Mr Pryde on the Motion of the Sea. 79 



In order to find the pressure at the surface of each of the 

 remaining spheres, from the poles towards the equator, he 

 proved that we must use the formula : 



TT"^ 7' S%Tb '/ (1 



o^/L'>nQ9^2 ^ —(1*000793)-^ = the force sought where r must 



be = the feet in the radius of the sphere, I = the latitude of 

 the place, and / = the hundreds of fathoms in the depth of 

 the sea. From this formula he deduced that at the depth of 

 2000 fathoms the force = -0564412 sin 21 at 4000 fathoms 

 the force = '0573588 sin 21, and at 7000 fathoms the force 

 = '0587636 si)i 21, while at the surface of the earth it = 

 '0555381 sin 21. This shows that at a depth of 7000 fathoms 

 the force had increased by about a I7tli part of itself. 



Having thus proved that the pressures towards the equator 

 were greater at the bottom of the sea than at the surface, and 

 the greater the depth the pressure increased the more rapidly, 

 he supposed a column of water reaching from the surface to 

 the bottom of the sea, and represented it by the line A B, 

 w^here 



B 



/V3C I v^3c 



A is the surface and B the bottom of the sea ; he supposed 

 forces applied at A and B each equal to the force acting 

 at C, the middle of the column ; then since the force at A 

 would be too great, and that at B too small, he applied a force 

 X in the opposite direction, at A, to reduce it to the true force ; 

 and also a force x at B in the same direction to increase it to 

 the true force acting there ; then applying two forces at C, 

 each equal to the former forces, he found that the four forces 

 marked 1 were in equilibrium, and might therefore be re- 

 moved, and there only remained the two forces marked x 

 acting in opposite directions, forming a couple, which must 

 therefore cause the point B to approach towards the equator, 

 and the point A to approach towards the pole ; thus proving 



