28 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



which these lines are traces and no effect could be recognized. Similarly if the 

 horizontal pendulum were attached to a large massive vertical pendulum 

 (rigid plumb-line) the displacement da/2 would escape detection. Neverthe- 

 less the potential possibility of the method, well illustrated by this example, 

 seemed to make it worth while to endeavor to develop it, for there are other 

 non-compensated micrometric deviations of the earth's diameter, to which it 

 would be directly applicable. 



16. Improved pendulum. The suspension of the symmetrical pendulum 

 was now modified so as to embody the suggestions contained in the above 

 work. The two pivots were supported on a single post of i-inch gas-pipe, 

 sunk into a hole in the concreted subfloor of the basement and secured with 

 plaster of paris. It was hoped, in this way, to obviate the possibility of tem- 

 perature disturbances in their immediate effect on the pendulum. Naturally, 

 the post was insulated from every other part of the apparatus, so that the 

 pendulum was quite free and independent. Its tin case was adjustably sup- 

 ported on the iron scaffolding carrying the mirrors, while the tank for the float 

 rested on an independent standard rising from the subfloor in question. It is 

 improbable that short of a special brick pier for the instrument a more advan- 

 tageous method of mounting could have been devised. It was therefore in- 

 teresting to observe how the whole apparatus would behave, on transition 

 from fall to winter conditions; i.e., to find the effect produced on turning on 

 the steam heat of the laboratory. The observations are given in the next 

 paragraph. 



17. Observations with the new pendulum. These observations are given 

 in fig. 1 8 in the usual way, the inclinations a, in seconds of arc, being con- 

 structed in their variations with time. To determine the constants of the 

 apparatus the micrometer method, similar to the above ( 1 1 , end) , was em- 

 ployed. The variation of x due to a twist of 12 of micrometer screw was 

 found to be # = 27, 26, 26 cm., or on the average 2.2 cm. per degree, whereas 

 the former value was # = 3.1 cm. Hence, since the other constants are the 

 same as above (the distance apart of the pivots being 7 5 cm. and the pitch of 

 the screw 0.125 cm., or 3-47Xio 4 cm. per degree of arc) 



io- 4 X 3 .47 =2I x J0 _ 6 radian 

 2.2X75 



or a. = 0.43% second of arc, nearly. This constant was used in the reductions. 

 In addition to the deviations x, the temperature of the room and the weather 

 conditions outside were taken daily. The latter showed no consistent influ- 

 ence and will be disregarded here. 



The first branch of the a curve (A A), from July 16 to August 23, shows an 

 initial ascent until July 20 and thereafter a fairly uniform descent. The tem- 

 peratures (as shown by the temperature curve, fig. 18) during the first half 

 of the observation period might suggest some relation, but they quite fail 



