34 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



purposes of the experiment. The additional braces have not been shown in 

 the figure, as they depend on purely local conditions, the base of each tetra- 

 hedron being at the pier and its apex at the corresponding common ends of 

 the pairs of rails, gc, g'h, g'i, and gd. All appurtenances like lenses, mirrors 

 and micrometers are attached with strong removable clamps, provided where 

 needed with rack-and-pinion attachment for focussing, etc. This allows of 

 an easy and indefinite modification of the sytem and is thus very convenient 

 for experimental purposes of the present kind. In the later work the telescope 

 rod kl, fig. 21, was discarded in favor of a tripod standing on the floor. 



It is finally necessary to describe the pivots of the horizontal pendulum, 

 and these are also given in fig. 20. Here p is a length of /^-inch gas-pipe fixed 

 in the wall with plaster. The outer end is split lengthwise and carries a collar 

 and set-screw I, so that the brass rod q fitting the pipe p snugly may be firmly 

 secured. The end of q carries the horizontal, very snugly fitting screw m of 

 /^-inch brass, which is tipped at n with the steel point of a darning needle. 

 The point of n is received by the socket of the horizontal pendulum. Thus 

 n may be rotated about qp and moved fore and aft or right and left for ad- 

 justment. The socket is a conical hollow of about 60 and of glass-hard steel. 



20. Equations. With regard to the apparatus just described, the size of 

 which was limited to conveniently fit the given pier, the following equations 

 may be used to obtain an estimate of the sensitiveness to be expected. 



Let <p be the inclination of the axis of the pendulum to the vertical and 6 an 

 angular excursion of the pendulum, measured from its position of equilibrium. 

 Let h be the normal distance of the center of gravity from the axis. The rise 

 of the latter above its lowest position is 



n 



( J ) y = h(i cos 6) sin <p = 2 



2 



and the energy potentialized, if the total mass is M, will be 



f\ 



( 2 ) W = 2Mgh sin <p sin 2 - 







which for small displacements corresponds to the torque Fh at the angle 9. 

 This torque is 



BW 



(3) -rr- = Mgh sin <f> sin 9 = Mgh <pd nearly 



ov 



or the total force F acting at center of gravity, or F/M per gram of mass M is 



In the above apparatus M= 1,245 grams, h = 8o cm. Hence per vanishing 

 interference ring, since the grating moves, if AA/" is the displacement of the 

 micrometer to bring back the center of ellipses to the fiducial sodium line 



(] AN/ 2 _A7V 



" D 5" 

 K. "2t\. 



where R is the distance of the point of the grating at the line of light corre- 

 sponding to the slit, from the axis of rotation. In the apparatus R= in on. 



