TECHNICAL EDUCATION OF THE PEOPLE IN UNTEGHNICAL LANGUAGE. JRead before Section III, Moyql Society of Canada, May 1894^ by a baillaimgA While the Eoyal Society of Canada, like its pro- totype of England, cannot descend to the education of the masses of mankind; it behoves It, though, as occasion may offer, to be suggestive of any impro- ved mode of doing so. Persons not destined to become scientists, pro- fessors or even professional men or women, must nevertheless be educated to an intelligence of the phenomena of life ; and it cannot be derogatory to the dignity of a society like this, to point out how it can be done without resorting to what is termed technology or technical tuition in the true sense of the word. ** Tyndall, says Spencer, possessed this faculty in a high degree. This constructive imagination, says he— for we are not concerned with mere remi- niscent imagination— here resulting in the creations of the poet and there in the discoveries of the man — 2 — of science, is the highest of human faculties. In common with successful investi^^'^tors in general, he displayed it in forming the conception of physical processes previously misinterpreted or uninterpreted ; and again in conceiving modes by which the actual relations of the phenomena could be demonstrated ; and again in divising fit appliances to this end. But to a much greater extent than usual, he displayed constructive ima2:ination in other fields. He was an exce.lent expositor, and good exposition implies much constructive imaginaiion. A prerequisite is the forming of true ideas of the mental states of those who are to be taught ; and a further prerequisite is the imagining of methods, by which, beginning with conceptions they possess, there may be built up in their minds the conceptions they do not possess. Of constructive imagination as displnyed in this sphere, men at large appear to be almost devoid ; as witness the absurd systems of teaching which in past tinies, and in large measure at present, have stupefied and still stupefy children, by presenting abstract ideas before they have any coucrete ideas from which they can be drawn. Whether as lecturer or writer profes- sor Tyndall carefully avoided this vicious practice. Mankind at large has a desire to understand the every -day lising of the sim and going d'jwn of the same, the phases of the moon, the wherefore of the t^des, the origtli of rivers and their ceaseless flow ; the s-hape, size, formation of the earth and how its component rocks, itscoa', its minerals have come to Le. It is not necessary he should be told how our — 3 — system is supposed to have been brought about by an aggregation of cosmic matter, or that Karth and Sun and planets are travelling together toward the cunstei ation Hercules; but it is pertinent for him to know something about his own make-up cr constitu- tion : his osseous, nuiscular, nervous, digestive, vascu- lar, venous and arterial systems ; that he may understand his ailings and n.inister to his require- ments. He must be made acquainted with the composi- tion and whereabouts of the component materials of his calling as of those of others. A knowledge of stone and wood comes to him of itself, he being in contact with them from earliest childhood ; but not so of glass, brick, delf, lime, paper, leather, cotton silk, etc. ; while wool may be surmised from being seen hanging to the very sheep it comes from, as feathers from birds, furs from our domestic animals ; and even woven fabrics may be guessed at, as to how and of what made up ; by noticin^j the component separate threads, interlacing with each other like the wicker work of a basket. The object lessons of the Kindergarten are ne- cessary at all ages : blocks to build up varied forms, balls and marbles to teach aL\tion and reaction, the angle of reflection equal to that of incidence, the pa- rallelogram of forces. Refraction can be tau^iht in a tea-cup j or when at play, illustrated by a stick thiust into a well or pond or river. There need be no technical terms made use of to illustrate the centre of gravity or how it is Ibund, — 4 - It is for the man of science to point out, suggest to the ordinary teacher how object lessons are to be imparted for the tuition of the million. Two men bearing on their shoulders, a log or other object larg- er at one end than the other, may think and some- times do, that each bears half the weight ; but let them lay it down and lift one end of it and then the other, as of a tapering spar, when they will be quick to see the difference and ihen take turns at shoulder- ing opposite extremities. Let any man be asked to cut into parts of equal cubical contents, a crooked or tapering stick of tim- ber, as a sawlog, or find the centre of gravity or bal- lancing point of a gun ; he may not readily think of or hit upon the plan of balancing it on a pivot, as you would a spoon or fork on the edge of a knife if required to divide it into parts of equal weight. | It is for the man of science, the technologist to reduce these things to writing, that the teacher in the kindergarten, the giver of the object lesson may know what to do and how to impart the know- ledge. In very many things, technical tuition by the man of science is not required. The teacher can him- self read up and see and tell how brick and delf and pottery and glass are made, and impart the know- ledge direct to the pupil ; and better still, he should see it done and take the student where he may see it also. He can explain how cotton grows and where and how made into thread and web, or warp and woof and tissue. He can tell how silk is spun and "what the silk worm feeds on ; how leather is of tan- ned hides and how made into boots and shoes ; how logs are cut into boards and made up into huts and houses and into furniture ; how glass is blown into bottle ibrm or cyUnder, the ends cut off, the cylinder split open, flattened ouf into sheets; how plate glass is cast and rolled and polished ; how the metals, like glass can be fused, run into molds; how paper is made up of rags and how rolled into sheets and again how type is put together into words and lines and pages and printed on the paper and made into books. He can tell his pupils where coal comes from and that it is not a manufactured article, or not made up by man, but formed in Earth's laboratories by na- tural elaboration and the lapse of ages ; how lime is made of stone by baking it and thus driving off its carbonic acid gas component. f ^ He can tell, explain a thousand things, ten thou" sand without the aid of the technologist ; but can he tell how the coal came there, of what it is composed ? No ! he must here take his clue from the geologist who will tell him of the woods and forests or plant life of the earth, of its waters, of how the waters are evaporated into clouds and wafted by the winds to colder mountain heights, where the vapor is condens- ed again and falls as rain, runs off in to rills and rivu- lets and rivers, carrying with it earth and sands dis- integrated from the parent rock by wind and wet and fiost and other agencies ; how these have form- ed deposits which ages and pressure and chemical ac- tion have hardened into stone. _6- Let the geologist write up in ordinary phraseo- logy the history of the world : that is, a nn*re sy- nopsis of it, or as much of it only as is i equin d to be known or can