56 Prof. H. Nagaoka on the Elastic Constants of 



with thin sheet lead underneath were interposed between the 

 four faces of the prism and the clamping screws. I, was 

 fixed to a solid iron frame. The central steel cylinder pro- 

 truding from I 2 was filed down to a sharp knife-edge on its 

 axis, coinciding with the central line of the prism. An agate 

 plane attached to another solid iron frame supported the knife- 

 edge and the twisting pulley P. To the cylinder above 

 referred to, a pulley P x of 14 centim. diameter was firmly 

 fixed ; a flexible string s 1 attached to a pin p on the circum- 

 ference of the pulley passed over it, and was tied to a light 

 wooden cross-bar c. Another string s 2 was attached to the 

 pulley, and instead of passing over it, was slung around 

 another pulley P 2 such that the line of passage s 2 from Pj to 

 P 2 was vertical. The string on going over P 2 in the opposite 

 direction to the former string was again let down vertical and 

 attached to the cross-bar. By hanging the weight at the 

 middle of the bar, the tension was the same in both strings 

 and gave rise to a couple = radius of the pulley X weight. 

 By this arrangement, the knife-edge did not support the load 

 producing the twisting couple, that of the prism, clamp, and 

 pulley being the only weight acting. The amount of torsion 

 was measured by observing the deflexion of two mirrors M x 

 and M 2 , one attached to the prism near the fixed clamp I\ 

 and the other near I 2 . The deflexions, as measured by a 

 vertical scale and two telescopes, were generally large com- 

 pared with those in flexure experiments, so that no micrometric 

 measurement was needed. The difference between the two 

 scale-readings gave the torsion between the two places where 

 the mirrors were fixed by special clamp screws. 



Denoting the sides of the prism by b and c, the torsion for 

 unit length by t, the twisting couple by N, and the rigidity 

 by fi, we get by (St. Venant's formula for the torsion of a rect- 

 angular prism the following expression for N 



r / 2«-l \w S2n-l-\7 



\ 2b ) ~\ 26 ) 



v e " +e 



It may be a question whether it is justifiable to use St. Venant's 

 formula in the present experiment, as the boundary conditions 

 are somewhat different from those considered by St. Venant 

 in deducing the above result. As the Jength of the prism was 

 large compared with its thickness, and as the twist t was 

 measured at points not very near the ends of the prism, the 

 result given by using the above formula will not be materially 



