 
 the Newtonian rings, increases with the difference of 
 phase, and this difference increases with the difference ot 
 velocities of the two pencils within the crystal, and with 
 the length of the path traversed with those velocities. 
 Both these increase with the inclination of the visual 
 ray to the axis of the crystal : since along the axis there 
 is no double refraction, which increases gradually from 
 that direction outwards up to a right angle. This, then, 
 explains the progressive increase of colour or order ot 
 tint in proceeding from the centre outwards. The 
 circular arrangement is a consequence of the symmetry 
 of the crystalline plate in all directions around its axis ; 
 the amount of double refraction being the same at 
 equal obliquities to that line in all directions around it, 
 as also the inciease of thickness traversed by rays 
 equally oblique in all directions to the surfaces of the 
 plate. It only now remains to explain how it happens 
 that, in this situation of the analyzing plate (at right 
 angles to the polarizing one), the tints are those of the 
 reflected, not of the transmitted series in the Newtonian 
 rings. And the reason is very similar to that by which, 
 in the colours of thin plates, the difference of phase is 
 assumed (justifiably assumed) to commence, not from 
 
 2 B
 
 3&6 ON LIGHT. 
 
 zero, but from half an undulation. Of the two partial 
 systems of waves that interfere, in the case considered, 
 that which belonged to the ordinary pencil in the crys 
 tal passes, as an extraordinary one, through the analyz- 
 ing plate. Now it is a law, susceptible of demonstra- 
 tion, but which it would lead us too far aside at present 
 to demonstrate that in the transition from an ordinary 
 to an extraordinary refraction, half an undulation is 
 gained. With the other portion of the interfering pencil, 
 no such transition takes place. Half an undulation then 
 has to be reckoned in addition to the phase-difference 
 due to the simple passage of the two rays through the 
 crystal just as is the case in the Newtonian reflected 
 rings, and with the same result. 
 
 (162.) If we follow out the same chain of reasoning 
 in the case when the analyzing plate is parallel to the 
 polarizing one, the conclusions will be identical up to 
 this last step. But here the cases differ. Neither of 
 the interfering pencils here at its entry into the second 
 tourmaline undergoes extraordinary refraction, and there 
 is accordingly no semi-undulation to be added to the 
 phase-difference. The rings, therefore, will have the 
 characters of the transmitted series of Newton's colours. 
 
 (163.) In the generality of uniaxal crystals, the tints 
 of the rings, when the crystal itself is colourless (or as 
 nearly as its colours will allow), follow a succession identi- 
 cal with that of the Newtonian colours of their plates. 
 I have elsewhere called attention, however, to several 
 instances of deviation from this rule, some of which are 
 .of so remarkable a nature as to deserve special mention.
 
 ON LIGHT. 387 
 
 The most remarkable is in the case of one variety of the 
 mineral called apophyllite which (from the peculiarity in 
 question) I have proposed to call Leucocyclite, in which 
 the rings are almost devoid of colour, being merely a 
 succession of dark and light circles, much more numerous 
 than the coloured ones usually seen, and the more re- 
 mote of which, from the centre, graduate into feeble 
 shades of purplish and yellowish light. The physical in- 
 terpretation of this phsenomenon is as follows. Since the 
 colours originate in the superposition of rings about a 
 common centre, differing in diameter for the several 
 coloured rays throughout the spectrum, (as already ex- 
 plained in Lecture VII.), it follows that in this case, no 
 such difference of diameter, or but a very slight one 
 exists. Now, for crystalline plates so cut, of a given 
 thickness, the apparent diameters of the rings seen are a 
 measure of the doubly refractive energy. The more in- 
 tense this energy the closer and more compact the sys- 
 tem of rings; for this obvious reason, that the same 
 difference of phases between the ordinary and extraordi- 
 nary pencils is developed at a less angle of inclination to 
 the axis ; and the difference of phases is a direct result 
 of difference of velocities in their internal propagation ; 
 and this again, of the doubly refractive energy. Hence 
 we conclude that in the leucocydite all the coloured rays 
 throughout the spectrum undergo equal, or very nearly 
 equal separation at a given angle of incidence, by double 
 refraction ; and that therefore in a doubly refracting prism 
 cut from this substance, the two spectra formed by a sun- 
 beam would be of precisely equal lengths, though un-
 
 388 ON LIGHT. 
 
 equally refracted, or that the highest index of refraction 
 would be accompanied with the least dispersive power. I 
 have not made the experiment, but that such would be 
 the case there can be no doubt. In the spectra formed 
 by an Iceland spar prism, the reverse is the case the 
 higher refractive index corresponding to a much higher 
 dispersive power, and the most refracted spectrum being 
 much longer and much more brilliantly coloured than 
 the least. 
 
 (164.) Another highly remarkable example of this kind 
 is found in the mineral called Vesuvian, a uniaxal crystal 
 of a greenish hue, which to a certain degree interferes 
 with the vivid development of its coloured rings. It does 
 not, however, prevent their being well observed and 
 they present this very singular anomaly, viz., that the 
 system of rings formed by the red rays is considerably 
 smaller than those formed by the violet, and in conse- 
 quence that the order of tints in the rings formed in 
 white light is inverted, so that, of the spectra formed by 
 a prism of this substance, the more refracted ought to be 
 the shorter, and the least coloured. This kind of ano- 
 malous action is, however, carried still further in another 
 variety of uniaxal apophylite, in a plate of which perpen- 
 dicular to the axis, rays of a medium refrangibility/rrw 
 no rings at all, so that for such rays the substance is singly 
 refractive. Proceeding from this medium refrangibility 
 towards either end of the spectrum, rings are formed, 
 contracting in diameter, as the red or violet end is ap- 
 \ reached, but most rapidly towards the red. It would 
 r;ot be too much to expect that if a prism could bo
 
 ON LIGHT. 389 
 
 formed of this mineral (unfortunately very rare), and a 
 bright point illuminated in succession with all the pris- 
 matic rays viewed through it, beginning with the red, 
 two images would at first be seen, the one formed by 
 ordinary refraction, fixed, the other gradually approach- 
 ing it ; at a certain stage of the illumination coinciding 
 with it ; then crossing to the other side and separating 
 more and more from it as the light verged more to the 
 extreme violet. The experiment, which would be a very 
 beautiful one, is recommended to the attention of those 
 in possession of such crystals which they may not be in- 
 disposed to sacrifice. 
 
 (165.) Of the colours developed by circular polarization. 
 Quartz, or ordinary rock crystal is uniaxal: and when 
 a plate of it of moderate thickness, cut from one of the 
 six-sided prisms in which it usually occurs at right angles 
 to its axis, is examined in the mode above described 
 with a polarizer and analyzing plate, a superb systerr 
 of coloured rings and black cross is exhibited but with 
 this peculiarity, that the cross does not come up to the 
 centre, and that the interior rings are blotted out and 
 obliterated by a round patch of coloured light; whose 
 tint, when the tourmalines are at right angles, varies with 
 the thickness of the plate ; being white when very thin, 
 and passing, for plates successively increasing in thick- 
 ness, through all the series of tints of Newton's trans- 
 mitted rings. Keeping to one plate, the tint also varies 
 on turning round the analyzing plate in its own plane, 
 and with this very extraordinary peculiarity, viz., that 
 while in some crystals a certain succession of colours is
 
 390 ON LIGHT. 
 
 observed, on turning it from right to left ; in plates of 
 the same thickness cut from other crystals the same suc- 
 cession is seen on turning it from left to right. Yet 
 more singular, is the fact that this inversion this right- 
 and-left-handedness in the succession of tints, corresponds 
 to, and is predictable beforehand from, the appearance 
 of certain small obliquely posited facets on the crystal 
 previous to polishing, which lean unsymmetrically in 
 some crystals to the right, in others to the left hand of 
 the axis held up straight before the eye. In all other 
 respects the crystals are identical.* A similar right-and- 
 left-handedness in the external form of their crystals, 
 accompanied with the very same optical phsenomena, 
 has been remarked by M. Pasteur in the salts called para- 
 tartrates and their crystallized acid. 
 
 (166.) The account given by the undulatory theory of 
 these phaenomena is this. Quartz (to adhere to our first, 
 chosen instance) is uniaxal, but it differs from Iceland 
 spar and others of that class in a most essential point 
 first noticed by Mr Airy, viz. : that the sphere and sphe- 
 roid representing the simultaneous surfaces of the ordi- 
 nary and extraordinary waves propagated within them, 
 though having a common axis, do not touch each other 
 internally. Hence, in the direction of that axis, though 
 there is, at a perpendicular incidence, no double refraction, 
 there is a difference of velocity in the two rays. Now 
 the theory at present adopted is, that owing to some 
 peculiarity at present not understood ; when a polarized 
 
 * Amethyst consists of thin alternate layers of right-handed and 
 left-handed quartz superposed, parallel to their axes.
 
 ON LIGHT. 391 
 
 ray (which may always be considered as compounded of 
 two circularly-polarized ones of opposite characters as 
 already stated, i.e., in which the particles of the ether cir- 
 culate in opposite directions) is incident on a quartz 
 plate, in this manner ; the crystal operates an analysis of 
 the ray and resolves it into two such rays circularly polar- 
 ized ; which it propagates as such, the one as an ordi- 
 nary, the other as an extraordinary one. On their em- 
 ergence at the opposite face of the plate they recompound 
 a plane-polarized ray ; but, having gained or lost on one 
 another, by reason of their difference of velocity in their 
 passage through it, a number of revolutions or parts of a 
 revolution proportional to the thickness of the plate, the 
 two circular rays at the instant of their reunion have no 
 longer a common zero-point as at their entry: and from this 
 it may be demonstrated* that the plane of polarization 
 of the recomposed will not be coincident with that of 
 the incident ray, but will have been turned round, 
 in the direction of the rotation of the ray which travels 
 fastest within the quartz, through an angle also propor- 
 tional to the thickness of the plate. As the angle of dis- 
 placement, moreover, differs for the differently coloured 
 rays of the spectrum ; the effect will be that, when passed 
 through an analyzing tourmaline the different colours 
 will be differently absorbed, and the result will be the 
 production of a compound tint in the beam finally deli- 
 vered into the eye, the colour of which will vary with 
 the rotation of that plate in its own plane, as observed. 
 
 * Our necessary limits forbid us to give the steps of the demon- 
 stration, which, however, are very obvious.
 
 392 ON LIGHT. 
 
 (167.) It is not in crystallized bodies only that this sing- 
 ular effect is produced. Strange as it may seem that a 
 colourless, transparent, and perfectly homogeneous^?/*/^ 
 should deviate the plane of polarization of a ray passing 
 perpendicularly through it at all; still strangei that it 
 should do so constantly in one direction for the same 
 fluid, but in opposite directions for' different fluids; 
 strangest of all, that even vapours should be found pos- 
 sessing the same property : such is the case. Thus, oil 
 of turpentine and its vapour turn the plane of polariz- 
 ation to the right hand, solution of sugar to the left, and 
 so for a variety of other substances.* This property has 
 been made the basis of an elegant instrument called the 
 saccharometer, by which the quantity of sugar contained 
 in a given solution is ascertained by simple inspection 
 of the tint so produced. 
 
 (168.) Struck by the fact, apparently so singular, of a 
 "right-and-left-handedness" inherent as it were in the 
 molecules of material bodies by the correlative fact of 
 such a tendency, or so to speak idiosyncrasy, manifest- 
 ing itself in the forms of crystals and again, in quite a 
 different field of scientific research, in the action of an 
 electrified cylindrical wire on a magnetized needle 
 placed parallel to its direction, (which turns the north 
 end of the needle to the right or to the left according to 
 the direction of the current along the wire) : it early 
 occurred to the writer of these pages that it was 
 
 * Mr Jellett, of Trinity College, Dublin, has, 1 am informed, 
 recently discovered a liquid which is right-handtd for one end of the 
 spectrum, but left-handed Tor the other 1
 
 ON LinHT. 393 
 
 scarcely possible such singularities should stand rn 
 no natural connexion. Between two of the cases ad- 
 duced the connexion had been proved by himself. It 
 remained to enquire whether the third could be brought 
 into obvious relation to the other two. Accordingly on 
 the I4th of March 1823, having prepared a long spiral 
 coil of copper wire enclosed in an earthenware tube, 
 furnished with a polarizing reflector at one end and an 
 analyzer at the other; by the kindness of the late Mr 
 Pepys, he was permitted to bring the coil into connexion 
 with the great magnetic combination of the London 
 Institution, consisting of one enormous couple, expressly 
 arranged for producing the greatest possible magnetic 
 effect. His expectation was that light would appear in 
 the dark polarized field on making the contact, and be 
 maintained during its continuance. The experiment, 
 however, proved unsuccessful. No direct action upon 
 light could so be made manifest. At a later period, 
 however (1845), by introducing into a similar coil a 
 certain highly refractive glass consisting chiefly or wholly 
 of borate of lead, as well as a variety of other solids 
 and liquids (water among others), Professor Faraday 
 succeeded in communicating, temporarily, and during 
 the continuance of the passage of the current, the pro- 
 perty in question to them. 
 
 (169.) Biaxal Crystals. By far the greater number 
 of crystallized substances do not present that single sym- 
 metry (symmetry on all sides of a single central line or 
 axis), which we have spoken of as indicative of a single 
 axis of double refraction, and of a spherical propagation
 
 39* ON LIGHT. 
 
 of the ordinary, and spheroidal of the extraordinary ray, 
 within them. In all or nearly all these, two lines in- 
 clined to one another at an angle greater or less accord- 
 ing to the nature of the substance can always be found 
 (either by a careful examination of the crystal in polar- 
 ized light through the faces of its natural form, or by 
 cutting and artificially polishing plates of it), which 
 possess the properties of such axes ; along which, that 
 is to say, refraction is single for a ray passing either way 
 out of the crystal ; and in which when examined in 
 polarized light with an analyzing plate between the eye 
 and the crystal, coloured rings are seen. The simplest 
 and readiest instance of a crystal of this kind is furnished 
 by a sheet of ordinary mica, such as may easily be pro- 
 cured in large sheets. If a sheet of this be held before 
 the eye in a polarized field perpendicularly (an analyz- 
 ing plate being interposed) and turned round in its own 
 plane, two portions will be found at right angles to each 
 other, in which the polarization of the incident light is 
 not disturbed, and the field remains dark. Of the two 
 planes perpendicular to the plate in which the plane of 
 polarization cuts it in these two positions, one is the 
 " principal section " of the plate, and contains its " optic 
 axes." These may be brought into sight by holding the 
 eye (armed with the analyzer) quite close to the mica, 
 and inclining the latter, either forward or backward in 
 one of these two section-planes so as to make an angle 
 of about 35 with the visual ray on either side of the 
 perpendicular. In either situation a set of coloured 
 .rings will be seen, not circular, but of an oval form,
 
 ON LIGHT. 395 
 
 about a common centre, and intersected, not by the two 
 arms of a black cross as in Iceland spar, but by one 
 vertical dark bar cutting centrally across them. This 
 dark bar is converted to a white one, and the colours 
 of all the rings changed to their complementary ones, 
 by turning the analyzing plate through 90 in its plane. 
 
 (170.) In mica, the angular separation of the optic 
 axes is too large to allow both these sets of rings to be 
 seen at once, so as to examine the nature of their 
 mutual connexion. In nitre however, in which it is 
 only about 5 (within the crystal), this may be very con- 
 veniently done, by cutting from the clear transparent 
 portion of a large hexangular-prismatic crystal (such as 
 may always be found in searching over a lot of the 
 ordinary commercial saltpetre) a plate about a quarter 
 of an inch thick, perpendicular to the axis of the prism, 
 and polishing its faces. If this be placed between two 
 crossed tourmalines, and held up against the light, the 
 normal phenomenon of the biaxal rings will be seen in 
 its utmost perfection, as in fig. 17, the upright and hori- 
 zontal lines in which indicate broad brushes as it were of 
 shadow, cutting across the system of ovals, and breaking 
 them up into four similar quadrants. If, retaining the 
 tourmalines in the same position, the nitre plate be 
 turned round in its own plane, this cross breaks up 
 into two curved arcs, as represented in fig. 18, cor- 
 responding to a movement through a quarter of a right 
 angle, then, as in fig. 19, corresponding to 45 of 
 change, and so on till after a quarter of a revolution 
 the original appeaiance of fig. 17 is restored. If the
 
 ON LIGHT. 
 
 tourmalines instead of being crossed, are laid parallel, 
 the forms of the ovals are the same, but the colours 
 complementary, and the cross and curved branches 
 white. 
 
 (171.) The forms of these curves are governed by a 
 
 Fig .17. 
 
 Fig. 18. 
 
 Fig. 19. 
 
 very simple and elegant general law, common to all 
 biaxal crystals, and applicable to every angular separa- 
 tion of the axis: and when this separation is small, as 
 in the case before us, they may be regarded as " lemnis- 
 cates," of which the property is this, that for every point 
 in the circumference of each oval the product (not as in 
 an ellipse the sum) of two lines drawn to the two centres 
 or foci, is invariable ; and for successive ovals proceed- 
 ing outwards from either focus, these products increase 
 in regular arithmetical progression. When the two foci 
 coincide, that is to say, when the two axes of the crys- 
 tal coalesce, and it becomes uniaxal, the ovals pass into
 
 ON LIGHT. 397 
 
 circles, and we fall back upon the circular rings and 
 cross proper to that class of bodies. 
 
 (172.) Neglecting the bending which the rays undergo 
 at their emergence from the posterior surface of the 
 crystal, or conceiving the eye as immersed within its 
 substance, it is evident that when looking in the direc- 
 tion of either of the foci of the ovals, the visual ray will 
 be directed along one of two axes, or lines of no double 
 refraction; while if looking towards any point in the 
 circumference of any one of the ovals, the visual ray will 
 traverse the crystal in such a direction that an ordinary 
 and extraordinary ray following that path shall gain or 
 lose on each other so many semi-undulations, or parts 
 of one, as shall correspond to the tint developed in that 
 direction and that, therefore, in all the directions 
 marked out by the circumference of each individual 
 oval, the tints being the same, the phase-difference, and 
 therefore the difference of velocities of the interfering 
 rays, and therefore again, the amount of double refraction 
 in that direction is the same. The forms of these ovals, 
 therefore, stand in immediate and intimate connexion 
 with the law of double refraction in such crystals, and 
 with the forms of the two wave surfaces belonging to the 
 ordinary and extraordinary rays. The theory of these 
 wave-surfaces belongs, however, to a higher department 
 of geometry than we could hope to make intelligible in 
 these pages. Suffice it to say that as delivered by M. 
 Fresnel and his followers it explains all the facts in the 
 most complete and satisfactory manner, and has even 
 led to the prediction, antecedent to observation, of some
 
 39^ ON LIGHT. 
 
 phaenomena so apparently paradoxical as to stand in 
 seeming contradiction with all previous optical ex- 
 perience ; and which any one, antecedent to their verifi- 
 cation by trial, would have pronounced impossible.* 
 
 (173.) One highly important conclusion from this 
 theory must, however, be noticed. The directions within 
 the crystal of the two axes of double refraction or the 
 " optic axes" stand in no abstract geometrical relation to 
 those of the angles and edges of its " primitive form," or 
 to its axes of symmetry. They are resultant lines deter- 
 mined by the law of elasticity of the luminiferous ether 
 within its substance as related to its crystalline form, and 
 to the wave-length of the particular coloured ray transmitted. 
 They are not, therefore, the same for all the coloured 
 rays. In the generality of biaxal crystals, the difference 
 of their situations and of the angle between the two, is 
 but small : but in some, as in the salt called Rochelle salt 
 (tartrate of soda and potash), it is very great, amounting 
 to at least 10, by which the direction within the crystal 
 of either axis for the extreme red rays differs from that 
 for the extreme violet. t In this salt the variation in po- 
 sition of the optic axes progresses pretty uniformly in 
 passing from a red to a violet illumination. In Car- 
 bonate of lead, on the other hand, it varies slowly in 
 
 * This alludes to the phenomena of what is called conical re- 
 fraction, pointed out by the late Sir Wm. R. Hamilton, as a neces- 
 sary consequence of Fresnel's theory, and demonstrated to exist at 
 a matter of fact, subsequently, by Dr Llcyd. 
 
 t See a paper by the author of these pages in Phil. Trans., 1820, 
 " On the action of crystallized bodies on homogeneous light," where 
 the singular phenomena to which this gives rise are fully described.
 
 ON LIGHT. 399 
 
 passing from red to green, but with increasing and finally 
 with extreme rapidity in the passage thence to violet. 
 
 (174.) It is time, however, to bring this long Lecture to 
 a conclusion. To describe the variety of splendid and 
 singular phaenomena, developed in every department of 
 physical enquiry by the use of polarized light, not one 
 of which has hitherto afforded any, the smallest, ground 
 for doubt as to the applicability of the undulatory theory 
 to its complete explanation, would require volumes. We 
 would gladly have said something of the magnificent 
 phenomena, exhibited by "macled" crystals,* and by 
 unannealed, or compressed glass ; of the changes pro- 
 duced by change of temperature on the optical relations 
 of bodies, and of the calorific and chemical rays of the 
 spectrum; but our limits forbid it. Suffice it to add, 
 that what the telescope and the microscope effect for us 
 in the discovery of outward and visible form, the proper- 
 ties of light, and especially of polarized light, effect in 
 subjecting to our intellectual vision the intimate structure 
 of material bodies. Within the compass of the smallest 
 visible atom they open out a world of wonders a uni- 
 verse sui generis, and for each atom of a different material 
 a different one all, however, related and bound together 
 in one vast harmony. 
 
 * These may find a place elsewhere. The phenomena alluded 
 ft have not, so far as I am aware, been hitherto described, t
 
 LECTURE IX. 
 ON SENSORIAL VISION.* 
 
 LOM what I have understood respecting the 
 objects of this Institution, as one equally 
 addressing itself to the cultivation of Phil- 
 osophy and Literature, I am led to believe 
 that the subject which I propose to bring before it, in 
 compliance with an invitation which I feel to be both 
 honourable and gratifying in no common degree, is one 
 not altogether foreign to them ; inasmuch as the history 
 of vision has both a strictly scientific and a more abstract 
 and philosophical bearing; the one referring itself to 
 material, the other to mental science. The one regards 
 only the means and adaptations by which we see, and the 
 other refers to the action of the mind itself in seeing, that 
 is, in interpreting the impressions produced on our visual 
 
 * This lecture was delivered before the Philosophical and Lite- 
 rary Society of Leeds, on the 3Oth September 1858, at the requesl 
 of that society.
 
