Intelligence and Miscellaneous Articles. 447 



sible empirically to displace the second nicol (and thereby the two 

 bands) so as to preserve the maximum of intensity to the simple 

 radiation the comparison of which would give the same result as 

 that of the total intensity. The neighbouring radiations are more 

 and more rapidly weakened in proportion as their distance from this 

 maximum increases ; and this circumstance diminishes the influence 

 of their differences of intensity (which increase with their distance 

 from the maximum) to such a degree as to render then negligible. 



In practice the system of nicol s and quartz plate is fixed in 

 the body of a small telescope placed opposite to the screen of the 

 photometer, upon the cone through the apex of which we view it. 

 This instrument, constructed with much precision by M. Duboscq, 

 tried with the Drummond light, an electric regulator or sun-light, 

 comparatively with the standard Carcel, immediately gave very pre- 

 cise results in spite of the difference of tint of those different 

 lights. — Comptes Rendus de VAcademie des Sciences, Sept. 26, 1881, 

 t. xciii. pp. 512, 513. 



A NEW DEMONSTRATION OF RIEMANN'S THEOREM. 

 BY M. CROULLEBOIS. 



M. Clausius* has presented Eiemann's theorem as a consequence 

 of Green's formula ; that important proposition can be demonstrated 

 more directly. The theorem is thus enunciated by Clausius : — 



Given tivo conducting bodies A and B, ivhich may either be insu- 

 lated or connected with the earth by a conductor ; in the vicinity of 

 these let there be any number whatever of other conducting bodies put 

 into communication ivitli the earth by means of conductors. While B 

 is in communication with the earth and A is insulated, this latter body 

 is charged with electricity up to a certain potential-level K. Let Q.j 

 be the quantity of electricity accumulated by influence upon B under 

 these circumstances. A is afterwards put into communication with 

 the earth, while B is insulated and charged ivith electricity to the 

 same potential-level K. Let Q J a be the quantity of electricity accumu- 

 lated upon A by influence under these circumstances. We shall have 



Let the two conductors A and B be initially accompanied by any 

 number of conductors, all connected with the earth — that is to say, 

 at the potential zero. Let us insulate A and bring it to the poten- 

 tial Y x ; the effect of this increase of potential will be to raise the 

 charge of A from to Q*, and to induce charges upon the other 

 conductors, and in particular upon B the charge Q^ ; we can put 



C a being the capacity of A, and Q a f) the coefficient of induction of A 

 upon B. 



Let us discharge A by putting it into communication with the 

 earth, and bring it to the potential V 2 ; there comes in like manner. 

 in this second state of equilibrium, for the charges acquired upon 

 B and induced upon A: — 



Qf=ofV a) Q,,';=e,';v = , 



* Theoric Mecanique de la Chakur, t. ii. pp. 38-44. 



