Solution of a Linear Differential Equation. 659 



Hence, since 



dR _ BT ___ l TJ2 ?!_ T2 



K " T * m 2 » 

 we have 



-13-9 X 10" 3 = 23*47 x 10~ 3 - 1 (17513) 2 . 10 14 . I* 



whence 



T = 2-2xl0- 12 sec*. 



Indications seem to point to molecular and intermolecular 

 effects of a highly complex nature, and until more definite 

 information is available as to the structure of the molecule, 

 it seems unlikely that a complete theory can be formulated. 



In conclusion, we desire to express our obligation to 

 Professor Taylor Jones, who suggested the research, for the 

 valuable interest he has taken in the work, especially in the 

 designing of the instrument employed in setting the speci- 

 men, the use of which has considerably enlarged the scope of 

 the method. 



Physics Laboratory, 



University College of N. Wales, Bangor, 



January 23rd, 1914. 



LXXIV. The Sum of an Infinite Series as the Solution of a 

 Linear Differential Equation. By I. J. Schwatt f. 



rpOfind 



S= t-^-- (1) 



Let u n denote the (n + l)st term of the series, then 



Un _ n 



u n -i w+6 

 or (n-+6)u n = rnu n „i, 



and 



X (nrJrQ)u n =zrSnUn-i=rX (?i + l)»« 



71=1 71=1 71=0 



* J. J. Thomson, in his ' Corpuscular Theory of Matter,' gives 

 10 _< cm. as the order of magnitude of the free path of a corpuscle, 

 and 10 7 cm. per sec. as that of the velocity, whence T=10"- u sec. 



t Communicated by the Author. 