 ON SENSORIAL VISION. 4OI 
 
 organs. It is to this latter division of the subject that I 
 shall chiefly address myself, while taking the opportunity 
 thus kindly afforded me of putting on record certain 
 visual phenomena which I have from time to time noticed, 
 belonging to that obscure class of impressions which 
 may be termed Sensorial Vision by which I mean visual 
 sensations or impressions bearing a certain considerable 
 resemblance to those of natural or retinal vision, but 
 which differ from these in the very marked particular 
 of arising when the eyes are closed and in complete 
 darkness. 
 
 (2.) Few persons, I suppose, are ignorant, as a matter 
 of personal experience, of the sort of appearances known 
 by the name of Ocular Spectra, which are produced by 
 the impression of a strong light on the retina of the eye, 
 and which continue to force themselves on the attention, 
 sometimes in a very pertinacious and disagreeable way 
 for some time afterwards, when the eyes are closed. In 
 one lamentable instance, that of an eminent Belgian 
 Philosopher, they have caused actual loss of sight ; and 
 in that of Sir Isaac Newton, their obstinate recurrence is 
 said to have deprived him of sleep for several days and 
 nights successively, and to have driven him to the verge 
 of distraction. These are cases when the stimulus of 
 light has been pushed to the extreme ; but when mode- 
 rate and regulated, these spectra admit of being studied : 
 and the laws of their production the singular and beau- 
 tiful phases they pass through their periodical extinc- 
 tion and renewal (which extend over a very considerable 
 interval of time from their first production), the orderly 
 
 2 c
 
 4O2 ON SENSORIAL VISION. 
 
 recurrence of the colours they assume, which are pecu- 
 liarly rich and various the singular effects of gentle pres- 
 sure on the eye, and partial light admitted through the 
 eyelids in modifying them or in renewing them when ex- 
 tinct all these offer a subject of much attraction and 
 interest. A very interesting memoir on them has been, 
 within these few years, communicated to the Royal 
 Society, by Dr Scoresby; but the subject is far from 
 being exhausted, and it is to the habit of attention to 
 such sensorial impressions, fostered by frequently watch- 
 ing the development of these spectra under a variety of 
 circumstances in my own case, that I attribute my having 
 been led to notice that other class of phaenomena of 
 which I shall presently speak, and which from their in- 
 conspicuousness, I suppose, escape the notice of most 
 people. 
 
 (3.) The production of Ocular Spectra refers itself, I 
 presume, to what I have described as the purely physical 
 branch of the general subject of vision. Their seat, it 
 can hardly be doubted, is the retina itself,* and their 
 production is in all probability, part and parcel of that 
 photographic process by which light chemically affects 
 the retinal structure, and of the gradual restoration of 
 that structure to its normal state of sensitiveness by the 
 fading out of the picture impressed. Cases are not want- 
 ing in artificial photography where an impression made 
 
 * In speaking of the retina, I would not be understood to express 
 any opinion on the disputed question whether the retina ana f omi- 
 cally so called or the choroid coa*. of the eye be really the seat of
 
 ON SENSORIAL VISION. 403 
 
 on sensitive paper dies out, and can be replaced by 
 another without the renewed application of any chemical 
 agent. 
 
 (4.) Thus considered, ocular spectra are quite as much 
 entitled to be considered as things actually seen, as the 
 retinal pictures of which they are the successors, or rather 
 remnants. It is quite otherwise with that other class of 
 visual impressions to which I now refer, and which differ 
 altogether from ocular spectra, not only in being for the 
 most part (though not always) much less vivid and much 
 more dreamy (if I may use the term without casting a 
 doubt on their reality as facts], but also in having no 
 reference or resemblance to any objects recently seen, or 
 even recently thought of. Of course, when I speak of 
 their reality as facts, I do so on the ground of their 
 admitting of being watched and studied with the same 
 sort of wide-awake attention which might be given to 
 any faint and fugitively-presented real object : though it 
 is no more possible to describe them accurately, much 
 less to draw them, than it would be to do so in the case 
 of objects dimly seen in the dusk of evening, and capri- 
 ciously appearing and disappearing. But this does not 
 preclude their being observed and described, pro tanto, 
 in general terms. 
 
 (5.) I fancy it is no very uncommon thing for persons in 
 the dark, and with their eyes closed, to see, or seem to 
 see, faces or landscapes. I believe I am as little vision- 
 ary as most people, but the former case very frequently 
 happens to myself. The faces present themselves in- 
 voluntarily, are always shadowy and indistinct in outline
 
 404 ON SENSORIAL VISION. 
 
 for the most part unpleasing, though not hideous ; ex- 
 pressive of no violent emotions, and succeeding one 
 another at short intervals of time, as if melting into each 
 other. Sometimes ten or a dozen appear in succession, 
 and have always, on each separate occasion, something of 
 a general resemblance of expression or some peculiarity 
 of feature common to all, though very various in individual 
 aspect and physiognomy. Landscapes present themselves 
 much more rarely but more distinctly, and on the few 
 occasions I remember, have been highly picturesque and 
 pleasing, with a certain but very limited power of vary- 
 ing them by an effort of the will, which is not the case 
 with the other sort of impressions. Of course I now 
 speak of waking impressions, in health, and under no 
 kind of excitement. When the two latter conditions are 
 absent, numerous instances are on record of both volun- 
 tary and involuntary impressions of this kind, and singular 
 as some of the facts related may appear, I am quite pre- 
 pared, from my own experience on two several occasions, 
 to receive such accounts with much indulgence. 
 
 (6.) A great many years ago, when recovering from 
 fever, my chief amusement for two or three days 
 consisted in the exercise of a power of calling up 
 representations both of scenes and persons, which 
 appeared with almost the distinctness of reality. One 
 of these scenes I perfectly recollect. A crowd was 
 assembled round a hole in the ice, into which a youth 
 had fallen. His mother was standing in agony on the 
 brink, and there were the floating fragments and some- 
 thing of a shadowy form under the blue transparent ice.
 
 ON SENSORIAL VISION. 405 
 
 In this case there was, of course, the excitability of nerve 
 connected with the remains of bodily disorder. On the 
 other occasion to which I allude, I had been witnessing 
 the demolition of a structure familiar to me from child- 
 hood, and with which many interesting associations were 
 connected : a demolition not unattended with danger to 
 the workmen employed, about whom I had felt very un- 
 comfortable. It happened to me at the approach of 
 evening, while, however, there was yet pretty good light, 
 to pass near the place where the day before it had stood; 
 the path I had to follow leading beside it. Great was 
 my amazement to see it as if still standing projected 
 against the dull sky. Being perfectly aware that it was a 
 mere nervous impression, I walked on, keeping my eyes 
 directed to it, and the perspective of the form and dis- 
 position of the parts appeared to change with the change 
 in the point of view as they would have done if real. I 
 ought to add, that nothing of the kind had ever occurred 
 to me before, or has occurred since. On this occasion, 
 no doubt, the daily habit of seeing the same object from 
 the same point of view for years would naturally give 
 great efficacy to the associative principle, and the fact 
 can only be regarded as an exemplification of a physio- 
 logical process which I shall presently have occasion to 
 speak of more particularly. 
 
 (7.) But it is not to phaenomena of this kind that I am 
 about specially to direct your attention. The human 
 features have nothing abstract in their forms, and they 
 are so intimately connected with our mental impressions 
 that the associative principle may very easily find, iu
 
 406 ON SENSORIAL VISION. 
 
 casual and irregular patches of unequal darkness, caused 
 by slight local pressure on the retina, the physiognomic 
 exponent of our mental state. Even landscape scenery, 
 to one habitually moved by the aspects of nature in as- 
 sociation with feeling, may be considered as in the same 
 predicament. There is nothing definite or structural in 
 its forms, which are arbitrary to any extent, and composed 
 of parts having no regular or symmetrical relations. It 
 is perfectly conceivable that the imagination may inter- 
 pret forms, in themselves indefinite, as the conventional 
 expressions of realities not limited to precise rules of 
 form. We all know how easy it is to imagine faces in 
 casual blots, or to see pictures in the fire. 
 
 (8.) But no such explanation applies to the class of 
 phaenomena now in question, which consist in the invol- 
 untary production of visual impressions, into which geo- 
 metrical regularity of form enters as the leading charac- 
 ter, and that, under circumstances which altogether pre- 
 clude any explanation drawn from a possible regularity of 
 structure in the retina or the optic nerve. 
 
 (9.) I was sitting one morning very quietly at my break- 
 fast-table doing nothing, and thinking of nothing, when 
 I was startled by a singular shadowy appearance at the 
 outside corner of the field of vision of the left eye. It 
 gradually advanced into the field of view, and then ap- 
 peared to be a pattern in straight-lined-angular forms, 
 very much in general aspect like the drawing of a fortifi- 
 cation, with salient and re-entering angles, bastions, and 
 ravelins, with some suspicion of faint lines of colour be- 
 tween the dark lines. The impression was very strong :
 
 ON SENSORIAL VISION. 407 
 
 equally so with the eyes open or closed, and it appeared 
 to advance slowly from out of the corner till it spread all 
 over the visual area, and passed across to the right side, 
 where it disappeared. I cannot say how long it lasted, 
 but it must have been a minute or two. I was a little 
 alarmed, looking on it as the precursor of some disorder of 
 the eyes, but no ill consequence followed. Several years 
 afterwards the same thing again occurred, and I recog- 
 nized, not indeed the same precise form, but the same 
 general character the fortification outline, the dark and 
 bright lines, and the steady progressive advance from left 
 to right. I have mentioned this to several persons, but 
 have only met with one to whom it has occurred. This 
 was a lady of my acquaintance, who assured me that she 
 had often experienced a similar affection, and that it was 
 always followed by a violent headache, which was not 
 the case with me. In this case the regularity of the pat- 
 tern was not great, but the lines were quite straight and 
 the angles sharp and well defined. Had it remained 
 stationary, it might be assumed that the retina had a 
 structure corresponding to the figure ; and that some 
 undue pressure might render that structure visible. But 
 such an hypothesis is precluded by the gradual transit of 
 the lines over every part of the visual area. 
 
 (10.) I come now to cases of perfect symmetry, and geo- 
 metrical regularity. The most ordinary class of patterns 
 of this sort I find to be formed only in darkness, and if 
 the darkness be complete, equally with open as with 
 closed eyes. The forms are not modified by slight pres- 
 sure, but their degree of visibility is much and caprici-
 
 408 ON SENSORIAL VISION. 
 
 ously varied by that cause. They are very frequent. In 
 the great majority of instances the pattern presented is 
 that of a lattice work; the larger axes of the rhombs 
 being vertical. Sometimes, however, the larger axes are 
 horizontal. The lines are sometimes dark on a lighter 
 ground, and sometimes the reverse. Occasionally at 
 their intersections appears a small, close, and apparently 
 complex piece of pattern work, but always too indis- 
 tinctly seen to be well made out. The lattice pattern if 
 constant, and if always upright, might be explained by 
 the habit of looking fixedly at a lattice window, with a 
 view to noting the order of succession of colours in the 
 Ocular Spectra, which this mode of viewing them shows 
 finely. Occasionally, however, the latticed pattern is 
 replaced by a rectangular one, and within the rectangles 
 occurs in some cases a filling in of a smaller lattice 
 pattern, or of a sort of lozenge of fillagree work, of which 
 it is impossible to seize the precise form, but which is 
 evidently the same in all the rectangles. Occasionally 
 too, but much more rarely, complex and coloured 
 patterns like those of a carpet appear, but not of any 
 carpet remembered or lately seen, and in the two or 
 three instances when this has been the case, the pattern 
 has not remained constant, but has kept changing from 
 instant to instant, hardly giving time to apprehend its 
 symmetry and regularity before being replaced by an- 
 other; that other, however, not being a sudden transi- 
 tion to something totally different, but rather a variation 
 on the former. 
 
 (i i.) Hitherto I have mentioned only rectilinear forms.
 
 ON SENSORIAL VISION. 409 
 
 I come now to circular ones. Having had to submit to a 
 surgical operation, I was put under the blessed influence 
 of chloroform. The indication by which I knew when 
 it had taken effect consisted in a kind of dazzle in the 
 eyes, immediately followed by the appearance of a very 
 beautiful and perfectly regular and symmetrical " Turks- 
 cap " pattern, formed by the mutual intersection of a 
 great number of circles outside of, and tangent to, a 
 central one. It lasted long enough for me steadily to 
 contemplate it so as to seize the full impression of its 
 perfect regularity, and to be aware of its consisting ot 
 exceedingly delicate lines ; which seemed, however, to be 
 not single but close assemblages of coloured lines not 
 unlike the delicate coloured fringes formed along the 
 shadows of objects by very minute pencils of light. The 
 whole exhibition lasted, so far as I could judge, hardly 
 more than a few seconds, and I should observe that I 
 never lost my consciousness of being awake, and in full 
 possession of my mind, though quite insensible to what 
 was going on. I spoke, but the words I am told I ut- 
 tered had no relation to what I know I meant to say. 
 
 (12.) After a considerable interval of time it became ne- 
 cessary to undergo another operation, which was also per- 
 formed under chloroform, but this time the dose was less 
 powerful, or differently administered. Again the " Turks- 
 cap" pattern presented itself on the first impression, 
 which I watched with much curiosity, but it did not 
 seem quite complete, nor was it identical with the former. 
 In the intersections of the circles with each other, I 
 could perceive small lozenge-shaped forms or minute
 
 ON SENSORIAL VISION. 
 
 patterns, but not clearly enough to make them well out 
 On both these occasions the patterns were far more 
 lively and conspicuous than the dim and shadowy forms 
 before spoken of, and probably belong to quite a differ- 
 ent class of phsenomena. 
 
 (13.) Since that time circular forms have presented them- 
 selves spontaneously, of the shadowy and obscure class, 
 on three occasions, one of them quite recently. On the 
 first of these, circular were combined with straight lines 
 forming a series of semicircular arches, supported by, or 
 rather prolonged beneath into, tall slender vertical 
 columns, the whole like small wirework ; mere lines, 
 and bright on a dark ground ; while another series of 
 similar arches and uprights darker than the general 
 ground appeared, intersecting the former so as to have 
 the dark uprights just intermediate between the bright 
 ones of the first set. On the second occasion the pattern 
 consisted of a very slender and delicate circular hoop, 
 surrounded with a set of other circles of the same size, 
 exterior tangents to the central circle and to each other. 
 On the third, the whole visual area was covered with 
 separate circles, each having within it a four-sided 
 pattern of concave circular arcs. All these phsenomena 
 were, however, much fainter than the chloroform exhibi- 
 tions, and of the order of the lattice patterns. 
 
 (14.) Now the question at once presents itself What 
 are these Geometrical Spectra? and how, and in what 
 department of the bodily or mental economy do they 
 originate 1 They are evidently not dreams. The mind 
 is not dormant, but active and conscious of the direction
 
 ON SENSORIAL VISION. 4U 
 
 of its thoughts; while these things obtrude themselves 
 on notice, and, by calling attention to them, direct the 
 train of thought into a channel it would not have taken 
 of itself. Retinal impressions they can hardly be, for 
 what is to determine the incidence of pressure or the 
 arrival of vibrations from without upon a geometrically 
 devised pattern on the retinal surface, rather than on its 
 general ground. The effect of some cause in the nature 
 of pressure I on one occasion experienced, and it mani- 
 fested itself quite differently, viz : as an Ocular Spec- 
 trum, consisting in a round, deep purple, feebly lumin- 
 ous spot, dying gradually away into darkness at the 
 borders; It was not exactly in the middle of the visual 
 area, and was caused by no external light : for it was 
 perceived one morning immediately on waking in the 
 morning twilight, and with the face shaded from a direct 
 view of the window. 
 
 (15.) It is quite clear that a regular geometrical pattern 
 cannot be suggested to the imagination by forms having 
 no regularity, however presented to it : so that the 
 explanation which in the other instances adduced might 
 have a certain plausibility, breaks down in these cases. 
 It may be said that the activity of the mind, which in 
 ordinary vision is excited by the stimulus of impressions 
 transmitted along the optic nerve, may in certain cir- 
 cumstances take the initiative, and propagate along the 
 nerve a stimulus, which, being conveyed to the retina, 
 may produce on it an impression analagous to that 
 which it receives from light, only feebler, and which, 
 once produced, propagates by a reflex action the seasa-
 
 412 ON SENSORIAL VISIOW. 
 
 tion of visible form to the sensorium. Still, even grant- 
 ing that such reflex action is possible, and the retina is 
 so impressed, the question remains Where does the 
 pattern itself or its prototype in the intellect originate 1 
 certainly not in any action consciously exerted by the 
 mind, for both the particular pattern to be formed and 
 the time of its appearance are not merely beyond our 
 will and control, but beyond our knowledge. If it be 
 true that the conception of a regular geometrical pattern 
 implies the exercise of thought and intelligence, it would 
 almost seem that in such cases as those above adduced 
 we have evidence of a thought, an intelligence, working 
 within our own organization distinct from that of our 
 own personality. Perhaps it may be suggested that 
 there is a kaleidoscopic power in the sensorium to form 
 regular patterns by the symmetrical combination of 
 casual elements, and most assuredly wonders may be 
 worked in this way. But the question still recurs in 
 another form : " How is it that we are utterly uncon- 
 scious of the possession of such a power ; utterly unable 
 voluntarily to exert it ; and only aware of its being ex- 
 erted at times, and in a manner we have absolutely no 
 part in except as spectators of the exhibition of its 
 results 1 " 
 
 (16.) But again, it may be urged that the particular 
 geometrical forms presented are familiar ones, and are 
 not created or invented pro re nata, but simply old ones 
 reproduced their reproduction being an act, not of 
 invention, but of memory. But against this view of the 
 matter there appears to me to exist an insuperable objec-
 
 ON SENSORIAL VISION. 413 
 
 tion. Memory does not produce its effect by creating 
 before the eyes a visible picture of the object remem- 
 bered. When Hamlet says, " Methinks I see my father," 
 we all know that the expression is a purely figurative 
 one, and have no need to be told, as in his reply to 
 Horatio's " Where ] my lord," (a question perfectly 
 natural to one who had just seen his ghost and knew 
 not but that it might still be present), that it is to the 
 " mind's eye," a merely figurative and metaphorical eye, 
 and not to that of the body, that the expression applies. 
 The act of reminiscence is a conscious and a mental act, 
 and if, under the influence of powerful excitement and 
 strong associations it ever results in the production of 
 a visible picture by the sort of reflex action I have 
 described, it must precede such formation or any how 
 not be itself called up by the picture of its own creation. 
 Of such cases whenever they occur (and I have related 
 what may be considered a case in point) the same 
 account is to be given as in that of certain eminent 
 painters, who are said to have declared that they see 
 upon the paper or the canvas the forms they are about 
 to delineate a quasi-image being formed on the retina by 
 the sympathy of the nerve with the brain, and its impres- 
 sion delivered back to the sensorium as that of a reality. 
 (17.) I ought perhaps to apologize for saying so much 
 about myself and my personal experiences in this line, 
 but the nature of the subject is such as to render this 
 inevitable ; and it is one which can only be elucidated 
 by the individual putting on record his own personal 
 contribution to the stock of facts accumulating. And
 
 ON SENSOR1AL VISION. 
 
 having gone so far in this direction, I may perhaps be 
 borne with if I add one or two more observations of a 
 similar personal nature, which, though not bearing on 
 the subject hitherto spoken of, seem to me not without 
 some interest as contributions to that mass of unaccount- 
 able or difficultly explicable facts with which the history 
 of vision teems so abundantly. 
 
 (18.) The first of these is one of constant occurrence 
 to myself in railway travelling. When looking out on a 
 sloping bank, the train going rapidly, if the sight be 
 directed fixedly out in one direction, all near objects 
 stones, grass tufts, &c., are of course seen as if drawn 
 out into horizontal lines. Now what I constantly per- 
 ceive is the appearance of slender obscure lines like 
 dimly seen dark wires at regular intervals asunder, cross- 
 ing those linear streaky images nearly at right angles, 
 and which always seem not to stand vertically up and 
 down, but as if they reclined backwards on the slope of 
 the bank. I find it best to let the eyes take their own 
 focus without endeavouring to adjust them to any 
 object. 
 
 (19.) It is generally taken for granted that to see any 
 object whatever, the best way is to look straight at it, 
 and get its image impressed on the centre of the retina. 
 This is certainly, however, not the case with a single 
 bright luminous point, if no brighter than a star of the 
 third or fourth magnitude, as any body may convince 
 himself by trying the experiment the first clear night. 
 When two such stars of equal magnitude, within a 
 degree or two of each other, are looked at, nothing is
 
 ON SENSCRIAL VISION. 415 
 
 easier than to make either of them disappear as if 
 blotted out from the sky, by looking full and fixedly at 
 it, while the other remains conspicuously visible. In 
 this way I find stars of the second magnitude consider- 
 ably enfeebled, though they cannot be made wholly to 
 disappear. Those of the first are but little affected. I 
 have found many persons incredulous on their first hear- 
 ing of this fact, who yet have satisfied themselves by 
 trial of its reality. I at one time believed that this 
 comparative insensibility of the centre of the retina 
 arose from the greater wear and tear consequent on 
 directing the attention continually to it, and habitually 
 directing it to any more conspicuous object, but I find 
 that the same thing happens to very young persons to 
 quite as great an extent in whom, of course, this cause 
 of deterioration cannot have gone so far as in adults. 
 There is reason to believe moreover, that this compara- 
 tive insensibility of the middle part of the retina to faint 
 impressions extends over a pretty considerable area, for I 
 find that in a room but feebly lighted, and with the back 
 to the light, it is possible by long looking fixedly in the 
 direction of an object of considerable angular diameter, 
 gradually to lose sight of it, and at length entirely cease 
 to see it and then, by an effort of the will, accompanied 
 with some kind of organic act in the eye itself, which I 
 know by sensation, but am unable to describe in words, 
 but which is not the action of adjusting the focus, it is 
 at once realized to sight, without any alteration of the 
 direction of the optic axis, or any motion given to the 
 head or person. It is an experiment which will not
 
 Al6 ON SENSORIAL VISION. 
 
 always succeed, and requires a peculiar adjustment 
 of the light, and of the comparative illumination of the 
 objects and the ground on which it is seen projected, 
 and perhaps also a peculiar state of nerve ; but when it 
 does succeed, the effect is exceedingly singular and 
 anomalous. 
 
