282 LECTURE XXX. 



Dalembert attempted, in his treatise on the motions of fluids, which was 

 published in 1744, to substitute for the suppositions of John Bernoulli, a 

 more general law, relating to all changes produced in the motions of a 

 system of bodies by their mutual actions on each other ; but his calculations 

 are more intricate and less easily understood, than some others which are 

 capable of an application equally extensive. The late Professor Kaestner 

 of Gottingen has defended Bernoulli against Dalembert's objections with 

 some success, and has in many instances facilitated and extended Ber- 

 noulli's theory; but there is often a singular mixture of acuteness and 

 prolixity in this author's works.* By the side of an intricate and difficult 

 fluxional calculation, he inserts a long string of logarithms for performing 

 a simple multiplication ; and in a work which comprehends the whole 

 range of the mathematical sciences, he does not venture to determine the 

 square root of 10 without quoting an authority. 



About the same time, the profound Leonard Euler applied himself, with 

 some success, to the examination of the motions of fluids, particularly as 

 they are connected with the subjects of seamanship and naval architecture ; 

 but the investigations of Euler are in general more remarkable for mathe- 

 matical address than for philosophical accuracy and practical application ; 

 although his calculation of the resistance of the air to the motions of pro- 

 jectiles may be employed with considerable advantage by the gunner. 



The beginning of the modern experimental improvements in hydraulics 

 may perhaps be dated from the investigations of Smeaton respecting the 

 effects of wind and water, which were published in the Philosophical 

 Transactions for 1759. His observations are of material importance 

 as far as they are capable of immediate application to practice, but he has 

 done little to illustrate their connexion with the general principles of me- 

 chanics. It was Mr. Borda that first derived from a just theory, about 10 

 years after, the same results, respecting the effects of undershot water 

 wheels, as Smeaton had obtained from his experiments. Before this time, 

 the best essay on the subject of water wheels was that of Elvius, published 

 in 1742 ; his calculations are accurate and extensive ; but they are founded, 

 in great measure, on the imperfect suppositions respecting the impulse of a 

 stream of water, which were then generally adopted. 



Our countryman Mr. Watt obtained, in 1769, a patent for his improve- 

 ments of the steam engine, which includes almost every essential change 

 that has been made since the time of Beighton. On a subject so important, 

 it cannot be superfluous to insert the words of the inventor, whose admirable 

 application of the sciences to practical purposes, most justly entitles him to 

 a rank among philosophical mechanics, not inferior to that of Ctesibius and 

 Dr. Hooke, 



" My method of lessening the consumption of steam, and consequently 

 fuel, in fire engines," says Mr. Watt, in his specification of his patent, 

 "consists of the following principles. First, that vessel in which the 

 powers of steam are to be employed to work the engine, which is called 

 the cylinder in common fire engines, and which I call the steam vessel, 

 must, during the whole time the engine is at work, be kept as hot as the 

 * Dissertationes Math, et Phys. 4to, Altenb. 1776. 



