ON Till. MODULUS OF TORSIONAL RIGIDITY OF METAL WIRES. 17 



(fig. 1), and also another on the lower rod B, beneath the gunmetal plate and just 

 above the mirror. This latter mark could be seen through the glass window in the 

 door of the heating jacket. The distance between these two marks was read every 

 few days by means of a cathetometer. The lengths from the marks to the jaws on 

 each of the rods E and B had previously been measured, and by subtracting these 

 distances, corrected for any difference of temperature, from the total length, the length 

 of the wire at the temperature of the observation was obtained. 



The radii of the wires were found by weighing a known length of the wire first in 

 air and then in water. The ends of the wire were filed square with the length, which 

 was then accurately measured. The wire was then wound up in the form of a spiral 

 and its volume found by weighing in air and afterwards in distilled water at a known 

 temperature. 



The lengths of the clamping rods, of the wires in the determination of their radii, 

 and the dimensions of the ring used in finding the moment of inertia of the vibrator, 

 were all measured on Professor POYNTINO'S measuring bench in the Physical Labora- 

 tory of the Birmingham University. This consists of a trolley running on a railway 

 underneath two vertical microscopes, which can be placed at any desired distance apart. 

 The microscopes have each a rock ing-plate micrometer,* by means of which a 

 length of -001 millim. can be measured. The article whose length is required is 

 placed under one microscope and a standard metre under the other. The trolley is 

 moved until the desired point on the article is under the first microscope, and the 

 reading of the standard metre under the second is noted. The trolley is then pushed 

 until the other point comes under the first microscope, and the scale is again read 

 through the second. In this way the distance between the two points is accurately 

 determined. The length of the standard metre was corrected to 0, at which 

 temperature it is certified correct. 



In obtaining the dimensions of the moment of inertia ring, two diameters at 

 right angles were measured, and then the ring was turned over and the same two 

 iliameters measured from the other side. 



The weight of the ring was 293 '3900 grammes. 



The mean radii were G'35078 centims. and 5'38859 centims. at 13'90 C. Hence 

 the moment of inertia at 13-90 C. = 10176'13 grm. cm. 2 



Corrections tu the Observed Periods of Vibration. 



In order tb.-it tin- observed periods at different temperatures may be comparable, it 

 is necessary that they should be corrected for the increased length and radius of the 

 \\ ire, and also for the expansion of the vibrator, at the higher temperatures. Two 

 other corrections might have been necessary, one for the logarithmic decrement of the 



* For description, see POYNTING, 'Phil. Trans.,' A, vol. 182, p. 589, 1891, or " The Mean Deiwity of the 

 Karth," p. 95. 



VOL. CVIV. A. D 