 (20.) It would lead me into too great a length of detail, 
 and I may also add, into a labyrinth of metaphysical 
 considerations, out of which I should find some diffi- 
 culty of getting disentangled, if I were to go into a dis- 
 cussion on those points of connexion between our 
 mental and our bodily organization which these facts 
 seem to suggest. There is a very curious chapter in 
 Stuart Mill's Treatise on Logic, devoted to the question 
 whether we are quite sure that every event has a cause. 
 He decides it, as every reasonable man must do, in 
 favour of the universality of the proposition, but he is 
 compelled to admit, as every one who considers it 
 closely must, I think, equally do, that the phaenomena 
 of the human will stand in a very peculiar relation to 
 that question ; and that granting volition to be a cause 
 of action, and granting the entire freedom of our will and 
 its complete independence to choose when a choice of 
 lines of action is brought before us, there is still the 
 question behind What determines the will? To this 
 question an answer must be found which will leave man 
 a moral and responsible agent. To choose the right 
 and to avoid the wrong, as such, must be left in his 
 power, and a freedom and independence of choice as 
 between these two grand lines of action must be left
 
 ON SENSORIAL VISION. 417 
 
 him, if we would not reduce him to a machine. So far 
 then, and to this extent, I do not see how it is possible 
 not to recognize an original causation, or at least one 
 which it is morally, intellectually, and logically impos- 
 sible for us to find an antecedent for by any power of 
 merely human inquiry. But still there arises this other 
 and further question What determines the will in cases 
 where a variety of modes of action exist ; all, so far as 
 we can see, equally open to choice? Mr Mill here 
 refers us to the associative principle ; and refers the 
 moral position of the individual to the education or 
 early discipline of this associating principle, by which 
 it may be habituated to suggest right and virtuous 
 courses of action among the many possible ones more 
 readily, more powerfully, and more suggestively (if one 
 may tautologize so far) than those of a contrary nature. 
 It is very evident that with the greatest rectitude of in- 
 tention, if a course of action the most conducive to the 
 interests of good do not suggest itself, or be not sug- 
 gested from without, the course actually adopted may 
 be one less so. It is then to the suggestive principle, 
 whatever that be, and however it may act, that we must 
 look for much that is determinant and decisive of our 
 volition when carried out into action, even when the 
 choice has been made between right and wrong in the 
 abstract; and the "way in which thoughts come into 
 our minds" is part and parcel of the nature and mode 
 of action of that principle if it be not merely another 
 form of words for the same thing. Of course this is a 
 subject so obscure and so mysterious, that it is quite 
 
 2 D
 
 418 ON SENSORIAL VISION. 
 
 out of the question to pretend to raise any theory state 
 any doctrine or say anything in the least degree satis- 
 factory, or on which any two opinions would agree, 
 about it. Still it strikes me as not by any means devoid 
 of interest, to contemplate cases where, in a matter so 
 entirely abstract, so completely devoid of any moral or 
 emotional bearing as the production of a geometrical 
 figure, we, as it were, seize upon that principle in the 
 very act, and in the performance of its office. 
 
 (21.) I will not, however, pursue this further, lest I get 
 bewildered myself and bewilder all who listen to me, and 
 it only remains for me to thank you for your patience 
 in listening to me so far, and to apologize once more 
 for dwelling upon my personal impressions. There is 
 one thing more I would add which is to congratulate 
 this town of Leeds on the existence within it of a society 
 of such a nature as that here assembled, and number- 
 ing among its members so many gentlemen of large and 
 liberal views, of extensive information and high acquire- 
 ments, both scientific and literary equally the orna- 
 ments of this their city, and of our common country.
 
 LECTURE X. 
 
 THE YARD, THE PENDULUM, AND THE 
 METRE. 
 
 CONSIDERED IN REFERENCE TO THE CHOICE OF A 
 STANDARD OF LENGTH.* 
 
 [HE attention of the public has of late been 
 strongly drawn to the subject of a proposed 
 alteration of our national system of weights 
 and measures, by the attempt made during 
 the last session of Parliament to carry through a bill, 
 having for its object the abolition of our existing system 
 in its entirety, and the introduction, in its place, of what 
 is known as the " French Metrical System." The bill, it 
 is true, was withdrawn after passing the second reading 
 (by which the House, as is usually supposed, " affirmed 
 
 * This Lecture or Essay was communicated to the Leeds Astrono- 
 mical Society, and read at a meeting of that Society on October 27, 
 1863.
 
 42O THE YARD, PENDULUM, AND METRE. 
 
 the principle of the measure"}, and it may therefore be 
 reasonably presumed that it will be brought forward 
 again in the next session, in the same or a modified 
 form. As the discussion it received in the House 
 seemed to be in no respect commensurate with the im- 
 mense importance and sweeping nature of the change 
 proposed, and with the exception of one or two rather 
 cursory notices in The Times, excited a marvellously 
 small amount of public interest pending its progress ; it 
 will not be amiss if, being called upon by the committee 
 of the Leeds Astronomical Society for an exposition of 
 some point of general interest in the form of a Lecture 
 or Essay, to be read at one of their Evening Meetings, 
 I select this for its subject ; and endeavour to place be- 
 fore you the several conditions which any standard or 
 typical unit of length which shall be assumed as the 
 basis of a system of measures and weights intended to 
 be national, and which may justly claim to be universal, 
 ought to fulfil; and to compare with these conditions, 
 in order to see how far they are fulfilled in fact, both 
 our actual standard, the French metre now in use, and 
 the length of the pendulum, which has been more than 
 once proposed as a natural unit of length. And this I 
 will endeavour to do in as elementary and familiar a 
 way as shall be consistent with perfect correctness. 
 Those of the present audience who are not already 
 familiar with the subject will thus be better enabled to 
 form an opinion as to the desirableness of the change 
 actually proposed, or of any legislative change in our 
 existing standard, and in our system of measures,
 
 THE YARD, PENDULUM, AND METRE. 421 
 
 weights, and coinage generally. And to such it will not 
 be amiss to observe in the outset that, the subject being 
 an exceedingly delicate and refined one, they must not 
 be surprised at seeing very minute quantities and very 
 small fractions treated as matters of much greater im- 
 portance than they may have been accustomed to regard 
 them. 
 
 (2.) The general subject of a national system of weights 
 and measures, be it observed, divides itself into two very 
 distinct and separate points of inquiry, viz. : first, What 
 is intrinsically the best and most available unit of linear 
 measure to adopt as a basis : and, secondly, what system 
 of numerical multiplication and aliquot sub-division of 
 such unit for measures of length, and of its derivative 
 units of area, of capacity, and of weight (for these all 
 refer themselves naturally and easily to the unit of linear 
 measure, or at least ought to do so) is most advantage- 
 ous either in a great mercantile community like our 
 own, or for the great mass of mankind in the ordinary 
 transactions of life. And it cannot be too strongly 
 impressed, and too perseveringly borne in mind, that 
 these two questions stand in no natural and necessary 
 relation to each other, but are perfectly independent. 
 We may resolve, with perfect logical consistency, either 
 to toss aside our present system in toto, and adopt the 
 metrical one in preference ; or to retain our fundamental 
 unit (the Imperial foot or yard), and decimalize our 
 system of denominations; or, lastly, by a slight, and, 
 practically speaking, imperceptible change in our present 
 standard, to bring it into conformity with our views of
 
 422 THE YARD, PENDULUM, AND METRE. 
 
 theoretical perfection (which, I shall show, may be 
 done). We may, too, retaining, all the convenience of 
 our existing denominations (so far as they are convenient) 
 superadd to them, by permissive legislation, the addi- 
 tional convenience of a decimal system for facility of 
 calculation : relying on its holding its ground if really 
 affording such facility, or working its way into general 
 use, and ultimately driving out the old system, if found 
 by the mass of the population to be practicably pre- 
 ferable. This last is the course I would myself prefer, 
 and I think it best to say so in the outset, lest those 
 who may take a contrary view should imagine a foregone 
 conclusion to be urged upon them under the semblance 
 of free inquiry. 
 
 (3.) It is unnecessary, of course, to observe that, the 
 measurement of length being required for almost every 
 purpose of construction as well as for every intelligible 
 statement of the sizes of material objects, the lengths 
 of journeys, the distances of places, &c. renders indis- 
 pensable the recognition, in every community, of some 
 common standard, some well-known and identifiable 
 unit, by whose repetition great, and by whose aliquot 
 subdivision small lengtns, distances, sizes, &c., may be 
 expressed in words and numbers. The common sense 
 of mankind, moreover, would naturally point, in the 
 selection of such unit, to some object of common oc- 
 currence, of moderate linear dimension, and of which 
 individual exemplars differed but little, or, if possible, 
 not at all in this respect ; so that appeal might at 
 once be made to such exemplar in case of a question
 
 THE YARD, PENDULUM, AND METRE. 423 
 
 arising as to the length of any object stated to contain 
 a given number of such units or its aliquots. A very 
 moderate experience would however suffice to convince 
 anybody that among natural objects of the same kind, 
 even those most common, perfect identity of length, of 
 breadth, of thickness, any more than of weight, is never 
 observed even a close approach to it rarely and a 
 very close one extremely so. Still, with all drawbacks 
 so arising on the adoption of a natural standard, the first 
 rude demand for such a standard would be easily enough 
 satisfied, and that in two ways, viz. : ist, by actually 
 fixing upon some individual among all the existing ob- 
 jects of the sort selected, to the exclusion of others or, 
 zdly, by the very natural, though somewhat more re- 
 fined conception of an ideal medium, or mean among a 
 very great multitude of such objects, such as might be 
 regarded as neither unusually great nor unusually little 
 ones of their kind. 
 
 (4.) Among objects of common occurrence, the 
 human person, or some distinct member of it would be 
 most likely to claim the attention of mankind as afford- 
 ing a standard of measure ; if only for the very obvious 
 reason that the relation of the sizes of material objects 
 to that of man mainly determines his facility of hand- 
 ling, or otherwise applying them to human uses. Ac- 
 cordingly, the height of a full grown person, the length 
 of his arm, his fore-arm (ulna or ell), his foot, his 
 band, his ordinary step, &c., would present, and is well 
 known to have presented itself among almost all com- 
 munities of mankind to their choice for this purpose.
 
 424 THE YARD, PENDULUM, AND METRE. 
 
 And so, among all nations whose measures have been 
 handed down to us, we find in speaking of the unit of 
 length, some members of the human person designated. 
 Thus, the bed of the gigantic king of Basan is related to 
 have measured eight cubits in length "after the cubit 
 (i.e., the fore-arm) of a man." The height of Goliath 
 the Philistine was "six cubits and a span." The bow 
 of Pandarus, described by Homer, was formed of 
 the horns of an Ibex, which grew out sixteen palms 
 (or hand -breadths) from his head. The Romans 
 reckoned their distances by intervals of 1000 paces 
 (millia passuum) whence our name for a mile, though 
 differing widely in reality. If, however, we may judge 
 from the great diversity in the actual lengths adopted 
 under the common name of " a foot " as the standards 
 of different nations, we shall see reason to believe that 
 the typical foot selected was usually that of an indi- 
 vidual some Chief, King, or High Priest, who could 
 claim pre-eminence among them as a man par excellence, 
 and who would seem to have been generally above the 
 average stature. Thus we find the Roman foot equi- 
 valent to 1 1 '6 of our inches ; the English to 1 2 ; the 
 Greek to 12*1; the French to 12-8; and the Egyptian 
 or"Drusian" to 13'! all of them (especially the two 
 last) in excess of the real length of the foot of a well- 
 proportioned man of medium stature (say 5ft. loin.) 
 which does not exceed lof, or at the most n inches. 
 
 (5 ) Another class of objects, which, from the univer- 
 sality of their occurrence in vast numbers, and their 
 general uniformity of dimension, would naturally occur as
 
 THE YARD, PENDULUM, AND METRE. 425 
 
 unit types, available for the measurement of small lengths, 
 or for the small aliquots of a larger unit, has been found in 
 the cereal grains of most common use, and of these, the 
 barley corn, and the rice grain, have found the preference. 
 Our inch, for instance, has been defined in an old statute 
 (now repealed) as the length of three grains of barley, 
 taken from the middle of the ear, and placed end to end. 
 And in a somewhat similar manner have been derived 
 from those cereals the smaller sub-divisions of the Heb- 
 rews and Hindoos ; while the larger have, in these, as in 
 other nations, originated in parts of the human person. 
 
 (6.) It is very evident, however, that types of this kind 
 admit of no precise and rigorous identification or inter- 
 comparison. The medium stature of a man is very dif- 
 ferent in different countries. That of an adult French 
 conscript for instance, is (or at least was in 1817) 5ft. 
 4in., as concluded from the measurement of 100,000 in- 
 dividuals, while the Belgian type, or mean adult stature, 
 has been placed at 5ft. yin. '8, and that of a Lancashire 
 non-manufacturing labourer, as high as 5ft. lofin. So 
 great a discordance as a result of local and secondary 
 circumstances, is of course fatal to the pretensions of the 
 human person as a natural type. So again of the cereals. 
 The difference of soil, climate, and cultivation must pro- 
 duce, and does in fact produce very great variety in the 
 medium size of grain grown in different countries, and 
 in different years : so that, even supposing them to be 
 measured by millions, the mean results would be found to 
 differ too much for the object in view. And the same 
 kind of objection holds good against having recourse to
 
 426 THE YARD, PENDULUM, AND METRE. 
 
 any kind of medium magnitude, among multitudes of 
 objects of a like species which occur in nature. Such 
 must, of necessity, be chosen among organic structures 
 of the animal or vegetable kingdom (for among inor- 
 ganic masses of whatever kind, nature presents no in- 
 stance of a mean or typical magnitude, as distinct from 
 the average of a number accidentally assembled, which 
 may differ to any extent from an average similarly taken 
 of an equal number elsewhere collected). And among 
 the former classes of objects, even were it possible to as- 
 semble and measure them in sufficient numbers to afford 
 a true typical mean, we should have no security for its 
 identity in different ages and climates. 
 
 (7.) We are driven then, in our choice of a universal 
 standard to the selection, either of some individual ob- 
 ject, (if such there be) natural or artificial, imperishable 
 in its nature, unsusceptible of variation by lapse of time 
 or decay, and indestructible by accident or else, to 
 some ideal or resultant length or magnitude (if such 
 there be), susceptible by its definition of being as it 
 were translated into a material expression, and marked 
 out as the result of some process which we are sure will, 
 in all ages and places reproduce the same identical 
 result. And besides these qualities of invariability, in- 
 destructibility and identical reproducibility it ought to 
 possess some obvious claim to general acceptation as of 
 common interest to all mankind, or at least to all the 
 civilized portion of it : an interest from which national 
 partialities and rivalries should be altogether excluded. 
 
 (8.) The individual human type is at once excluded
 
 THE YARD, PENDULUM, AND METRE. 427 
 
 by these conditions. Supposing the foot of the most re- 
 markable person who ever lived to be marked out on 
 steel or adamant, it would be at the mercy of fire, earth- 
 quake, loss in political convulsions, and a hundred other 
 forms of destruction or disappearance, without the pos- 
 sibility of reappeal to the original form. Of human 
 works, the most permanent, no doubt, and the most im- 
 posing as well as generally interesting and respected, are 
 those mighty monumental structures which have been 
 erected as if for the purpose of defying the powers of 
 elementary change. Take the vastest of them that to 
 which appeal has been often made for this very purpose 
 the great pyramid of Cheops. When built it was 481 
 ft. in height, and the square area of its base was 764 ft 
 in the side. The height is now only 451 ft. and the side 
 of the base only 746 ; and the sole means by which we 
 are now enabled to determine the original height consists 
 in a block of the exterior marble casing which will in 
 all probability disappear in the hands of " the curious " 
 within the next century. Nature presents to us but one 
 material object which combines all the requisites enumer- 
 ated, and combines them all in perfection viz. : the 
 globe itself that we inhabit. And in that globe we find 
 only two naturally-defined lengths which unite the re- 
 quisites of individuality to identify them under every 
 change of human relations and even of geological revol- 
 utions and catastrophes, and of universality, so as to 
 stand in the same relation to both hemispheres and to 
 all meridians viz. : the earth's polar axis, and its 
 equatorial circumference. For the latter, the equatorial
 
 428 THE YARD, PENDULUM, AND METRE. 
 
 diameter might be more advantageously substituted : but 
 that we have good reason to believe the equator to be 
 not strictly circular, but in some degree elliptic, the pro- 
 portion of its greatest and least diameters not being yet 
 precisely known, though very much nearer to equality 
 than that of the equatorial and polar diameters. This 
 however would not prevent its mean equatorial diameter 
 from being assumed in preference to its circumference, 
 were not the polar axis, for very obvious reasons, prefer- 
 able to both. Of the latter, and indeed of all three 
 (thanks to the elaborate geodesical surveys which have 
 been made within the century last elapsed), we possess 
 a knowledge so precise as to render them perfectly avail- 
 able for our purpose. 
 
 (9.) Of lengths which exist not marked by the dimen- 
 sions of any material object, but which are defined by 
 the nature of things and by physical relations, and which 
 are susceptible of exact determination and of being 
 marked off on a scale, and so of becoming materialized 
 for practical reference ; there have been proposed only 
 three which can be considered theoretically, and of these 
 only one practically available. These are, ist, the vel- 
 ocity of light or the space travelled over by light in some 
 definite time (say the ten-millionth part of a second, 
 which would give a modulus of about 100 feet) ; adly, 
 the length of an undulation of a ray of light of some 
 definite refrangibility a length so minute as to require 
 multiplication a million-fold to give a modular unit ; and 
 3dly, the length of a pendulum vibrating seconds under 
 certain definite and normal circumstances or rather
 
 429 
 
 that of an ideal seconds-pendulm supposed to be placed 
 at the extremity of the earth's polar axis. To this is 
 in effect equivalent, and derivable from it, as a mere 
 arithmetical conclusion, the space fallen through by a 
 heavy body on the same place by the earth's attraction 
 in a second of time. The modulus so obtained is there- 
 fore a measure of the earth's total attractive power (in- 
 dependent of centrifugal force arising from its rotation), 
 as that derived from the length of its diameter is of its 
 total bulk, and equally unalterable and universal. As 
 for the other two which depend on the nature of light, 
 the difficulty and delicacy of the processes they would 
 involve render all idea of resorting to either of them 
 purely visionary. 
 
 (10.) The linear dimensions of the earth then, on the 
 one hand, and the linear measure of its attractive force 
 embodied in the pendulum on the other, are the two, 
 and, so far as we can see, the only two available sources 
 of the invariable and universal standard length which 
 we seek. And it is curious to observe that while the 
 French after considering both of them threw aside the 
 pendulum in favour of the metre (or ten millionth of the 
 meridian quadrant); the English on the other hand, by 
 the Act of Parliament in 1824, which repealed the old 
 statute already alluded to (and so threw aside the 
 principle of resorting to an organic type) did in effect, 
 at that time, adopt the pendulum as their ultimate resort. 
 For while that act declares that a certain metallic bar 
 made by Bird in 1760 when at the temperature of 62 
 Fahr. should, without any further reference to its origin,
 
 43 THE YARD, PENDULUM, AND METRE. 
 
 be considered the standard yard of the British empire, 
 it provided for its recovery and reproduction in case of 
 the total destruction or loss of it and all its authentic 
 copies and facsimiles, by a declaration that its length is 
 36 inches, such that 39-13929 of them are equal to the 
 length of a pendulum vibrating seconds in vacuo and at 
 the sea-level, in the latitude of London. The report of 
 the French commissioners also in 1798 which led to the 
 enactment of the metrical system, is careful to state that 
 in the event of the total loss or destruction of all 
 material representatives of the metre its value would be 
 easily recoverable from a numerically specified relation 
 between its length and that of the pendulum vibrating 
 seconds at Paris, which had been determined with great 
 accuracy by Borda, one of the commissioners. So that, 
 practically speaking, in the event of the total destruction, 
 by political convulsions, of every authentic yard and 
 metre (supposing any written record of our existing 
 knowledge to survive them) the metre would have been 
 recovered, not by the laborious and costly process 
 of remeasuring the French meridian arc, but by the in- 
 finitely more summary one of a precise repetition of 
 Borda's experiments and the exact re-application of all 
 his corrections and reductions. 
 
 (i i.) For the reproduction of the English yard, a simi- 
 lar repetition of those experiments in London which led 
 to the adoption of the number 39'i3929 in. as the mea- 
 sure of the pendulum would, in such an event, no doubt 
 have been, at that epoch, resorted to ; though in depart- 
 ure from the wording of the act, which speaks of a
 
 THE YARD, PENDULUM, AND METRE. 431 
 
 pendulum vibrating seconds, not at but in the latitude of 
 London : a very different thing, as General Sabine has 
 pointed out in his " Account of Experiments to determine 
 the figure of the Earth by means of a Pendulum vibrating 
 Seconds in different latitudes" For the object would have 
 been then, as it really was on the occasion of the actual 
 destruction of the parliamentary standard in 1834, not 
 to produce a theoretically better, but as far as possible to 
 reproduce the same identical length by the most summary 
 process ; without undertaking circumnavigatory voyages, 
 or entering on any theoretical discussion. The new act 
 necessary for legalizing the standard so arising would 
 probably have sanctioned this procedure, and we should 
 have thenceforward had a standard of a purely local 
 character, assuming for the fundamental basis the indi- 
 vidual seconds pendulum in London. 
 
 (12.) This, however, is not now the case. On the de- 
 struction of the standard of 1760 by the burning of the 
 Houses of Parliament, the new standard was constructed, 
 not by any measurement of the length of the pendulum 
 (for in the ten years elapsed since 1826 very grave 
 doubts had been raised, or rather very serious sources 
 of error pointed out in the processes used for the pur- 
 pose on the former occasion) but, by an assemblage 
 and most careful comparison of all the scales and stand- 
 ards of any authority which could be got together re- 
 sulting in the production of one primary and a great 
 many secondary standards, in all human probability ab- 
 solutely identical with that destroyed. The act, more- 
 over, (of 1855,) which constituted that one our legal yard,
 
 432 THE YARD, PENDULUM, AND METRE. 
 
 and named the others in a certain order as its successors 
 in the event of its destruction or loss, omitted the clause 
 identifying its length with any numerical multiple of the 
 pendulum. In fact, then, our yard is a purely individual 
 material object, multiplied and perpetuated by careful 
 copying ; and from which all reference to a natural origin 
 is studiously excluded, as much as if it had dropped 
 from the clouds. Apart, then, from the extraordinary 
 pains taken in its construction, and from the singularly 
 fortunate but at the same time purely accidental coinci- 
 dence which I shall presently mention, it has no preten- 
 sions whatever to be regarded as a scientific unit. 
 
