THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



NO V EMBER 1919. 



LI. The Bessel-Clijford Function, and its applications. 

 By Sir CtEORGE GtREEnhill *. 



VETRITERS on Stability, statical and dynamical, as 

 ▼ » of a beam, strut, and whirling chain or shaft, 

 are compelled to introduce the Bessel Function to provide 

 a complete solution. 



The ordinary function is employed usually as given in the 

 text-book ; but attention should be directed to a forgotten 

 posthumous memoir by Clifford, ' Mathematical Papers,' 

 p. 346, 1882, where he makes a start with the function, 

 which we may denote after him by C(V), defined as the sum 

 of the positive integral, k, powers of «r, x k , divided by the 

 square of the factorial h, Uk. 



The following applications are intended to show the 

 advantage of Clifford's notation. 



1. It is convenient to change the sign of ,r, and to make, 

 according to this definition, 



9(*> - s£T(-*)*/(II*)*-; . . . . (l) 



thus, in the notation of the ordinary Bessel Function, the 

 Clifford Function C(» = J (2 \/x). 



In the definition of the ordinary Exponential Function 



9 • «-* = 2(-*)*/II*; (2) 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 38. No. 227. Nov. 1919. 2 N 



