244 Mr. K. D. Oldham on the Modulus of Cohesion of Ice. 



equals m ; so that the total depth to which a glacier could be 

 forced down a slope is 



D= - 



fju cot /3 — 1 



Or if p represent the thickness of the glacier at the head of the 

 slope ; and r that at the lowest point to which it can be forced, 



D = ^±^. ...... (V.) 



fju cot /3 — 1 v y 



Suppose T to be the total pressure which, if applied at a, 

 would be required to impel the glacier, as a whole, through 

 and out of the basin a b c ; then 



T = P + S 



= D(1 + /* cot <2) + D(> cot /3-1) 



=yuX>(cot(9+cot/3) (VI.) 



But as the pressure which can be transmitted at a is only m, 

 we get the greatest value for D when 



m = ijlD (cot 6 + cot /3), 

 or 



-TV W 



yu.(cot6> + cot/3)' 



supposing the thickness of the glacier at the lower end to be 

 the same as that -at the head of the lake ; but if there be any 

 difference, D cannot be greater than 



m + Z -y 



^->(cot0+cot/3)' * " * ' t vli -) 



z being the thickness at the upper, and y at the lower end of 

 the lake-basin. 



As, however, it will not always be necessary or convenient 

 to find the maximum value of D, but rather of ab (that is, the 

 maximum distance to which motion could be transmitted 

 through a glacier as a whole), this may easily be deduced 

 from the above formulae ; for if L represent the extreme dis- 

 tance to which motion can be transmitted, then D = L sin 6 or 

 L sin /3, as the case may be. Substituting this in (III.) and 



m + x — y 



or 



L= . '" ' " * „ .... (VIII.) 

 sin o + juu cos cr v ' 



yu,cos/3— sin/3 ' ^ '* 



