342 PHILOSOPHICAL TRANSACTIONS, [anNO 17 5Q. 



a minute; with that velocity wherewith it struck the wheel: but the wheel being 

 incumbered by friction and resistance, and yet moving 6o turns in a minute, it 

 is plain, that the velocity of the water must have been greater than 6o circum- 

 ferences before it met with the wheel. Let now the cord be wound round the 

 cylinder, but contrary to the usual way, and put a weight in the scale; the 

 weight so disposed, which may be called the counter-weight, will endeavour to 

 assist the wheel in turning the same away, as it would have been turned by the 

 water: put therefore as much weight into the scale as, without any water, will 

 cause it to turn somewhat faster than at the rate of 6o turns in a minute: sup- 

 pose 63 ; let it now be tried again by the water, assisted by the weight ; the 

 wheel therefore will now make more than 60 turns ; suppose 64 ; hence we con- 

 clude the water still exerts some power in giving motion to the wheel. Let the 

 weight be again increased, so as to make 644- turns in a minute without water: 

 let it once more be tried with water as before; and suppose it now to make the 

 same number of turns with water as without, viz. 644^; hence it is evident, that 

 in this case the wheel makes the same number of turns in a minute, as it would 

 do if the wheel had no friction or resistance at all; because the weight is equiva- 

 lent thereto; for were it too little, the water would accelerate the wheel beyond 

 the weight ; and if too great, retard it ; so that the water now becomes a regula- 

 tor of the wheel's motion ; and the velocity of its circumference becomes a mea- 

 sure of the velocity of the water. 



In like manner, in seeking the greatest product, or maximum of effect; hav- 

 ing found by trials what weight gives the greatest product, by simply multiplying 

 the weight in the scale by the number of turns of the wheel, find what weight 

 in the scale, when the cord is on the contrary side of the cylinder, will cause the 

 wheel to make the same number of turns the same way, without water; it is 

 evident that this weight will be nearly equal to all friction and resistance taken 

 together; and consequently, that the weight in the scale, with twice* the weight 

 of the scale, added to the back or counter-weight, will be equal to the weight 

 that could have been raised, supposing the machine had been without friction or 

 resistance; and which multiplied by the height to which it was raised, the pro- 

 duct will be the greatest effect of that power. 



The Quantity of Water expended is found thus: 



The pump made use of for replenishing the head with water was so carefully 

 made, that no water escaping back by the leathers, it delivered the same quantity 

 of water at every stroke, whether worked quick or slow; and as the length of 

 the stroke was limited, consequently the value of one stroke (or on account of 

 more exactness \'l strokes) was known, by the height to which the water was 



• The weight of the scale makes part of the weight both ways. — Orig. 



