Interferometer to the Horizontal Pendulum. 505 



and down motion is needed for the insertion of these appurten- 

 ances. The rods cd and hi are not in the same horizontal or 

 the same vertical plane, so that the systems may be superposed 

 as stated. 



In the course of the work it appeared, however, that the 

 framework of simple pipe was annoyingly subject to tremors. 

 It was found necessary to lengthen the rods gd and ge, g'i and 

 g'h to over a meter in length. Hence it was preferable to bolt 

 the pairs of parallel rails together for increased stiffness and to 

 secure the ends of each pair with a wide tetrahedral brace of 

 gas pipe, abutting at the pier, against horizontal and vertical 

 displacement. So adjusted, the system was light and rigid and 

 easily modified for the different 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, ge and g'h, gi and gd. All 

 appurtenances like lenses, mirrors, 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 system and is thus 

 very convenient for experimental purposes of the present kind. 

 Finally the telescopes T and T are preferably supported on an 

 independent tripod resting on the floor, the arm M being 

 removed. It will be remembered that the sodium line of the 

 spectrum and not the vertical crosshairs of the telescope is used 

 for reference. 



It is finally necessary to describe the pivots of the horizon- 

 tal pendulum, and these are also given in fig. 2. Here p is a 

 length of 1/4 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 fit- 

 ting screw m of 1/4 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. Thusw may be rotated 

 about qp and moved fore and aft or right and left, for adjust- 

 ment. The socket is a conical hollow of about 60° in glass 

 hard steel. 



3. 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 cf> be the inclination of the axis of the pendulum to the 

 vertical and 6 an angular excursion of the pendulum, meas- 

 ured from its position of equilibrium. Let h (fig. 1) be the 



