THE ABSOLUTE VALUE OF THE ACCELERATION OF GRAVITY 

 DETERMINED BY THE RING PENDULUM METHOD. 



The use of a ring- pendulum for the determination of the absolute value of the acceleration 

 of gravity was first proposed by Dr. T. C. Mendenhall, who in 1S98 presented to the National 

 Academy of Sciences a brief report of some preliminary experiments made by Prof. A. S. Kim- 

 ball at the Worcester Polytechnic Institute. The use of the method as an ordinary laboratory 

 exercise in the physics department of the institute (in charge of Professor Kimball) had shown' 

 that even with rather roughly constructed apparatus results were obtained agreeing well with 

 each other and with the approximately known value of the constant at that point. It seemed 

 desirable, therefore, that a careful examination and test of the method should be made, since the 

 importance of a knowledge of the value of this constant is so great and the known methods of 

 determining it are so few that any process which may serve as a check upon these methods can 

 not fail to be of value. Accordingly a grant from the Bache fund of the Academy was made to 

 Dr. Mendenhall by the trustees of this fund to enable him to procure the apparatus necessary 

 for a more exacting test of the method. During the two succeeding years some preliminary 

 work was done under his direction by Dr. Edward Rhoads at the Worcester Polytechnic 

 Institute, consisting mostly of a study of some points relating to the theory of the method and 

 the design of a part of the apparatus. Dr. Mendenhall being at that time unable to give 

 further attention to the investigation, it was placed in my hands; the material turned over to me 

 consisting of the unfinished pendulum case, and some notes by Dr. Rhoads, to which I am glad 

 to acknowledge indebtedness. It is only, however, at intervals during the past two years that 

 the work has been under way, the greater part of this time having been devoted to the comple- 

 tion of the pendulum case and other accessory measuring apparatus, and more especially to the 

 completion of the rings. 



Geometrically, the ring pendulum is a figure bounded by two plane parallel surfaces and two 

 concentric cylindric surfaces whose axis is perpendicular to the plane faces, and it is to be vibrated 

 on a knife edge resting on an element of the inner cylindric surface. The relation between the 

 dimensions of the ring, the period, and " g" is quite simple, the most interesting point being the 

 existence of a particular ratio of the inner and outer radii which makes the period depend only 

 on the value of the outer radius; that is, the period is very insensitive to changes in the inner 



radius. This ratio, =^3" is one which gives a very deep, and hence a very rigid, ring. For a 



convenient coincidence interval of about 6 minutes (with a one-second clock beat) — that is, a 

 period of about I s . 003 — the external diameter should be about 28. *5 cm. and the inner 16.65 cm. 

 The ring can be swung from any internal element and by so doing irregularities of density or 

 figure, not otherwise easily discovered, can be detected and their effects to an extent eliminated. 

 This matter will be discussed more in detail later, but the above considerations are enough to 

 suggest the three points on which the desirability of the ring pendulum method will certainly 

 depend, namely: 



I. A definite and easily observable length to measure — the external diameter of the ring. 

 II. The great rigidity of the pendulum, hence but slight departure from its measured figure when suspended. 

 III. Detection of, and partial correction for, nonhomogeneity of pendulum. 



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