[46] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



of the formula (105); the rest of the table was calculated by means of the series (113). 

 In the former part of the calculation, six places of decimals were employed in calculating the 

 functions M , &c. given by (103). The last figure was then struck out, and five-figure loga- 

 rithms were employed in multiplying the four functions M , M' Q , M e , and 1 - M e by 



- , and by L, as well as in reducing the right-hand member of (105) to the form k + \/ - 1 A/. 



4 



The terms of the series (113) were calculated to five places of decimals. That these series are 

 sufficiently convergent to be employed when lit = 1-5, might be presumed from the numerical 

 values of the terms, and is confirmed by finding that they give k = 1*952, and k'= V\S3. For 

 til = 1-5 and a few of the succeeding values, the second and third of the series (113) were 

 summed directly as far as W -5 inclusively, and the remainders were calculated from the formulae 

 (114). Two columns are annexed, which give the values of ttl'k and ttt 2 &', and exhibit the law 

 o/ the variation of the two parts of the force F, when the radius of the cylinder varies, the 

 nature of the fluid and time of oscillation remaining unchanged. Four significant figures are 

 retained in all the results. 



The numerical calculation by means of the formulas (103), (104), (105) becomes very 

 laborious when many values of the functions are required. The difficulty of the calculation 

 increases with the value of ttt for two reasons, first, the calculation of the functions M a , &c. 

 becomes longer, and secondly, the moduli of the numerator and denominator of the fraction in 

 the right-hand member of (105) go on decreasing, so that greater and greater accuracy is 