 (13.) Let us now consider the claim which the pen- 
 dulum, in the abstract, as a measure of the earth's gravi- 
 tation, can advance for its reception as a fundamental 
 and universal standard of length (and here, incidentally 
 it may be remarked that, as a length, it is not more in- 
 convenient than the metre, being within about a quarter ot 
 an inch the same).* One of the reasons assigned by the 
 French Savans for their rejection of it in favour of the 
 metre, and, as would appear, the only one which 
 weighed with them (for their other reason ostensibly 
 advanced is a mere appeal to the political passions of the 
 time) was the dependence of the length of the pendulum 
 
 The metre has this inconvenience, as compared with the yard 
 that while the latter can be readily extemporized by a man of 
 ordinary stature (and often is so in practice) by holding the end of a 
 string or ribband between the finger and thumb of one hand at the 
 full length of the arm extended horizontally sideways, and marking 
 the point which can be brought to touch the centre of the lips 
 (facing full in front) ; the former is considerably too long to afford 
 the same facility.
 
 THE YARD, PENDULUM, AND METRE. 433 
 
 on the time of its vibration ; as if the 86,4ooth part of a 
 day which we call a second of time were not as definite 
 and as invariable a quantity as the ioo,oooth part which, 
 in their rage for decimalization, they proposed to call 
 one ; and as if they might not have fixed on a pendulum 
 vibrating 100,000 times in a day (which would have given 
 a very near approach to our yard). But their stumbling- 
 block was the introduction of an extraneous element, 
 f ime, at all, into the subject : as if the length of the 
 day were not as much an invariable, universal, and 
 physical element as the dimensions of the earth or its 
 gravitation. But in this they seem to have overlooked 
 the fact that their adoption of the quadrant of a meridian 
 for the base of their system does really admit this ex- 
 traneous element, time, into that system, though in a much 
 more insidious way. For the total bulk or mean radius 
 and the total mass or gravitating energy of the earth 
 remaining the same, the ellipticity of its meridians, and 
 therefore their absolute length, depends on the period 
 of its rotation or the length of the day. The same ob- 
 jection, to be sure, if it be one, would equally apply to 
 the adoption of the polar axis, or the equatorial diameter 
 of the earth ; and the only way to exclude all ideas of 
 time and force from a metrical system, and render it 
 purely metrical, i.e., dependent on geometrical magnitude 
 alone, would be to take for a fundamental unit the 
 radius, diameter, or circumference of a sphere, or the 
 side of a cube, equal in volume to that of the earth. 
 And perhaps were a tabula rasa made ; were the 
 ground totally unoccupied and the whole matter to do 
 
 2
 
 434 THE YARD, PENDULUM, AND METRE. 
 
 over again, this would be as good a unit as could be 
 proposed. 
 
 (14.) But the true objection to the choice of the pen- 
 dulum for a universal unit of measure lies, not in any 
 metaphysical and abstract considerations of this kind ; 
 but in the uncertainty which prevails, and must neces- 
 sarily always prevail as to the true length of that normal 
 or ideal pendulum which shall stand equally related to 
 the whole globe, and from which the mean length cor- 
 responding to any assigned latitude can be calculated : 
 that is to say, the length of a pendulum which would 
 swing seconds at the pole of the terrestrial spheroid 
 an uncertainty which, as I shall proceed to show, must 
 affect the result of every attempt to deduce it with the 
 precision the subject requires from experiments made on 
 the surface of our planet : however refined the methods 
 employee.' and however numerous and diversified the 
 geographical stations at which they may be instituted. 
 
 (15.) In practice, the mean length of the polar or 
 equatorial pendulum is concluded from an assemblage of 
 the observations of the times of oscillation of one and 
 the same invarial le pendulum at a multitude of geo- 
 graphical stations in all accessible latitudes in both 
 hemispheres : no *wo combinations agreeing in giving 
 the same precise length, by reason of the local deviations 
 of the intensity of gravity due to the nature of the soil, 
 and the configuration of the ground immediatety beneath 
 and around the places of observation. Now, since the 
 pendulum cannot be observed at sea, the whole sea- 
 covered surface of the globe is of necessity excluded
 
 THE YARD, PENDULUM, AND METRE. 435 
 
 from furnishing its quota of observations to the final or 
 mean conclusion. And the influence of this, it should 
 be observed, is not self-compensating as that of local 
 inequalities of mere density on land would be, but tells 
 all in one direction. For water being, on the average, 
 not more than one-third the weight of an equal bulk of 
 land (such land as the earth's surface consists of) and 
 only -fj- of the mean density of the globe, the force of 
 gravity at the surface of the sea is less than at the sea- 
 level on land by the attractive force of as much material 
 taken at twice the specific gravity of water, or at Aths 
 that of the globe, as would be required to raise the bot- 
 tom to the surface. Supposing then the difficulty of 
 observing the pendulum at sea overcome, and that the 
 whole surface of the globe were dotted over with stations 
 of observation equally distributed over sea and land, 
 from whose intercomparison it were required to derive 
 the mean co-efficient of terrestrial gravitation, or the mean 
 length of the polar pendulum ; it is evident that the sea 
 stations would everywhere conspire to give a less result 
 than the land. According to Dr Young (Phil. Trans., 
 oL cix., page 93) the attraction of an extensive flat 
 mass of any thickness on a point in the middle of its 
 surface is three times that of a sphere of the same mate- 
 rials having that thickness for its diameter. And from 
 this it is very easy to conclude that, supposing the sea to 
 have a mean depth of four miles (which seems not im- 
 probable) the mean defalcation of gravity at its surface, 
 due to the deficiency of attracting matter, would be three 
 times the attraction of a sphere four niles in diameter
 
 436 THE YARD, PENDULUM, AND METRE. 
 
 and T^-ths of the earth's mean density that is by a 
 simple calculation TW> or rather less than one i Sooth 
 part of the whole attraction of the earth a fraction far 
 too large, as well as far too uncertain in its amount 
 either at any given spot or in general, not to vitiate irre- 
 mediably any conclusion as to the ultimate result of the 
 operation. 
 
 (16.) Similarly, if we look to the reductions to the 
 sea level necessary for stations in the interior of conti- 
 nents, we shall find that they depend, partly on the 
 diminution of gravity due to the height above the sea- 
 level, or to the increase of distance from the earth's 
 centre, which always tells in diminution of gravity ; and 
 partly on the protuberant matter, be it mountain or 
 elevated table-land immediately beneath and around the 
 pendulum, which always tells in favour of increased gravi- 
 tation. The former portion is rigorously calculable, and 
 therefore need not trouble us, but the latter is in an ex- 
 treme degree uncertain in particular localities, and in a 
 general estimate falls very short of compensating for the 
 sea-deficiency. For the mean height of the European 
 continent is only 1342 feet; of Asia 2274; of North 
 America 1496 ; and of South America, 2302. The 
 mean is 1840 feet, or rather more than a third of a 
 mile, which, on the same principle of reckoning, would 
 be equivalent to about nriroth part only of the total 
 gravity, which has to be reduced to one-third of its 
 amount, or to i-45oooth, inasmuch as the proportion of 
 land to water over the whole globe is only that of 5 1 to 
 146, or about i to 3. This is the mean effect of the
 
 THE YARD, PENDULUM, AND METRE. 437 
 
 elevated matter to increase gravitation. That of mere 
 elevation above the sea-level to the height of of a mile 
 (similarly reduced) is, however, one 36oooth in the oppo- 
 site direction, or to diminish it and the difference or 
 one 180,000 of the whole is effective not to compensate 
 but to add to the sea-deficiency. 
 
 (17.) To obtain the real length of the normal pendu- 
 lum then we must go out of our own globe, and ascer- 
 tain the true co-efficient of gravity from astronomical 
 facts ; and, as the only one available for the purpose, 
 compute the distance fallen through by the moon in a 
 second of time towards the earth from a tangent to her 
 orbit. This, it is evident, is independent of the influence 
 of those local inequalities which affect the pendulum 
 measurements. But, on the other hand, it must be re- 
 membered ist, That our knowledge of the distance in 
 question depends on our previous knowledge of the 
 moon's distance, which, in its turn, depends on that of 
 the earth's diameter, and therefore presupposes the 
 metre to be accurately known. For any aliquot error in 
 the metre will produce an equal aliquot error in the 
 moon's distance estimated in metres, and therefore also 
 in the linear deflection per second from the tangent to 
 the orbit. 2d, That this linear deflection, or approach 
 of the moon to the earth in one second of time, is the 
 result of the joint attraction of the earth on the moon 
 and of the moon on the earth, and is in effect the sum of 
 the spaces fallen through by the moon towards their com- 
 mon centre of gravity, in virtue of the earth's attraction, 
 and by the earth towards that point in virtue of the
 
 4?8 THE YARD, PENDULUM, AND METRE. 
 
 moon's. Now the mass of the moon is about one 88th 
 part of that of the earth, so that one 88th part of the force 
 that draws them together is due to the moon. By so 
 much then must the space fallen through be diminished, 
 to get that due to the earth's alone. Suppose, now, that 
 the moon's mass assumed should be in error by a 5oth 
 part of its whole amount (and Laplace's estimate of it 
 differs by as much from that at present received) and 
 we shall find ourselves landed, from this cause of uncer- 
 tainty alone, in an error to the extent of nearly one 
 4oooth of the quantity sought. 
 
 (18.) Lastly, our knowledge of the moon's mass is 
 mainly derived from its effect in producing the phseno- 
 menon of nutation, which it does through the medium of 
 the earth's ellipticity, so that not only the dimensions, 
 but the figure of the earth are thus mixed up in our 
 attempt to derive the length of the normal pendulum from 
 the moon's motion. 
 
 (19.) I cannot but consider then that the uncertainty 
 of the one mode of obtaining the length of the normal 
 pendulum, and the non-independence of the other, unfit 
 it for being received as the ultimate scientific basis of a 
 universal standard ; whatever merit it may possess in an 
 abstract and metaphysical point of view and that the 
 true and only practical use of the pendulum in relation 
 to such a standard is the ready, cheap, and perfectly un- 
 objectionable means its measurement, at a determinate 
 spot and under defined circumstances, affords of recover- 
 ing it when lost, by the recorded statement of its length 
 in terms of such standard.
 
 THE YARD, PENDULUM, AND METRE. 439 
 
 (20.) The causes of uncertainty which tell with such 
 very appretiable effect on the local determination of 
 the force of gravity by the pendulum, have little or no 
 influence on the local curvature of the surface of equili- 
 brium, and absolutely none on the measures of large 
 arcs of the meridian. Suppose, for example, a sea of 
 four miles in depth, and of great extent, to cover one 
 part of the earth's surface. Its surface water will gravi- 
 tate less by one i Sooth part of its proper weight, owing 
 to the deficiency of attracting matter below it ; and, the 
 diminution of gravity growing less and less in descend- 
 ing (being proportional to the height of a particle above 
 the bottom), the whole weight of the column of water 
 vertically above a given spot will be diminished by one 
 36ooth part, so that to maintain the equilibrium, one 
 36ooth part of four miles, or one Qooth of a mile, t.e., 
 about six feet of additional water, must be heaped on : a 
 mere infinitesimal of the radius of curvature of its surface, 
 which is that of the earth itself. 
 
 (21.) Let us now see how far the French metre, as it 
 stands, fulfils the requirements of scientific and ideal 
 perfection. It professes to be the io,ooo,oooth part of 
 the quadrant of the meridian passing through France 
 from Dunkirk to Formentera, and is therefore, scientifi- 
 cally speaking, a local and national, and not a universal 
 measure. The earth's equator is not a perfect circle, 
 but slightly elliptic, and the meridians of places differ- 
 ing in longitude are therefore not all of the same length. 
 The difference, however, is so trifling (the ellipticity of 
 its equator being not more than a thirtieth part of that
 
 440 THE YARD, PENDULUM, AND METRE. 
 
 of its meridian) that to raise an objection against the 
 practical reception of the metre, either perse, or as a sub- 
 stitute for the yard, on this score, would savour of hyper- 
 criticism. A more serious objection is the choice made 
 of the circumference of the meridional or generating 
 ellipse of the terrestrial spheroid in preference to its 
 axis of revolution. This is a blemish on the very face 
 of the system a sin against geometrical simplicity. 
 Still, were the length of the metre as determined by the 
 French geometers rigorously exact, or correct within 
 limits which the much more extensive measurements of 
 meridian arcs since made elsewhere than in France have 
 proved to be attainable, this would be only a matter of re- 
 gret, and could hardly, of itself, be drawn into an argument 
 /or its rejection. But this is far from being really the 
 case. The metre, as represented by the material stand- 
 ard adopted as its representative, is too short by a 
 sensible and measurable quantity, though one which 
 certainly might be easily corrected. To show this it 
 will be necessary to enter into some detail. 
 
 (22.) In effect, that standard is declared, in the An- 
 nuary of the Bureau des Longitudes, to be equal to 
 39^37079 British imperial standard inches. The quad- 
 rant of the French meridian then ought, if this be correct, 
 to be 393,707,900 such inches, or 32,808,992 feet. And 
 by whatever aliquot part of its whole length the true 
 quadrant exceeds this, by that same aliquot of its length 
 is the metre, so stated, erroneous. 
 
 (23.) Mr Airy, by a combination of the whole series of 
 meridian arcs whose measures had been obtained in
 
 THE YARD, PENDULUM, AND METRE. 44! 
 
 every part of the globe in 1830, was led to conclude for 
 the value of the minor or polar axis of the terrestrial 
 spheroid, 41,707,620 feet ; while the late Professor Bessel, 
 pursuing a course similar in its general principle that is 
 to say, using all the measured arcs, great and small, in 
 combination one with another, and taking the most 
 probable mean among the (necessarily) discordant results, 
 obtained by combining them two and two arrived at a 
 value very slightly different, viz., 41,707,314 feet The 
 mean of these gives, as the result of this mode of proced- 
 ure, 41,707,467. 
 
 (24.) Quite recently, M. Schubert in a very elaborate 
 memoir which appears as part of the ist vol., yth series, 
 of the Memoirs of the Petersburg Academy, has pointed 
 out the inconvenience, and necessarily discordant results 
 which the combination by pairs of a multitude of small 
 arcs, each of itself insufficient to afford any precise 
 measure of the ellipticity, affords; and assigned his rea- 
 sons for restricting the inquiry in the first instance into 
 the length of the polar axis, as an element unique in 
 itself, and common to all the meridians: deducing it 
 separately from each of the most extensive arcs, the Rus- 
 sian, the Indian, and the French, each taken independ- 
 ently; comparing the three values so obtained, and 
 thence concluding the final result. In this manner he 
 obtains the following three values of the axis, viz. : 
 
 From the Russian arc (of 25 2Of in extent) 41, 71 1, 019-2 feet 
 Indian (of 21 21' ) 41, 712, 534-2 feet 
 French,, (of 12 22' ) 4 1,69 7, 496-4 feet. 
 
 In concluding for these a mean, or final value, M.
 
 442 THE YARD, PENDULUM, AND METRE. 
 
 Schubert however, arbitrarily, and as I think quite inde- 
 fensibly, rejects altogether the result of the French arc, 
 and assigns to the Russian double the weight of the 
 Indian ; a mode of precedure in which he will find, I 
 presume, few to agree with him. A much fairer, indeed 
 the only fair way to treat them, is obviously to ascribe to 
 each of the separate results in taking the mean / , a 
 weight proportional to the total extent of the arc, and 
 this gives for the length of the axis 41,708,710-0 feet. 
 Comparing then the final results of the two modes of 
 procedure we find, 
 
 From the former, 41,707,467 feet. 
 
 And from the latter, 41,708,710 
 
 which differ only by 1243 feet, or less than \ of a mile 
 so that their mean or 41,708,088-5 f. is in all probability 
 within a furlong, or one part in 64,000 of the truth. 
 
 (25.) From each of the great arcs of Russia and India, 
 M. Schubert then obtains a separate value of the equa- 
 torial or the larger axis of the elliptic meridian to which 
 it belongs; and by a similar treatment of the arc of Peru, 
 which, lying under the equator, is especially favourable 
 for the purpose, he obtains a third value of the equa- 
 torial diameter. The three diameters of the equatorial 
 ellipse thus obtained, with the angles they include at the 
 centre (which are the differences of longitude of the re- 
 spective meridians, and which are as favourably arranged 
 for the purpose as the nature of the case seems to admit), 
 suffice for the determination of the major and minor axis 
 of the equator, regarded as an ellipse, and the longitudes 
 in which they lie, viz. :
 
 THE YARD, PENDULUM, AND METRE. 443 
 
 Axis major = 41,854,800 feet, in long. 38 44' E. from 
 Paris (one end falling about half-way between Mount 
 Kenia and the east coast of Africa, the other in the 
 middle of the Pacific Ocean). 
 
 Axis minor = 41,850,007 feet, in long. 128 44' E. from 
 Paris (one end falling on Waygiou, one of the Molucca 
 Islands, and the other at the mouth of the Amazon 
 River), giving an ellipticity of one 888oth, or about one- 
 thirtieth part of that of the meridians as already stated. 
 
 (26.) The figure of the equator, and its dimensions 
 thus obtained, the exact equatorial diameter correspond- 
 ing to any given longitude is easily calculated. And by 
 comparing this with the polar axis, the precise ellipticity 
 of the meridian for that longitude may be computed. 
 And executing this computation for Paris, M. Schubert 
 finds ^g- for the ellipticity of the French meridian. 
 
 (27.) With these data, viz., a Polar axis of 41,708,088 
 feet, and an ellipticity of 5^75- which certainly may lay 
 claim to greater precision than anything previously 
 obtained, I shall now proceed to calculate the true length 
 of the quadrant of the French meridian, for which pur- 
 pose the following very simple and convenient formula 
 may be used,* viz. : 
 
 Q=5 A (i + 2m + Qm* + 38^* ) 
 
 * For the present purpose it is necessary to carry out the cal- 
 culation to the cube of the ellipticity but in cases where the 
 square of that fraction may be neglected, the following simple rule 
 for finding the circumference of an ellipse is worth remembering. 
 On the longer axis of the ellipse describe a circle, and between this 
 and the ellipse, describe a small circle having its centre in the pro- 
 longation of the minor axis, and touching the ellipse externally, and
 
 444 THE YARD, PENDULUM, AND METRE. 
 
 in which Q represents the length of the quadrant re- 
 quired, A that of the polar axis, if the circumference of 
 a circle whose diameter is i, and m, one fourth part 
 of the fraction expressing the ellipticity, or in this 
 
 Executing the calculation the result is. ..32,813,000 feet. 
 Substract 10,000,000 metres = 32,808,992 
 
 Remain, excess 4,008 
 
 for the excess of the true quadrant over that assumed 
 as the basis of the metrical system, that is to say, one 
 8194 aliquot part of the whole, or one 2o8th of an inch 
 on the whole metre, which is therefore the quantity by 
 which the French standard is actually too short. 
 
 (28.) It must not be denied that this is a very wonder- 
 ful approximation, and in the highest degree creditable 
 to the science, skill, and devotion of the French astrono- 
 mers and geometricians who carried on their operations 
 under every difficulty, and at the hazard of their lives in 
 the midst of the greatest political convulsion of modern 
 times. And adopted as it is over a large portion of 
 Europe ; were the question an open one what standard a 
 new nation, unprovided with one, unfettered by usages 
 of any sort, and in the absence of any knowledge 
 of the existence of the British yard, should select ; there 
 could be no hesitation as to its adoption (with that very 
 slight correction above pointed out which would in no 
 
 the circumscribed circle internally. The circumference of this small 
 Circle is the difference between those of the ellipse and of the larger 
 or circumscribing circle.
 
 THE YARD, PENDULUM, AND METRE. 445 
 
 way interfere with its practical use a correction which 
 the French themselves might, under such circumstances, 
 consent to adopt). But the question now arising is 
 quite another thing, viz. : whether we are to throw over- 
 board an existing, established, and, so to speak, ingrained 
 system adopt the metre as it stands, for our standard 
 adopt moreover its decimal sub-divisions, and carry 
 out the change into all its train of consequences j to 
 the rejection of our entire system of weights, measures, 
 and coins. If we adopt the metre we cannot stop short 
 of this. It would be a standing reproach and anomaly 
 a change for changing's sake. The change, if we 
 make it, must be complete and thorough. And this in 
 the face of the fact that England is beyond all question 
 the nation whose commercial relations, both internal and 
 external, are the greatest in the world, and that the 
 British system of measures is received and used, not only 
 throughout the whole British empire (for the Indian 
 " Hath" or revenue standard is denned by law to be 18 
 British imperial inches) but throughout the whole North 
 American continent, and (so far as the measure of length 
 is concerned) also throughout the Russian empire ; the 
 standard unit of which, the Sagene, is declared by an 
 imperial ukase to contain exactly seven British imperial 
 feet, and the Archine and Vershock precise fractions 
 of the Sagene, Taking commerce, population, and 
 area of soil then into account, there would seem to be 
 far better reason for our continental neighbours to 
 conform to our linear unit could it advance the same, 
 or a better a priori claim, than for the move to come
 
 446 THE YARD, PENDULUM, AND METRE. 
 
 from our side. (I say nothing at present of decimaliza- 
 tion). 
 