be taken in, retained by men who have had no classical education, cannot afford it or have no time for it even if they could ; so much as a man, a farmer or mechanic or intelligent laborer should know or is desiious of knowing, that he nay uot be or appear to others absolutely ignorant of the c>ur- rounding world. ; ^^ - r ^ * ^^ We need not go back to the very chaos of Gene- sis ; but s:art with the supposition that Earth was made a molten globe with vapor all around it, con- densins: inio water as the crust cooled down into what we now call granite. Our every-day fellow man can understand this and how the inner work- ings of the material in fusion, have done on a gran- der scale what vo canoes and earthquakes are still doing in a diminished way ; to wit : have thrown the crust or rind of the earth into humps and ridges; precisely as the crust upon a pie is upheaved into hummocks, fumeroles by the action of the imprisoned steam beneath. ; The waters of the earth will now have settled into the hollows, forming seas and lakes and oceans, and have lelt dry the portruding continents and islands. The unequal surface velocity of rotation at and near the equator and in higher latitudes, and the action of the sun, will have caused winds, the winds waves, the waves disintegration of the coasts; and that, with the detritus brought down by river-^ fr om the heights lo wieh th-j wind driven evaporation from the waters has ascended, the super etrata or hiyers above the granite. Forests now appear and let it b 3 by the fiat of the Creator. They grow for ages, luxuriant in heat and carbonic acid gas until soin3 cataclysn, sJine mighty cyclone, niny-be, fells them to the earth, and there they lie and rot and are elaborated into peat and lignite and finally into coal, or may-be the pro- cess of transformation is not as yet complete when by surface subsidence the strata 2:0 beneath the waters ; and are in time covered by other sedimen- tary depjsits, in their turn to become, as before, hardened into stone. '^f^ The surface is upheaved again and other fo- rests formed whit-h again in turn are elaborated into coal and so on through countless ages forming al- ternate layers of coal and stone for man's future re- quirements. - And when the waters have sufficiently cooled down, they are peopled with moUusca; later on with fish, the mammoth whale and some other mammalia ; the air with winged life, the land with quadrupeds, etc, until finally man appears upon the earth and finds every thing provided for his existence : his nourishment in its surface soil, its fish and fowl and other animal food ; wood for constructive purposes, and stone ; coal for fuel in its bowels ; and in its veins and fissures gold and silver, copper, ores of iron and other meta's and some of them found native ; the — 8 — skins and furs of animals to cloth his nakedness, and preserve his bodily heat, and a benign creator to care for all his needs. Nor will our pupil be slow at understanding how, if w^e can not tell the absolute length of life of mountain chains, there relative ages may be pro- cinimed by a study of the nature and number of the non conformant strata lying at their bases; while the relation of these strata to each other in regard to priority of formation is evidenced by the progres- sive or gradual transition from the first, the lowest forms of life, to the higher and more perfect forms found imbedded in the strata; and an examination of existing glaciers and of their moraines will leave no doubt in the man's mind as to how the great ' erratics, the monstrous bowlders to be met with in our latitudes, have been torn from the mountain summits to the North of us, and moved southward by the rivers of plastic slowly flowing ice of the so called glacial epoch, as evidenced by their abraded sur- faces and rounded angles, the striaB along their route ; and as the author is witness to every year, by bowld- ers from (-arouge and higher up the St. Lawrence which become frozen in the under surface of the batture or shore ice and several of which have been thus transported and dropped on the very beach op[;osite his country residence, som 20 miles below and some of these again taken up and moved still further by a similar or analogue process. The astronomer now steps in and in a concise and plainly written form, instructs the ti acher how — 9 — to explain the motion of the earth upon its axis and around the sun, making use of some such simile as that of a bycicle coursing around a circular path with something in the centre illustrative of the sun — a gas or an electric light for instance, making the simile more natural — where the progressive motion of the cycle is illustrative of that of the planet around its pri- mary, its motion in a twelve months ; the revolution of the larger wheel, the earths' rotation on its axis, its daily motion ; while the small or stearing wheel may represent the satellite or moon accompanying the earth, revolving also as it goes ; and on account of the diifering. velocities of the two wheels around their respective axes, the larger thus successively presenting every portion of its periphery to the smaller, producing the effect of the moan's rotation about the earth. But this revolution of the earth about its axi^ may be ocularly demonstrated in an hour or less by a rehearsal on a smaller scale of Foucault's experiment of the pendulum in the Pantheon, and which the wri- ter often had occasion to repeat when giving lessons to his pupils in engineering and surveying, to wit : by suspending an iron or a billard ball or any other, by a string to a nail or hook in the ceiling of his studio, starting it to oscillate, say in a direction pa- rallel to one side of the room or apartment, or to one of the component flooring boards or ceiling battens, or to a line or straight edge on a table beneath the ball ; when it will be noticed that in less than one hour, in fact, in the fraction of an hour a consider- — 10 — able v«iriation in the direction of the swi-iging plane has taken place ; and, that the rotation or twisting of the suspending string does not affoct the direction of the plane of oscillation may be seen in a few se- conds by any one holding up his watch by the end of the chain, causing the watch to oscillate as the pen- dulum of a clock, while at the same time twisting the chain around between his fingers. Or, and hs he has also often done himself in lec- turing on astronomy to his students : let there be npon a stand in the centre of a room' a candle, lamp or other source of light and let this be the sun ; then through the shorter diameter of an apple or an orange or through and through the stem or axis thrust a knitting needle, or the handle of a pen, incline it as required to the angle of elevation of the pole and holding it constantly parallel to that direction, or pointing to the pole of the heavens or supposed to be, walk around the luminary with this simile of the earth, rotating it the while in your lingers, around its axis, and you illustrate in this way day tind night at any one point: their equality at the equinoxes, their disparity at the solstices and show how one pole is lighted at one season of the year and the other when you are half way around the sun ; a clove, a tack or the end of a match stuck into the apple in your own latitude representing the position of the observer. And