TOL LI.] PHILOSOPHICAL TRANSACTIONS. 351 



to that of 10 : 5.2, that hi, nearly from 4 : 3 to 4 : 2. In those experiments 

 where the heads of water and quantities expended are least, the proportion is 

 nearly as 4:3; but where the heads and quantities are greatest, it approaches 

 nearer to that of 4 : 2 ; and by a medium of the whole, the ratio is that of 

 3 : 2 nearly. We have seen before, in the observations on the effects of undershot 

 wheels, that the general ratio of the power to the effect, when greatest, was 

 3:1; the effect therefore of overshot wheels, under the same circumstances 

 of quantity and fall, is at a medium double to that of the undershot :" and, as 

 a consequence thereof, *' that nonelastic bodies, when acting by their impulse 

 or collision, communicate only a part of tlieir original power ;" the other part 

 being spent in changing their figure, in consequence of the stroke. 



The powers of water computed from the height of the wheel only, compared 

 with the effects, as in column 10, appear to observe a more constant ratio: for 

 if we take the medium of each class, which is set down in column 11, we shall 

 find the extremes to differ no more than from the ratio of 10 : 8,1 to that of 

 10:8.5; and as the 2d term of the ratio gradually increases from 8.1 to 8.5, by 

 an increase of head from 3 inches to 11, the excess of 8.5 above 8.1, is to be 

 imputed to the superior impulse of the water at the head of 1 1 inches above 

 that of 3 inches: so that if we reduce 8.1 to 8, on account of the impulse of 

 the 3-inch head, ' we shall have the ratio of the power, computed on the height 

 of the wheel only, to the effect at a maximum as 10 : 8, or as 5 : 4 nearly :' and 

 from the equality of the ratio between power and effect, subsisting where the 

 constructions are similar, we must infer, that the effects, as well as the powers, 

 are as the quantities of water and perpendicular heights multiplied together re- 

 spectively. 



//. Concerning the Most Proper Height of the Wheel in Proportion to the 



Whole Descent. 

 We have already seen, from the preceding observation, that the effect of the 

 same quantity of water, descending through the same perpendicular space, is 

 double, when acting by its gravity on an overshot wheel, to what the same pro- 

 duces when acting by its impulse on an undershot. It also appears, that by in- 

 creasing the head from 3 inches to 11 , that is, the whole descent, from 27 inches 

 to 35, or in the ratio of 7 to Q nearly, the effect is advanced no more than in 

 the ratio of 8.1 to 8 4, that is, as 7:7.26; and consequently the increase of 

 effect as not l-7th of the increase of perpendicular height. Hence it follows 

 that the higher the wheel is in proportion to the whole descent, the greater 

 will be the eflect;' because it depends less on the impulse of the head, and more 

 on the gravity of the water in the buckets: and if we consider how obliquely the 

 water issuing from the head must strike the buckets, we shall not be at a loss to 