 (29.) Let us see then how this part of the matter stands. 
 Taking the polar axis of the earth as the best unit of 
 dimension which the terrestrial spheroid affords (a. 
 better a priori unit* than that of the metrical system) we 
 have seen that it consists of 41,708,088 imperial feet 
 which, reduced to inches, is 500,497,056 imperial inches. 
 Now this differs only by 2944 inches, or by 82 yards 
 from 500,500,000 (five hundred million and five hundred 
 thousand) such inches and this would be the whole error 
 on a length of 8000 miles which would arise from the 
 adoption of this precise round number of inches for its 
 length, or from making the inch, so defined, our funda- 
 mental unit of length. Suppose, then, that any length 
 were proposed in English measure, and we desire to 
 know what decimal fraction such length were of the 
 earth's axis. We have only to express it in inches and 
 decimals, and from the number so stated take off its 
 thousandth part (a calculation involving only the writing 
 down the number twice over, removing the figures of the 
 
 * A writer in Quesneville's Moniteur Scientifique, No. 163, v. 736, 
 argues that itinerary measures ought to be based on the circumfer- 
 ence of the globe and not on its axis by reason that the decimal 
 principle of sub-division, if carried out, would apply to the decimal 
 graduation of the quadrant adding that "the greatest advantage 
 of the French system is in reality its decimal division" but_/2>r- 
 getting to add that the decimal division of the quadrant was intro- 
 duced in France, but was abandoned by common comsttt ez>en in 
 France, and can never be reintroduced. In the " Mondes" (Suppl. 
 38, p. 616) the same argument is advanced, and the same answer 
 applies.
 
 THE YARD, PENDULUM, AND METRE. 447 
 
 under line three places to the right and subtracting), and 
 the thing is done, and vice versa* Suppose now the 
 same length stated in French metres, and we would 
 ascertain what decimal fraction it is of a quadrant of the 
 French meridian. The number of metres assigned must 
 be divided by 8194 either by a long division sum or by 
 the use of a table, before the proper number to be sub- 
 tracted can be found. Which then is the shorter pro- 
 cess ? and which, both scientifically and practically, the 
 preferable unit 1 
 
 (30.) If we are to legislate at all on the subject then, 
 the enactment ought to be to increase our present stand 
 ard yard (and of course all its multiples and submultiples) 
 by one precise thousandth part of their present lengths, 
 and we should then be in possession of a system of 
 linear measure the purest and most ideally perfect im- 
 aginable. The change, so far as relates to any practi- 
 cal transaction, commercial, engineering, or architectural, 
 would be absolutely unfelt, as there is no contract for 
 work even on the largest scale, and no question of 
 ordinary mercantile profit or loss, in which Q\\Z per miUe 
 in measure or in coin would create the smallest difficulty. 
 Neither could it be doubted that our example would b<; 
 
 * Strictly speaking for the conversion and reconversion we should 
 subtract one 999th and add one loooth. But the difference is only 
 one part in a million which can never be of the slightest importance. 
 Per contra the conversion of the metre according to the process here 
 stated leads to a result which, though exact in parts of the French 
 meridian, is erroneous in parts oi the mean terrestrial meridian by 
 a considerably larger proportional part, and this is what we really 
 wimt to know.
 
 448 THE YARD, PENDULUM, AND METRE. 
 
 very speedily followed both in America and Russia, so 
 soon as the reason of the thing and the trifling amount 
 of the change came to be understood. And even with- 
 out legislation the relation between the proposed new or 
 geometrical measure and the imperial ones is so simple 
 and striking fixing itself so easily in the memory, and the 
 conversion from one to the other so ready, that, were 
 there no other reason, it might almost be questioned 
 whether it would be worth while to make the change. 
 
 (31.) But there is another reason, and I think a decisive 
 one. Hitherto I have said nothing about our weights 
 and measures of capacity. Now, as they stand at pre- 
 sent nothing can be more clumsy and awkward than the 
 numerical connexion between these and our unit of 
 length. A grain is denned as the weight of distilled 
 water, so that 252724 of such grains at the freezing 
 temperature, or 252-46 at that of 62 Fahr. which is the 
 standard temperature of our imperial yard, shall fill a 
 cubic inch. Of such grains, so defined, the pound con- 
 tains 7000, the ounce 43 7 , and the gallon of water at 
 62", 70,000. According to this system, the cubic foot of 
 water at our standard temperature weighs 997-145 oz., 
 falling short of 1000 02. by very nearly 3 oz. However 
 tempting this approximation might appear, still, in the 
 absence of any more cogent reason, the commissioners 
 who recommended our system of weights and measures 
 legalized in 1824 forbore to recommend such a change 
 in the ounce (about ij grain) as would have brought it 
 about ; though the rule that a cubic foot of water weighs 
 1000 ounces is still handed down as a rough and ready
 
 THE YARD, PENDULUM, AND METRE. 449 
 
 way of converting cubic measure into weight. But were 
 we to adopt the geometrical instead of the present imperial 
 standard the linear foot being increased by one thou- 
 sandth, the cubic foot would be increased by three times 
 that aliquot, or would become 1*003 times our present 
 cubic foot and so would make up just the deficient 
 three ounces, or at least so very nearly that a legislative 
 change in the ounce, increasing it by only one part in 
 8000, or by one i8th part of a grain, would bring every- 
 thing into decimal coincidence, by making the ounce and 
 the cubic foot the links of connexion between weights 
 and measures instead of the grain and the cubic inch, as 
 at present. As regards our measures of capacity, the con- 
 nexion would be equally consecutive, as a decimal one, 
 between the cubic foot and the half pint, which for the 
 purpose in view, ought to have a distinct name (such as 
 a " tumbler" or a " rummer" or a " beaker"") and which 
 would contain exactly one xooth part of a cubic foot, 
 with whatever liquid or solid matter it might be filled. 
 And thus the change which would place our system of 
 linear measure on a perfectly faultless basis, would at the 
 same time rescue our weights and measures of capacity 
 from their present utter confusion, and secure that other 
 advantage, second only in importance to the former, of 
 connecting them decimally with that system on a regular, 
 intelligible and easily-remembered principle ; and that by 
 an alteration practically imperceptible in both cases, and 
 interfering with no one of our usages or denominations. 
 
 (32.) On the subject of decimalization, it will be ga- 
 thered from what I have said that I would make any de- 
 
 2 F
 
 45 THE YARD, PENDULUM, AND METRE. 
 
 cimalized denominations which anybody might agree to 
 buy, sell, or contract by, permissive. There seems to be 
 a doubt whether such is now the case, and if so the law 
 should I think be altered. But I would leave untouched 
 all our present denominations and their relations to the 
 standard and the only new measure I would legalize 
 would be a " module" (or some other name at present un- 
 occupied) of 50 geometrical inches being the ten millionth 
 of the polar axis, or its half, the "geometrical cubit" of 
 25 such inches leaving its use quite voluntary. 
 
 COLLINGWOOD, Sept. 30, 1863. 
 
 ADDENDUM. 
 
 (33.) Since the foregoing remarks were written my 
 attention has been called by the Astronomer Royal to 
 a very elaborate memoir by Captain Clarke, in voL 
 xxix. of the Memoirs of the Royal Astronomical Society, 
 whose conclusions, though differing from those of M. 
 Schubert in some particulars (as in making the equator 
 more elliptic) yet, so far as the present subject is con- 
 cerned, tend in the same direction, and that, as regards 
 the aliquot error of the metre, even more strongly. 
 
 (34.) Captain Clarke assigns for the three axes of the 
 earth the following values : 
 
 Polar axis 4i,7O7>536 feet 
 
 Or in inches 500,490,432. 
 
 Longer equatorial axis 41,852,970 feet. 
 
 Shorter do. do 41,842,354
 
 THE YARD, PENDULUM, AND METRE. 451 
 
 Longitude of the vertex of the longer axis=i3 58' 30' 
 east or 11 35' 15" E. of Paris) whence it is easy to 
 conclude as follows : 
 
 Diameter of equator in the longitude of Paris. ..41, 852, 695 feet. 
 Ellipticity of the Paris meridian .............. , ......... TSTS sa y sr? 
 
 (35.) Calculating now the quadrant from this ellip- 
 ticity, and from Captain Clarke's polar axis, we find it 
 32,814,116 feet, which exceeds ten million metres by 
 5124 feet, being in excess of that above found (4008) 
 by 1116 feet; and corresponding to an aliquot error of 
 one part in 6404, or on the metre itself to one i63d part 
 of an inch. The aliquot error in our "geometrical 
 yard" is also somewhat increased by the adoption of 
 this polar axis, viz., to one part in 52,310, or to about 
 one i453d part of an inch on the yard. 
 
 (36.) As this memoir of Captain Clarke contains by far 
 the most complete and comprehensive discussion which 
 the subject of the earth's figure has yet received, and 
 must be held as the ultimatum of what scientific calcula- 
 tion is as yet enabled to exhibit as to its true dimen- 
 sions and form this conclusion will of course be con- 
 sidered to supersede that arrived at in the foregoing 
 pages. 
 
 COLLINCWOOD, Oct. 11, 1863. 
 
 P.S. Some slight subsequent corrections made by CapL 
 Clarke in his calculations, founded on data quite 
 recently published, make the polar axis approximate 
 still more nearly to 500,500,000 inches.
 
 XL 
 
 ON ATOMS.* 
 
 "I sing of atoms." Rejected Addressee 
 
 DIALOGUE. Hermogenes et Hermione interloquuntur. 
 
 | E R M I O N E. What strange people those 
 Greeks were? I was reading this morning 
 about Democritus, " who first taught the 
 doctrine of atom's and a vacuum." I suppose 
 he must have meant that there is such a thing as utterly 
 empty space, and that here and there, scattered through 
 it, are things called atoms, like dust in the air. But then 
 I thought, "What are these atoms]" for if this be true, 
 then, these are all the world, and the rest is nothing! 
 
 Hermogtnes. Yes. That is the natural conclusion: 
 unless there be something that does not need space 
 to exist in ; or unless there be things that are not mate- 
 
 * From the Fortnightly Review.
 
 ON ATOMS. 453 
 
 rial substances ; or unless space itself be a thing: all 
 which is deep metaphysic, such as I arn just now rather 
 inclined to eschew. But, dear Hermione, how am I 
 to answer such a host of questions as you seem to 
 have raised all in a breath ? The Greeks ! Yes ; they 
 were a strange people so ingenious, so excursive, yet so 
 self-fettered ; so vague in their notions of things, yet so 
 rigidly definite in their forms of expressing them. Ex- 
 tremes met in them. In their philosophy they grovelled 
 in the dust of words and phrases, till, suddenly, out of 
 thei r utter confusion, a bound launched them into a new 
 sphere. There is a creature, a very humble and a very 
 troublesome one, which reminds me of the Greek mind. 
 You might know it for a good while as only a fidgety, 
 restless, and rather aggressive companion, when, behold, 
 hop ! and it is away far off, having realized at one 
 spring a new arena and a new experience. 
 
 Hermione. Don't! But a truce to the Greek mind 
 with its narrow pedantry and its boundless excursiveness. 
 The excursiveness was innate, the pedantry superinduced 
 the result of their perpetual rhetorical conflicts and 
 literary competitions. I have read the fifth book of 
 Euclid and something of Aristotle ; so you need not talk 
 to me on that theme. Do tell me something about these 
 atoms. I declare it has quite excited me ; 'specially be- 
 cause it seems to have something to do with the atomic 
 theory of Dalton. 
 
 Hermogenes. Higgins, if you please. But the thing, 
 as you say, is as old as Democritus, or perhaps older ; 
 for Leucippus, Democritus's master, is said to have
 
 454 ON ATOMS. 
 
 taught it to him. Nay, there is an older authority still, 
 in the personage (as near to an abstraction as a tradi- 
 tional human being can be) Moschus (not he of the 
 Idyls). But the fact is that the notion of THE ATOM 
 the indivisible, the thing that has place, being, and power 
 is an absolute necessity of the human thinking mind, 
 and is of all ages and nations. It underlies all our 
 notions of being, and starts up, perse, whenever we come 
 to look closely at the intimate objective nature of things, 
 as much as space and time do in the subjective. You 
 have dabbled in German metaphysics, and know the 
 distinction I refer to. 
 
 Hermione. You don't mean to say that we are nothing 
 but ATOMS 1 Place ! being ! power ! Why, that is I, it 
 is you, it is all of us. Nay, nay. This is going too 
 fast 
 
 Hermogenes. Perhaps it is. (You have forgot thought, 
 by-the-by, and will.) But I am not going to make a 
 single hop quite so far. We shall divide that into two 
 or three jumps, and loiter a little in the intermediate 
 resting-places. But, to go back to your atoms and a 
 vacuum. What does a vacuum mean ? 
 
 Hermione. Vacuum ? Why, emptiness, to be sure ! 
 I mean empty space. Space where no thing is. I am 
 not so very sure that I can realize that notion. It is 
 like the abstract idea of a lord mayor that Pope and 
 Atterbury talk about ; and in getting rid of the man, the 
 gold chain and the custard are apt to start up and vindi- 
 cate their claim to a place in the world of ideas. And 
 yet I do mean something by empty space. I mean dis-
 
 ON ATOMS. 455 
 
 tance I mean direction: that steeple is a mile off, and 
 not here where we sit ; and it lies south-east of us, and 
 not north or west. And if the steeple were away, I 
 should have just as clear a notion of its place as if I saw 
 it there. There now ! But then distance and direction 
 imply two places. So there are three things anyhow that 
 belong to a vacuum ; and let me tell you, it is not every- 
 thing that three things positively intelligible can be 
 " predicated " of (to speak your jargon). 
 
 Hermogenes. Dear me, Hermione ! how can you twit 
 me so? Jargon! Every speciality has its "jargon." Even 
 the Law, that system of dreams, has its " jargon " the 
 more so, to be sure, because it is a system of dreams, or 
 rather of nightmares (God forgive me for saying so !). 
 Well , then, you seem to have tolerably clear notions 
 about a vacuum at least, I cannot make them clearer. 
 Much clearer, an yhow, than Des Cartes had, who main- 
 tained that if it were not for the foot-rule between them, 
 the two ends of it would be in the same place. Still, 
 there is much to be said about that same Vacuum, espe- 
 cially when contrasted with a Plenum, which means (if it 
 mean anything) the exact opposite of a vacuum. In other 
 words, a " jam," a " block," a " fix." But, on the whole, 
 I lean to a vacuum. The other idea is oppressive. It 
 does not allow one to breathe. There is no elbow-room. 
 It seems to realize the notion of that great human 
 squeeze in which we should be landed after a hundred 
 generations of unrestrained propagation.* One does no 
 
 * For the benefit of those who discuss the subjects of Population, 
 War, Pestilence, Famine, &c., it may be as well to mention that the
 
 ON ATOMS. 
 
 understand how anything could get out of the way of 
 anything else. 
 
 Hermione. Do come back to our dear atoms. I love 
 these atoms : the delicate little creatures ! There is 
 something so fanciful, so fairy-like about them. 
 
 Hermofrenes. Well they have their idiosyncrasies. I 
 mean, they obey the laws of their being. They comport 
 themselves according to their primary constitution. They 
 conform to the fixed rule implanted in them in the in- 
 stant of their creation. They act and react on each 
 other according to the rigorously exact, mathematically 
 determinate relations laid down for them ab initio. They 
 work out the preconceh 2d scheme of the universe by 
 their their col 
 
 Hermione. Their? Stop, stop ! my dear Hermogenes. 
 Where will you land us ? Obey laws ! Do they know 
 them 1 Can they remember them 1 How else can they 
 obey theml Comport themselves according to their 
 primary constitution ! Well, that is so far intelligible : 
 they are as they are, and not as they are not. Conform 
 to a fixed rule ! But then they must be able to apply 
 the rule as the case arises. Act and react according to 
 
 number of human beings living at the end of the hundredth gene- 
 ration, commencing from a single pair, doubling at each generation 
 (say in thirty years), and allowing for each man, woman, and child 
 an average space of four feet in height, and one foot square, would 
 form a vertical column, having for its base the whole surface of the 
 earth and sea spread out into a plane, and for its height 3674 times 
 the sun's distance from the earth ! The number of human strata 
 thus piled one on the other would amnui>* to 460, 790,000,000,000.
 
 ON ATOMS. 457 
 
 determinate relations ! I suppose you mean relations 
 with each other. But how are they to know those re- 
 lations 1 Here is your atom A, there is your atom B (I 
 speak as you have taught me to speak), and a long in- 
 terval between them, and no link of connexion. How 
 is A to know where B is ; or in what relation it stands to 
 B ? Poor dear atoms ! I pity them. 
 
 Hermogenes. You may spare your sympathy. They 
 are absolutely blind and passive. 
 
 Hermione. Blind and passive ! The more the wonder 
 how they come to perceive those same relations you talk 
 about, and how they " comport themselves," as you call 
 it (act, as I should say), on that perception. I have a 
 better theory of the universe. 
 
 Hermogenes. Tell it me. 
 
 Hermione. In the beginning was the nebulous matter, 
 or Akasch. Its boundless and tumultuous waves heaved 
 in chaotic wildness, and all was oxygen, and hydrogen, 
 and electricity. Such a state of things could not pos- 
 sibly continue ; and as it could not possibly be worse, 
 alteration was here synonymous with improvement. 
 Then came 
 
 Hermogenes. Now it is my turn to say, Stop ! stop ! 
 Solvuntur risu tabula. Do let us be serious. Remem- 
 ber, it was you who began the conversation. Je me snis 
 settlement laisse entrainer. The fact is, I have only so far 
 been trying you, and I see you are >apt. There lies the 
 real difficulty about these atoms. These same "relations" 
 in which they stand to one another are anything but
 
 458 ON ATOMS. 
 
 simple ones. They involve all the " ologies " and all the 
 "ometries," and in these days we know something of 
 what that implies. Their movements, their interchanges, 
 their "hates and loves," their "attractions and repul- 
 sions," their " correlations," their what not, are all deter- 
 mined on the very instant. There is no hesitation, no 
 blundering, no trial and error. A problem of dynamics 
 which would drive Lagrange mad, is solved instanter, 
 " Solvitur ambulando" A differential equation which, 
 algebraically written out, would belt the earth, is inte- 
 grated in an eye-twinkle ; and all the numerical calcu- 
 lation worked out in a way to frighten Zerah Colburn, 
 George Bidder, or Jedediah Buxton. In short, these 
 atoms are most wonderful little creatures. 
 
 Hermione. Wonderful indeed ! Anyhow, they must 
 have not only good memories, but astonishing presence 
 of mind, to be always ready to act, and always to act 
 without mistake, according to " the primary laws of their 
 being," in every complication that occurs. 
 
 Hermogenes. Thou hast said it ! This is just the point 
 I knew you must come to. The presence <T/"MIND is what 
 solves the whole difficulty ; so far, at least, as it brings it 
 within the sphere of our own consciousness, and into 
 conformity with our own experience of what action is. 
 We know nothing but as it is conceivable to us from our 
 own mental and bodily experience and consciousness. 
 When we know we act, we are also conscious of will 
 and effort ; and action without will and effort is to us, 
 constituted as we are, unrealizable, unknowable, incon- 
 ceivable.
 
 ON ATOMS. 459 
 
 Hermione. That will do. My head begins to turn 
 round. But I hardly fancied we had got on such an 
 interesting train. We will talk of this again. More 
 to-morrow. Now to the feast of flowers the children are 
 preparing. 
 
 COLUNGWOOD, Aug. 16, i86a
 
 " Mens agitat molem et magno se corpore miscet" 
 
 ]HAT is it that we ought to understand by 
 the theory of any natural phenomenon I 
 This is a question not without its importance 
 when we are told, as we so frequently are, 
 that it is useless to inquire into causes: that, in fact, 
 causes are to us as though they were not ; seeing that 
 all we can ever attain to is the observation and registry 
 of constant laws of phenomenal sequence: in other 
 words, that phenomenon succeeds phenomenon, event 
 event, according to certain rules, which are all we have 
 any business to inquire into. 
 
 (2.) It is unfortunate for this doctrine that within the 
 range of every individual's momentary experience there 
 occurs the phenomenon of volition ; and that there are 
 
 * From the Fortnightly Review.
 
 ON THE ORIGIN OF FORCE. 461 
 
 large classes of phenomena, and those most important 
 ones, which, we are quite sure, take place in virtue of 
 such volitions, and without which we are equally sure 
 they would not take place at all. In that peculiar 
 mental sensation, clear to the apprehension of every one 
 who has ever performed a voluntary act, which is present 
 at the instant when the determination to do a thing is 
 carried out into the act of doing it (a sensation which, 
 in default of a term more specifically appropriated to it, 
 we may call that of effort) we have a consciousness of 
 immediate and personal causation which cannot be dis- 
 puted or ignored. And when we see the same kind of act 
 performed by another, we never hesitate in assuming for 
 him that consciousness which we recognize in ourselves : 
 and in this case we can verify our conclusion by oral 
 communication. The first step in the way of generaliza- 
 tion thus taken, the next is obvious enough. Though a 
 flight rather than a step, it forces itself on our thoughts with 
 ever-increasing cogency, the more it is dwelt upon, and 
 the more utterly abortive all attempt to render any other 
 account of that deep mystery of nature mechanical 
 force is found to be. Whenever, in the material world, 
 what we call a phenomenon or an event takes place, we 
 either find it resolvable ultimately into some change of 
 place or of movement in material substance, or we en- 
 deavour to trace it up to some such change ; and only 
 when successful in such endeavour we consider that we 
 have arrived at its theory. In every such change we re- 
 cognize the action of FORCE. And in the only case in 
 which we are admitted into any personal knowledge of
 
 462 ON THE ORIGIN OF FORCE. 
 
 the origin of force, we find it connected (possibly by in- 
 termediate links untraceable by our faculties, but yet 
 indisputably connected} with volition, and by inevitable 
 consequence, with motive, with intellect, and with all those 
 attributes of mind in which and not in the possession 
 of arms, legs, brains, and viscera personality consists. 
 In limiting thus the domain of physical theory, we keep 
 on the outside of the apparently interminable discussions 
 and difficulties as to the origin of the will itself, which 
 seem to have culminated in some minds in the denial 
 of volition as a matter of fact, and in the dictum of 
 Judge Carleton,* that what men term the will, is " simply 
 a passive capacity to receive pleasure from whatever 
 affects us agreeably at the time." 
 
 (3.) It may, however, be said, and indeed there are 
 not wanting those who appear very much disposed to 
 say, if not totidem verbis, at least by strong implication, 
 that the conception of Force itself, as part and parcel of 
 the system of the material universe, is superfluous and 
 therefore illogical. They argue thus. All we know of 
 material phenomena, it is true, resolves itself into the 
 transference of motion from matter to matter. This, 
 however, may be effected by mere collision. Now, when 
 A strikes B, and motion is thereby communicated from 
 A to B, why not at once admit this as a sequence ? Why 
 interpose an unknown agent, or intermedium, Force, as 
 part of the process? Having come to regard Heat, 
 Light, Electricity, and the " imponderables " generally, 
 
 * " Proceedings of the American Philosophical Society," ix. p. 
 136 Report of Meeting of January 2, 1863.
 
