UNIVERSITY OF CALIFORNIA 
 
 ANDREW 
 
 SMITH 
 
 HALLIDIE: 
 
 1868 1901 
 
ASTKONOMICAL INVESTIGATIONS. 
 
30tronomtai Jfabesttgattons, 
 
 THE COSMICAL RELATIONS 
 
 REVOLUTION OF THE LUNAK APSIDES, 
 
 OCEANIC TIDES. 
 
 BY 
 
 HENRY F. A. PRATT, M.D. 
 
 LONDON: 
 JOHN CHURCHILL AND SONS, NEW BURLINGTON STREET. 
 
 MDCCCLXV. 
 
LONDON : 
 
 BENJAMIN PARDON, PRINTER, 
 PATERNOSTER ROW. 
 
PREFACE. 
 
 WHEN Pilate asked the question, What is truth? the 
 apocryphal gospel of Nicodemus affirms that he was told 
 in reply, that Truth is from heaven : but that it is on 
 earth, among those who, when they have the power of 
 judgment, are governed by truth, and form right judg- 
 ment. 
 
 Three conditions are thus declared to be necessary to the 
 enunciation of the truth in all cases: the power of judg- 
 ing, the acceptance of true evidence, and the formation of 
 a right judgment. 
 
 In Astronomical Science the combination of these con- 
 ditions is very rare, for the power, when unconsciously 
 severed from the will, fails to recognise the value of the 
 evidence; or else, comprehending its force, permits it to 
 remain unverified, as though valueless; the sense of the 
 imperative duty of forming the right judgment, when the 
 true evidence is presented, being only too often wanting, 
 here as elsewhere, in those who have the power of judging, 
 but not the courage to face the consequences of their judg- 
 ment : for, perhaps unfortunately, those with whom, by an 
 almost universal sufferance, if not necessarily, the power 
 of judging is permitted to rest in this science, are parties 
 in any issue that may be raised in which accepted theories 
 are controverted, and thus are virtually made the judges 
 
 105138 
 
VI PREFACE. 
 
 in their own cause; for the unlearned public admits its 
 incompetence to decide in such cases ; but, as a consequence 
 of this special interest, they almost unavoidably read all 
 evidence that may be submitted to them through the dis- 
 torting lens of their own preconceived opinions. 
 
 In the judgment of facts, however, on which observation 
 can be brought to bear, and where prejudice must yield 
 to the determining and determined results of a rigid 
 scrutiny, they will, themselves, become truthful witnesses 
 when their attention is sufficiently roused to the bearings 
 of any given fact to the verification of which they are 
 invited. The Author, therefore, now appeals to them, the 
 practical astronomers, who are also through the force of cir- 
 cumstances the judges in his cause, to test the value of his 
 views as to the true cosmical relations of the revolution 
 of the lunar apsides, and the teachings that can be drawn 
 from tidal phenomena considered in their oceanic origin ; 
 confident that if they can be once led to see the importance, 
 not to say the necessity, of reconsidering accepted theories 
 on these points, through a new and possibly true bearing 
 of the actually observed facts, the true evidence on which 
 their judgment ought to be based, the right judgment will 
 come, and these Astronomical Investigations not have been 
 written in vain. 
 
THE COSMIOAL RELATIONS 
 
 REVOLUTION OF THE LUNAR APSIDES. 
 
INTRODUCTION. 
 
 THE following paper on "The Cosmical Relations of the 
 Revolution of the Lunar Apsides" was written at the 
 suggestion of a friend, who considered the author's astro- 
 nomical opinions of sufficient importance to deserve a 
 formal discussion, and therefore kindly offered to commu- 
 nicate them to the Royal Society. It was accordingly 
 placed in the hands of one of the secretaries of that 
 Society, but returned by him as not suitable for the con- 
 sideration of its members. 
 
 Perhaps it was declined because an attempt has been 
 made in it to free an abstruse and difficult subject from 
 the technicalities and obscurities in which it is commonly 
 involved, by reducing the principles through which some 
 of the phenomena resulting from revolving motion, combined 
 with a gravitating attraction in a complex system, ought 
 to be interpreted, to simple geometrical demonstrations, 
 stripped of algebraic formulae and symbolic calculations : 
 though it may have been because the views advanced in 
 it do not agree with the opinions of the day. 
 
 However this may be, the author regrets that an oppor- 
 tunity for discussion has been denied to him, for he 
 conceives the whole subject to be of sufficient importance 
 to deserve examination, notwithstanding any seeming un- 
 scientific method in the manner in which it is approached ; 
 while, if learned societies decline to discuss unaccepted 
 
 B 
 
2 INTRODUCTION. 
 
 opinions, either because they are opposed to those held by 
 the greater part of their members, or else fear that they 
 may compromise themselves as a body, by seeming for a 
 time to endorse views which may turn out to be incorrect, 
 but can only be tested by such a searching inquiry as it is 
 in their power to institute, it becomes evident that they 
 have fallen away from the end proposed in their institution, 
 and, instead of aiding, render themselves real impediments 
 to the advance of science. 
 
 The author still desires that his opinions may be ex- 
 amined, in order, if they are incorrect, that their fallacy may 
 be established: he therefore now publishes them, but in 
 the form in which it was proposed to submit them to the 
 Royal Society, in order that his readers may have exactly 
 the same opportunity of judging their merits. 
 
 The progress of science is unfortunately beset by two 
 classes of difficulties, each of them presenting peculiar 
 impediments to the onward movement. The first of these 
 accompanies the observation and determination of pheno- 
 mena and facts, and is sometimes so impenetrable that a 
 series of successive patient observers has been necessary in 
 order to establish a single relation.* The second lurks in 
 the path of the interpreter of observed and determined 
 phenomena and facts, and often leads him to give a false 
 value to the results of observation, f 
 
 As the intrinsic worth of facts is measured, not only by 
 the difficulty with which the knowledge of them has been 
 gained, but also by the importance of the lesson which 
 they appear to teach, there is always a tendency in the 
 
 * Until the time of Copernicus, the earth was supposed to be stationary. 
 "What a long period and series of observers passed away before its actual 
 motion was determined ! That is, under the present order of science. 
 
 f As hi the case of Bradley, who discovering the apparent, interpreted it 
 as an actual nutation of the earth's polar axis, and attributed it to the in- 
 fluence of attraction acting upon the assumed preponderating equatorial 
 mass of the earth. 
 
INTRODUCTION. 3 
 
 mind of the successful observer to estimate his facts (or 
 supposed facts), by the labour which their attainment has 
 cost him, and to interpret them more or Jess through his 
 own preconceived opinions hence there is always a pos- 
 sibility, nay, perhaps even a strong probability, that every 
 newly ascertained fact will be at first misinterpreted.* 
 
 Even in those cases in which facts have not been over- 
 estimated, an importance is often given to the opinion of 
 their discoverer in proportion to their actual value, so that 
 he is raised into an authority on the subject, and his inter- 
 pretation considered as certain as the fact which he inter- 
 prets all other methods of interpretation being most pro- 
 bably overlooked ; so that it is possible that simultaneously 
 with the knowledge of fresh facts a false method of inter- 
 pretation may arise and be perpetuated for an indefinite 
 time, the authority of a name being thus rendered an 
 obstacle to the discovery of the truth. f 
 
 The science of Astronomy has been in all ages peculiarly 
 exposed to this influence. Its facts are always learnt by 
 slow processes and with very great difficulty, while they 
 are, at the same time, so important, that every discoverer 
 becomes an authoritative exponent of opinion ; and yet, 
 unfortunately, in order to become a discoverer a peculiar 
 training is necessary, which perforce involves the adoption 
 of preconceived opinions, so that, a given theory having once 
 
 * This was done by Galileo, who, when he discovered that balls of diffe- <* 
 rent weights appeared to take the same time in falling from the same height 
 to the earth, rashly generalized that gravity acted equally upon all masses 
 of matter at the same distance, forgetting that his experiments were on so 
 small a scale, as compared with the mass of the earth, that differences could 
 not be made perceptible to the senses of man, which nevertheless reason and 
 philosophy show must exist. See On Eccentric and Centric Force, Part I., 
 sec. 1, and Part III., sec. 10. 
 
 f This is strikingly seen in the case of Sir Isaac Newton, who, recognis- 
 ing the cosmical influence of gravity as a source of attraction, rashly gene- 
 ralized the principle that it was the saarc^_pjjth^jnotions of the heavenly ' ' 
 bodies, instead of a tendency in their constituent matter to draw them } 
 together,~~and bring them to a state of union and rest. 
 
 B 2 
 
4 INTRODUCTION. 
 
 been accepted, every succeeding phenomenon will be of 
 necessity read and interpreted through that theory.* 
 
 In this science, from the earliest ages, but certainly from 
 the time of Copernicus downwards, the almost constant 
 obstacle to onward progress has been the misinterpretation of 
 observed phenomena. Every fact added to the general stock, 
 when once it has been established, is an actual gain. The 
 whole group of recognised facts forms the common store 
 from which all interpreters must draw the bases of their 
 inductions ; but, though the facts are (perhaps) admitted by 
 all, and even beyond the reach of question, any method of 
 interpretation may be far from being so. And therefore, 
 and as long as a possibility of error exists, every new system 
 of interpretation is entitled to a hearing, and those who with- 
 hold this right expose themselves to the risk of opposing 
 the advance of that truth which every inquirer is in reality 
 labouring to define and put within the reach of all.f 
 
 The writer of these pages, after a patient and careful 
 examination of the whole subject, has come to the conclusion, 
 
 * The predicted existence and subsequent discovery of the planet Neptune, 
 through the perturbations caused by its mass, is given as a triumphant proof 
 of the truth of the theory of universal gravitation. In reality it only shows 
 that an attraction is seated in matter which acts at immense distances, and, 
 when acting excentrically, alternately accelerates and retards the motion of 
 those bodies on which it is acting, and causes relatively slight deviations 
 from their true paths. It gives no further proof of the truth of the New- 
 tonian interpretation or theory of universal gravitation than does the calcu- 
 lation and prediction of eclipses, which is quite independent of that theory. 
 
 t The theory of universal gravitation was constructed on a basis of mis- 
 interpreted facts, and then became a groundwork of preconceived opinions 
 through which a misinterpretation of subsequently discovered facts was 
 provided for and perpetuated. Thus, Sir Isaac Newton read, in the 
 apparent, an actual variability in the moon's motion, and attributed this 
 assumed variability to the attraction of the earth ; and then, observing the 
 effects of attraction in planetary perturbations and the tides, promulgated 
 a scheme which, when once it was accepted, became the source of all sub- 
 sequent interpretations ; so that already recognised phenomena, as recession . 
 and precession, as well as every fresh discovery, such as the apparent 
 nutations of the earth's polar axis, were interpreted by and read as further 
 proofs of its accuracy. 
 
INTRODUCTION. 5 
 
 that by studying the mutual relations of the whole series of 
 observed phenomena from a new point of .view, in which 
 they are combined into groups, each of which is referred 
 to certain distinct causes, principles can be developed more 
 philosophic in themselves, and at the same time more 
 easily subjective to examination and verification, and more 
 facile of comprehension, and results elicited from these 
 principles, under which far greater scope is given to the 
 present limited range of astronomical theory. 
 
 The present range of astronomical vision, as far as the 
 system of which the earth is a component part is concerned, 
 is centred in the sun, to which motion has at length been 
 attributed, and even the direction of that motion conjectured ; 
 so that the picture presented to the mind's eye is that of the 
 solar system hurrying through space, and possibly revolving 
 in an extensive orbit, the relations, range, and period of 
 which are not even attempted to be surmised. 
 
 Grand as this ideal picture may be, and perfect, as far as 
 it goes, it is yet a very limited one, when contrasted with 
 the results which can be drawn from a more careful examina- 
 tion of the mutual relations of the observed phenomena ; for, 
 under such an examination, it can be shown that the solar 
 system, vast and complicated though it be, is but a single 
 member of a wonderful compound system, the general scheme 
 and relations of which can be depicted : thus, the solar system 
 is hurrying round an as yet unrecognised body or central 
 sun* which is itself again hurrying round an also unrecog- 
 nised body or centric sunf each of these bodies lying on 
 what may for convenience be termed the plane of the 
 zodiac, though in reality the actual planes of the orbits of 
 motion are inclined to each other. J 
 
 * See On Orbital Motion, by the author. (London : John Churchill and 
 Sons.) Par. 12. 
 
 f This body is not mentioned in Orbital Motion. The author has only 
 demonstrated its existence since the publication of that work. 
 
 J See Orbital Motion, Notes 96 and 117. 
 
6 INTRODUCTION. 
 
 Moreover, the actual measures of the respective periods of 
 these several bodies exist ; for the lunar cycle (of recession) 
 is the measure of the time occupied by the sun in revolving 
 in its orbit, while the terrestrial cycle (of precession) is the 
 measure of the period occupied by the central sun in its 
 revolution.* 
 
 But the manner in which the phenomena can be made to 
 speak does not end here ; on the contrary, it can be shown 
 that the centric sun is itself in motion nay, more than this, 
 although so far its period cannot be determined, the direction 
 in which it is moving can be ascertained, when singularly 
 enough it is found that the observed motion at present attri- 
 buted to the sun is that of the centric sun, which, instead of 
 revolving on the plane of the zodiac, like the component 
 members of its system, is passing through (or across) that 
 plane, f 
 
 In order to understand these several relations, it is necessary 
 to regard the whole compound system as spheroidal in cha- 
 racter ; and to consider all these motions as taking place on 
 the surface of the assumed spheroid but with this difference, 
 that the orbit of the centric sun is a great circle of the 
 spheroid, while the other bodies are revolving on its surface ; 
 so that, while the plane of motion of the centric sun is through 
 the centre of the spheroid, the general direction of the planes 
 of the orbits of the other bodies is parallel to a segment of 
 its surface ; in consequence of which the plane of the orbit 
 of the centric sun may be said in general terms to be at right 
 
 * See Orbital Motion, Notes 25 and 81. 
 
 f See Fig. 1. See also Orbital Motion, Fig. 1, where the path of the 
 central sun should be treated as that of the centric sun. The evidence of 
 the motion of the centric sun is drawn from the difference in period between 
 the revolution of the terrestrial apsides and equinoctial points. The great 
 difference between the periods of these two simultaneous revolutions in 
 opposite directions, is owing to the path of the centric sun being across 
 the zodiac. 
 
INTRODUCTION. 7 
 
 angles to the common plane of motion of the members of its 
 system.* 
 
 The centric sun is in reality revolving round a point or 
 body situated within, and probably (relatively) in the neigh- 
 bourhood of the centre of the spheroidal system but still 
 excentric in the path of the centric sun.f 
 
 This focal body of the orbit of the centric sun has pecu- 
 liar relations to all of the bodies forming the entire system. 
 It lies upon and is the common focus of the axes of their 
 poles in the North Celestial Pole, and thus can be very pro- 
 perly termed the Celestial Polar Centre. It is an attracting 
 body. It has drawn the bulk of the solid matter of the earth 
 into the northern hemisphere. It is the source of attraction 
 of the magnetic needle ; and by its attraction maintains the 
 stability of the polar axis of the earth and of the other mem- 
 bers of the system. Its attraction varies with the distance 
 through which it acts ; and it is this varying attraction, 
 acting upon the earth by slow degrees, through long periods 
 of time or cycles, that has produced a large proportion of the 
 physical changes in the constitution of the earth ; and besides 
 this, it is probably the primary source of the electrical and 
 magnetic currents which pervade the whole system, and 
 become, from time to time, visibly sensible in the Northern 
 Lights. $ 
 
 Three simple but well- recognised principles, acting through 
 the relations determined by the spheroidal system just 
 described, when rightly and carefully applied to the inter- 
 pretation of the observed phenomena, at once throw a fresh 
 
 * The simplest way of studying these relations is to view the centric sun 
 as moving in a direction parallel to the mean polar axis, or from north to 
 south, while the other bodies are passing respectively from west to east. 
 
 f This excentricity will have a double aspect ; for though it may not be 
 great with reference to the volume of the imaginary spheroid, it would 
 yet, relatively to the volume and mass of the earth, cause immense differ- 
 ences in its actual distance in the different and ever- varying positions of 
 the entire system and its relative parts. 
 
 See Orbital Motion, Note 95. 
 
8 INTRODUCTION. 
 
 flood of light upon the physical history of the earth. These 
 principles are 
 
 First. The mutual attraction which the several bodies have 
 for each other, and especially the increase which takes place 
 in this attraction inversely as the distance diminishes, and 
 vice versd* 
 
 Second. The inclination of the planes of the several orbits 
 to each other and to the equators of their proper bodies ; f 
 and, 
 
 Third. The excentricity of the several focal bodies.:}: 
 
 The source of the first of these principles is, probably, 
 an inherent tendency in all matter to combination, union, 
 
 * This attraction is twofold in its character : between a primary and its 
 satellites, when it acts concentrically, resisting the force which maintains 
 the persistent motions of the satellites round it, and tending to draw them 
 into itself, thus becoming a true centric force, as in the case of Jupiter and 
 its moons, a due balance between this attraction and the active motive force 
 maintaining the systemic relations ; and between any two (or more) other 
 bodies, as between Jupiter and the earth, when it acts eccentrically, tending 
 to disturb the systemic relations, and produce what are termed perturbations. 
 The Newtonian theory has failed to discern the force of this distinction. 
 
 f This inclination is the cause of one form of variation in the degree of 
 attraction that acting through the polar axis, since it causes a regular 
 alternate variation in the distance between the revolving body and the 
 celestial polar centre. 
 
 There are three ways in which orbital inclination might originate : 
 
 1. Through the eccentric attraction of a remote concentric body, as 
 explained in Orbital Motion, Note 117, and Fig. 13. 
 
 2. Through alternate systemic concentration and expansion, also indi- 
 cated in Orbital Motion. 
 
 3. During the progressive motion of the centric sun across the zodiac, 
 the inclination of the zodiacal plane would diminish as its centre was 
 approached, and increase again after it was passed. 
 
 The two former appear to be both of them in operation, the one acting 
 on the plane of the moon's orbit, the other on that of the earth. 
 
 J This provides for another form of variation in the degree of attraction. 
 
 The probable cause of excentricity has been discussed in Eccentric and 
 Centric Force and Orbital Motion. There is another way of accounting for 
 jt : by regarding each revolution as an act of projection, under which 
 circumstances the law of projection given by the author in the works just 
 referred to would be followed, and the revolving body increase its velocity 
 of motion as it increased its distance from the focal body of its orbit. 
 
INTRODUCTION. 9 
 
 rest;* while the second and third appear to depend upon 
 the varied modifications and modifying action of the first, 
 when resolved into the several forces drawn from the mutually 
 re-acting bodies, and their antagonistic relations to the active 
 force through which the persistent motions of the universe 
 are maintained. f However this may be, it is sufficient to 
 regard them here as principles drawn from the actual and 
 observed phenomena, when, read in and through them, a 
 wonderful provision is at once found for all the changing 
 relations of the whole system. 
 
 Thus, to apply them to the earth considered as a spheroid 
 of revolution in equilibrium .J The bulk of the land is in 
 
 Perhaps both forms are in actual cosmical operation, the excentricity of the 
 celestial polar centre depending upon the motion of the centric sun follow- 
 ing the laws of projection ; while the secondary and tertiary, or more remote 
 forms, result from the simultaneous motion of both primary and secondary 
 alternately towards and from each other. Two causes seem to be in opera- 
 tion, determining variations in the planes of orbit that re-acting upon the 
 moon's path (Orbital Motion, Note 117), and that acting upon the ecliptic 
 (Orbital Motion, Note 119) ; it is, therefore, not unlikely that two causes, 
 resulting in two forms of excentricity, primary and subordinate, are simul- 
 taneously acting and producing the combined result. 
 
