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



80° to 32°, and this would produce a slight contraction. But 

 as the weight of the mass would not be affected, in order to sim- 



Fig. 2. 



plify our reasoning we may leave this contraction out of consi- 

 deration. Any one can easily satisfy himself that the assump- 

 tion that E E' is equal to P' P does not in any way affect the 

 question at issue — the only effect of the contraction being to 

 increase by an infinitesimal amount the work done in descending 

 the slope, and to diminish by an equally infinitesimal amount 

 the work done in the vertical descent. If, for example, 16 

 foot-pounds represent the amount of work performed in descend- 

 ing the slope, and 2 foot-pounds the amount performed in the 

 vertical descent, on the supposition that E' E does not contract 

 in passing to the pole, then 16*0048 foot-pounds will represent 

 the work of the slope, and 1*9952 foot-pound the work of ver- 

 tical descent when allowance is made for the contraction. But 

 the total amount of work performed is the same in both cases. 

 Consequently, to simplify our reasoning, we may be allowed to 

 assume P' P to be equal to E E'. 



The slope E P being 18 feet, the slope E' P' is consequently 

 14 feet ; the mean slope for the entire mass is therefore 16 

 feet. The mean amount of work performed by the descent of 

 the mass will of course be 16 foot-pounds per pound of water. 

 The amount of work performed by the vertical descent of P / P 

 ought therefore to be 2 foot-pounds per pound. That this is 

 the amount will be evident thus : — The transference of the 2 

 feet of water from the equatorial column to the polar disturbs 

 the equilibrium by making the equatorial column too light by 

 2 feet of water and the polar column too heavy by the same 

 amount of water. The polar column will therefore tend to sink, 

 and the equatorial to rise till equilibrium is restored. The dif- 

 ference of weight of the two columns being equal to 4 feet of 

 water, the polar column will begin to descend with a pressure 

 of 4 feet of water ; and the equatorial column will begin to rise 

 with an equal amount of pressure. When the polar column 



