自然哲学的数学原理-3

ing and important, and had attracted considerable investigation.He, however, was the first to determine the law of the production of these colours, arid, during the same year made known theresults of his researches herein to the Royal Society. His modeof procedure in these experiments was simple and curious. Heplaced a double convex lens of a large known radius of curvature,the flat surface of a plano-convex object glass. Thus, fromUFE OF SIR ISAAC NEWTON. 25their point of contact at the centre, to the circumference of thelens, he obtained plates of air, or spaces varying from the extremestpossible thinness, by slow degrees, to a considerable thickness. Letting the light fall, every different thickness of thisplate of air gave different colours the point of contact of thelens and glass forming the centre of numerous concentric colorednags. Now the radius of curvature of the lens being known, thethickness of the plate of air, at any given point, or where any particular colour appeared, could be exactly determined. Carefullynoting, therefore, the order in which the different colours appeared, he measured, with the nicest accuracy, the different thick*nesses at which the most luminous parts of the rings were produced, whether the medium were air, water, or mica all thesesubstances giving the same colours at different thicknesses ; theratio of which he also ascertained. From the phenomena observed in these experiments, Newton deduced his Theory of Fits ofEASY REFLECTION AND TRANSMISSION oflight. It consists in supposing that every particle of light, from its first discharge from a luminous body, possesses, at equally distant intervals, dispositions tobe reflected from, or transmitted through the surfaces of bodiesupon which it may fall. For instance, if the rays are in a Fit ofEasy Reflection, they are on reaching the surface, repelled,thrown off] or reflected from it; if, in a Fit of Easy Transmission,they are attracted, drawn in, or transmitted through it. By thisTheory of Fits, our author likewise explained the colours ofthick plates.He regarded light as consisting of small material particlesemitted from shining substances. He thought that these particles could be re-combined into solid matter, so that "gross bodiesand light, were convertible into one another ;" that the particles oflight and the particles of solid bodies acted mutually upon eachother ; those of light agitating and heating those of solid bodies,and the latter attracting and repelling the former. Newton wasthe first to suggest the idea of the POLARIZATION of light.In the paper entitled An Hypothesis Explaining Properties ofLight, December, 1675, our author first introduced his opinions respecting Ether opinions which he afterward abandoned and again26 LIFE OF SIR S.。AC 1SEWTON.permanently resumed " A most subtle spirit which pervades" ahbodies, and is expanded through all the heavens. It is electric,and almost, if not quite immeasurably elastic and rare. " By theforce and action of which spirit the particles of bodies mutuallyattract one another, at near distances, and cohere, if contiguous ;and electric bodies operate at greater distances, as well repellingas attracting the neighbouring corpuscles ; and light is emitted,-reflected, refracted, inflected and heats bodies ; and all sensationis excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from theoutward organs of sense to the brain, and from the brain into themuscles." This "spirit" was no anima mundi ; nothing furtherfrom the thought of Newton ; but was it not, on his part, a partial recognition of, or attempt to reach an ultimate material force,or primary element, by means of which, " in the roaring loom oftime," this material universe, God s visible garment, may bewoven for us ?The Royal Society were greatly interested in the results ofsome experiments, which our author had, at the same time, communicated to them relative to the excitation of electricity in glass ;and they, after several attempts and further direction from him,succeeded in re-producing the same phenomena.One of the most curious of Newton s minor inquiries related tothe connexion between the refractive powers and chemical composition of bodies. He found on comparing the refractive powersand the densities of many different substances, that the formerwere very nearly proportional to the latter, in the same bodies.Unctuous and sulphureous bodies were noticed as remarkable exceptions as well as the diamond their refractive powers being twoor three times greater in respect of their densities than in thecase of other substances, while, as among themselves, the one wasgenerally proportional to the other. He hence inferred as to thediamond a great degree of combustibility ;a conjecture whichthe experiments of modern chemistry have shown to be true.The chemical researches of our author were probably pursuedwith more or less diligence from the time of his witnessing someLIFE OF .SIR ISAAC NEWTON. 