Sir John Conroy on a new Photometer. 423 



the semi major axes of the other ellipses are 



a + 9? a + b. ..a+ — , &c; 



while to find b n} the semi minor axis of the (n + l)th ellipse, 

 we have 



(a+^ 2 ^bl=a^b\Abl=b' + na\ + ^. . (12) 



Let Q Q 1 = 2c, then we have 



a 2 =b 2 + <?, (13) 



and the equation to the (w + l)th ellipse is 



y 2 



^ + na\+~ 6 2 + naX+^~ 

 4 4 



Let # w be the abscissa of the point in which this is cut by the 

 line y = b, then 



(n 2 ^\?\ / n 2 \ 2 \ 



a 2 + naX -I — ?—-] ( ndk -\ — ; — I 



* ; W • • < 15 > 



6 2 + naX-{ — t— 

 4 



Substituting for a and giving w the values 0, 1, 2, 3, &c. in 

 order, we can obtain values for x , x Yy x 2 &c, and determine 

 thus the position of the lines. A plane grating ruled in this 

 manner would form at Q x without aberration an image of Q for 

 light of the given wave-length X. Of course it would be open 

 to the objection which holds against all such aplanatic arrange- 

 ments, viz. that they are only good for light of one definite 

 wave-length. If the grating were used for light of a different 

 refrangibility, the image formed would suffer from aberration. 



LX1II. A new Photometer. 

 By Sir John Conroy, Bart., M.A.* 



HAYING recently made a considerable number of photo- 

 metric observations, and learnt by experience the 

 difficulty which attends all such determinations, I venture to 

 bring before the Society the description of a new form of 

 photometer which appears to possess certain advantages over 

 those in use. All such instruments, with the exception of the 

 wedge-photometer, are essentially arrangements for comparing 

 the illuminating-power of two lights, and therefore do not 



* Communicated by the Physical Society; read April 28, 1883. 

 2H2 



