Chapter XV: Introduction (11)

36. AFTER this it is shewn, from the proportion of the equatorial diameter of the earth to its axis, how the same may be determined of any other planet, whose density in comparison of the density of the earth, and the time of its revolution about its axis, are known. And by the rule delivered for this, it is found, that the diameter of the equator in Jupiter should bear to its axis about the proportion of 10 to 9[276], and accordingly this planet appears of an oval form to the astronomers. The most considerable effects of this spheroidical figure our author takes likewise into consideration; one of which is that bodies are not equally heavy in all distances from the poles; but near the equator, where the distance from the center is greatest, they are lighter than towards the poles: and nearly in this proportion, that the actual power, by which they are drawn to the center, resulting from the difference between their absolute gravity and centrifugal force, is reciprocally as the distance from the center. That this may not appear to contradict what has before been said of the alteration of the power of gravity, in proportion to the change of the distance from the center, it is proper carefully to remark, that our author has demonstrated three things relating hereto: the first is, that decrease of the power of gravity as we recede from the center, which has been fully explained in the last chapter, upon supposition that the earth and planets are perfect spheres, from which their difference is by many degrees too little to require notice for the purposes there intended: the next is, that whether they be perfect spheres, or exactly such spheroids as have now been mentioned, the power of gravity, as we descend in the same line to the center, is at all distances as the distance from the center, the parts of the earth above the body by drawing the body towards them lessening its gravitation towards the center[277]; and both these assertions relate to gravity alone: the third is what we mentioned in this place, that the actual force on different parts of the surface, with which bodies are drawn to the center, is in the proportion here assigned[278].

38. THE next effect of this figure of the earth is an obvious consequence of the former: that pendulums of the same length do not in different distances from the pole make their vibrations in the same time; but towards the poles, where the gravity is strongest, they move quicker than near the equator, where they are less impelled to the center; and accordingly pendulums, that measure the same time by their vibrations, must be shorter near the poles than at a greater distance. Both which deductions are found true in fact; of which our author has recounted particularly several experiments, in which it was found, that clocks exactly adjusted to the true measure of time at Paris, when transported nearer to the equator, became erroneous and moved too slow, but were reduced to their true motion by contracting their pendulums. Our author is particular in remarking, how much they lost of their motion, while the pendulums remained unaltered; and what length the observers are said to have shortened them, to bring them to time. And the experiments, which appear to be most carefully made, shew the earth to be raised in the middle between the poles, as much as our author found it by his computation[279].

39. THESE experiments on the pendulum our author has been very exact in examining, inquiring particularly how much the extension of the rod of the pendulum by the great heats in the torrid zone might make it necessary to shorten it. For by an experiment made by PICART, and another made by DE LA HIRE, heat, though not very intense, was found to increase the length of rods of iron. The experiment of PICART was made with a rod one foot long, which in winter, at the time of frost, was found to increase in length by being heated at the fire. In the experiment of DE LA HIRE a rod of six foot in length was found, when heated by the summer sun only, to grow to a greater length, than it had in the aforesaid cold season. From which observations a doubt has been raised, whether the rod of the pendulums in the aforementioned experiments was not extended by the heat of those warm climates to all that excess of length, the observers found themselves obliged to lessen them by. But the experiments now mentioned shew the contrary. For in the first of them the rod of a foot long was lengthened no more than 1/9 part of what the pendulum under the equator must be diminished; and therefore a rod of the length of the pendulum would not have been extended above ⅓ of that length. In the experiment of DE LA HIRE, where the heat was less, the rod of six foot long was extended no more than 3/10 of what the pendulum must be shortened; so that a rod of the length of the pendulum would not have gained above 3/20 or 1/7 of that length. And the heat in this latter experiment, though less than in the former, was yet greater than the rod of a pendulum can ordinarily contract in the hottest country; for metals receive a great heat when exposed to the open sun, certainly much greater than that of a human body. But pendulums are not usually so exposed, and without doubt in these experiments were kept cool enough to appear so to the touch; which they would do in the hottest place, if lodged in the shade. Our author therefore thinks it enough to allow about 1/10 of the difference observed upon account of the greater warmth of the pendulum.

