1020 Prof. Akimasa Ono on the First Root of 



In this work, in which 336 aurora photograms from the 

 above expedition are reproduced, calculated and discussed, 

 there is also a chapter treating of the very same problems 

 that, are discussed in Vegard's paper. In tins chapter 

 (pp. 157-212), of which the title is " Sur l'absorption et 

 l'intensite lumineuse des rayons corpusculaires penetrant 

 dans l'atmosphere terrestre en suivant des trajectoires non 

 rectilignes/' there are, in addition to the necessary formulae, 

 also a number of numerical calculations of trajectories in 

 the atmosphere applied to the auroral phenomena. 



I will content myself with this reference, without going 

 into the questions of priority. 



CYIII. On the First Root of Bessel Functions of Fractional 



Order. 

 To the Editors of the Philosophical Magazine. 



Gentlemen, 



AS pointed out by Dr. J. R, Airey in the February issue 

 of the Phil. Mag., the first root of Bessel functions of 

 fractional order appears to play an important role in the 

 solution of physical problems, e. g. the elastic stability of 

 tapered long struts*. If we assume that the moment 

 of inertia I of the cross-section at any distance x from the 

 free end of a strut is represented by 





where i! is the value of I at the other fixed end x = l, and 

 n is a constant independent of x, then the critical load is 



P=(l-1) 2 ^^. • ..... (2) 



In this equation E is the modulus of elasticity, and z 1 is the 

 first root of the Bessel function J_i^ (V), 



2-n 



Now calculating the value of ll—^\ z-f for several 



' (-I)'-' 



assigned values of ??, we observe that it can be approxi- 

 mately represented by a linear function of n, thus : 



2 



c +kn. 



(.-»■,■ 



* "On the Stability of Long Struts of Variable Section," Akimasa 

 Ono. Memoirs of the College of Engineering, Kyushu Imperial 

 University, vol. i. No. 5 (1919). 



