EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 27 



In the apparatus used above, <f>=io- 2 and R=io 2 cm., (3 2 =io~ s . These 

 are moderate; the former could easily be reduced. Hence, 



io- 8 Xio 2 

 A/v = - ^ = lo- 4 cm. 



Even in the case of the present apparatus, therefore, about three interference 

 rings should vanish (potentially) between the positions hvb and h'v'b'. 



A similar comparison might be made for the position of the horizontal 

 pendulum normal to the plane of the diagram, in relation to the first and final 

 conditions discussed. But the lines are now oblique and require two or more 

 projections, and this additional complication is superfluous here. 



Contractions of the pendulum itself must be negligible, as these merely dis- 

 place the center of gravity in the plane of the pendulum and are otherwise 

 not amplified. Tidal forces have approximately the same value in the two 

 positions, or may be allowed for. There remains, therefore, the contraction 

 of the earth itself, which changes from a sphere of radius r to an oblate ellip- 

 soid with its minor axis r \/i /3' 2 in the direction of motion p'. In a general 

 way we may state at the outset that as the triangle is a part of the earth, its 

 distortion could not be recognized for the lack of an independent base of com- 

 parison. But the question is advantageously approached, specifically, as fol- 

 lows. Fig. 17, which contains the sphere and the ellipsoid in question, shows 

 that the diameter p is displaced to q and that the angle a moves over a distance 



5 = rdd/sm 6 nearly 



where dO is the angle between p and q and = 45 nearly. But the displace- 

 ment 5 is the contraction of r cos or 



s = r cos 



2 



Hence, 



cin ifl 



I, nearly. 



The same angular deviation occurs between the two tangents or bases pro- 

 longed, since the equation of the ellipse referred to the circumscribed circle is 



x rsinB, y r\/i (P cos 6, 



& 



dd= t -sm 20 = 0V 4 nearly. 

 4 



Hence, the two angles, if 



as above 



seeing that in the position h'v'b' the angle a does not change. The displace- 

 ment from p to q, therefore, keeps the center of gravity in the normal plane in 



