170 Dr. Young’s Hydraulic Investigations. 
error of the remaining 3 6 is j T , according to my mode of 
calculation, and —• according to Mr. Dubuat's ; so that on 
the whole, the accuracy of the two formulae may be con- 
sidered as precisely equal with respect to these experiments. 
In the six experiments which Dubuat has wholly rejected, 
the mean error of his formula is about and that of 
mine -' T . In fifteen of Gerstner’s experiments, the mean 
error of Dubuat’s rule is one third, that of mine one fourth; 
and in the three experiments which I made with very fine 
tubes, the error of my own rules is one fifteenth of the whole, 
while in such cases Dubuat’s formulae completely fail. I have 
determined the mean error by adding together the logarith- 
mic ratios of all the results, and dividing the sum by the 
number of experiments. It would be useless to seek for a 
much greater degree of accuracy, unless it were probable that 
the errors of the experiments themselves were less than those 
of the calculations ; but if a sufficient number of extremely 
accurate and frequently repeated experiments could be ob- 
tained, it would be very possible to adapt my formula still 
more correctly to their results. 
In order to facilitate the computation, I have made a table 
of the coefficients a and c for the different values of d, all the 
measures being still expressed in French inches. 
fi 
