VOL. 



LI.] : PHILOSOPHICAL TRANSACTIONS. 347 



Maxims and Observations deduced Jrom the foregoing Table of Experiments. 

 Maxim 1. That the virtual or effective head being the same, the effect will be 

 nearly as the quantity of water expended. — ^This will appear by comparing the 

 contents of the columns 4, 8, and 10, in the foregoing sets of experiments. 



Maxim '1. That the expence of water being the same, the eff^ect will be nearly 

 as the height of the virtual or effective head. — This also will appear by com- 

 paring the contents of columns 4, 8, and 10, in any of the sets of experiments. 



Maxim 3. That the quantity of water expended being the same, the effect is 

 nearly as the square of its velocity. — This will appear by comparing the contents 

 of columns 3, 8, and 10, in any of the sets of experiments. 



Maxim 4. The aperture being the same, the effect will be nearly as the cube 

 of the velocity of the water, — ^This also will appear by comparing the contents of 

 columns 3, 8, and 10. 



Obs. 1. On comparing column 2d and 4th, tab. i. it is evident, that the vir- 

 tual head bears no certain proportion to the head of water : but that when the 

 aperture is greater, or the velocity of the water issuing therefrom less, they ap- 

 proach nearer to a coincidence : and consequently in the large opening of mills 

 and sluices, where great quantities of water are discharged from moderate heads, 

 the head of water, and virtual head determined from the velocity, will nearly 

 agree, as experience confirms. 



Obs. 2. On comparing the several proportions between the power and effect in 

 column 11, the most general is that of 10 to 3 ; the extremes 10 to 3.2 and 10 

 to 2.8; but as it is observable, that where the quantity of water, or its velocity, 

 that is, where the power is greatest, the 2d ratio is greatest also : we may there- 

 fore well allow the proportion subsisting in large works, as 3 to I . 



Obs. 3. The proportions of velocities between the water and wheel in column 

 12, are contained within the limits of 3 to 1 and 2 to 1 ; but as the greater ve- 

 locities approach the limit of 3 to 1, and the greater quantity of water approach 

 to that of 2 to 1, the best general proportion will be that of 5 to 2. 



After the experiments above mentioned were tried, the wheel, which had ori- 

 ginally 24 floats, was reduced to 12; which caused a diminution in the effect, on 

 account of a greater quantity of water escaping between the floats and the floor ; 

 but a circular sweep being adapted thereto, of such a length, that one float en- 

 tered the curve before the preceding one quitted it, the effect came so near to 

 the former, as not to give hopes of advancing it by increasing the number of 

 floats beyond 24 in this particular wheel. 



Part II. Concerning Overshot Wheels. 

 In the former part of this essay, we have considered the impulse of a confined 



Y Y 2 