 * See Eccentric and Centric Force, Part I., sec. 3, and Part III., 
 sec. 10 ; and Orbital Motion, Chap. III., par. 112 and 113. 
 
 f See Eccentric and Centric Force, Part IV., sec. 7 ; and Orbital 
 Motion, par. 165. 
 
 In a spheroid of revolution of equal density, the centre of gravity is on 
 and at the centre of the axis of revolution ; so that radii drawn from the 
 same latitude to its centre of gravity, or any point of its polar axis, will be 
 of equal length. In a spheroid of revolution of unequal density, the centre 
 of gravity will still be on the axis of revolution ; but radii drawn to it from 
 the same latitude will be longer in the less dense than the more dense por- 
 tions, equilibrium being preserved in the parallel planes of revolution by an 
 increase in volume on the one side compensating for an increase in density 
 on the other. 
 
 It must be remembered, that in a spheroid of revolution, there will be 
 a physical tendency to elongate the polar axis at one set of velocities, 
 just as there may be a physical tendency to shorten it at another. Thus, 
 if a body like the earth is revolving with a low velocity of revolution 
 with regard to its axis of motion, determined by the number of revo- 
 lutions accomplished in a given time, but with a high velocity of transition, 
 as between its equatorial surface and space, its equatorial fluid particles 
 
10 INTRODUCTION. 
 
 the northern hemisphere ; and of the water in the southern. 
 The land, as a whole, has a greater specific gravity than the 
 water : hence the centre of gravity of the earth will be north 
 of the equator ; and, as it is in revolution, on its polar axis. 
 But since the earth is necessarily in equilibrium, a plane 
 parallel to its equator, and drawn through its centre of 
 gravity, would divide it into two portions of equal weight, 
 but unequal volume ; for the polar axis is divided by it into 
 two unequal parts, the shortest of which is in the northern 
 hemisphere, the centre of figure being in the southern or 
 larger portion ; so that the greatest volume of matter lies 
 south of the plane drawn through the centre of gravitj\ On 
 the other hand, the equatorial plane may be considered to 
 pass through the centre of figure, and so give an approximate 
 equality in volume to the two hemispheres. But now a pre- 
 ponderance of weight is found in the northern hemisphere, 
 it is heavier than the southern : hence the centre of figure 
 becomes a true centre of suspension the polar axis the line 
 of suspension, the celestial polar centre the centre of attrac- 
 tion towards which the suspension is directed. The relations 
 of the earth, primarily considered, are thus not unlike those 
 of a balloon; its greater volume, but diminished density, 
 being in the southern hemisphere the suspending power that 
 force which maintains the movements of the whole system. 
 
 Under this view, increase in volume is used revulsively to 
 compensate for diminution in density, in order to preserve 
 individual equilibrium, and with it the stability of the polar 
 
 will recede upon its axial motion, and seek a diminished velocity in the 
 polar regions, and thus tend to elongate the polar axis. To develop cen- 
 trifugal force, it is necessary that the velocity of revolution, as well as that 
 of transition, should be high, and that there should be free scope for the 
 action of the antagonistic forces. The latter condition could probably only 
 be attained in a spheroid of revolution, the whole of whose surface consisted 
 of fluid particles. That centrifugal force is not in action at the earth's equator 
 is demonstrated by the equatorial currents, whether of the ocean or atmo- 
 sphere. But if it is not in action, then another reason is given for affirming 
 that the earth's polar axis is its longest diameter. See Orbital Motion. 
 
INTRODUCTION. 11 
 
 axis. The same principle holds good on the several planes 
 of revolution ; so that, if a plane be taken through the polar 
 axis, the hemisphere containing the most land will be opposed 
 by an hemisphere containing most water, that is to say, the 
 water line will be higher in proportion as its surface area 
 increases, the radius of volume drawn from the centre of 
 figure longer in that hemisphere where there is least land.* 
 
 Owing to this primary difference in the relative densities 
 of land and water, and the fluid nature of the more 
 voluminous and less dense element water variations in the 
 equilibrium of the earth, from whatever cause they may 
 originate, will be necessarily accompanied by a variation 
 in the level of the water line; the law of this variation 
 being, that under the influence of a disturbing cause the 
 water will flow to that point whose relative density has 
 diminished, from the point where it has been increased, f 
 
 This is the primary law of revulsion in equilibrium. Its 
 tendency when called into action will be to cause a tide 
 to pass from one hemisphere into the other, and it is in 
 reality a modification of the law under which gases recede 
 from the centre of the earth. 
 
 In considering the action of this law upon the earth in its 
 cosmical relations, it must be remembered that increase in 
 
 * This is strikingly illustrated on the eastern shore of the Pacific Ocean, 
 where the water maintains a higher level than on the western Atlantic ; 
 although physical causes, taken by themselves, would make the Atlantic 
 the highest. 
 
 f The same law holds good when the relative gravity of either hemi- 
 sphere (divided by a plane through the polar axis) is disturbed in any other 
 way, as by an addition to its volume ; so that, if a wave were generated on 
 the equator at any point, there would be a tendency to generate a similar 
 wave at the opposite side of the equator ; and thus two waves would result, 
 180 apart, the latter originating in the law of revulsion, in order that the 
 stability of the earth's axis as a spheroid of revolution may be maintained. 
 This revulsive law will cause any two waves travelling round the earth, to 
 whatever cause they may owe their commencement, to preserve an interval 
 of 180, and therefore, in a great measure, regulate the velocity, and preserve 
 the synchronism of the tides. (See Oceanic Tides, by the author.) 
 
12 INTRODUCTION. 
 
 gravity is only another way of expressing increased subjection 
 to the influence of an attracting force ; so that, inter alia, the 
 same particles of matter would be heavier at the North 
 Pole than at the South Pole, because at the North Pole they 
 would be nearer to, and therefore more subjected to the 
 influence of the celestial polar centre. 
 
 It results from this, that the land in the northern hemi- 
 sphere is, from position, relatively heavier than that in the 
 southern, as well as indeed the water;* hence from this 
 cause there will be an increased revulsive effect in the 
 southern hemisphere, so that its volume in figure will be 
 greater than that of the northern.! Besides this, owing to 
 this combined form of attraction and revulsion acting 
 through the polar axis of the earth, there will be a tendency 
 to elongate that axis ;J so that the earth's true figure will 
 
 * Even with, reference to the centre of gravity of the earth, the same 
 particles of surface matter will be heavier in the northern than in the 
 southern hemisphere in the same latitude, because the distance from the 
 centre of gravity increases in passing to the south, owing to the excentricity 
 of the earth's centre of gravity. 
 
 f It is through this revulsive action that the ovoid form of the earth 
 results, the broad end of this figure being thus placed in the southern 
 hemisphere. 
 
 J The relations of the polar axis and equatorial diameter are inverse to 
 each other. As the one elongates, the other contracts. A provision is 
 found for this alternation in the ocean beds, more particularly that of the 
 Atlantic, which, as a longitudinal indentation in the earth's crust, becomes 
 deeper and narrower as the polar axis is elongated, thus causing the con- 
 traction of the equatorial diameter. 
 
 Some of the phenomena which appear to contradict the revulsive theory 
 are caused by these relations ; for, as a consequence of the subsidence of 
 the bed of the Atlantic, the coast of Greenland will be slowly submerged, 
 dragged down by the sinking ocean bottom, while the lateral or corrugating 
 tension will often reach a point at which the crust of the earth will crack 
 and recoil, some of the strata yielding. In this manner, sudden elevations 
 will occur, often of very considerable extent. These will be more liable to 
 happen at the margins of the ocean, and in the neighbourhood of the 
 tropics. For the same reason, in approaching the poles, these sudden 
 releases from tension will progressively increase in ratio towards the poles. 
 Every exceptional case will be found susceptible of explanation when care- 
 fully studied in all its relations through sound views of physics. 
 
INTRODUCTION. 13 
 
 approximately resemble that of an egg, having its base or 
 broad end in the southern hemisphere.* 
 
 From variations in position on the earth's surface, the 
 effects of variation in the position of the earth in space have 
 now to be considered. 
 
 If it were possible that by very slow degrees, extended 
 over long periods of time, the earth was alternately drawing 
 near to and receding from the celestial polar centre, it would 
 follow, as a necessary result, that a cyclical revulsive tidal 
 wave, co-extensive in its volume with the degree of variation 
 in distance, would be alternately passing from one hemi- 
 sphere to the other, which would be read on the surface of the 
 earth as a variation in the level of the land. 
 
 But such a variation has taken place, nay, is still pro- 
 gressively taking place on the surface of the earth ; indeed, 
 the evidence of it the alternate oscillations in its level is 
 a primary means of distinguishing between the great geolo- 
 gical epochs. 
 
 , * Sir Isaac Newton assumed that the figure of the earth was that of an 
 ! oblate spheroid on purely theoretical grounds. This figure has never been 
 I demonstrated, and the geometrical results drawn from actual measurement 
 are against it ; for arcs of the meridian become longer as they approach 
 the poles, which at once proves that the earth's polar axis is the longest- 
 _ Astronomers get out of this difficulty, in order to maintain their theory, by 
 affirming that this elongation of the arcs of the meridian is due to the fact 
 that gravity acts vertically from the surface of the earth ; but in affirming 
 f this, they in reality give up the Newtonian theory altogether ; for it refers 
 gravity to the centre of gravity, irrespective of the earth's figure. The fact 
 is, that the direction of gravity, with reference to the surface of the earth, 
 cannot be determined experimentally ; for the spirit-level will always give 
 an horizon at right angles to the plumb-line. But how can it be proved 
 that this agrees with the level of the surface of the earth, or the horizon of 
 oceanic water at rest ? This is an assumption, and, in all deviations from 
 the perfect sphere, an unphilosophical one. In a spheroid, the horizon of 
 the spirit-level (or of isolated surfaces of still water) will only agree with 
 the horizon of figure at the poles and the equator (or its equivalent). But 
 if this is so, then no correction is to be made for differences in the direction 
 of gravity in calculating the true arcs of the meridian ; and their progressive 
 increase from the equator to the poles is a positive demonstration that the 
 earth's polar axis is longer than its equatorial diameter. 
 
14 INTRODUCTION. 
 
 If it were further possible that these alternate variations 
 in level could also resolve themselves into variations in 
 degree, so that during one series of the cycles of change 
 the earth was drawing successively nearer and nearer to the 
 celestial polar centre, and during another series of such 
 cycles receding further and further from it, then the 
 revulsive tidal wave would be itself a variable one, increasing 
 in volume during its serial recession from, and diminishing 
 in volume during its serial re- approximation to, the celestial 
 polar centre.* 
 
 But the actual oscillations of the earth's surface level have 
 varied considerably in degree according to the results drawn 
 from geological research ; the degree of alternate subsidence 
 and re-elevation at any given point having been much more 
 extensive on some occasions than on others. 
 
 Now, these varying relations are not only accounted for, 
 but rendered necessary by the theoretical extension of the 
 astronomical system here advocated ; for, if the central sun 
 is passing round the centric sun in an orbit inclined to its 
 
 * At first sight this appears to be a contradiction to the principle of 
 revulsion laid down. It is, however, only a modification of that principle, 
 which can be easily made intelligible ; for it is owing to the inclination of 
 the orbit of the central sun that this cyclical tidal wave exists. Now this 
 inclination is a variable one, attaining its maximum when the centric sun is 
 most remote from the celestial polar centre, and reaching zero at its point 
 of greatest proximity ; so that the actual wave (or alteration in the level of 
 the land) will be the greatest when the whole system is furthest from the 
 celestial polar centre, although the land will attain its maximum of eleva- 
 tion, simultaneously with a minimum tidal wave, when the whole system 
 is nearest to the celestial polar centre. 
 
 These seemingly incongruous relations arise from the blending of two 
 orders of waves, that dependent on the revolution of the centric sun, under 
 which the water has made its greatest recession from the circumpolar 
 regions (especially the northern), when nearest to the celestial polar centre ; 
 and that dependent on the revolution of the central sun, which, since it is 
 due to the inclination of its orbit, sinks to a zero point at that period, but 
 attains its maximum when the centric sun's tide has returned to the circum- 
 polar regions : so that the gross result is that the motion of the centric 
 sun makes a slow but determined serial change in the degree of the alter- 
 nations in the level of the land caused by the revolution of the central sun. 
 
INTRODUCTION. 15 
 
 equator, it will then be alternately drawing near to and 
 receding from the celestial polar centre, with its whole 
 system ;* while further, if the celestial polar centre holds 
 an excentric position in the orbit of the centric sun, it follows, 
 as a matter of course, that the centric sun in its revolution 
 carries its whole compound system alternately nearer to 
 and further from the celestial polar centre :f so that, the 
 cycle of precession being taken as the cycle of the central 
 sun's period (the centric sun's path, of course, representing 
 an unknown series of such cycles), during one-half cycle it 
 would be drawing near to the celestial polar centre, J and 
 the revulsive tidal wave would be ebbing from the northern 
 hemisphere to the southern, and from the polar regions to 
 the equatorial; the effect on the surface of the earth being 
 that the land forming its equatorial belt would be slowly 
 subsiding into the retreating waters, that in its circumpolar 
 regions, especially the northern, as gradually emerging 
 from them ; while during the next half cycle it would be 
 receding from that centre, and the tidal wave would now be 
 passing from the southern hemisphere to the northern, or 
 ebbing in the equatorial regions and flowing in the polar ; 
 the land now rising in the equatorial and subsiding in the 
 circumpolar regions. || Moreover, as during succeeding cycles 
 in precession, the centric sun would be advancing in its 
 path, or moving round the celestial polar centre, and at 
 the same time varying its distance from it, it is evident that 
 these alternations must vary in degree, and the tidal wave 
 be the greatest the oscillations in the level reach their 
 
 * Fig. 2. t Ibid. 
 
 J Or passing from its point of greatest remoteness from, to that of 
 greatest proximity to, the centric sun. Its point of greatest proximity to the 
 centric sun will be its point of greatest proximity to the celestial polar 
 centre in that revolution. 
 
 Or passing from its point of greatest proximity to, to that of greatest 
 remoteness from, the centric sun. 
 
 II See Orbital Motion, Notes 22, 95, and 268. 
 
16 INTRODUCTION. 
 
 maximum when the centric sun was furthest from the 
 celestial polar centre.* 
 
 Another consequence flows from these changing relations ; 
 for, in drawing near to the celestial polar centre, an actual 
 concentration with a diminution in excentricity takes place 
 in the solar system ;f while increase in proximity to that 
 centre enables it to receive renewed force or energy 
 from it.J 
 
 These, which are only some of the first and most prominent 
 results drawn from the present attempt at a re-interpretation 
 of well- recognised astronomical phenomena, have this peculiar 
 feature, that while grouping the phenomena themselves into 
 classes, and then tracing each class to its -direct cause, and so 
 drawing the outline of a more perfect system than any that 
 has yet been proposed, they fulfil this further condition of 
 such a system, that they indicate the astronomical measure 
 of the cosmical changes which have taken place, and are 
 taking place on the earth's surface pointing to the cycle of 
 precession as the great geological "day," or revolution and 
 further indicating the source of variation, in the effects pro- 
 duced during that cycle. 
 
 Such an astronomical measure must exist, seeing that from 
 whatever cause variations in the earth's individual relations 
 may originate, their nature proves that they are cosmical in 
 character, and, therefore, responsive to a cosmical cause which 
 permeates the whole system, of which the earth is a relatively 
 remote member : hence every system which does not point to 
 it is inadequate to the end for which it is proposed. Astro- 
 nomy must furnish the link which binds the sciences together, 
 and unravels some of their obscurities providing the basis 
 through which all their relations are to be read, their relative 
 
 * See Fig. 2. 
 
 t See Orbital Motion, Notes 52, 96, 119, 138, and 173 ; and Eccentric and 
 Centric Force, Part IV., sects. 1, 4, and 7. 
 J See Orbital Motion. 
 See Ibid., Note 268. 
 
INTRODUCTION. 17 
 
 quantities determined ; and, above all, the geologist, the 
 zoologist, and the botanist must turn to the astronomer for 
 the clue to possibly missing links in the chain of their 
 science. 
 
 The interpretation and grouping of astronomical phenomena 
 is very simple. 
 
 1. The moon passes round the earth from west to east ; 
 its passage causing the sidereal heavens, including the sun, 
 to appear to pass from east to west. 
 
 2. The visible hemisphere of the moon gravitates to the 
 centre of gravity of the terrestrial system, in consequence of 
 which the sidereal heavens pass round its circumference as it 
 passes round the earth, and give it an apparent revolution on 
 its axis. 
 
 3. The earth revolves upon its polar axis from west to 
 east; the passage of a given meridian round that axis causing 
 the sidereal heavens, including both sun and moon, to appear 
 to pass round it from east to west. 
 
 These are the individual motions of the terrestrial system. 
 
 4. The terrestrial system passes round the sun from west to 
 east, its passage causing the sidereal heavens to appear to 
 pass round it from east to west ; while, owing to that passage, 
 the sun appears to move through the signs of the zodiac from 
 west to east.* 
 
 The difference between the sidereal and synodic lunar 
 
 * Three distinct phenomena singly and simultaneously furnish the measure 
 of the period occupied by the terrestrial system in passing round the sun. 
 
 1. The sun passes through all the signs of the zodiac, and returns to its 
 point of departure, thus making a complete apparent revolution in space, 
 which is the reflection of the actual revolution of the earth. 
 
 2. The same star returns to the meridian with the sun that is to say, 
 the solar and sidereal meridian once more coincide as measures of time 
 the earth having in the interim made one more revolution on its axis with 
 reference to the sidereal heavens than with regard to the sun ; and 
 
 3. The sidereal and synodic points of departure of the lunar revolution 
 once more coincide, the moon having in the interim made one more revo- 
 lution round the earth, with reference to the stars than with regard to 
 the sun. 
 
18 INTRODUCTION. 
 
 month and the sidereal and solar day is caused by the pro- 
 gressive motion of the earth. 
 
 5. The sun* moves round the central sun from west to 
 east. This passage causes the point at which the earth's 
 annual revolution round the sun is completed, to recede from 
 the central sun from east to west ;f which recession is read in 
 the heavens by a passage of the zodiac from west to east 
 round the lunar node ; so that the complete recession of that 
 node is the measure of the period of the revolution of the 
 solar system in space. J 
 
 This is accompanied by an advance of the lunar apsides, 
 which pass once through the signs of the zodiac, but twice 
 from conjunction to opposition, in (approximately) the same 
 period, depending on the attraction of the central sun; ,by 
 an oscillation or variation in inclination of the moon's path, 
 caused by a variation in that attraction, as the earth alter- 
 nately draws near to and recedes from that body;|| by an 
 apparent nutation of the polar axis of the earth, determined 
 by the actual stability of that axis or fidelity with which it 
 points to the celestial polar centre, in consequence of which 
 it appears to nutate with reference to any intermediate star ;*[ 
 and, further, by a progressive variation in the length of the 
 lunar synodic revolution.** 
 
 These phenomena constitute a single cycle to which the 
 name " lunar cycle" may, for convenience, be given, since its 
 most readily interpreted unit is" the lunar recession. It is 
 determined by the revolution of the sun, and is the measure 
 of the period of that re volution, ff It resolves itself into 
 two groups : the first and shortest comprehends the apsidal 
 
 * The sun revolves upon its axis, and the planetary systems revolve 
 
 round it, with their individual and systemic motions ; but these can be 
 passed over here. 
 
 t See Orbital Motion, Fig. 3. % See Ibid., Notes 25 and 170. 
 
 See Ibid., Note 167. || See Ibid., Note 117. 
 
 f See Ibid., Note 79. ** See Ibid., Fig. 20. 
 ft See Ibid., par. 48. 
 