40. THERE is a third effect, which the water has on the earth by changing its figure, that is taken notice of by our author; for the explaining of which we shall first prove, that bodies descend perpendicularly to the surface of the earth in all places. The manner of collecting this from observation, is as follows. The surfaces of all fluids rest parallel to that part of the surface of the sea, which is in the same place with them, to the figure of which, as has been particularly shewn, the figure of the whole earth is formed. For if any hollow vessel, open at the bottom, be immersed into the sea; it is evident, that the surface of the sea within the vessel will retain the same figure it had, before the vessel inclosed it; since its communication with the external water is not cut off by the vessel. But all the parts of the water being at rest, it is as clear, that if the bottom of the vessel were closed, the figure of the water could receive no change thereby, even though the vessel were raised out of the sea; any more than from the insensible alteration of the power of gravity, consequent upon the augmentation of the distance from the center. But now it is clear, that bodies descend in lines perpendicular to the surfaces of quiescent fluids; for if the power of gravity did not act perpendicularly to the surface of fluids, bodies which swim on them could not rest, as they are seen to do; because, if the power of gravity drew such bodies in a direction oblique to the surface whereon they lay, they would certainly be put in motion, and be carried to the side of the vessel, in which the fluid was contained, that way the action of gravity inclined.

41. HENCE it follows, that as we stand, our bodies are perpendicular to the surface of the earth. Therefore in going from north to south our bodies do not keep in a parallel direction. Now in all distances from the pole the same length gone on the earth will not make the same change in the position of our bodies, but the nearer we are to the poles, we must go greater length to cause the same variation herein. Let M I L K (in fig. 117) represent the figure of the earth, M, L the poles, I, K two opposite points in the middle between these poles. Let T V and P O be two arches, T V being most remote from the pole L; draw T W, V X, P Q, O R, each perpendicular to the surface of the earth, and let T W, V X meet in Y, and P Q, O R in S. Here it is evident, that in passing from V to T the position of a man’s body would be changed by the angle under T Y V, for at V he would stand in the line Y V continued upward, and at T in the line Y T; but in passing from O to P the position of his body would be changed by the angle under O S P. Now I say, if these two angles are equal the arch O P is longer than T V: for the figure M I L K being oblong, and I K longer than M L, the figure will be more incurvated toward I than toward L; so that the lines T W and V X will meet in Y before they are drawn out to so great a length as the lines P Q and O R must be continued to, before they will meet in S. Since therefore Y T and Y V are shorter than P S and S V, T V must be less than O P. If these angles under T Y V and O S P are each 1/90 part of the angle made by a perpendicular line, they are said each to contain one degree. And the unequal length of these arches O P and V T gives occasion to the assertion, that in passing from north to south the degrees on the earth’s surface are not of an equal length, but those near the pole longer than those toward the equator. For the length of the arch on the earth lying between the two perpendiculars, which make an angle of a degree with each other, is called the length of a degree on the earth’s surface.

42. THIS figure of the earth has some effect on eclipses. It has been observed above, that sometimes the nodes of the moon’s orbit lie in a straight line drawn from the sun to the earth; in which case the moon will cross the plane of the earth’s motion at the new and full. But whenever the moon passes near the plane at the full, some part of the earth will intercept the sun’s light, and the moon shining only with light borrow’d from the sun, when that light is prevented from falling on any part of the moon, so much of her body will be darkened. Also when the moon at the new is near the plane of the earth’s motion, the inhabitants on some part of the earth will see the moon come under the sun, and the sun thereby be covered from them either wholly or in part. Now the figure, which we have shewn to belong to the earth, will occasion the shadow of the earth on the moon not to be perfectly round, but cause the diameter from east to west to be somewhat longer than the diameter from north to south. In eclipse of the sun this figure of the earth will make some little difference in the place, where the sun shall appear wholly or in any given part covered. Let A B C D (in fig. 118.) represent the earth, A C the axis whereon it turns daily, E the center. Let F A G C represent a perfect globe inscribed within the earth. Let H I be a line drawn through the centers of the sun and moon, crossing the surface of the earth in K, and the surface of the globe inscribed in L. Draw E L, which will be perpendicular to the surface of the globe in L: and draw likewise K M, so that it shall be perpendicular to the surface of the earth in K. Now whereas the eclipse would appear central at L, if the earth were the globe A G C F, and does really appear so at K; I say, the latitude of the place K on the real earth is different from the latitude of the place L on the globe F A G C. What is called the latitude of any place is determined by the angle which the line perpendicular to the surface of the earth at that place makes with the axis; the difference between this angle, and that made by a perpendicular line or square being called the latitude of each place. But it might here be proved, that the angle which K M makes with M C is less, than the angle made between L E and E C: consequently the latitude of the place K is greater, than the latitude, which the place L would have.

