"^^^ ^ IMAGE EVALUATION TEST TARGET (MT-3) // i z 1.0 I.I 1.25 !« 2.0 1.8 \'^ IIIIII.6 V] A 1 1111 • 1 tliat It the salmon be dead the wem'ht is increased." After much discussion, and several learned and elaborate answers had been prepared, it occurred to one more sage than the rest to say " try it." Of course the result was that the weight was increased by tliat of the sfdmon, whether it were alive or dead. 13 ut to return — their notions on the subject of AI. chanical Force were of the vaguest, most confused description ; they had no conception of the dilference between force as 24 ! i| used to produce motion, and force used to keep bodies at rest, and with respect to velocity and motion itself their views were by no means clear ; and tlicir other mechanical laws were no truer or more useful than the one we have given. The law in Hydrostatics which w^e now jn'oceed to notice is not a glaring one in absmdity, but one of the best of their dogmas, inasmuch as Example from tlicrc was euougli of vcrification of it Hydrostatics. ^^ make it by no means improbable. In fact, as far as their knowledge went, it was by no means a bad hA^pothesis. It is this, " Nature abhors a vacuum." This law was an approach to a scientific one, it was wTong, but still the reasons for it were better tlian those they usually had, and the method of establishing it something approaching the true one. Ey it could be explained suction, as it is improperlycalled, of various kinds, tlie action of bellows with their spouts immersed in water, tlie action of pmnps, the foct that a column of w^ater or other fluid may be sustained in an inverted vessel, and other phenomena of this class. These were thus iccncralized or re- duced to follow a uniform law, and if sucli a law happened to be true it would most certainly explain the phenomena. It was by no means a very violent assmnption th.'it it was a law of Nature, that there should be no vacant 25 space so long as it was possible for substance to fill it, and until experience or experiment shewed the contrary, it was as good a theory as any other. Indeed the notion of fluid pressure is a very difficult one to grasp fully, even when it is clearly explained, and to find it out was a task worthy of the great men who discovered it. I am afraid that few of those who refer all the occurrences I have mentioned to their true cause, the pressure of the atmosphere, could give any very clear ex- planation of the how. We shall see presently by what kind of proof the true theory was established in this as well as in other cases. lor the present we see that some of the old dogmas were absurd, depending for their proof on notliing but men's arbitrary fancy, not borne out by facts, and in some cases not even submitted to the ordeal of experiment ; that others were somewhat more satisfactory, having a semblance of demonstration to prove them. But we may regard it as the distinguish- ing feature of ancient Philosophy, which tainted all the attempts made by Piiilosophers at Physical Scicnce,that a theory was to them the more beauti- ful, the more free it was from the debasing and trammelling disturbance of verification. That was most to be admired which was too beautiful for men to wish to interfere with, too abstruse for 26 ancient mc thod in Physi- cal Science. men to cavil at, too deep for tlie vulgar at least to understand. Science, whether mental or phy- inadequacy of ^ical, was too lo% a thing, too noble in itself, to have anything to do (so they thought) with the life, comforts or practice of man ; it was to raise man to be akin to Deity, not to teach him to live and act as man. However much there may have been of beauty and of truth in some of these views, as far as Physical discovery was concerned, such a tendency of mind was most vicious in its effects, having the end of leading men to despise the only true and safe method of discovery, — yet had they noble views of tlie dignity and beauty of Knowledge, and the sublimity of Science, and so much, is there true and good in their conceptions, so much of mental acumen and ingenuity in their researches, that it is almost with regret that we are obliged to confess the inadequacy of their methods, and in Physical IIow much to . '' be adnuied in Scicucc, at Icast, to couiparc them to the Philosopher Tliales, who contem- plating too earnestly the stars, fell into the water. On which has been shrewdly observed, if he had looked in the water he mii>'ht have seen the stars, but looking at the stars he could not sec the water. Plato says : " An astronomer must be the I i. 27 riato, Epino wisest of men ; his mind must be duly discip- lined in youth. Especially is mathe- vv-^'o^% matical study necessary, both an acquaintance with the doctrine of numloers, and also with that other branch of matliematics, which, closely connected as it is with tlie science of the heavens, we very absurdly call geometry, the measure of the earth." We may then conclude that we advrtagcl. °' are indebted to ancient philosophy for these benefits : 1. Considerable geometrical knowledge. 2. A strong behef in the importance of the deductive method of estabhshing a science, when first principles of it are known. 3. AVhen certain phenomena recur in regular ordCT, we may infer that they proceed from some determinate law, which must be guessed first, and verified afterwards. It is in the reducing to order the processes implied in this last law that later discoveries have made so many advances,— the manner in which observations must be made to suggest a probable hj'l)othesis, and the manner in which the verifi- cation or rejection of the assumed law is to be carried out ; for in general the guesses of philo- Bophers were very wide of truth, and verification was l)y no means indispensable in every case. 28 |v ' ' S'ili We will now proceed to trace briefly as we are able, how it was that science learned to tlirow off the trammels, w^ith wliich a blind adherence to Aristotelian teaching had shackled it, to be taug'lit that, as Ilerschel so wtII puts it, "The liberty of speculation whicli we possess in the domains of theory, is not like the wild license of the slave broke loose from his fetters, but rather like that of tlie free man wdio has learned the lessons of restraint, in the school of just subordi- nation." One of the first, and by far the most distin- guished, of tliose who early perceived the impor- tance of lal)orious verification of laws by experiment, was Hipparchus. He devoted himself to the study of astronomy, and the pro1)lcm he proposed to himself was to ac- count for the celestial phenomena on the hypo- thesis of circular motion — that is to say, to represent geometrically such motion, not to give anv reason for it, such as attraction. The first tiling to be found out was evidently, how did tlie heavenly bodies move, or appear to move. A much later problem would be, wliy do they do so ? The 1 ')orious observations tliat he made, wonderful • their accuracy, (when we consider the nature ul tlie instruments with which he worked, no telescopes, no transit instruments, Hipparchus. 