6oo 



NATURE 



\Oct. 1 8, 1883 



will be 4/8ths of 3 . So with the other intermediate points. 

 In this way, then, Digges enabled a much greater accuracy to be 

 altained in this circle reading. 



The next great improvement after that of Digges was one made 

 by M. Vernier, a Frenchman, who, in about the year 1631, in- 

 vented the instrument which bears his name. The following is 

 the arrangement. Let the scale on which the measurements are 

 made be divided into a certain number of parts. Take a second 



" j1 _ 



. ' 1 ' : ' ' 1 1 n 1 1 1 1 1 1 8 



1 1 1 1 1 1 11 1 1 



Fig. 6.— Vernier reading to tenths of divisions. 



scale called the vernier, shorter than the first by the length of 

 one of its divisions, and make the number of divisions in this 

 vernier equal to the number of divisions in the scale. Then 

 each of the divisions of the vernier, will be less than each of the 

 parts of the scale, by a fraction having one for its numerator, 

 and the number of divisions in the scale or vernier respectively 

 for its denominator. Thus if the number of divisions be ten 

 (see Fig. 6), and the vernier equal in length to nine of such 



""'Wl IJi' i Vi"" "'V 



';'::__ "-rzr. 



Fig. 7.— Vernier shown in Fig. 6 reading to three-tenths. 



parts has also ten divisions, each of these divisions will be 

 shorter l.y l/icth than each of the parts of the scale. If the 

 number of divisions be seventeen (see Fig. S) the different parts, 

 of the vernier will be less by '/17th than each of the divisions 

 of the scale. So when the numter of divisions is thirty (see Fig. 9), 

 the parts of the vernier will be less by i/joth than thedivisions of 

 the scale. The arrangement, how ever, is not limited to straight 

 scales. It may also be used for the determination of small 



I 



_LL 



: 1 1 1 1 1 1 1 1 



I I I II : 1 : i ,1 I I i II 



t -N 



" 



Fig. 



-Vernier reading to seventeenths. 



fractions of degrees on a circle. Fig. 10 represents a vernier 

 giving tenths of degrees on a circle. It need hardly be said 

 that the vernier may be construcied to give readings upon 

 the inner as well as the outer edge of the graduation. 



In using the vernier the observer looks along it until he meets 

 a coincidence, that is for a point where one of the divisions on 

 the scale c< ir.cides with a division on the vernier. If this occurs 

 at the eighth division, then the observation is some whole num- 



FlG. 9.— Application of vernier to circle reading to one-tenth of a degree. 



ber, and 8/loths, 8/l7ths, or 8/30ths, according as the scale used 

 is elivided into ten, seventeen, or thirty parts. In Fig. 7 the 

 coincidence occurs at the third division ; the reading in that 

 case would be some whole number and 3/ioths. 



To the instrument of Tycho Brahe, then, the vernier, which 

 can be adapted to it, has now been added. Of course by taking 

 divisions enough the measurement may be made as fine as pos- 



sible. A vernier of 100 divisions may replace the vernier of 

 10, of 17, or of 30 divisions. Seventeen divisions have been 

 chosen to show that the principle isjiot limited to tenths. Any 

 number of divisions may be taken. A very fine degree of accu- 

 racy can be attained then in angular measurement, owing to the 

 introduction of the vernier, and that is why there is what is 

 practically a vernier upon almost every measuring instrument in 

 every workshop and laboratory. The question next arises 

 whether with the introduction of the vernier the limit of accu- 

 racy has been reachetl, or whether it be possible to go beyond 

 this. A negative reply may be made to this question. The 



Fig. 10. — Application of vernier to circle reading to ten seconds of arc. 



limit of accuracy has not here been reached. In order to get 

 more accuracy in this angular measurement, it is only necessary 

 to add some branch of physical science to those geometrical 

 considerations by means 1 of which circles have been so finely 

 divided. The astronomer culls certain portions out of the 

 science of optics, and uses them for bis | urpose. It is perfectly 

 clear that the reason a limit is reached with an arrangement of 

 the nature of the vernier is, that at last the divisions get so small 

 that the eye cannot distinguish them, so that optical principles 

 have to lie appealed to to increase the power of the eye. 



Before discus- ing this question of whether it be possible to 



Fig. 11. — Horizontal section of the human eye. 



select some principle of optics, by the application of which the 

 power of the eye may le increased, it will be well to con- 

 sider in what it is that that power consists. Fig. II will 

 give a rough notion of those parts of the eje which specially 

 relate to this matter. First comes the curved surface Cn, the 

 cornea, and next Aq, the small anterior chamber which contains 

 the aqueous humour. Behind this comes Ir, the iris, which 

 limits the amount of light entering the eye, this being imme- 

 diately succeeded by Cry, the ciystalline lens. Then comes the 

 large posterior chamber of the eye which contains the vitreous 

 humour. Behind this the optic nerve enters the eyeball, ex- 