INTRODUCTION. 19 
 
 revolution and oscillation in plane of the moon's orbit ; the 
 second, the complete recession of the nodes, the revolution in 
 nutation, and the variation in the lunar synodic period, the 
 difference in period occupied by these two being caused by, and 
 a primary measure of, the motion of the central sun in space.* 
 
 6. The central sun moves round the centric sun from west 
 to east. This passage causes the earth's equinoctial points to 
 recede round the zodiac from east to west. This is known 
 as the precession of the equinoxes ; a complete revolution in 
 precession being the measure of the central sun's period. f 
 
 It is accompanied by an advance in the terrestrial apsides, 
 by a variation in the obliquity of the ecliptic, by an apparent 
 nutation of the earth's polar axis, || and by a progressive 
 variation in the length of the tropical^[ year, these pheno- 
 mena constituting the terrestrial cycle.** They are parallel 
 in their teaching value to those in the lunar cycle, and, like 
 tbe latter, are divisible into two groups. The first and shortest 
 includes the apsidal revolution and variation in the obliquity 
 of the ecliptic ; the second, the precession of the equinoctial 
 point, the apparent nutation, and the variation in length of 
 the tropical year. The difference in the period of these two 
 groups is caused by the motion of the centric sun, and is of 
 such a great proportionate extent, because that body is pass- 
 ing across, and not revolving within, the zodiac.ft 
 
 7. The centric sun is passing round the celestial polar 
 centre from north to south,* on the plane of its polar axis. 
 This change in direction (from an approximate equatorial to 
 an approximate polar plane) causes it to move across the 
 zodiac, and has been hitherto read by astronomers as the 
 proper motion of the sun. JJ 
 
 * See Orbital Motion, Note 138. f See Ibid., Note 81. 
 
 + See Ibid., Note 138. See Ibid., Notes 96 and 119. 
 
 || See Ibid., Note 79. II See Ibid., Fig. 20 and Note 173. 
 
 ** See Ibid., par. 49. ft See Ibid., Notes 119 and 138. 
 
 JJ See Ibid., Fig. 1. There treated as the orbit of the central sun. 
 
 c 2 
 
20 INTRODUCTION. 
 
 These phenomena have been examined and discussed else- 
 where ; and the grounds for grouping them in the manner 
 here indicated, carefully weighed.* The whole subject has 
 been considered under a fresh aspect, and from an entirely 
 new point of view, in the paper on " The Cosmical Value of 
 the Revolution of the Lunar Apsides," and the strict coinci- 
 dence in the results drawn from this double process amounts 
 to an absolute demonstration of the accuracy of the view 
 now advocated, f 
 
 It is of course desirable, in offering a new theory to the 
 world, to give, where it is possible, some clear and simple 
 test by which its real value can be subjected to a rigid 
 scrutiny. "When Orbital Motion was published, the author 
 invited the Astronomer Royal and the practical astronomers 
 of England to make a search for the central sun, whose bear- 
 ings and relative position in space he ventured to indicate.^ 
 He now formally invites those gentlemen to verify his views 
 of the true significance of the phenomenon known as apsidal 
 advance. The test is a simple one. He affirms that the 
 lunar perigee, in passing from conjunction to conjunction, 
 only advances through half of the signs of the zodiac. 
 He is not aware that this is a recognised fact. He offers 
 it as a predication, and challenges its admission or dis- 
 proval. He is willing to stake the truth of his whole 
 theory upon the results of observation on this single point, 
 and waits for the revelations of such observation without 
 anxiety, fully conscious that they will agree with his pre- 
 diction. 
 
 But if they do agree with his prediction if it should be 
 discovered and admitted that two revolutions of the lunar 
 
 * See Orbital Motion, passim. 
 
 f The proofs are drawn from one series of phenomena in Orbital Motion. 
 They are now drawn from another and perfectly distinct set of relations, 
 both of which demonstrate the same causes as being in operation. 
 
 % See letter dated 18th October, 1863, published in the Times newspaper 
 
INTRODUCTION. 21 
 
 apse are necessary, in order that it may advance through all 
 the signs of the zodiac, this position will have been reached, 
 as a result of this crucial test, that apparently incompatible, 
 not to say impossible, conditions are found to be coexistent 
 for how can the same relations make simultaneously an entire 
 revolution in space when computed from one point, and only 
 a half revolution when computed from another ? And then 
 the author is confident that there will be no escape from the 
 dilemma in which astronomers will find themselves but the 
 acceptance of his theory. 
 
 HEREFORD, 15th March, 1865. 
 
12. 
 
THE COSMICAL RELATIONS 
 
 OF THE 
 
 REVOLUTION OF THE LUNAR APSIDES. 
 
 AMONGST the many interesting phases of motion which 
 present themselves to the thoughtful observer in the study 
 of physical astronomy, the revolution of the lunar apsides 
 is by no means the least instructive. In studying this phe- 
 nomenon, it is surprising to find how lightly it is touched 
 upon, even by some of those who have elaborately discussed 
 the whole field of astronomical change ; for, beyond a dry 
 description of the fact, and sometimes an attempt at a 
 mechanical explanation of it, it is for the most part passed 
 over in silence. 
 
 And yet, perhaps, this is not surprising, for in reality it 
 presents a double anomaly under the received theory of 
 gravitation; and hence it may still be regarded as an 
 astronomical enigma, possibly containing the elements of an 
 unsolved problem. 
 
 For these reasons it presents a fair field for investigation, 
 and in a careful examination of its actual relations data 
 may even be found for a more extended and comprehensive 
 view of the whole subject. 
 
 The relations of the moon's orbit, known by astronomers 
 
24 THE COSMICAL RELATIONS OF 
 
 as its apsides, are indicated by an imaginary and purely 
 theoretical line, which is supposed to pass through the 
 relatively long axis of the moon's nearly circular path 
 round the earth. They are determined by the excentric 
 position of the earth in that orbit, under which the moon 
 during its transit round varies its distance from the earth, 
 alternately drawing near to and then receding from it, and 
 are in fact assumed to lie upon, and hence are referred to a 
 line passing at any given time from the point of the moon's 
 greatest proximity to, through, and thence to the point of its 
 greatest recession from the earth. 
 
 The designations of the points where the moon crosses the 
 line of its apsides "are perigee and apogee respectively; the 
 perigeal point being, of course, that of greatest proximity. 
 
 The revolution of the lunar apsides, the probable cause 
 of which is about % to be considered, is this, that the perigeal 
 and apogeal points of the moon's orbit do not represent 
 fixed points in space, that is to say, it is found under obser- 
 vation that their relations are not constant, whether to the 
 sun on the one hand or the zodiac on the other, but pro- 
 gressively changing, for they are advancing in the order 
 of the signs ; so that, starting from conjunction with the sun 
 in 4J years, the moon's perigee is found to be in opposition 
 to that orb ; and in a second 4| years, having still continued 
 to advance, it will have returned to conjunction once more; 
 and thus in every 9 years the lunar apse makes a complete 
 revolution in space with reference to the sun. 
 
 The anomalies which this revolution presents are to the 
 astronomer very clear for, 
 
 1st. Its period is only 9 years ; that of the recession of 
 the lunar nodes being 18 while 
 
 2nd. It advances in space, whereas the lunar nodes recede, 
 or move in an exactly opposite direction. 
 
 And it is on this account that a purely mechanical ex- 
 
THE REVOLUTION OF THE LUNAR APSIDES. 25 
 
 planation of the phenomenon has been adopted, in order to 
 separate it completely from the ordinarily recognised effects 
 of the laws of gravitation. 
 
 On attentively considering this revolution, it is difficult 
 to dissociate it from the recession of the lunar nodes, 
 although not only have these two concurrent circumstances 
 no phenomenon in common, but they even appear at first 
 sight to be in all their relations opposed to each other, since 
 it takes somewhat more than two periods of the one to 
 complete the full period of the other, and they are moving in 
 opposite directions. 
 
 In the relations of the half period of nodal recession to the 
 whole period of apsidal revolution, the first link in a possible 
 chain of evidence does, however, seem to present itself, as a 
 guide to further inquiry. Another link can be drawn from 
 an associated phenomenon, which more closely connects them, 
 for the moon's orbit has not a permanent degree of obliquity 
 to the ecliptic, but oscillates to and fro across it, a single 
 oscillation exactly coinciding with one revolution of the 
 apsides ; a complete or to and fro oscillation being performed 
 in somewhat less time than a complete recession of the lunar 
 nodes. 
 
 Thus, the revolution of the lunar apse exactly coincides 
 with the oscillation of the lunar orbit, that is to say, during 
 one revolution of the apse the orbit crosses the ecliptic in 
 one direction, and in the next revolution recrosses it in the 
 other, while both of these associated phenomena have a 
 definite relation to the period of lunar nodal recession. 
 
 But the oscillation of the lunar orbit is evidently a single 
 to and fro act, depending upon a definite cause which pro 
 duces a regularly oscillating result. 
 
 j Hence the first inference is, that a single revolution of the 
 lunar apsides is in reality the measure of only half a phe- 
 riomenon, half of an actual revolution in space. 
 
 J 
 
26 THE COSMJCAL RELATIONS OP 
 
 And yet that the lunar apse does make two revolutions 
 during a single recession of the nodes cannot be denied. 
 
 Is it possible to reconcile such an evident discrepancy ? 
 
 Perhaps an examination of the relations of the terrestrial 
 apsides may throw some light upon it. 
 
 These, like the lunar apsides, are revolving in space, and, 
 like them, are advancing in the order of the signs ; but, as 
 was to be expected from the difference in time occupied by a 
 lunar and a terrestrial revolution, their period is greatly pro- 
 longed, the perihelion point of the earth taking some 21,000 
 years to pass through all the signs of the zodiac or make a 
 complete circle in space. 
 
 But the advance of the terrestrial apse in space is not 
 the only parallel relation between these two revolutions, 
 for there is a precession of the terrestrial equinoxes which 
 bears the same relation to the terrestrial orbit that the reces- 
 sion of its nodes does to the lunar ; and then there is a 
 progressive, theugh slow, variation in the obliquity of the 
 ecliptic which parallels the oscillations of the lunar orbit ; so 
 that there are two sets of precisely similar phenomena, one of 
 them affecting the terrestrial orbit, the other the lunar. 
 
 The question which now suggests itself is, What relations 
 do each of the three phenomena of either set bear to the 
 similar phenomena of the other ? 
 
 It is a question easily answered ; for, while the equinoxes 
 pass round the zodiac against the order of the signs or 
 retreat along them once in some 25,868 years, the terrestrial 
 apsides pass round it in the order of the signs or advance 
 along them once in some 21,000 years, while the ecliptic 
 oscillates to and fro once in the same period as the apsides 
 revolve. 
 
 The points of accord between the two sets of phenomena 
 are thus at once seen to be, that the period of precession 
 in the one, like that of recession in the other, is the longest, 
 and so marks the longest revolution ; while the period of 
 
THE REVOLUTION OF THE LUNAR APSIDES. 27 
 
 oscillation of the ecliptic (to and fro) coincides with that of 
 the revolution of the apsides; and, on the other hand, the 
 points of difference are these, that the terrestrial apsides 
 revolve but once during the oscillation of the ecliptic and 
 retreat of the equinoxes, whereas the lunar apsides revolve 
 twice during a single oscillation, (to and fro) of the lunar 
 orbit and recession of the nodes. 
 
 This difference in phenomena, which otherwise are so very 
 similar as to appear to illustrate a general principle and 
 depend on a similar cause, is very remarkable ; and yet, after 
 all, it is not so very unexpected, for it affirms what was 
 suggested at the outset, that the revolution of the apsides 
 is part and parcel of a single act to which the three several 
 coincident phenomena belong. 
 
 But, if the revolution of the apsides illustrates, in com- 
 bination with oscillation and recession, a single act, How is 
 it that this act occupies two revolutions of the apse in the 
 lunar orbit, and but one in the terrestrial ? 
 
 How, indeed? In order to answer this question another 
 must be asked, the answer to which will, perhaps, throw some 
 light upon this remarkable difference. With reference to 
 what is the revolution of the lunar apse computed ? And 
 when this has been replied to, it must be considered with 
 reference to what the revolution of the terrestrial apsis is 
 calculated. 
 
 Now, the revolution of the lunar apsis is computed from 
 the sun that is, from a departure from conjunction with, 
 to a return to that relation to that orb; whereas the re- 
 volution of the terrestrial apsis is measured by a direct 
 reference to the signs of the zodiac. This is an important . 
 difference, for it is possible that the lunar apsis might make 
 an apparent revolution in space (from conjunction to con- 
 junction), and yet only pass through half the signs of the 
 zodiac in doing so. 
 
 To realize the possibility of this seeming paradox, a single 
 
28 THE COSMICAL RELATIONS OF 
 
 assumption is required, that the sun itself is describing an 
 orbit in space round an excentric focal, and, as yet, undis- 
 covered body or central sun, the period of which coincides 
 with, and is measured by, what for convenience may be 
 termed the lunar cycle. 
 
 If, for a moment, this could be conceded, the explanation 
 would become very easy ; for then 
 
 1st. The passage of the sun in its orbit would cause a 
 retreat of the terrestrial system round that orbit, which would 
 be recognised on the zodiac by the recession of the lunar 
 nodes. 
 
 2nd. It would cause the central sun (were that body 
 visible) to appear to advance in the order of the signs, and 
 complete a full apparent revolution during the full revolution 
 of the sun ; the revolution of the sun being thus read in the 
 skies by an apparent revolution of the central sun ; and 
 
 3rd. As it approached the central sun the orbit of the 
 moon would become gradually more inclined to its equator, 
 crossing the ecliptic in doing so ; while, as it receded from 
 that body, the moon's orbit would become less inclined to its 
 equator, and thus recross the ecliptic. 
 
 Admitting these three results as necessary consequences of 
 the assumed revolution of the sun, another has now to be 
 claimed ; or, 
 
 4th. That the lunar apsides would always rest upon or 
 point to the apparently advancing central sun ; the moon 
 at its perigee lying between the earth and the central 
 sun. 
 
 This, of course, it would do, in virtue of the attraction of 
 that body ; but now, what would happen from these mixed 
 relations? Why, 
 
 1st. That the central sun, as it advanced in the order of 
 the signs of the zodiac, would carry the lunar apsides with 
 it, pari passu. 
 
 2nd. That in doing this it would cross the retreating 
 
THE REVOLUTION OF THE LUNAR APSIDES. %9 
 
 terrestrial system, or receding node, twice in each revolution, 
 at the opposite sides of the sun's orbit. 
 
 3rd. That each time that it crossed the lunar node, the 
 terrestrial system then lying between it and the sun, the 
 perigeal point of the moon would be in opposition. 
 
 4th. That each time that it was in quadrature with the 
 points where it crossed the lunar node, the sun would lie 
 between it and the terrestrial system, and the lunar perigeal 
 point thus necessarily be brought into conjunction. Hence, 
 
 5th. That in passing from conjunction with the lunar 
 node to quadrature with the point where that conjunction 
 occurred (or actual opposition with the lunar node), the 
 lunar perigeal point would be passing from opposition to 
 conjunction; and, 
 
 6th. That in passing from opposition to the lunar node, 
 to conjunction with it, the lunar perigeal point would be 
 passing from conjunction back again to opposition. 
 
 That is to say, as the central sun passed from conjunction 
 through opposition to conjunction again with the terrestrial 
 system, the lunar perigeal point would make a single com- 
 plete apparent revolution (with reference to the sun). 
 
 But this would occur twice during a single retrograde 
 motion of the node, actual revolution of the sun, or apparent 
 revolution of the central sun. 
 
 Hence two revolutions of the lunar apsides would neces- 
 sarily coincide with a single recession of the lunar nodes. 
 
 Such an explanation as this of the revolution of the lunar 
 apsides, would strictly accord with the theory of gravitation ; 
 for the attraction of the central sun would cause the apsidal . 
 line always to point towards it. 
 
 fi The possibility of such a theory as the one here offered 
 being the true explanation -of the form of motion under 
 discussion, can hardly be denied. The manner in which it 
 extends the received astronomical generalizations, and widens 
 the field of investigation, must now be briefly considered, 
 
30 THE COSM1CAL RELATIONS OF 
 
 in order to determine how far it is a probable, as well as a 
 possible way of accounting for a very interesting phenomenon. 
 The first consequence that flows from it is the change in 
 the value which it gives to the phenomenon of recession; 
 which amounts to a remodelling of opinions on this branch 
 of the subject. 
 
 If the recession of the lunar nodes were the only form of 
 recession recognised in practical astronomy, then the value 
 now claimed for it might be called in question, because of 
 the antecedent revolutions of the earth and moon, which 
 ought to be accompanied by, and so occasion, similar results. 
 But these revolutions are accompanied by, and do occasion 
 recession ; and it is by the recessions which follow their 
 motions, that these motions in space have been identified; 
 but, owing to the recessions which they occasion differing 
 in form, the actual identity in principle of their teaching 
 value has been overlooked. 
 
 The first and simplest form of recession is that of the 
 whole heavens round the earth during its axial revolution, 
 upon which the difference between day and night depends. 
 Similar to this is that of the heavens round the moon during 
 its passage round the earth, perceived through its diurnal 
 advance amongst the heavenly bodies. 
 
 The second form of recession is that recognised only after 
 an interval of time, under which the whole aspect of the 
 heavens differs, say in the winter, from its appearance in 
 the summer ; for here the heavenly bodies recede once round 
 the earth and the sun during the annual revolution of the 
 former, and occasion the difference between solar and sidereal 
 time ; owing to which the sidereal year comprises one more 
 axial revolution of the earth than the solar year, though 
 occupying exactly the same period of time the effect of the 
 progressive advance of the earth round being to lengthen its 
 axial revolution with regard to the sun, by which process the 
 sidereal revolution in excess is broken up into fragments, one 
 
THE REVOLUTION OF THE LUNAR APSIDES. 31 
 
 of which is added to and included in each solar day ; so that 
 here the annual sidereal recession is occasioned by the pro- 
 gressive or orbital motion of the earth, and is confessedly 
 a measure of its annual revolution round the sun. 
 
 The same form of recession is witnessed as the moon tra- 
 verses its orbit, for its sidereal period is shorter than its 
 synodic ; so that it also performs one more revolution in 
 each year, when computed from a fixed star, than when its 
 course is measured from the sun; this sidereal revolu- 
 tion in excess being also, like the last mentioned, broken 
 up into fragments, one of which is added to and included 
 in each of its synodic revolutions, this added revolution 
 being thus a further measure of the earth's progressive 
 motion round the sun in space. 
 
 On considering these several recessions, they are found to 
 be measures of revolutions in space, exactly defining the 
 periods of either of the revolutions indicated, viz., the axial, 
 and then the orbital, motion of the earth ; and, finally, the 
 orbital motion of the moon, their peculiarity being that the 
 sidereal heavens recede (or move from east to west) round 
 the revolving or advancing body. 
 
 In the recession of the lunar nodes, and the precession of 
 the terrestrial equinoxes, this peculiarity is reversed ; for 
 here the sidereal heavens advance with reference to the 
 retreating node or equinoctial point, or pass from the west to 
 the east ; so that if this change in the direction of the 
 apparent motion can be accounted for, the inference becomes 
 a demonstration that these recessions also are measures of the 
 periods of revolution of other concentric revolving bodies. 
 
 And yet nothing is perhaps easier than to account, and 
 that most satisfactorily, for the change in the direction of the 
 apparent motion ; for all that is necessary is to remember 
 that the whole of the first forms of recession are with 
 reference to the moving earth or its satellite to whose 
 motions they are directly referred ; so that, as the terrestrial 
 
32 THE COSMICAL RELATIONS OF 
 
 system moves through space, the sidereal heavens must pass 
 round it, against its actual motion. 
 