in the same or a similar manner can the phases of the moon be made plain and how eclipses of the sun and moon occur, total, partial, annular, and how the discovery of the velocity of light was — 11 — brought about by Eoemer, while comparing the act- ual and calculated or tabulated times of occultation of the satellites of Jupiter or of their eclipses, and reappeareuces, and what that velocity is and how arrived at. No endeavour need be made to cram your man with such abstruse subjects as aberration and nu- tation ; nor is it nessary that the average pupil be told what means the 'erm " precession of the equi- noxes and of its period of 23,000 years or so "; but tell him of our planetary system, its compo::ent members, their approximate relative sizes and distances. A word about Yenus may not be out of place and of how, being an inferior planet or between us and the sun, it can never vary its apparent distance from the latter by more than a given angular amount or distance, being thus some times in the twilight an evening, then a morning star ; while the superior planets, like Jupiter m ly bj seen at all angles from the sun or even in almost direct oppo- sition to it. All this can be shown on a table or the floor with the helpof afew balls or marbles or an orange for the sun ; and even without such a ijuncts, by a mere pencil sketch on paper ; though bettf^r, quicker and easier of apprehension by the concrete method of th^ objects in relief. Now in geometry, the pupil can easily be made to see how the three angles of a plane triangle make up two right angles, by cutting off and putting to- gether the component angulars of any triangle drawn on paper, or on cardboard or on the easily to — 12 — be divided lid or botton of an ampty cigar box or f^heet of tin or the like ; and how, by assuming the diameter of the earth's orbit about the sun, as a base line, taking one angle now and the other six months hence, the third or angle at the apex is obtained, and how the distance of the sun thereby compares with the length of base assumed and how it thus becomes known. The practical man will not yearn for any thing more than this , he will not care to be told how this distance may also be obtained by a transit of Venus or of Mercury accross the sun's disk. He is now readv to admit that one can reach he stars and measure them and their distances from us and from each other and understand what mean such distances when expressed in terms of the velocity of light. Latitude can easily be made plain to our man as being equal to the angle of elevation of the pole or of Polaris when on a horizontal line with the former or when in elongation, or as he would be told, discarding technical phraseology : when on a line parallel with the horizon or perpendicular or at right angles to a plumb-line ; by showing him that from pole to equator being 90" or a right anq^le, and from zenith to horizon also a right angle ; therefore taking equals irom equals, the remainders must be equal. Our pupil young or old can soon be made to see and in fact is likely to see for himself that the earth revolves, and from West to East in 24 hours of his clock time j and knowing that a circle is divided into — 13 — 360 degrees, is not slow at discovering that every hour corresponds to 15', every minute of time to 15 minutes of space or longitude or to the quarter of one degree, and he can then understand how the captain by his chronometer can tell his longitude at sea ; he now appreciates the necessity for the utmost precision in such time keepers, their setting and ra- ting, and he sees how longitudes of places can be com- pared under the times simultaneously telegraphed by the instantaneous flash of electricity. But there are matters for the million where the data to be used cannot be obtained nor taught by elementary modes and where calculus of the highest order must be resorted to, as in the preparation of the nautical almanac or ephemerides, for the gui- dance of the mariner at sea and the determination of the exact figure of the earth, and relative positions of points upon its surface. The untutored may smile incredulously at such an apparently useless array of figures involved in the obtaining of the time or exact longitude, and at that, of only one single spot on the earth's surface; but when he reflects, that the earth being only abjut 25,000 miles in circum- ference, a minute of the compass is but the 2 1,600th part of the circle and can be but slightly greater than an ordinary mile — 6076 ft. instead of 5280 — or what is called a knot, a marine, nautical or geogra- phical mile ; a second of space or the 60th part of a minute, only 100 f t ; and when he recollects that an ocean greyhound now leaps over or- covers this dis- tance of 100 feet in 2 seconds of time ; he sees, he — 14 — fully takes in and appreciates that fraction of a mi- nute which may lie between his vessel and a breaker, betw^een a live craft and a w^reck, in one word, be- tween life and death ; and it is thus the vulgar be- come wedded to the necessity for accuracy so unerring. Again our man or pupil, and without more tech- nology than the mere mention of the thing, may be made to see at a glance how .spherical areas are arriv- ed at ; for, first, to see that the area of a plane tri- angle is just half that of its corres[)onding parallelo- gram requires no geometrical endeavour. Now, do not teli him that the area of a circle is equal to the square of the diameter into decimal .7854 or about 782 per cent of its enclosing square. He will not understand that as it is not brought home to him by his own process of reasoning ; but what he can see, the argument r< aching the mind through the eye, is that the area of the circle is equal to its circum- ference into half the radius ; for he will mentally or with pencil parcel it out into triangles by drawing lines from the centre to the circumference, and of each of thee components the area is that of the base into half the height or radius — and thus he also sees that the area of the semi-circle and of the sector is to be arrived at by a like process of the length of arc into half the radius. The segmental area strikes him at once as the difference between that of the sec- tor and that of the triangle ; and the area of a lune iri, in an analogous manner, made just as p'ain to his untutored perception, as the difference between a semi-circle and a segment on th3 same base, by a mere repetition of the process for the segment. — 15 — Here then arrive we at the component tiiangu- lar spaces into which the surface of a ball, or sphere, the earth may be divided or of which a spherical or spheroidal area as that of a melon, an orange may be conceived to be made up ; for Ihis very structure exists in nature in the component ungulae or wedged like shapes or solids of which the ribbed melon is composed ; and the orange after the renioval of the outer skin or rind, reveals the same wedge-Lke struc- ture, the base or surface of each elemental ungula, supposing it developed, being like unto a double seg- ment or two segments base to base, or the middle sec- tion of a prolate spindle by a plane through its longer axis, affording thus an idea of how to get its area. But to do the thing correctly, and s >, more easy : let this surface of the ungula be cut in two at the equator or half way betwen its poles or apices, and