TORSIONAL OSCILLATIONS OF WIRES. 429 



azine, July 1894), were obtained by superposing the experimental curves upon sets of 

 curves of the required form, and choosing the one which gave best correspondence. 

 A re-calculation of the values, by the method now employed, was made, in order to 

 get a strict comparison of the earlier results with those more recently obtained. 

 Table IV. contains the values so found. The columns headed n', a', b' contain the 

 values of the quantities n, a, and b given in the First Paper. The column headed b" 

 contains the values of b, calculated by the present method, with the old unit for y 

 (0"364 times the new unit used in the Second Paper and the present paper). The 

 columns headed n, a, and b give the values found by the present method in the new 

 unit. The values of n and a are independent of the y-vmit. Table VI. is, in part, a 

 reproduction of Table II. of the First Paper. Values of y are given in the top row, 

 and corresponding values of x + a' are given in sets of three rows, each set correspond- 

 ing to one experiment. The middle row of each set gives the experimentally observed 

 values of x + a' ; the upper row of each gives the values of x + a f calculated by means 

 of the values of n', a', and b', given in Table IV. ; and the lower row gives the values 

 of x + af calculated by means of the values of n, a', and b", given in that table. The 

 new values are, on the whole, just as suitable as the old values, and are accordingly 

 used in the subsequent discussion. 



Relations between n and b. 



It was pointed out, in the Second Paper, that, throughout the three series of experi- 

 ments therein described, the value of the product nb was, within possible experimental 

 errors, constant. The basis for this statement is exhibited graphically in figs. 5, 6, 7. 

 In these figures the values of log nb are plotted as ordinates against the values of n 

 as abscissae. The average values of log nb was in each case taken to be 2*3. By 

 means of the re-calculated values of n and b for the series described in the First Paper, 

 a similar diagram (fig. 8) was obtained for that series. With the single exception 

 of experiment P, all the points group very well about a straight line having a positive 

 slope. This implies the existence of a Critical Angle (see Second Paper) throughout 

 the series of experiments described in the First Paper ; so that, by a proper choice of 

 the y-unit, the value of nb might have been made constant in that series also. For 

 the equation 



ny n (x + a) = nb 



may be written in the form 



ny' n (x + a) = nb(-\ 



by making ky' = y, i.e., by taking as the unit a quantity k times greater than the 