29 I no mural circles, not even a clock; instruments so indispensable to tlie observer,) are of the great- est value now ; and the geometrical representa- tion of the motions lie observed, complicated and ingenious as tliey are, are in reality, as far as tliey go, statements of the results which later theory has established, the actual form in which modern analysis has thrown the solution of the problem of the Lunar and Planetary motions. He really laid down a method of representing actual appearances, as far as his ob- rf'S'scfeu!; servation went, although no progress ^•'^'" was made towards the discovery of the law which was the cause of such motions. Hipparchus left the science of Astronomy en- riched witli a number of most valuable observa- tions, and an explanation of some of the hea- venly appearances ; he also left data, as he himself tells us, for the use of later philosophers on cer- tain plc^netary motions which he himself was not able satisfactorily to determine. The next name of note to which we shall allude, is that of Ptolemy. His work consisted prin- cipally of arranging and correcting the observa- tions and results of previous astronomers, and to him is due a complete statement of the History of Astronomy at his time. He made also some important discoveries, and Ptolemy. 30 Ilis Theory. set fortli plainly wliatis called tlie Ptolemaic sys- tem of tlic motions of the planets. He placed the eartli in the centre of all tlie planetary mo- tions ; the sun and all the planets were made to revolve ahout it ; and by the aid of artifices like that alluded to above — that is, bv various com- binalions of circular motions — he gave a very fair explanation of the dilFerent planetary motions. This theory is now too much decried as absurd, and it is asked why so much more complicated a system was not earlier replaced by the simpler one, with which every school-boy is familiar, which makes the sun the centre of all the planets' motions. It must be remarked that it is very difficult to grasp fully ideas contrary to experience, still less to make a theory in direct contradiction as would at first seem of the evidence of the senses. It was hard to believe that this earth vast as it ap- peared, should be in rapid onward motion and ra})id revolution about its axis, while the sun which seemed to move, and of whose size they had little means of judging, was stationary. Again Mc must remember that there were really strong grounds for accepting the theory of an- other and more satisfactory kind. Eclipses could be predicted by it, as well as by the later theory, and for rough observation, with equal precision. I) Reasons for it. 31 Also we must recollect thattlie theory of tlie earth's motion appeared incon- sistent with the fact that the stars preserve always the same apparent place with respect to the earth. It was but natural to suppose, that if the earth moved in an orbit, it would seem sometimes nearer and sometimes farther ofP, and that the stars would not appear always the same distance from one another; just as in walk- ing round a field, trees anywhere near the field would look differently placed according as you went nearer or farther off from them. If the trees were very far off, this difference would not be so evident. It was not easy all at once, for men to satisfy themselves, that the stars were so very far off, that not only the size of tlie earth itself, but of its orbit, which is 190,600,000 mdes across, was very small compared with their dis- tance, so small that it made no difference where in its orbit the earth was. Another reason was, that it was proved that Yenus and Mercury must exliibit phases like the moon if the sun were really the centre of planetary motion, and no such phenomena had been observed as yet. There was then good reason for retaining the Ptolemaic Theory until it could be shewn that another would explain the planetary motions more simply 32 Copernicus. andmore accurately, and also answer satisHictorlly tlie reasons brought against it. Copernicus was the man wlio had courage and talent enough to defend the solar sys- tem which we now receive ; for in those days (early in the 10th century), it required no little courage to attack notions and prejudices of lon^j; standini?, and which Divine and Pliiloso- pher were prepared to defend. Those opposed to Copernicus were rather the latter than the former, lor the religious opposition to the new discoveries which were said to he op- posed to the scriptures, had not yet taken any decided part. But for centuries past the labours of all, with few and honourable exceptions, Avho had any pretensions to learning, had been restrict- ed chiefly to transcribing and commenting, and bigotry was the order of the day, any who pre- sumed to attempt to oversetthe established opinion were persecuted with the most deadly hatred, as the poet has happily said — They stfincl Lockcil up lonjetbcf liaiid in hand, Every one leads as he is led, The siaraa bare ]iath they tread ; And dani'e like fiiiries a I'mtastic round, But noitiier chano'e their motion nor their Quoted by Whewell, Hist. Ind. Science. ground. Copernicus and his pupils however held their ground, and soon afterwards the discoveries of 83 Galileo, afforded tlie most wonderful verification of the system of Copernicus. By the Galileo proves /» i i copernicua' Qiscovery of tlic telcscopc he was en- abledtosuewnot only that the planet Jupiter with his moons, was, as it were, an epitome of the solar system, but that Venus shewed the phases which objectors had asserted must be the case, if the earth as well she, revolved about the sun. Galileo was hence enabled to confirm Coperni- cus' Theory of the solar system, in a most satisfac- tory manner, though he had to endure a still larger share of persecution on account of his opinions, than Copernicus had. As yet the cumbrous geo- metrical machinery which the system of circle upon circle had introduced, remained untouched ; it was reserved for the intellect and perseverance of Kepler to discover not merely as Ilip- parchus had done, a way of represent- ing nearly the motions of the planets, but one which should exactly and simply represent their actual motions. Instead of being satisfied with the old system of epicycles, which were botli com- plicated, and, with the improved powers of obser- vation, by no means accurate, he tried innumera- ble other hypotheses ; his works are especially valuable, not only on account of what he dis- covered, but also by shewing wherein he failed, Kepler. 