we have two spherical triangles, where the pupil on being told of it, will see that the angle at the apex is the so called spherical exces--, or the excess over two right angles or 180*"; for, as is evident the angles at the base of every such- component triangle ot the hemisphere are both right angles as of all meridians where cut by the equator; and as their respective areas vary as the angles at the apices or summits, therefore becomes it evident even t ) the non tech- nologist that the areas of spherical triangles are pro- portional to their respective spherical excesses and that this is also true of spherical polygons ; and now, beginning with the area of the tri-rectangular tri- angle or one eighth of the whole sphere ; dividing it by 90, we get the area of a bi-rectangalar of which — 16 — the spherical excess is one degree, the 60th part of this being for one minute, the 60th of this last for one second and, shifting the point : the 10th, the 100th, the 1000th of this for the corresponding de- cimals. These figures of cours;? are for the sphere of which tae diam. is 1 or unity, so that squaring the diameter whatever it may be and multiplying, our practical mechanic can arrive by a mere addition of the tabulated areas, or rather by first multiplying the respective figures for one degree, one minute, one second and its unit decimals by the number thereof in the given spherical excess, at the area of any component section of the earth, a dome or other figure of the kind however large or small. And in another direction, the practical mechanic with a little elementary geometry, may be led to work out a variety of problems. For instance, it so hap- pens that the square of the hypothenuse or largest side of any right angled triangled is equal to the sum of the squares upon the other sides, and therefore can a right angle be laid out by the aid of any three num- bers as 3 and 4 and 5 or of any multiples therof, enabling our man to calculate the length of laddtr needed lo reach a certain height, or length of stay or strut or brace or inclined member or diagonal ; and the perpendicular in a semi-circle to any point in the diameter is a mean proportional between the parts of said diameter. Applying this, the radius of a rail- way curve can be found by measuring the length of cori or straight line joining any two points in the curve, and the versed sine or distance at the centre — 17 — of the cord between it and the curve ; when, squaring the half cord and dividing by the versed sine, and extracting the square root or looking for it in exist- ing ril;les for the purpose, there comes the balance of the diameter which adding to the versed sine and halving the result, gives the radius required ; and in a similar manner could the size of a tree be arrived at of which there remained but a portion of the stump. Now going into physica, to vary the tuition, and not tire out the individual by dwelling too much at length on one and the same the^ie : the pressure of the atmosphere cjin be illustrated by rolling a sheet of paper into a cylindrical or tube-like form, applying it air tight to the palm of the hand at one end, apply- ing the mouth to it and sucking out the air at the other, when it will immediately collapse or the oppo- site sides of it come together at the centre. Suction and the common pump may be illus- trated by a straw, or better by a glass tube with coloured liquid — the weight of the air and amount of pressure at the level of the earth, by a comparison with that of a column of water sustained in a vacuum, and proved again by the relative weights of water and of mercury and the corresponding heights of these substances in their respective tubes. Thus also will be understood how a siphon or curved pipe or con- duit with its bend or apex upwards, and on condition that its vertical height do not extend beyond that to which, under the pressure of the atmosphere, water will ascend in a tubii devoid of air, may be made l6 — 18 — empty out a lake or reservoir, or pour one sea into another ; provided the air be pumped from it, and the height of the intervening ridge or ground not more than 30 feet above the level of the water drawn from, unless dug into or tunneled for the purpose, the delivery leg of the siphon longer than the other and the surface of the water in the river or lake pumped to, at all times below that of the lake or pond or sea pumped from, with both ends of the siphon, of course, always under water. And he can see for himself if incredulous of tel ling, that this pressure of the atmosphere, as shown by a barometer decreases as he ascends to mountain heights or balloon altitudes ; and will then be ready to give credence io the assertion of the man of science, that though at 5 miles high one half the weight of air is left below one, the upper portion from its less density may and probably does extend to some 50 miles above the surface ; while his concep- tion of the phenomenon may be enhanced by the simile of a depth or height of 50 ft. of feathers, or even of a room full, which however light or almost withoul weight at top, a person lying under would certainly feel the weight of. Our pupil wdll now see how the barometer can be applied to the measurement of aliitudes and atmos- phiric pressures ; he will notice how when rising, the surface of the mercury in the tube is convex and the contrary or concave when falling, and will thus know if the mercury be rising to fair or falling to foul weather ; and he will gain credence, confidence — lo- in the foretelling of the weather by the bureau of meteorology or so called Govt. Observatory, founded on observations of the behaviour of the mercurial column under vicissitudes of rain and shine and wind and calm. He will now be ready to admit that water must boil or bubble under a less pressure of the air at an elevation above the earth's surface, and that it there- fore can not be made hot enough to scald, unless under an air tight cover he.ivy enough to stand the uplifting force of steam at 212° or that of water boiling at the earth's surface ; or if not heavy enough, to be tied or wei2:hted down till the water is hot and that this again must afford, which it does, an approximate mode of estimating altitudes; and thus all the phenomena of heated and lighter air and water will be made easy to him, and why smoke ascends and balloons follow suit ; and will under- stand the spontaneous rising of hot water to distri- bute heat through our dwellings ; and ventilation, and how air may be compressed and used for motor power, and even liquified by cold and pressure, and water frozen and water vaporized or made steam of and its force increased indefinitely by boiling under pressure ; a foot of snow being considered equivalent to an inch of water, a cubic inch of water to a cubic foot of steam, a foot of air an ounce or so, specific gravities and the like. And how much more of a popular nature may be imparted without the aid of science proper, and in fact almost every thing an intelligent man or woai*a^ laborer or mechanic may care to know about* for - 20 - instance : put one pin in a table througli a sheet of paper and with a string and pencil show how a circle of any radius may be la d out on the ground. Now put in two pins at a distance between them and let the string or rope be of the full length of the trans- verse or