• BY A. E. BLACKMAN. 377 



In effect their masses may be considered concentrated 

 at their centres of mass (centres of gravity) so far as 

 distances beyond their circumferences are concerned, but 

 within their circumferences the law of variation, as far as 

 distances are concerned, depends in homogeneous masses 

 directly with regard to those centres, because anywhere 

 within a spherical shell of matter the forces of the particles 

 of the shell are self-destructive. From this it is evident 

 that a body falling towards the earth is continually acted 

 upon by an increasing force until it reaches in general 

 the surface, after which, if its way were clear to the centre 

 of the earth, the force would fall off to nothing — thus 

 there is a place of maximum force — the effective surface, 

 very approximately sea-level over the ocean, and rising 

 over that level as a comparatively smooth surface over the 

 land, averaging its level. 



Now, it is well-known that a pendulum's rate of swing 

 depends upon the force of gravitation and its length as 

 an equivalent simple pendulum — one in which all the 

 matter is supposed concentrated at its centre of oscillation. 

 Take two pendulums synchronised, one placed within a 

 heavy shell— of lead, say — and the other vertically above 

 and immediately outside; the one above experiences the 

 full force of all' the matter in the world, provided there 

 be nothing else above 'its horizontal plane, whereas the 

 one within is deprived of the force due to the mass of the 

 shell. Consequently, the pendulum within loses relatively 

 to that outside. 



The weight of the world being some six thousand 

 milhon billions of tons, any mass we could make use of 

 for our shell would be so extremely small in comparison 

 that the loss of force by its self-destruction, as far as the 

 pendulum within is concerned, can only make a very 

 small difference in its rate of vibration, notwithstanding 

 the fact that the virtual proximity largely compensates— 

 the earth's distance being gravitationally its radius, or, 

 roughly, seven milhon yards, to the few yards of the shell 

 from the outside pendulum. Thus a mass of a few tons 

 in the shell is virtually many billions of tons in its 

 comparative effect. 



By well-known mathematical formulae, after securing 

 the ratio of times of the clocks as indicated by dials and 

 special optical arrangements, we can calculate how many 