 As soon as the motion of the sun, however, comes into 
 question, these relations are at once changed, and another 
 principle comes into operation one very familiar to those 
 observers who are in the habit of studying the consequences 
 of motion. Any one who has travelled much by rail can 
 hardly have failed to notice that, in inspecting the country 
 as he passes rapidly by it, the most distant objects appear to 
 advance with reference to any intermediate one or, in other 
 words, that the nearest object recedes from the more distant 
 one with which its relative position is compared, as the 
 observer passes it, being left behind by the passing train, 
 with which the distant body seems to advance. 
 
 Now, this is precisely what happens whether in lunar 
 recession or equinoctial precession, that is to say (in the 
 former), as the sun advances in space, the signs of the zodiac, 
 or most distant visible objects, advance, seem to advance 
 with the advancing sun, and thus allow the terrestrial 
 system, with its terrestrial observer, to fall slowly behind 
 them : and hence it appears 
 
 That the lunar nodes or terrestrial system recede upon 
 the zodiac, because the earth is an intermediate object between 
 the moving sun and relatively fixed zodiacal belt ; so that 
 it can be fairly -held that in this, as in the previously noticed 
 instances, recession is the measure of the period of a revo- 
 lution, that accomplished by the sun in passing round the 
 focal body of its orbit. 
 
 The existence of a central sun has, of course, to be in- 
 ferred, since that body has not, so far, been discovered ; 
 but there need be no difficulty here, for no body has, as 
 yet, been recognised as revolving in an empty orbit, and 
 it is contrary to all analogy that the sun should present 
 the first instance of such a body. 
 
 Assuming the existence of a central sun, it would be 
 
THE REVOLUTION OF THE LUXAR APSIDES. 3# 
 
 necessarily passing round the zodiac iu the order of the 
 signs, during the revolution of the sun, just as the sun passes 
 round the zodiac in the same order during the revolution 
 of the earth : this passage being a reflection of the actual 
 passage of the sun round it : and in this passage it would 
 carry the apsidal line with it. 
 
 Conceding these relations, and they amount to a philo- 
 sophical demonstration, it becomes evident that the three 
 associated phenomena of revolution of the apsides, recession 
 of the nodes, and oscillation of the orbit, form a cycle of 
 concurrent events, a lunar cycle, whose period they deter- 
 mine; the interpreting significance of which is, that it is 
 the measure of the time occupied by the sun in passing once 
 round the central sun or focal body of its orbit. 
 
 But even beyond this the lunar apse can be made to speak, 
 since the fact that two of its revolutions occupy a shorter 
 period than one recession of the nodes is not without its 
 special value ; for owing to the change in the direction of the 
 apparent motion of recession, under which from passing from 
 east to west, when the motions of the moon and earth are 
 being considered, and thus occasioning the difference between 
 sidereal and solar time, by rendering the former periods 
 shorter than the latter, it passes from west to east when 
 the motion of the sun (or other concentric body) is being 
 examined the sidereal heavens are now advancing upon 
 the synodic revolution instead of receding from it, and hence 
 the point of conjunction is regained before the sidereal rela- 
 tions are resumed. But through this significant fact it is 
 learned that the body with which it is associated, the 
 central sun, is itself in motion. 
 
 This, however, is not surprising ; for it is clearly demon- 
 strated by the terrestrial cycle (of precession of the equinoxes, 
 revolution of the apsides, and variation in the obliquity of 
 the ecliptic), which, from being in its three associated phe- 
 nomena parallel to the lunar cycle, must have a similar 
 
 D 
 
34 COSMICAL RELATIONS OF REVOLUTION OF LUNAR APSIDES. 
 
 interpreting value ; so that not only the fact of the motion, 
 but the actual period of the revolution, of the central sun, 
 is defined. 
 
 Nor do the signs of motion drawn from apsidal revolution 
 cease, even here ; for the terrestrial apsides, in their period 
 of some 21,000 years, indicate a recession in time from the 
 period of precession (some 25,868 years). And since reces- 
 sion in time now stands for progression in space, or changing 
 relations in the body to which it is imputed, it is thus shown 
 that the body round which the central sun is passing is also 
 in motion. 
 
 From these conclusions, which have been necessarily 
 thrown together in a highly condensed form, it becomes 
 evident that a careful examination of the phenomenon known 
 as apsidal revolution can be made very fruitful in results ; 
 but these results only point to the outlying portions of a 
 vast field of inquiry, extended research in which will more 
 than amply repay the persevering investigator. 
 
GEOMETRICAL DEMONSTRATIONS. 
 
 FIG. I. 
 The Centric Solar System passing across the Zodiac. 
 
 Z D C. The zodiac. 
 
 C O. The path of the centric sun across the zodiac. 
 
 a. The centric sun. 
 
 e. The central sun. 
 
 i. The sun. 
 
 o. The earth. 
 
 u. The moon. 
 
 c c. The orbit of the central sun, round a, the 
 
 centric sun. 
 
 5 s. The orbit of the sun, round e, the central sun. 
 
 1 1. The orbit of the earth, round t, the sun. 
 
 m m. The orbit of the moon, round o, the earth. 
 
 D2 
 
36 GEOMETRICAL DEMONSTRATIONS. 
 
 The centric sun, a y in moving from C to O passes across 
 the plane of the zodiac, while the several members of its 
 system are revolving on that plane, within the zodiacal 
 belt. 
 
 It becomes evident from considering this diagram, that 
 the plane of the zodiac represents the equator of the centric 
 sun, and the paths of the members of its system, which are 
 continuously passing round it within the circle of the zodiac, 
 while the plane of its own path lies on its polar axis or at 
 right angles to its equatorial plane ; so that, while the mem- 
 bers of its system are passing from west to east, it is moving 
 in a direction which, with reference to the polar relations 
 to space (absolutel} r ), ultimately resolves itself into north and 
 south. 
 
 The ultimate passage of the whole system from the zodiac, 
 or the varying angular relations of the zodiac to the mean 
 plane of the system passing through it, which must be 
 occurring, unless compensating processes are at work, are 
 not considered here. The time required to verify such 
 changes would be incalculable, the data being as yet not 
 ascertained, and the phenomena elicited coincident if not 
 identical with those which establish the so-called motion of 
 the sun, but actual motion of the centric sun. 
 
GEOMETRICAL DEMONSTRATIONS. 
 
 37 
 
 FIG, II. 
 
 The varying relations of the Central Solar System to the 
 Celestial Polar Centre, at definite positions on the Centric 
 Sim's Orbit. 
 
 A B C D. A circle representing the orbit of the centric sun. 
 
 E. The centre of that circle. 
 
 F G. Excentric or focal points within that circle. 
 
 H. The centric sun. 
 
 a e. The plane of the orbit of the central sun. 
 
 e o. The equator of the centric sun.* 
 
 * The equator of the centric sun is parallel to that portion of the circle of 
 its path at which it is found at any given time ; hence, e, being more distant 
 from that circle than a, a e is necessarily inclined to i o. 
 
38 GEOMETRICAL DEMONSTRATIONS. 
 
 a e. The central sun at opposite points of its orbit. 
 
 E a, E e. Radial lines showing the relative distance of a 
 and e from E. 
 
 The line E e is longer than the line E a : therefore, at a 
 the central solar system, and with it the earth, is nearer to E, 
 the celestial polar centre, than at e. At G this difference 
 increases, but at F it diminishes ; that is to say, it increases 
 with the increasing distance of H, and diminishes with its 
 diminishing distance, from the focal body. A great prin- 
 ciple is demonstrated by this variation in the difference, 
 for, although at Gr the attracting force is more remote from 
 a H c than at E or F, it acts with greater relative force on 
 a than on c. and therefore tends to increase the inclination of 
 a c ; but at F, though nearer to a H e y it has increased its 
 proximity, and with this the force of its attraction more 
 rapidly upon e than upon a, and therefore tends to diminish 
 the inclination of a e ; so that the inclination of the orbit of 
 the central sun is thus shown to diminish with the approxi- 
 mation of the centric sun to the celestial polar centre, and to 
 increase with the recession of that body from it. 
 
 In virtue of this principle, the inclination of the orbit of 
 the central sun will be least, when the centric sun is nearest 
 to the celestial polar centre, and greatest when it is furthest 
 from it ; and also in virtue of it, when the centric sun is 
 nearest to the celestial polar centre, there will be a maximum 
 of elevation in the land in the northern hemisphere of 
 the earth, or elongation of its polar axis ; and a minimum 
 oscillation in the level of the land as the central sun passes 
 round the centric sun : whereas, when the centric sun is 
 furthest from the celestial polar centre, there will be a, 
 minimum elevation of the circumpolar land, or elongation 
 of the polar axis ; and a maximum of oscillation in level 
 during the central sun's revolution. 
 
 The variation in the obliquity of the ecliptic will be 
 determined by the same law, but the oscillation in the plane 
 
GEOMETRICAL DEMONSTRATIONS. 
 
 of the moon's orbit appears to depend upon the excentric^ 
 attraction of the central sun. See Orbital Motion. 
 
 Another principle is taught by this diagram ; for if the 
 polar axes point to the centre of the celestial polar centre, 
 and not to the centre of the orbit of the centric sun, then 
 the equator of the centric sun would be inclined to its own 
 orbit at all points of its course but those of greatest 
 proximity to and remoteness from the celestial polar centre, 
 this inclination varying in degree, progressively, with its 
 position in space. 
 
 According to the law of projection established in Eccentric 
 and Centric Force and Orbital' Motion, the excentricity of the 
 celestial polar centre in the orbit of the centric sun may be 
 an indication that the path of the centric sun is the result of 
 a single projection, the measure of one act : and therefore 
 the polar axes may all point to the true centre of the celestial 
 polar centre, and cause the variation indicated in even all of 
 the orbits ; but these variations (if existent) are probably not 
 commensurable, and must be distinguished from those recog- 
 nised under observation, with which they would, of course, be 
 blended. 
 
 In every case it is, perhaps, possible that focal excentricity 
 may be a result of the law of projection ; but if this were so, 
 then each revolution would indicate a single subordinate act 
 of projection, and each orbit would be traversed at a velocity 
 which increased with recession from, and diminished with 
 regression towards, the focus of motion. 
 
40 
 
 GEOMETRICAL DEMONSTRATIONS. 
 
 FIG. III. 
 
 Apparent path of the Central Sun round the Zodiac, with the 
 Moon 1 8 perigee a<-<-onip(inyiij, and uhcayx point-in y to the 
 Central Sun. 
 
 Z Z 2 Z 3 Z 4 . The zodiac or sphere of *the fixed stars the 
 circle of comparison to which each revolu- 
 tion in space should be referred. 
 
 C C 8 . The apparent path of the central sun round the 
 
 zodiac on the one hand, and the sun on the 
 other. 
 
 S. The sun, regarded as a relative centre of rest. 
 
 C C 2 . The central sun, at two of the quadratic points 
 
 of its apparent orbit. 
 
GEOMETRICAL DEMONSTRATIONS. 41 
 
 E E 2 . The earth, at two of the quadratic points of its 
 
 orbit. 
 
 M M 2 . The moon in perigee, at two quadratic points of 
 
 its orbit. 
 
 The terrestrial system being at E, with the moon, M, in 
 perigee and conjunction, the sun is at S, and the central 
 sun at C, all of them lying on the line ESC Z Z being the 
 point on the zodiac to which any change in their mutual 
 relations will be referred ; the moon, M, being between the 
 earth, E, and the sun, S, while the central sun, C, is between 
 the sun, S, and the zodiac, Z. 
 
 If the central sun, C, be now supposed to have traversed 
 one quarter of its apparent path, it will be at C 2 , between 
 S and Z 2 , its position in space being marked by Z 2 . During its 
 passage from C to C 2 it will have traversed one quarter of 
 the zodiac, from Z to Z 2 , carrying the moon's perigeal point 
 with it, so that the moon's perigee will have advanced from 
 M to M 2 , also traversing one quarter of the zodiac, from 
 Z to Z 3 ; while, during this double advance of the central 
 sun and the moon's perigee, the terrestrial system will have 
 receded from E to E 2 , so that the moon's perigee is now 
 in opposition, the earth l} T ing between the moon and the 
 sun : and thus the lunar apsides will have described half 
 a revolution with reference to the sun, but only a quarter 
 revolution in space. 
 
 Moreover, the points of the lunar nodes, when the terres- 
 trial system was at E, were Z and Z 3 , or, like the apsides, on 
 a line with the sun and the central sun : they are now found 
 to be Z 2 , and Z 4 , still on a line with the sun and the central 
 sun, but in quadrature with Z and Z 3 , having receded round 
 one quarter of the zodiac, the one node from Z 3 to Z 2 , the 
 other from Z to Z*. 
 
 Further, at E the sun lies between C, the central sun, and 
 E, the terrestrial system, so that here the terrestrial system 
 is in opposition to the central sun ; but at E 2 the terrestrial 
 
42 GEOMETRICAL DEMONSTRATIONS. 
 
 system lies between S, the sun, and C, the central sun, or 
 is in conjunction with the central sun : so that there is an 
 inversion in the relations of conjunction and opposition, 
 under which, when the moon's perigee is in conjunction with 
 the sun, the terrestrial system is in opposition to the central 
 sun ; and when the moon's perigee is in opposition to the sun, 
 the terrestrial system is in conjunction with the central sun. 
 
GEOMETRICAL DEMONSTRATIONS. 
 
 FTG. IV. 
 
 The Revolution of the Lunar Apsides. 
 
 Z Z 3 Z 3 Z 4 . The zodiac, or circle of comparison . 
 
 C. The central sun, regarded as a relative centre 
 
 of rest. 
 S S 2 S 3 S 4 . The sun at. the quadratic points of its orbit. 
 
44 GEOMETRICAL DEMONSTRATIONS. 
 
 E E 2 E 3 E 4 . The relative positions of the earth at the indi- 
 cated positions of the sun in its orbit. 
 m r s v. The orbit of the sun. 
 n u o. The orbit of the earth. 
 
 a e p i. The orbit of the moon. 
 
 a p. The lunar apsides. 
 
 When the sun advances in its orbit, m r a c, from S to S 2 
 the terrestrial system retreats round the ecliptic;, n n o, from 
 E to E 2 , the moon's perigeal point p, on a E j), simultaneously 
 advancing round a e p i, the moon's orbit, to p on a E 2 p, 
 because it always lies between the earth and the central sun. 
 
 At S the moon's perigee is in conjunction with the sun, 
 because the sun now lies between the terrestrial system and 
 the central sun ; and the line Z Z 3 indicates the line of the 
 lunar apsides and the position of the lunar nodes. 
 
 At S 2 , on the other hand, the moon's perigee is in oppo- 
 sition to the sun, because the terrestrial system now lies 
 between the sun and the central sun, the moon's perigee still 
 being between the earth and the central sun; so that, although 
 the sun has only traversed a quarter of its orbit, or passed 
 from S to S 2 , and along the zodiac from Z to Z-, the perigeal 
 point of the moon has passed from conjunction to opposition, 
 or made half of its apparent revolution in advance : but when 
 this apparent semi-revolution is measured on the zodiac, the 
 moon's perigee is found only to have advanced from the 
 line Z Z 3 to the line Z 2 Z 1 , or from Z 3 to Z 4 , between which 
 point on the zodiac and the earth the moon's perigee now 
 lies, so that it has in reality only advanced a quarter revolu- 
 tion in space, the other quarter revolution having resulted 
 from the recession of the terrestrial system or lunar nodes, 
 which now occupy the line Z 2 Z 4 instead of the line Z Z ;{ . 
 
 The apparent path of the central sun, were it visible or 
 recognised (and the advance of the moon's perigee), is shown 
 by the arc of the zodiac, Z 3 Z 4 ; for at E 8 the moon's perigee 
 
GEOMETRICAL DEMONSTRATIONS. 45 
 
 and the central sun lie between E and Z 3 , but at E 2 S 2 they 
 lie between E 2 and Z 4 , having thus traversed one quarter 
 of a circle in space as measured upon the zodiac, so that the 
 actual path of the sun from S to S 2 , or on the zodiac from 
 Z to Z 2 , must give an apparent path to the central sun or 
 lunar perigee from Z 3 to Z 4 . 
 
 The retreat of the node in the same period is shown on the 
 arc Z Z 4 , for at E S the terrestrial system lies between 
 S and Z, but at E 2 S 2 it is between S 2 and Z 4 ; so that the node 
 has made a quarter recession as measured on the zodiac, 
 from Z to Z 4 . 
 
 As the sun continues to advance from S 2 to S 3 , the terrestrial 
 system continues to recede from E 2 to E 3 , while the moon's 
 perigee continues to advance from p on "E 2 to p on E 3 , because 
 it always points to the central sun ; so that at E 3 S 3 the 
 terrestrial system is once more in opposition with the central 
 sun, the moon's perigee in conjunction with the sun : but 
 this happens on the opposite side of the sun's orbit, for the 
 sun has only passed through half of its path, the lunar nodes 
 made only a half circle of recession, and the lunar apsides 
 a half circle of advance ; and yet the moon's perigee during 
 this half circle of advance has passed from conjunction 
 through opposition to conjunction again. 
 
 When the sun passes to S 4 , the terrestrial system recedes 
 to E 4 , when it is again in conjunction with the central sun, 
 the lunar perigee in opposition to the sun, and at S the 
 original relations are restored ; so that while the sun has 
 passed from S through S 2 , S 3 and S 4 back again to S, the 
 terrestrial system or lunar node has receded from Z through 
 Z 4 , Z 3 and Z 2 back again to Z, and the lunar apsides have 
 advanced from Z 3 through Z 4 , Z, and Z 2 back again to Z 3 , or 
 but a single revolution ; and yet during this single revolu- 
 tion the moon's perigee will have passed twice from con- 
 junction through opposition back again to conjunction, or 
 
46 GEOMETRICAL DEMONSTRATIONS. 
 
 made two apparent revolutions when measured from the sun, 
 this apparent discrepancy having been occasioned by mea- 
 suring the revolution of the lunar apsides from the sun 
 instead of from the zodiac. 
 
 Were the central sun a visible body, then the terrestrial 
 apsides would in the same manner describe two revolutions as 
 computed from it, during the single revolution which they 
 actually make round the zodiac. 
 
OCEANIC TIDES. 
 
P E E F A C E. 
 
 IN the following pages an attempt has been made to explain 
 the origin of the tides, upon simple and intelligible, and 
 yet philosophic, principles. The view that the semi-diurnal 
 tide is in reality caused by alternate equatorial and polar 
 waves, originating simultaneously, and yet, from the circum- 
 stances of their genesis, following each other at some twelve 
 hours' interval, approves itself to the mind as having reason- 
 able grounds upon which to rest its claim for acceptance. 
 The further view that the so-called diurnal wave, and the 
 differences in the elevation of the respective semi-diurnal 
 waves, originate in the superposition of direct and reflected 
 waves that irregularities or apparent divergencies from 
 deductions drawn through any hitherto offered theory, 
 whether in the equatorial regions or Pacific Ocean, arise 
 from the relations of the respective coast lines to the direct 
 waves, and the manner in which the direct, the reacting, 
 and the reflected waves cross each other at definite points 
 of their several courses and that the absence of sensible 
 tides is due to the want of an extensive concentrating or 
 reflecting coast, is also a rational one, and deserving of con- 
 sideration : while the conclusion that revulsion, due to the 
 action of the individual gravity of the earth, and called into 
 play by the inherent necessity for preserving its equilibrium 
 
 E 
 
50 PREFACE. 
 
 as a spheroid of revolution, is a powerful agent in deter- 
 mining the synchronism of the regularly observed tidal 
 phenomena, requires only to be pointed out for its import- 
 ance to be recognised. 
 
