254 Mr Peake, A Novel Instrument for Illustrating 



bar, which was lashed securely to the pointer, the change in the 



moment of inertia and in the gravitational restoring couple of the 



swinging system being easily calculated from measurements of the 



dimensions, position, and weight of the added rod. 



In the first of these methods a 20 gramme weight when 



suspended at a horizontal distance from the axis of 3'86 cms. 



produced a deflection of 123 divisions on the B scale, hence the 



„. , ,. 20x3-86 



controlling force per div. = — — r^r — gramme cms., or 



20 x 3'86 x 981 „ , 0rt 1 

 =^= = 6,160 dyne cms. 



In the second method the time for a complete oscillation under 

 normal adjustment was - 782 seconds. Let us call this T . 



Let I Q and G represent respectively the moment of inertia of 

 the system about the axis of suspension and the controlling couple 

 in dyne cms./radians for very small angles of displacement, under 

 this same adjustment, before the addition of the brass rod. 



Let also T ly I x , and O x stand respectively for the new periodic 

 time, etc., after the addition of the brass rod. 



T x was found to be 1*18 sees. 



Then (1) T^ZitsJ^, 



(2) *\-*V£- 



These equations may be written thus : 

 (1) J.-G.(@*. 







(2) h- 



^®" 







Subtracting 













Il- 



ls- 



= (6?! — G ) 



®' + ^ 



(2tt) 2 





n . 



_(27r)*{ii 



-/o}+(^o- 



-Gi) 



T , 



01 ' ^o— yT2_7 1 2 



Now I x — I Q = change in moment of inertia ) due to addition of 

 and 6r — G x = change in gravitational control j brass rod. 



The particulars of brass rod were as follows : 

 Length 107 5 cms. 



Width 1*25 cms. (Negligible in calculating /.) 

 Centre of gravity 8*62 cms. above axis. 

 Weight 36*74 grammes. 



