﻿38 Dr. W. Peddie on 



found that, in all my observations hitherto made, such arbi- 

 trariness is notably absent ; and I have been able to obtain an 

 extremely accurate empirical formula for the representation of 

 the results. 



The results here given refer only to a single iron wire whose 

 extremities were soldered into holes drilled axially in stout 

 brass rods. The length of the wire was 89' 1 centim., and its 

 diameter was 0*1011 centim. The one rod was firmly clamped 

 in a vertical position, with the wire suspended from it ; and 

 to the other rod was attached, sym metrically and horizontally, 

 a heavy lead ring of considerable moment of inertia. In per- 

 forming the observations, one experimenter increased the 

 torsional oscillations of the system up to a predetermined 

 maximum, taking care to avoid as far as possible any swing 

 of the system like that of an ordinary pendulum. Whenever 

 the required maximum oscillation was attained, the system 

 was left to itself, except in so far as any marked swing of 

 the latter kind was damped out in such a way as not to in- 

 terfere, by friction or otherwise, with the torsional oscillations. 

 Another observer commenced at once to take readings of the 

 maximum elongation by means of a telescope placed a few 

 yards off. The scale was fastened round the outer circum- 

 ference of the lead ring, and a fixed pointer was placed close 

 in front of it. At first readings were taken at the end of each 

 complete oscillation ; subsequently, as the time-rate of decay 

 of the oscillations became less, readings were taken at the end 

 of two, three, five, or more, complete oscillations. A curve 

 was then plotted with the scale-readings as ordinates and the 

 number of swings as abscissae. The oscillations were found 

 to be almost isochronous, so that the axis of abscissas was 

 practically a time-axis. In almost all cases the curve showed 

 traces of ordinary pendulum oscillations, but a smooth curve 

 could easily be drawn on the average through the observed 

 points so as to avoid all such irregularities. It would serve 

 no useful purpose to give here the full details of each experi- 

 ment. Their general nature will be seen from the curves 

 shown in fig. 1, and the special data given in Table II. will 

 be found sufficient for each. In fig. 1 the curves give the 

 data obtained from observation, and the points show positions 

 calculated from the respective equations in Table I. 

 It was found that equations of the form 



t/"(a:+a)=b, (1) 



where a, b, and n are constants, applied with great accuracy 

 in each case Table I. gives details on this point. 