 At the same time, in giving publicity to his opinions on 
 these and other involved points, the Author is well aware 
 that in some respects they embody generalizations drawn 
 from insufficient data : but on such a subject this was only to 
 be expected, and further investigations will serve to clear 
 up all apparent obscurities and seeming inconsistencies. He 
 does not profess to have devised a perfect theory : he rather 
 claims to have traced principles through the instrumentality 
 of which he hopes that such a theory will be ultimately attain- 
 able ; but the demonstration of true principles, as guides to 
 interpreting observed phenomena, is a very important step ; 
 and this he believes that it will be ultimately recognised that 
 he has accomplished. He now submits the results of his 
 inquiries to the criticism of his readers, that they may be 
 fairly tested, and their true value determined. 
 
 UEREFOKD, March 1865. 
 
OCEANIC TIDES. 
 
 GREAT as has been the advance in scientific investigation 
 of late years, and more especially great, as well as generally 
 successful, the efforts that have been made to bring the 
 results of these investigations, and the laws through which 
 they are explained, to the level of the untrained mind, one 
 branch of science at least can be pointed out which has not 
 kept pace with the general onward movement ; for, while 
 on the one hand those most familiar with the subject admit 
 that the ordinary scientific explanation reaches very few 
 cases,* on the other a popular theory of the tides has yet to 
 be written. 
 
 The general belief, in accordance with the view which is 
 indeed still given in some of the best and latest practical 
 astronomical works, f is that the disturbing body, as the 
 moon or sun, attracts the water on that side of the earth 
 which is the nearest to it more than it attracts the great 
 
 * See Tides and Waves, by G. B. Airy, M.A., F.R.S., Astronomer 
 Royal, par. 14. 
 
 f See A Handbook of Descriptive and Practical Astronomy, by Geo. F. 
 Chambers, F.R.G.S,, p. 149. 
 
 E2 
 
52 OCEANIC TIDES. 
 
 mass of the earth, and therefore tends to raise the water 
 from the earth on the side next to or immediately under 
 it, but that it also attracts the great mass of the earth more 
 than it attracts the water upon the side most distant from 
 itself, and therefore tends to draw the earth from the water 
 on the side most distant from itself : and thus produces exactly 
 the same effect as if a force tended to draw the water away 
 from the earth on that side. So that the disturbing body is 
 held to raise the water on two opposite sides of the earth at 
 the same time, and this by its direct action ; the heaped up 
 waters tending to a line passing through the centre of the 
 earth and that of the disturbing body. 
 
 This theory is probably still offered to the unlearned public 
 because of its simplicity, and because although the greatest 
 mathematicians and the most laborious observers of the 
 present age have agreed equally in rejecting its founda- 
 tions they still compare all their observations with its 
 results, in consequence of the singular agreement of these 
 results with the actual phenomena, to explain which they 
 are applied:* but, at any rate, from whatever motive, it is 
 still put forward, and this is much to be regretted, because 
 the prestige of authority is thus given to the dissemination 
 of error ; for an eminent living astronomer the present 
 Astronomer Royal has said of this theory, f " That it is 
 one of the -most contemptible theories that was ever applied 
 to explain a collection of important physical facts. It is 
 entirely false in its principles, and entirely inapplicable in 
 its results." 
 
 This theory has been called the Equilibrium theory, and 
 it is known by that name, because its results are drawn from 
 the assumed conditions of water at rest. 
 
 Laplace, in his investigations utterly disregarding this 
 
 * See Tides and Waves, par. 64. 
 f See Ibid. 
 
OCEANIC TIDES. 53 
 
 theory, took a different starting-point, and very properly 
 and sagaciously treated the tides as fluid in motion ; but 
 even his investigations, though they are allowed to be one 
 of the most splendid works of the greatest mathematician 
 of the past age, offer for the most part results rather of 
 a negative than of a positive kind ; -for he, at last, took 
 refuge in the assumption that all that we are certain of 
 is, that the disturbances of the seas will be periodical as 
 the forces that cause those disturbances, but that their 
 times of maximum or minimum are not necessarily the 
 same as the times of maximum or minimum of the forces,* 
 which any accurate observer could have told him before he 
 commenced his investigations. 
 
 The present Astronomer Royal, in his elaborate treatise 
 on Tides and Waves, advances a wave theory in explanation 
 of tidal phenomena : but though, in speaking of it, he says 
 that he hopes it will be found that something has been added 
 to the preceding investigations of motion, possessing in some 
 degree a practical character, still he admits that, even in 
 the state in which he leaves it, it reaches very few cases ;f 
 and the impartial examiner of his investigations is reluctantly 
 compelled to admit that this is the case, though it has been 
 said of his theory, that it has entirely superseded every pre- 
 vious theory on the subject, and that it will prove for many 
 years to come the only sound foundation of our knowledge 
 of the theory of the tides. J 
 
 In the course of his investigations, he calls attention to an 
 interesting fact, which, however, might have been predicated 
 from prima facie evidence, that in a tidal river affected by a 
 general current towards the sea, and subject to friction, the 
 low water in the upper part may be higher than the high 
 
 * See Tides and Waves, par. 121. 
 
 f See Ibid., par. 14. 
 
 + See Advertisement to the Encyclopedia of Astronomy. 
 
54 OCEANIC TIDES. 
 
 water near the sea.* This fact is a very important one, as 
 bearing upon the whole subject, for it proves that river tides 
 are derived tides, or true waves, having special laws of their 
 own, which very possibly differ from the laws governing the 
 motions of the great primary or oceanic tides ; so that a 
 theory, drawn from tlie study of the wave current in canals, 
 and thus specially applicable to this form of derived tidal 
 wave, may be inapplicable to, and therefore unfitted for, 
 the interpretation of the laws governing the oceanic tides. 
 
 It is clear, therefore, from the admission of the most 
 recent, as well as confessedly most eminent, authority on the 
 subject, that an adequate scientific theory of oceanic tides is 
 still wanting, and, as a consequence of this, that a popular 
 explanation of them has yet to be written. 
 
 The ordinary tidal phenomena such as the manner in which 
 the most easily observed or semi-diurnal tide, in the progres- 
 sive variations in its periods and range, follows the varying 
 relative positions and inclinations of the moon and the sun 
 are so well known that they need not be dwelt upon here ; for 
 the intimate relations between this tide and the phases of 
 the moon clearly establish the fact that, regarding the tides 
 as evidences of disturbed equilibrium in the earth's fluid 
 particles, the moon and the sun, in their changing relations 
 with the surface of the earth during its axial rotation, are 
 the disturbing bodies. They do more than this, indeed ; for, 
 since in the semi-diurnal tides the influence of the sun only 
 makes itself felt by diminishing the range of the tide during 
 the moon's passage to quadrature, and increasing it again 
 during its return to the syzygies, in a manner that is well 
 understood, the lunar tide is thus learnt to be the only one 
 that, in the north of Europe at any rate, is commonly sensible : 
 and thus it is perceived that the disturbing influence, what- 
 ever may be its nature, chiefly emanates from the moon. 
 
 * See Tides and Wares, pars. 343 and 508. 
 
OCEANIC TIDES. 55 
 
 Under the theory of gravitation, the influence exercised by 
 the disturbing bodies is attributed to the attracting power 
 dependent on, and inherent in, their mass ; and although 
 this view has been disputed by some, even in the present 
 day, it is found to account for and satisfactorily explain a 
 larger series of observed tidal phenomena than any theory 
 that has been proposed in its stead, and therefore will be 
 taken as the basis of the following inductions. 
 
 The preponderating influence of the moon as a disturbing 
 body, is, by the theory of attraction, at once accounted for, 
 since the law of gravity being that its attraction diminishes 
 inversely with the squares of the increasing distance, although 
 the mass of the sun is so much greater than that of the moon, 
 the latter is so much nearer to the earth than the former, 
 that through proximity its disturbing force is rendered the 
 more potent of the two. 
 
 This is the first induction drawn from the theory of gravity. 
 In its application it will presently be found most important, 
 not only in determining the relative strengths of the moon 
 and the sun in their action upon the water of the earth, but 
 actually in limiting the sphere of the action of the moon ; for, 
 it being granted that the nearer the attracting body the 
 greater its attracting influence, it follows that the attracting 
 influence of the earth, referred to its centre, upon the water 
 on its surface, lying between it and the inoon, and therefore 
 exposed equally to the direct influence of both, through 
 acting from only -g^th of the distance through which the 
 moon exercises its power, must be proportionably greater 
 than that of the moon ; so that, when it is remembered 
 that, in addition to this, the mass of the earth vastly pre- 
 ponderates over that of the moon r * it is at once perceived, 
 
 * The mass of the earth being regarded as unity, that of the moon is 
 computed as 0-0114, so that it would take very nearly 88 moons to make 
 one earth, their densities being equal. 
 
56 OCEANIC TIDES. 
 
 and must be unhesitatingly admitted, that the moon cannot 
 heap up the waters of the earth under itself, that is, on 
 a line between its own centre and the centre of the earth ; 
 since, when two similar forces are acting in a similar 
 manner, but in direct antagonism to each other, the action 
 of the weaker force must be controlled by, and subordi- 
 nated to, that of the stronger ; so that a single demonstra- 
 tion, drawn from an extension of the very principle upon 
 which it rests to the phenomena which it has been supposed 
 to explain, at once proves the fallacy of the Equilibrium 
 theory, based as it is upon the view that the water is at 
 rest. 
 
 This being the case and that it is the case can hardly 
 be denied the question now very naturally suggests itself: 
 Since the attraction of the earth is so much stronger upon 
 anything lying on its surface than that of the moon, both 
 through preponderance of mass and proximity, how can the 
 attraction of the moon disturb the equilibrium of the water 
 spread over the surface of the earth? 
 
 Difficult as the problem involved in this question may at 
 first seem, it is in reality susceptible of a very ready and, at 
 the same time, intelligible solution, for all that is necessary 
 is to remember that it is the direct antagonism of the attrac- 
 tions of the earth and the moon that neutralizes the latter ; 
 and since the influence of gravity in each instance radiates 
 as from a centre, this direct antagonism can only exist on the 
 direct line between the centres of the moon and the earth* 
 diminishing rapidly from this to the circumference of the 
 hemisphere of which this right line of direct antagonism 
 may be taken as the centre ;f so that the angular relations of 
 any given point of the surface of this hemisphere to the relative 
 centres of the earth and the moon are very important elements 
 
 * That is, at B in the figure. 
 
 t That is, in passing from B towards A or C in the figure. 
 
OCEANIC TIDES. 57 
 
 in determining the relative strength of the disturbing 
 force that can, at any given time, be exercised by the 
 latter. 
 
 Through this induction the very significant result is gained, 
 that the attraction of the moon, or of any other similarly 
 disturbing body, does not tend to draw the water, spread 
 over the surface of the earth, from its centre, but imparts 
 motion to it, introducing a circulation which commences 
 at the periphery of the disturbed hemisphere, and is 
 directed towards its superficial centre, thus primarily 
 affecting its surface. Hence the lesson is learnt that 
 every attracting disturbing body acts by introducing 
 motion amongst the disturbed fluid particles;* the general 
 tendency of which motion, when unmodified, is, in the first 
 instance, towards the superficial centre of the disturbed 
 hemisphere. 
 
 This view at once introduces an important modification 
 in the otherwise universal law of gravity, for it is now seen 
 that when acting through free space from a remote mass 
 upon the surface of a spherical or spheroidal body whose 
 inherent attraction is opposed to its own on the direct or 
 common line of their mutual attractions, the attraction 
 radiating from the remote mass, which unopposed would 
 diminish with the increase of distance, through the intro- 
 duction of the antagonising similar force against which it is 
 now acting, actually inverts this law, since, as its radiating 
 lines of force diverge from the common line of direct anta- 
 gonism, their disturbing action on the surface of the spherical 
 or spheroidal body increases with their increasing distance 
 from the centre of action. j 
 
 * So that it does not attract vertically from the centre of the disturbed 
 body, but obliquely, in a direction more or less inclined to the surface at 
 the point of attraction, the motive power increasing with the increasing 
 obliquity till the right angle is reached, where a maximum is attained. 
 
58 
 
 OCEANIC TIDES. 
 
 This very important principle can 
 be easily illustrated and established 
 geometrically ; for if A B C be 
 considered to represent the outline 
 of the surface of a disturbed hemi- 
 sphere, E its centre, B its superficial 
 centre, and D the disturbing body, 
 then the right line D E, passing 
 between the centres of the disturbed 
 and the disturbing bodies, will re- 
 present the line of common action 
 or direct antagonism, along which, 
 at B, the disturbing influence of D 
 will be nil; from which point, as 
 the disturbing radius D B increases 
 progressively in length to D A or 
 D C, although the actual quantity 
 of attracting force from D is as 
 progressively diminishing in a geo- 
 metrical ratio to the points A C, on 
 the lines D A, D C, at which points 
 it attains its relative minimum, yet, owing to the ratio of 
 angular inclination between the lines E A and D A, the 
 relations of antagonism, which have been as progressively 
 diminishing from E B to E A, at A are nil] so that the 
 actually weakened force D A has, from being unopposed by 
 the force E at A, attained there its greatest power of 
 expressing itself, and hence acts at A most readily ; through 
 its action, imparting motion along the superficies A B 
 towards B, to any fluid particles subjected to its influence 
 there. 
 
 It follows from this that the disturbing attracting body 
 acts upon the fluid particles of the disturbed body, not by 
 drawing them further (or lifting them) from its centre, but 
 by imparting motion to them round, or, as it might not 
 
OCEANIC TIDES. 59 
 
 inaptly be termed, parallel to, that centre, in a direction 
 towards the central line of common action ; so that the 
 primary source of the tides is motive, not lifting, in its 
 expression, owing to the circumstances under which it is 
 brought into operation.* 
 
 A singular philosophical inference flows from this, no lees 
 than that if the earth and the moon could be regarded as 
 fixed bodies in space, that is, in themselves absolutely mo- 
 tionless, the attraction of the moon would, under these 
 circumstances, introduce motion into the waters of the earth, 
 by drawing them, or causing them to flow, towards that point 
 of the surface of the earth, or rather of the ocean, that was 
 immediately under itself, f 
 
 This purely ideal view of the subject will be found to be 
 of great value in further investigations, for it practically 
 illustrates the origin of the lunar and other similarly caused 
 tides; but though the flow thus produced would, under 
 the imaginary fixed relations that have been indicated, be 
 persistent, it will be convenient to regard it as expressing 
 itself under the form of a succession of waves which, com- 
 mencing from the periphery (circumference) of the dis- 
 turbed hemisphere, would progressively advance as a series 
 of concentric circles, increasing in magnitude (within certain 
 limits) as the}' converged, as well as in the rapidity of their 
 flow ; so that the direction of their flow would be correctly 
 indicated by a series of radiating lines converging in an 
 equal degree upon a central (superficial) point. 
 
 It would appear, at first sight, as though this view were 
 
 * That is, the disturbing force is not cannot be vertical in its action, 
 but oblique, according to the principle that has been laid down. 
 
 f But as the attraction of the earth would prevent the advancing waters 
 from accumulating or heaping themselves up under the moon, a reflux 
 would be originated in the form of under- currents, to preserve the equili- 
 brium of the earth, so that the double attraction would thus introduce a 
 double or to-and-fro motion- -an actual circulation of the waters of the 
 earth. 
 
60 OCEANIC TIDES. 
 
 directly opposed to the principle which has been just laid 
 down, that the attraction of the moon cannot heap up water 
 under itself, since the uncorrected inference would be, that 
 the progressive increase in the magnitude of the waves, 
 as they converged, must necessarily lead to the piling up, 
 or accumulation, of the waters directly under the moon. 
 This, however, has been shown to be impossible : hence, even 
 at this early stage a modification has to be introduced into 
 this primary simple theory; one consistent with, and de- 
 pendent upon, the antagonising causes which are at once 
 originating and controlling the imparted motion. This is to 
 be found in the principle that this progressive increase in 
 magnitude cannot go on beyond a certain point,* which 
 in this supposed fixed, disturbed hemisphere would be in- 
 dicated by a circle drawn some 45 or thereabouts from its 
 periphery. Hence, in this disturbed hemisphere the con- 
 centrating waves would within certain limits progressively 
 increase in magnitude to the 45, at or about which point 
 they would reach their maximum. 
 
 The reason why this should be the case will at once appear, 
 on considering the properties of the assumed sphere, whose 
 surface is supposed to be acted upon by the attraction of 
 a body influencing it from without ; for this attraction, in 
 obedience to the law of gravity, will increase rapidly in 
 strength with the rapidly diminishing distance up to 45 ; 
 but very slightly and slowly from that point, owing to the 
 small amount and gradual nature of the diminution in dis- 
 tance that now takes place ; whereas, the antagonism of the 
 attraction of the disturbed body referred to its centre, which 
 is equal to zero at the periphery, or circumference of the 
 superficies of the disturbed hemisphere, where it is all but 
 
 * Because the centric force of the earth will cause the accumulating 
 waters to subside and flow off in the form of under -currents, whose 
 direction will be towards the point from which the superficial wave 
 started, to supply for the water which rises there, in order to preserve the 
 general equilibrium. 
 
OCEANIC TIDES. 61 
 
 inoperative, will increase very slowly up to 45, owing to 
 the slow variation in the angular relations of the two forces, 
 which are still considerable, but from that point it rapidly 
 increases its power of expressing its action, with the rapidly 
 diminishing angle, to its maximum of entire control at ,the 
 central point, where the angular relations cease in the right 
 line of direct antagonism. 
 
 The consequences of these relations are now intelligible 
 enough ; for while the direct action of the disturbing 
 body, so far almost unopposed, causes the successive tidal 
 waves to flow towards the 45th parallel, where the highest 
 (direct) tide will be gained, the hitherto all but inoperative, 
 but now less perfectly, and gradually less and less opposed, 
 centric action of the earth coming into play diffuses the 
 accumulated waters again, and so prevents the culmination 
 of the tidal wave reaching the central point of the surface 
 of the supposed immoveable hemisphere.* 
 
 Under these imaginary relations the tendencies of the two 
 forces are brought out into bold relief, in order to show that 
 the unmodified action of the disturbing body is to heap up, 
 and the centric action of the disturbed body to diffuse, the 
 tidal wave ; but, tinder the view that has been, so far, 
 examined, the actual phenomena, as observed in nature, 
 have been inverted, the periphery of the disturbed hemi- 
 sphere having been regarded as diffused in its persistent 
 relations, the centre of course as concentrated, and this it 
 is which has created the difficulty in applying the principles 
 that have been indicated to the actual facts which they will 
 presently have to explain. 
 
 The manner in which these artificially constructed diffi- 
 culties disappear, in the actual phenomena that have to be 
 
 * The attraction of the earth at all times tends to diffuse those waves 
 which disturbing action would otherwise accumulate. Hence, direct 
 tidal waves will, by diffusion, be scarcely appreciable in their mensurable 
 range ; a combination of other causes, and especially reflection, being 
 necessary to render them sensible as tides. 
 
62 OCEANIC TIDES. 
 
 interpreted, is very remarkable ; for, impart a rotating motion 
 to the hitherto fixed sphere, or let the earth, as it does in 
 fact, revolve upon its axis, and the diffused periphery of 
 the disturbed hemisphere, hitherto represented by a great 
 circle of the sphere, is at once concentrated into two points, 
 the extremities of the axis of rotation or poles of the earth,* 
 while the hitherto central point, towards which the disturbing 
 body acts, is itself converted into a great circle of the sphere, f 
 This is a remarkable change to have been produced by the 
 simple act of axial revolution, but its consequences will be 
 found yet more remarkable than they probably at first 
 appear. 
 
