EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 13 



was no explosion (marked e in the graph) due to blasting under the hill, as 

 after the occurrence of such a disturbance. In fact, the values of a range 

 within 26 seconds and are often as large as that per day, whereas in paragraph 

 5, for the case of the apparatus without a float, the whole limit of variation 

 was not above 1.5 seconds. 



In fact, the two slit images frequently separated to a distance exceeding 

 x = 36 cm., or nearly as many seconds (compared with the isolated maximum 

 of 8 cm. above), while the distance between mirror and scale was but .0 = 900 

 cm. (compared with 2,000 cm. above). The apparent change of inclination 

 of the line determined by the pendulum pivots is thus, in the present case of 

 the float, registered about 17 or 18 times larger than the above similar case 

 without a float, whereas there should be no difference. At least, it is difficult 

 to conceive how the float, which practically compensates the weight of the 

 pendulum, can introduce any seriously variable torque around the vertical axis. 



In fig. ioa, let ABG be the horizontal projection of the lower pivot, the 

 center of buoyancy, and the 

 center of gravity of the pendu- 

 lum. Then, with the correspond- 

 ing notation, the forces involved 

 will be A -\-B = G, the couples 

 involved, Ah and Bh, very nearly, 

 if h is the distance AG. The 

 effective couple is thus Ch, the 

 vector sum of Ah and Bh. If 

 the angle between A G and BG is 

 , the couple Ch may be resolved 

 into a normal couple A" and a 

 parallel couple H equal to Bht 

 nearly, whose axis is essentially 

 horizontal. In fig. 1 06, where AZ FIG. 10. 



is the vertical and AF the line of 



pivots at an angle <f> to AZ, the horizontal couple H may be again resolved 

 into a couple whose axis is normal to AF, which is ineffective, and another P 

 whose axis is parallel to AF, where P = Bhtip, nearly. Now, although P is of 

 the second order of small quantities, it does not follow that it is inappreciable, 

 for if B is replaced by Vpg, where p is the density of water at the given 

 temperature, the buoyancy couple is Vpghep. If the observed deflection is 0, 

 the couple due to any simultaneous change of inclination will therefore be 



and the tilt 



a = <p(d-Vpe/Af) 



Hence only if p remains constant, will 



with a corresponding value free from e for T' T. 