84 His discoveriea. for lie lias preserved records of botli successes and failures, with equal fidelity and almost equal af- fection. After years of toil spent in examining his various guesses, he at last announced his great discovery that the planets move round the sun, in curves called ellipses, like that in the figure ; (the properties of which curve had been well known to the ancients,) the SLin being not in the centre, but in a point called the focus, rather nearer to one end of the longest diameter. He also discovered laws about the time of the body in its path, and the area which it swept out about that point ; which however simple when discovered, were hard enough to guess simply from observation. These laws, guesses at first, among innumerable wrong guesses, were established by induction, that is by long and laborious trial, observation, and comparison of results, and were the first great steps made in the science of Astronomy. Thus the old complicated system was replaced by one simple and beautiful, Upset the old ^^^^ ^^^® tauut cxprcsscd by Alphonso system. Castilc, that if he had been consulted at the creation he would have contrived the universe on a simpler and better plan, fell to the ground. Nothing however had yet been done to explain the reason of the motion, of which the circumstances were now determined. 85 Lord Bacon. Philosophers had busied themselves entirely with the Jioio, and had not attempted the tohy ; those that is, who with clear views of the only safe way of making discovery, objected to accept absurdities on the dictum of others. Tney had used the inductive process of verification to some extent, but without precisely knowing the power of the agent, with which they worked. Prancis Bacon reduced to a system, the method which he set forth with the utmost confidence as the only one adapted for the prose- cution of discoveries in Physical Science, for ar- riving at Physical laws, no less than explaining Physical facts. It was reserved for Newton, he whose name stands foremost in every department of science, to establish the physical cause of heavenly motions. Others had fancied that the cause of planetary motion was attraction to the sun. Milton even has : — " What if the sun Be centre to the world, and other stars, By his attractive virtue and their own Incited, dance about him various rounds." Some had observed that the attraction must be less, the further off the body were, and had even suggested the true law, as a guess ; or from vague reasoning, that, if it were anything hke light, poured forth from the sun, it must of ne- Newton. 36 cessity, from geometrical considerations, follow such law. This law is called that of the inverse square of the distance. You may understand what it means in this way : Suppose a body placed at a certain distance from the sun, it would be pulled towards it with a certain force ; if put at one-half the distance, it would be pulled witii four, i. e. twice two times as much force ; if at one-third the distance, with nine, i. e. three times three times as much force ; if at one-fourth, with four times four or sixteen times as much force : and so on. To Newton fell the task of verifying this law in the fullest possible manner. He first endea- voured to shew, that the moon was retained in her orbit by the attraction of the earth; and, thoudi foiled once bv liavino: taken the erroneous Discovers gra- JT^easure of tlic carth then in use, he vitation. ^y^g enabled in the most triumphant manner to verify it, when the more correct mea- sure was afterwards put forth. AYith a surpassing intellect, to which we can- not but accord most unbounded admiration, he invented methods of calculation first, and solved the problem of the moon's motion in two ways. Explains fully "^^ slicwcd tliat if thc motion of one moon's motion, i^^jy attracted by anotlicr, be such as Kepler had observed, it must be because it is 87 attracted in the way mentioned above ; and lie also shewed, that if we suppose the attraction of one body to another to be according to this law, tlie motion nmst necessarily be such as Kepler had observed. He also proved Kepler's other laws by his process. Thus, then, the ob- served motion will give the physical law which is the cause of it, namely, tlie attraction to the centre. Or, reversing tlie question, the assumed law will give motion in accordance with obser- vations ; and each of tliese propositions may be regarded as a proof of the other, just as a mul- ti|)lication sum will prove a division, and a divi- sion sum a multiplication. Nor v^as this all. Tlie sun attracts the moon in a similar way, though not nearly so much as the earth does, because it is so much further off ; but it attracts it enoui?h to draw it a little from its orbit, some- times one way, soinetimes another. Newton applied his method with success, to explain and compute these variations, inequalities they are called, in the moon's motijn. His method, beautiful and wonderful as it is, required the intellect of Newton to use it ; with his method no one up to the present day has done anything further. Clever men can just read and understand his works, and that is all. 38 New methods needed. As Wliewell strikingly remarks, " The ponderous instrument, so effective in Lis hands, has never since been grasped by one who could use it for such purposes ; and we gaze at it with admiring curiosity, as on some gigan- tic implement of war, Avhich stands idle amongst the memorials of ancient days, and makes us wonder what manner of man he was who could wield as a weapon, what we can hardly lift as a burden." The need, however, produced the pro- cesses recpnred ; for in science, as in other things, the demand produces the supply. Newton's method had been strictly founded on geometry, but geometrical methods were no longer enough ; the gigantic implement was replaced by more penetrating and more subtle instruments; the battle-axe, so to speak, was replaced by the rifle. Mathemati- cians invented new methods of calculation, and mathematical analysis by which, when Newton had shewn the way, the problem of the moon's motion has been still more completely deter- mined,— methods by which symbols are made to think for us, as it were, and mathematical pro- cesses represent the intense thought, which was too much for the mind of man; and by these means all Newton's and many other problems can be easily and accurately solved. National jea- of analysis in veuted. 