On the Effects of Changes of Temperature on Metal Wires. 181 



bulk-modulus, and it is impossible, except on strict experimental evi- 

 dence, which has not so far been forthcoming, to suppose that there is 

 any invariable numerical relation between the two latter moduli. 

 Wertheim, it may be remarked, imagined that he had found evidence 

 of an increase of the Yoiing's modulus from C. to 100 C. and a 

 diminution from 100 C. to 200 C. This result is negatived, as 

 Messrs. Kohlrausch and Loomis notice, by the fact that if "two 

 tuning forks are in vibration, and one of them is heated, the number 

 of vibrations changes in the manner demanded by the assumption of a 

 decrease of elasticity for increasing temperatures." 



It was found by Messrs. Macleod and Clarke,* in an experiment on 

 the change of frequency of a tuning fork produced by alteration of 

 temperature, that the period was increased by the fraction 11 x 10~ 5 

 for one degree of rise of temperature. The amount of this change due 

 to expansion was very small in comparison with that due to diminu- 

 tion of the Young's modulus. For the linear expansion of steel is 

 about 1*2 x 10~ 5 per degree, and as the period of a fork is altered in 

 the direct ratio of the square roots of its corresponding linear dimen- 

 sions before and after the expansion, if there is no change of modulus, 

 the period was augmented by the expansion, by the fraction - 6 x 10~ 5 

 for each degree rise of temperature. Hence the increase of period due 

 to diminution of the Young's modulus was about 10'4 x 10~ 5 for each 

 degree rise of temperature. And as the period is inversely as the 

 square root of the Young's modulus, the fractional diminution of the 

 Young's modulus must have been twice this amount or 20'8 x 10~ 5 for 

 each degree rise of temperature. It will be seen below that the 

 change of Young's modulus for mild steel is, according to our experi- 

 ments, a diminution of about the same amount, though no doubt the 

 change may be very different for different specimens of material. 



In the 'Philosophical Magazine' for June, 1899, Mr. G. A. Shake- 

 spear has described an application of an interference method to the 

 investigation of Young's modulus for wires, and has given values of 

 the temperature-changes found by measurements made in this way. 

 Thus it was found that the final value of the Young's modulus was for 

 copper, iron, steel, and hard brass lower at the higher temperature 

 than that at the lower temperature by the respective percentages 3 '6, 

 1*6, 3'2, and 3. Also it was noticed that repeated heating and cooling 

 of the specimen seemed to produce an augmentation of the tempera- 

 ture-change of the modulus, the material apparently settling down to a 

 steady state. 



The method adopted by Mr. Shakespear was to elongate the speci- 

 men of wire (which was in each case about 28 cm. long and 0'75 mm. 

 in diameter) by applying a weight of about 2 kilos. The elongation 

 changed the difference of path of two rays from the same source, and 

 * 'Phil. Trans.,' vol. 171, Part I, 1880. 



