64 



A quantitative check of this theory by means of the 

 curvature of the a vs. t curve of Fig. 2 at its maximum seems 

 out of the question, since the distances involved are not very 

 accurately known, and since flow of water around the sides of 



the steel plate and even bending of the plate may have been 



a 

 quite appreciable. The factor (1 - ■■ '??^ ) , urtiich would describe 



the narrowing of the curve near the maximum due to the surface 

 effect in the absence of a steel plate, has the value 0.S6. 

 This figure is only slightly less than the ratio of the curva- 

 tures of the observed and theoretical curves in Fig. 2; apparent- 

 ly therefore the steel plate had a surprisingly slight effect, 

 or else the measurements of radius were falsified by bending of 

 the mirror with which the photographs were taken, or by distortion 

 of the surface. A similar situation exists with regard to the 

 period. The experimental errors just mentioned could not falsify 

 the observed period, but they could affect the calculated period, 

 which is proportional to a-nj.' "^^^ period calculated from (7) 

 is T (oo) - .0297 sec, assuming normal atmospheric pressure and 

 fresh water (p ■ 1.00), If only the fi*ee surface were present, 

 (llf) would modify this to T^(h) - .026g. The observed period is 

 T - -028 , and the difference between this and T (h) could be amply 

 accounted for by the effect of gas pressure alone, without radiation 

 damping or any effect of the steel plate. 



The complete theory of the motion in the presence of a 

 free or rigid surface, as worked out in Appendix 5, predicts that 



