VOL. LI.] PHILOSOPHICAL TRANSACTIONS. 355 



water, when acting by its impulse, and by its weight, under the titles of under- 

 shot and overshot wheels ; we might naturally proceed to examine the effects 

 when the impulse and weight are combined, as in the several kinds of breast- 

 wheels, &c, but, what has been already delivered being carefully attended to, 

 the application of the same principles in these mixed cases will be easy, and re- 

 duce what is to be said on this head into a narrow compass : for all kinds of 

 wheels where the water cannot descend through a given space, unless the wheel 

 moves with it, are to be considered of the nature of an overshot wheel, accord- 

 ing to the perpendicular height that the water descends from ; and all those 

 that receive the impulse or shock of the water, whether in an horizontal, per- 

 pendicular, or oblique direction, are to be considered as undershots. And 

 therefore a wheel, which the water strikes at a certain point below the surface 

 of the head, and after that descends in the arch of a circle, pressing by its 

 gravity on the wheel ; " the effect of such a wheel will be equal to the effect of 

 an undershot, whose head is equal to the difference of level between the sur- 

 face of the water in the reservoir and the point where it strikes the wheel, 

 added to that of an overshot, whose height is equal to the difference of level, 

 between the point where it strikes Hie wheel and the level of the tail-water." 

 It is here supposed, that the wheel receives the shock of the water at right an- 

 gles to its radii ; and that the velocity of its circumference is properly adapted 

 to receive the utmost advantage of both these powers ; otherwise a reduction 

 must be made on that account. 



Part III. — On the Construction and Ejects of Windmill Sails. 

 In trying experiments on windmill-sails, the wind itself is too uncertain to 

 answer the purpose : we must therefore have recourse to an artificial wind. 

 This may be done two ways ; either by causing the air to move against the ma- 

 chine, or the machine to move against the air. To cause the air to move 

 against the machine in a sufficient volume, with steadiness and the requisite 

 velocity, is not easily practised : to carry the machine forward in a right line 

 against the air, would require a larger room than could conveniently be met 

 with. What is found most practicable therefore, is to carry the axis of the 

 sails progressively round in the circumference of a large circle. On this idea* 

 a machine was constructed as follows. 



* Some years ago Mr. Rouse, an ingenious gentleman of Harborough in Leicestershire, set 

 about trying experiments on the velocity of the wind, and force thereof upon plain surfaces and 

 windmill-sails : and much about the same time Mr, EUicott contrived a machine for the use of the 

 late celebrated Mr. B. Robins, for trying the resistance of plain surfaces moving through the air. 

 The machines of both these gentlemen were much alike, though at that time totally unacquainted 

 with each other's inquiries. But it often happens, that when two persons think justly upon the 

 same subject, their experiments are alike. This machine was also built upon the same idea as the 

 foregoing J but diftered in having the hand for the first mover, with a pendulum for its regulator, 



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