 ON THE ORIGIN OF FORCE. 463 
 
 some upon more, others on less, cogent evidence, as 
 " modes of motion," they seem to consider Force itself 
 as included in the same category, and think there is 
 "reason to believe that it depends on the diffusion of 
 highly-attenuated matter through space."* This doctrine 
 goes to resolve the entire assemblage of natural phaeno- 
 mena into the mere knocking about of an inconceivable 
 number of inconceivably minute billiard balls (or cubes, 
 or tetrahedrons, if that be preferred), which once set in 
 motion and abandoned to their mutual encounter and 
 impact, work out the totality of natural phsenomena. 
 With the amount of forethought and intelligence called 
 for in the initiatory disposal of the place and movement 
 of every individual of this multitude ; to work out for 
 countless ages the orderly sequence of observed facts, 
 by their blind conformity to the laws of collision, those 
 disposed to adopt such a view of nature would probably 
 concern themselves little. Their actual disposal at the 
 present moment is afaif accompli; and from this point 
 it would be possible, at least in imagination, if we knew 
 the present position and movement of every particle of 
 matter in the universe, to work backwards, up to any 
 epoch which we might choose to assign as that of crea- 
 tion, by a simple reversal of the velocity and direction of 
 each : nay, having thus ^//created the world, the mole- 
 cules would of themselves work out a pre-existent order 
 of things into all past eternity : an image of what might 
 have existed in the past (though it did not) seen, as it 
 were, reflecte i in the future. 
 
 * North British Review, vol. xl. p. 41.
 
 464 ON THE ORIGIN OF FORCE. 
 
 (4.) This simplification (if such it be) of our view of 
 material action is altogether untenable ; nor will it be 
 difficult I think (and certainly not superfluous), to show 
 that such an arrangement must of necessity be rapidly 
 self- destructive, and must result in the gradual but 
 speedy dying away of all relative motion, and the reduc- 
 tion of the universe either to a single block of matter 
 moving uniformly on, for ever, in one direction, without 
 relative motion of its parts ; or else in the dispersion into 
 space, and absolute final dissociation of its molecules. 
 
 (5.) For, be it observed, force (except in the sense of 
 bodily extrusion) being non-existent, our billiard-balls 
 must of necessity be supposed inelastic. Elasticity im- 
 plies force. If this be disallowed, if elasticity be not 
 force, but collision, each billiard-ball (each ultimate 
 atom, that is to say) must be itself a universe in miniature 
 composed of other more minute ones, moving and collid- 
 ing, inter se to give them that resilience which we term 
 elasticity, but which, in this view of the matter, is nothing 
 but "clash." Now what is to prevent these ultimate 
 atoms of the second order, animated with velocities im- 
 mense, as compared with their mutual distances, coercea 
 by no mutual attractions, subject to no control but from 
 their mutual collisions ; from dispersing themselves out 
 in all directions into space and abdicating their functions 
 as a group ? If we waive this objection (which, how- 
 ever, is fatal) nothing is gained. The original objection 
 applies in its full force to these sub-atoms, and so on ad 
 infinitum. 
 
 (6.) Now, in the collision of inelastic bodies, vis viia
 
 ON THE ORIGIN OF FORCE. 46$ 
 
 is necessarily and invariably destroyed. The destruction 
 may be total, or may fall short of totality in any propor- 
 tion according to the directness of the impact, and the pro- 
 portion of the moving masses ; but whenever contact oc- 
 curs between such bodies, vis viva disappears, and, once 
 lost, is gone for ever. Taking such a system in its entirety 
 (where force exists nof), there is no possibility of its re- 
 production. There is therefore a necessary and unceas- 
 ing drain on the vis viva of such a system. Everything 
 which constitutes an event, whatever its nature, exhausts 
 some portion of the original stock. Such a system has 
 no vitality. It feeds upon itself, and has no restorative 
 power. All relative motion in it tends rapidly to decay, 
 or at all events to a final state, when there will occur no 
 more collision, i.e., when phenomena cease altogether ; 
 when the minimum of vis viva consistent with the con- 
 servation of momentum is attained ; and nothing remains 
 but either a single caput mortuum, journeying through 
 space, or a multitude of such, travelling different ways; 
 having parted company never to meet again. 
 
 (7.) It will of course be urged that this reasoning takes 
 for granted the law just mentioned of the conservation of 
 momentum estimated in any given direction : since we 
 cannot assert a priori that two inelastic bodies, after col- 
 lision, must move on with a common velocity and un- 
 changed joint momentum. Of course it does so. But 
 the object of the hypothesis we are combating is to ex- 
 hibit collision as a substitute for force; i.e., to give an 
 account of the acknowledged laws of motion without in- 
 troducing the conception of force. We are therefore 
 
 2 G
 
 ON THE ORIGIN OF FORCE. 
 
 justified, when arguing against it, in assuming all the 
 results of those laws as established truths : they being, 
 in effect, the very things which the hypothesis is framed 
 to account for. The law in question, constituted as the 
 material universe is, is absolute and universal : and no 
 view of matter and motion can be a true one which is 
 incompatible with it. 
 
 (8.) The inward pressure of an etherial medium sur- 
 rounding the sun upon the earth and planets, suggested 
 by Newton as a mode of escape from the metaphysical 
 difficulty of attraction at a distance, is either only another 
 form of the collision theory above combated, or an 
 evasion of the difficulty by substituting repulsive for 
 attractive force. If the ether press by its elasticity, be- 
 sides supposing its particles endowed with the neces- 
 sary amount of repulsion ; what, it must be asked, but a 
 repulsion emanating from the sun (and thereby equilibrat- 
 ing and rendering ineffective its inward pressure) is to 
 keep it from rushing in on all sides, and destroying that 
 inequality of density on which its supposed inward pres- 
 sure depends 1 If not, its agency must be simply that 
 of an inert resisting medium, rendering the continued 
 revolution of the planets round the sun impossible, and 
 causing them, while it lasts, to rotate on their axes in a 
 direction contrary to that of their orbital motion, as a direct 
 consequence of the more rapid abstraction of motion 
 from their outer than from their inner hemispheres. The 
 hypothesis of Le Sage which assumes that every point of 
 space is penetrated at every instant of time by material 
 particles, sui generis, moving in right lines in every possible
 
 ON THE ORIGIN OF FORCE. 467 
 
 direction, and impinging upon the material atoms of 
 bodies ; as a mode of accounting for gravitation, is too 
 grotesque to need serious consideration ; and besides, will 
 render no account of the phenomenon of elasticity. Be- 
 sides this, I am not aware of any other attempt to embody 
 in a tangible form the notion of a substitute for the con- 
 ception of dynamical force arising out of the elementary 
 conceptions of motion and inertia. There is a tendency 
 indeed, of late apparent, to attribute the elastic pressure 
 of a gas on its containing envelope, as due to the collisive 
 shock of its particles conceived as existing in a continual 
 state of vibration, or of circulation round each other. 
 But the maintenance of such vibrations or revolutions in- 
 volves the supposition of inter-molecular coercive forces, 
 and is not, therefore, to be classed with such attempts. 
 
 (9.) If it be true, then, that the conception of FORCE 
 as the originator of motion in matter without bodily con- 
 tact, or the intervention of any intermedium, is essential 
 to a right interpretation of physical phenomena ; and if 
 it be equally so, on the other hand, that its exertion 
 makes itself manifest to our personal consciousness by 
 that peculiar sensation of effort which is not without its 
 analogue in purely intellectual acts of the mind; it comes, 
 not unnaturally, to be regarded as affording a point of 
 contact, a connecting link between these two great de- 
 partments of being between mind and matter the one 
 as its originator, the other as, its recipient. The control 
 we possess over the external world we are sure must 
 arise from a capacity somehow inherent in the intellec- 
 tual part of our nature, to originate or call into action
 
 468 ON THE ORIGIN OF FORCE. 
 
 this one and only agent which matter obeys in its changes 
 of form and situation. We may hesitate about admitting 
 into the system of created things around us so vast an 
 amount of additional or extraneous vis viva, as the total- 
 ity of animal exertion since the first introduction of life 
 upon earth would seem to imply. But this is not neces- 
 sary. The actual force necessary to be originated to give 
 rise to the utmost imaginable exertion of animal power 
 in any case, may be no greater than is required to re- 
 move a single material molecule from its place through 
 a space inconceivably minute no more in comparison 
 with the dynamical force disengaged, directly or indirectly, 
 by the act, than the pull of a hair trigger in comparison 
 with the force of the mine which it explodes. But without 
 the power to make some material disposition, to originate 
 some movement, or to change, at least temporarily, the 
 amount of dynamical force appropriate to some one or 
 more material molecules, the mechanical results of 
 human or animal volition are inconceivable. It matters 
 not that we are ignorant of the mode in which this is 
 performed. It suffices to bring the origination of dyna- 
 mical power, to however small an extent, within the 
 domain of acknowledged personality. 
 
 (10.) It will perhaps be objected to this, that the prin- 
 ciple so generally cited, and now so universally recog- 
 nized as a dominant one in physics that of the " con- 
 servation of force " stands opposed to any, even the 
 smallest amount of arbitrary change in the total of 
 " force " existing in the universe. This principle, so far 
 as it rests upon any scientific basis as a legitimate conclu-
 
 ON THE ORIGIN OF FORCE. 469 
 
 sion from dynamical laws, is no other than the well- 
 known dynamical theorem of the conservation of vis viva 
 (or of " energy," as some prefer to call it) supplemented to 
 save the truth of its verbal enunciation, by the introduc- 
 tion of what is called " potential energy," a phrase which 
 I cannot help regarding as unfortunate, inasmuch as it 
 goes to substitute a truism for the announcement of a 
 great dynamical fact. No such conservation, in the 
 sense of an identity of total amount of vis viva at all 
 times, and in all circumstances, in fact, exists. So far 
 as a system is maintained by the mutual actions and re- 
 actions of its constituent elements at a distance (/.<?., by 
 force), vis viva may temporarily disappear, and be sub- 
 sequently reproduced between certain limits. Collision, 
 indeed, betwen its ultimate atoms, regarded as absolutely 
 rigid, and therefore inelastic (for that which cannot change 
 its figure can have no resilience), cannot take place without 
 producing a permanent destruction of it, which there 
 exists no means of repairing. And here we may remark 
 that, this being the case, to ascribe to such atoms any 
 magnitude becomes not only superfluous, but embarrass- 
 ing. The system of Boscovich has to be accepted in 
 its integrity, if absolute permanence is to be one of the 
 conditions insisted on ; and they come to be considered 
 as mere localizations of inertia and such other attributes, 
 including the centralization of force if any other than 
 this there be which belong to our notion of material 
 substance. The conservation of energy, then, is in effect 
 no conservation at all in any strict sense of the term, 
 unless so supplemented. It is a fact dynamically demon-
 
 47O ON THE ORIGIN OF FORCE. 
 
 stratable that the total amount of vis viva in any moving 
 system abandoned to the mutual reaction of its particles, 
 while depending at every instant of time, solely for its 
 magnitude, on the then relative situation of those par- 
 ticles (or being, in algebraical phrase, a function of their 
 mutual distances), has a maximum value which it cannot 
 exceed, and a minimum below which it cannot descend. 
 Let its state then be what it will, there is sure to be a 
 certain amount of vis viva by which its actual falls short 
 of its extreme possible value ; and to say that the amount 
 of this deficiency added to the actual present amount 
 will make up the maximum, is neither more nor less than 
 a truism : whether expressed in so many words, or by say- 
 ing that the potential together with the actual energy of 
 the system is invariable ; or, again, in other words, that 
 when certain changes have taken place in the relative 
 situations of the parts of the system, what it has lost in 
 actual it has gained in potential energy. When in speak- 
 ing of a mechanical combination we say that what is lost 
 in time is gained in power, though equally a translation 
 in ordinary language of a dynamical equation, the terms 
 ued refer to different modes of viewing the expendi- 
 ture of force. But in the case before us they stand in 
 their nakedness of similar meaning and convey to the 
 mind no equivalence available for any purpose of rea- 
 soning. If, indeed, we could be assured, d, priori, that the 
 system is one of simple or compound periodicity in which 
 a certain lapse of time will restore every molecule to 
 identically the same relative situation with respect to all 
 the rest ; we should then be sure that in the nature ot
 
 ON THE ORIGIN OF FORCE. 471 
 
 things there would take place periodically, so to speak, 
 i winding up from a lower to a higher state of potential 
 energy, to be subsequently exchanged for newly-created 
 vis viva. But as we can have no such a priori assur- 
 ance, can only assume such restoration to be possible, 
 and can see no means of effecting it, if possible, other- 
 wise than by foresight and prearrangement ; the one 
 equally with the other is an unknown function, vari- 
 abk within unknown limits, and susceptible of fluc- 
 tuations to an unknown extent, nor can we have any, 
 the smallest, right to assert that what is expended in the 
 one form is, necessarily, laid up in reserve for further use 
 in the other. It would be very diffcult, I apprehend, to 
 show whether in the winding up of a clock, or the build- 
 ing of a pyramid, taking into consideration all the various 
 modes in which vis viva disappears and reappears in the 
 expenditure of muscular power, the evolution of animal 
 heat, the consumption of the materials of our tissues 
 (laying aside all question as to the evolution of force 
 from intellectual effort), the propagation of vibratory 
 motion, and a thousand other modes of transfer; the total 
 vis viva of this our planet is increased or diminished. 
 That it should remain absolutely unchanged during the 
 process is in the last degree inconceivable. The amount 
 of vis viva latent in the form of heat or molecular 
 motion in the sun and planets in our immediate system 
 may bear, and probably does bear, a by no means inap- 
 pretiable ratio to that more distinctly patent in the form 
 of bodily motion in the periodical circulation of the 
 planets round the sun, and the sun and planets round
 
 472 ON THE ORIGIN OF FORCE. 
 
 their axes. The latter amount fluctuates to and fro 
 according to laws easily calculable ; but the former we 
 have no means whatever of computing, and to what ex- 
 tent, or within what limits, it may be variable, we a"e 
 altogether ignorant. 
 
 (n.) In what is here said, it is by no means intended 
 to call in question the validity or to underrate the impor- 
 tance of those remarkable physical investigations which 
 have resulted in exhibiting heat as one of the forms in 
 which vis viva reappears in the apparent destruction of 
 motion. That all heat consists in molecular tremor (or 
 circulation), and is therefore accompanied with the 
 alternate development and disappearance of vis viva 
 within a limited space and quantity of matter accorling 
 to the dynamical laws of such tremulous or rotating move- 
 ments, may very readily be granted. But that there are 
 no forms of internal molecular movement other than 
 heat, and what we now speak of as its " correlated 
 forces " in which vis viva may be temporarily stored up, 
 to make its appearance ultimately in a form cognizable 
 to our senses, is what can by no means be so readily ad- 
 mitted. Nor (while accepting with all due admiration 
 as approximate truths these great revelations as to the 
 mutual convertibility of these correlatives according to 
 the measure of vis viva appropriate to each) shall we 
 advance any nearer to a rational theory of any one of 
 them, till it- shall be shown with much more distinct- 
 ness than at present appears, in what these molecular 
 movements themselves consist ; by what forces (in the 
 dynamical acceptation of the term) they are controlled ;
 
 ON THE ORIGIN OF FORCE. 473 
 
 in what manner, or by what mechanism, they are propa- 
 gated from one body to another ; and how their mutual 
 interconversion is effected. In referring them to the 
 action of dynamical force upon matter, and in getting 
 rid of the " imponderables " (other than the luminiferous 
 ether) we are at length fairly entered on the construction 
 of a theory of their phaenomena, in what, as above re- 
 marked, must be considered the true acceptation of that 
 term in physics : and once satisfied that dynamical force 
 itself is a phenomenon sui generis; that it is not a result 
 of collision an educt from the duality Inertia and 
 Motion; one of those correlatives, in short, to which 
 the epithet " Physical forces " has of late been so gene- 
 rally, and, in my opinion, so very improperly applied, we 
 have reached the point where theory ends and specula- 
 tion begins, where we cease to inquire into the causes 
 of phaenomena, and direct our consideration thencefor- 
 ward to their reasons. 
 
 (12.) The universe presents us with an assemblage of 
 phaenomena, physical, vital, and intellectual the con- 
 necting link between the worlds of intellect and matter 
 being that of organized vitality, occupying the whole 
 domain of animal and vegetable life, throughout which, 
 in some way inscrutable to us, movements among the 
 molecules of matter are originated of such a character as 
 apparently to bring them under the control of an agency 
 other than physical,* superseding the ordinary laws 
 
 * Take for instance the formative ntsus, which determines the 
 production of a supernumerary finger in the human hand. Here is 
 no gradual change from generation to generation, no first develop-
 
 474 ON THE ORIGIN OF FORCE. 
 
 which regulate the movements of inanimate matter, or, 
 in other words, giving rise to movements which would not 
 result from the action of those laws uninterfered with ; 
 and therefore implying, on the very same principle, the 
 origination of force. The first and greatest question 
 which Philosophy has to resolve in its attempts to make 
 out a Kosmos, to bring the whole of the phenomena 
 exhibited in these three domains of existence under the 
 contemplation of the mind as a congruous whole, is, 
 
 ment of a rudimentary joint followed in slow succession after centuries 
 of hereditary improvement, by the others, up to the perfect member. 
 It starts at once into completeness. The change in the working-plan 
 of the whole hand has been carried out at once, by a systematic 
 engraftment of blood-vessels and nerves into effective connexions 
 with the centres of nutritive, mechanical, and sensitive action in the 
 frame, as if by some preconceived arrangement. [Since this was 
 written I have been informed of two or three instances of super- 
 fluous thumbs. They were imperfectly formed, not movable, and 
 so far might be considered rudimentary.] 
 
 In direct reference to this point I would call the reader's atten- 
 tion to a very striking passage in the Croonian Lecture for 1865, 
 delivered before the Royal Society by Prof. Beale, where, after 
 stating that " phcenomena occur in the simplest form of living 
 matter, which never have been, and which," he believes, " never 
 can be explained upon any known physical or chemical laws " he 
 goes on to say, 
 
 " Living matter is not a machine, nor does it act upon the prin- 
 ciples of a machine, nor is force conditioned in it as it is in a machine, 
 nor have the movements occurring in it been explained by physics, 
 or the changes which take place in its composition by chemistry. 
 The phenomena occurring in living matter are peculiar, differing 
 from any other known phenomena ; and therefore, until we can ex- 
 plain them, they may well be distinguished by the term vital. Not 
 the slightest step has yet been made towards the production of 
 matter possessing the properties which distinguish living matter from 
 matter in every other known state." Proceedings of the Royal 
 Society, xiv. p. 282, No. 72.
 
 ON THE ORIGIN OF FORCE. 475 
 
 whether we can derive any light from our internal con- 
 sciousness of thought, reason, power, will, motive, design 
 or not : whether, that is to say, nature is or is not more 
 interpretable by supposing these things (be they what they 
 may) to have had, or to have, to do with its arrange- 
 ments. Constituted as the human mind is, if nature be 
 not interpretable through these conceptions, it is not 
 interpretable at all ; and the only reason we can have 
 for troubling ourselves about it is either the utilitarian 
 one of bettering our condition by " subduing nature " to 
 our use through a more complete understanding of its 
 " laws," so as to throw ourselves into its grooves, and 
 thereby reach our ends more readily and effectually ; or 
 the satisfaction of that sort of aimless curiosity which 
 can find its gratification in scrutinizing everything and 
 comprehending nothing. But if these attributes of mind 
 are not consentaneous, they are useless in the way of ex- 
 planation. Will without Motive, Power without Design, 
 Thought opposed to Reason, would be admirable in 
 explaining a chaos, but would render little aid in account- 
 ing for anything else.
 
 XTII, 
 
 ON THE ABSORPTION OF LIGHT BY 
 COLOURED MEDIA, 
 
 VIEWED IN CONNEXION WITH THE UNDULATORY THEORY.* 
 
 |HE absorption of light by coloured media is 
 a branch of physical optics which has only 
 since a comparatively recent epoch been 
 studied with that degree of attention which 
 its importance merits. The speculations of Newton on 
 the colours of natural bodies, however ingenious and 
 elegant, can hardly, in the present state of our know- 
 ledge, be regarded as more than a premature general- 
 ization ; and they have had the natural effect of such 
 generalizations, when specious in themselves and sup- 
 ported by a weight of authority admitting for the time 
 of no appeal, in repressing curiosity, by rendering further 
 inquiry apparently superfluous, and turning attention 
 
 * The substance of this paper was read before the Section of 
 Physics of the British Association, at Cambridge, 1833. Some in- 
 accuracies of wording are corrected, but nothing introduced bear- 
 Ing on the views more recently entertained as to the conversion of 
 motion into heat-vibration.
 
 ON THE ABSORPTION OF LIGHT, ETC. 477 
 
 into unproductive channels. I have shown, I think 
 satisfactorily, however, in my Article on Light,* that the 
 applicability of the analogy of the colours of thin plates 
 to those of natural bodies is limited to a comparatively 
 narrow range, while the phenomena of absorption, to 
 which I consider the great majority of natural colours 
 to be referrible, have always appeared to me to consti- 
 tute a branch of photology sui generis to be studied in 
 itself by the way of inductive inquiry, and by constant 
 reference to facts as nature offers them. 
 
 (2.) The most remarkable feature in this class of 
 facts consists in the unequal absorbability of the several 
 prismatic rays, and the total abandonment of anything 
 like regularity of progress in this respect as we proceed 
 from one end of the spectrum to the other. When we 
 contemplate the subject in this point of view, all idea of 
 regular functional gradation is at an end. We seem to 
 lose sight of the great law of continuity, and to find our- 
 selves involved among desultory and seemingly capri- 
 cious relations, quite unlike any which occur in other 
 branches of optical science. It is, perhaps, as much 
 owing to this as to anything, that the phaenomena of 
 absorption in some recently-published speculations, and 
 in the view which Mr Whewell has taken in his Report 
 of the progress and actual condition of this department 
 of natural philosophy, read to this meeting, have been 
 characterized as peculiarly difficult to reconcile with the 
 undulatory theory of light. In so far as I have above 
 
 * This refers to the Article on Light published in the " Encyclo- 
 paedia Metropolitana" in 1826-7.
 
