Connected with the Earth's Field of Force. 151 



general conclusion, namely, the existence of an eqnator- 

 ward force. For a parallelopiped the eqnatorward force 

 is approximately proportional to the average elevation of 

 its upper face above the surface of the fluid. 



For a body of irregular shape the existence of such a 

 force may be inferred by a comparison of the potential 

 of such a body floating at the equator, with its potential 

 at some other latitude; the potential of the displaced 

 fluid must be included in the calculation. The force 

 itself may be conveniently evaluated by using for calcu- 

 lating the pressures the familiar transformations. 



/ / V cos a dS = III -- dx dy dz. 



The integral on the left is extended over the submerged 

 surface and also, merely to form a closed surface, over 

 the cap formed by the geoid surface within the solid, the 

 cap being bounded by the ' ' water-line. ' ' The integral on 

 the right is a volume integral over the solid bounded by 

 the submerged surface and by the cap.^^ 



The statement on page 137 with regard to the force 

 which tends to turn a floating body, so as to bring its axis 

 of length into the prime vertical in low latitudes and into 

 the meridian in high latitudes applies to a body in general 

 conforming to the curvature of the earth and lying oblique 

 to the meridian, with a uniform elevation of its upper 

 surface above the surface of the liquid. In low north 

 latitudes the northern end, being nearer to latitude 45°, 

 where the equatorward pull is a maximum, would be 

 drawn toward the equator more strongly than its southern 

 end. This would tend to bring the axis of greatest length 

 into the prime vertical. In high north latitudes (above 

 45°) the southern end would be drawn more strongly 

 toward the equator and the force would tend to bring the 

 axis of length into the meridian. This force resembles 

 somewhat the force acting on the bar on an Eotvos 

 balance, but has a different cause. 



The motion of matter toward the earth's equator 

 would, of course, have an effect on the position of the 

 earth's axis of rotation. It has been assumed that the 

 masses involved were negligible in comparison with 



^^See almost any accomit of the potential function, as for example 

 Peirce's Newtonian Potential Function, 3d Ed., page QQ. 



