THE YARD, PENDULUM, AND METRE. 439 



(20.) The causes of uncertainty which tell with such 

 very appretiable effect on the local determination of 

 the force of gravity by the pendulum, have little or no 

 influence on the local curvature of the surface of equili- 

 brium, and absolutely none on the measures of large 

 arcs of the meridian. Suppose, for example, a sea of 

 four miles in depth, and of great extent, to cover one 

 part of the earth's surface. Its surface water will gravi- 

 tate less by one i Sooth part of its proper weight, owing 

 to the deficiency of attracting matter below it ; and, the 

 diminution of gravity growing less and less in descend- 

 ing (being proportional to the height of a particle above 

 the bottom), the whole weight of the column of water 

 vertically above a given spot will be diminished by one 

 36ooth part, so that to maintain the equilibrium, one 

 36ooth part of four miles, or one gooth of a mile, i.e., 

 about six feet of additional water, must be heaped on : a 

 mere infinitesimal of the radius of curvature of its surface, 

 which is that of the earth itself. 



(21.) Let us now see how far the French metre, as it 

 stands, fulfils the requirements of scientific and ideal 

 perfection. It professes to be the io,ooo,oooth part of 

 the quadrant of the meridian passing through France 

 from Dunkirk to Formentera, and is therefore, scientifi- 

 cally speaking, a local and national, and not a universal 

 measure. The earth's equator is not a perfect circle, 

 but slightly elliptic, and the meridians of places differ- 

 ing in longitude are therefore not all of the same length. 

 The difference, however, is so trifling (the ellipticity of 

 its equator being not more than a thirtieth part of that 



