ON THE MODULUS OF TORSIONAL RIGIDITY OF MKTAI, WIKKS 21 



laboratory. After repeated heatings for long periods to one temperature, the increase 

 with time at that temperature gradually became smaller and smaller, and in some cases 

 became zero ; but if then the wire was heated to a higher temperature and subsequently 

 brought back to the lower one again, the increase with time at that temperature 

 still went on. This effect could not be due to any disturbing cause, such as the 

 oxidation of the surface of the wire or a gradual lengthening under the tension, for 

 these would have the opposite effect, and cause an apparent diminution in the 

 rigidity. The wires were quite bright ;it the end of the experiments, and the length 

 was measured at intervals and in many cases was quite constant. In the case of 

 gold and the softer metals, however, it increased slightly (hiring the experiment*, and 

 the periods obtained were corrected on this account. 



Under these circumstances it is evidently impossible to determine accurately the 

 manner in which the rigidity is affected by the change of temperature, for such 

 change is complicated by the varying time effect. It was thought that the most 

 useful information would be obtained by plotting the values of the rigidity modulus 

 against the corresponding temperatures, and drawing a curve through the first points 

 obtained at each temperature. The alteration of rigidity per 1 C. rise of temperature 

 at the ordinary lalx>ratory temperature was then found by drawing the tangent to 

 this curve at 15 C. In this manner a coefficient /3 was obtained for each wire such 

 that for temperatures in the neighbourhood of 15 C. n t = n )6 (l ftl), n lb being the 

 value of the modulus at 15 C. 



In addition to the determinations of the periods of vibration, observations of the 

 logarithmic decrement of the amplitudes of the oscillations were taken at each 

 temperature, as already described. These will be found among the results which 

 follow. At the end of the rigidity determinations for each wire, a series of observa- 

 tions was usually taken to ascertain the manner in which the logarithmic decrement 

 and the torsional period varied with the amplitude of vibration, amplitudes up t<> 

 about 10 being used. The main observations for the rigidity determinations were 

 all taken at the constant average amplitude of 14 minutes. 



Observations at 126 C. were only taken with a few of the wires, for great trouble 

 was experienced through the heating jacket leaking when heated to this temperature. 



In the account which follows, the complete set of curves and tables of results are 

 given for a few only of the metals experimented on. These serve as examples of the 

 11 u- tin id of experimenting and as models of the results obtained. 



It would be well to remark here that only in a few instances was more than one 

 specimen of the metal in question experimented on. The values given for the rigidity 

 modulus and its temperature coefficient would be only approximately true for any 

 other specimen, for it is a well-established fact that the values of the rigidity modulus 

 of any substance given by different specimens of the same material are not the same. 

 The cases in which more than one sample was experimented on were those in which 

 the " time effect " was least, as it seemed possible that in these OMeo the temperature 



