in the Use of Bifilar Suspensions. 439 



By proper choice of: constants we could get a more or less 

 empirical formula of this type which would cover a very 

 large range, but it is obviously impossible to apply such a 

 formula to the early part of the creep, as it would involve 

 the assumption that x was infinite when t was zero. 



It might be suggested that the formula 



o no 



y=a + Mog(l + cQ, (11) 



could be applied to express the whole range of the creep in 

 agreement with analogous effects in electric absorption*. Any 

 particular creep can be expressed empirically by this formula 

 over a very large range, but it was not found advantageous 

 to develop an expression along these lines for the special 

 case of our problem. For, supposing we take this equation 

 as representing . the initial creep, then by superposition of 

 effects we get for the solution to our problem 



y = b log (1 + ct') - 2blog (1 + ct' -T) + 2blog(l + ct'- XL) - 

 + (-!)" 2Mog(l + c?^T), . . (12) 



where a = Q, since we take ?/ = when £ = 0, and t r = the 

 time from the start of the initial creep. If t equals the time 

 from the nth reversal, then by putting £' = £ + rcT we get 



y = 61og(l + c* + nl , )-261og(l + c* + (rt-ljT) + 261og(l + c«+(w-2)r)- 



-f (-1)" 2b\og(l + ct). . . (13) 



Now assuming the equation 



# = D + 



ae-« 



where a= — D, for the initial creep, since we take */ = 

 when t = 0, we get by the same method as the above 



y=-Da-e- kt ')-2D(l-e-W-V) + 2D(l-e-w- 2 V) 



+(-l) w 2D(l~e-W'-» T >), . . . (14) 



and putting t' = t + nT we get 



;/ = D(l-^-^' tT )— 2D(l-<?-*'+(»- 1 > T )+ ... 



+(-l) n 2D(l-e- kt ), . . . (15) 



which reduces at once to equation (8) when nT is large 

 compared with T. It is to be noted that we have here a 

 much more concise development of equation (8). The former 

 method was presented as offering a closer insight into the 



* H. A. Wilson, Proc. R<w. Soc. A. vol. lxxxii. p. 417 (1909). 



2 G 2 