43. THE next effect, which follows from this figure of the earth, is that gradual change in the distance of the fixed stars from the equinoctial points, which astronomers observe. But before this can be explained, it is necessary to say something more particular, than has yet been done, concerning the manner of the earth’s motion round the sun.

44. IT has already been said, that the earth turns round each day on its own axis, while its whole body is carried round the sun once in a year. How these two motions are joined together may be conceived in some degree by the motion of a bowl on the ground, where the bowl in rouling on continually turns upon its axis, and at the same time the whole body thereof is carried straight on. But to be more express let A (in fig. 119) represent the sun B C D E four different situations of the earth in its orbit moving about the sun. In all these let F G represent the axis, about which the earth daily turns. The points F, G are called the poles of the earth; and this axis is supposed to keep always parallel to it self in every situation of the earth; at least that it would do so, were it not for a minute deviation, the cause whereof will be explained in what follows. When the earth is in B, the half H I K will be illuminated by the sun, and the other half H L K will be in darkness. Now if on the globe any point be taken in the middle between the poles, this point shall describe by the motion of the globe the circle M N, half of which is in the enlightened part of the globe, and half in the dark part. But the earth is supposed to move round its axis with an equable motion; therefore on this point of the globe the sun will be seen just half the day, and be invisible the other half. And the same will happen to every point of this circle, in all situations of the earth during its whole revolution round the sun. This circle M N is called the equator, of which we have before made mention.

45. NOW suppose any other point taken on the surface of the globe toward the pole F, which in the diurnal revolution of the globe shall describe the circle O P. Here it appears that more than half this circle is enlightned by the sun, and consequently that in any particular point of this circle the sun will be longer seen than lie hid, that is the day will be longer than the night. Again if we consider the same circle O P on the globe situated in D the opposite part of the orbit from B, we shall see, that here in any place of this circle the night will be as much longer than the day.

46. IN these situations of the globe of earth a line drawn from the sun to the center of the earth will be obliquely inclined toward the axis F G. Now suppose, that such a line drawn from the sun to the center of the earth, when in C or E, would be perpendicular to the axis F G; in which cases the sun will shine perpendicularly upon the equator, and consequently the line drawn from the center of the earth to the sun will cross the equator, as it passes through the surface of the earth; whereas in all other situations of the globe this line will pass through the surface of the globe at a distance from the equator either northward or southward. Now in both these cases half the circle O P will be in the light, and half in the dark; and therefore to every place in this circle the day will be equal to the night. Thus it appears, that in these two opposite situations of the earth the day is equal to the night in all parts of the globe; but in all other situations this equality will only be found in places situated in the very middle between the poles, that is, on the equator.

47. THE times, wherein this universal equality between the day and night happens, are called the equinoxes. Now it has been long observed by astronomers, that after the earth hath set out from either equinox, suppose from E (which will be the spring equinox, if F be the north pole) the same equinox shall again return a little before the earth has made a compleat revolution round the sun. This return of the equinox preceding the intire revolution of the earth is called the precession of the equinox, and is caused by the protuberant figure of the earth.

49. SINCE the sun shines perpendicularly upon the equator, when the line drawn from the sun to the center of the earth is perpendicular to the earth’s axis, in this case the plane, which should cut through the earth at the equator, may be extended to pass through the sun; but it will not do so in any other position of the earth. Now let us consider the prominent part of the earth about the equator, as a solid ring moving with the earth round the sun. At the time of the equinoxes, this ring will have the same kind of situation in respect of the sun, as the orbit of the moon has, when the line of the nodes is directed to the sun; and at all other times will resemble the moon’s orbit in other situations. Consequently this ring, which otherwise would keep throughout its motion parallel to it self, will receive some change in its position from the action of the sun upon it, except only at the time of the equinox. The manner of this change may be understood as follows. Let A B C D (in fig. 120) represent this ring, E the center of the earth, S the sun, A F C G a circle described in the plane of the earth’s motion to the center E. Here A and C are the two points, in which the earth’s equator crosses the plane of the earth’s motion; and the time of the equinox falls out, when the straight line A C continued would pass through the sun. Now let us recollect what was said above concerning the moon, when her orbit was in the same situation with this ring. From thence it will be understood, if a body were supposed to be moving in any part of this circle A B C D, what effect the action of the sun on the body would have toward changing the position of the line A C. In particular H I being drawn perpendicular to S E, if the body be in any part of this circle between A and H, or between C and I, the line A C would be so turned, that the point A shall move toward B, and the point C toward D; but if it were in any other part of the circle, either between H and C, or between I and A, the line A C would be turned the contrary way. Hence it follows, that as this solid ring turns round the center of the earth, the parts of this ring between A and H, and between C and I, are so influenced by the sun, that they will endeavour, so to change the situation of the line A C as to cause the point A to move toward B, and the point C to move toward D; but all the parts of the ring between H and C, and between I and A, will have the opposite tendency, and dispose the line A C to move the contrary way. And since these last named parts are larger than the other, they will prevail over the other, so that by the action of the sun upon this ring, the line A C will be so turned, that A shall continually be more and more moving toward D, and C toward B. Thus no sooner shall the sun in its visible motion have departed from A, but the motion of the line A C shall hasten its meeting with C, and from thence the motion of this line shall again hasten the sun’s second conjunction with A; for as this line so turns, that A is continually moving toward D, so the sun’s visible motion is the same way as from S toward T.

