ON THE HISTORY OF HYDRAULICS AND PNEUMATICS. 359 



which is here attributed to a pound. His calculations of the motions of 

 fluids, in some very intricate cases, are very ingenious and satisfactory, and 

 they are in general sufficiently confirmed by well imagined experiments. He 

 examines the force of the Avind acting on the sails of a windmill, but by 

 another mistake in calculation, which Maclaurin has detected, of two angles 

 which answer the conditions of the determination, he has taken the wrong 

 one, and assigned that position of the sail as the most effectual, which pro- 

 duces absolutely no effect at all. 



It may be objected to Bernoulli's calculations, that some of the circum- 

 stances which are necessarily neglected in them, produce a very material effect 

 in the results of all experiments; but it must be allowed that the corrections 

 required, on account of this unavoidable omission, may easily be deduced 

 from simple experiments, and then applied to the most complicated cases. 

 It is, however, a more material objection, that the fundamental law of the 

 preservation of ascending force can only be adopted with certain limitations; 

 thus, when a small stream passes through a large reservoir, Bernoulli is 

 obliged to suppose the whole of its force consumed by the resistance which it 

 meets. The immediate mode, in which the accelerating forces must be sup- 

 posed to act, remains also wholly undetermined; and it was principally for 

 this reason, that John Bernoulli attempted to substitute, for his son's calcula- 

 tions, a method of deducing the motions of fluids more immediately from the 

 gravitation of their different parts. The peculiarity of- John Bernoulli's 

 mode of investigation consists in his imagining the weight of each indi- 

 vidual particle to be transferred to the surface of the fluid, causing there a 

 pressure in the direction of gravity; and he examines the manner in which 

 this force must operate, in order to produce every acceleration which is re- 

 quired for the motion of fluids, in vessels of all imaginable forms. 



Maclaurin, in his treatise of fluxions, investigated several of the proper- 

 ties of fluids in his usual concise and elegant manner. His remarks on the 

 positions of the sails of windmills and of ships are peculiarly interesting: he 

 added much to what had been done respecting the effects of the wind, and 

 showed the possibility of arranging the sails of a ship in such a manner as to 

 make her advance with a greater velocity than that of the wind itself. At 

 that time, however, the science of hydraulics had been too little assisted by 