longer diameter of the proposed ellipsis, and join the ends or tie them to the pins and with the string held taut and the pencil or graver carried around, you w^ill have laidout ihe curve, such a one as you obtain on obliquely cutting through a cone, or through a W( 11 made beet root, carrot, parsnip, or even the handle of a bropm or the like. Our pupil will now^ see that each of the radii veciores — call them plain radii or rays or lines drawn from the centres or the foci — makes an equal angle with the ciicumfeience or curve, or more correctly with the tangent drawn through the point of contact ; and if he has forgotten the lesson : than the angle of incidence is equal to the angle of reflection ; illustrate it to him again with a ball and straight edge, or to make the simile more perfect, curve the ruler or a mere plasterer's lath, maintaining it in position by three or more nails; when our man will see that as to all appearences the lines from the foci do meet the outer edge of the figure under equal angles, therefore that a ball, if projected from one focus towards the periphery, will rebound and reach or pass through the other focus, and he w4ll understand how as well as balls, rays of light and heat and sound from one focus must be repercusstd towards the other, rendering plain to him the coveted secret of the — 21 — whispering gallery in St. PauVs Cathedral, London ; as well how under circumstances analogous, a person may be heard better at a greater distance than if nearer by. Again, this double centred curve is that in which our Earth and all the planets travel round the sun, our moon around its mother Earth, and all the satellites as of Jupiter and other planet-s, about their primaries ; and from a few points in this magic curve, its whole periphery can be traced out ; yes : in the s«me way as the engineer, given three points in his curve, can run it out for miles if necessary, amidst the waters and the forests of the Earth ; so can the astronomer trace out among the starry forests of the heavens, the path of each member of the solar sys- , tern ; and when a comet heaves in sight, tell its velo- city, to within what distance it will approach the sun situated in one of its foci, its excentricity or distance of the focus from the centre of the curve, and finally both of its diameters and the total circuit or periphery of its orbit around the sun ; and predict with ahnost unerring accuracy when it will heave in sight again, on its return trip to our sun, and even though it should be absent for a hundred years or more. Now for the parabola, the section of a cone by a plane parallel to its slant side — cut one from a well conditioned elongated turnip or a beet-root after parting or paring off the head — ^ the pupil has no use for knowing what an ordinate or an abscissa i-?, or that the si^uare of the former is in constant ratio with the u — 22 — 1 Jitter, From the nature of the section he will see that it is and must be an open curve of which the legs can never come together but must go on, if pro- longed, widening their distance to infinity, and he will then see how, if a comet travel in an ellipsis around the sun, it must again heave in sight some day ; while one coming towards us along one leg of a para- bola, and after circuiting around the sun, its focus or its centre, must leave us to return no more ; unless as in political astronomy it be swerved from its course by side issues on its way. ' Again, trace out the parabola on paper or a board, not by the scientific modes of doing t^o, and may -be too abstruse to understand or teach ; but by applying the solid section or portion cut from the cone with its face towards the paper, and run your pencil round iis margin. Now assume the focus { but that your man may not be led to think that it can or should be found by fudging, point out to him, whether he is likely to remember it or not, how this centre can be got by simple geometrical construction : halv- ing an ordinate, drawing from the half point a line to the summit or apex of the curve, and from the same half point, a perpendicular to this to meet the axis or median line, at a point the distance of which from the assumed ordinate equals and gives the dis- tance of the centre fro:n the apex. From the focus draw a line to any point in the curve, and from that point a parallel to the axis, and tell him again that each ol' these lines makes equal angles with the curve, and that the angle of the incident ray being there- fore equal to that of the reflected , a ball or ray of — 23 — light or sound projected or sent forth trom the focus to the side, will rebound or go off in a direction paral- lel to the central or the median line of the parabola. And if this pirabolic paper section be cut out and made to stand on end, or even half of it, and it be turned or swept around, we shall be in presence of the so called paraboloid, illustrative of which a tumbler, tea cup, or a ladle may do duty ; and as all sectionsof it through the vertical or axis must be and are alike, our pupil will now see how, if the summit or the apex of an elongated figure of the kind be cut away and the mouth applied just at the focus, we have the speaking trumpet in which, instead of the sound spreading on all sides, as where uttered in the open, its vibrations are concentrated by the tube and the whole force of the voice thus turned in any re- quired direction and therefore heard at a much greater distance. And he will see and understand how, as in a light house, the rays from the focus of the fire, instead ol spreading as do those of the sun and moon and stars, or of a lamp or candle towards all points of the horizon and up and down and every where ; will on the c )ntrary, after striking the curved surface of the purposely made paraboloidal reflector, be concentrat- ed into a bun .le, so to say, and thus go forth on their errand of humanity. He will be ready now to grasp the idea of how a stone projected obliquely upward into space, and which, if there were no retardatory causes, would hurry on in the saine straight lino in the direction — 24 — pointed to, does, under the influence of gravity or of its own weight, curve more and more as it ascends, towards its mother planet, until it reaches to the summit of its throw, and then it falls again, describ- ing as it descends, the selfsame curve, but facing or turned the other way, each half the counterpart of its fellow, each half the half of a paiabola, and of the same parabola ; or, falling beyond the vertical through the apex of the curve, to the self same distance it was projected from ; and thus will he understand how the artillerist can, with a ball or shot of given weight, and given force of powder impact and at a given or calculated angle or inclination upward from the hori- zon, be made to fall just where required into the stronghold of the enemy on land or into a ship at sea, of either of which there are many quick and simple modes of ascertaining the distance off. Our every-day man can be taught by simple means how to tell his distance from a far off object of which he knows he size or height. The difficulty often times is not in doing but in conceiving now and what to do. If he is told that sound travels, say in round numbers 1000 ft. per second, and is taught by observing the pendulum of a seconds clock, to beat seconds in his mind, and