ACOUSTICS AND GRAVITATION. 



81 



since for t = 0, y = 0. Equation (3) may be written 

 (4) i = ( 



where /3 and A are constants. 



Such an equation will necessarily fail in the lapse of time, since A is the limit 

 of y in (3) ; whereas experimentally y probably increases indefinitely. On the 

 other hand, however, thermal instabilities are always present, apart from 

 stress, so that equation (2) can only refer to the stress part of the phenomenon. 

 Furthermore, the exact time of the beginning of viscous deformation can not be 

 adequately specified, since there are a few minutes of irregularity in exchanging 

 the weight and placing the fringes. The initial observation (t = 0) is thus 

 inevitably a few minutes late. Hence an equation which fits the data of the 

 first 30 minutes nearly enough for practical purposes is all that could be at 

 issue. Yet even this modest expectation is not realized. Thus if we combine 

 the first and third, second and fourth observations, the data are, for example: 



Wire : Drawn. 



io*A = 100 125 



lo 1 /? = 90 54 



io 8 C = 79 



10* AN at ioo m = 125 



A rapidly increases and /3 diminishes in the lapse of time (here about an 

 hour or two) . If Aj3 = C, the equation takes the form 



indicating that at least another power of time must also occur in the denomi- 

 nator if the equation is to reproduce the data. The reduction is thus not 

 simple. 



There would not, however, be any real hardship in adapting a function by 

 which the amount of twist at any definite time after twisting could be accu- 

 rately computed. The real difficulty lies in the time-loss in the shifting of the 

 weight, and the subsequent adjustment, for fringes, etc. Twist is thus not 

 imparted suddenly or all at once. The initial time (* = 0) is too indefinite. 

 Again, since the balance-beam remains horizontal, but one-half of the wire 

 is twisted, the other remaining without stress and idle, unless two symmetrical 

 torsion-heads, one at each end of the wire, are used. For these reasons I 

 discontinued the present method temporarily in favor of the next, 71, where 

 t is very large, the yield proportionally small, and where certain advantages of 

 stability would accrue to the method. It indicates the importance to be 

 attached to the thermal coefficient of rigidity. 



70. Absolute viscosity of the wire. The curves given may be used to obtain 

 the absolute viscosity 17 of the wire, for the given rate of twist and diameter, 

 and at any time after twisting. As but half the wire is used, the full torque 

 FL (where L is the half length of the beam (n cm.), F the weight of the 



