184: C. Barus — Viscosity of Solids. 



whose position is x and whose distance apart is dx (x> I), dur- 

 ing the time t be 



dip = - qjdx. 



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 oppo- 

 site viscous motions which take place on any section, only 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 l\ be 

 kept at a given constant temperature and be of the same tem- 

 per throughout. Let those parts also, of the wire above the 

 index be of the same or any uniform temper ; but let them be 

 heated to different constant temperatures. Thus let the vis- 

 cous detorsion between x—0 and x—V be typified by <p' '; be- 

 tween x=r and w=p, by <p 3 ; between x=j3 and x=a by <p\ 

 between x=a and x—L by <p 1 ; in which the differences of <p^ 

 <p, <p z are evoked by differences of temperatures of the parts of 

 the wire to which these data refer, whereas <p' may differ from 

 all these by any increment of temper, as well as of tempera- 

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

 parts in question, on the index whose position is %=l', will be 



PL dx ,. /*« dx v PP dx _ , Pi dx 

 J a x ^Jp x *Jy « t/o L—x 



where L—V—l. Hence the motion, <fi, of the index is 



^ = l '(^ ln a +(pln ]j + ^ ln j)~ l(p ' ln T 

 Now if the experiment is so conducted that <p 1 ^=cp 3 =(p / , and 

 l—V— -Z, which implies uniformity of temper throughout the 

 wire from to Z, then 



$=l(<p- <p') In 



which suggests the most convenient method of experiment. 

 If it is possible to heat the upper wire uniformly throughout 

 its length, this equation takes the form (p=l (y> — <p r ) ln#. If <p' 

 is negligible relatively to <p, this method leads to absolute results. 

 There is another case which facilitates experiment. Let 

 <p=<p„ <p = 0, 1=1'. Then 



i/; = lq) i In 2 + l(q)—(p^ In — . 



If the behavior of the wires for <p =<p i (i. e. for the case in 

 which the upper wire has the uniform temperature correspond- 



