MECHANICS. 



iicient for the purpose is received from 

 the superior level h. 



The weights of the water in the seve- 

 ral buckets, however, are not equally 

 effective in turning the wheel; this 

 will be easily perceived. If any water 

 were contained in the highest bucket 

 Hi its weight would press upon the 

 axle O in the direction H O. This 

 weight would be entirely sustained by 

 the supports of the wheel, and would 

 contribute in no degree to its motion. 

 From the several buckets a b c, &c., 

 conceive the lines a A, b B, cC, &c. 

 drawn perpendicular to the horizontal 

 diameter F G. The weight of the water 

 in the bucket a has the same effect in 

 making the wheel revolve as if that 

 weight acted at A, by the arm or lever 

 A O. In the same way the weights of 

 the water in the several buckets bed 

 and e have the same effect as if they 

 acted at the points B C D E. Now it 

 is very evident, that the more remote 

 from the centre O a given weight acts, 

 the more effective will that weight be in 

 turning the wheel ; and therefore, the 

 water in the buckets near F is propor- 

 tionally more effective than that in those 

 near H. The same may be said of the 

 buckets e' d 1 c'. As, however, the water 

 begins to flow from each bucket as it 

 descends from the end F of the horizon- 

 tal diameter, these buckets, e' d 1 c', pro- 

 duce a less effect than those edc imme- 

 diately above them, in proportion as 

 they contain a less weight of water. 



Jn order to increase the power of 

 overshot water-wheels, engineers have 

 given considerable attention to the con- 

 struction of the buckets, which should 

 be so shaped as to retain as much of the 

 water as possible until they reach the 

 lowest point L, but to retain none after 

 they pass that point : in fact, each 

 bucket should be empty on arriving at 

 the lowest point L, but should remain 

 filled until it come as near as possi- 

 ble to that point : to attain this, va- 

 rious forms of buckets have been 

 suggested. That which has been gene- 

 rally considered best is represented in 

 fig. 21. 



This bucket is formed of three 

 planes ; A B is in the direction of the 

 radius of the wheel, and is called the 

 start, or shoulder; BC is called the 

 arm, and C H the wrist. These buckets 

 are so constructed, that when A B 

 makes an angle of 35 with the vertical 

 diameter of the wheel, the line A D is 

 horizontal ; and the area of the figure 



AD C B is equal to 

 that of F C B A; so 

 that as much water is 

 retained in the bucket in 

 this position as would 

 fill F C B A : the whole 

 of the water is not dis- 

 charged until C D be- H 

 comes horizontal, which 

 takes place when the 

 line A B is very near the 

 lowest point. 



In attempting to keep 

 all the descending buck- 

 ets filled, it should not 

 be forgotten, that the increased pres- 

 sure upon the supports of the axle pro- 

 duces an increased resistance from fric- 

 tion ; and therefore, that there is neces- 

 sarily a certain distance from the highest 

 and lowest point, within which a weight 

 in a descending bucket is a positive impe- 

 diment to the motion of the wheel. This 

 will be readily understood by commenc- 

 ing with the extreme cases of the high- 

 est and lowest buckets themselves. If 

 these be filled, the weight of the water 

 which they contain will, as we have 

 before stated, have no effect whatever 

 in turning the wheel, but will press on 

 the supports of the axle with its entire 

 force; the friction, being proportional 

 to the perpendicular pressure, will there- 

 fore be increased ; and hence an addi- 

 tional resistance to the effect of the 

 water in the descending buckets will 

 be created : thus it appears, that water 

 in the highest and lowest buckets is a 

 positive resistance to the motion of the 

 wheel. Now, suppose the buckets a a' 

 near the highest and lowest points be 

 filled, two effects will then be produced ; 

 an additional pressure on the axle ; and 

 therefore an increased resistance will be 

 created on the one hand, and a moving 

 force with the leverage A O will be 

 brought into action on the other hand : 

 but when the buckets a a' are very near 

 the highest and lowest points, the lever- 

 age A O will be very small, while the 

 increased pressure on the axle will be 

 very great. Thus the increased resis- 

 tance may be greater than the moving 

 force which is gained ; and therefore, on 

 the whole, a loss of power will ensue. 



From this reasoning, it is apparent 

 that there is a certain distance from the 

 highest and lowest points at which the 

 momentum, or moving power of the 

 water in the buckets is only equal to 

 resistance arising from friction, which 

 its own weight creates ; and it is very 