 They must be examined through the known tenden- 
 cies of the two forces that have been now seen to be 
 in operation. It has been shown that the disturbing body 
 exercises its direct action by introducing motion (or causing 
 a flow of the tide) from the periphery (or circumference) 
 of the hitherto considered fixed hemisphere towards its 
 centre. It has also been shown that the introduction of 
 motion, round an axis of the hitherto stationary sphere, 
 transfers the periphery of the fixed hemisphere, with all 
 the persistent relations and tendencies which attach them- 
 selves to it, to the two extremities of the axis of revolution. 
 
 The first consequence of this is a very remarkable one, 
 for the action of the moon upon the superficial waters of the 
 earth having been proved to be to impart motion to them 
 in a determinate direction, it is now clear that this direction 
 must primarily be from the poles towards the equator ; while 
 the centric force of the earth having been proved to have 
 a tendency to diffuse the accumulating waters over a surface 
 
 * The persistent local relations to the disturbing body are, of course, 
 here referred to. 
 
 t That is, the equatorial regions, so that the introduction of axial rota- 
 tion not only does away with the difficulties involved in the concentrating 
 influence of a disturbing body, but actually diffuses the effects of disturbing 
 attraction. 
 
OCEANIC TIDES. DO 
 
 which may, for facility of description, be termed the equa- 
 torial regions, and forms an extensive belt encircling the 
 earth, it follows, first from the relations of areas, and second 
 from the relations of the 45th parallel, that the motion and 
 range of the tides, when unmodified, will be most sensible 
 in the circumpolar regions, and become necessarily insig- 
 nificant in the equatorial.* 
 
 This diffusing power of the centric action of the earth 
 deserves careful study. It is not immediately destructive 
 to the motion of the waters advancing from the polar regions, 
 but spreads out, or progressively widens, the area of the 
 motion. Hence, in the first instance, the wave initiated in 
 the polar regions will have a radiating character as it ap- 
 proaches the equator ; but the radiation, as will be seen 
 presently, will tend westwards, f 
 
 In consequence of this property of the centric action of the 
 earth, it can and does offer no direct barrier to the advancing 
 waters when they reach the equator ; hence, the tidal wave 
 coming direct from the polar regions and progressively 
 increasing its motion, at least to the 45th parallel, owing to 
 the progressive increase in the strength of the force under 
 which it acts, will, in obedience to the laws of projection 
 and motion, although it reaches the equator as a much 
 thinner wave, not die out there, but pass on into the opposite 
 hemisphere J 
 
 From this tendency the first distinction in the character 
 of the tidal wave is learned ; for it is now found to be direct 
 from the polar regions towards the equatorial, and reactive 
 from the equatorial regions towards the poles. 
 
 * This only applies to the direct tidal waves, and does not affect the 
 actual or observed tides, except in so far as it shows the tendencies of par- 
 ticular regions of the revolving sphere. 
 
 f This tendency will probably hardly show itself till the equatorial 
 regions are approached, since in the temperate regions the tendency in the 
 atmospheric and oceanic currents is eastwards. 
 
 That is, unless obstructed in its course. 
 
64 OCEANIC TIDES. 
 
 It has been shown that the introduction of rotation to 
 the earth concentrates the continuous direct disturbing 
 action of, say the moon, in the polar regions.* This is 
 only strictly accurate when the poles are regarded as points 
 of persistent direct action (which they alone are), for the 
 whole of the hemisphere under the moon is really subject, 
 more or less, to its disturbing influence ; but rotation modifies 
 that influence in this wise : the meridian for the time being 
 under the moon may be considered to divide the moving 
 disturbed hemisphere into two halves, one of which/ the 
 eastern, quoad its angular motion, is opposing and passing 
 away from its direct action moving against it ; while 
 the other is moving with, or in the same line as that 
 direct action expresses itself on the surface of the earth. 
 The consequence of this is, that the rotation of the earth 
 neutralizes, or renders insensible, the direct disturbing 
 action of the moon (quoad wave genesis) westward of the 
 meridian, over which, for the time, it is to be found, and 
 intensifies the sensible expression of that action eastwards 
 of the same meridian. f 
 
 From these remarkable relations, another important phe- 
 nomenon in the history of the genesis of the tidal wave 
 is found, that, in the equatorial regions, the direct action 
 of the moon causes a wave of water to follow it in its 
 apparent course, or pass from the east in a westerly direc- 
 tion. J This wave, though really direct, quoad the action 
 of the moon, can, from its relations to the axial motion 
 of the earth, be very properly termed the receding wave. 
 
 * That is to say, practically reduces its persistent direct power of 
 expressing itself to a minimum of surface ; in reality to two points, the 
 poles. 
 
 t This is self-evident and universally admitted. See Tides and Waves. 
 
 % This wave, judging from its relations to the new and full moon on 
 the eastern equatorial regions of the coasts of Africa and South America, 
 follows the moon at an interval of 4 hours or 60 in distance which 
 represents the angle at which the moon exercises a maximum of disturb- 
 ing force. 
 
OCEANIC TIDES. 65 
 
 The centric force of the earth will tone this wave down, 
 as it does all regular tidal waves in the equatorial regions, 
 causing it to diffuse itself towards the north and south 
 as it passes westwards; thus giving it, as a whole, a ra- 
 diating tendency, those portions which pass off towards 
 the north or the south forming, in reality, reactive waves, 
 similar in character to those already described, though 
 differing in the direction of their origin.* 
 
 The two extremes of the primary modification introduced 
 by the axial motion of the earth into the tidal wave have 
 now been shown. Their leading features deserve careful 
 study, more particularly that, in their directions, they are 
 transverse to each other ; the polar waves primarily flowing 
 with the meridians, or north and south ; the equatorial 
 passing with the parallels of latitude, or in the line of the 
 equator towards the west. But it must be remembered 
 that, from these extremes, as the points of genesis of the 
 wave approach each other (in passing respectively north 
 and south), the direction of motion gradually changes, until, 
 at the mean, it has become parallel each to each, or merged 
 in the same line ; so that (theoretically), regarding the 
 surface of the waters from the moon, the general direction 
 of the lines of motion would be radiating from a point 
 under the moon to the eastern circumference of the visible 
 hemisphere, straight at the equator and the polar extre- 
 mities^ but gradually curving from these towards the mean, 
 with the concavity of the curves on either side of the equator 
 directed towards their respective poles. 
 
 * That is to say, these originate in a wave moving parallel to the equator ; 
 whereas the others proceed from waves moving towards the equator. 
 
 t Straight at the equator, because the motion there is always in the line 
 of attraction straight at the poles, because there the change in direction 
 is the slowest curved at the mean, or 45th parallel, because from the 60th 
 to that parallel the oblique action of the moon is most felt, and therefore 
 the change in direction from the polar meridian to the equatorial parallel 
 most rapid. 
 
 + Because at the poles the moon is always acting in the direction of the 
 
 F 
 
66 OCEANIC TIDES. 
 
 In noticing the transverse relations of the extreme direc- 
 tions of the tendencies of motion of the direct tidal wave 
 at the equator and the poles, it is worthy of remark, that 
 the results reached here are the exact reverse of those 
 previously drawn from theory ; for Professor Airy, in 
 examining Laplace's investigations, says (Tides and Waves, 
 par. 103) : 
 
 " Thus we obtain the result, that at the equator the water 
 moves only north and south, resting for an instant at the 
 change of motion: in every other part of the earth the 
 water is always moving with some velocity; but the cur- 
 rent is perpetually changing its direction. At the poles 
 the velocity is constant, and the direction is always trans- 
 verse to the meridian which passes through the luminary." 
 
 A very little reflection will show that this latter view 
 cannot be correct ; for the direction of the general tendency 
 of the motion must be determined by the length of time 
 that the line of direction of the originating force is actually 
 or comparatively undisturbed. Now, at the equator this 
 force always acts transverse to the meridian, so that the 
 direct tendency there cannot be north and south ; while 
 at the poles the velocity of rotation is so low, as compared 
 to that at the equator, that the direction of the originating 
 force is changed very slowly, so that the tendency of 
 the general direction of the motion (during a short interval 
 of time) will much more nearly approach that of the meri- 
 dians than one transverse to them.* 
 
 meridian over which, it is crossing at the time ; but as the polar waves pass 
 towards the equator, or north and south, the moon in moving to the west 
 draws them after it, seeing that they are becoming relatively to the moon 
 more and more east of it. 
 
 * Instead of following the moon round the pole, as the mathematical 
 theory infers, the wave will advance to the equator, and be emancipated 
 from the power of the moon's attraction as the moon passes the meridian 
 90 from its meridian of genesis (or even sooner) ; hence, from the proximity 
 of the meridians to each other in the polar regions, the scope for curve is 
 very slight in proportion to that for extension. 
 
OCEANIC TIDES. 67 
 
 In considering the general tendency to a mean curvilinear 
 character, in the direction imparted to the moving waters 
 by the axial motion of the earth, another consequence has 
 been incidentally brought out, which must be now more 
 distinctly referred to. The extreme direction of this ten- 
 dency has been shown to be at the poles, primarily north 
 and south, and at the equator invariably westward. Hence 
 the impulse imparted at the poles is primarily north and 
 south; but this impulse is being constantly (and at first 
 even more vigorously*) renewed in a modified direction, so 
 that, as the wave of water passes towards the equator, it is 
 warped towards the west ; this warping if it may be so 
 termed being caused by the axial motion, which is con- 
 stantly changing the direction of the renewed impulse. 
 The consequence of this is, the extremes of direct action 
 being at the equator and the poles, that at the 45th 
 parallel, or thereabouts, a mean is gained; the unmodified 
 direction there (or in the circumpolar regions of which that 
 parallel may be held to represent the centre) being S.W. 
 and KW. respectively. From this mean point, proceeding 
 towards the poles, the polar direction will be progressively 
 increasing, and towards the equator the equatorial. 
 
 Now, this 45th parallel will not only represent a mean 
 point, but a mean area, forming, as it does, the centre of 
 the circumpolar regions. f Hence, at this parallel, three 
 significant relations are combined a mean of area, a mean 
 in direction, and a maximum in height.^ 
 
 * As regards the ratio of increasing strength of the attraction of the 
 disturbing body. 
 
 f The temperate regions are called circumpolar, because of their rela- 
 tions to the polar regions. A designation drawn from geometrical position 
 is perhaps more convenient than one taken from physical relations. 
 
 J This maximum in height refers to the height produced by disturbing 
 attraction : it extends from the 60th to the 45th parallel ; although a 
 maximum relation, it will hardly produce a sensible effect on the observed 
 (or reflected) tides, unless by combining or coinciding with them in some 
 regions or localities. 
 
 F2 
 
68 OCEANIC TIDES. 
 
 Read through, these relations, the first inference is, that 
 in the circumpolar regions the direct tidal wave will attain 
 its greatest elevation or range ; that in the northern hemi- 
 sphere, its mean, unmodified direction will be towards the 
 S.W., and in the southern towards the N."W. ; the westerly 
 direction being, moreover, increased in each instance by 
 the tendency which the waves will have, as they advance 
 towards the equator, to lag behind the rotating surface of 
 the earth.* 
 
 Hence, for convenience of interpretation, and yet with 
 great general accuracy, the mean or circumpolar may be 
 taken as the direction of the direct tidal waves passing 
 from the polar regions towards the equatorial; while in 
 the reacting tidal waves, which pass from the equator 
 towards the poles, this transmitted direction will be con- 
 tinued that is to say, in the northern hemisphere the 
 reacting waves will pass to the N.W., and in the southern 
 to the S.W., or exactly cross the direct waves ; f but here, 
 since the waves are passing from a high to a lower rotating 
 velocity (as regards the earth's axial motion), they will 
 have a tendency to advance upon the rotating earth, or 
 incline eastwards of their direct course.} 
 
 A clear view of the mean direction of the primary or 
 direct tidal wave can now be gathered, according to the 
 
 * In the circumpolar regions, or temperate zones, the tendency is, in 
 reality, to advance upon the rotating motion or pass eastwards, as is seen 
 in the atmospheric and oceanic currents in these regions. Hence the 
 theoretical tendency to lag behind the earth's axial motion cannot come 
 into play until the equatorial regions are approached, where true recession 
 will commence. In waves passing from the equator to the poles the ten- 
 dency to move eastwards will be increased as the wave gradually passes 
 from a higher to a lower rotatory velocity, by its carrying a proportion of 
 the higher velocity with it. 
 
 t It is well known by all observers, that waves cross and re-cross 
 each other in all directions and at all angles, without interfering with each 
 other's course. 
 
 J So that, in the circumpolar regions, they will increase the general 
 tendency to pass eastwards. 
 
OCEANIC TIDES. 69 
 
 parallel through which it is being traced, since it is found 
 to resolve itself into three principal waves, each possessing 
 distinctive characteristics drawn from the position of the 
 region of its genesis. 
 
 1st. The northern direct which passes through the 
 northern circumpolar to the equatorial regions in a S.W. 
 direction, and, crossing the equator, enters the southern 
 hemisphere as a reacting wave ; 
 
 2nd. The southern direct which passes through the 
 southern circumpolar to the equatorial regions in a N.W. 
 direction, and, crossing the equator, continues its course 
 through the northern hemisphere in the same general 
 line, though slightly diminishing its inclination westwards 
 as it advances to the north ; and 
 
 3rd. The equatorial direct, or receding which is found 
 in the equatorial regions, and passes to the west in a direc- 
 tion generally parallel to the equator ; which also sends off 
 reacting waves during its passage, which are radiating in 
 their origin, but more or less inclined, in the northern 
 hemisphere, to the N.W., and in the southern to the S.W.* 
 
 It must be remembered that each of these waves, when 
 taken singly, and in its unmodified form, has, in reality, 
 a comparatively slight range ; f so that even collectively, 
 as will be seen presently, they can be only the primary 
 cause of the observed tides ; the nature of the actual tides is 
 to be learnt from the manner in which these primary waves 
 are modified by combination, and otherwise. Hence the 
 modifying causes of the primary waves have now to be 
 consider ed.J 
 
 * So that the course of the direct tidal wave will be definite for every 
 parallel, and can be determined in any region of the globe by the parallel 
 which it is crossing and the range through which it has already moved. 
 
 f In elevation. 
 
 J Although the direct tides are treated as waves, they are perhaps more 
 correctly periodic currents flowing through the oceans in the directions 
 indicated, and only seem to make themselves sensible as tides by flowing 
 on to an extensive opposed coast line after a long range. 
 
70 OCEANIC TIDES. 
 
 It must be conceded that the primary waves can only 
 be expected to be traced in the ocean, or rather on their 
 flowing on to an oceanic coast, after passing over an 
 extensive and uninterrupted surface of water ; and that, 
 in reality, even here, they have not a sufficient range to 
 make themselves, in all cases, readily sensible in an 
 unmodified form;* indeed, in their purity, they could 
 only be present if the revolving earth were covered with 
 a tolerably uniform and deep layer of water ; under which 
 conditions the ordinary means of detecting them would 
 be wanting, f Hence, theoretically, they can only be used 
 to indicate the direction towards which, at a given point of 
 the earth, the unmodified wave would tend, in order thus 
 to learn how modifying causes can be, and most probably 
 are, brought into play ; but thus used, they will be found 
 to be of very great value. 
 
 It is at once evident that the principal modifying cause is 
 to be found in the configuration of the several continents 
 which form the boundaries of the oceans and seas into 
 which the collected waters of the earth are, for the most 
 part, divided ; which, by opposing obstruction to the free 
 passage of the waves, change the direction of their course, 
 reflecting them, and thus producing a change of motion in 
 another, also determinate, direction. Hence in reflection 
 a form of recoil from an obstructing boundary the true 
 source of a large proportion of the observed tides, and 
 certainly of the observed semi-diurnal tides on the coast 
 of Europe, will be found. 
 
 The general law of reflection that its angle will equal 
 the angle of incidence is well known, and need not be 
 
 * Thus in Europe, unless they aid in forming the tides in the North Sea 
 and on the west coasts of Scotland and Ireland, they have not been 
 observed ; although in the equatorial regions of the east coasts of America 
 and Africa they form the observed tides. 
 
 t Because, under these circumstances, there would be no coasts for them 
 to flow on to or past. 
 
OCEANIC TIDES. 71 
 
 dwelt upon here. Its unmodified expression in the ocean 
 would be this, that if the equatorial plane of the earth 
 could be converted into a solid obstacle to the passage of 
 the waves of water, then in the northern hemisphere that 
 flowing from the N.E. would be reflected to the N.W., 
 and, in the southern hemisphere, that from the S.E. to the 
 S.W. ; while, if a solid meridional plane could be passed 
 through its polar axis, then the receding wave coming 
 from the E. would be reflected back upon itself, or towards 
 the E., while that coming from the ET.E. would be reflected 
 towards the S.E., and that from the S.E. towards the N.E., 
 each variation in angle making itself felt. 
 
 Simple as these laws are, however, in practice, it is very 
 difficult to apply them, owing to the generally irregular 
 form of the several boundaries of the ocean, and owing to 
 modifications in them, caused by friction, on the one hand, 
 and the tendency, determined by the axial motion of the 
 earth, to introduce certain definite currents or lines of 
 direction, on the other. Other causes also will, necessarily, 
 be in operation, such as those which govern the laws of 
 projection under which the waves of water are moving, 
 and determine the application of the secondary forces 
 engaged in producing them; but any reference to these 
 would be widening the field of discussion too much. They 
 must, therefore, be passed over as subordinate to the great 
 primary causes which are at work ; but, perhaps, the most 
 important is to be found in the fact that the reflected water 
 is reflected in a medium of equal density to itself that is, 
 in itself for the reflection takes place in water ; so that 
 when it occurs at an angle, the line of reflection will be 
 more or less curvilinear. Hence the reflection of the tidal 
 wave becomes a special, and even complicated, study ; but, 
 notwithstanding the diificulty of the analysis of the problem 
 involved in this branch of the subject, certain guides can 
 be found of great value : thus, in the circulation of the 
 
72 OCEANIC TIDES. 
 
 atmosphere, it is now a well-known empirical fact that, 
 while in the tropics the prevailing current is from E. to 
 W., owing to the tendency in the fluid particles to lag 
 behind the diurnal motion, in the temperate zones this 
 order is inverted, the current here moving from "W. to E., 
 or advancing on the diurnal motion. This, doubtless, is 
 caused by the earth's axial motion, and most probably 
 depends, at least in part, upon the different actual velocity 
 of rotation at the respective regions indicated ; but, if this 
 is the case and in the present state of knowledge on the 
 subject it can hardly be called in question then the same 
 tendency will be present in the circulating waters of the 
 ocean, and though, owing to the restraining action of the 
 several coast lines, it cannot express itself in the same 
 manner, nevertheless it will be acting as an important 
 modifying cause in the determination of the great oceanic 
 tidal waves. 
 
