TORSIONAL OSCILLATIONS OF WIRES. 617 



single points show the values of n and 6 in the first series of experiments, Roman 

 numerals being used to indicate the points corresponding to the first twelve experi- 

 ments of the series. Points surrounded by circles indicate the values of n and Q in the 

 second series, the values of N given in Table IV. being placed alongside. The crosses 

 give the results of the third series of experiments. 



Explanation of Diagrams. 



Fig. 2 has just been discussed. Fig. 1 shows the curves obtained from the readings 

 in the experiment 20.7.94 (2). The abscissae give the number of complete oscillations 

 which have taken place since the commencement of the experiment. The ordinates of 

 the upper curve represent the excess of the positive elongations over 20. The ordinates 

 of the lower curve represent the defect of the negative elongations from 20. The 

 ordinates of the middle curve are the means of simultaneous ordinates of the upper 

 and lower curves. This curve, therefore (p. 612), shows the elongations referred to the 

 zero about which they are symmetrical. Points on that curve which correspond to the 

 abscissas I, 2, 3, 5, 7, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, are taken. The straight 

 line in the figure is drawn on the average through points, whose ordinates are obtained 

 by taking the logarithms of each of the above-noted abscissa? increased by 9, and whose 

 abscissas are the logarithms of the corresponding ordinates of the middle curve. From 

 that line the values of n and b were deduced in the manner stated on p. 614. Only the 

 lowest point, whose abscissa is 1*42, lies to any extent off the line. The second lowest 

 point corresponds to the ordinate 20'5 in the middle curve. If the ordinate were 19 '9 

 the point would be on the straight line, so that the discrepancy is only 1*5 per cent. 



Fig. 3 illustrates the determination of limits (p. 616) between which the value of 

 the product nb must lie. The points in that figure have been plotted, in the way 

 just described, from the results obtained in the fourth experiment made on the date 

 3.8.94. In one case the value 12 was given to a, and nb had the value 195. Within 

 experimental errors, all the points lie on the straight line. In the upper system of 

 points, a and nb have the values 14 and 167 respectively, and the convexity of the 

 system towards the origin is apparent. In the lower system, a and nb have the values 

 10 and 221 respectively, and it is evident that there is a tendency towards concavity 

 to the origin. 



The points in fig. 4 constitute a similar set for the experiment of date 18.12.95. 

 When a =10, ?i&=182, the system of points is convex towards the origin. When 

 a = 9, nb = 205, the system is practically straight; and the rectilinearity is even more 

 complete in the lowest set of points, with the values a = 8, nb = 217. 



The numbers in Table VII. give the observational data from which the upper and 

 lower curves in fig. 1 were plotted. The first, third, fifth, &c, numbers give the scale 

 readings for the positive elongations, the second, fourth, sixth, &c, numbers give the 

 scale readings for the negative elongations. The number of scale divisions contained 

 in a complete revolution of four right angles was 46*1. Hence, to get the plotted 



