On Electricity in the Act of Muscular Contraction, 53 



which, as x increases without limit, approaches to c + log \ogos 

 or log log {x>^)i where x or s" is a constant, which may be found 

 by computation. 



Now as X increases without limit, we have 



log (l + ^ + ^ + [ +-. + 7,)=logiogM; 



so that the expression to which (l — o) (^"o') 



\}~~t) •••(! ) approximates arithmetically is not 



as was before observed, but 



The expression here discussed was calculated by Legend re, 

 and tabulated up to ^=1229. (See Tlieorie des JVombres, 

 tab. IX. vol. i.) The value of c, as derived from x= 1229, is 

 •581078; as derived from ,r=1213, it is -580693; and as de- 

 rived from ,27 = 94-7, it is '58101 ; and it is not improbable that 

 its theoretical value is the constant •5771213 of the ordinal 

 series. It may be observed, that the difference between this 

 constant and that which enters in the sum of the reciprocals 

 of the primes corresponds exactly with the analytical value of 

 this constant y ; for the value of this difference is 



(| + logi) + (j + log|) + (i+log|) + ... «<Zm/., 



and the value of y is 



(l+log.) + (l + logi) + (i+log|) + (l+!ogi) + ... 

 ad infijiitum. 



The preceding investigations may be made available for the 

 determination of the law which regulates the occurrence of 

 numbers which are composites of two primes, of three primes, 

 &c. ; but I have not hitherto investigated this part of the sub- 

 ject with sufficient minuteness. 



VI. On the Development of Electricity in the Act of Muscular 

 Contraction. By M. Becquerel*. 



I HAVE repeated unsuccessfully the experiment of M. Du 

 Bois Reymond, relative to the production of an electric 

 current in the act of muscular contraction, making use of the 

 arrangements which he indicated in a letter addressed to 

 * From the Comptes Rendus for May 28, 1849, 



