TRANSACTIONS OF SECTION A. 287 



d. Experiment b repeated. 



e. Experiment a repeated. 



/. The coefficient due to damping was determined. An oscillation being set up, a 

 number of swings of the needle were observed, and the log. decrement of the 

 deflections calculated. 



Let 0, and 6n + 1 be two excursions of the needle measured on the same side 

 of the zero and separated by n complete oscillations. 



Let - log - — i-_ = log- a. 

 n ° 8n + l ° 



Then if 6 is the observed excursion of the needle due to an instantaneous 

 impulse applied when the needle was at rest near the zero point, and fi.8 the ex- 

 cursion that would have occurred had there been no resistance to the motion of the 

 needle, 



I tan" *L 



2tt log a 



/3 =a 

 If we write a = 1 + z where z is small, 



P 4 1.32 4W 



\128 16 W 

 __„ 4 / 77 _55 1 5 R 



V2408 384 jt 2 96 ttV 

 + &c, 

 or 



/S = 1 + 0-25000s 



- 0-11908s 2 

 + 0-07369s 3 



- 0-05158s 4 



— a convenient expression sufficiently accurate for most practical cases. 



The time of oscillation was determined as follows : — The needle was brought 

 to rest, started by discharging a condenser through the galvanometer exactly at the 

 beat of a chronometer ; by listening to the beats the periods of the first five swings 

 of the needle were observed and registered, a certain number (usually ten) of oscil- 

 lations were then counted, and the periods of five successive swings again measured, 

 and so on. 



The mean of the first five observations, the second five, and so on were 

 treated as the time of the 2nd, 16th, 30th, &c, oscillation. No sensible change 

 in period due to extent of oscillation was observed. 



In this manner results agreeing within 0-1 per cent, were readily obtained. 



The galvanometer was inclosed in an iron chest of J in. wrought iron with a 

 small opening to admit the light to the needle. The zero of the instrument re- 

 mained very constant even when the period of oscillation was large — 25 seconds 

 for example. 



The needles were made of little pieces of watch spring hardened and well mag- 

 netised ; the lower series being attached to a brass disc fixed to an aluminium 

 wire perpendicular to the plane of the disc, and vertically over its centre. 



The results obtained are now given : — 



Glass condenser as first set up. 



1st series of experiments Cap. = 0-00697 mfds. 

 2nd „ „ „ =0-00694 „ 



3rd „ „ „ = 0-00696 „ 



Mean 0-00696 „ • 



