VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 



19 



the knife edge and reversed. The azimuth adjustment was tested by means of a similar level, 

 pivoted, and provided with a glass contact point which rested against the face of the ring over 

 the knife edge (see tig. 12). Evidently if the ring is not at right angles to the knife edge, a rota- 

 tion of it around the edge will result in a motion of the level bubble; and a simple calculation 

 shows that this device with a 5" level is more sensitive than is necessary to enable one to adjust 

 to within the limits (± 8') indicated as desirable in the discussion under theory. After the ring 

 was adjusted two stop screws (S, S,. fig. 11), 

 rigidly fastened to an axis fixed to the bot- 

 tom of the case, were swung into position 

 and set until they made simultaneous con- 

 tact with both sides of the ring. They 

 served to locate permanently the correct 

 plane, and the ring was always tested with 

 respect to them before and after each _ Line of 

 swing. 



Mechanical arrangements were of course 

 provided for lowering, raising, and starting 

 the pendulum from outside the case, and 

 these operated without at all displacing the 

 ring from its proper position. 



•2. Temperatun correction. — From the 

 pendulum formula: 



T 2 =KR 



Fig. 12. 



find: 



AT 



ffjer 



_/~ 



s± 



where 6 is the coefficient of thermal expan- 

 sion of the ring, and JT the small change 

 in period produced by the small changes in 

 temperature Ad. Using the measured co- 

 efficient of expansion for the two rings, the 

 values of AT have been calculated. There 

 were two thermometers in the pendulum 

 case, one near the bottom of the ring, the 

 other above the middle, and as they usually 

 differed by less than u. 1° (_'.. the mean (of 

 their readings at the beginning and end of 

 a swing) was taken as the temperature of 

 the ring. 



3. Amjilit'iil, correction. — At the begin- 

 ning and end of each set of observations, 

 the double amplitude was measured and the 

 reduction to an infinitesimal arc obtained by graphical interpolation from the usual expression: 



W 



T 



[jk ( "> 



,u <", + ",)"- 



I 

 L92 



(«,- 



,,] 



The initial half amplitudes were about 1 12' and the final averaged about 35'. 



■i. Pressun correction. — The average pressure inside the pendulum case during observations 

 was about 1 cm. of mercury, at which pressure corrections for buoyancy and entrained air are 

 negligible. 



