346 Mr. C. Bams on the Change of the Order of Absolute 



there is no shearing. Then 2d<f>jdt = 2Q t is the common 

 angular velocity, per unit of length, with which the shear is 

 increased. Consider an elementary cylindrical shell whose 

 length / is the effective length of either half of the wire w w 

 (fig. 2), and whose right section is 2irr dr. Then the amount 

 of force distributed uniformly over 2irrdr will be 



j- Vmrdr , iat . . * 



df=V t — j— (Z2(V). ..... (4) 



Multiplying by r, and integrating between and p, the radiu s 

 of the steel wire, 



iP\=^2C„ (5) 



where P/2 is the weight at the end of the lever-arm X, per 

 effective half of the wire. In any given adjustment P\/7rp 4 = A 

 = constant. Hence 



V=A/SO, (6) 



In these equations it has been assumed that \j)r d dr = 7j t \r d dr. 



Hence under all circumstances r\ t is a mean value defined by 

 these integrals. 



14. Results obtained with the apparatus § 12, are given in 

 Tables IV. to VII. Here p is the radius, I the length of each 

 effective half of the steel wire. P is the total force (being 

 the weight plus the weight of the scale-pan) acting at the 

 end of the lever A (see fig. 2). The rate of twist is given 

 under t, and 2 <I> is the total yield during the interval of 

 experiment. N denotes the actual scale-reading observed by 

 the telescope (scale-distance from mirror, II = 200 centim.) 

 at the time given ; and 2 </> is the viscous angular motion 

 between two right sections of the steel wire 1 centim apart. 



In the second half of the tables, 2 C* is the time-rate of 

 change of 2(f), computed for consecutive intervals of 500 

 seconds each. The final column contains the corresponding 

 absolute viscosity. All times are reckoned from the moment 

 of twisting. To obtain 2C* I availed myself of graphic 

 methods*, these being in conformity with the mean accuracy 

 of the work. Table IV. contains results for the wire No. 1, 

 already tested in Table I. Three twists are applied, alter- 

 nately in opposite directions. In Table V. the same wire is 

 similarly examined, after it has been softened by heating to 



* Of course a set of smoother values might be obtained by computing 

 the constants of the curves <£ from Kohlrausch's exponential formula, and 

 the tangents from the values obtained, 