39 lousy, too, played its part in the cause of science, and caused the Newtonian theory to be subject- ed to the most searching tests, from the shape of the earth, the motions of pendulums, the dis- turbances of the heavenly bodies, before it was universally accepted. Suffice it to remark, that it rests on the firmest footing of inductive rea- soning that is possible to conceive. And in taking leave of tliis very hasty and im- perfect sketch of the discovery and verification of the theoiv of gravitation, we cannot avoid allud- ing to a well-known and most extraordinary instance of its verification, the discovery of Discovery of ^^^^ P^^^^^ Ncptunc. If the attrac- Neptuue. ^^qq Qf orravitatiou be universal, and the planets move round the sun urder the action of his attraction, they must draw one another sliglitly from their orbits round the sun by their attraction of one another. The calculation of the amount of tlvsh disturbance is difficult enough when the attrac '' >\i' body is known, but to calculate the magnitude ai.u position of an unseen and un- known body, merely by its disturbing efPect on another, was a problem that might well terrify the most accomplished mathematicians. This was, however, done in the case of the planet Neptune. The observed place of the planet Uranus diba-ieed with the calculated place by 4iO EUi a small, though in the present state of astronomic science, appreciable amount. It had been sup- posed that an unknovvn exterior planet might produce this effect, and from the difference be- tween the computed and actual places, Adams and Leverrier, about the same time, calculated independently the orbit and place of the new planet and directed observers where to look for it. The planet thus predicted vr^ observed by Professor Challis at the Cambridg. jbservatory in Endand, in the place which Mam's Astro- '-' . ■"•, my, wcaie'3 Adam's had assigned, twice before it was recognized in Berlin by Dr. Galle, who was searchini? according? to Leverrier's directions ; but the foreign astronomer had the good fortune to be the iirst to pronounce the observed star a planet ; the glory of the discovery is, by general consent, divided between these distinguished men. This in- stance is one of the most striking that could be adduced, to exhibit the advance of astrono- my in theoretical development, and practical application; the mathematician, the observer, the instrument maker, almost equally indispen- sable ; it illustrates the immense strides that deductive science had made in the department of purely mathematical analysis; it furnishes an additional proof of the Newtonian system of 41 gravitation, and it adds its quota of praise to tlie combination of theory, experiment, and me- chanical skill, that go to the formation of good astronomical instruments. We must endeavour to notice a few illus- trations of a more generally interesting and intelligible kind, but it was impossible to say anything on the union of experiment and theory, and not dwell more or less at leni^th on the science of astronomv, even at the risk of being to some extent tedious ; since it is the most perfect exemplification of the beauty of the inductive method of verifying laws ; of the importance of geometry ; and also of a point on which little has yet been said, the importance of practical excellence in the formation of instru- ments. Let us, in passing, observe on the con- nection between theory and practice in this. It Theory and IS kuowu that light, iu passiug through ftnmient mik". g^^^^, watcr, or othcr transparent '"'s- substance, is separated into various colours. Careful experiment furnished the law of separation, and mathematical calculation based on this, pointed out how to take lenses made of proper material and of proper powers to remedy the defect produced by this colour, in the picture presented to the eye, when the lenses were used for the formation of tele- i& I > I I til scopes. Again, experiment showed that hght travels in straight lines, which, by reflection or refraction are bent after certain laws ; these laws were subjected to careful experimental proof, and then theory showed the best form of lens to be used, in order that the picture formed by them might be as distinct as possible. Theory having furnished the conditions of a good lens, mechani- cal skill came into play to carry out its sugges- tions ; so that a good telescope cannot be obtained without careful experiment, theoretical calcu- lation, and a careful and skilful artizan. And now let us revert to the simple laws of mechanics and hydrostatics of which we pre- viously took notice. Archimedes had in very early times arrived at just views of some statical questions, and even the fundamental property of fluids ; this knowledge, however, was but of the individual, and had long been forgotten ; everything had to be discovered over again. Galileo shewed the ab- cihiukai (lis- surdity of Aristotelian notions with respect to force and motion, and by careful experiments made on bodies shding down inclined planes, wliich, moving slowly, could be easily observed, made considerable advance to- wards clear views on these matters; he also Archimedes. 