ON THE MODULUS OF TORSIONAL RIGIDITY OF METAL WIRES. 53 



a horizontal metal tube some 20 centum*, long, can be fomssed on to tin- wire. leing 

 r<Mlerteil downwards by a right-angled prism. The path of the raA0flted lieam is 

 almost vertical and is in a plane perpendicular to the wire. In this manner perfect 

 illumination is secured, and when looking at the .standard metre no shadows are seen 

 along the graduation lines. 



In determining the coefficient of expansion of the gunmetal liar it was supported in 

 a similar manner to the standard metre. The fiducial marks were near the ends of 

 the bar and were made by brightly polishing the surface and then drawing a fine 

 needle at-ross. The marks were protected from the water by two short glass tul)es 

 \\liicli had been ground level at the bottom and were held firmly against the bar by 

 stout elastic bands, a ring of thin sheet indiarubber being placed between. 



In experimenting, the trough containing the wire under test was left under the 

 microscopes only while readings were being taken. It was moved off along the line 

 to be heated up. At each temperature about half-an-hour was allowed after the 

 required temperature had been obtained before the readings were taken. During 

 this period the heating and stirring were continual. The trough was then wheeled 

 under the microscopes and adjusted in position, so that the marks were approximately 

 under the cross wires. The heating and stirring were then stopped- -for the shaking 

 rendered the image indistinct and by means of the rocking plates the marks were 

 adjusted on to the cross wires. The temperature was then noticed and the trough 

 wheeled away. The readings of the micrometer scales were then taken. This was 

 repeated three or four times at each temperature, and in general there was no 

 difficulty in obtaining a very close agreement. 



The expansions were taken at various temperatures up to 90 C., and after each 

 observation the distance between the microscopes was checked by wheeling the 

 standard metre beneath them. This precaution was necessary in order to see that 

 the heat did not warp the stands and thus alter the positions of the microscopes, but 

 only in a few cases was it necessary to apply a correction on this account. 



The coefficients of expansion of all the wires used in the rigidity experiments we re- 

 determined, with the exception of the very soft metals lead, cadmium, and tin, which 

 were found to draw out slightly under the necessary tension, especially at the higher 

 temperatures. The coefficients of expansion of these metals would have to be found 

 from bars of the material, but in the present research it was not necessary to know 

 them with great accuracy on account of the fact that the rigidity determinations in 

 these cases were not so accurate as with the harder wirea The values given in 

 LUPTON'S tables (1901) were therefore used. 



Before determining the coefficients of expansion, the wires which had been bent 

 into spirals for weighing in air and water in the determination of their radii were 

 straightened and annealed in the same manner as before the determination of their 

 rigidities. 



The lengths of the wires at the different temperatures were plotted against the 