27?t the uractical operations in that science at the Apothecary s atGrantham. DE NATURA ACIDORUM is a short chemical paper, onvarious topics, and published in Dr. Horsley s Edition of hisworks. TABULA QUANTITATUM E r GRADUUM COLORIS was inserted iii the Philosophical Transactions ;it contains a comparative scale of temperature from that of melting ice to that of asmall kitchen coal-fire. He regarded fire as a body heated so hotas to emit light copiously ; and flame as a vapour, fume, or exhalation heated so hot as to shine. To elective attraction, bythe operation of which the small particles of bodies, as he conceived, act upon one another, at distances so minute as to escapeobservation, he ascribed all the various chemical phenomena otprecipitation, combination, solution, and crystallization, and themechanical phenomena of cohesion and capillary attraction. Newton s chemical views were illustrated and confirmed, in part, atleast, in his own life-time. As to the structure of bodies, he wasof opinion" that the smallest particles of matter may cohere bythe strongest attractions, and compose bigger particles of weakervirtue; and many of these may cohere and compose bigger partides whose virtue is still weaker ; and so on for divers successions, until the progression end in the biggest particles, on whichthe operations in chemistry and the colours of natural bodies depend, and which by adhering, compose bodies of sensible magnitude."There is good reason to suppose that our author was a diligentstudent of the writings of Jacob Behmen ; and that in conjunctionwith a relative, Dr. Newton, he was busily engaged, for severalmonths in the earlier part of life, in quest of the philosopher stincture. " Great Alchymist," however, very imperfectly describes the character of Behmen, whose researches into thingsmaterial and things spiritual, things human and things divine, aifordthe strongest evidence of a great and original mind.More appropriately here, perhaps, than elsewhere, may begiven Newton s account of some curious experiments, made in hisown person, on the action of light upon the retina, Locke, whowas an intimate friend of our author, wrote to him for his opinionon a certain fact stated in Boyle s Book of Colours. Newton, in2S LIFE OF SIR ISAAC NEWTON.his reply, dated June 30th, 16(Jl, narrates the following circumstances, which probably took place in the course of his opticalresearches. Thus :" The observation you mention in Mr. Boyle s Book of ColoursI once tried upon myself with the hazard of my eyes. Themanner was this;I looked a very little while upon the sun in thelooking-glass with my right eye, and then turned my eyes into adark corner of my chamber, arid winked, to observe the impression made, and the circles of colours which encompassed it, andhow they decayed by degrees, and at last vanished. This I repeated a second and a third time. At the third time, when thephantasm of light and colours about it were almost vanished, intending my fancy upon them to see their last appearance, I found,to my amazement, that they began to return, and by little andlittle to become as lively and vivid as when I had newly lookedupon the sun. But when I ceased to intend my fancy upon them,they vanished again. After this, I found, that as often as I wentinto the dark, and intended my mind upon them, as when a manlooks earnestly to see anything which is difficult to be seen, Icould make the phantasm return without looking any more uponthe sun ; and the oftener I made it return, the more easily I couldmake it return again. And, at length, by repeating this, withoutlooking any more upon the sun, I made such an impression on myeye, that, if I looked upon the clouds, or a book, or any brightobject, I saw upon it a round bright spot of light like the sun,and, which is still stranger, though I looked upon the sun withmy right eye only, and not with my left, yet my fancy began *omake an impression upon my left eye, as well us upon my right.For if I shut my right eye, or looked upon a book, or the clouds,with my left eye, I could see the spectrum of the sun almost asplain as with my right eye, if I did but intend my fancy a littlewhile upon it;for at first, if I shut my right eye, and looked withmy left, the spectrum of the sun did not appear till I intended myfancy upon it; but by repeating, this appeared every time moreeasily. And now, in a few hours time, I had brought my eyesto such a pass, that I could look upon no blight object with eithereye, but I saw the sun before me, so that I durst neither writeLIFE OF SIR ISAAC NEWTON. 29nor read ; but to recover the use of my eyes, shut myself up inmy chamber made dark, for three days together, and used allmeans to divert my imagination from the sun. For if I thoughtupon him, I presently saw his picture, though I was in the dark.But by keeping in the dark, and employing my mind about otherthings, I began in three or four days to have some use of my eyesagain ; and by forbearing to look upon bright objects, recoveredthem pretty well, though not so well but that, for some monthsafter, the spectrum of the sun began to return as often as I beganto meditate upon the phenomena, even though I lay in bed at midnight with my curtains drawn. But now I have been very wellfor many years, though I am apt to think, if I durst venture myeyes, I could still make the phantasm return by the power of myfancy. This story I tell you, to let you understand, thaj; in theobservation related by Mr. Boyle, the man s fancy probably concurred with the impression made by the sun s light to producethat phantasm of the sun which he constantly saw in bright objects. And so your question about the cause of phantasm involves another about the power of fancy, which I must confess istoo hard a knot for me to untie. To place this effect in a constantmotion is hard, because the sun ought then to appear perpetually.It seems rather to consist in a