43 shewed that bodies fall with the same speed, whatever their weights. Among other discoveries which he made, one of the most remarkable, and most valuable, is the common pendulum, which will afford our next illustration of the union of theory with ex- periment. Observing' the oscillations of a lamp in a cathedral, he noticed that, however much or little it swung, it performed its oscillations in the same time. Experiment con- Pendulum. . , , . . vmced him that his observations were true, and clocks constructed to count the oscilla- tions of a pendulum became very accurate regis- ters to measure time. So far, it was independent of theory. But soon it was shewn by calcu- lation, that, if the force of the gravitation of the earth on a body continued always the same, then the regular beat of a pendulum was a necessary consequence. Tliis, then, is most important. Experience tells us that clocks keep time more or less correctly, according to the perfection of Theory and tlieirmechamsm. Theory shews that experiment. ^]^^g ^g ncccssarily thc case, and leads us to attribute trifling deviations to nothing but defective mechanism, or inevitable disturbance (slight, though it be) by the resistance of the air. Or to view it in a different aspect ; if we assume the regular beat of the pendulum to be a fact ea- 44 if tablisliedby observation, we obtain a proof of tlie constancy of the tendency of bodies to the earth i. e. that bodies weigh the same always at the same place. Nor is this all, the force of gravity regulates the time of the beat ; Theory tells ex- actly how the time and the force of gravity are connected by a simple formula. Suppose then that pendulums of the same length do not beat the same at difiPerent places on the earth, the inference will be that gravita- tion to the earth, the same at the same place is different at different places ; for example, will shew that a body weighs less at the equator of the earth, than it does near the poles. And this enables us to prove the rotation of the earth, to prove what certainly seems otherwise most likely, that the celestial vault with the stars and planets does not turn about the earth, but the earth rotates on its axis, inside it. This, the difference of beat of a pendulum shows in the following way. You know that the effect of making a Proves rota- '^ tion of earth, body movc in a circle about another is that it will fly off unless some force to the centre keeps it at the same distance. This ten- dency to fly off is called the centrifugal tendency. If the earth spin on its axis, a man at the equator would fly off were it not for the attraction of the earth, which is much more powerful than this ten- ! 45 dency. Nevertheless, he will press somewhat less heavily on the earth at the Equator than any- where else, because the centrifugal tendency in- creases the farther the body is from the axis; The pendulum oscillation shews as it ought to do, that the tendency to the earth is less at the equa- tor than elsewhere. Or again, reversing the question ; assume tlie rotation of the earth as an experimental fact, we have at once the means, by somewhat refined calculations, of finding how far the equator is from its axis, and by a series of or- And determines ganizcd cxperimcnts at different parts its shape. Qf j^]^q earth for determinins: its fi^'ure. And all this follows from Galileo's observed law of pendulum motion, and tlie theoretical proof that his law was correct. It is possible to measure arcs of the earth in different parts, and thus de- termine its shape ; the result is that its shape de- duced from the measurement, agrees Avell with the results from pendulum experiment. Not long after Gahleo's discovery of the pen- dulum, so important in its results, Stevinus made a simple and elegant discovery, on which the whole science of statical mecha- nics may be made to depend. Sup- pose an endless string Imng over a smooth double w^edge, with its base horizontal. It will remain at rest, and evidently will do the Stevinus' sliiiicul dis- covery. 46 K. m same if the loop below be cut off, because tlie tendency of the loop to pull it round one way, being the same as that to pull it the other, tlie loop may be removed. Hence the strings lying on the two sides balance, i. e. weights which balance one another on inclined planes, are pro- portional to their lengths. We have mentioned the overthrow of the supposition that nature abhorred a vacuum, and have asserted that the pressure of the atmosphere, Hydrostaticai ^^^ ^^^® causc to whicli all thc phe- law established, nomcua attributed to the above were to be referred. It was found that a pump would not raise water to a orreater heis^ht than 34 feet, so that nature had no objection then, to tolerate a vacuum „ . „. above the water. Torricelli made an Torricelli, Descartes, experiment with a column of mer- cury, and produced a vacuum above Pascal. \l 47 it at a Sinaller height ; the vacuum which we have often seen in a barometer tube. Descartes previous to this, had attributed the support of a column of mercury to tlie pressure of the air. This assumption Pascal proved by taking the barometer up a mountain, where the atmospheric r,ru n, xt- pfcssurc wfts of coursc less, and found Whewelrs Hist. ■'• of lud. Sciences, tlic supportcd columu less than be- " fore, by several inches. This fact being once established, hydrostatical science was carried on with a zeal which led to other impor- tant discoveries, on which our limits will not allow us to enlarge. We have mentioned one or two cases in wliich early science made use of laws for the explana- tion of phenomena, which, however untrue, were yet not violently absurd ; which in fact, were good enough as hypotheses; though later discovery overturned them. We must in many cases com- mence with an hypothesis, and only reject it when we meet with a better. To be able to make a good hypothesis, and examine fairly its Qualifications of truth, arc the great qualifications of a Phiiosopiier. jj philosoplicr. Hc must not be so wedded to the productions of his own ingenuity, that he will not reject them if they are not borne out by facts. He will imitate Newton, who re- jected for a time his own wonderful discovery of 48 gravitation, because of a slight numerical dis- crepancy in tlie result, a discrepancy so slight that many would have made it of no account. He will ])e like Kepler, who rejected one ingenious explanation of planetary motion after another, on account of trilling dilference between his theory and the observations apphed to test it. And not like the servile commentators on xiristotle, who indignantly rejected any statement, at variance with the dicta of the great master ; and in order to support his theories from rude interference, clothed them in language more and more ambi- guous, reducing science to be the art of talking unintelligibly on subjects ofwhichwe are ignorant. We are about to notice an extraordinary case in which rival theories seemed for a time almost equally probable; explained the circmii stances of nature to some extent with equal accuracy, and with equal inability to account fully for all phenomena. Optics as we have observed before, may be made to some extent a geometrical study. But there are certain phenomena which it seems impossible to explain, without knowing something of the consti- tution of light itself ; how it is produced, and wdiy it is that it follows the laws which experiment shews it to do. Newton supposed that light consisted of very minute particles, emitted in all directions from lumi- Thoories of Physical Optics. Newton's and Hnyghen's Theories. 