242 Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 



rough sandstone has been determined by Mr. Hopkins* to be 

 20°. Now, as the base of a glacier has imbedded in its sub- 

 stance quantities of rock (for, if not, there could be no erosive 

 power), the coefficient of friction must be greater than tan 20° 

 or -577. In the following calculations I have taken it at only 

 •2, so that there shall be no chance of exaggeration f. 



The next point to be determined is, what pressure acting 

 parallel to the surface of the bed would be required to force a 

 glacier en masse through and out of a lake-basin which it had 

 filled in its onward course. In the figure let gg represent a 



glacier flowing over its bed dabce, and let a b c represent the 

 longitudinal section of a rock-basin which it has filled : it is 

 required to determine the lowest pressure which will cause 

 the prism be hi to be forced up the inclined plane b c. Then 



P=wsin# + ^wcos 6, 

 where P is the pressure, expressed for convenience in vertical 

 feet of ice, to the weight of the prism, /jl the coefficient of re- 

 sistance, and 6 the angle of the slope b c. In this equation 

 to sin 6 is constant; for to varies as cosec 6, and is always equal 

 to the resistance due to a column of ice in height equal to the 

 depth of the lake-basin, which may be called D ; and since 

 to sin #=D, /jlw cos 6 will equal [mD cot 6 ; so that the equation 

 becomes 



P=D+/J)cot<9, 

 or P = D(1+A6cot0) (I.) 



Thus P increases approximately as cot 6. 



* Quoted by the Key. T. G. Bonney, M.A. (Quart. Journ. Geol. Soc. 

 vol. xxvii. p. 322, 1871). 



t Inasmuch as a glacier could not (if a rigid body) flow down an angle 

 of less than 20° by its own weight, and as the upper surface of glaciers is 

 known to move when the inclination is much less, it is evident that the 

 resistance of ice to change of shape cannot be very great, or, in other 

 words, that under a comparatively small pressure it apparently behaves 

 as a viscous body. But this does not affect the question of whether the 

 base slides over its bed : if the angle of slope be but 5° it could not, 

 though that might be an angle sufficiently steep to allow the upper 

 portions to slide over the lower. 



