280 LECTURE XXX. 



determination of the oscillations of fluids in bent tubes, was a good begin- 

 ning of the investigation of their alternate motions in general. 



The accurate experiments of Poleni were published in 1718. He has the 

 merit of having first distinctly observed that the quantity of water dis- 

 charged by a short pipe is greater than by a simple orifice of the same 

 diameter ; although there is some reason to suppose that Newton was before 

 acquainted with the circumstance. 



In 1 727, Mr. Bouguer received a prize from the Academy of Paris for his 

 essay on the masts of ships, which is said to be ingenious, but by no means 

 practically useful. He was, probably, tempted by this encouragement to 

 continue his application to similar studies ; and, about twenty years after- 

 wards, he published his valuable essay on the construction and manoeuvres 

 of ships, which appears to have superseded all that had been done before 

 respecting the subjects of his investigation. 



The first researches of Daniel Bernoulli concerning the properties and 

 motions of fluids, bear also the date of 1727. This justly celebrated man 

 was as happy in his application of mathematics to natural philosophy, as he 

 was ready and skilful in his calculations. The greatest part of his hydraulic 

 theorems are founded on the principle first assumed by Huygens, and called 

 by Leibnitz the law of living or ascending force, which is confessedly only 

 true where there is no loss of velocity, from the imperfection of the elasticity 

 of the bodies concerned ; for it is only with this limitation that the motions 

 of any system of bodies are always necessarily such as to be capable of 

 carrying the common centre of gravity to the height from which it has de- 

 scended while the bodies have been acquiring their motions. This law of 

 ascending force is of considerable utility in facilitating the solution of a great 

 variety of problems. It is certain that mechanical power is always to be 

 estimated by the product of the mass of a body into the height to which it 

 is capable of ascending ; and whatever objections may have been made to the 

 employment of this product as the measure of the force of a body in motion, 

 which is indeed an expression inconsistent with a correct definition of the 

 term force, yet it must be confessed, on the other hand, that some of the best 

 English mathematicians have fallen into material errors for want of paying 

 sufficient attention to the general principle. Bernoulli estimates very justly 

 in this manner the mechanical power of a variety of natural and artificial 

 agents, and among the rest he examines that of gunpowder ; but, from an 

 accidental combination of errors, he states the force of a pound of gun- 

 powder as equivalent to the daily labour of 100 men, while, in fact, the 

 effect which is actually obtained from two tons of powder is no greater than 

 that 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 wind 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 

 produces absolutely no effect at all. 



* Fluxions, 2 vols. 4to, Edin. 1742, art. 914. 