49 nous bodies, and on this theory explained many phenomena of vision. Huyg-liens had about tlie same time imagined that it was produced hke sound, by the vibration of a subtle fluid, pene- trating all transparent substances. If so, as Mith sound, the vibration must be in equal times. The pendulum law furnished the law of vibration in equal times for theory to work upon ; would this law explain more appearances than the other, the emissive theory of light ? At first it would have seemed not. Eor instance,— if light go through a hole, there is a spot of light formed on a f ^n placed to receive it, determined by the shcipe of the hole. This is easy enough to explain if we suppose the particles of light to be shot straight through it ; but if ''we follow the analogy of sound, we should expect all the screen to be illuminated, since sound can be heard in all directions after passing through the hole. Eigid calculation, however^ shewed that it was all right ; that, if the waves were very much smaller than the hole, as those of light are, which are excessively minute, they would only go straight through. Eut if at all to be comapred with the hole in size, as those of sound, which are several feet in length, they would spread in all directions after passing through the hole. This theory too, accounted 50 for the shadovrs of objects not having defined sharp edges, but gradually fading away as we observe them to do. Ou applying the test of investigation, they ought to be sharp and dis- tinct on the emissive, but not on the wave theory. Eut theory teaches that, if it be true that light is produced by waves, these waves must in- terfere in certain cases, so that two streams of light actually produce darkness. A delicate experiment showed, however wonderful it may seem, that it is possible to produce dariiness by two streams of light. Let us take an illus- iiiustrati-i cf tration ; if a stone be thrown into a interference, pond, circular wfivcs sprcad in all directions. You could imagine another stone, dropped in directly after, so as to make waves which should fall exactly between the first waves and produce still water again. So it is that two waves of light or sound may follow one another in such a way, as to neutralize each other's effects. This discovery, due to experiment, was a wonderful confirmation of the wave theory, for there is no means of accounting for such dark- ness if the light were emitted or shot forth, and the emissive theory was therefore at fault. Also, theory shewed that, if light were the result of waves, there must be a bright spot m 51 Shadow of Sphere. the middle of the dense shadow of a sphere ; this bright spot may actually be seen if the experiment be carefully made ; another wonderful confirmation of theory. To take another illustration ; Newton had observed that, if two pieces of glass touched, which were slightly curved, there were brilliant rings of variou.s colours about the spot of contact, with Newton'3 ^l^ck Hugs bctwecn. The utmost ''°^'- that the emissive theory could do in explanation, was to assert that there might be, between the bright rings, rings only half as bright; the theory of waves shewed that the rings must be quite dark. Experiment gives black and not half bright lings. TJie various extraordinary and beautiful phenomena of what Polarization. '^ ^^^^^^ pokrizcd light, are on the whole consistent with the undulatory, and inconsistent with the emissive theory of light. Time will show whether any other theory may arise, which offers a better explanation of all the appearances. Per the present it must be consi- dered almost certain, that, if the right theory be not now laid down, the true one is but some slight modification of it. We have hitb'^rto dwelt chiefly on the more abstruse discoveries, for the prosecution of which a very considerable degree of know- 1 ■ ■'( 1,1 53 ledge is actually necessary. It were hopeless to attempt to pursue the law of gravitation into its inevitable consequences, establish the stability of the Solar System, and account for the various departures from the first broad statement of results, as has been done by Clairault, D'Alembert, Lagrange, t'orruj'ab- • Laplace and others, too numerous to "''"'• mention ; or even to foUow the m- vestigation of others in these matters, without considerable natural ability, and considerable mathematical skill. In respect of the theory of hn-ht, the same observation holds good. J3ut there are no sciences in which the value of the inductive ard dedttctive is more fully brought out ; and t uerefore, at the risk of bemg tedious and'obscure,! have dwelt on them somewhat at leno'th, since they show how the experimental proof suggests the theoretical, the theoretical paves the" way to further convincing experiment. We will now notice other branches of science to which a knowledge of mathematical proces- ses is not so indispensable. The Science of Chemistry is one that plays a most important nart in the industrial sciences and Chemistry, i'"^ '^ . .