49. THE moon will have on this ring the like effect as the sun, and operate on it more strongly, in the same proportion as its force on the sea exceeded that of the sun on the same. But the effect of the action of both luminaries will be greatly diminished by reason of this ring’s being connected to the rest of the earth; for by this means the sun and moon have not only this ring to move, but likewise the whole globe of the earth, upon whose spherical part they have no immediate influence. Beside the effect is also rendred less, by reason that the prominent part of the earth is not collected all under the equator, but spreads gradually from thence toward both poles. Upon the whole, though the sun alone carries the nodes of the moon through an intire revolution in about 19 years, the united force of both luminaries on the prominent parts of the earth will hardly carry round the equinox in a less space of time than 26000 years.

50. TO this motion of the equinox we must add another consequence of this action of the sun and moon upon the elevated parts of the earth, that this annular part of the earth about the equator, and consequently the earth’s axis, will twice a year and twice a month change its inclination to the plane of the earth’s motion, and be again restored, just as the inclination of the moon’s orbit by the action of the sun is annually twice diminished, and as often recovers its original magnitude. But this change is very insensible.

51. I SHALL now finish the present chapter with our great author’s inquiry into the figure of the secondary planets, particularly of our moon, upon the figure of which its fluid parts will have an influence. The moon turns always the same side towards the earth, and consequently revolves but once round its axis in the space of an entire month; for a spectator placed without the circle, in which the moon moves, would in that time observe all the parts of the moon successively to pass once before his view and no more, that is, that the whole globe of the moon has turned once round. Now the great slowness of this motion will render the centrifugal force of the parts of the waters very weak, so that the figure of the moon cannot, as in the earth, be much affected by this revolution upon its axis: but the figure of those waters are made different from spherical by another cause, viz. the action of the earth upon them; by which they will be reduced to an oblong oval form, whose axis prolonged would pass through the earth; for the same reason, as we have above observed, that the waters of the earth would take the like figure, if they had moved so slowly, as to keep pace with the moon. And the solid part of the moon must correspond with this figure of the fluid part: but this elevation of the parts of the moon is nothing near so great as is the protuberance of the earth at the equator, for it will not exceed 93 english feet.

52. The waters of the moon will have no tide, except what will arise from the motion of the moon round the earth. For the conversion of the moon about her axis is equable, whereby the inequality in the motion round the earth discovers to us at some times small parts of the moon’s surface towards the east or west, which at other times lie hid; and as the axis, whereon the moon turns, is oblique to her motion round the earth, sometimes small parts of her surface toward the north, and sometimes the like toward the south are visible, which at other times are out of sight. These appearances make what is called the libration of the moon, discovered by HEVELIUS. But now as the axis of the oval figure of the waters will he pointed towards the earth, there must arise from hence some fluctuation in them; and beside, by the change of the moon’s distance from the earth, they will not always have the very same height.

~BOOK III~.

~CHAP~ I.

Concerning the cause of COLOURS inherent in the LIGHT.

AFTER this view which has been taken of Sir ISAAC NEWTON’S mathematical principles of philosophy, and the use he has made of them, in explaining the system of the world, &c. the course of my design directs us to turn our eyes to that other philosophical work, his treatise of Optics, in which we shall find our great author’s inimitable genius discovering it self no less, than in the former; nay perhaps even more, since this work gives as many instances of his singular force of reasoning, and of his unbounded invention, though unassisted in great measure by those rules and general precepts, which facilitate the invention of mathematical theorems. Nor yet is this work inferior to the other in usefulness; for as that has made known to us one great principle in nature, by which the celestial motions are continued, and by which the frame of each globe is preserved; so does this point out to us another principle no less universal, upon which depends all those operations in the smaller parts of matter, for whose sake the greater frame of the universe is erected; all those immense globes, with which the whole heavens are filled, being without doubt only design’d as so many convenient apartments for carrying on the more noble operations of nature in vegetation and animal life. Which single consideration gives abundant proof of the excellency of our author’s choice, in applying himself carefully to examine the action between light and bodies, so necessary in all the varieties of these productions, that none of them can be successfully promoted without the concurrence of heat in a greater or less degree.

