230 PROCEEDINGS OF THE GEOLOGICAL SOCIETY. [Jan. 20, 



mean distance, has travelled 500 miles from the centre. And the 

 labouring force which has carried it through this space, in whatever 

 way it has acted, must be equivalent to the product of the moving 

 pressure and the space through which it has acted ; that is, it must 

 be equivalent to the weight of 1^000,000 of a mile of water, multiplied into 

 500 miles. 



This is the same as ^ of a mile of water, multiplied into one mile ; 

 or one mile of water multipUed into 2^ of a mile of elevation. 



That is, one cubic mile of water rising through 25^0 of a mile (or 

 about 2^ feet) would supply the power necessary to carry the drift 

 which occupies one average mile at the mean distance from the centre 

 of distribution. 



Instead of one cubic mile of water, we may take a square of ten 

 miles, iJo of a mile deep ; and this mass, rising through 2^ of a mile, 

 will produce the effect now spoken of. 



Taking any radius drawn from the centre of the annulus, the part 

 of this radius which lies on the annulus is 600 miles. On each of these 

 600 miles, we suppose drift to rest. Each portion of drift has 

 travelled a different distance from the centre. But at each different 

 distance from the centre, there may be a different quantity of drift 

 upon the average ; the quantity probably decreasing as we recede 

 from the centre. Let us suppose, for the sake of calculation, that 

 the quantity diminishes exactly in proportion as the distance increases; 

 so that at the distance of 200 and 800 miles, the quantities on a square 

 mile are as four and one respectively. 



On this supposition, the labouring force requisite to carry the drift 

 which lies on each square mile of the same radial line, would be the 

 same. It would take the same labouring force to carry 1^000,000 of a 

 mile through 500 miles (the mean radius) as to carry 4oo;ooo through 

 200 miles to the inner edge of the annular space ; or i;6oboo through 

 800 miles, to the outer edge of the annulus. In each case, the amount 

 of force requisite would be, as before, the weight of 2000 of a mile of 

 water, raised through one mile. 



Here the labouring force requisite to carry the drift to the whole 

 of the 600 miles which lie along this radius, would be -^ or •^, of a 

 mile of water raised through one mile (600 X2-^=2o=~io)' 



Now taking the whole semi-annulus, the length of the mean semi- 

 circle, of which the radius is 500 miles, is about 1500 miles. 



Hence if we suppose the radial tracts a mile wide just spoken of to 

 make up the semi-annulus, the force requisite to distribute the whole 

 mass of drift will be 1500X^, or 450 cubic miles of water raised 

 through one mile. 



Now though these radial tracks do not make up the annulus, being 

 too broad within the mean distance and too narrow beyond it, this 

 excess and defect balance each other ; and therefore we arrive at the 

 conclusion that 450 cubic miles of water raised a mile high would 

 produce an effect equivalent to the dispersion of the whole body of 

 northern drift. 