^ . theory entiroiy j,|-g ^^f[ [^ jts various romiiicaiions the result ot ex- ' n -r • n 1 i-1 11 periuicut. i^ tiie science of Lite, and the wen being of mankind ; yet the laws which govern 53 its operations are as yet to a great extent un- known, while those that are known are entirely experimental. It is beyond almost all others a science of number-, and proportions, and exact quantitative distribution of elements. Its theories admit of proof by there being always an invariable result, from performance of the same operations. There would seem to be fewer disturbances, few- er apparent exceptions to its laws, and no special mathematical learning is required, either to pre- dict the circumstances of future, or account for those of past experiments. Experiment will give the laws of combination, the exact proportion of ingredients tliat goes to the formation of natural compounds of elements ; and exact quan- titative analysis is one of the most beautiful and useful results from this knowledge, a know- ledge which none need despair of obtaining. The theories of Chemistry are of a simple and easily applicable kind, which do not even demand intense concentration of thought. It is therefore, one of the most popular as well as useful of studies — by its aid the secret poisoner cannot hope to escape the hands of justice — the scarcely less deadly assassin, who for a small profit adulterates our food and poisons our drink, is detected in his nefarious proceedings. By its aid the languid pulse is restored to vigorous ac- 54i .1 !■ tion, the diseased system to health ; and if we in- clude under the designation of Chemistry, the va- rious branches of experimental philosophy, we may add : by it, is the miner enabled to descend with safety into an atmosphere as inflammable as gun-powder — by it, is the soil rendered more fertile, and the destructive insect no longer able to carry on its ravages — by it, is the mine venti- lated and rendered wholesome — by it is the light- ning conveyed harmlessly to the ground. The science of Medicine is of itself a most ample illustration of the good and evil of induc- Medicai Theo- ^^^^ generalization. From the days Ties iaductive. ^j^g^ mcus' surgical skill enabled them to bind up a wound with healing herbs, to the present day, has the healing art been one es- pecially venerated and cultivated by mankind. Savage tribes treat the pretenders thereto with reverence ; civilized races shew their willingness to be relieved from the ills that flesh is heir to, by swallowing potions which they half believe will completely remove every disease, pain, or annoy- ance. Yet the laws of healing are entirely experi- mental. Observation, keen quicksighted obser- vation, puts a man on making experiments to veri- fy his suspicion of the efficacy of a certain re- medy. The instinct of animals, points out the virtues of this or that herb. Science finds out 55 the method of extracting the virtue, and leaving the useless portion behind. Take an instance or two, — a man grievously Discovery of ^fflictcd with aguc, is forced by neces- quiniae. gj^y. ^q ^j-'i^^]^ thc bittcr watcr in which some trees are lying ; he recovers : the cure is traced to the properties of the water, and thence to the bark of the trees. Prom this bark science extracts the quinine, known as a specific for ague. A soap boiler finds in his vats a substance Discovery of wliich corrodcs his vessels, and which iodine. jg different from any substance before known. The analysis of this by a scientific chemist produces one of the most singular and important chemical elements, iodine. Its presence is traced to the ashes of sea plants used in the manufacture ; to the sea water itself, and other marine products, among others, iTerschei, Nat. *« spougc. Dr. Coiudct of Gcueva Phil., page 51. remembered that burnt sponge had been used as a remedy for goitre, an unsightly glandular enlargement to which the moun- taineers of Switzerland are especially subject. He thought of trying its effect on those thus afflicted, and the result is the discovery of the most efficacious remedy for all such affections. Such are some of the ways in which discove- PF^ TSSSS^Bmimmm * 1) 1 t/'l iPi I. "i 56 ries are made. Experience or experiment are the only implements with which chemical science works ; it is from experience only tliat we know what will be the effect of putting a lump of sugar into water, of burning a stick in the fire, of mixing various colours, of the combining of elements. And philosophy teaches us that nothing is lost or dissipated. A philosopher w^ould deduce the weight of the smoke from the coals consumed, and the ashes left ; while an ordinary observer would imagine a loss of that consumed. We have then arrived at a class of sciences in which the deductions are simple, while the experimental processes are as boundless as nature herself. It is possible for a man, hav- ing no other ideas than those of space and motion, to reason out for himself all the propositions of geometry, and, having arrived at the laws of motion, solve for himself the motion of bodies under any conceivable law, w^hether DiflfcrcncG 1)G" tween chemistry gucll laW Cxist lu UaturC Or UOt ; tllC and pure and -, t- • , ^ • ji t'jj I'l mixed mathema- QUly limit bcmg tUC limit tO WlllCll he can carry his deductive proces- ses ; but he cannot reason out, that lemon-juice is a specific for scurvy, or that blue and yellow powders mixed will appear green to the naked eye, but blue and yellow mixed, under a micros- cope. 57 Eefore concluding, we must allude briefly to a class of sciences, or more properly empirical arts, which are still more dependent on experiment than any strictly natural science, of which the laws are simple and determinate, and capable of being followed out into their results. It were next to impossible to find anything more uncertain than the duration of human life, and any calculations based on it would seem at first to share in this uncertainty. It is however pos- sible, by very careful collection of instances, to reduce the uncertainty to mathematical value. On the whole, averages are nearly the same; the average height of thermometers, barometers, etc,, are more and more nearly alike, the longer the successive intervals of time, the greater the number of instances collected, and so it can be settled as a fact, quite accurately enough to reckon upon, that a man's life in a certain country, under certain circumstances, is worth so many years' purchase, and that by paying into a common stock a certain sum an- Theory and • i i • practice iu life nually, a man may msure to nis family, if he be called away by death, a certain provision. But yet in the various cases that may occur of life annuities, insurance for a limited number of years, insurance on the joint lives of several individuals, etc., problems occur V' y 58 of very considerable intricacy, and requiring very considerable mathematical skill to calculate the fair amount of contribution ; that individuals may not pay more than is necessary, or companies be ruined by insufficient subscription. Accord- ingly respectable offices grudge hardly any salary to secure the services of a first rate mathemati- cian, on whose reasoning from the given data they can rely. Here again, in a simple practical matter, is theory absolutely necessary to enable the practical matter to be carried out fairly and safely. Political economy is another of these arts, „ ,.,. , which men are learning but by slow Political econ- *-* *' omy almost an (Jeffrces. If it bc uo lougcr true experimental o *-" ^ science. ^^g^^ natious do not learn by experi- ence, the laws of government, supply and de- mand, taxation, military strength, and legislative enactments, are being but by slow degrees ar- rived at. Some Physical Laws are still waiting to be fully elucidated by the searching test of careful experiment, and a series of tabulated observa- tions. Such are the laws of the direction and force of magnetic cur- rents in the earth and their physical cause, of meteorologic phenomena and storms, and cli- Meteorology. 