 In the actual ocean currents, therefore (though these are 
 quite distinct from the tides, and are the expression of the 
 uniform, as the latter are of the varying, circulation of the 
 earth), guides to the true direction of the tidal wave will 
 be found; thus, take for an example the Atlantic Ocean, 
 which, from being the best known, furnishes the most 
 readily intelligible illustration of the principle which it is 
 now sought to establish. In this ocean the equatorial 
 current flows from E. to "W. On reaching the coast of 
 South Am erica it finds, in that coast, a more or less trian- 
 gular or wedge-shaped obstacle, which divides it into two 
 streams, one of which passes towards the Gulf of Mexico, 
 the other towards Cape Horn. The apex of this obstacle, 
 however, is not on the line of the equator, but south of it 
 some 6 or 7. Hence the great mass of the equatorial 
 current will necessarily be directed into the Northern 
 Ocean. This is the stream which has now to be con- 
 sidered. Guided by the general outline of the coast, rather 
 
OCEANIC TIDES. 73 
 
 than reflected from it (the direct reflection being impeded 
 by the pressure of the water outside that which reaches the 
 coast line), it proceeds in a general north-westerly direction 
 past the West Indian Islands (sending oflshoots, or derived 
 currents, on its course into the Caribbean Sea and Gulf of 
 Mexico) to the coast of North America, directed and guided 
 by which, again, and aided by the circulating tendency 
 (eastwards) of the region which it is gaining, it now moves, 
 to the N.E., and, in the form of the Gulf Stream, reaches 
 the coast of Europe, where again, divided by the British 
 Isles, it sends its streams north and south.* 
 
 Under this view, the accuracy of which is hardly 
 questionable, the Atlantic equatorial current and Gulf 
 Stream become a single continuous river in the Ocean, 
 sending out branches and changing its direction according 
 to intelligible laws. But, if this is the case, then the 
 oceanic tides, which only differ from the oceanic currents 
 in being intermitting in their flow, will obey the same 
 laws and tend towards the same direction : thus, supposing 
 the moon to be full on the meridian of Christiania, its action 
 will be vertical in the equatorial regions on the western 
 coast of Africa, so that its disturbing power here will be 
 nil, though in the polar regions it will be in full operation 
 hence the receding equatorial wave has not yet commenced, 
 though the direct polar waves are flowing ; as the equatorial 
 regions pass to the east under the moon,f the receding equa- 
 torial wave will commence its flow, passing to the west, 
 
 * So that the circumstances in which it is called into play on the 
 Atlantic coasts convert the reflecting influence of those coasts into guiding, 
 rather than direct reflecting, media. 
 
 f Many theorists confuse the motion of the moon with its apparent 
 motion. Its actual motion is from west to east, and is the cause of the 
 diurnal variation in the time of the high water of the semi-diurnal tides. 
 Its apparent motion is from east to west, and is a reflection of the axial 
 motion of the earth. Hence the axial motion of the earth is the cause of 
 the crest of the tidal wave lying always to the east of the moon, on the 
 equator, and passing from east to west. 
 
74 OCEANIC TIDES. 
 
 towards the meridian over which the moon is lying, the 
 mean of which will probably be some 45 from that 
 meridian ; the polar waves in the meantime passing 
 north and south respectively, inclining to the W., and 
 then from the circumpolar regions passing respectively 
 N.W. and S.W. Disregarding the origin of these waves, 
 and now looking upon them as simply three waves moving 
 at the same time, the one due W. on the equator, the 
 other N.W. in the South Atlantic, and S.W. in the north 
 What will their several courses be ? 
 
 Studying these through their several directions on the 
 terrestrial globe,* they will be easily followed ; for, first 
 the receding wave, like the great equatorial current, will, 
 on impinging on the wedge-shaped coast of South America, 
 divide into two waves, by far the larger of which will pass 
 into the northern hemisphere, in the track of the Gulf 
 Stream; then the South Atlantic wave (owing to the 
 general inclination of the passage between the two oceans 
 being in the direction of its own course) will pass, almost 
 entirely, as a receding wave, into the North Atlantic, 
 following the equatorial wave ; while the North Atlantic 
 wave, sweeping in a south-westerly curve across the 
 Atlantic, inclining more and more to the west as it 
 approaches the equatorial regions, will be reflected, almost 
 entirely, on the opposite curve back into the northern 
 hemisphere, following the general direction of the equa- 
 torial wave, and therefore accompanying the southern re- 
 acting wave. 
 
 It would thus appear that in the Atlantic Ocean these 
 three waves pass from the equatorial regions into the 
 North Atlantic, where, after flowing round the coast of 
 America and carrying the flood-tide with them, they cross 
 
 * Diagrams are not used, because, from their flat surface, they can be 
 made to give but a very faint idea of the true relations. A terrestrial 
 globe should be referred to by the reader. 
 
OCEANIC TIDES. 75 
 
 the Atlantic, in the direction of the Gulf Stream, and so 
 bring the flood-tide to Europe.* 
 
 If this is the case, then the oceanic co-tidal lines are at 
 once shown to be inaccurate, even in their name, since the 
 same wave cannot reach the west and east coast of the 
 temperate zone of the North American Ocean at the same 
 time. They rather point to the order of succession, and help 
 to measure the time of transit of the tide from the one coast 
 to the other, f 
 
 The general course of the three waves having been thus 
 briefly indicated, their relations to each other have now to 
 be examined, in order, if possible, through these to learn the 
 origin of the North Atlantic semi-diurnal tides ; since their 
 combination, under the views now given, would only account 
 for a single tide in each sidereal day. These relations are 
 to be learnt by considering the relative spaces (linear areas) 
 that have to be passed through by each from their point of 
 genesis to their common point of reflection, determining 
 the period at which the shortest and most direct wave 
 reaches this common point, learning its velocity of motion 
 by computing how long after the transit of the moon over 
 the meridian of this common point it reaches it, and so 
 discovering, approximately, how long it has taken to per- 
 form its thus accurately determined course ; and then, 
 
 * So that the Atlantic tidal wave, as a wave, is equatorial in its origin, 
 and passes round the coast of America, and so across the Atlantic to 
 Europe. 
 
 f The co-tidal lines of the Atlantic have been drawn under the impres- 
 sion that the Atlantic tidal wave is, in each instance, a single wave, which, 
 starting from the Antarctic regions, passes between Africa and South 
 America, simultaneously causing a tide on each of these coasts ; then 
 crosses the equator, and, spreading over the North Atlantic, carries the flood- 
 tide with it to Europe on the one side, and North America on the other. 
 Moreover, they have been adapted to what Professor Airy has styled 
 "the miserable equilibrium theory;" so that even he does not consider 
 them very reliable : indeed, he says, "it is impossible to receive one of 
 Mr. Whewell's speculations on the tides of the Atlantic." See Tides and 
 Waves. 
 
76 OCEANIC TIDES. 
 
 through comparing the actual space traversed in this 
 period with that which has to be traversed by the other 
 waves, in this way to arrive at an approximation of the 
 probable period which these would occupy in passing 
 through their more extended course. In doing this, the 
 first thing to be noticed is that the polar waves, from 
 having the same linear areas to traverse, will occupy the 
 same periods respectively,* and therefore will meet at their 
 common point of reflection, so that in reality the relations 
 of only two waves have to be considered, the equatorial 
 and the polar ; and here, for the first time, the probable 
 origin of the semi-diurnal tide is foreshadowed.f 
 
 Of these two waves, the receding or equatorial, as being 
 the shortest, the least modified, and at the same time the 
 one whose origin can be most readily referred to the position 
 and direct action ^of the moon, which it simply follows, 
 offers the readiest data for the solution of the problem under 
 examination. 
 
 Now, in the Atlantic Ocean, this wave has a determinate 
 distance equal to a mean of some 45 to traverse; for the 
 distance between the continents of Africa and South America 
 say between Cape St. Catherine and Cape St. Eoque 
 is about 45. But 45 are equal to three hours of mean 
 time, as measured by the earth's axial rotation. Hence 
 the moon's period, or the time which it takes in passing 
 from the one continent to the other, is thus found to be 
 three hours. The time occupied by the receding wave can 
 also, and as readily, be learnt; for at the full and new 
 
 * The ovoid figure of the earth will give the southern polar wave a greater 
 surface to traverse than the northern has to pass over ; but on the whole 
 area this difference will be relatively slight, and need not be regarded 
 here. 
 
 f When it has been recognised and admitted that the semi-diurnal tides 
 originate in these waves, it will be further seen that the diurnal tide is 
 caused either by one of these receiving an undue prominence in range, or else 
 from a reflected and a direct wave meeting each other, but not absolutely 
 coinciding. 
 
OCEANIC TIDES. 77 
 
 moon, when the moon crosses the meridian of St. Roque 
 at about two o'clock of Greenwich mean time, the tide is 
 not high at that point till six; so that the receding or 
 equatorial wave does not culminate there till four hours 
 after the moon has crossed the meridian, or seven hours 
 after it left its meridian of genesis at the west coast of 
 Africa.* 
 
 These relations are most important, and deserve very 
 careful study; for through them the Atlantic equatorial 
 regions can be made to the oceanic tides what the base 
 line of a triangle is to its sides in the geometrical measure- 
 ment of distance a starting-point from which to determine 
 their relations to each other. 
 
 The problem sought to be solved is this : admitting that 
 one of the semi-diurnal tides is equatorial in its origin, is 
 it possible that the other is derived from the polar waves? 
 If it is, then the semi-diurnal tides being, speaking in round 
 numbers, about twelve hours apart, the polar tides, starting 
 from the same meridian at the same time, should reach 
 a determinate position on the equator twelve hours after the 
 equatorial wave. Hence, since the Atlantic equatorial wave 
 reaches Cape St. Roque four hours after the moon, then 
 the polar waves should arrive there yet twelve hours later. 
 The issue raised, therefore, is this: Is it probable nay, 
 possible that the polar waves would occupy this time? 
 
 To answer this question with approximate correctness, 
 the meridian of Greenwich offers itself, by position, as the 
 best point of departure in the relative calculations. Now, 
 the meridian of Greenwich is some 35 east of the meridian 
 of Cape St. Roque, or, in round numbers, some two hours in 
 mean Greenwich time ; f but the tidal wave takes six hours to 
 
 * The same ratio is observed on the east coast of Africa, where this 
 tidal wave also follows the moon after an interval of about 4 hours equal 
 to some 60 of longitude. 
 
 f The meridian of Greenwich offers itself as a convenient point of depar- 
 
78 
 
 OCEANIC TIDES. 
 
 traverse this distance, or three times as long as the moon. 
 Then, again, the distance to be traversed by the polar wave 
 is about three times that passed over by the equatorial. 
 It ought, therefore, on a primd fade view, to take thrice 
 the time, or eighteen hours ; and so reach Cape St. Roque 
 some twelve hours after it, which is the interval between 
 the semi-diurnal tides. 
 
 A more careful analysis will only confirm the strict accord 
 between the results determined by observation and required 
 by theory; for the equatorial distance is some 35 (not 30), 
 and therefore represents 2 h 20 m in mean time ; so that six 
 hours is one hour less than thrice that : but then the moon 
 does not commence its action till after it has crossed the 
 meridian, and has reached a commensurate angular distance 
 from it, and then with a minimum of relative attracting 
 force ; and, on the other hand, the curved path of the polar 
 wave is necessarily longer than 90, probably equal to three 
 times 35 or 105 ; so that the polar wave is initiated earlier 
 than the equatorial, and by a maximum, the equatorial 
 beginning later, and with a minimum, of the moon's attrac- 
 tion. Hence, while on the one hand the moon's position 
 renders three times its own time necessary to the motion 
 of the equatorial waters, it on the other causes three times 
 the time to be sufficient for the greater relative linear area 
 traversed by the polar wave, by imparting a higher velocity 
 to that wave as it advances. But beyond this, another very 
 important element revulsion, caused by the action of the 
 gravity of the earth to preserve its individual equilibrium 
 
 ture in this calculation ; but disregarding this, and only considering the 
 geometrical relations of the culminating wave to the meridian over 
 which the moon is passing, the 60 interval represents that point in the 
 angular relations of the relative attractions of the moon and the earth, on 
 the surface of the latter, at which the moon exercises its greatest disturb- 
 ing influence ; so that the crest of the equatorial or receding wave probably 
 always follows the moon at this interval, but yet requires an extensive 
 coast on which to impinge, to make itself sensible in its true relations. 
 
OCEANIC TIDES. 79 
 
 as a spheroid of revolution, and with this the stability of 
 its polar axis aids in generating and maintaining the actual 
 synchronism of the observed tidal waves, and causes an 
 interval in time, equal to half a sphere in linear distance, 
 to intervene between them.* 
 
 If this is the case and that it is the case can hardly 
 be doubted, since no other satisfactory way of accounting 
 for semi-diurnal tides seems to be attainable then it becomes 
 evident that disturbing bodies, acting over the earth's 
 equator, simultaneously initiate two classes of tidal waves 
 equatorial and polar which, starting from a given meridian 
 at the same time, though 90 apart, reach a determinate 
 point on the equator some twelve hours after each other, 
 and are then propagated from the equator towards the poles 
 as the observed tides, following each in the track of the 
 other, with the same interval persisting between them.f 
 
 Some significant results flow from this induction; for, if 
 the polar wave reaches the equator some eighteen hours after 
 the moon has left the meridian from which it started, it 
 follows that when it reaches the equator, though eighteen 
 hours behind the moon in fact, it is six hours in advance of 
 it in position, since the moon will now be on a meridian 90 
 to the east of it. Hence, during the last twelve hours of its 
 course, as a direct wave, it has been unaided by the moon's 
 
 * If the earth, is so poised in space that its northern hemisphere gravi- 
 tates to the north celestial pole, then, under whatever circumstances the 
 tidal waves may originate, the revulsive tendency of the earth, generated 
 by its individual gravity, and indicated by the stability of its polar axis, 
 would cause an interval equal to an hemisphere to intervene between 
 them : as, if a single wave were passing round the globe, or two waves 
 in nearer proximity than 180, the polar axis would oscillate round its 
 centre or vary its position ; this is obviated by the law of revulsion, which, 
 preserving the interval of 180 between them, as shown by the actual 
 synchronism of the tides, causes the one to counterpoise the other, and so 
 maintains the stability of the axis of revolution. 
 
 f The admirable manner in which this arrangement, by preserving the 
 synchronous relations of the tides, aids in maintaining the stability of the 
 earth's polar axis, is obvious. 
 
80 OCEANIC TIDES. 
 
 attraction as it will continue during the remainder of its 
 existence as a wave, since the moon's direct influence, once 
 having ceased, cannot be resumed on that individual wave, 
 which is now subject solely to the laws of projection, reflection, 
 and equilibrium. And hence, when it reaches the coast of 
 England as a reflected wave some twenty-four hours later, 
 although the " establishment of each port" is determined by 
 the then position of the moon, and, owing to the laws governing 
 the earth's equilibrium, can be so computed with exactness, 
 nevertheless the actual wave has no other relations than those 
 determined by the laws of equilibrium to the then position of 
 the moon, seeing that its relations with that body are only 
 and simply these : that it was set in motion by it some two 
 revolutions earlier; so that, although the influence of the 
 moon in determining the tides was primarily learned by the 
 persistent relations of the establishment of the given port to 
 its phases, it is now seen that a just inference was drawn from 
 a mistaken interpretation, itself originating in a coincidence, 
 in which either phenomenon only stood indirectly to the other 
 in the relation of cause and effect. 
 
 Accepting this theory as a probably accurate explanation 
 of the observed tides, many of the hitherto unexplained tidal 
 phenomena will receive a ready solution : thus, the highest 
 spring-tide and the lowest neap would necessarily follow the 
 respective phases of the moon at an interval equivalent to 
 the one recognised under observation, because the wave would 
 occupy that time in moving from its point of genesis round 
 the coast of North America and across the Atlantic. Then 
 the slight range of the tides in the equatorial, as compared 
 with that in the temperate, or circumpolar regions, is intel- 
 ligible ; since the former is a direct or diffused, the latter a 
 reflected, and therefore more or less concentrated, wave. 
 And further, the great range of the derived tides in channels 
 and rivers is accounted for, seeing that it depends upon vary- 
 ing degrees of concentration, and the direction of the mouth 
 
OCEA.NIC TIDES. 81 
 
 and general course, with reference to the special wave from 
 which that under examination is derived. 
 
 The theory of the tides in channels or canals has been 
 already fully discussed by the present Astronomer Royal,* it 
 need not therefore be considered here ; but in examining it, 
 care must be taken in determining from which wave the tide 
 under review has been most probably derived. Thus that in 
 the Amazon will originate alternately in the equatorial and 
 polar direct waves ; that in the St. Lawrence will be a lateral 
 divergence from the great reflected wave moving in the 
 course of the Gulf Stream ; while that in the English and 
 Irish channels, and the Severn, &c., will be the direct 
 expression of this reflected wave. 
 
 In the same manner, the comparative freedom from tides 
 found in the Pacific can be accounted for, since here there is 
 no equivalent for the reflecting continent of South America, 
 the mass of islands found in their course tending rather to 
 break up the direct (diffused) waves ; while the reacting waves, 
 which are also diffused, are able, for the most part, to cross 
 each other, and pass on in their original directions into the 
 opposite hemisphere, until concentration makes them sen- 
 sible. But even here the sources of the derived wave can 
 
 * It is not a little singular that the very basis of Professor Airy's wave 
 theory, drawn from the observation of short waves, is, that in the hollow of 
 the wave, after its crest has passed, the water is retreating, or flowing con- 
 trary to the direction of the wave that is to say, that its stream moves 
 towards the lowest level of the water. In long waves this is not the case, 
 for then, as in the English Channel, the flow continues in the direction of 
 the wave after its crest has passed ; since the water runs up channel some 
 three hours after its height is falling, or until the mean range has been 
 reached. The same holds good of the ebb tide, when the flow continues 
 against the rising water. 
 
 Professor Airy has also left the phenomenon of stationary waves 
 unnoticed, such as those seen in " Races " and the like. These invert the 
 relations of moving waves ; the broken crest, as well as of course the 
 steepest side, being directed towards, or meeting, the flowing water. This 
 condition it is that makes the passage of races dangerous, since the stream 
 carries the vessel into and under the opposed broken water. 
 
82 OCEANIC TIDES. 
 
 generally be indicated as, in the Gulf of California, from 
 the alternate equatorial and South Polar reacting waves 
 from which also the tides in India and the Persian and 
 Arabian Gulfs will be chiefly derived, those in China, Japan, 
 &c., being, probably in part, aided by reflection ;* but 
 indeed, owing to the land being chiefly massed in the 
 northern hemisphere, the diffused Pacific waves have but 
 little facility for concentration, and will, in great part, be 
 equatorial and antarctic in their origin. Even on the east 
 coast of Africa they will probably be rather direct than 
 reflected in their sensible effects, f while on its west coast 
 they will be expressions of the direct antarctic wave.J So 
 little, however, is known of the tides in the Pacific, that 
 no generalization can be made upon them with any degree of 
 reliability, except that its waters are so much more diffused 
 than those of the Atlantic, that diffusion will most probably, 
 unless in exceptional cases, be the principal characteristic of 
 its tides. 
 
 In the north of Europe again, and especially in the North 
 Sea, it is possible that the direct wave coming from the 
 Arctic regions may meet, and apparently combine, with the 
 reflex wave arriving from the coast of North America. || 
 
 * The combinations of the so-called diurnal with the semi-diurnal wave, 
 as at Petropaulovski, which give the semblance of a single tide in the day, 
 will arise from a direct or a reacting wave intervening between two tides, 
 and so preventing one of the low waters by rising as the other is falling. 
 
 f The interval between the passage of the moon across the meridian and 
 the arrival of the crest of the wave some four hours appears to indicate 
 this. 
 
 J Diffused offshoots of it. 
 
 Want of coincidence in the diffused waves and imperfect reflection and 
 concentration are probably the cause of the slight range and seeming irregu- 
 larities of the tides in the Pacific ; accidental, or rather intermitting causes, 
 sometimes leading to the predominance of the one, and sometimes of the 
 other, of the three principal direct waves. 
 
 || What has been termed the diuraal tide is, in reality, a want of exact 
 coincidence in the simultaneously moving waves. Though it is possible 
 that in some regions, or under certain conditions, a revulsive wave may be 
 
OCEANIC TIDES. 83 
 
 If these inductions are true, and they certainly offer a 
 reasonable and probable explanation of the several recognised 
 tidal phenomena, then it must be admitted that, instead of 
 the semi-diurnal tides observed in Europe being alternately a 
 single wave following the moon, or a double one following 
 the moon and sun, they are, -in each instance, a reflected 
 wave, and point to at least six classes of waves as being in 
 operation in producing them. 
 
 1st. The direct diffused waves, passing from the poles 
 towards the equator. 
 
