416 DR. F. HORTON ON THE MODULUS OF TORSIONAL RIGIDITY OF 



The Results of the Experiments. 



In order to calculate the modulus of rigidity it is necessary to know the moment of 

 inertia of the movable cylinder of the vibrator when in the two positions shown in 

 fig. 1. The mass and dimensions of the cylinder were therefore accurately determined. 



They were 



Mass of cylinder = 2 '0987 grammes, 



Mean diameter of cylinder = 5'5841 millims. at 13*5 C., 



Diameter of longitudinal hole = 1-4490 13'5 C., 



Length of cylinder = 11-0202 13-5 C., 



Diameter of transverse hole = T4956 ,, 13'5 C., 



from which moment of inertia of the cylinder with its axis vertical (fig. 1, first 

 position) = '0878115 gramme cm. 2 at 13'5 C., and moment of inertia about the axis 

 of rotation when in the second position (fig. 1) = '263747 gramme cm. 2 at 13'5 C. 



The coefficient of expansion of the cylinder had been determined and was 

 00001937, from which the moments of inertia of the cylinder in the two positions 

 at the standard temperature 15 C. are 



I' = '263762 gramme cm. 2 , I = '087817 gramme cm. 2 

 The periods obtained with the first fibre experimented on were 



Cylinder on vibrator in first position, Tj = 8'47 140 at 13-11 C., 



second T' = 14-34857 12'99 C., 

 first T 3 = 8-46916 13'15 C., 



Mean of the two periods in first position, T = S'47028 at 13'13 C. 



These periods, T and T', have now to be corrected to the values they would have 

 if the temperature had been 1 5 C. ; correcting, therefore, on account of the alteration 

 of rigidity of the fibre and of the dimensions of the fibre and vibrator, we get the 



corrected periods 



T = 8'46967 sees, and T' = 14 '34745 sees., 



Length of the fibre, I = 11 '268 centims., 

 Mean radius, r = '001058 centim. 



The formula for the modulus of rigidity is 



n = 



which gives for the modulus of rigidity of this fibre at 1 5 C. the value 



2'965 x 10" dynes per sq. centim. 



