ACOUSTICS AND GRAVITATION. 103 



minutes. With the air -damping the period is increased to something like 20 

 minutes or 30 minutes, so that it practically creeps. 



Instead of using the torsion coefficient t of the filament, it is more convenient 

 to introduce the linear modulus a, so that the force is/=a#. If the semi- 

 length of the needle is r, it is obvious that 



(2) t = ar* 



We may now employ the equation for the attracting force /, in terms of the 

 masses M and m and their distance apart ^ = 4.24 cm., Ax being the observed 

 double amplitude of static displacement. Thus 



, Mm A* 

 /==7 __ = a _ 



whence 



a R* 



no attention being, for the present purposes, given to the attraction of the mass 

 M for the straw shaft zr, weighing 0.28 gram, but remote. If we introduce 

 equation (i), equation (3) becomes finally 



, , 



(4) y 



If we insert the data specified, 



2ir 2 X 0.0495 (- 



7 = /^.^ a ./ 0.0786 = 5.7 X io~ 8 

 (6) 2 Xn 2 949X0.59 



This value is below the standard value and needs further correction. To apply 

 such corrections now would be idle ; for it is first obviously necessary to learn 

 to control the enormously variable excursions of the needle Ay. The subject 

 will be resumed presently. Since 



t 



the above data give a = io~ 6 X4.49 and the torsion coefficient * = ar 2 =io~* 



X5-43- 

 The large early double amplitudes Ay as compared with later values, in- 



duced me to make a series of observations throughout a number of successive 

 weeks, in half-hour periods. Before doing this, however, it was thought safer 

 to actually cement the hooks of the quartz fiber to the torsion-head above and 

 to the needle below. This was done at a slight sacrifice of the end of the 

 fiber by accident, so that the coefficient a is a little larger than above. These 

 observations are shown in figures 119, 120, beginning on July 17. They do 

 not differ as a whole from the older data, with a needle hooked into sharp 

 triangles, with which they were compared. 



85. Long-period observations in the lapse of time. These are given in scale 

 readings y in figures 119, 120, etc. The actual displacement of the shot m is 

 x = o.oi455y. The attracting mass M is placed on one side or the other of m, 



