274 UR. ROYSTON-PIGOTT. 



of the glass. The focal length may be approximately deter- 

 mined thus : 



_ £ 12 12 



J ~ 1 ~ 1 ~ 2 



»«+2 + - 6^+2 + ;^ 8| + 



Also, 

 Then, 



6i "^ ' 13 

 = 1-38666. 



rs _ 1 X G _ ^ 

 r+ s "~ 1 + 6 ~ 7 ' 



1 _ A 1 



^ i — 7 X 2-305(35 



= -61813; 



and \i. = 1"61813, 



the refractive index. 



A further correction may he added for thickness, as follows : 

 If t be the thickness of the lens at the centre, s the radius 



of the surface next the object on the stage, r the radius of the 



surface next the eye, the approximate focal length must be 



increased by^ 



In the case before us of the crossed lens, supposing the 

 more convex surface be placed next the object r = I, /x — 1 

 = 0-61813, and if we suppose the lens to be tV^^ of an inch 

 thick, t = O'l, and the correction for increasing /, which 

 nearly = 1-38666, 



_ 0-618131^ Q'l ^ l-38f)66|2 



— ^ 1-(J1813 ^ 



which, reduced, = 00382085 x 1922853 -^ 1-61813 



= 1-188318 X 0-382085 



= -0454038 

 but/ = 1-3866666 



/ then = 1-4320704 = 1-43207. 



Hence, 



u — 1 now = —r- X — = — X iT nr5777 = 0*59853. 



The error by neglecting thickness amounts to the difference 

 between the two values of fx, viz. — 



1-61813 

 1-59853 



001960 



* It is remarkable that the correction for the thickness does not depend 

 at all upon the radius of the surface next the object, but only upon the 

 radius of the surface furthest from the object. 



