Oct. 1 8, 1883] 



NATURE 



603 



dispersion will have been got rid of, and the deviation will have 

 been rttained, and this is exactly what takes place in the modern 

 compound, or, as it is called, achromatic lens. By building up 

 a lens in this way we can get a much belter image of the carbon 

 poles of the lamp than before. This compound, achromatic 

 lens, when used in a combination, is called the object-glass, 

 because it is pointed to the object. But w hen it is a question of 

 the combination of lenses, there is something else to be con- 

 sidered besides the mere formation of images. It is not enough 

 to consider merely this, because when we spoke of the action of 

 a convex lens in aiding us to read the vernier, we found that if 

 an image was to be obtained the rays entering the eye must be 

 practically parallel. In that case the rays always come to a 

 focus at the same point. If the rays are not parallel, but diver- 

 gent rays, then their focus will vary with the varying distance of 

 the source of light. 



In combining lenses together, then, it is important to bear in mind 

 the fact that the rays of light which, after passing through the 

 lenses ultimately reach the eye, must be parallel ones. Let us 

 consider that arrangement which obtains in the telescope. In the 

 simple form of this instrument, A (Fig. 13), representing the object- 

 glass, receives the rays of light and forms an image of the distant 

 arrow, from which they are supposed to flow, in exactly the 

 same way that the lens we used just now formed an image of the 

 carbon poles on the screen. 



This image, then, having been observed, the eye views the distant 

 object as if the object itself were placed at B. Remember no» 

 the way in which the eye was enabled to read the vernier placed 

 close to it, and the action of the convex eyepiece of the :elescope 

 will be very obvious. In just the same way as the divergent 

 rays coming from the vernier were grasped by the convex lens, 

 and rendered parallel, so in this case the convex e) epiece of the 

 telescope grasps the divergent rays from the image, reduces them 



Fig. 16.— Model of U 



to the necessary condition of parallelism, and thus enables the 

 image of the object to be clearly formed upon the retina of the 

 observer's eye. 



We have, then, got so far that by means of an object-glass we 

 produce an aerial image, and by means of a convex lens we 

 can view this image under conditions which enable another 

 image of it to be formed on the retina. It is at once obvious 

 that we can do something more than thi=, for if we place a 

 concrete thing such as a cross wire at the same distance in 

 front of the convex lens as the aerial image, or, in other words, 

 at the focal distance of the object-glas, we shall see both the 

 nerial image and the concrete thing, be it a cro-s wire or what 

 not, both together. Now imagine that we can obtain an aerial 

 image in this way of a star, and that side by side with this image 

 of the star we observe the cross wire. It is quite clear that if we 

 have any means of getting the cross wire to bisect the image of 

 the star we shall have a much more accurate method of pointing 

 at the celestial body, and therefore of measuring the angle 

 between two celestial bodies, than was possible on the old system 

 of sights without telescopes. 



Suppose this telescope of ours to supplant the pointer of the 

 old instrument of Tycho Brahe, consider the extreme accuracy of 

 iis observation as compared with that of the pointer in Tycho's 

 quadrant, and it w ill be seen how vastly the application of these 

 optical principles has added to the instrumental powers of the 

 astronomer. 



3. How Optics enables us to Replace the Vernier by a Micrometer. 

 — But we have not yet done with optics. Its principles have 

 been applied in yet another manner, but still, like these two 

 applications which we have considered, tending to increase the 



power of accurately measuring minute angular distances of 

 space. 



Fig. 14 shows a simple model which has been designed to 

 illustrate the principle of the instrument called the micrometer. 

 This instrument places in the hands of the astronomer the power 

 of measuring with extreme accuracy the most minute distances. 

 It consists of two vertical wires, one, A, fixed, the other, B, 

 movable by the rotation of a very perfectly cut screw, seen at c. 

 The head of the screw, d, is divided into ico parts, and read 

 by means of a vernier to i/ioooths. 



This system of threads moving over certain small distances 

 which can be accurately measured by means of a micrometer 

 screw, can replace the cross wires to which we have just referred, 

 and there are two very notable applications of this principle to 

 which reference must now be made. When the object-glass is 

 used for astronomical purposes, it is naturally arranged to bring 

 the rays which fall upon it from a celestial body, and which are 

 practically parallel, to a focus which represents the actual focus 

 of the lens for such rays, and which is called the principal focus. 

 But it is not necessary that the rays which fall upon such a lens 

 should be parallel. The lens acts under other conditions with 

 this proviso, that the more the rays diverge from the body in 

 front of it, or, in other words, the nearer the object is to it, the 

 greater will be the distance behind the lens of the point at which 

 the aerial imaire is formed. 



Fig. 17.— Micrometer arranged for demonstration with the electric light. 



Here in a few words we have a statement of the arrangement 

 used in the microscope, and a moment's thought will show that 

 such an arrangement may le applied to the vernier instead of 

 the small lens, to which reference has already been made. Nay, 

 we can go further than this, it may be applied to the circle itself, 

 and help us to measure small fractional divisions of its parts with 

 yet greater accuracy than is possible by the aid of the vernier. 

 The way in which this is managed is as follows : — The micro- 

 scope is turned towards the circle, so that its divisions may le 

 plainly seen in the field of view, and the position of the wire, on, or 

 between any division may represent a certain position which is 

 to be measured by means of the circle. The micrometer head 

 may now be used to tell us the exact distance in i/ioooths of a 

 revolution between the po.-ition occupied by the whe in the first 

 instance, and the position of the wire when it exactly lies on the 

 next division. By determining, according to the graduation of 

 the circle, the number of thousandths of parts as indicated by the 

 micrometer which lie between each division, it is obvicus that 

 the exact angular distance between such a position and the 

 next division of the circle can be accurately determined. Such 

 an operation as this is called a "lun," and practically such a 



