ON dubuat's hydraulic theorem. 309 



XII. 



Trantformation of Mr. Dnhuafs Hydraulic Theorem, Bif 

 Thomas Young, M,D. F,R,S. 



To Mr. NICHOLSON. 

 SIR, 



i 



N the course of some investigations respecting the mo- Dubuat's hy- 

 tion of the blood, and the rause of fever, I have had occa- transformed, 

 sion to employ the rules derved from the hydraulic experi- 

 ments of Dubuat ; and haviudj reduced them into a more 

 correct form than those which are mentioned in the second 

 volume of my Lectures on Natural Philosophy, p« 225, I 

 beg leave to make public, through the medium of your 

 Journal, the formula which I have obtained. 



Dubuat's rule, reduced to English inches, is "^ — b, 



h 



and V — 153 [*/ cZ — -2) . ( — -} — ; ^ — -001) 



I being the length of a pipe, d its diameter, h the height 

 of the reservoir, and tj the velocity in a second. Now 



hA.xzznxii — M, when n is infinite, for the fluxion ''J^JL 



becomes ultimately ~ ; and th6 same is very nearly true 



when n is any large number: we may therefore express 

 the hyperbolical logarithm, taking n zr l6, in the terms 

 d i tV — S 4-1-,; and the whole formula may be changed into 

 another, which will often be more convenient, in this manner, 

 making c-h^\-^\yV=. 153 (v^(/ — -2) . (— ^ + ''Sl±l 



— '0012.) This expression will be found as near the truth, 

 in all cases, as can be supposed to have been correctly as- 

 certained by Pubuat's experiments. 



I am, SIR, 



Your very obedient servant, 



THOMAS YOUNG. 



Wdhech Street, 22 Nqv, 



XIII. 