audibly to his own hearing by saying 0, 1,2, 3, 4, 5 &c., or told to make a pen- dulum for himself with a plumb bob, or stone and line of given length (39.1383" or 39 }"), he can then calculate how far off is the thunder bolt by the lapse of time between the instnntaneous light of flash and sound thereof ; and if miles away when he can hear the midday gun, his miles into seconds will tell him — 25 — just how much past noon it really is or should be by his watch when the sound reaches him. And when I say that to count seconds, one must begin with nought or zero, it is that to appreciate the first interval, there must be a starting point, and whether audibly or mentally, it must be haid or thought, or the first second cannot even be approxi- mately guessed at. Our hankerer after knowledge had thought be- fore this lesson on the velocity of sound, that the dis- charges of a line of musketry were successive as the sounds thereof, and could not make out how it should be possible for each succeeding shot to be fired in so small a fraction of a second after the one iuimediate- ly preceding it, and be succeeded at equal intervals by the next and next and next; but now he under- stands that the firing is really simultaneous along the line, and that it is because, of his position at one end of the line or further off, that the sounds reach his hear successively, due to the increased dis- tance each has to travel. And if he be posted near the centre of :he column ; then will he hear a double series of separate reports reaching him simultaneous- ly in pairs proceeding from the centre or point oppo- site to him and successively towards each extremity of the line of fire. Echo may also be here explained as existing when a sound reaching and being reflected back from a non absorbent rock or wall, &c., is heard a second time ; provided the point from which the sound goes forth h at a distance of at least 90 ft. from the repeating — 26 — or repercussive surface ; as, if not, the echo and the sound would be heard together and confounded with each other, and this echo may be several times re- echoed as the celebrated Woodstock echo repeating 20 times, while that at Simon etta castle near Milan reechoes 40 times. An inkling can also be imparted of how the vibra- tions of chords of stringed instruments as violins, guitars, harps, pianos, &c. produce sounds, the lowest noise audible as a continued sound by a string stout or long, or just taut enough to vibrate 16 times in one second of time, the octave by doubling the num- ber of vibrations, and the successive octaves by doubl- ing and doubling again, and by making the strings suc- cessively thinner, shorter tauter ; and how the in- termediary notes of the octave are due to numbers of vibrations of intermediate frequency but propor- tionally so between those of each successive octave, and how when a siring tuned to a certain pitch, bo- comes elongated more or less under continuous fin- gering or striking by a piano hammer, the note be- comes false, flat if too loose, sharp if too tauth and has to be rectified by tightening or loosening the screw or key, an openition called tuning ; and while on the subject of vibrations, our friend may be made to un- derstand that in an analogous manner the compo- nent colours of white or sun light, travelling as it does at 180,000 miles in one second of time, in undula- tions of sny one 40,000th inch ampl. more or less, strike the retina with the tremendous and to us incomprehen- sible velocity of 500 millions of millions of vibrations in 3, second j the greater or less frequency of vibration in — 27 — that unit of time, producing in us the impression of the component colours of the rainbow or those into which white light is decomposed by a prism of glass, and how. What has already been said of bundling together rays of light to do duty in a light house, is sufficient for the pupil to conceive and admit how by the use of lenses of certain forms and at certain distances apart, telescopes are constructed to aid the eye in reaching, seeing to greater distances, microtcopes to magnify. The eye retains the impression of an object seen or looked at, during one eighth of a second of time. This tells how many optical illusions are to be ex- plained ; as of a continuous line or circle or other figure produced by the quick brandishing of an in- cnndescent coal, or of a stick one end of which has been thrust into the fire, and while still aglow, moved through the periphery of the figure aescribed in the eighth part of a second, or mnde continuous by moving the luminous point eight times per second. This retention of the impression by the retina, pro- duces the effect, when passing rapidl}^ in a railway train through an iron lattice or trussed bridge, that all the diagonal members or struts and ties are being thrown into a violent state of oscillation or wave or whip-like motion. Another effect the writer has noticed is that in passing rapidly before a pile of pipes with their ends or apertures turned towards you, the circular open- ings appear oval or elongated in the direction of, your motion. — 28 — The magic wheel or cylinder where objects and animals inay be seen in motion, though at a stand srill in the picture, is explainable in the same manner. In dealing now a day with such quick travelling matters as light and electricity 180,000 miles in one second of time, and of the millons of vibrations per second of the retina caused by the entrance into the eye in that time of as many undulations or waves — one may make some approach to a conception of such a subdivision of the second of time by considering that one can easily during tow beats of the seconds pen- dulum, count to ten and even to twenty, but as two tens, to avoid the delay of the two syllable numbers from 12 to 20. Now take a book containing say 1000 folios of thin paper in an inch ; and holding it, so the thumb will touch the corners while they are made to pass under it, will be a division, a sensible and visible division of the second into a thousand parts, if it took a second to do so ; but this can be done in the 10th part of a second or 10 times in one second and thus we arrive at the division of the second into 10,000. Again let a wheel be supposed of which the peri- phery or circumference is 1000 inches, and each inch milled into 1000 parts, this fraction of an inch being conceivable by the above mode of 1000 folios of thin paper to an inch. The whole periphery is therefore divided into 1000 x 1000 or 1000,000 parts. This circumference ot 1000 inches gives a diameter of only 26 i ft. or so, and as such a wheel might be made to revolve once per second ; we thus arrive at a, so to say, ocular proof or conception of the division — 29 — of a second of time into a million parts. Again, as gold leaf is supposed to be only the 100 thousandth part of an inch in thickness, there would be 100 of them to each folio or hvaf of our supposed division of the peri- phery into 1000 parts per inch and thus the mind is capable of conceiving such minutia as the 100 mil- lionth of a second, and the 100 thousandth of an inch in space. Well, our object-lesson pupil has now been taught many things ; but to make his teachings gene- ral, let us hint at how, as well as lines and areas both plain and curved, he may alsocOver solids; and to this effect give him but one rule for