 478 ON THE ABSORPTION OF LIGHT 
 
 described the phasnomena in appropriate terms, it will 
 be evident that a certain difficulty must attach to their 
 reduction under the dominion of any theory, however 
 competent, ultimately, to render a true account of theih. 
 Where such evidence of complication and suddenness 
 of transition subsists on the face of any large assemblage 
 of facts, we are not to expect that the mere mention of 
 a few general propositions, like cabalistic words, shall 
 all at once dissipate the complication, and render the 
 whole plain and intelligible. If we represent the total 
 intensity of light, in any point of a partially-absorbed 
 spectrum, by the ordinate of a curve whose abscissa in- 
 dicates the place of the ray in order of refrangibility, it 
 will be evident, from the enormous number of maxima 
 and minima it admits, and from the sudden starts and 
 frequent annihilations of its value through considerable 
 amplitudes of its abscissa, that its equation, if reducible 
 at all to analytical expression, must be of a singular and 
 complex nature ; and must at all events involve a great 
 number of arbitrary constants dependent on the relation 
 of the medium to light, as well as transcendents of a 
 high and intricate order. We must not, therefore, set 
 it down to the fault of either of the two rival theories if 
 we do not at once perceive how such phenomena are 
 to be reconciled to the one or to the other ; but rather 
 endeavour to satisfy ourselves whether there be, in the 
 first instance, anything in the phenomena, generally 
 considered, repugnant either to sound dynamical prin- 
 ciples, or to the notions which those theories respectively 
 involve as fundamental features.
 
 BY COLOURED MEDIA. 479 
 
 (3.) Now, as regards only the general fact of the ob- 
 struction and ultimate extinction of light in its passage 
 through gross media, if we compare the corpuscular and 
 undulatory theories, we shall find that the former appeals 
 to our ignorance, the latter to our knowledge, for its 
 explanation of the absorptive phsenomena. In attempt- 
 ing to explain the extinction of light, on the corpuscular 
 doctrine, we have to account for the light so extinguished 
 as a material body, which we must not suppose anni- 
 hilated. It may, however, be transformed ; and among 
 the imponderable agents, heat, electricity, &c., it may 
 be that we are to search for the light which has become 
 thus comparatively stagnant. The heating power of the 
 solar rays gives a prima facie plausibility to the idea of 
 a transformation of light into heat by absorption. But 
 when we come to examine the matter more nearly, we 
 find it encumbered on all sides with difficulties. How is 
 it, for instance, that the most luminous rays are not the 
 most calorific, but that, on the contrary, the calorific 
 energy accompanies, in its greatest intensity, rays which 
 possess comparatively feeble illuminating powers ? These 
 and other questions of similar nature may perhaps admit 
 of answer in a more advanced stage of our knowledge ; 
 but at present there is none obvious. It is not without 
 reason, therefore, that the question, " What becomes of 
 light?" which appears to have been agitated among the 
 photologists of the last century, has been regarded as one 
 of considerable importance as well as obscurity by the 
 corpuscular philosophers. 
 
 (4.) On the other hand, the answer to this question
 
 480 ON THE ABSORPTION OF LIGHT 
 
 afforded by the undulatory theory of light is simple and 
 distinct. The question, " What becomes of light ? " 
 merges in the more general one, "What becomes of 
 motion ? " And the answer, on dynamical principles, is, 
 that it continues for ever. No motion is, strictly speak- 
 ing, annihilated ; but it may be divided, and the divided 
 parts made to oppose and, in point of ultimate effect, 
 counteract each other. A body struck, however perfectly 
 elastic, vibrates for a time, and then appears to sink into 
 its original repose. But this apparent rest (even abstract- 
 ing from the inquiry that part of the motion which may 
 be conveyed away by the ambient air), is nothing else than 
 a state of subdivided and mutually-compensating motion, 
 in which every molecule continues to be agitated by an 
 indefinite multitude of internally-reflected waves, propa- 
 gated through it in every possible direction, from every 
 point in its surface on which they successively impinge. 
 The superposition of such waves will, it is easily seen, at 
 length operate their mutual counteraction, which will be 
 the more complete, the more irregular the figure of the 
 body and the greater the number of internal reflections. 
 (5.) In the case of a body perfectly elastic and of a 
 perfectly regular figure, the internal reflection of a wave 
 once propagated within it in some particular direction 
 might go on for ever without producing mutual destruc- 
 tion ; and in sonorous bodies of a highly elastic nature 
 we do in fact perceive it to continue for a very long time. 
 But the least deviation from perfect elasticity resolves our 
 conception of the vibrating mass into that of a multitude 
 of inharmonious systems communicating with each oiucr.
 
 BY COLOURED MEDIA. 481 
 
 At every transfer of an undulation from one such system 
 into that adjacent, a partial echo is produced. The 
 unity of the propagated wave is thus broken up, and a 
 portion of it becomes scattered through the interior of 
 the body in dispersed undulations from each such system, 
 as from a centre of divergence. In consequence of the 
 continual repetition of this process, after a greater or less 
 number of passages to and fro of the original wave across 
 the body (however perfect we may suppose the reflec- 
 tions from its surface to be), it becomes frittered away 
 to an insensible amplitude, and resolved into innumer- 
 able others ; crossing, recrossing, and mutually compen- 
 sating each other, while each of the secondary waves so 
 produced is in its turn undergoing the same process of 
 disruption and degradation. 
 
 (6.) In this account of the apparent destruction of 
 motion, I have purposely supposed the body set in vibra- 
 tion to be insulated from communication with any other. 
 In the case of a perfectly or highly elastic body struck in 
 air, it will vibrate so long that a great part of its motion 
 is actually carried off in sonorous tremors communicated 
 to the air. But in the case of an inelastic or imperfectly 
 elastic body, the internal process above described goes 
 on with such excessive rapidity, as to allow of very few, 
 and those rapidly degrading, impulses to be communi- 
 cated from its surface to the air. 
 
 (7.) In my Article on Sound,* I have explained, on this 
 principle of internal reflection and continual subdivision, 
 
 * Published like that on Light, above cited, in the EncyclopceJta 
 Metropolitana, 1829-30. 
 
 2 H
 
 482 ON THE ABSORPTION OF LIGHT 
 
 in a medium consisting ofloosely-aggregated earth inter- 
 mixed with much air, the hollow sounds which are often 
 attributed to the reverberation of subterrannean cavities, 
 and in particular the celebrated instance of this kind of 
 sound heard at the Solfaterra near PozzuolL The dull 
 and ill-defined sound thus produced from a succession of 
 partial echoes is there assimilated to the nebulous light 
 which illuminates a milky medium when a strong beam 
 is intromitted. If we suppose, now, such a mass of 
 materials insulated from communication with the exter- 
 nal air by some sound-tight envelope, these partial echoes, 
 when they reach the surface in any direction, will be all 
 sent back again as so many fresh impulses, till at length 
 it will become impossible to assign a point within the 
 mass which will not be agitated at one and the same 
 moment by undulations traversing it in every possible 
 phase and direction. Now the state of a molecule, un- 
 der the influence of an infinite number of contradictory 
 impulses thus superposed, is undistinguishable from a 
 state of rest. 
 
 (8.) The only difficulty, then, which remains in the 
 application of the undulatory theory to the absorptive 
 phaenomena, is to conceive how a medium (i.e., a combin- 
 ation of asthereal and gross* molecules) can be constituted 
 so as to be transparent, or freely permeable to one ray 
 or system of undulations, and opake, or difficultly per- 
 
 * By gross molecules, or gross bodies, I understand the ponderable 
 constituents of the material world, whether solid, liquid, or gaseous ; 
 using the term in contradistinction to aethereal, which has refer- 
 ence to the lurniniferous aether.
 
 BY COLOURED MEDIA. 
 
 483 
 
 meable to another, differing but little in frequency. Now 
 it is sufficient for our present purpose if, without pretend- 
 ing to analyze the actual structure of any optical medium, 
 we can indicate structures and combinations in which 
 air, in lieu of the aether, is the undulating medium, and 
 which shall be either incapable of transmitting a musical 
 sound of a given pitch, or shall transmit it much less 
 readily than sounds of any other pitch, even those nearly 
 adjacent to it. For that which experiment, or theory so 
 well grounded as to be equally convincing with experi- 
 ment, shows to be possible in the case of musical sounds, 
 will hardly be denied to have its analogue or represen- 
 tative among the phaenomena of colour, when referred to 
 the vibrations of an aether. 
 
 (9.) An example of an acoustic combination, or com- 
 pound vibrating system, incapable of transmitting a 
 
 musical sound of a given pitch, is furnished by the pipe 
 A E, which, after proceeding singly a certain length A B, 
 at B branches off into two equal and symmetrically dis- 
 posed pipes B C and b c, which reunite again at D d, and 
 there again constitute a single pipe D E, whose direction
 
 484 ON THE ABSORPTION OF LIGHT 
 
 shall (like A B) bisect the angle between the branches. 
 The branches, however, are of unequal length, the one 
 BCD being longer than the other, by a quantity equal 
 to half the length of the undulation or pulse of the musi- 
 cal note in question. It is evident, then, that if that 
 note be sounded at A, each pulse will subdivide itself at 
 B b, and the divided portions will run on along the two 
 branches with equal intensities till they reunite at D d. 
 They will arrive there, however, in opposite phases, and 
 will therefore counteract each other at their point of re- 
 union, and in every point of their subsequent course 
 along the pipe D E; so that on applying the ear at E 
 no sound should be heard, or at best a very feeble one, 
 arising from some slight inequality in the intensities 
 wherewith the undulations arrive by the longer and 
 shorter pipe a difference which may be made to dis- 
 appear, by giving the longer a trifle larger area for its 
 section.* 
 
 (10.) Suppose now that the pipes instead of being 
 cylindrical were square, and that the whole surface of 
 one side of a chamber were occupied with the orifices 
 A of such pipes, leaving only such intervals as might be 
 necessary to give room for their due support, and for 
 
 * I ought to observe, that I have not made the experiment de- 
 scribed in the text, nor am I aware that it has ever been made ; but 
 it is easy to see that it ought to succeed, and would furnish an apt 
 enotfgh illustration of the principle of interference. Instead of a 
 pipe, inclosing air, a canal of water might be used, in which waves 
 of a certain breadth, excited by some mechanical contrivance at one 
 end, would not be propagated beyond the point of reunion, D, of 
 the twn canels i^Jto which the main channel, A B, was divided.
 
 BY COLOURED MEDIA. 485 
 
 their subdivision according to the condition above ex- 
 plained ; and suppose, further, that the other ends (E) 
 of all the reunited pipes opened out, in like manner, into 
 another chamber, at some considerable distance from the 
 first, and separated from it by masonry or some material, 
 filling in all the intervals between the pipes, so as to be 
 completely impervious to sound. Things being so dis- 
 posed, let the whole scale be sounded, or a concert of 
 music performed in the first chamber, then will every 
 note, except that one to which the pipes are thus ren- 
 dered impervious, be transmitted. The scale, therefore, 
 so transmitted, will be deficient by that note, which has 
 been, to use the language of photologists, absorbed in its 
 passage. If several such chambers were disposed in 
 succession, communicating by compound pipes, ren- 
 dered impervious (or wwtuned, as we may term it) to so 
 many different notes, all these would be wanting in the 
 scale on its arrival in the last chamber ; thus imitating a 
 spectrum in which several rays have been absorbed in 
 their passage through a coloured medium. 
 
 (i i.) In my Article on Light, above referred to, Art. 505, 
 I have suggested, as a possible origin of the fixed lines 
 in the solar spectrum, and (pan ratione) of the deficient 
 or less bright spaces in the spectra of various flames, that 
 the same indisposition in the molecules of an absorb- 
 ent body to permit the passage of a particular coloured 
 ray through them, may constitute an obstacle, in limine, to 
 the production of that ray from them. The following easy 
 experiment will explain my meaning. Take two tuning 
 forks of the same pitch, and heating the ends of them,
 
 ON THE ABSORPTION OF LIGHT 
 
 fasten with sealing-wax, on one of them one, and on the 
 other two, disks of card (all equal in size), on the inner 
 surfaces, having the plane of the card perpendicular to 
 that of a section of the fork through the axes of both its 
 branches. The cards on that fork which has two, should 
 have their surfaces about a tenth of an inch asunder, and 
 their centres just opposite ; and the other fork should be 
 brought into unison with it by loading its undisked 
 branch with additional wax, equal in weight to the disk 
 and wax on the other. Now strike the forks, and a re- 
 markable difference will be perceived in the intensity of 
 their sounds. The fork with one disk will utter a clear 
 and loud sound, while that of the other will be dull and 
 stifled, and hardly audible, unless held close to the ear. 
 The reason of this difference is that the opposite branches 
 of the fork are always in opposite states of motion, and 
 that in consequence the air is agitated by either the two 
 branches vibrating freely, or by both loaded with equal 
 disks, with nearly equal and opposite impulses ; whereas 
 in the case of a fork furnished with only one disk, a 
 greater command of the ambient medium is given to the 
 branch carrying it, and a much larger portion of uncount- 
 eracted motion is propagated into the air. Here, then, we 
 have a case in which a vibrating system in full activity 
 is rendered, by a peculiarity of structutre, incapable of 
 sending forth its undulations with effect into the sur- 
 rounding medium ; while the very same mass of matter, 
 vibrating with the same intensity, but more favourably dis- 
 posed as to the arrangement of its parts, labours under 
 no such disability.
 
 BY COLOURED ME'^IA. 
 
 (12.) The disked tuning fork is a most instructive in- 
 strvment, and I shall not quit it until I have availed my- 
 self rf its properties to exemplify the easy propagation of 
 vibra ions, of a definite pitch, through a system compara- 
 tively much less disposed to transmit those of any other 
 pitch. Take two or more forks in unison, and furnish 
 each of them with a single disk of the size of a large 
 wafer, looking outwards. Having struck one of them, 
 let its iisk -be brought near to that of the other, 
 centre opposite to centre, and it will immediately 
 set the o.her in vibration, as will be evident by the 
 sound produced by it when 
 the first fork is stopped, as 
 well as by ts tremors, sensible 
 to the hand which holds it. 
 The communication of the 
 vibration is much more power- 
 ful and complete when a 
 small loop of fine silver wire 
 is fixed to one of the forks, 
 and brough: lightly into con- 
 tact with tie other, with its 
 looped or convex side. Ima- 
 gine now a series of such 
 forks and locps arranged as in the annexed figure, and 
 let the first, A, be maintained in vibration by any excit- 
 ing cause, as, for instance, by sounding a musical note 
 opposite to its disk, A, in unison with its pitch. The 
 vibrations sc excited will, as is evident, run along the 
 whole line, tiough with diminishing intensity, to the last
 
 488 ON THE ABSORPTION OF LIGHT 
 
 fork. Here, then, we have a case analogous to the e?sy 
 transmission of a ray of definite colour, accompanied vith 
 its gradual extinction, in traversing a considerable thick- 
 ness of the absorbing medium. If we would ava'd the 
 actual contact of the vibrating systems, we may conceive 
 an arrangement like that here depicted, where, ii place 
 of forks, straight bars, disked at both ends and supported 
 at their centres, are used to form the vibrating siries. 
 
 (13.) When two disked tuning forks slightly out of 
 unison are opposed to each otherj the vibrations of one 
 are still communicated to the other, even wh<n they differ 
 sufficiently to produce audible and pretty rapid beats. 
 But the communication in this case is less complete, and 
 the sound produced feebler, than in that of perfect uni- 
 son, and the degradation of intensity in tie communi- 
 cated sound is very rapid as the forks recede from 
 unison. We have here a fact analogous to the appear- 
 ance of a bright line in the spectrum situtted between 
 dark spaces, and as it is not difficult to imagine corn-
 
 BY COLOURED MEDIA. 489 
 
 binations of the nature above mentioned, in which seve- 
 ral different notes shall be transmitted, while the inter- 
 mediate one, finding no unisons, or near approaches to 
 unison in the systems established, shall be extinguished ; 
 so by analogy we may perceive how ?ny number of 
 bright and dark lines may be produced in a spectrum 
 unequally absorbed. 
 
 (14.) The case last put is entirely analogous in its 
 principle to that of a phsenomenon which is described in 
 my Treatise on Sound, and of which, at the time of the 
 publication of that Treatise, I believed myself to have 
 been the first and only observer, though I have recently 
 learned to rectify that impression, and have great plea- 
 sure in referring the experiment, which is a remarkably 
 easy and striking one, to Mr Wheatstone, the author of 
 so many other ingenious and instructive experiments in 
 this department of physics. If a tuning fork be held 
 over the open end of a pipe pitched in unison with it, 
 the pipe will speak by resonance. (If the fork be disked, 
 and the aperture of the pipe be nearly covered by the 
 disk, the tone brought out is one of a clearness and 
 purity quite remarkable.) Now both Mr Wheatstone 
 and myself have observed that if two forks, purposely 
 pitched out of unison with each other, so as to yield the 
 beats of imperfect concords, be at once held over the 
 orifice, the pipe will, at one and the same moment, yield 
 both the notes, and will utter loud beats, being actually 
 out of unison with itself. In proportion, however, as 
 the pitch of one or other fork deviates from that to which 
 the length of the pipe corresponds, and which the pipe
 
 49<> ON THE ABSORPTION OF LIGHT 
 
 alone would utter, the resonance of its tone is feeble, and 
 beyond a certain interval becomes inaudible. 
 
 (15.) The dynamical principle on which these and 
 similar phaenomena depend is that of " forced vibrations/' 
 as it is stated in the Essay on Sound above referred to, 
 or, more generally, in a more recent publication (Cab. 
 Cyclop., volume on Astronomy), in terms as follow : 
 " If one part of any system, connected either by material 
 ties or by the mutual attractions of its members, be con- 
 tinually maintained by any cause, whether inherent in 
 the constitution of the system or external to it, in a state 
 of regular periodic motion, that motion will be propa- 
 gated throughout the whole system, and will give rise in 
 every member of it, and in every part of each member, 
 to periodic movements, executed in equal periods with 
 that to which they owe their origin, though not neces- 
 sarily synchronous with them in their maxima and mini- 
 ma." The general demonstration of this as a dynamical 
 theorem is given in the Essay on Sound already referred 
 to, and its applicability to the transmission of light 
 through material bodies is indicated in a note thereto 
 appended. 
 
 (16.) The mode, then, in which we may conceive the 
 transmission of light through gross media to be per- 
 formed, so as to bring the absorptive phaenomena within 
 the wording of this principle, is, to regard such media 
 as consisting of innumerable distinct vibrating parcels 
 of molecules, each of which parcels, with the portion of 
 the luminiferous aether included within it (with which it 
 is connected, perhaps, by some ties of a more intimate
 
 BY COLOURED MEDIA. 4QI 
 
 nature than mere juxtaposition), constitute a distinct 
 compound vibrating system, in which parts differently 
 elastic are intimately united and made to influence each 
 other's motions. Of such systems in acoustics we have 
 no want of examples in membranes stretched on rigid 
 frames, in cavities stuffed with fibrous or pulverulent 
 substances, in mixed gases, or in systems of elastic 
 laminae, such as boards, sheets of glass, reeds, tuning 
 forks, &c., each having a distinct pitch of its own, and 
 all connected by some common bond of union. In all 
 such systems the whole will be maintained in forced 
 vibration so long as the exciting cause continues in 
 action, but the several constituents, regarded separately, 
 will assume, under that influence, widely different ampli- 
 tudes of oscillation, those assuming the greatest whose 
 pitch taken singly is nearest to coincidence with that of 
 the exciting vibrations. Everybody is familiar with the 
 tremor which some particular board in a floor will 
 assume at the sound of some particular note of an organ ; 
 but when that note is not sounded, it is sufficiently 
 apparent that the board is no less occupied in perform- 
 ing its dynamical office of transmitting to the soil below, 
 or dispersing through its own substance and the con- 
 tiguous bodies, the motion which the oscillation of the 
 air above is continually imparting to it. 
 
 (17.) As we know nothing of the actual forms and 
 intimate nature of the gross molecules of material bodies, 
 it is open to us to assume the existence, in one and the 
 same medium, of any variety of them which may suit 
 the explanation of phenomena. There is no necessity
 
 492 ON THE ABSORPTION OF LIGHT 
 
 to suppose the luminiferous molecules of gross bodies 
 to be identical with their ultimate chemical atoms. I 
 should rather incline to consider them as minute groups, 
 each composed of innumerable such atoms ; and it 
 may be that in what are called uncrystallized media, 
 the axes or lines of symmetry of these groups may have 
 no particular direction, or rather all possible directions, 
 or the groups themselves mav DC unsymmetrical. Such 
 a disposition of things would correspond with a uniform 
 law of absorption, independent of the direction of the 
 transmitted ray; while in crystallized media a uniformity 
 of constitution and position of these elementary groups, 
 or rather of the cells or other combinations which they 
 may be regarded as forming with the interfused aether, 
 may be readily supposed to draw with it differences in 
 their mode of vibration, and even different disposals of 
 their nodal lines and surfaces, according to the different 
 directions in which undulations may traverse them : and 
 which may not impossibly be found to render an account 
 of the change of tint of such media according to the 
 direction of the rays in their interior, as well as of the 
 different tints and intensities of their oppositely polar- 
 ized pencils; of which latter class of phenomena, 
 however, I shall immediately have occasion to speak 
 further. 
 
 1 (18.) But as my present object is merely to throw out, 
 as a subject for examination, a hint of a possible explana- 
 tion of the phenomena of absorption, on the undulatory 
 theory, I shall not now pursue its application into any 
 detail, nor attempt the further development of particular
 
 BY COLOURED MEDIA. 493 
 
 laws of structure competent to apply to this or that phae- 
 nomenon. I will, however, mention one or two facts in 
 acoustics which appear to me strongly illustrative of cor- 
 responding phenomena in the propagation of light. 
 The first of these is the impeded propagation of sound in 
 a mixture of gases differing much in elasticity as com- 
 pared with their density. The late Sir J. Leslie's experi- 
 ments on the transmission of sound through mixtures of 
 hydrogen with atmospheric air sufficiently establish this 
 remarkable effect. It would be desirable to prosecute 
 those experiments in larger detail, but hitherto I am not 
 aware of anybody having ever repeated them. It would 
 be interesting, for instance, to inquire whether the im- 
 pediment offered by such a mixture of gases be the 
 same for all pitches of a musical note, or not ; and how 
 far this phenomenon might be imitated by mixing actual 
 dust of a uniform size of particle, such as the dust of 
 Lycoperdon, &c. ; or aqueous fog, and how far such mix- 
 ture would affect unequally sounds of different pitches. 
 
