110 Prof. Kichard Threlfall on the 



points of soldering. The thread is prepared by simply 

 drawing down a needle by hand, leaving the thicker portions 

 attached. The thin part was generally about 12 inches long. 

 The ends are then easily joined to the similar ends, project- 

 ing from the brass work. The whole having been clamped 

 so as to let the vibrator swing freely, it is brought into order 

 by heating the thick portions till they become soft and stretch 

 slightly. Two sets of observations were made with threads 

 prepared and supported in this way. Of these, one was much 

 better than the other — that with the heavy vibrator — and 

 that alone will be used, for the reason that the small vibrator 

 was of unknown brass ; while the coefficient of expansion of 

 the other was determined from a sample cut from the same 

 rod. The time of vibration (taken from sets of two hundred 

 vibrations each) was first determined under a pressure of a 

 few centim. of mercury, and at a low temperature. Steam 

 was then turned through the steam-jacket, and after a known 

 period the time of vibration was again taken. The tempera- 

 ture inside the vibration-tube and in the hollow in the block 

 was determined in a subsequent experiment, where the 

 conditions as to steam-supply were made as nearly identical 

 as possible with those obtaining during the vibrations. The 

 observations made were very numerous and very concordant. 

 Two hundred vibrations took about 11 minutes 39 seconds, and 

 the sets differed only by two or three tenths of a second. 

 Time was taken from a rated stop-watch. Nineteen sets were 

 taken at a mean temperature of 22° C, and fourteen sets at a 

 mean temperature of 98*5° C. for the fibre, and 67° C. for 

 the brass. In order to obtain a result from these measure- 

 ments we require to know the coefficient of expansion of the 

 brass, and for some purposes of the quartz also. The coeffi- 

 cient of linear expansion of the brass was found, by the method 

 of Matthiessen (Phil. Trans. 1866), in a manner that will be 

 described, to be -000020264 between 79° and 35° C. This 

 was considered to be the coefficient of expansion over the 

 range 23°-68° used in the observation. For most practical 

 purposes we are only concerned to know the change in the 

 torsion produced by heating a twisted quartz fibre, and for 

 this it is sufficient to know the expansion of brass. To get 

 the coefficient of the modulus of rigidity we require to know 

 besides the expansibility of fused quartz and the length of 

 the thread used. The former we have attempted to get by 

 Matthiessen's method applied to masses of fused quartz, but 

 with only partial success. Even assuming that an extension 

 to threads of the coefficient so found were admissible, the 