all, as he was taught one rule for all areas, by compuiing and putting together the component triangles of which every area can be conceived to be made up The prismoidal formula is what is required, where only plane areas are to be made up; or when circular, segmental, ellip- tical or the like, found ready made in books, the areas added, their sum multipliod and the pro- duct divided, all by simple arithmetic ; .and when dealing with complex forms, how to be sub-divided and the contents added or their differences taken. And as said before, the duty of the technologist or scientific man is to suggest simple modes of doing things which the kindergarten teacher may not dream of; such as cubing a piece of statuary, a chair, a plant-like form, a man or living animal, by putting it or him into a tub, or box filled with water or with sand and note the difference of level when taken out. Teach the mechanic, the founder how to compute ^ 30 — in advance the weight of an intricate casting of orna- mental schroll work from that of the model, by their respective spticific gravities or weights and a simple rule of three. How a rough stone picked from a quarry on the roadside may be cubed if necessary by an arithmetical comparison of its weight with that of a cubic ft. or inch of the same material under the heading of specific gravities ; and how, conversely, without any means at hand of getting at the weight of a tub of butter or other article capable of being cubed; the weight itself would follow by mere com- paraison with that of a foot or inch of like material. The delivery of a stream or river, by its area of cross section into its average velocity in ft. or yards per second or per minute, and the whole into horse power by the height in lbs. into the head or height of fall and a division of the foot-pounds by the ordinary assumption of 33 or in round numbers say 30,000 lbs. raised one foot high in one minute of time. The draught of a pontoon or vessel by a compu- tation of its weight and a comparison thereof with that of water. A mental process for instance of arriving at the weight of a foot in length or area of iron or other scantling, by simply bearing in mind the weight of a cubic ft. thereof, say 480 lbs., being 40 lbs. for an inch-foot, area, 5 lbs. for a foot square and | thick ; whence for instance a bar 3 x i will give for one ft. of it the quarter of 15 lbs. and the same size scantlino- if of wood at 48 lbs. per cubic foot, one tenth of such result. ^ 31 — Fraunhoffer's lines would be greek to our indivi- dual ; but he must be told what ihey mean and how by the help of them we know the i omponent materials of other worlds. And now let him know something of his own make up : of how he breathes and what ; how the atmosphere is a mixture of oxygen and nitrogen or azote, say one to four with some carbonic acid gas ; how the latter is destructive of animal life and to be detected in a well and accidents avoided by trying with a candle or a lamp let down into it, it being heavier than air and settling to the bottom, or how in a cellar a dog may breathe and die of it or be affected more or less, or himself if lying down, while if standin with, no instru- ments, no models, no apparatus; how the first object at h ind or in sight may bj made to do duty as said befoie : as a broom handle for a cylinder, a beat-root, parsnip, carrot for a cone ; an orange for a sphere and its component ungulae, a pencil in a cup of water for refraction, a bit of mirror for reflection, a lath and marble for action and reaction, a taut string between the fingers for a straight line, a folded sheet of paper for a ruler or straight edge, while a double fold brings forth a right ang e or a pair or 4 of them when developed, another fold an angle of 45°, and s j on ; a lamp or other source of light, the sun ; a cup for a parobaloid, a string, a pulley and some weights, a hammer, naih>, etc ; a book illustra- tive of how small thicknesses or amplitudes may be conceived or measured by piling them together and counting the number of them in an inch or in a given portion of an inch and other self suggestive modes to the technologist by which he may make his mean- ing full and facile of understanding. And further to help our man in the conception of infinitesimals, direct his mind to the fact that in the seed must be the elements o' every portion of the plant or tree : its trunk and branches, twigs and leaves and blossoms. Look at the insect you cjni ^ 36 — hardly see with the naked eye : it also has its orga- nisms of vitality — heart and lungs and circulation of the blood, its digestive apparatus and its nervous system ; and if its whole body be but the lOOth of an inch or the 6000th part of the lineal dimensions of a man or of any animal of like dimension, and the blood corpuscles in proportion to its size of veins and arteries which in us and them are the 600th of an inch, then must our man admit that these same corpuscles in the insect can be but the 3,600.000 of an inch. And in a manner, may -be, more sensible by being visible to the eye and which can be felt and handled ; take the result at which the gold beater, the maker of gold leaf or gilding gold, arrives, when he has j spread out his f' cube of solid gold into a sheet 20 ft. square and therefore 400 ft. in area, in which the f' area is contained 147,000 times and — you cannot deny ] your senses — the tickness of the leaf can not exceed the 236,000th part of an inch. Apply the same process to a drop of soap suds : this you can blow into a bubble of such diam., that the thickness of the film will hardly exceed the millionth of an inch and there you see it and can touch it and have proof po- sitive of the truth of the assertion. What precedes is all in the way of " object les- sons " (legons de cJioses) but there are other lessons * quite as important to be taught, and w^hich do not seem ever to have been dreamed of a< yet by any one, or to form part of any system : I allude to " word lessons" (legons demotsj or what should or might be called such. Children of many years of age : 10, 15 and — 37 — even 20 and many of Tiiaturer age ignore the mean- ing of hundreds of words with which they should be made familiar and without a knowledge of which they never can be considered as having a practical educa- tion, fitting them for the duties and conceptions of every-day life. 1 hey do not understand what they read ; they cannot join in conversation nor appre- ciate, for they know not +he meaning of many of the words made use in their surroundings. The writer has been witness to and noticed this for 40 years past in is own family and the families of others. Children at school and college and in convents know their catechism and their history and grammar and they can read correctly and fluently of a story, tale or novel where the words alluded to do not occur and if they do or did their meaning is not, would not be understood, because forsooth the teacher knowins: them, or may-be not, he or she, imagines that the pupil knows them also, and that it never enters his or her mind to tell the pupil what they mean. There are children by the thousand and up to all ages who can not read the time of day by clock or watch, unable to recite in succession the months of the year or even the days of the week. In fact they do not know what constitutes such subdivision of the