■584 Proceedings of the Royal Irish Academy. 



thinking tliat the changes in steep and lofty rock -masses, such as the 

 Aiguilles of Mont Blanc or the JVTatterhorn, are entirely due to 

 weathering, and not to the squeezing down of the masses by gravity. 

 The e:ffective action of gravity upon a cone or pyramid, in squeezing 

 it down, can be easily shown to be likely to produce a change of 

 shape only if the matter was soft, but none if hard. A mass of rocks, 

 with vertical sides, is acted on by changes of temperature and mois- 

 ture, rain, frost, snow, and air, so as to gradually degrade it ; but 

 conceive all of these agencies absent, the sole force acting on its 

 gravity — and although this is 289 times at least as great as the centri- 

 fugal at the equator — it could not be concluded, nor has it ever been 

 proved that gravity has caused such a mass to be in the slightest 

 degree flattened. If rocks were so plastic that ^i-^g could mould 

 them, all the earlier mountains would have been long since flattened 

 down. A force more than two hundred and eighty times as great 

 as the greatest amount of centrifugal force has acted for more than 

 fifty centuries on the pyramids of Egypt and other structures raised by 

 man, and yet not the smallest compression can be proved. It is there- 

 fore inconceivable that the very small force resulting from the angular 

 velocity of the earth could produce any such effect. If a fly-wheel or a 

 mill-stone continues to rotate with a small angular' velocity, no change 

 in its form can be observed. But if it received such a rapid rotation 

 as to create a centrifugal force very much greater than gravity, 

 instead of changing its shape it breaks to pieces. ISTo instance has 

 ever been recorded of a fly-wheel or a mill-stone, rotating at their 

 usual angular velocities, having received the slightest change in its 

 form. Yet the angular velocity of a mill-stone or fly-wheel is 

 usually many thousand times as great as the angular velocity of the 

 earth. 



Por every mountain slope, whose inclination exceeds the angle 

 made by the normal at any point of a sphere to the direction of cen- 

 trifugal from any gravity, has a force acting on it far exceeding cen- 

 trifugal force at the equator. If a be radius of a base of a conical 

 mountain, and h its height, then gravity acts on its slope with a force 



_ „ , in order that this force = /. 



"^v '''' + ^^^ 



«*+A' , ,. , a" h 1 



or^^l.f^^Y)-i=/=^l(l-^ZUc.), 

 a \aj a o, 



or the ratio of height to its base would be ^tt nearly. 



A mountain with a base 478 miles and a height of 1 mile is acted 

 on by a force equal to that of centrifugal force. 



A mountaia 5 miles high, with a base of 100 miles, is acted on by 



