Mr. J. Croll on the Physical Cause of Ocean-currents. 255 



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. one foot-pound as the work of vertical descent. 



Now it will be found, as we shall presently see, that if we cal- 

 culate the mean amount of work performed in descending the 

 slope from the equator to the pole, 17 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 18 feet. The water 

 at the top of the mass which descended from E to P' descended a 

 slope of only 16 feet. The mean descent of the whole mass is 

 therefore 17 feet. And this gives 17 foot-pounds as the mean 

 amount of work per pound of water in descending the slope ; 

 this, added to the 1 foot-pound derived from vertical descent, 

 gives 18 foot-pounds as the total amount of work per pound of 

 the mass. 



I have in the above reasoning supposed 2 feet of water accu- 

 mulated 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 18 foot-pounds per pound of water, supposing we had con- 

 sidered 3 feet, or 4 feet, or even 18 feet of water to have accu- 

 mulated on the polar column before vertical motion took place. 



I have also, in agreement with Dr. Carpenter's mode of repre- 

 senting 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, how- 

 ever, 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. 



I have also represented the level of the ocean at the equator as 

 remaining permanent while the alterations of level were taking 

 place at the pole. But in representing the operation as it would 

 actually take place in nature, we should consider the equatorial 

 column to be lowered as the polar one is being raised. We 

 should, for example, consider the two feet of water P' P put upon 

 the polar column as so much taken off the equatorial column. 

 But in viewing the problem thus we arrive at exactly the same 

 results as before, as we shall presently see. 



Let P (fig. 2), as in fig. 1, be the surface of the ocean at the pole, 

 and E the surface at the equator, there being a slope of 18 feet 

 from E to P. Suppose now a quantity of water, E E ; , say, 2 feet 

 thick, to flow from off the equatorial regions down upon the 

 polar. It will thus lower the level of the equatorial column by 

 2 feet, and raise the level of the polar column by the same 

 amount. I may, however, observe that the two feet of water in 

 passing from E to P would have its temperature reduced from 



