and on the Maximum Effect of Machines, 



417 



solution of the problem in the first edition of the "Principia" 

 which he materially altered in the succeeding editions. In the 

 first edition (book 2nd, prop. 37.) he infers, that the reaction is 

 equal to the weight of a column of water of which the base is 

 equal to the area of the orifice, and the height equal to that 

 of the surface of the water above the orifice. In the succeed- 

 ing edition, the subject is more fully discussed in the 36th prop, 

 of the second book, where he infers (cor. 4.) that, when the 

 area of the surface B is indefinitely large compared with that 

 of the orifice, the reaction is, what it was afterwards in a dif- 

 ferent manner demonstrated to be by D. Bernoulli. Sir Isaac 

 Newton further observes, that he found, by admeasurement, 

 the area of the orifice in a thin plate to be to that of the sec- 

 tion of the contracted vein, at the point of its greatest contrac- 

 tion, in the ratio of \/ 2 : 1 nearly. He takes the reaction, 

 therefore, to be greater than what he understood it to -be when 



he published the first edition, in the ratio of \/ 2 : 1 nearly. 

 He refers, however, more to experiment than to theory for a 

 solution of this question ; and many valuable experiments have 

 since been made on effluent water ; yet I cannot find that the 

 results of any direct experiments have been published which 

 go to determine the precise amount of this reaction. 



Sir Isaac Newton suggested (Principia, first edit. p. 332.) a 

 method by which the reaction may be easily measured. If 

 the vessel be suspended like a pendulum, he observes, it will 



New Series, Vol. 3. No. 18. June 1828. 3 H recede 



