their different reflexibility; a quality not yet discoursed of.

In the next particular, where M. Huygens would shew that it is not necessary to mix all colours for the production of white; the mixture of yellow, green, and blue, without red and violet, which he propounds for that end, will not produce white but green, and the brightest part of the yellow will afford no other colour but yellow, if the experiment be made in a room well darkened, as it ought, because the coloured light is much weakened by the reflexion, and so apt to be diluted by the mixing of any other scattering light. But yet there is an experiment or two mentioned in my letter in the Transactions, No. 88, by which I have produced white out of two colours alone, and that variously, as out of orange and a full blue, and out of red and pale blue, and out of yellow and violet; as also out of other pairs of intermediate colours. The most convenient experiment for performing this was that of casting the colours of one prism upon those of another, after a due manner. But what M. Huygens

can deduce from hence I see not. For the two colours were compounded of all others, and so the resulting white, to speak properly, was compounded of them all, and only decompounded of those two. For instance, the orange was compounded of red, orange, yellow, and some green; and the blue of violet, full blue, light blue, and some green, with all their intermediate degrees; and consequently the orange and blue together made an aggregate of all colours to constitute the white. Thus if one mixes red, orange, and yellow powders to make an orange; and green, blue, and violet powders to make a blue; and lastly, the two mixtures to make a grey; that grey, though decompounded of no more than two mixtures, is yet com

pounded of all the six powders, as truly as if the powders had been all mixed at once. This is so plain that I conceive there can be no further scruple, especially to them who know how to examine whether a colour be simple or compound, and of what colours it is compounded: which, having explained in another place, I need not now repeat. If therefore M. Huygens would conclude any thing, he must shew how white may be produced out of two uncompounded colours; which when he hath done, I will further tell him why he can conclude nothing from that. But I believe there cannot be found an experiment of that kind, because, as I remember, I once tried by gradual succession the mixture of all pairs of uncompounded colours, and though some of them were paler and nearer to white than others, yet none could be truly called white. But it being some years since this trial was made, I remember not well the circumstances, and therefore recommend it to others to be tried again.

In the last place, had I thought the distinctness of the picture, which (for instance) a twelve feet objectglass casts into a darkened room, to be so contrary to me as M. Huygens is pleased to affirm, I should have mended my theory in that point before I propounded it. For that I had thought on that difficulty you may easily guess by an expression somewhere in my first letter, to this purpose, that I wondered how telescopes could be brought to so great perfection by refractions, which were so irregular. But to take away the difficulty, I must acquaint you first, that though I put the greatest lateral errors of the rays from one another to be about of the glass's diameter, yet their greatest error from the points on which they ought to fall will be but of the diameter; and h Phil. Trans. vol. vi. p. 3079: No. 80, for Feb. 19, 1671-2.

then that the rays, whose error is so great, are but very few in comparison to those which are refracted more justly for the rays, which fall upon the middle parts of the glass, are refracted with sufficient exactness, as also are those that fall near the perimeter, and have a mean degree of refrangibility. So that there remain only the rays, which fall near the perimeter, and are most or least refrangible, to cause any sensible confusion in the picture. And these are yet so much further weakened by the greater space, through which they are scattered, that the light, which falls on the due point, is infinitely more dense than that which falls on any other point round about it. Which, though it may seem a paradox, yet is easily demonstrable. Yea, although the light, which passeth through the middle parts of the glass, were wholly intercepted, yet would the remaining light convene infinitely more dense at the due points than at other places. And by this excess of density, the light, which falls in or insensibly near the just point, may, I conceive, strike the sensorium so vigorously that the impress of the weak light, which errs round about it, shall in comparison not be strong enough to be animadverted, or to cause any more sensible confusion in the picture than is found by experience. This, I conceive, is enough to shew why the picture appears so distinct, not withstanding the irregular refraction. But if this satisfy not, M. Huygens may try, if he please, how distinct the picture will appear when all the lens is covered, excepting a little hole next its edge on one side only. And if, in this case, he please to measure the breadth of the colours thus made at the edge of the sun's picture, he will perhaps find it approach nearer to my proportion than he expects.

This letter is printed in the Phil. Trans. vol. viii. p. 6108, No. 97, Oct. 6, 1673. Huygens' name is however suppressed. 2 A

VOL. II.

Sir,

CCLIII.

NEWTON TO COLLINS.

Cambridge, April 9, 1673.

Having perused Mr. Gregory's candid reply", I have thought good to send you these further considerations upon the differences that still are between us. And first, that a well polished plate reflects [rays] at the obliquity of 45 degrees more truly than direct ones, seems to me very certain. For the flat tuberculæ or shallow valleys, such as may be the remains of scratches almost worn out, will cause the least errors in the obliquest rays, which fall on all sides the hill, excepting on the middle of the foreside and backside of it; that is, where the hill inclines directly towards, or directly from the ray. For if the ray fall on that section of the hill, its error is in all obliquities just double to the hill's declivity: but if it fall on any other part of the hill, its error is less than double, if it be an oblique ray, and that so much the less by how much the ray is obliquer; but if it be a direct ray, its error is just double to the declivity, and therefore greater in that case. I presume Mr. Gregory, if you think it convenient to transmit this to him, will easily apprehend me. How the charge may be varied at pleasure in my telescope will

I See Gregory's letter of March 7, 1673, No. ccxii. p. 246..

of glass or crystal, whose sides, BC and BD, are not flat but spherically convex, so that the rays which come from G, the focus of the great concave A, may by the refraction of the first side BC be reduced into parallelism, and after reflexion from the base CD be made by the refraction of the next side BD to converge to the focus of the eyeglass H. The telescope being thus formed, it appears how the charge may be altered by varying the distances of the glasses and speculum.

As for the objection that Mr. Gregory's telescope will be either overcharged, or have too small an angle of vision, &c., I apprehend that the difference between us lies in limiting the aperture of the eyeglass. Mr. Gregory puts it equal to that of the little concave, but I should rather determine it by this proportion : that if a middle point be taken between the eyeglass and its focus, the apertures of the eyeglass and concave be proportional to their distances from that point. That is, suppose AB the little concave, EF the eyeglass, GH their common focus or image, and K the mean dis

A

B

G

E

K

I

H

F

tance between GH and EF, from the extremities of AB draw AK and BK butting on the eyeglass at F and E, and EF shall be its aperture. The reason of this limitation is, that the superfluous light which comes on all sides of the speculum AB to the space GH, in which the picture of the object is made, may fall beside the eyeglass. For if it should pass through it to the eye, it would exceedingly blend those parts of the picture with which 'tis mixed, and such are those parts of it, which extend themselves beyond the lines AK, BK. As I remember I said in my former letter, that the scattering light, which falls on the eyeglass, will