That such is the case is further evident from the following considerations. Before the polar column begins to descend, it is heavier than the equatorial by the weight of one foot of water; but when the column has descended half a foot, the polar column is heavier than the equatorial by the weight of only half a foot of water; and, as the column continues to descend, the force with which it descends continues to diminish, and when it has sunk to P the force is zero. Consequently the mean pressure or weight with which the one foot of water P′ P descended was equal to that of a layer of half a foot of water; in other words, each pound of water, taking the mass as a whole, descended with the pressure or weight of half a pound. But a half pound descending one foot performs half a foot-pound; so that whether we consider the _full pressure acting through the mean distance, or the mean pressure acting through the full distance, we get the same result_, viz. a half foot-pound as the work of vertical descent. Now it will be found, as we shall presently see, that if we calculate the mean amount of work performed in descending the slope from the equator to the pole, 3½ foot-pounds per pound of water is the amount. The water at the bottom of the mass P P′ moved, of course, down the full slope E P 4 feet. The water at the top of the mass which descended from E to P′ descended a slope of only 3 feet. The mean descent of the whole mass is therefore 3½ feet. And this gives 3½ foot-pounds as the mean amount of work per pound of water in descending the slope; this, added to the half foot-pound derived from vertical descent, gives 4 foot-pounds as the total amount of work per pound of the mass. I have in the above reasoning supposed one foot of water accumulated on the polar column before any vertical descent takes place. It is needless to remark that the same conclusion would have been arrived at, viz., that the total amount of work performed is 4 foot-pounds per pound of water, supposing we had considered 2 feet, or 3 feet, or even 4 feet of water to have accumulated on the polar column before vertical motion took place. I have also, in agreement with Dr. Carpenter’s mode of representing the operation, been considering the two effects, viz., the flowing of the water down the slope and the vertical descent of the polar column as taking place alternately. In nature, however, the two effects take place simultaneously; but it is needless to add that the amount of work performed would be the same whether the effects took place alternately or simultaneously.