28 ART. 6.— S. KUSAKABE : 



j /T6g + l)[/T58I + l)F[A9t + l)? 



^- A ' ?- L /'(73t+j)n/'(^+i)r 



so that the difference of the two is 



r(82r+i)(r(52i+i)]- 



& log- 



(r(73t+l)p/'(43l + l) 



Now, the value given by ç x is what is called set by engineers and 

 the value of y)\ is its increase caused by the second cycle. Comparing 

 the absolute values of these two, we easily see that the latter is very 

 small. In a particular case, indeed, where 2t = 10, the value of r n is 

 [3-825 MoglO] while that of ?', is only [0-238 MoglO} , which falls 

 almost within the limits of error of observation, or wdiich may be 

 neglected without any serious error. Thus we have 



Proposition VIII. Suppose that we give a set to a specimen by 

 twisting it through a definite angle. A second twisting through the same 

 angle causes little or no further set. 



Lastly, referring to the equations (6) and (7) we see that, since ?} 

 is a function of several variables, it may have any value whatever, 

 within certain limits, when the amount of couple actually acting upon 

 the specimen i.e. p or n is given. Also, from (17) we see that, when p 



or n and -/? are given, — — — or ■ - ■ may have several different values. 



' ö ' Ap An 



Thus we have : 



Proposition IX. Not only may the .specimen be brought to any 

 twisted, state, within wide limits, by a given definite couple, but it may have 

 more than one gradient in passing through that state. 



As a particular case of the above, if both p or n and r t are zero, 

 the specimen is actually free from any external couple and also it is 

 free from any residual. In every respect, there is no external differ- 

 ence between such a piece and a virgin one. Tested with couple, 

 however, it retains latent traces of the twist from which it was lately 



