1878.] Dr. A. Schuster on the Spectra of Metalloids. 383 



2 2m+l n+1 A(s—m) A(s—n— l) A(s—p) 

 2s + l "m+T 2^+1 A(s) 



2 2m+l ?i A(s— 1— m) A(s — ?i) A(s— 1— 

 27^1 ~^+T 2^+1 A(s-l) 



2 m A(s — m) A(s— n— 1) A(s— 1— p) 

 2.s-l m + 1 A(s-l) 



It is now a matter of easy algebraical work to put these three terms 

 together by the aid of the essential property of the function A(r). 

 If we put the second and third terms together we shall get 



2 (m—n)(s—p) A(s — m — l)A(s — n)A(s—p) 



+ l)(2tt + T) (s-m)(2s—2n-T) Aj7) ~' 



and the first term is equal to 



2 (2m + 1)Q + l)(2g - 2m - l)(g - w) A (s - m - 1 ) AQ - n) AQ —p ) _ 

 U+T ' O + 1 )(2/i + l)(s - m)(2* - 2% - 1) A(s) ' 



the aggregate of the last two expressions is 



2 A(s— m— 1) A(s— ?i) A(s— p) t 

 2F+T A(i) 5 



as it should be. 



1 may observe that the definite integral was discussed by Dr. N. C. 

 Schmit in a dissertation published at Brussels in 1858 ; but no simple 

 result is there obtained. 



III. " On the Spectra of Metalloids. Spectrum of Oxygen." By 

 Arthur Schuster, Ph.D., F.R.A.S. Communicated by J. 

 Clerk Maxwell, F.R.S., Professor of Experimental Physics 

 in the University of Cambridge. Received April 25, 1878. 



(Abstract.) 



The many unexplained phenomena attending the passage of elec- 

 tricity through gases will probably for some time to come occupy the 

 attention of experimental physicists. It is desirable that the subject 

 should be approached from as many different sides as possible. One 

 of our most powerful instruments of research is the spectroscope, but 

 before it can be applied to the study in question we have to settle the 

 chemical origin of the different spectra, which we observe in vacuum 

 tubes, and to discuss in what way such spectra are liable to change 

 under different circumstances. A special investigation has to be made 