2. ’TIS true, our author has not made so full a discovery of the principle, by which this mutual action between light and bodies is caused; as he has in relation to the power, by which the planets are kept in their courses: yet he has led us to the very entrance upon it, and pointed out the path so plainly which must be followed to reach it; that one may be bold to say, whenever mankind shall be blessed with this improvement of their knowledge, it will be derived so directly from the principles laid down by our author in this book, that the greatest share of the praise due to the discovery will belong to him.

3. IN speaking of the progress our author has made, I shall distinctly pursue three things, the two first relating to the colours of natural bodies: for in the first head shall be shewn, how those colours are derived from the properties of the light itself; and in the second upon what properties of the bodies they depend: but the third head of my discourse shall treat of the action of bodies upon light in refracting, reflecting, and inflecting it.

4. THE first of these, which shall be the business of the present chapter, is contained in this one proposition: that the sun’s direct light is not uniform in respect of colour, not being disposed in every part of it to excite the idea of whiteness, which the whole raises; but on the contrary is a composition of different kinds of rays, one sort of which if alone would give the sense of red, another of orange, a third of yellow, a fourth of green, a fifth of light blue, a sixth of indigo, and a seventh of a violet purple; that all these rays together by the mixture of their sensations impress upon the organ of sight the sense of whiteness, though each ray always imprints there its own colour; and all the difference between the colours of bodies when viewed in open day light arises from this, that coloured bodies do not reflect all the sorts of rays falling upon them in equal plenty, but some sorts much more copiously than others; the body appearing of that colour, of which the light coming from it is most composed.

5. THAT the light of the sun is compounded, as has been said, is proved by refracting it with a prism. By a prism I here mean a glass or other body of a triangular form, such as is represented in fig. 121. But before we proceed to the illustration of the proposition we have just now laid down, it will be necessary to spend a few words in explaining what is meant by the refraction of light; as the design of our present labour is to give some notion of the subject, we are engaged in, to such as are not versed in the mathematics.

6. IT is well known, that when a ray of light passing through the air falls obliquely upon the surface of any transparent body, suppose water or glass, and enters it, the ray will not pass on in that body in the same line it described through the air, but be turned off from the surface, so as to be less inclined to it after passing it, than before. Let A B C D (in fig. 122.) represent a portion of water, or glass, A B the surface of it, upon which the ray of light E F falls obliquely; this ray shall not go right on in the course delineated by the line F G, but be turned off from the surface A B into the line F H, less inclined to the surface A B than the line E F is, in which the ray is incident upon that surface.

7. ON the other hand, when the light passes out of any such body into the air, it is inflected the contrary way, being after its emergence rendred more oblique to the surface it passes through, than before. Thus the ray F H, when it goes out of the surface C D, will be turned up towards that surface, going out into the air in the line H I.

8. THIS turning of the light out of its way, as it passes from one transparent body into another is called its refraction. Both these cases may be tried by an easy experiment with a bason and water. For the first case set an empty bason in the sunshine or near a candle, making a mark upon the bottom at the extremity of the shadow cast by the brim of the bason, then by pouring water into the bason you will observe the shadow to shrink, and leave the bottom of the bason enlightned to a good distance from the mark. Let A B C (in fig. 123.) denote the empty bason, E A D the light shining over the brim of it, so that all the part A B D be shaded. Then a mark being made at D, if water be poured into the bason (as in fig. 124.) to F G, you shall observe the light, which before went on to D, now to come much short of the mark D, falling on the bottom in the point H, and leaving the mark D a good way within the enlightened part; which shews that the ray E A, when it enters the water at I, goes no longer straight forwards, but is at that place incurvated, and made to go nearer the perpendicular. The other case may be tryed by putting any small body into an empty bason, placed lower than your eye, and then receding from the bason, till you can but just see the body over the brim. After which, if the bason be filled with water, you shall presently observe the body to be visible, though you go farther off from the bason. Let A B C (in fig. 125.) denote the bason as before, D the body in it, E the place of your eye, when the body is seen just over the edge A, while the bason is empty. If it be then filled with water, you will observe the body still to be visible, though you take your eye farther off. Suppose you see the body in this case just over the brim A, when your eye is at F, it is plain that the rays of light, which come from the body to your eye have not come straight on, but are bent at A, being turned downwards, and more inclined to the surface of the water, between A and your eye at F, than they are between A and the body D.

