in a new Jorm of Refractometer. 399 
The effect is es aaa of the position of the glass plate, 
provided its surface is kept ase with the corresponding 
mirror. Suppose, diievetora that 
is in contact with the latter and fet 
ed, fig. 4, represent the common 
surface. et ¢=hi= thickness of 
the glass, i=angle of incidence, r= 
angle of refraction, n=index of re- 
fraction, 4= wave-length of light. 
Let ef represent the image of the 
8 
other mirror, and put n,=—. 
It can be rendily, pela dg ste : O..- eke 
that the path of t Fier. 
hat 
given in the figure, where one of the rays follows the path 
gnmh, and the other the path rofh. Suppose the mirrors cd 
and ¢ parallel, Then as has been previously shown, the 
curves of a erence are concentric circles, formed at an 
infinite dis Therefore the rays gn, ro, whose ath ” to 
be traced, sein an allel, and from the point A they coincide. 
Their difference of path is 2nm—2h/—op, and their diftseenas 
of phase is 
: _2nm 2hi op 2n,.t 2t.n 
AG a aed A cosr 
2t ‘ esis 
—z(% tan ¢—tan7) sin7, whence 
p=— [m, cos i—n cos 7] (7) 
Let it be proposed to find the value of , which renders any 
Saiiviar ring achromatic. The condition ‘of achromatism, as 
given by Cornu, is “P9, which gives 
+2¢ (cose —n sin CR )=0. 
r aa rs dn da) 
sin 7 dr 2 
We have =, whence — = PreecdiI , whence 
sin dn sinécosr 
+ 2t ond 
¥ cosr dA 
dn_ 2a, 
By Cauchy’s fe ] =a +—2 
y Cauchy’s formula we have n= =a, +5. > Whence — a. 
