106 



Mr. H. Tomlinson. The Influence of 



this result it was assumed that the number of degrees of torsion pro- 



, , 1A . v ,,t, m 90*43 + 1(181-02) 

 duced with 10 grams in each of the pans, T, was ^ , 



a 



or 90-47. 



The value of the modulus of torsional elasticity in grams per square 

 centimetre can be found from the formula — 



_ L x D x P x 360 



where L is the length of the wire in centimetres, S the section in square 

 centimetres, P the number of grams in each pan, n the number of degrees 

 of torsion, r s the modulus of torsional elasticity determined by the 

 statical method, and D is the arm of the couple P X D in centimetres. 

 The value of D was determined very carefully by a wire gauge reading 

 toy^oth of a millimetre, due allowance being made for the thickness of 

 the silk thread, and proved to be 0*96(58 cm. The value of L varied 

 in the different experiments from 650 to 800 era., and within the 

 limits of errors of observations the strain, as in the above experiment, 

 was exactly proportional to the stress. The diameter of each of the 

 wires was very nearly 1 mm., and in only one instance* was the value 

 of n carried beyond 200°. As far as could be ascertained the torsional 

 stress never exceeded the limit of elasticity, the recovery being in all 

 instances apparently perfect. f 



As soon as the determination of the modulus of torsional elasticity 

 by the statical method had been satisfactorily concluded, the modulus 

 was redetermined by the method of torsional vibrations. The time of 

 vibration was in the case of each wire taken from the mean of a large 

 number of observations, first with only the graduated plate attached 

 to the wire, and again when the moment of inertia of the plate had 

 been supplemented with a hollow ring df copper, turned true inside 

 and outside, and of which the moment of inertia could be calculated 

 with considerable accuracy. The error likely to arise in the determi- 

 nation of the modulus of torsional elasticity by the kinetical method 

 would not in any case be greater than O'l per cent. In the next table 

 will be found the results obtained by both methods : — 



* That of platinum in which the value of n was 210. 



f This does not necessarily imply perfect elasticity, as for this the recovery of the 

 wire on the removal of the stress should be instantaneous. Whether this was so 

 could not, of course, be ascertained. 



