ON THE MODI' I. is OF TORSIONAL RIGIDITY OF METAL WIRES. 47 



The values given in the above table were uot in all cases found from the range l 

 temperatures C. to 100 C. The experiments <>t N \i II:I;SKV and those of KUPFFKH 

 on iron, platinum, and silver, were only performed over a small range of temperature, 

 from about 5 C. to 25 (V. while tin- numliere of SI-II.KKKR and BENTON apply to 

 temperatures between 186 C. and + 20 C. It must also be pointed out that 

 KOHLRAUSCH and LOOMIS, PISATI and TOMLINSON, give formulae showing that the 

 alteration of rigidity with temperature does not follow a linear law ; KOHLRAUSCH 

 and LOOMIS, and TOMLINSON, finding that the rate of decrease per degree rise of 

 temperature increases with the temperature, a view with which PISATI'S. results, with 

 a few exceptions, agree. The values given by KOHLRAUSCH and LOOMIS are very 

 different from those obtained by other olxservers, a result no doubt due in part to the 

 fact that the wires they used had not been subjected to any annealing process. These 

 authors state that observations taken on different days could not be compared, and 

 from their tables it is seen that the period of torsional oscillation decreased from day 

 to day. This means an increase of rigidity with time, an effect to which I have drawn 

 special attention in this paper, and which, in unannealed wires, is quite large. 



A fault common to all the experiments which have hitherto been made by the 

 dynamical method, is that sufficient precautions were not taken to insure that during 

 the observations at high temperatures the wire was every where throughout its length 

 at the same temperature. The average temperature of the wire must generally have 

 been considerably below the temperature indicated by the thermometers. This was 

 found to lie the case when experimenting with the first form of apparatus used in tin- 

 present research. Under these circumstances, the observed rate of alteration of 

 rigidity with temperature would be less than the actual alteration, and the temperature 

 coefficients obtained would be too small. In the present research the values of the 

 temperature coefficients for iron and steel, as given by experiments with the old form 

 of apparatus, are less than the values obtained with the apparatus in its final form. 



The results of KUPFFER and of NAPIERSKY are only of interest from an historical 

 point of view, they differ very considerably from those obtained by more recent 

 observers. One great fault in their experiments is that the amplitudes of oscillation 

 were extremely large. In PISATI'S experiments, too, the amplitude of vibration was 

 90 at tli. I it Binning of each observation, and the rigidity of the wire (the length of 

 which was 65 centims.) must have been considerably altered by being subjected to 

 this treatment. 



M' the more recent experiments, those of SCH^CFER stand out as comprising the 

 largest number of materials. As already stated, he employed the statical method of 

 experimenting, observing the torsional deflections of a wire under a constant couple. 

 The temperatures worked at were, in general, only two, the temperature of the 

 lalxn-atory and that of boiling liquid air, and the rate of alteration of rigidity with 

 temperature was assumed to be constant between them. The main object of this 

 work was, however, to compare the temperature coefficient of the torsion modulus 



