_' DR. F. HORTON ON THE EFFECTS OF CHANGES OF TEMPERATURE 



temperatures a curve, and not a straight line, was obtained. The form of the curve 

 was similar to that given by gold, iron, &c., and suggests that the departure from the 

 linear law is due to the gradual increase of rigidity with time. 



The value of the modulus at 15 C. for commercial copper is n l6 = 37956 x 10 U 

 dynes per sq. centim., and the " temperature coefficient " ft = '0004074. 



The modulus of rigidity is thus considerably less, and the temperature coefficient 

 rather greater, than in the case of pure copper. 



The logarithmic decrements of the amplitudes of oscillation were about four times 

 as large as those obtained with the pure copper wire, indicating a much greater 

 internal viscosity in the case of this commercial copper. 



PART III. 



SUMMAKY AND COMPARISON OF RESULTS. 



The results of the experiments may be summarised as follows : 



1. In all the materials examined, with the exception of pure copper and of steel, 

 the modulus of rigidity at one temperature is not constant, but increases as time goes 

 on. The rate of increase of rigidity with time is greater the higher the temperature, 

 and repeated heatings to the same temperature gradually lessen the rate of alteration 

 with time at that temperature, but even in the course of months of experimenting the 

 increase of rigidity with time cannot be entirely eliminated. 



2. The diminution of the modulus of rigidity per degree rise of temperature 

 between 10 C. and 100 C. is constant for pure copper and for steel, but not for any 

 of the other materials examined. 



3. In the case of the metals iron, gold, tin, lead, and commercial copper, the 

 rigidity-temperature curve is of such shape as to suggest that if it were possible to 

 obtain the values of the rigidity modulus at the different temperatures, all within a 

 very short space of time (so as to avoid the " time effect "), the resulting curve would 

 be a straight line. 



4. In the case of the metals platinum, silver, and aluminium, the shape of the 

 rigidity-temperature curve shows that the effect of the gradual increase of rigidity 

 with time is such as to make the alteration with temperature approximate more 

 closely to a linear law than would be the case if the observations were all taken 

 within a very small interval of time. For these metals, therefore, the decrease of 

 torsional elasticity per 1 C. rise of temperature increases with the temperature. 



5. In general, the effect of heating to a high temperature is to increase the value 

 of the rigidity modulus at low temperatures. [This applies even to pure copper, of 

 which the modulus of rigidity at the ordinary laboratory temperature is slightly 

 greater after the wire has been heated to higher temperatures. The rigidity of steel 



