20 ART. 6.— S. KUSAKABE : 



Let the principle of superposition be assumed to hold good for 

 the case of yielding, and take for granted the following relation, no 

 matter how or from what hypothesis it may have been obtained, 



r}=klogt.* (1). 



To simplify the matter, let us suppose that a definite amount of 

 couple begins to act at the origin of time and remains acting for an 

 infinite time ; and also that after each unit of time — in my experi- 

 ments it was one minute — the couple is increased by the same 

 amount. Then, the total amount of the yielding at the instant T=p 

 is given by 



T i = Vp + r tv-\ + + r h + r n = MogI\p + 1 } (2). 



where r is a well-known symbol for Gamma-function. 



If a negative couple were to act at the instant T=p + 1 and after- 

 wards, increasing in its absolute amount step by step like the positive 

 couple, the yielding due to this negative couple at the instant T=p + r 

 would evidently be 



y=-Mogr{r+l) 

 Hence, if the couple increases for the first p minutes and then remains 

 constant for the following r minutes, the yielding at the instant 

 T=p + r is 



V =kloglJp + r+l}-MogI\r+l}=klog^^±^-. (3). 



Again, if the couple after an increase for the first p minutes, 

 remains constant for the next r minutes, and then decreases step by 

 step during last n minutes, the yielding at the instant T=p + r + n, as 

 it may easily be seen, is given by 



* In Page 15, we had the formula i) = r-r,) = A: logt, where r is the value of r at the time 

 t = l, so that the expression for the yielding i.e. q = hlogt holds good only for t >1. When the 

 present paper is under the press, it is kindly noted by Mr.JS. Sano, that it is better to take a 



form n = k log , where e is a constant, than to take the form given in the text. It is very 



good of him to have given me so much of other valuable remarks. The author would like to 

 thank him for all his kindness. 



