204 Eev. H. Moseley on the Mechanical Possibility [Jan. 7, 



of the rock, the projections of which insert themselves into its mass, and 

 into the cavities of which it moulds itself. 



4thly. The friction of the ice in contact with the bottom and sides so 

 sheared over or abraded. 



If the whole mechanical work of these several resistances in a glacier 

 could be determined, as it regards its descent, for any relatively small time, 

 one day for instance, and also the work of its weight in favour of its 

 descent during that day, then, by the principle of " virtual velocities" (sup- 

 posing the glacier to descend by its weight only), the aggregate of the work 

 of these resistances, opposed to its descent, would be equal to the work of 

 its weight, in favour of it. It is, of course, impossible to represent this 

 equality mathematically, in respect to a glacier having a variable direction 

 and an irregular channel and slope ; but in respect to an imaginary one, 

 having a constant direction and a uniform channel and slope, it is possible. 



Let such a glacier be imagined, of unlimited length, lying on an even 

 slope, and having a uniform rectangular channel, to which it fits accurately, 

 and which is of a uniform roughness sufficient to tear off the surface of 

 the glacier as it advances. Such a glacier would descend with a uniform 

 motion if it descended by its weight only, because the forces acting upon 

 it would be uniformly distributed and constant forces*. The conditions of 

 the descent of any one portion of it would therefore be the same as those 

 of any other equal and similar portion. The portion, the conditions of 

 whose descent it is sought in this paper to determine, is that which has de- 

 scended through any given transverse section in a day ; or, rather, it is one 

 half this mass of ice, for the glacier is supposed to be divided by a vertical 

 plane, passing through the central line of its surface, it being evident that 

 the conditions of the descent of the two halves are the same. The mea- 

 surements which have been made of the velocities of the surface-ice at 

 different distances from the sides, make it probable that the differences of 

 the spaces described in a given time would be nearly proportional to the 

 distances from the edge in a uniform channel t ; and the similar measure- 

 ments made on the velocities at different depths on the sides that, under 

 the same circumstances, the increments of velocity would be as the distances 

 from the bottom. This law, which observation indicates as to the surface 



* It is supposed that the weight is only just sufficient to cause the descent. 



f Prof. Tyndall measured the velocity of the surface of the Mer de Glace at a series of 

 points in the same straight line across it at a place called Les Ponts. The distances of 

 these points in feet along the line up to the point of greatest velocity are set off to a 

 scale in fig. 1 ; and the space in feet through which each point would pass in thirtj>six 

 days, if its velocity continued uniformly the same, is shown by a corresponding line at 

 right angles to the other. The extremities of these last lines are joined. It will be seen 

 that the line joining them is for some distance nearly straight ; if it were exactly so, the 

 law stated in the text would, in respect to this ice, be absolutely true. Fig. 2 shows in 

 the same manner the spaces described in thirty-six days by points at different depths on 

 the side of the Glacier du Geant, as measured by Prof. Tyndall at the Tacul. See Phil. 

 Trans. Royal Society, vol. cxlix. part 1, pp. 265, 266. [The figures referred to in this 

 note accompany the MS. of the paper.] 



