Now； subducting the diameter of the hole from the length and breadth of the image； there remains 13 inches the length； and 2 3/8 the breadth； comprehended by those rays； which； passing through the centre of the said hole； which that breadth subtended； was about 31'； answerable to the sun's diameter； but the angle which its length subtended was more than five such diameters； namely 2 degrees 49'。 〃Having made these observations； I first computed from them the refractive power of the glass； and found it measured by the ratio of the sines 20 to 31。 And then； by that ratio； I computed the refractions of two rays flowing from opposite parts of the sun's discus； so as to differ 31' in their obliquity of incidence； and found that the emergent rays should have comprehended an angle of 31'； as they did； before they were incident。 〃But because this computation was founded on the hypothesis of the proportionality of the sines of incidence and refraction； which though by my own experience I could not imagine to be so erroneous as to make that angle but 31'； which in reality was 2 degrees 49'； yet my curiosity caused me again to make my prism。 And having placed it at my window； as before； I observed that by turning it a little about its axis to and fro； so as to vary its obliquity to the light more than an angle of 4 degrees or 5 degrees； the colors were not thereby sensibly translated from their place on the wall； and consequently by that variation of incidence the quantity of refraction was not sensibly varied。 By this experiment； therefore； as well as by the former computation； it was evident that the difference of the incidence of rays flowing from divers parts of the sun could not make them after decussation diverge at a sensibly greater angle than that at which they before converged； which being； at most； but about 31' or 32'； there still remained some other cause to be found out； from whence it could be 2 degrees 49'。〃 All this caused Newton to suspect that the rays； after their trajection through the prism； moved in curved rather than in straight lines； thus tending to be cast upon the wall at different places according to the amount of this curve。 His suspicions were increased； also； by happening to recall that a tennis…ball sometimes describes such a curve when 〃cut〃 by a tennis…racket striking the ball obliquely。 〃For a circular as well as a progressive motion being communicated to it by the stroke；〃 he says； 〃its parts on that side where the motions conspire must press and beat the contiguous air more violently than on the other； and there excite a reluctancy and reaction of the air proportionately greater。 And for the same reason； if the rays of light should possibly be globular bodies； and by their oblique passage out of one medium into another acquire a circulating motion； they ought to feel the greater resistance from the ambient ether on that side where the motions conspire； and thence be continually bowed to the other。 But notwithstanding this plausible ground of suspicion； when I came to examine it I could observe no such curvity in them。 And； besides （which was enough for my purpose）； I observed that the difference 'twixt the length of the image and diameter of the hole through which the light was transmitted was proportionable to their distance。 〃The gradual removal of these suspicions at length led me to the experimentum crucis； which was this： I took two boards； and； placing one of them close behind the prism at the window； so that the light must pass through a small hole； made in it for the purpose； and fall on the other board； which I placed at about twelve feet distance； having first made a small hole in it also； for some of the incident light to pass through。 Then I placed another prism behind this second board； so that the light trajected through both the boards might pass through that also； and be again refracted before it arrived at the wall。 This done； I took the first prism in my hands and turned it to and fro slowly about its axis； so much as to make the several parts of the image； cast on the second board； successively pass through the hole in it； that I might observe to what places on the wall the second prism would refract them。 And I saw by the variation of these places that the light； tending to that end of the image towards which the refraction of the first prism was made； did in the second prism suffer a refraction considerably greater than the light tending to the other end。 And so the true cause of the length of that image was detected to be no other than that LIGHT consists of RAYS DIFFERENTLY REFRANGIBLE； which； without any respect to a difference in their incidence； were； according to their degrees of refrangibility； transmitted towards divers parts of the wall。〃＇1＇
THE NATURE OF COLOR Having thus proved the composition of light； Newton took up an exhaustive discussion as to colors； which cannot be entered into at length here。 Some of his remarks on the subject of compound colors； however； may be stated in part。 Newton's views are of particular interest in this connection； since； as we have already pointed out； the question as to what constituted color could not be agreed upon by the philosophers。 Some held that color was an integral part of the substance； others maintained that it was simply a reflection from the surface； and no scientific explanation had been generally accepted。 Newton concludes his paper as follows： 〃I might add more instances of this nature； but I shall conclude with the general one that the colors of all natural bodies have no other origin than this； that they are variously qualified to reflect one sort of light in greater plenty than another。 And this I have experimented in a dark room by illuminating those bodies with uncompounded light of divers colors。 For by that means any body may be made to appear of any color。 They have there no appropriate color； but ever appear of the color of the light cast upon them； but yet with this difference； that they are most brisk and vivid in the light of their own daylight color。 Minium appeareth there of any color indifferently with which 'tis illustrated； but yet most luminous in red； and so Bise appeareth indifferently of any color with which 'tis illustrated； but yet most luminous in blue。 And therefore Minium reflecteth rays of any color； but most copiously those indued with red； and consequently； when illustrated with daylightthat is； with all sorts of rays promiscuously blendedthose qualified with red shall abound most in the reflected light； and by their prevalence cause it to appear of that color。 And for the same reason； Bise； reflecting blue most copiously； shall appear blue by the excess of those rays in its reflected light； and the like of other bodies。 And that this is the entire and adequate cause of their colors is manifest； because they have no power to change or alter the colors of any sort of rays incident apart； but put on all colors indifferently with which they are enlightened。〃＇2＇ This epoch…making paper aroused a storm of opposition。 Some of Newton's opponents criticised his methods； others even doubted the truth of his experiments。 There was one slight mistake in Newton's belief that all prisms would give a spectrum of exactly the same length； and it was some time before he corrected this error。 Meanwhile he patiently met and answered the arguments of his opponents until he began to feel that patience was no longer a virtue。 At one time he even went so far as to declare that； once he was 〃free of this business；〃 he would renounce scientific research forever； at least in a public way。 Fortunately for the world； however； he did not adhere to this determination； but went on to even greater discoverieswhich； it may be added； involved still greater controversies。 In commenting on Newton's discovery of the composition of light； Voltaire said： 〃Sir Isaac Newton has demonstrated to the eye； by the bare assistance of a prism； that light is a composition of colored rays； which； being united； form white color。 A single ray is by him divided into seven； which all fall upon a piece of linen or a sheet of white paper； in their order one above the other； and at equal distances。 The first is red； the second orange； the third yellow； the fourth green； the fifth blue； the sixth indigo； the seventh a violet purple。 Each of these rays transmitted afterwards by a hundred other prisms will never change the color it bears； in like manner as gold； when completely purged from its dross； will never change afterwards in the crucible。〃＇3＇
XII。 NEWTON AND THE LAW OF GRAVITATION We come now to the story of what is by common consent the greatest of scientific achievements。 The law of universal gravitation is the most far…reaching principle as yet discovered。 It has application equally to the minutest particle of matter and to the most distant suns in the universe； yet it is amazing in its very simplicity。 As usually phrased； the law is this： That every particle of matter in the universe attracts every other particle with a force that varies directly with the mass of the particles and inversely as the squares of their mutual distance。 Newton did not vault at once to the full expression of this law； though he had formulated it fully before he gave t