 2nd. The receding a diffused wave, passing westwards in 
 the equatorial regions. 
 
 3rd. The reacting diffused waves, passing from the 
 equator towards the poles. 
 
 4th. The reflected concentrated waves, in the North 
 Atlantic, passing from the east coast of America to the west 
 coast of Europe. 
 
 5th. The derived concentrated waves, passing into the 
 several channels and rivers diverging from the ocean ; and, 
 
 6th. The synchronous or revulsive not distinct waves, but 
 rather a controlling and guiding tendency, imparting a 
 periodicity to any and all of the other waves, in order 
 thus to maintain the equilibrium and general stability of 
 the terrestrial globe in its variable relations. 
 
 But then, again, these six classes of waves are resolvable 
 into two the equatorial and the polar which, as reflected 
 from the equatorial regions, alternately form the semi-diurnal 
 tides recognised under observation on the coasts of, or that 
 diverge from, the North Atlantic Ocean ; so that, if this 
 theory is true, the North Atlantic semi-diurnal tides are 
 derived alternately from diffused waves, originating simul- 
 taneously in the equatorial and polar regions of the earth, 
 which, owing to the conditions and circumstances of their 
 
 generated, to preserve the equilibrium of the earth and the stability of its- 
 polar axis as a spheroid of revolution. 
 
84 OCEANIC TIDES. 
 
 
 
 genesis, reach the north-east coast of South America some 
 twelve hours after each other, and are then reflected, as con- 
 centrated waves, round the east coast of North America and 
 across the Atlantic Ocean to Europe, constituting in this part 
 of their course the observed tides. 
 
 London : Benjamin Pardon, Printer, Paternoster Row. 
 
London, New Burlington Street, 
 April, 1865. 
 
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 Bowman's Practical Chemistry 7 
 
 Do. Medical do. ..7 
 
 Fownes' Manual of Chemistry . . 12 
 
 Do. Actonian Prize .. ..12 
 
 Do. Qualitative Analysis . . 12 
 
 Fresenius' Chemical Analysis. . 12 
 
 Galloway's First Step . . 12 
 
 Do. Second Step ..12 
 
 Do. Analysis .. ..12 
 
 Do. Tables .. ..12 
 
 Griffiths' Four Seasons .. 13 
 
 Horsley's Chem. Philosophy .. 16 
 
 Mulder on the Chemistry of Wine 20 
 
 Plattner& Muspratton Blowpipe22 
 
 Speer's PathoL Chemistry . . 26 
 
 Button's Volumetric Analysis . 27 
 
 CLIMATE. 
 
 Barker on Worthing 4 
 
 Bennet on Mentone 6 
 
 Dalrymple on Egypt 10 
 
 Francis on Change of Climate . . 12 
 
 Hall on Torquay 14 
 
 Haviland on Climate 14 
 
 Lee on Climate 18 
 
 Do. Watering Places of England 18 
 McClelland on Bengal .. ..19 
 McNicoll on Southport .. ..19 
 Martin on Tropical Climates . . 20 
 Moore's Diseases of India . . 20 
 Scoresby-Jackson's Climatology 24 
 Shapter on South Devon . . . . 25 
 
 Siordet on Mentoue 25 
 
 Taylor on Pau and Pyrenees . . 27 
 
 DEFORMITIES, &c. 
 
 Adams on Spinal Curvature . . 3 
 
 Barwell on Clubfoot . . . . 4 
 
 Bigg on Deformities . . . . 6 
 
 Do. on Artificial Limbs . . 6 
 
 Bishop on Deformities . . 6 
 
 Do. Articulate Sounds .. 6 
 
 Brodhurst on Spine . . . . 7 
 
 Do. on Clubfoot . . 7 
 Godfrey on Spine .. ..13 
 
 Hugman on Hip Joint . . 16 
 
 Taniplin on Spine . . . . 27 
 
 & SOTS' CAIA18CT1. 
 
 DISEASES OF WOMEN 
 
 AND CHILDREN. PAOK 
 Ballard on Infants and Mothers 4 
 Bennet on Uterus ...... 6 
 
 Do. on Uterine Pathology.. 6 
 Bird on Children ...... 7 
 
 Bryant's Surgical Diseases of 
 
 Children .......... 7 
 
 Eyre's Practical Remarks ..11 
 Harrison on Children .. ..14 
 
 Hood on Scarlet Fever, &c. ... 16 
 
 Kiwisch (ed. by Clay) on Ovaries 9 
 Lee's Ovarian <fc Uterine Diseases 18 
 
 Do. on Diseases of Uterus 
 Do. on Speculum 
 Seymour on Ovaria 
 Smith on Leucorrhcea . . 
 Tilt on Uterine Inflammation 
 Do. Uterine Therapeutics 
 Do. on Change of Life . . 
 Underwood on Children . . 
 Wells on the Ovaries 
 West on Women 
 
 Do. (Uvedale) on Puerperal 
 Diseases 30 
 
 GENERATIVE ORGANS, 
 
 Diseases of, and SYPHILIS. 
 
 Acton on Reproductive Organs 3 
 Coote on Syphilis . ..10 
 
 Gant on Bladder.. . ..13 
 
 Hutchinson on Inherited Syphilis 1 6 
 Judd on Syphilis . . . 17 
 
 Lee on Syphilis .. ... 18 
 
 Parker on Syphilis . ..21 
 
 Wilson on Syphilis . ..31 
 
 HYGIENE. 
 
 Armstrong on Naval Hygiene 4 
 Beale's Laws of Health . . . . 5 
 
 Do. Health and Disease . . 5 
 
 Bennet on Nutrition 6 
 
 Carter on Training 8 
 
 Chavasse's Advice to a Mother . . 9 
 Do. Advice to a Wife . . 9 
 Dobell's Germs and Vestiges of 
 
 Disease 11 
 
 Do. Diet and Regimen ..11 
 
 Granville on Vichy 13 
 
 Hartwig on Sea Bathing . . . . 14 
 
 Do. Physical Education 14 
 
 Hufeland's Art of prolonging Life 16 
 
 Lee's Baths of Germany 
 Moore's Health in Tropics 
 Parkes on Hygiene . . . 
 Parkin on Disease . . 
 Pickford on Hygiene 
 Robertson on Diet . . 
 Routh on Infant Feeding . 
 Rumsey's State Medicine . 
 TnnstalPs Bath Waters 
 
 Wells' Seamen's Medicine Chest 30 
 Wife's Domain 
 
 Wilson on Healthy Skin 
 
 31 
 
 Do. 
 Do. 
 
 on Mineral Waters .. 31 
 on Turkish Bath . . . . 31 
 
 MATERIAMEDICA and 
 
 PHARMACY. 
 
 Baseman's Magnacopia . . . . 5 
 
 Beasley's Formulary . . . . , . 5 
 
 t>o. Receipt Book .. .. 5 
 
 Div, Book of Prescriptions 5 
 
 Frazer*s Materia Medica . . .. 12 
 
 Nevins' Analysis of Pharmacop. 20 
 
 Pereira's Selecta e Praescriptis 21 
 
 MATERIA MEDICA and 
 PHARMACY continued. 
 
 fAOE 
 
 Pharmacopeia Londinensis . . 22 
 Prescriber's Pharmacopoeia . . 22 ^ 
 Royle's Materia Medica .. ..24 
 Squire's Hospital Pharmacopeias 26 ... 
 Do. Companion to the Phar- 
 macopeia 26 
 
 Steggall's First Lines for Che- 
 mists and Druggists . . . . 26 
 Stowe's Toxicological Chart . . 27 
 
 Taylor on Poisons 27 
 
 Waring's Therapeutics . . . . 29 
 Wittstein's Pharmacy .. ..31 
 
 M1EDICINE. 
 
 Adams on Rheumatic Gout ; . 3 
 Addison on Cell Therapeutics . . 3 
 Do. on Healthy and Dis- 
 eased Structure 3 
 
 Aldis's Hospital Practice . . . . 3 
 
 Anderson on Fever 4 
 
 Austin on Paralysis 4 
 
 Barclay on Medical Diagnosis . . 4 
 Barlow's Practice of Medicine 4 
 
 Basham on Dropsy 5 
 
 Brinton on Stomach 7 
 
 Do. on Ulcer of do 7 
 
 Budd on the Liver 8 
 
 Do. on Stomach 8 
 
 Camplin on Diabetes 8 
 
 Chambers on Digestion . . . . 8 
 
 Do. Lectures 8 
 
 Davey's Ganglionic Nervous 
 
 System 11 
 
 Eyre on Stomach 11 
 
 French on Cholera 12 
 
 Fuller on Rheumatism .. .. 12 
 
 Gairdner on Gout 12 
 
 Gibb on Throat 13 
 
 Granville on Sudden Death .. 13 
 
 Gully's Simple Treatment .. 13 
 
 Habershon on the Abdomen .. 13 
 
 Do. on Mercury .. ..13 
 
 Hall (Marshall) on Apnoea .. 14 
 
 Do. Observations .. 14 
 
 Headland Action of Medicines 14 
 
 Hooper's Physician's Vade- 
 
 Mecum 13 
 
 Inman's New Theory .. ..16 
 
 Do. Myalgia 16 
 
 James on Laryngoscope .. .. 17 
 Maclachlan on Advanced Life . . 19 
 Marcet on Chronic Alcoholism . 19 
 Meryon on Paralysis . . . . 20 
 
 Pavy on Diabetes 21 
 
 Peacock on Influenza .. ..21 
 Peet's Principles and Practice 
 
 ofMedicine 21 
 
 Richardson's Asclepiad . . . . 23 
 
 Roberts on Palsy 23 
 
 Robertson on Gout 24 
 
 Savory's Compendium . . . . 24 
 
 Semple on Cough 24 
 
 Seymour on Dropsy 25 
 
 Shaw's Remembrancer .. ..25 
 
 Smee on Debility 25 
 
 Thomas' Practice of Physic .. 27 
 Thudichum on Gall Stones . . 28 
 Todd's Clinical Lectures . . . . 28 
 Tweedie on Continued Fevers 29 
 Walker on Diphtheria .. ..29 
 
 Wells on Gout 30 
 
 What to Observe at the Bedside 1 9 
 
 Williams' Principles 30 
 
 | Wright on Headaches . . . . 31 
 
CLASSIFIED INDEX. 
 
 MICEOSCOPE. 
 
 PAGE 
 
 " Beale on Microscope in Medicine 5 
 Carpenter on Microscope . . . . 8 
 Schacht on do 24 
 
 MISCELLANEOUS. 
 
 Acton on Prostitution 
 Barclay's Medical Errors . . , 
 Bascoine on Epidemics 
 
 Bryce on Sebastopol 
 
 Cooley's Cyclopaedia 
 
 Gordon on China 13 
 
 Graves' Physiology and Medicine 13 
 
 Guy's Hospital Reports 
 Harrison on Lead in Water . 
 Hingeston's Topics of the Day. 
 
 Lane's Hydropathy 
 
 Lee on Homo30p. and Hydrop. 
 London Hospital Reports.. . 
 
 Marcet on Food 
 
 Massy on Recruits 
 
 Mayne's Medical Vocabulary . . 20 
 
 Part's Case Book 21 
 
 Redwood's Supplement to Phar- 
 macopoeia 23 
 
 Ryan on Infanticide 24 
 
 Snow on Chloroform. . 
 Steggall's Medical Manual 
 
 M 
 
 26 
 Do. Gregory's Conspectus 26 
 
 Do. Celsus 26 
 
 Whitehead on Transmission . . 30 
 
 NEEVOUS DISOEDEES 
 AND INDIGESTION. 
 
 Birch on Constipation . . . . 6 
 
 Carter on Hysteria 8 
 
 Downing on Neuralgia .. ..11 
 
 Hunt on Heartburn 16 
 
 Jones (Handneld) on Functional 
 
 Nervous Disorders 17 
 
 Leared on Imperfect Digestion 18 
 Lobb on Nervous Affections . . 19 
 Radcliffe on Epilepsy . . . 22 
 Reynolds on the Brain . . . 23 
 Do. on Epilepsy . . . 23 
 Rowe on- Nervous Diseases .. 24 
 Sieveking on Epilepsy . . . 25 
 Turnbull on Stomach . . 28 
 
 OBSTETRICS. 
 
 Barnes on Placenta Prsevia . . 4 
 Hodges on PuerperalConvulsions 15 
 Lee's Clinical Midwifery .. .. 18 
 
 Do. Consultations 18 
 
 Leisliman's Mechanism of Par- 
 turition 18 
 
 Mackenzie on PhlegmasiaDolens 19 
 Pretty's Aids during Labour . . 22 
 Priestley on Gravid Uterus . . 22 
 Ramsbotham's Obstetrics . . . . 23 
 Do. Midwifery.. .. 23 
 
 Sinclair & Johnston's Midwifery 25 
 Smellie's Obstetric Plates. . . . 25 
 Smith's Manual of Obstetrics . . 26 
 
 Swayne's Aphorisms 27 
 
 Waller's Midwifery 29 
 
 OPHTHALMOLOGY. 
 
 Cooper on Injuries of Eye . 9 
 
 Do. on Near Sight ... 9 
 
 Dalrymple on Eye 10 
 
 Dixon on the Eye 11 
 
 on Ophthalmoscope . 15 
 
 ouse on Strabismus . . . 15 
 
 on Impaired Vision 15 
 
 OPHTHALMOLOGY-^/"- 
 
 Hulke on the Ophthalmoscope 
 
 Jacob on Eye-ball 
 
 Jago on Entoptics 
 
 Jones' Ophthalmic Medicine . 
 | Do. Defects of Sight . . . 
 
 Do. Eye and Ear 
 
 Xunneley on the Organs of Vision 21 
 
 Walton on the Eye 29 
 
 Wells on Spectacles 30 
 
 PHYSIOLOGY. 
 
 Carpenter's Human 8 
 
 Do. Comparative . . . . 8 
 
 Do. Manual 8 
 
 Heale on Vital Causes .. ..14 
 O'Reilly on the Nervous System 2 1 
 Richardson on Coagulation . . 23 
 
 Shea's Animal Physiology 25 
 
 Virchow's (ed. by Chance) Cel- 
 lular Pathology 8 
 
 PSYCHOLOGY. 
 
 Arlidge on the State of Lunacy. 4 
 Bucknill and Tuke's Psycholo- 
 gical Medicine 8 
 
 Conolly on Asylums 9 
 
 Davey on Nature of Insanity . . 11 
 Dunn's Physiological Psychology 1 1 
 Hood on Criminal Lunatics .. 16 
 Millingen on Treatment of Insane 20 
 
 Noble on Mind 21 
 
 Williams (J. H.) Unsoundness of 
 Mind 30 
 
 PULMONAEY and CHEST 
 
 DISEASES, &c. 
 Alison on Pulmonary Consump- 
 tion 3 
 
 Billing on Lungs and Heart 6 
 
 Bright on the Chest .... 7 
 
 Cotton on Consumption .. 10 
 
 Do. on Stethoscope . . 10 
 
 Davies on Lungs and Heart 10 
 
 Dobell on the Chest . . . . 11 
 
 Fenwick on Consumption . . 11 
 
 Fuller on Chest 12 
 
 Do. on Heart 12 
 
 Jones (Jas.) on Consumption 17 
 
 Laennec on Auscultation . . 18 
 
 Markham on Heart . . . . 20 
 
 Richardson on Consumption 23 
 
 Salter on Asthma . . . . 24 
 
 Skoda on Auscultation . . 20 
 
 Thompson on Consumption 27 
 
 Timms on Consumption . . 28 
 
 Turnbull on Consumption 28 
 
 Waters on Emphysema . . 29 
 
 Weber on Auscultation . . 29 
 
 EENAL and UEINAEY 
 DISEASES. 
 
 Acton on Urinary Organs . . 3 
 
 Beale on Urine 5 
 
 Bird's Urinary Deposits . . . 6 
 
 Coulson on Bladder 10 
 
 Hassall on Urine 14 
 
 Parkes on Urine 21 
 
 Thudichum on Urine . . . 28 
 
 Todd on Urinary Organs . . . 28 
 
 SCIENCE. 
 
 Baxter on Organic Polarity . . 5 
 
 Bentley's Manual of Botany . . 6 
 
 Bird's Natural Philosophy . . 6 
 
 SCIENCE continued. 
 
 PAOK 
 
 Craig on Electric Tension . . 10 
 Hardwich's Photography.. .. 14 
 
 Hinds' Harmonies 15 
 
 Howard on the Clouds .. ..16 
 
 Jones on Vision 17 
 
 Do. on Body, Sense, and Mind 17 
 
 Mayne's Lexicon 20 
 
 Pratt's Genealogy of Creation . . 22 
 Do. Eccentric* Centric Force 22 
 Do. on Orbital Motion . . . . 22 
 Price's Photographic Manipula- 
 tion 22 
 
 Rainey on Shells 23 
 
 Reymond's Animal Electricity 23 
 Taylor's Medical Jurisprudence 27 
 Unger's Botanical Letters . . 29 
 Vestiges of Creation 29 
 
 SUEGEEY. 
 
 Adams on Reparation of Tendons 3 
 
 Do. Subcutaneous Surgery 3 
 Anderson on the Skin . . . . 3 
 
 Ashton on Rectum 4 
 
 Barwell on Diseases of Joints . . 4 
 Brodhurst on Anchylosis . . . . 7 
 Bryant on Diseases of Joints . . 7 
 
 Callender on Rupture 8 
 
 Chapman on Ulcers 9 
 
 Do. Varicose Veins . . . . 9 
 Clark's Outlines of Surgery . . 9 
 
 Collis on Cancer 9 
 
 Cooper (Sir A.) onTestis .. .. 10 
 
 Da (S.) Surg. Dictionary 10 
 Coulson on Lithotomy .. ..10 
 Curling on Rectum 10 
 
 Do. onTestis 10 
 
 Druitt's Surgeon's Vadc-Mecum 11 
 
 Ferguson's Surgery 11 
 
 Gant's Principles ot Surgery .. 13 
 Heath's Minor Surgery and 
 
 Bandaging 15 
 
 Higginbottom on Nitrate of Silver 15 
 
 Hodgson on Prostate 15 
 
 Holt on Stricture 15 
 
 James on Hernia 17 
 
 Jordan's Clinical Surgery .. 17 
 
 Lawrence's Surgery 18 
 
 Do. Ruptures 18 
 
 Liston's Surgery 18 
 
 Logan on Skin Diseases .. ..19 
 
 Macleod's Surgical Diagnosis . . 19 
 
 Do. Surgery of the Crimea 19 
 
 Maclise on Fractures 1! 
 
 Maunder's Operative Surgery . . 20 
 Nunneley on Erysipelas . . ..21 
 
 Pirrie's Surgery 22 
 
 Savage's Female Pelvic Organs 24 
 Smith (Hy.) on Stricture .. ..25 
 
 Do. on Haemorrhoids . . . . 25 
 
 Do. (Dr. J.) Dental Anatomy 
 
 and Surgery 26 
 
 Squire on Skin Diseases : . . 26 
 Steggall's Surgical Manual . . 26 
 Teale on Amputation . . . . 27 
 Thompson on Stricture . . . . 27 
 
 Do. on Prostate . . . . 27 
 
 Do. Lithotomy and Lithotrity 27 
 Tomes' Dental Surgery . . . . 28 
 
 Toynbee on Ear 28 
 
 Wade on Stricture 2'j 
 
 Watson on the Larynx . . . . 29 
 Webb's Surgeon's Ready Rules 29 
 Williamson on Military Surgery 30 
 Do. on Gunshot Injuries 30 
 Wilson on Skin Diseases . . . . 31 
 
 Do. Portraits of Skin Diseases 31 
 Yearsley on Deafness .. ..31 
 
 Do. on Throat 31 
 
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