ACOUSTICS AND GRAVITATION. 107 



mediate quantitative agreement, the indentations of the Ay and A0 curves 

 show a close agreement in sequence and less occui rence of lag. This brings the 

 ultimate interpretation nearer at hand. The evidence is in fact very striking, 

 and to indicate it more forcibly I have numbered the successive temperature 

 cusps on A0 i to 29, in crder to coordinate them v/ith the corresponding 

 similarly numbered cusps on the Ay curves. 



86. Short-period observations. It is to this subject that the present paper 

 is to be mainly devoted, with the object of discerning whether the balls on the 

 needle may not be treated as in uniform or ultimately in uniformly varied 

 motion. It will, therefore be convenient to compute the Newtonian constant 

 on simple principles throughout, but merely as a criterion of the degree to 

 which the condition specified has been realized. 



With these reservations we may, therefore, in first place ignore the friction 

 coefficient of the medium (air) and the elastic coefficient ot the fiber; more- 

 over, at the outset, disregard the attraction of the mas? M for the straw rhaft, 

 a correction which can afterwards be applied. Under these circumstances 

 the double amplitude A* of either ball may be written Ax = g't 2 /2, where g' 

 is the effective acceleration and t the period of the alternating attraction, the 

 latter regarded constant and consecul ively positive and negative. Under the 

 limitations stated, the attracting force is f=yMm/R 2 and the mass actuated 



2m. Hence g = ~^>' whence 



2/Y 



But in 83, x = 0.01455 y, where y is the displacement reading on the centimeter 

 scale in the telescope. If for short alternations of the period t, Ay is the 

 double amplitude observed in the telescope, 



_~ o.o 1 45 5 Ay 

 = ~~~ 



Hence, if we put R = 4.2^ cm., M = Q4p grams, then 



7 = icr 4 Xii.o Ay// 2 



or, if we express t in minutes, as observed, 



7 = io- 8 30.6(Ay/* 2 ) 



Thus it is merely necessary to divide the double telescopic amplitude by the 

 square of the time in minutes, apart from the constant. This would be very 

 easy if the motion of the needle were not at times cobwebby, so much so that 

 I have frequently passed a wire around it, inside the case, several times to 

 insure myself of its freedom. 



In figures 122 and 123 I have given the data (scale readings successive 

 minutes apart) obtained on July 5 for one-minute and two-minute periods 

 in the switch-over of M. The turning-times of M are indicated by little 

 circles. Since the needle is invariably drifting, it is necessary to compute the 