9. THIS we hope is sufficient to make all our readers apprehend, what the writers of optics mean, when they mention the refraction of the light, or speak of the rays of light being refracted. We shall therefore now go on to prove the assertion advanced in the forementioned proposition, in relation to the different kinds of colours, that the direct light of the sun exhibits to our sense: which may be done in the following manner.

10. IF a room be darkened, and the sun permitted to shine into it through a small hole in the window shutter, and be made immediately to fall upon a glass prism, the beam of light shall in passing through such a prism be parted into rays, which exhibit all the forementioned colours. In this manner if A B (in fig. 126) represent the window shutter; C the hole in it; D E F the prism; Z Y a beam of light coming from the sun, which passes through the hole, and falls upon the prism at Y, and if the prism were removed would go on to X, but in entring the surface B F of the glass it shall be turned off, as has been explained, into the course Y W falling upon the second surface of the prism D F in W, going out of which into the air it shall be again farther inflected. Let the light now, after it has passed the prism, be received upon a sheet of paper held at a proper distance, and it shall paint upon the paper the picture, image, or spectrum L M of an oblong figure, whose length shall much exceed its breadth; though the figure shall not be oval, the ends L and M being semicircular and the sides straight. But now this figure will be variegated with colours in this manner. From the extremity M to some length, suppose to the line _n o_, it shall be of an intense red; from _n o_ to _p q_ it shall be an orange; from _p q_ to _r s_ it shall be yellow; from thence to _t u_ it shall be green; from thence to _w x_ blue; from thence to _y z_ indigo; and from thence to the end violet.

11. THUS it appears that the sun’s white light by its passage through the prism, is so changed as now to be divided into rays, which exhibit all these several colours. The question is, whether the rays while in the sun’s beam before this refraction possessed these properties distinctly; so that some part of that beam would without the rest have given a red colour, and another part alone have given an..orange, &c. That this is possible to be the case, appears from hence; that if a convex glass be placed between the paper and the prism, which may collect all the rays proceeding out of the prism into its focus, as a burning glass does the sun’s direct rays; and if that focus fall upon the paper, the spot formed by such a glass upon the paper shall appear white, just like the sun’s direct light.

The rest remaining as before, let P Q. (in fig. 127.) be the convex glass, causing the rays to meet upon the paper H G I K in the point N, I say that point or rather spot of light shall appear white, without the least tincture of any colour. But it is evident that into this spot are now gathered all those rays, which before when separate gave all those different colours; which shews that whiteness may be made by mixing those colours: especially if we consider, it can be proved that the glass P Q does not alter the colour of the rays which pass through it. Which is done thus: if the paper be made to approach the glass P Q, the colours will manifest themselves as far as the magnitude of the spectrum, which the paper receives, will permit. Suppose it in the situation _h g i k_, and that it then receive the spectrum _l m_, this spectrum shall be much smaller, than if the glass P Q were removed, and therefore the colours cannot be so much separated; but yet the extremity _m_ shall manifestly appear red, and the other extremity _l_ shall be blue; and these colours as well as the intermediate ones shall discover themselves more perfectly, the farther the paper is removed from N, that is, the larger the spectrum is: the same thing happens, if the paper be removed farther off from P Q than N. Suppose into the position θ γ η ϰ, the spectrum λ μ painted upon it shall again discover its colours, and that more distinctly, the farther the paper is removed, but only in an inverted order: for as before, when the paper was nearer the convex glass, than at N, the upper part of the image was blue, and the under red; now the upper part shall be red, and the under blue: because the rays cross at N.

12. NAY farther that the whiteness at the focus N, is made by the union of the colours may be proved without removing the paper out of the focus, by intercepting with any opake body part of the light near the glass; for if the under part, that is the red, or more properly the red-making rays, as they are styled by our author, are intercepted, the spot shall take a bluish hue; and if more of the inferior rays are cut off, so that neither the red-making nor orange-making rays, and if you please the yellow-making rays likewise, shall fall upon the spot; then shall the spot incline more and more to the remaining colours. In like manner if you cut off the upper part of the rays, that is the violet coloured or indigo-making rays, the spot shall turn reddish, and become, more so, the more of those opposite colours are intercepted.

