tjydraulic Investigations. \q$ 



the mean error of his formula is about -5V, and that of mine 

 Vt» In fifteen of Gerstner's experiments, the mean error 

 of Dubuat's rule is one third, that of mine one fourih; 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 lo- 

 garithmic 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 ex- 

 tremely accurate and frequently repeated experiments could 

 be obtained, 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 t wk 

 the measures being still expressed in French inches* 



Table of Coefficients for French Inches. 



For example, in the last experiment, where d is 1, / 4, 

 and h 27 1, we have a = -0000259, h 



Vol. 33. No, 130. Feb, 1809. 



«/ : d f QQ182 



516, 



