242 



Mr. A. Mallock. The Physical 



[June 6, 



Fig. 5. 



adjustments are complete, the axis of the india-rubber is the con- 

 tinuation of the line DE. 



In the statical measures two silk threads were attached to A, one 

 carrying the plumb-bob K, and the other the small weight W. W 

 was drawn to one side as shown, care being taken that the horizontal 

 projection of AH was at right angles to AB, and that HL was 

 horizontal. The distance HK was then measured with a scale, and 

 the angle through which the moment due to the horizontal com- 

 ponent of force acting along AH turned the bar AB was read on the 

 divided circle F. 



The section of the specimens of india-rubber used in these experi- 

 ments being approximately square, and the reaction against torsion of 

 a square prism being 0*883 that of a circular cylinder of the same 

 area,* it follows that, since the torsional rigidity of similar prisms 

 varies as the fourth power of the linear dimensions of their section, 

 therefore the circular cylinder which has the same torsional rigidity 

 as a square prism whose side is a, has a radius equal to (a/"") ^O'SSS. 



In fig. 4 let AB = 2R, 



CC = I = length of the india-rubber, 

 HK = x, 

 AK = X, 



= angle through which the india-rubber is turned, 



expressed in circular measure, 

 s = sectional area of india-rubber, 

 W = weight hung from H. 

 Then if n = coefficient of rigidity 



and r = (>*/*-) (0-883)*, 



_ 2nwix 



* See Thomson and Tait, < Nat. Phil.,' vol. 1, Part II, p. 257. New Edition. 



