WATER. 



velocity of a river its fquare root ; this gives the velocity 

 at the furface ; and by fubtrafting the fame fquare root, 

 we get the velocity at the bottom. 



N. B. 2.618 — ,/ 2.618 = I, and .382 + ^/ .382 = I ; 

 which it may be ufeful to remember, with reference to this 

 laft rule. 



Dr. Young made a comparifon of his general theorem, as 

 above, with forty experiments extrafted from the colleftion 

 which ferved as a bafis for Du Buat's calculations ; and he 

 found that the mean error of his formula is -j^-th of the whole 

 velocity, and that of his own iVth only. But, omitting the 

 four experiments, in which the fuperficial velocity only of a 

 river was obferved, and in which he calculated the mean velo- 

 city by Dii Buat's rules, the mean error of the remaining 36 

 is but 3-5-th, according to Dr. Young's mode of calculation, 

 and -TT-th according to M. Du Buat's ; fo that, on the whole, 

 the accuracy of the two formulas may be confidered as pre- 

 cifely equal with refpeft to thefe experiments. 



In the fix experiments which Du Buat has wholly rejefted, 

 the mean error of his formula is about TrVth, and that of 

 Dr. Young's TTsth. In fifteen of Gerftncr's experiments, 

 the mean error of Du Buat's rule is id, that of Dr. Young's 

 ^th ; and in the three experiments which Dr. Young 

 made with very fine tubes, the error of his own rules is -rVth 

 of the whole ; while in fuch cafes Du Buat's formuls com- 

 pletely fail. 



It would be ufelefs to feek for a much greater degree of 

 accuracy, unlefs it were probable that the errors of the expe- 



riments themfelves were lefs than thofe of the calculations. 

 But if a fufficient number of extremely accurate and fre- 

 quently repeated experiments could be obtained, it would 

 be very poffible to adapt Dr. Young's formula ftill more 

 correftly to their refults. 



In order to facilitate the computation. Dr. Young made' 

 tables of the co-efhcients a and c for 44 different values of 

 a, both in French and Englirti inches, which may be feen 

 in the Philofophical Tranfaftions for 1808 ; but inftead of 

 inferting them, we fhall give a far more extended table, 

 which we have carefully deduced from Dr. Young's formula- 

 and table, and put it in a form more direftly applicable to 

 praftice. 



Let d reprefeni four times the hydraulic mean depth of 

 an open canal. 



Note. — The hydraulic mean depth is the area of the feftion 

 through which the water runs, divided by fo much of the 

 circumference of that feftion as is touched by the water. 



Not£ alfo. — In cafe of clofe pipes running a full bore of 

 water, the diameter of the pipe is four times the hydrau- 

 lic mean depth. 



s reprefents the fine of the inchnation of the water's 

 furface ; that is, the height of the head or rife, divided by 

 the length or diftance of the flope in which fuch rife takes 

 place. 



V, the mean velocity per fecond, in inches. 



The other fymbols ufed in the theorem are (hewm at the 

 head of the different columns of the Table. 



Dr. Thomas 



