1919] HENDRICKS— TORSION 429 



about each other several times (more than shown). On h, k two 

 loops of this thread are placed, instead of one, and in such a way 

 that the inner part on m, n comes between the inner parts of the 

 two loops on h, k when the clamp is closed. A piece of fine copper 

 wire (/), several cm. long, is attached to one-half of the clamp. 

 This can be adjusted by bending so as to counterbalance the holders 

 opposite. The entire device weighs somewhat over i gm. Since 

 the mirrors are placed at some distance from the vertical axis, 

 slight corrections are necessary for accurate work. In order to 

 measure the growth in length of the point holding this clamp, a 

 linear scale, fastened vertically, was used. With care this measure- 

 ment could be made with fair accuracy. 



In its simplest terms, torsional rigidity may be looked upon 

 as "resistance to twisting." In earlier experiments it was esti- 

 mated by balancing a measured deflection in the part of the 

 vine used against a measured twist in a very fine wire. As 

 this required additional apparatus, as the readings were rather 

 difficult to make satisfactorily, and as the results were not very 

 accurate, it will not be described in detail. The success of the 

 present method, which is not open to these objections, depends 

 on making the frame light, compact, and with small resistance to 

 the air. In making a determination by the present method, the 

 period of oscillation of the frame is timed. This is, in fact, a com- 

 mon method in physical laboratories. As may bq learned from 

 any textbook in physics,^ the law governing this may be stated as 

 follows : If a circular wire of length L and radius of cross-section R 

 suspends a body whose moment of inertia is iv , and if the coeflficient 

 of torsional rigidity of the material of this wire is n, then the period 

 of oscillation in sec onds of th is body is given by the following equa- 

 tion: 7= (i/i?^)l/87rA'L-^w. From this, » = 87ri^L-^-Pi?l It is 

 more convenient, however, to use the diameter {D) of the vine, and I 

 always use the same frame and am dealing with comparative values 

 only. Consequently, the expression actually used is L-^ T^D^, 

 which equals what may be called the coefficient of rigidity. This 

 may be defined for our purposes as the relative measure of the resist- 

 ance offered to twisting through a unit angle of an average unit length 



3 For example, Watson, W., A text-book of physics. Longmans, Green & Co. 

 1900. p. 205. 



