THE YARD, PENDULUM, AND METRE. 437 



elevated matter to increase gravitation. That of mere 

 elevation above the sea-level to the height of \ of a mile 

 {similarly reduced) is, however, one 36oooth in the oppo- 

 site direction, or to diminish it and the difference or 

 one 180,000 of the whole is effective not to compensate 

 but to add to the sea-deficiency. 



(17.) To obtain the real length of the normal pendu- 

 lum then we must go out of our own globe, and ascer- 

 tain the true co-efficient of gravity from astronomical 

 facts; and, as the only one available for the purpose, 

 compute the distance fallen through by the moon in a 

 second of time towards the earth from a tangent to her 

 orbit. This, it is evident, is independent of the influence 

 of those local inequalities which affect the pendulum 

 measurements. But, on the other hand, it must be re- 

 membered ist, That our knowledge of the distance in 

 .question depends on our previous knowledge of the 

 moon's distance, which, in its turn, depends on that of 

 the earth's diameter, and therefore presupposes the 

 metre to be accurately known. For any aliquot error in 

 the metre will produce an equal aliquot error in the 

 moon's distance estimated in metres, and therefore also 

 in the linear deflection per second from the tangent to 

 the orbit. 2d 3 That this linear deflection, or approach 

 of the moon to the earth in one second of time, is the 

 result of the joint attraction of the earth on the moon 

 and of the moon on the earth, and is in effect the sum of 

 the spaces fallen through by the moon towards their com- 

 mon centre of gravity, in virtue of the earth's attraction, 

 and by the earth towards that point in virtue of the 



