OF ARTS AND SCIENCES. 



291 



the ordinary form of illumination, however, the advantage of a high 

 pow er would Dot be bo apparent. 



The value of one division of the micrometer depends both on the 

 magnifying power of the microscope and on the pitch of the microme- 

 ter-screw. Those who advocate a low magnifying power usually pre- 

 fer a screw having a small pitch. Further observations are needed 

 to determine the best relation between the pitch of the screw and the 

 magnifying power of the objective. The following are the values of 

 one revolution of a i\\v of the micrometer-screws which have been 

 used in the comparison of standards: — 



Value nf 

 1 division. 



Inch. Observer. 



.0001000 Chaney, 1880, new objectives, 



.0000428 Rogers, 1880, Comparator,— 



erver. 

 Troughton, 1708, 

 Kater, 1818, 



Hassler, 1- .0001000 



Baily, L832, .0000-300 



Baily, 1844, .0000253 



Bache, 1856, May, .0000333 



Bache, 1856, October, .oooiOOO 



Hilgard.Saxton Comparator, .0001000 

 Clarke, 1866, .0000286 



Chaney, 1880, old objectives, .0000319 | i With i in. and amplifier 

 Tresca, 1880, 0.301 fi = .0000118 Internat. Comrn., 1.0 ^ 



With 1 in. objective, 

 Willi i in. objective, 

 With I in. objective, 

 With i in. and amplifier, 

 With 1 in. objective, 

 With } in. objective, 

 With J in. objective, 



Value of 



1 division. 



Inch. 



.0000058 



.0000197 

 .0000087 

 .0000047 

 .0000028 

 .0000079 

 .0000035 

 .0000019 

 .0000011 

 .0000394 



The writer is inclined to the opinion that one can measure with cer- 

 tain/;/ only what one can see. 



(b.) The best method of illumination for opaque objects. 



I cannot better illustrate the necessity for a proper illumination in 

 making exact measurements, than by saying that I have been obliged 

 to reject a series of observations extending over a period of four 

 months, for the simple reason that I finally discovered that during all 

 this time I have never once seen, the actual lines ruled, but only their 

 image. I used a parabolic reflector, giving a beautiful white line on a 

 black background. The lines were traced upon a steel surface nickel- 

 plated, their width being about one ten-thousandth of an inch. Inves- 

 tigation showed that the positions of the lines could be changed by an 

 amount more than half their width, by shifting the position of the par- 

 abolic reflector. 



The method of illumination employed by Baily and Sheepshanks 

 seems to me radically defective. With the microscopes used by Sheep- 

 shanks I found myself unable to separate lines ruled on a polished steel 

 plate, though separated by an interval of only one-thousandth of a 

 centimeter. As already stated, I have used with great satisfaction the 