disposition of the sensorium tomove the imagination strongly, and to be easily moved, both bythe imagination and by the light, as often as bright objects arelooked upon."JThough Newton had continued silent, yet his thoughts wereby no means inactive upon the vast subject of the planetary motions. The idea of Universal Gravitation, first caught sight of, soto speak, in the garden at Woolsthorpe, years ago, had graduallyexpanded upon him. We find him, in a letter to Dr. Hooke,Secretary of the Royal Society, dated in November, 1679, proposing to verify the motion of the earth by direct experiment,namely, by the observation of the path pursued by a body fallingfrom a considerable height. He had concluded that the pathwould be spiral ; but Dr. Hooke maintained that it would be aneccentric ellipse iu vacuo, and an ellipti-spiral in a resisting medium. Our author, aided by this correction of his error, and by30 LIFE OF SIR ISAAC NEWTON.the discovery that a projectile would move in an elliptical orbilwhen under the influence of a force varying inversely as thesquare of the distance, was led to discover " the theorem bjwhich he afterwards examined the ellipsis ;" and to demonstratethe celebrated proposition that a planet acted upon by an attractive force varying inversely as the squares of the distances willdescribe an elliptical orbit, in one of whose foci the attractiveforce resides.When he was attending a meeting of the Royal Society, inJune 1682, the conversation fell upon the subject of the measurement of a degree of the meridian, executed by M. Picard, aFrench Astronomer, in 1679. Newton took a memorandum oithe result; and afterward, at the earliest opportunity, computedfrom it the diameter of the earth : furnished with these new data,he resumed his calculation of 1666. As he proceeded therein,he saw that his early expectations were now likely to be realized ;the thick rushing, stupendous results overpowered him ; he became unable to carry on the process of calculation, and intrustedits completion to one of his friends. The discoverer had, indeed,grasped the master-fact. The law of falling bodies at the earth ssurface was at length identified with that which guided the moonin her orbit. And so his GREAT THOUGHT, that had for sixteenyears loomed up in dim, gigantic outline, amid the first dawn of aplausible hypothesis, now stood forth, radiant and not less grand,in the mid-day light of demonstrated truth.It were difficult, nay impossible to imagine, even, the influenceof a result like this upon a mind like Newton s. It was as if thekeystone had been fitted to the glorious arch by which his spiritshould ascend to the outskirts of infinite space spanning the immeasurable weighing the imponderable computing the incalculablemapping out the marchings of the planets, and the far-wanderings of the comefs, and catching, bring back to earth some clearernotes of that higher melody which, as a sounding voice, bearsperpetual witness to the design and omnipotence of a creatingDeity.Newton, extending the law thus obtained, composed a seriesof about twelve propositions on the motion of the primary planetsLIFE OF SIR ISAAC NEWTON. 31about the sun. These were sent to London, and communicatedto the Royal Society about the end of 1683. At or near this period, other philosophers, as Sir Christopher Wren, Dr. Halley,and Dr. Hooke, were engaged in investigating the same subject ;but with no definite or satisfactory results. Dr. Halley, havingseen, it is presumed, our author s propositions, went in August,1684, to Cambridge to consult with him upon the subject.Newton assured him that he had brought the demonstration toperfection. In November, Dr. Halley received a copy of thework ; and, in the following month^ announced . it to the RoyalSociety, with the author s promise to have it entered upon theirRegister. Newton, subsequently reminded by the Society of hispromise, proceeded in the diligent preparation of the work, and.though suffering an interruption of six weeks, transmitted themanuscript of the first book to London before the end of April.The work was entitled PHILOSOPHI/E NATURALIS PRINCIPIAMATHEMATICA, dedicated to the Royal Society, and presentedthereto on the 28th of April, 1685-6. The highest encomiumswere passed upon it; and the council resolved, on the 19th ofMay, to print it at the expense of the Society, and under the direction of Dr. Halley. The latter, a few days afterward, communicated these steps to Newton, who, in a reply, dated the 20thof June, holds the following language :" The proof you sent meI like very well. I designed the whole to consist of three books ;the second was finished last summer, being short, and only wantstranscribing, and drawing the cuts fairly. Some new propositionsI have since thought on, which I can as well let alone. Thethird wants the theory of comets. In autumn last, I spent twomonths in calculation to no purpose for want of a good method,which made me afterward return to the first book, and enlarge itwith diverse propositions, some* relating to comets, others to otherthings found ouf last winter. The third I now design to suppress. Philosophy is such an impertinently litigious lady, that aman had as good be engaged in liw-suits as have to do with her.I found it so formerly, and now I can no sooner come near heragain, but she gives me warning. The first two books withoutthe third will not so well bear the title of P/iilosophicc Naturalis332 LIFE OF