13. THIS I think abundantly proves that whiteness may be produced by a mixture of all the colours of the spectrum. At least there is but one way of evading the present arguments, which is, by asserting that the rays of light after passing the prism have no different properties to exhibit this or the other colour, but are in that respect perfectly homogeneal, so that the rays which pass to the under and red part of the image do not differ in any properties whatever from those, which go to the upper and violet part of it; but that the colours of the spectrum are produced only by some new modifications of the rays, made at their incidence upon the paper by the different terminations of light and shadow: if indeed this assertion can be allowed any place, after what has been said; for it seems to be sufficiently obviated by the latter part of the preceding experiment, that by intercepting the inferior part of the light, which comes from the prism, the white spot shall receive a bluish cast, and by stopping the upper part the spot shall turn red, and in both cases recover its colour, when the intercepted light is permitted to pass again; though in all these trials there is the like termination of light and shadow. However our author has contrived some experiments expresly to shew the absurdity of this supposition; all which he has explained and enlarged upon in so distinct and expressive a manner, that it would be wholly unnecessary to repeat them in this place[280]. I shall only mention that of them, which may be tried in the experiment before us. If you draw upon the paper H G I K, and through the spot N, the straight line _w x_ parallel to the horizon, and then if the paper be much inclined into the situation _r s v t_ the line _w x_ still remaining parallel to the horizon, the spot N shall lose its whiteness and receive a blue tincture; but if it be inclined as much the contrary way, the same spot shall exchange its white colour for a reddish dye. All which can never be accounted for by any difference in the termination of the light and shadow, which here is none at all; but are easily explained by supposing the upper part of the rays, whenever they enter the eye, disposed to give the sensation of the dark colours blue, indigo and violet; and that the under part is fitted to produce the bright colours yellow, orange and red: for when the paper is in the situation _r s t u_, it is plain that the upper part of the light falls more directly upon it, than the under part, and therefore those rays will be most plentifully reflected from it; and by their abounding in the reflected light will cause it to incline to their colour. Just so when the paper is inclined the contrary way, it will receive the inferior rays most directly, and therefore ting the light it reflects with their colour.

14. IT is now to be proved that these dispositions of the rays of light to produce some one colour and some another, which manifest themselves after their being refracted, are not wrought by any action of the prism upon them, but are originally inherent in those rays; and that the prism only affords each species an occasion of shewing its distinct quality by separating them one from another, which before, while they were blended together in the direct beam of the sun’s light, lay conceal’d. But that this is so, will be proved, if it can be shewn that no prism has any power upon the rays, which after their passage through one prism are rendered uncompounded and contain in them but one colour, either to divide that colour into several, as the sun’s light is divided, or so much as to change it into any other colour. This will be proved by the following experiment[281]. The same thing remaining, as in the first experiment, let another prism N O (in fig. 128.) be placed either immediately, or at some distance after the first, in a perpendicular posture, so that it shall refract the rays issuing from the first sideways. Now if this prism could divide the light falling upon it into coloured rays, as the first has done, it would divide the spectrum breadthwise into colours, as before it was divided lengthwise; but no such thing is observed. If L M were the spectrum, which the first prism D E F would paint upon the paper H G I K; P Q lying in an oblique posture shall be the spectrum projected by the second, and shall be divided lengthwise into colours corresponding to the colours of the spectrum L M, and occasioned like them by the refraction of the first prism, but its breadth shall receive no such division; on the contrary each colour shall be uniform from side to side, as much as in the spectrum L M, which proves the whole assertion.

15. THE same is yet much farther confirmed by another experiment. Our author teaches that the colours of the spectrum L M in the first experiment are yet compounded, though not so much as in the sun’s direct light. He shews therefore how, by placing the prism at a distance from the hole, and by the use of a convex glass, to separate the colours of the spectrum, and make them uncompounded to any degree of exactness[282]. And he shews when this is done sufficiently, if you make a small hole in the paper whereon the spectrum is received, through which any one sort of rays may pass, and then let that coloured ray fall so upon a prism, as to be refracted by it, it shall in no case whatever change its colour; but shall always retain it perfectly as at first, however it be refracted[283].

