Effect of Temperature on Modulus of Rigidity. 397 



The methods of mental division and mental determination 

 of square roots are given here only for the sake of interest. 

 The author does not intend to recommend them for practical 

 use until he has had sufficient experience of their merits or 

 otherwise. 



But the method of mental multiplication has serious claims 

 to oar attention (already mentioned), and very little ex- 

 perience with it makes* one feel that if one had been brought 

 up on it from childhood in place of the ordinary method, 

 then the multiplication of large numbers would have its 

 terrors considerably lessened. 



XL IV, The Effect of Temperature on the Modulus of Rigidity, 

 and on the Viscosity of Solid Metals. By Kei Iokibe and 

 SuKEAKI SAKAI *. 



1. Introduction. 



THE effect of temperature on the modulus of rigidity of 

 different metals has been a favourite subject of many 

 investigators. In most of the previous investigations the 

 range of temperature was very limited, not much exceeding 

 300° C. Kohlrausch & Loomis f, Pisati J, and Tomlin- 

 son § investigated the effect of temperature on rigidity below 

 300° C, and proposed the formula of the form 



n t = n (l-at-/3t 2 ), 



where n t and ?i are the values of rigidity at t° and 0° respec- 

 tively. Experiments have also been made by Katzenelsohn ||, 

 Gray, Blyth & DunlopH, and Sutherland**, the latter 

 confining his researches to the softer metals, such as lead, 

 zinc, tin, and magnesium, which had been neglected by 

 former investigators. He also obtained a formula of the 

 type 



-=i-( T y 



N \T /' 



where N is the value of rigidity at absolute zero, and T the 

 melting-point in absolute scale. 



* Communicated by tbe Authors. 

 f Pugg. Ann. vol. cxli. p. 481 (1870). 



X Nuovo Cithento, ser. 3, vol. i. p. 181 ; ii. p. 137; lv. p. 152; v. 

 pp. 34, 135-145 (1877-79). 



§ Proc. Roy. So«. vol. xl. p. 343 (1886). 

 || Beibl. vol. xii. p. 307 (1888). 

 f Proc. Roy. Soc. vol. lxvii. p. 180 (1900). 

 ** Phil. Mag-. (5) vol. xxxii. p. 31 (1891). 



