VALUE OF ACCELERATION OF GRAVITY— MENDENHALL. 17 



Hence, to determine ^'R, we have 



j;.M(R+J'R) 2 = ^MR 2 +gJ///R'- 

 and — 



A nt 

 The ratio y can be found by the aid of the graphical construction figure 10; in this way 



the corrections ^'R, and J'R„ have been found, which are to be added to the minimum values of 

 R, and R 2 to give the effective radii of the rings. 



In all the length measurements it was the custom to make five or more successive contacts 

 and readings of the moving contact against fixed contact; the other carriage and ring would then 

 be put on the ways, and five or more contacts and readings taken of ring against end stop and 

 moving stop against ring; the ring would then be moved and another series of contacts taken of 

 stop against stop. In case the primary object happened to be to measure diffen noes in diameter, 

 zero readings (stop against stop) would be less frequently taken. 



MEASUREMENT OF THE PERIOD. 



The pendulums were swung in a brass air-tight case (see figure 11 page 18) on an agate knife 

 edge of 120° angle. This was given its final grinding and polishing by Mr. E. G. Fisher of the 

 United States Coast and Geodetic .Survey, whose kindness I am glad to acknowledge. A coinci- 

 dence method was used for comparing the period of the pendulums with the beat of the standard 

 mean solar clock of the Washburn Observatory, kindly made available by Prof. G. C. Comstock. 

 The arrangement was as follows: on the flat face of the pendulum toward the observer were etched 

 eight very fine radial lines about 3 mm. long, symmetrically distributed at intervals of 45°, and 

 at about the distance (2 cm.) from the outer circumference where, as determined above, their 

 effect on the period would be a minimum. Thus, while one line was immediately over the knife 

 edge, the opposite one was vertically underneath and executing the longest possible linear arc of 

 vibration. This line was observed with a telescope of considerable magnifying power, and was 

 brilliantly illuminated for an instant once every two seconds. This was very simply brought 

 about by the use of the flash apparatus belonging to one of the United States Coast and Geodetic 

 Survey one-half second pendulum outfits, loaned through the courtesy of Superintendent Titt- 

 man. The horizontal slit of the apparatus was periodically opened by the clock circuit, while on 

 the slit was focussed the horizontal image of a Nernst glower, in such a manner that the beam 

 afterwards fell upon the etched line on the ring. The linear amplitude at the beginning of a 

 swing was from S to 9.5 mm., and at the end from 3 to 5 mm.; with the magnification used, the 

 coincidence of the etched line with the cross wire of the telescope could lie determined with ample 

 accuracy. The times of coincidence were noted on a chronometer whose rate with respect to the 

 clock was followed closely, and all intervals reduced to clock seconds. Finally, from observations 

 for which I am indebted to Professor Comstock, the mean rate of the clock was determined and 

 the corresponding correction applied. As the observations extended almost continuously over a 

 period of more than two weeks, it is safe to say that diurnal variations of clock rate do not affect 

 the result. 



Further points to be considered in connection with the determination of T are — 



1. Adjustment of the ease and pendulum. 



2. Temperature corrections. 



3. Amplitude corrections. 

 1. Pressure corrections. 



5. Corrections for vibration of the support. 

 1. The principal adjustments are to have the knife edge horizontal and the plane of the 

 pendulum at right angles to it. The leveling of the edge was tested with a 5" level supported on 

 80.369°— vol 10—11 2 