 (19.) The other fact in the science of acoustics which 
 I would notice as illustrative of a corresponding phseno- 
 menon in photology, is one observed by Mr Wheatstone, 
 which I have his permission to mention. In attempting 
 to propagate vibrations along wires, rods, &c., to great 
 distances, he was led to remark a very great difference 
 in respect of facility of propagation between vibrations 
 longitudinal and transverse to the general direction of 
 propagation. The former were readily conveyed with 
 almost undiminished intensity to any distance ; the latter 
 were carried off so rapidly by the air, as to be incap-
 
 494 ON THE ABSORPTION OF LIGHT, ETC. 
 
 able of being transmitted with any considerable intensity 
 to even moderate distances. This strikes me as ob- 
 viously analogous to the ready transmissibility of a ray 
 polarized in one certain direction, through a tourmaline 
 or other absorbing doubly-refracting crystal, while the 
 oppositely-polarized ray (whose vibrations are rectangu- 
 lar to those of the first) is rapidly absorbed and stifled, 
 i.e., dispersed, by the agency of the colouring matter 
 which acts the part of the air in Mr Wheatstone's experi- 
 ment, and self-neutralized by the opposition of its sub- 
 divided portions as above explained. 
 
 SLOUGH, October 19, 1833.
 
 XIV. 
 
 ON THE ESTIMATION OF SKILL IN 
 TARGET-SHOOTING. 
 
 jjAPPENING to be present at an archery 
 meeting at St Leonard's not long ago, I was 
 struck, on examining the target, by observ- 
 ing a much less degree of concentration of 
 " hits," as indicated by the marks left on them about 
 the centre and within the " gold '.' (accompanied by a 
 rapidly-increasing frequency of marks within the imme- 
 diately-surrounding circles, proceeding thence outwards 
 from the centre), than could be at all reconciled with my 
 own preconceived impression of what ought to be the 
 proportional numbers, according to what I then con- 
 sidered as results afforded by a legitimate application of 
 the calculus of probabilities to such a question. The 
 proportional numbers of hits in the several areas dis- 
 tinguished as gold, red, blue, white, black, marked out 
 by equidistant rings of 4 '8 inches each in breadth, sur- 
 rounding the gold circle of that radius, ought, accord-
 
 496 ON THE ESTIMATION OF 
 
 ing to the statement given by myself in my review 
 of M. Quetelet's work on Probabilities,* to run as fol- 
 lows: In the gold (out of 500 hits), 107; in the red 
 annulus, 106; in the blue, 101; in the black, 97; and 
 in the white, 89; supposing the target (terminating with 
 the white) to receive half the entire number (1000) of 
 arrows discharged; which in the case observed was 
 not far from the truth. Whereas by the actual record 
 of that day's shooting, handed to me afterwards, the 
 proportional numbers corresponding to a total of 500 
 hits were: Gold, 31; red, 89; blue, 121; black, 140; 
 white, 119. This discordance with observation, being 
 far too great to be attributable to ordinary casualty (the 
 whole number of arrows discharged on the day in ques- 
 tion being upwards of 7000), led me, of course, to 
 re-examine the reasoning on which the first expectation 
 had been grounded. And so enlightened, I was at no 
 loss to discover its fallacy, affording, as it does, a good 
 example of the necessity of close attention to the word- 
 ing of all reasonings on questions of probability. It 
 was, in fact, traceable to the wording of a proposition 
 perfectly true, and, as applied to the case where it was 
 employed in another inquiry, correctly applicable, viz.,t 
 " Suppose a ball dropped from a given height, with the 
 intention that it shall fall on a given mark. Fall as it 
 may, its deviation from the mark is error; and the prob- 
 ability of that error .... decreases in geometrical 
 
 * Essays from the Edinburgh and Quarterly Reviews, &c., && 
 Longman, 1857. P. 401. 
 
 1 Essays, &c, &c. Pp. 398, 399.
 
 SKILL IN TARGET-SHOOTING. 
 
 progression as the square of the error increases in arith- 
 metical." Now, it is perfectly true that the deviation 
 of the point of incidence from the mark is error. But 
 it is something more special. It is error in that one 
 particular direction in which the point of incidence lies 
 from the mark aimed at. In estimating, therefore, the 
 probability of striking a target at a certain definite dis 
 tance from the centre aimed at, we must multiply the prob- 
 ability of striking a determinate point at that distance 
 from the centre, by the number of points within the 
 extent of the target which actually do lie at that distance 
 from it, without regard to the directions in which they 
 lie : i.e., we have to multiply the fractional number ex 
 pressing the abstract probability of committing a given 
 error out of an indefinite number of equally possible ones, 
 by a number proportional to the degree of opportunity 
 which the circumstances of the special case afford for 
 its commission. In this case that degree of opportunity 
 is evidently measured by, and proportional to, the length 
 of the circumference of the circle about whose centre, 
 at the distance specified, an arrow may strike, or a ball 
 drop from a height. 
 
 (2.) Reasoning on this (the correct principle in the 
 case of target-shooting), any one conversant with mathe- 
 matical analysis will find no difficulty in arriving at the 
 following singularly neat and simple formula for the prob- 
 ability of missing, in any one single shot, a circular area 
 of given radius (r), at whose centre the shooter aims.* 
 
 * The demonstration of this formula is annexed in the form of a 
 note at the end of this essay. 
 
 3 I
 
 498 ON THE ESTIMATION OF 
 
 Denoting by a the radius of the circular area with- 
 in which his skill would, on the average of an im- 
 mense number of shots, enable him to plant half the 
 total number discharged; and by M the fraction ex- 
 pressing the probability in question, certainty being ex- 
 pressed by i, we shall have 
 
 while for H the probability of hitting the same area 
 
 we have 
 
 H=\ M 
 
 (3.) From these expressions, knowing the value of a, 
 which is the inverse measure of the skill of the shooter 
 (being less the greater that skill), it is easy to calculate 
 his chance of hitting a circle of any given radius in a 
 single shot. And, reversing the question, his skill 
 (measured by the fraction j ) may be ascertained, by 
 observing what percentage of shots he can plant, on a 
 large average, from a given distance, within a circle of 
 any given radius (r). For that percentage being the 
 numerical expression of his probability of hitting the 
 circle, or the value of If, or i M, M is known, and a 
 will be given by the formula. 
 
 y 
 ~ 
 
 I Log. 2 
 
 Log. M. r - >~ Log. (iH) 
 
 Thus, if a marksman be observed to plant 9 per 
 cent of his arrows within a circle of one foot in 
 diameter at the distance of one hundred yards we have
 
 SKILL IN TARGET-SHOOTING. 499 
 
 r = i . ff= _2_: j/ = .21, whose logarithm is o '0409 6, 
 100 100 
 
 I 30103 
 that of 2 being +0*30103: so that a = \ ^j 
 
 f. f. in. f. in. 
 
 = 1-355 = J '4 f j whlch > doubled, gives 2 '8 ^ for 
 
 the diameter of a target which he might make an even 
 bet to hit at the first shot. And according to the values 
 of this constant, so determined in the case of each 
 several competitor, ought their names to be arranged in 
 a prize-list, the smaller values ranking higher than the 
 larger. 
 
 (4.) If the object of the competition be merely to 
 arrange the competitors correctly in order of skill at 
 the moment, without deducing for each any definite and 
 normal numerical result expressive of his absolute skill, 
 and comparable with others derived from practice with 
 targets of other dimensions, and at other distances ; it is 
 evident that the trouble of any such computation as the 
 above may be spared, since the same precise order must 
 necessarily result from merely tabulating the total num- 
 ber of hits of each competitor (practising with an equal 
 number of arrows, and at one and the same distances). 
 Were the number of shots allowed to each immensely 
 large, the same order of merit and the same set of values 
 of the constant a would result from a record of the hits 
 within the total area of each of the several circles marked 
 out by the outer circumferences of the gold, red. blue, 
 black, and white colours. The only use of these rings 
 is to give opportunity for a variety of prizes, and that 
 piquancy and interest to the result of a day's shooting
 
 5OO ON THE ESTIMATION OF 
 
 which arises from the element of luck mixing itself in the 
 competition. This it does the more, the fewer the shots 
 allowed to each, nor can it be eliminated, so as to make 
 skill the sole determining power, but on the average of 
 very enormous numbers, such as, for instance, ten or 
 twenty thousand arrows discharged by each marksman. 
 Every shooter, of course, aims to the best of his ability, 
 exclusively with a view to hit the centre of the gold ; 
 nor is it conceivable that, having that intention, there 
 should exist in any individual such specialty of aiming 
 as should disperse his shots, failing the gold, so as to 
 strike preferentially (say) the blue, rather than the red 
 ring on one side of it and the black on the other. 
 
 (5.) The following table shows the respective num- 
 bers of "hits" per 1000 shots, which may be expected 
 to occur on a calculation from our formulae, within the 
 several coloured areas of the five equidistant rings (con- 
 sidering the central gold as the first ring) into which an 
 ordinary target is divided. Considering its diameter as 
 divided into ten equal parts, the outside diameters of 
 those rings will be respectively 2, 4, 6, 8, 10; their radii, 
 ! 2 > 3j 4> 5 ') an( l the areas of their containing circles, 
 in the proportion of the squares of these numbers, i, 
 4, 9, 1 6, 25, so that the areas of the several coloured 
 spaces form the progression i, 3, 5, 7, 9. The usual 
 rule of valuation, then, which accords to hits in any of 
 the rings (from the white inwards), values in the propor- 
 tion of these numbers ; assumes the probability of hitting 
 to be in the simple proportion of the area struck (as 
 would be the case were the shooting entirely at random),
 
 SKILL IN TARGET-SHOOTING. 
 
 SOI 
 
 and the merit to increase as the probability, so estimated 
 diminishes. The range in this table of the quantity a, 
 or what may be termed the probable error from the 
 centre of a single shot, includes what may be taken as 
 the extremes of good and bad shooting : 
 
 TABLE I. 
 
 
 Probable hits per thousand in the 
 
 
 a 
 
 "Gold 
 o i. 
 
 Red 
 
 I 2. 
 
 Blue 
 
 2 
 
 Black 
 3 4- 
 
 White 
 4 5- 
 
 Misses 
 5 to QO. 
 
 I 
 
 500 
 
 438 
 
 42 
 
 20 
 
 o 
 
 o 
 
 2 
 
 159 
 
 341 
 
 290 
 
 J 47 
 
 50 
 
 13 
 
 3 
 
 74 
 
 191 
 
 235 
 
 208 
 
 146 
 
 146 
 
 4 
 
 42 
 
 117 
 
 I6 4 
 
 177 
 
 161 
 
 339 
 
 S 
 
 27 
 
 78 
 
 116 
 
 137 
 
 142 
 
 500 
 
 6 
 
 19 
 
 55 
 
 85 
 
 106 
 
 118 
 
 6 I7 
 
 7 
 
 14 
 
 4 1 
 
 65 
 
 82 
 
 96 
 
 702 
 
 8 
 
 II 
 
 3i 
 
 Si 
 
 66 
 
 78 
 
 763 
 
 Q 
 
 9 
 
 25 
 
 40 
 
 54 
 
 65 
 
 807 
 
 10 
 
 7 
 
 20 
 
 33 
 
 45 
 
 54 
 
 841 
 
 (6.) For the purpose of comparing this theory with 
 practice, I have been favoured with the series of an- 
 nual reports of the practice at the Grand National 
 Archery Meeting, with their target lists, and awards of 
 prizes, for fifteen successive years, commencing with 
 1850; which record the hits made by each competitor 
 in each of the colours, from specified distances, and 
 with specified numbers of arrows. The number of shots 
 delivered amounts, collectively, to upwards of half a 
 million; and excluding 169 cases in which it is noted 
 that the shooter did not deliver all his arrows, and those 
 comparatively much more rare ones in which the record 
 of the shots is incompatible with the awarded value 
 from some other cause than a mere misprint (which can 
 generally be rectified), to 474,384; of which 168,239 
 were hits, and 306,145 misses, on a target of 48 inches in
 
 502 ON THE ESTIMATION OF 
 
 diameter, which gives 4-8 in. for the unit of our a. This 
 gives as a general average, 644 misses per 1000 shots; 
 and therefore were the distances all alike, or for an 
 average distance of 80 yards, would correspond to a 
 value of a in our table, of very nearly 6^, or to a mean 
 probable deviation of a single shot, of 30 '4 in. ; the 
 total number of competitors being 2075 (reckoning the 
 same individual appearing in several lists as so many 
 distinct competitors), shooting at 430 targets. As the 
 causes of linear deviation may be considered as increas- 
 ing proportionally to the distance, and as in fixing the 
 average distance as above at 80 yards, (strictly 79'!,) the 
 number of arrows discharged at each distance is taken 
 into account ; this may be regarded as a fair estimate of 
 our national proficiency in archery, and as comparable, 
 in the terms of its statement, with what may be obtained 
 at a future period, or in other countries. 
 
 (7.) Jn deducing the results embodied in the follow- 
 ing tables, the numbers of hits made by all the shooters 
 at each target in its several colours were summed 
 separately. The results so obtained for all the targets 
 for each class of shooters, and for each distance, in 
 each year of the series, were then grouped together and 
 summed, and the fifteen sets of annual sums so ob- 
 tained, united into general sums, as exhibited below in 
 Table II., to shorten which it is to be borne in mind 
 that of the lady competitors, 853 in number, each de- 
 livered 96 arrows at 60 yards, and 48 at 50;* and the 
 
 In the year 1850 the arrows delivered by each lady were only 
 72 and 36 at the same distances.
 
 SKILL IN TARGET-SHOOTING. 
 
 503 
 
 gentlemen, numbering 1222, 144 arrows at 100 yards, 
 96 at 80, and 48 at 60 yards : the number of targets 
 being, for the former, 164, and for the latter 266. 
 
 TABLE II. 
 
 Class of 
 shooters. 
 
 Dis- 
 tance 
 in 
 yards. 
 
 Total 
 No. of 
 arrows 
 de- 
 livered. 
 
 Numbers of hits in the several 
 colours. 
 
 Misses. 
 
 Gold. 
 
 Red. 
 
 Blue. 
 
 Black. 
 
 White. 
 
 Ladies 
 Do 
 
 60 
 
 50 
 
 100 
 
 80 
 60 
 
 81696 
 40848 
 175968 
 117312 
 
 58560 
 
 1722 
 
 1364 
 1873 
 2516 
 
 2553 
 
 4927 
 3799 
 5365 
 7061 
 6651 
 
 7279 
 
 5i45 
 8239 
 10137 
 8455 
 
 8572 
 5640 
 10629 
 12067 
 8983 
 
 8688 
 
 5159 
 11605 
 12058 
 7752 
 
 "50508 
 19741 
 138257 
 73473 
 24166 
 
 Gentlemen 
 Do 
 
 Do 
 
 Sums total 
 
 
 474384 
 
 10028 
 
 27803 
 
 39255 
 
 45891 
 
 45262 
 
 3<*>i4S 
 
 (8.) To compare these results with theory, and ascer 
 tain how far the distribution of the hits in each series 
 corresponds with our formula, the best way will be to 
 deduce, in each, five separate values of a the constant 
 appropriate to each, from ist, the hits in the gold; 2d, 
 the sum of those in the gold and red ; 3d, the sum of 
 those in the gold, red, and blue, and so on. These, it 
 is manifest, in each series ought to agree inter se, though 
 different for different series. Applying, then, the ex- 
 pression given in (3.) for a to these entries of "hits" 
 in Table II. on this principle, we derive corresponding 
 values of our constant or modulus as in the annexed 
 table (Table III), in the first division of which it is set 
 down in units and decimals, as in Table I. ; while in the 
 second are entered the same values reduced to inches 
 and decimals by the multiplier 4-8.
 
 ON THE ESTIMATION OF 
 
 TABLE III. 
 
 Class. 
 
 Dis- 
 tance 
 in 
 yards. 
 
 Values of ft as deduced from the numbers of 
 hits falling within the circles externally 
 limiting the 
 
 Mean 
 value 
 of a. 
 
 Gold. 
 
 Red. 
 
 Blue. 
 
 Biack. 
 
 White. 
 
 Ladies 
 Do 
 
 60 
 
 SO 
 
 100 
 
 80 
 60 
 
 5'74 
 4-518 
 8-048 
 5'654 
 3 '943 
 
 S-7I5 
 4'53 
 8-125 
 
 5-693 
 4-027 
 
 in. 
 27'432 
 ai'743 
 38-998 
 27-388 
 19-324 
 
 5'777 
 4-631 
 8-232 
 5-823 
 4-170 
 
 5-867 
 4'75i 
 8-311 
 5-925 
 4-275 
 
 6 '003 
 4-882 
 8-476 
 6-086 
 4-425 
 
 5-8i3 
 4-662 
 8-238 
 5-836 
 4-168 
 
 Gentlemen 
 Do 
 
 Do 
 
 
 Ladies 
 Do 
 
 60 
 50 
 100 
 
 80 
 60 
 
 in. 
 
 27-380 
 21-685 
 38-631 
 27-141 
 18-928 
 
 in. 
 27730 
 22*231 
 39'5i2 
 27-950 
 
 2O'OI2 
 
 in. 
 28-163 
 
 22 "804 
 39-893 
 28-438 
 20-519 
 
 in. 
 28-812 
 23-432 
 40-686 
 29,210 
 
 21 "239 
 
 in. 
 27-903 
 22-379 
 
 39-544 
 28 '025 
 20-004 
 
 Gentlemen 
 Do 
 
 Do 
 
 (9.) Although the general agreement of the results in 
 each horizontal line of this table is quite sufficient to 
 afford a highly satisfactory verification of the theory, 
 it is impossible not to be struck with the uniform 
 and steady increase (though small) in the value of a 
 in proceeding from the gold outwards. There occurs 
 not throughout the whole table a single instance in 
 which this progressive dilatation is not maintained. For 
 this there must be a reason; and the only rational 
 account of it, so far as I can perceive, is this : Were the 
 number of shooters infinite, including (indifferently) every 
 gradation of skill, from absolute random shooting up to 
 absolute certainty of striking the point aimed at : the 
 result of their combination would be one from which in- 
 dividual skill would be entirely eliminated ; and the 
 distribution of the hits would be regulated purely and 
 simply by the intention of hitHng the centre. The skill 
 in that case (on which the value of a depends) would be 
 the average skill of the whole human race ; and the value
 
 SKILL IN TARGET-SHOOTING. 505 
 
 of a would conform to that average. But the number of 
 shooters at each target being limited, never more than 
 six, and sometimes not more than two or three (owing 
 to our rejection of those scores where the arrows were not 
 all delivered), the distribution of the hits oy. each results 
 from the summation or superposition of several series of 
 numbers graduated according to the values of so many 
 different specified values of a as a modulus ; the inter- 
 mediate values being absent : and it by no means follows 
 that such a series of sums will follow the law of gradation 
 of either separately, or accommodate itself rigorously to 
 an average modulus ; any more than it would follow that 
 a curve whose ordinate is the sum of the ordinates of (say), 
 two concentric circles should itself be a circle. Suppose, 
 for instance, we were to ground our calculation of an 
 average modulus or value of a on a series of hits given 
 by summing up each separate column of Table I. This 
 would give the following series : Gold, 862 ; Red, 1337 ; 
 Blue, 1 121 ; Black, 1042; White, 910, on a total num- 
 ber of 10,000 shots. And from this deducing five several 
 values of a by the use of the formula of (3), after the 
 manner of those in Table III., we should obtain the 
 
 series, 
 
 <*= 2771, 3-340, 3-931, 4-399, 4-809, 
 
 which exhibits (only in a much more exaggerated form) 
 precisely the sort of dilatation in question. This being 
 then the tendency, in the case of each particular target, 
 a similar tendency will of course be exhibited by the 
 successive values resulting from a combination of any 
 number.
 
 506 ON THE ESTIMATION OF 
 
 (10.) The same principles apply of course equally to 
 rifle-shooting as to archery, provided the target aimed at 
 be circular. If rectangular, and especially if an elon- 
 gated rectangle, the same formulae will not apply ; and 
 the appropriate formulae would be necessarily much more 
 complex and their results proportionably more difficult 
 of calculation. This is a strong argument for the use 
 of circular targets : for, though for the mere decision of 
 the order of merit in a distribution of prizes almost any 
 impartial rule, rough and readily applicable, may suffice, 
 the same cannot be said when the object is to obtain a 
 true numerical measure of the national skill in the use 
 of that great weapon : for which purpose it is highly 
 desirable that the data afforded by our rifle prize meet- 
 ings should be preserved, collected, and reduced syste- 
 matically. 
 
 NOTE. 
 
 Demonstration of the formula in (2.) and ($.) 
 
 The probability of committing the specific error r (all errors pre- 
 senting equal facility for their commission) is proportional to 
 E ( kr"-), the characteristic sign E being used to denote the expo- 
 nential or anti-logarithmic function ; and k being some certain con- 
 stant to be determined or eliminated. And in the case of aiming at 
 the central point of a circular target, the degree of facility afforded 
 for the commission of a lineal error r t no matter in what direction, 
 is proportional to 2vr, the circumference of a circle of that radius, 
 or, simply to r : so that the probability of planting a shot some- 
 where on the circumference of that circle is measured by r. E (kr-), 
 and therefore the probability of making a hit anywhere within its 
 area is proportional tofrdr. E ( kr*) taken between the limits 
 o and r. Representing certainty therefore by i ; this probability 
 (which we have denoted by H in the foregoing pages) will be ex-
 
 SKILL IN TARGET-SHOOTING. 507 
 
 pressed numerically by such a multiple of this integral, so taken, as 
 to give I for its value when r is infinite : which gives 
 
 ff=i- E(-kr*) ; and therefore M= E (kr*). 
 
 Now, when r = a, the radius of that circle within which just half 
 the total number of arrows strike ; the probabilities of hitting and 
 missing that circle are equal : so that H and M are in that case 
 each = . We have, consequently, 
 
 E (-M = i, 
 and eliminating k, we obtain 
 
 Log. Jtf = -J, log. (}); 
 or, 
 
 -cjf 
 
 COLLINGWOOD, June 8, 1866. 
 
 NOTANDUM. 
 
 The experiment suggested in 9 of Lecture XIII. has been made 
 by Herr G. QUINCKE, with complete success. A full account of it 
 will be found in Poggendorff's Annalen, voL cxxviii. pp. 177, et sey. 
 
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