362 



Prof. J. R. Young on the Evaluation of 



Animal (continued). 

 Veal, raw 873 



... boiled .... 911 

 Beef, raw 880 



... boiled .... 942 

 Ox-lung 931 



Purified muscular Jihre Jrom 

 various animals. 



Fibre of eel . . 



''';.j ' Sdltnon . 



.« ' herring . 



... haddock 



... flounder 



pigeon 

 lamb 



908 

 982 

 914 

 988 

 988 

 775 

 916 



Fibre of sheep 

 .». calf . 



ox 

 sow 



928 

 993 

 935 

 893 



Proximate -principles of ani- 

 mals, calculated from the 

 quantity of nitrogen as de- 

 termined by Mulder. 



Pure proteine . . . 1006 



albumen 

 fibrine . 

 caseine . 

 gelatine . 

 chondrine 



996 



999 



1003 



1128 



910 



LIV. On the Evaluation of the Sums of Neutral Series. By 

 J. R. Young, Professor of Mathematics in Belfast Col- 

 lege^. 



THE attention of several analysts has been called of late to 

 the series 1 — 1 + 1 — 14- 1 , and the long-prevail- 

 ing doctrine that the sum of this series to infinity is neces- 

 sarily — , is beginning to be questioned, and the true charac- 



ter of it to be recognised. There is danger however of mis- 

 take arising in another direction, for it has been affirmed that 



this series cannot be — , even when regarded as the limit of 



the converging cases of the general series 1 —x-\^x^—a^-\-x'^... 

 It is my wish in the present communication to point out the 

 error of this statement, and to notice the circumstances which 

 appear to have led to it. 



And in the first place I would observe, that when the series 

 in question is intended to represent that which the general 

 converging series becomes in the extreme case of a; = 1, it is 



considered as identical with I — 1 + 1^ — 1^ + I'* I""', or 



rather, — indicating more explicitly the connexion of this ex- 

 treme case with the general series of converging cases that it 

 terminates, — it is considered as identical with 



\ G0/\ 00/ \ 00/ **"\ 00/ 



Again, the general expression for n terms of the series 1 — x 

 * Communicated by the Author. 



