— 6 — 



Remark. — On onr rotarn from the ozcnrsion, wo found that Iho wod^c-xhapod 

 appendage for the break circuit amincjornont of the K pendulum lind boon sli^^htlr 

 scraped bj one of the screw nails u.sod to fix the lid of its box. This of course ia 

 awkward : but if wo suppose it to l)e a mere loss of mass nnaccompanio<l bj any further 

 change, wo may apply the following correction. 



Let I =momcnt of inertia almut tlio knife-edge of the pendulum, 

 K=radius of gyration about the knife-edge, 

 L = length of simple ctjuivalent pendulum, 

 z=distanco of the centre of mass from tho knife-edge, 

 m=mass of tho pendulum, 

 M = mi the moment of mass, 

 8m=raas3 scraped off, 

 p=distancc of tho scrapc.l portion from tho knifo-odgo. 



Then 



f = w V -^ to first approximation. 



9 



It _\ iL 



but L= -^ 



Therefore by differentiation and reduction 



^_M _ »M_ 



L ~I M 

 bat SI = p' 8»i 



and JM = p 8m 



8L . 8M 8M 



whenco U"** ~1 ''"nP 



but K'=Lx 



Hence *5i= P ^"^ ( ?_ _i\ 

 L ~~z «I \ L / 



8< _ 1 p 8m / p \ 



t ~2"i m\ L ~7 

 Had we accurately wei^fhed the pendulum Insfore packing it np, wc might 

 have determined 8m by reweighing it. Snpposehowevcr that 8m is .1 gr. which ia 

 certainly an over-estimate. Then, since 

 p=110. era. 

 x=r 87. „ determined experimentally by balancing the pondulnm 



horizontally. 

 L=98.1 cm. estimated from / and g. 

 M=2824 gr. 

 we havc^_ _!_ HO .1 /IIP _ ^ \ 

 t 'Z 87 282-i \yo7l / 



= .0000027 

 which is within the errors of experiments, as will I» seen by comparing the (imoa 

 of a Single oscillation bsforo and after tho excursion. 



