18. MICROSCOPES are of two sorts. One kind is only a very convex glass, by the means of which the object may be brought very near the eye, and yet be seen distinctly. This microscope magnifies in proportion, as the object by being brought near the eye will form a broader impression on the optic nerve. The other kind made with convex glasses produces its effects in the same manner as the telescope. Let the object A B (in fig. 158) be placed under the glass C D, and by this glass let an image be formed of this object. Above this image let the glass G H be placed. By this glass let the rays, which proceed from the points A and B, be refracted, as is expressed in the figure. In particular, let the rays, which from each of these points pass through the middle of the glass C D, cross in I, and there let the eye be placed. Here the object will appear larger, when seen through the microscope, than if that instrument were removed, in proportion as the angle, in which these rays cross in I, is greater than the angle, which the lines would make, that should be drawn from I to A and B; that is, in the proportion made up of the proportion of the distance of the object A B from I, to the distance of I from the glass G H; and of the proportion of the distance between the glasses, to the distance of the object A B from the glass C D.
19. I SHALL now proceed to explain the imperfection in these instruments, occasioned by the different refrangibility of the light which comes from every object. This prevents the image of the object from being formed in the focus of the object glass with perfect distinctness; so that if the eye-glass magnify the image overmuch, the imperfections of it must be visible, and make the whole appear confused. Our author more fully to satisfy himself, that the different refrangibility of the several sorts of rays is sufficient to produce this irregularity, underwent the labour of a very nice and difficult experiment, whose process he has at large set down, to prove, that the rays of light are refracted as differently in the small refraction of telescope glasses as in the larger of the prism; so exceeding careful has he been in searching out the true cause of this effect. And he used, I suppose, the greater caution, because another reason had before been generally assigned for it. It was the opinion of all mathematicians, that this defect in telescopes arose from the figure, in which the glasses were formed; a spherical refracting surface not collecting into an exact point all the rays which come from any one point of an object, as has before been said[330]. But after our author has proved, that in these small refractions, as well as in greater, the sine of incidence into air out of glass, to the sine of refraction in the red-making rays, is as 50 to 77, and in the blue-making rays 50 to 78; he proceeds to compare the inequalities of refraction arising from this different refrangibility of the rays, with the inequalities, which would follow from the figure of the glass, were light uniformly refracted. For this purpose he observes, that if rays issuing from a point so remote from the object glass of a telescope, as to be esteemed parallel, which is the case of the rays, which come from the heavenly bodies; then the distance from the glass of the point, in which the least refrangible rays are united, will be to the distance, at which the most refrangible rays unite, as 28 to 27; and therefore that the least space, into which all the rays can be collected, will not be less than the 55th part of the breadth of the glass. For if A B (in fig. 159) be the glass, C D its axis, E A, F B two rays of the light parallel to that axis entring the glass near its edges; after refraction let the least refrangible part of these rays meet in G, the most refrangible in H; then, as has been said, G I will be to I H, as 28 to 27; that is, G H will be the 28th part of G I, and the 27th part of H I; whence if K L be drawn through G, and M N through H, perpendicular to C D, M N will be the a 28th part of A B, the breadth of the glass, and K L the 27th part of the same; so that O P the least space, into which the rays are gathered, will be about half the mean between these two, that is the 55th part of A B.