[DAWES] A REVERSIBLE PENDULUM 129 



The product of P^ into these factors is equal to {P''^ — A) to small 

 quantities of a second order where 



\8 



X" , -i . mL \, 



7 2MhJ' 



^=( r-+^+4r + -^, )To' 



The T-, x^, curve is therefore parallel to the P-, x~, curve and 

 below it at a distance A . 



For oscillations about the second knife edge the T'", .r-, curve is 

 similarly parallel to the P'-, x-, curve and below it at the distance 



\8 x^ / 2M{L~-h)/ 



Solving the equations of the T-, T'~ curves for the value of Po" and 

 taking account of the fact that h/'L for this particular design of 

 pendulum is small or nearly unity according to the knife-edge from 

 which h is measured, the value of Po" is shown to be less than Pq- 



by ( — -\ h — ) Pq- the correction for the buoyancy of the air 



\ 8 TT" I '^ 



disappearing. 



6. Set of Values. 



The following is a set of values (C. G. S. Units) 

 x-i 33.664 x{' 1133.3 x. 2.262 x{~ 5.117 



Pi 2.016 Pi^ 4.064 Po 1.994 T{~ 3.976 



P'l 2.060 P'l^ 4.244 P'o 1.978 PV 3.912 



These values give the curves of Figure 2. The (Period)- coordinate 

 of the point of intersection is Pq- = 3.999. 



In making these observations the am.plitude of swing at no time 

 exceeded 1/100 and scarcely fell to half value in one thousand oscil- 

 lations so that the values of the first two term.s of the reduction 

 factor, a-/8 and X^/tt-, were extremely sm.all. 



Taking the value of the added mass on account of the motion of 

 the air surrounding the pendulum as one half the mass of air equal to 

 the pendulum in volum.e ^7/=. 00015. 



The value of ft? is therefore 3.999 X (1- .00015) and the value of 

 "g" calculated therefrom is 980.41 as compared with the accepted 

 value at Toronto, viz. 980.46. 