16. NOR yet will these colours after this full separation of them suffer any change by reflection from bodies of different colours; on the other hand they make all bodies placed in these colours appear of the colour which falls upon them[284]: for minium in red light will appear as in open day light; but in yellow light will appear yellow; and which is more extraordinary, in green light will appear green, in blue, blue; and in the violet-purple coloured light will appear of a purple colour; in like manner verdigrease, or blue bise, will put on the appearance of that colour, in which it is placed; so that neither bise placed in the red light shall be able to give that light the least blue tincture, or any other different from red; nor shall minium in the indigo or violet light exhibit the least appearance of red, or any other colour distinct from that it is placed in. The only difference is, that each of these bodies appears most luminous and bright in the colour, which corresponds with that it exhibits in the day light, and dimmed in the colours most remote from that; that is, though minium and bise placed in blue light shall both appear blue, yet the bise shall appear of a bright blue, and the minium of a dusky and obscure blue: but if minium and bise be compared together in red light, the minium shall afford a brisk red, the bise a duller colour, though of the same species.

17. AND this not only proves the immutability of all these simple and uncompounded colours; but likewise unfolds the whole mystery, why bodies appear in open day-light of such different colours, it consisting in nothing more than this, that whereas the white light of the day is composed of all sorts of colours, some bodies reflect the rays of one sort in greater abundance than the rays of any other[285]. Though it appears by the fore-cited experiment, that almost all these bodies reflect some portion of the rays of every colour, and give the sense of particular colours only by the predominancy of some sorts of rays above the rest. And what has before been explained of composing white by mingling all the colours of the spectrum together shews clearly, that nothing more is required to make bodies look white, than a power to reflect indifferently rays of every colour. But this will more fully appear by the following method: if near the coloured spectrum in our first experiment a piece of white paper be so held, as to be illuminated equally by all the parts of that spectrum, it shall appear white; whereas if it be held nearer to the red end of the image, than to the other, it shall turn reddish; if nearer the blue end, it shall seem bluish[286].

18. OUR indefatigable and circumspect author farther examined his theory by mixing the powders which painters use of several colours, in order if possible to produce a white powder by such a composition[287]. But in this he found some difficulties for the following reasons. Each of these coloured powders reflects but part of the light, which is cast upon them; the red powders reflecting little green or blue, and the blue powders reflecting very little red or yellow, nor the green powders reflecting near so much of the red or indigo and purple, as of the other colours: and besides, when any of these are examined in homogeneal light, as our author calls the colours of the prism, when well separated, though each appears more bright and luminous in its own day-light colour, than in any other; yet white bodies, suppose white paper for instance, in those very colours exceed these coloured bodies themselves in brightness; so that white bodies reflect not only more of the whole light than coloured bodies do in the day-light, but even more of that very colour which they reflect most copiously. All which considerations make it manifest that a mixture of these will not reflect so great a quantity of light, as a white body of the same size; and therefore will compose such a colour as would result from a mixture of white and black, such as are all grey and dun colours, rather than a strong white. Now such a colour he compounded of certain ingredients, which he particularly sets down, in so much that when the composition was strongly illuminated by the sun’s direct beams, it would appear much whiter than even white paper, if considerably shaded. Nay he found by trials how to proportion the degree of illumination of the mixture and paper, so that to a spectator at a proper distance it could not well be determined which was the more perfect colour; as he experienced not only by himself, but by the concurrent opinion of a friend, who chanced to visit him while he was trying this experiment. I must not here omit another method of trying the whiteness of such a mixture, proposed in one of our author’s letters on this subject[288]: which is to enlighten the composition by a beam of the sun let into a darkened room, and then to receive the light reflected from it upon a piece of white paper, observing whether the paper appears white by that reflection; for if it does, it gives proof of the composition’s being white; because when the paper receives the reflection from any coloured body, it looks of that colour. Agreeable to this is the trial he made upon water impregnated with soap, and agitated into a froth[289]: for when this froth after some short time exhibited upon the little bubbles, which composed it, a great variety of colours, though these colours to a spectator at a small distance discover’d themselves distinctly; yet when the eye was so far removed, that each little bubble could no longer be distinguished, the whole froth by the mixture of all these colours appeared intensly white.

19. OUR author having fully satisfied himself by these and many other experiments, what the result is of mixing together all the prismatic colours; he proceeds in the next place to examine, whether this appearance of whiteness be raised by the rays of these different kinds acting so, when they meet, upon one another, as to cause each of them to impress the sense of whiteness upon the optic nerve; or whether each ray does not make upon the organ of sight the same impression, as when separate and alone; so that the idea of whiteness is not excited by the impression from any one part of the rays, but results from the mixture of all those different sensations. And that the latter sentiment is the true one, he evinces by undeniable experiments.