Viscosity of Solids and its Physical Verification. 189 



of steel* are a sufficient guarantee for the remarks of this 

 paper j but as the above paragraphs clearly show that data 

 tending to throw light on the ultimate nature of viscosity are 

 urgently called for, I shall add some further experimental 

 results. To obtain these I made use of a perfected form of the 

 differential apparatus described elsewhere f. 



For several purposes touched upon in the course of the 

 present work it is necessary to indicate the theory of the said 

 differential apparatus more fully than was done in the earlier 

 paper. This I will briefly do here. 



Given a continuous straight steel wire, of length L, to which 

 a convenient rate of twist, t, has been imparted. Consider 

 two right sections whose distance apart is the unit of length, 

 and let 2c/> be the amount of viscous angular motion of the 

 first relative to the second during the given small time t and 

 for the fixed rate of twist r. To fix the ideas, let the wire be 

 adjusted vertically, and provided with an index to register 

 angular motion at a distance I' above the lower end. Then 

 will the motion at the index due to the viscous detorsion of 

 two sections whose position is x, and whose distance apart 

 is dx {x>V) i during the time t be 



/' 



dyjr=—d>dx. 



x 



For at every section the viscous motion is such that if the 

 contiguous parts immediately below the section slide in a given 

 direction, the parts immediately above it slide in equal amount 

 in the opposite direction. Again, of the two equal and opposite 

 viscous motions which take place at any section, only the 

 motion of the part nearest the index will influence it. 



This premised, suppose, furthermore, that the parts of the 

 wire below the index, the parts whose position is to V ', be 

 kept at a given constant temperature and be of the same temper 

 throughout. Let those parts also of the wire above the index 

 be of the same or any other uniform temper, but let them be 

 heated to different constant temperatures. Thus let the viscous 

 detorsion between x = and x=V be typified by fa; between 

 x = l' and x = /3 by fa\ between x = @ and x = <x by </>; between 

 x= a and x—h by fa : in which the difference of fa, (/>, fa are 

 evoked by differences of temperature of the parts of the wire 

 to which these data refer, whereas fa may differ from all these 

 by an increment of temper of any value, as well as of tempe- 

 rature. Then the influence of the viscous detorsion in each of 



* Amer. Journ. [3] xxxii. p. 444, 1886; ibid, xxxiii. p. 20, 1887. 

 t Amer. Journ. [3] xxxiv. p. 2, 1887. 



