314 The Rev. 0. Fisher on Mr. Mallet's 



tion probably diminishes as the pressure increases. Hence 



8 P- 

 .'. the work= „ — e/c 2 . 



O jJU 



But the whole work on a vertical section was found to be 



P 2 



— ek* ; hence the whole work along the plane of shearing is 



A 6 



2f- of the work along the vertical section. This work will not 



be evenly distributed, but will be greatest upon the unit of the 



length nearest A, where the space moved over will be eAB, and 



the force upon it is/*'. Hence work upon the last unit=/u/eAB, 



i P x-Pa , 

 = fjJe j 



p. 



upon the suppositions made, this becomes 

 =±Vek. 



And the work upon a square mile of section on the same suppo- 

 sitions was found to be 



fPBek. 



Hence the work, and therefore the heat, upon the last unit of the 

 plane of shearing, where it will be greatest, is only one fifth of 

 the work and heat respectively on a unit of the vertical section. 



This result seems unfavourable to the view that the heat 

 arising from friction of the rocks along horizontal planes can 

 account for the heat concerned in producing even metamorphistn. 



It must be fully understood that the results just arrived at 

 with respect to the heat developed at a vertical section, as well 

 as along the plane of shearing, have reference not to any probable 

 values, but to a superior limit which must be greater than the 

 greatest possible. In fact they involve several impossible as- 

 sumptions, all of which make it too large. These are : — 



(1) That the contraction from cooling takes place in the matter 

 of the nucleus and not in the crust. 



(2) That the above circumstance allows the coefficient of con- 

 traction to be nearly four times as large as it would be on the 

 more probable supposition. 



(3) That the pressure increases to the utmost attainable value, 

 viz. that of a column of rock 2000 miles long, before yielding 

 takes place. 



(4) That when yielding does take place, the pressure at the 

 place of yielding entirely vanishes. 



The above assumptions, besides making the amount of heat 

 impossibly great, also localize it to an impossible degree, as may 

 be seen by observing that BB' would be lessened by diminish- 