SIR ISAAC NEWTON.Principia Mathematicia ; and thereupon I had altered it to this,De Motu Corporum Libri duo. But after second thought I retain the former title. It will help the sale of the book, which Iought not to diminish now tisyours."This "warning" arose from some pretensions put forth by Dr.Hooke. And though Newton gave a minute and positive refutations of such claims, yet, to reconcile all differences, he generously added to Prop. IV. Cor. 6, Book I, a Scholium, in whichWren, Hooke and Halley are acknowledged to have independently deduced the law of gravity from the second law ofKepler.The suppression of the third book Dr. Halley could not endureto see. " I must again beg you" says he," not to let your resentments run so high as to deprive us of your third book, wherein your applications of your mathematical doctrine to the theoryof comets, and several curious experiments, which, as I guess bywhat you write ought to compose it, will undoubtedly render itacceptable to those who will call themselves philosophers withoutmathematics, which are much the greater number." To thesesolicitations Newton yielded. There were no "resentments," however, as we conceive, in his "design to suppress." He soughtpeace ;for he loved and valued it above all applause. But, inspite of his efforts for tranquillity s sake, his course of discoverywas all along molested by ignorance or presumptuous rivalry.The publication of the great work now went rapidly forwards,The second book was sent to the Society, and presented on the2d March ; the third, on the 6th April ; and the whole was completed and published in the month of May, 1686-7. In the second Lemma of the second book, the fundamental principle of hisfiuxionary calculus was, for the first time, given to the world ; butits algorithm or notation did not appear till published in thesecond volume nf Dr. Wallis s works, in 1693.And thus was ushered into existence The PRINCIPIA a workto which pre-eminence above all the productions of the humanintellect has been awarded a work that must be esteemed ofpriceless worth so long as Science has a votary, or a single worshipper be left to kneel at the altar of Truth.LIFE OF SIR ISAAC NEWTON. 33The entire work bears the general title of THE MATHEMATICALPRINCIPLES OF NATURAL PHILOSOPHY. It consists of three books:the first two, entitled, OF THE MOTION OF BODIES, are occupiedwith the laws and conditions of motions and forces, and are illustrated with many scholia treating of some of the most generaland best established points in philosophy, such as the density andresistance of bodies, spaces void of matter, and the motion ofsound and light. From these principles, there is deduced, in thethird book, drawn up in as popular a style as possible and entitled,OF THE SYSTEM OF THE WORLD, the constitution of the system ofi he world. In regard to this book, the author say^" I had, indeed,composed the third Book in a popular method, that it might be readby many ; but afterwards, considering that such as had not sufficentlyentered into the principles could not easily discover thestrength of the consequences, nor lay aside the prejudices to whichthey had been many years accustomed, therefore, to prevent disputes which might be raised upon such accounts, I chose to reducethe substance of this Book into the form of Propositions (in themathematical way), which should be read by those only who hadfirst made themselves masters of the principles established in thepreceding Books : not that I would advise any one to the previousstudy of every Proposition of those Books." "It is enough itone carefully reads the Definitions, the Laws of Motion, and thethree first Sections of the first Book. He may then pass on tothis Book, and consult such of the remaining Propositions of thefirst two Books, as the references in this, and his occasions shall require." So that " The System of the World" is composed both" in a popular method," and in the form of mathematical Propositions.The principle of Universal Gravi ition, namely, that everyparticle of matter is attracted by, or gravitates to, every otherparticle of matter, icith a force inversely proportional to thesquares of their distances is the discovery w? ich characterizesThe PRINCIPIA. This principle the author deduced from the motion of the moon, and the three laws of Kepler laws, whichNewton, in turn, by his greater law, demonstrated to be true.From the first law of Kepler, namely, the proportionality ofLIFE OF SIR ISAAC NEWTON.the areas to t。ie times of their description, our author inferredthat the force which retained the planet in its orbit was alwaysdirected to the sun ; and from the second, namely, that everyplanet moves in an ellipse with the sun in one of its foci, he drewthe more general inference that the force by which the planetmoves round that focus varies inversely as the square of its distance therefrom : and he demonstrated that a planet acted uponby such a force could not move in any other curve than a conicsection ; showing when the moving body would describe a circular, an elliptical, a parabolic, or hyperbolic orbit. He demonstrated, too, that this force, or attracting, gravitating power resided in every, the least particle ; but that, in spherical masses, itoperated as if confined to their centres ; so that, one sphere orbody will act upon another sphere or body, with a force directlyproportional to the quantity of matter, and inversely as the square