Mr. C. H. Bennington on a New Photometer. 475 



If we write out a Table expressing these relations in a manner 

 similar to that employed for the particular case of ^ = 2 in a pre- 

 ceding article, we shall obtain a square array of signs (q* to a 

 side) which will form an inverse orthogonal matrix corresponding 

 to the type q . q .q . . . (to i terms) . 



[Part II. to follow.] 



LXI. Description of a New Photometer. 

 By C. H. Bennington, M.A. Cantab* 



"T IGHT varies inversely as the square of the distance." 



-«-J is a pinhole in an opake screen, papered and lighted 

 behind. A scale extends 1 foot halfway from to the observer. 

 An opaline screen x slides on the scale. 



Times. 

 Suppose when x is visible set at 1 foot from 0, 01 



can be photographed in j 



.'. when x is only visible at yL of a foot from 0_, 0~\ 

 can be photographed in J 



My photometer is based on the above principle. 



1 



12 2 



< 



A is a small compound microscopef sliding tight in a tube B, 

 at the end of which in a T l 5 -inch diaphragm is an opaline micro- 

 photograph x. B slides tight in another tube C which has a 

 ^-inch diaphragm y. D is an eyepiece fixed to A, fitting the 



in the given system of sign-progressions. The proof of the theorem is pre- 

 cisely the same as for the case previously considered, where q=2; viz. it 

 may he shown that the sum above denoted by 2 is equal to 





j>i,p 2 , «*«,/*»! 



each of the q i terms of which new sum vanishes except that one in which 

 the variable /x system is identical with the given X system of the 5th roots 

 of unity, for which term the fraction becomes equal to qK 



* Communicated by the Author. 



f The eye-tube of a small telescope answers the purpose. 



212 



