MECHANICS. 



19 



centre of Cavity O' through the arch 

 O E, in order to turn the body over 

 the edge D. 



XL 



It is evident that a much less eleva- 

 tion of the edge A will effect this, than 

 that which would be necessary to raise 

 the centre O through the arch O E in 

 the former case. 



The danger of loading carriages hea- 

 vily at the top, when the lower parts of 

 the vehicle are comparatively unloaded, 

 is accounted for in this, way, and also 

 the danger arising from persons stand- 

 ing up in a boat. In these cases, the 

 centre of gravity is raised, and the faci- 

 lity with which the vehicle may be over- 

 turned is proportionally increased. 



If it be attempted to support a body 

 upon a sharp point, considerable diffi- 

 culty will be felt owing to the practical 

 impossibility of keeping the centre of 

 gravity of the body vertically over the 

 point on which it is sustained. If, how- 

 ever, a motion of rotation be communi- 

 cated to the body, and it be made to 

 spin on ^the point, it will be found to 

 be balanced with comparative ease. In 

 this case, the centre of gravity in each 

 revolution of the body assumes every 

 possible position round the point, and 

 has an equal tendency to make the body 

 incline in all directions round it. Con- 

 sequently, its tendency to make the 

 body incline in any one direction, is 

 after half a revolution counteracted by 

 an equal tendency to make it incline in 

 the opposite direction ; and provided the 

 motion of rotation be sufficiently rapid, 

 these opposite tendencies follow in such 

 quick succession, that they counteract 

 each other as effectually as if they acted 

 simultaneously. 



CHAPTER V. On Water considered 

 as a Mectianical Agent. 



(47.) WHEN w r ater descends from any 

 Jevel to a lower one, its weight during 



the descent may be used as a mecha- 

 nical agent. That this may be possible, 

 it is only necessary that there should 

 be a sufficient supply of water at the 

 superior level, and that there should be 

 means of carrying it off after its descent, 

 so as to prevent, by its accumulation, 

 the equalization of the two levels. The 

 most usual means of giving motion to 

 machinery by this power is a wheel, on 

 the circumference of which the weight 

 of the water is made to act in its descent, 

 in a direction as nearly as possible at 

 right angles to the radii ; this pressure, 

 however, acting only at one side of the 

 wheel. Wheels driven by this power 

 are of two kinds, the overshot wheel 

 and the breast-wheel. 



The diameter of an overshot wheel' is 

 nearly equal to the difference of the 

 levels of the water by which it is moved. 

 A section of such a wheel at right angles 

 to its axle is represented in Jig. 1 9. The 



rim is furnished with buckets w r hich re- 

 ceive the water as it descends from the 

 superior level h. The buckets from the 

 top H of the wheel to the end F of the 

 horizontal diameter F G are constantly 

 full of water, while those from F to a 

 point a', where the side of the bucket 

 becomes level or horizontal, are only 

 partially filled; those from a' to the 

 lowest point L being empty. It is evi- 

 dent that the buckets on the other side, 

 G, of the vertical diameter H L, will be 

 all empty. 



In this state the wheel will be turned 

 round by the weight of the water hi 

 the buckets, since that weight acts 

 entirely on one side, H F L, of the 

 wheel, and is not counterpoised by 

 an equal weight on the other side ; 

 and the wheel will continue to be 

 turned so long as a supply of water suf- 

 c 2 



