THE AID OF THE ACHROMATIC FRINGES. 85 



On submerging the above plate of thickness = 0.202 cm. in benzol, it was 

 found that the length =13 cm. of air- tube sufficed to center the spectrum 

 ellipses in the red when completely exhausted. Hence the limiting AN for 

 one tube would be 293 X io~ 6 X 13 or 0.0038, whence 



AN/e = 0.0038/0. 202 = 0.0188 



as the range of possible accommodation. The ellipses entered on exhaustion 

 at the violet and reached the yellow at above p = 5o cm., the temperature 

 being about 20 C. This would agree with the increment given by the Billet 

 compensator (0.0123), at 20 and a pressure difference of 53.3 cm. 



In a later experiment at the temperature 16.5, = 46 cm. was observed 

 giving for the y. increment 



0.01367X46/289X0.202 = 0.0108 



also agreeing with the corresponding datum of the Billet compensator (0.0107). 

 Unless the ellipses are very strong, however, and not too large, it is difficult 

 to set the air compensator to a centimeter of pressure, which is equivalent 

 to about two units in the fourth place of /JL. 



The air compensator is thus not very convenient unless the experimental 

 equipment is elaborate. A single tube will only give Ax and not 2Ax, unless 

 it is shifted from one ray to the other; but this is dangerous, as it is liable to 

 modify the fringes. Hence the double-tube method is almost essential, which 

 implies a definite distance apart of the tubes and the same annoyance intro- 

 duced by the Billet apparatus. The latter, though it requires special standard- 

 ization, is much more easily manipulated. 



Work of the same kind as that given in table 6 was carried out at greater 

 length, but with no essential improvement in the results as a whole. As there 

 are three terms, viz, the one in Ax, the one in (BB'), and the temperature 

 correction from 8.5, all about of the same order, to be added to the n' of ben- 

 zol, better agreement is hardly to be expected, unless a plane parallel optic 

 trough is used. 



62. Micrometer measurements. The use of a screw micrometer in case 

 one of the separated mirrors in figure 79 was suggested above. Experiments 

 of this kind are given in table 7. The mirror N' was in this case preferably 

 separated at b, each half being on a screw normal to the face. The adjustment 

 (first made for trial with an unseparated mirror) proved to be very easy. The 

 two mirrors replace the single mirror, the apparatus being nearly in adjustment. 



In this case, if the plate is put successively in the two beams, the displace- 

 ment of micrometer is again twice that (AN) which corresponds to the thick- 

 ness e of plate, and if i is the angle of incidence (here 2 = 47 I0/ ) 



cos *' 