59 matology, in which investigations our own Cana- dian observatories are playing their part. As a last illustration of the manner in which such laws are discovered, I will direct your attention to a case in which what has been observed, may or may not lead to a discovery. Possible future ^hc magnetic current, that which discovery. dirccts thc nccdlc to the pole, is subject to variations both in intensity and direc- tion. There is one such variation that takes a period of ten years to go through all its changes and recur to the original circumstances. Now it was observed that certain changes in spots on the sun's disc took the same time, ten years, before they assumed the same appear- ance. Can it be that changes in the sun's spots have anything to do with magnetic currents on the earth's surface? If future investigation throw more light on this, which may be only an accidental coincidence, or may be the operation of a cause producing an effect, it is possible that this observation may aid in determining the cause of the current, or the nature of the spots, or both. But, ladies and gentlemen, I have already trespassed on your patience too long. If considering my audience to consist to a great extent of persons more or less scientific, I have tried to give too much science, or too many of the w^ 60 i~ 1 Vi hard terms wliicli make simple ideas hard to grasp ; if by striving to be instructive I have not only failed in this, but also failed to be interest- ing, I would only hope that something which may have been said may not have been said altogether in vain. In conclusion of this review of my subject, in which I am conscious that the more interesting topics have been more hastily dismissed, and that much has been omitted that might have been said, let me warn you that mighty as is the power of tlie inductive method to discover truth, it has its dangers if indolently or carelessly applied. The race of man in its infancy fell into error by the tendency to seize too liastily on a law and refine and reason upon it. Eeing delighted with their new found powers of thought and reason, men could Conclusion. .^ . i i i • not wait to examme on what basis their reasoning was founded ; they forgot that to build high they must dig deep ; and were anxious to rear a goodly and ornamental pile, and finish the structure without taking heed to the foundation. And in a practical age, so called, the same impatience after results mani- fests itself. It is the danger into which a young and progressive people are liable to fall ; they cannot bear enough in mind the proverb " fes- tina lente," " hasten slowly,'* and have patience 61 to wait for the results of laborious investigation. They find it hard to stop to gain enough of the theoretical knowledge which will make then- practical knowledge useful. A great and glo- rious future may be opening out before us, but it depends on us now to a great extent liow great and* how glorious it may be — whether the growth be of a sound and lasting character, or like a mushroom, sprouting in a night. We live in an age which reverses the old sup- position that science has nothing to do with nature or with man. We consider that science may enter into everything rather than be supe- rior to everything. We do not try to prove to men that they are to render themselves indepen- dent of the laws of nature, but to render them- selves masters of them. Science is like an ele- phant's trunk, that will pick up a pin or rend an oak. But in order to use this instrument pro- perly, it must be really science, really knowledge, not a vague smattering, not a servile appropria- tion of the works of others. Every one may be more or less scientific. It is a noble thing to trace the laws of nature, and to rise from the contemplation of nature to nature's God. Eut let us remember that we shall not be men worthy of the name if we only seek after knowledge for the purposes of sensual ease or pecuniary profit. 62 This is not the way to be great and noble ; this is not the way to secure tlie glorious birthright of humanity, neither will it compass the end sought. It is only by aiming at something high, that we can achieve at all ; only by aiming at perfection that we reach excellence. We can never tell what good to mankind may result from the prosecution of science in any direction. Who would have supposed that the dreams of Kepler would lead to the explication of the laws which govern the universe ; that the gropings of the alchemist after gold and an immortal elixir, would lead to the useful and now indispensable science of chemistry. That a shrewd man ob- serving a lamp swinging in a cathedral should by this observation enable us to weigh the earth and determine its shape. Let us not be content with a log shanty when we can build a goodly stone mansion. Men in Canada have eyes and ears, brains and intellects, as well as stal- wart arms and manly hearts. Let them put them to good use. Let societies of arts and manufactures flourish. Let universities and colleges do their work in instilling sound theoretical knowledge, and, as far as may be, sound practical instruction. Let each and all keep eyes and ears about them to take advan- tage of all the opportunities of improvement 63 offered. The time is now, now to lay a solid foundation of tlie greatness of nations to come. Who loves not knowledgo ? Who shall rail Against her beauty ? May she mix With men and prosper. Who shall fix Her pillars ? Let her work prevail. FINIS.