year, or even what a year is, the equinoxes and the solstices, what the meaning is of such words and when the thing expressed oicurs; what a bissextile year and why, or how made up. What are taxes ; water, poor and school rates; and the answer to this leads to the explanation of: what a municip ility, a city, town, a village and a ward, — a councillor, an alderman, a — 38 — . mayor; a proprietor, an occupant, a tenant; what tithes are, excise, custom duties, protection as against free trade, an examining warehouse, gjods in bond. Geographies now a day tell us that a territory ruled by a king, is cilled a kingdo.n ; by an emperor an empire ; but in other respects the difference between the former and between them and a pre- sident of a republic and their respective functions are not explained and never taught at school. What means a Legislature, a Government, the House of Commons, the House of Lords. Congress, a Senate, Privy Co mcil, municipal or city council, a committee, a commission and the duties of the functionaries of all such ; a diocese, a parish, township, a city or peoples' representative, a deputy, a legislative councillor, a senator, minister, a parliament, a session or a sitting; the Governor and his attributes ; a minister of crown lands, public works, canals & railways, of the interior, of marine and fisheries, of mil & def ; a secretary of state, an attorney or solicitor general ; a whipper in, a sergeant-at-arms, usher of the black rod ; the duties of a " speaker, " a prime mi«iister ; a czar, mikado, sultan, bey, shah, dey ; a mother country and a colony; the funi*tions of a magistrate, a judge, a sheriff and the difference between a police court, the superior court and couris of revision, appeals, an exchequer court, the supreme court, a circuit court, the Crown and what not; and a thousand other things words, expressions never taught in SL.*hools and yet which should be : how wine and beer and cheese and butter, bread are made — whence come salt, coal oil, truffles, asphalt, cioutchouck ; what is a manufac- _ 39 — tory, a foundry, a smithy, puddling and rolling mills, etc. Steernge, saloon, intermediate passengers ; shares, debentures at, above and below par ; dis- count, premium, at a; dividend, stocks, bulls and bears; flour, jjork, etc., firm, easy, dull ; agent, edition of a book, newspaper, etc., editor, bail, security, cash, instalm(-nt — passenger, freight, mixed train — staflf, med.. Gov. Genls' — quarantine — wholesale — retail — bankruptcy — assignee — liquidation — li- quidator ; to Day so much in the dollar, creditor, debtor, broker, stock broker ; — via, by the way of, by such and such a route — Gen. Frt. tc. Pas. Agt — to wire — to cable — going N., S., E., W. ; explan in what direction from place of publication — right, left bank of river — local mail, stopping at all places where there is a P. O. — docked : put into a dock — payable " at sight " — explain stock quotations (below, above par) — market quotations, market loeak, barley quiets corn (htll^ lard firmer^ cotton stead tj-^ — baled hay — hamper — crate (of delf, cabbage, etc.); an alias, an alibi, extradition — estale (so and so) insolvents — inventory — water tight (vessel) compartments, sa- loons anndsJilps (less motion in pitching) Now a very good way of teaching a host of such words is to give the pupil every day a lesson at reading portion of a common or ordinary news-paper : the advertisements more especially of every descrip- tion where some one or oilier or several of these words occur. The moment a word heaves in sight of which you have reason to beleive the reading pupil — 40 — probably does not know the meaning or acceptation or how it is to b^ interpreted under the circumstances; let the reader stop until the word has been explained and then proceed until another necessitates his ministry. And look at the many abbreviations never found in reading h'story, stories and the like. — How can the child know unless told, that ss. is to be read steam- ship, Nfid., Newfouudland, Col. and Cal., Colorado, California, Ont. Ontario, B. C. British Columbia, N. S. Nova Scotia, Me. Maine, Vt. Vermont, Ar. Ari- sona, Ark. Arkansas, Wy. Wyoming, Md. Mary- land, P. 0. Post Office, P. Q. Province of Quebec, P. E. I. Prince Edward Island, Co. company, Bros, brothers, lb. pound, cwt. a hundred weight, a stone 14 lbs., a quintal 112 lbs. manfg. Co. manufactur- ing Co., C. P. II., I C. R., Q. C, Quebec Central, G. T. R , U. P. R., P. S. post script, ad-addendum or addenda, H. M. S., His or Her majesty's ship Canada, Sappho, etc. — 7.55 P. M. — 3.02 A. M., M. D.— B.N. A. British North America — Phone 94, Tele- phone No. R. M. S. Royal Mail Steamer — brigt. brigantine, etc. In the foregoing, the author assumes that men, otherwise uneducated; and, possibly, not even know- ing how to read or write ; 'Lher for want of means, or time or taste or aptitude for such tuition ; are nevertheless curious or desirous of understanding the salient traits of the phenomena of life. He thinks they would be better for a certain amount of geometrical, physical, astronomical, geolo- — 41 — gical, biological and other knowledge ; more satis- fied with themselves, less jealous of their educated fellows ; less liable, when left to their own com- munings, to brooding in ill humor over their evils real or imaginary, of nourishing ideas of communism, anarchy and mischief; their minds being then stored witli materials for reflection on the greatness and goodness of the Deity. The education of the masses should not go too far beyond mere reading, writing and arithmetic and the object-lessons here proposed. The injunc- tion : '' educate the people " must not be mis- interpreted, as it certainly is in far too many cases Education must be special to the calling of the indi- vidual, a truth which Lady Aberbeen is now trying hard to inculcate : servants, nurses, cooks must learn how to minister unto the wants of others. Too much grammar, literature, music, embroidery, con- chology and the like, unfits the farmer's daughter for the duties of her husband's sphere in life. Collegial, University tuition are ill adapted to the farmers' son, if he is to follow in the footsteps of his sire; though enough of chemistry to be imparted in a few object lessons and enough of botany are essential to his success in agri., horti., sylvi. and arboriculture. Let us beware of 'Hoo much education" there is a danger of overdoing the thing and thus causing or inciting our should be agriculturists to be dissa- tisfied with their parents' mode of livelyhood, flock- ing towards cities and towns or populated centres ; there to become second and third class professionals of — 42 — every hue, with little or nothing to do; with mis- chief and discontent and anarchical tendencies fol- lowing in the wake. There must not be too much sacred history, too much catechism ; Sunday is the day for that : it is so by divine injunction ; let week days be devoted to object lessons in sewing, garden- ing, cooking, and in the teachings of husbandry : as how to dig, and ditch, and drain and plough and fence in, and cultivate, and erect buildings for the farm, the whole in miniature while at school, and in reality thereafter, for let it not be forgotten that God has said "six days shalt thou labor" and good, hard, honest work is the prayer the most congenial to the Deity.