204 OUTLINES OF NATURAL PHILOSOPHY. 



the greatest and least velocities, as computed in the 

 last proposition. 



The mean velocity is, therefore, v V v -f _ . 



The formulas of Du BUAT have been reduced to great 

 simplicity by PHONY, so that they are free from 

 logarithms, and require nothing more than the ex- 

 traction of a square root. Reclierches Physico-Ma- 

 tUematiques sur la Theorie des Eaux Courantes. Pa- 

 ris 1804. 



Let V, as before, be the mean velocity ; A the length 

 of an open canal, or of a close pipe ; z the difference 

 of level of its two extremities ; R the radius, defined 

 as in Du B,UAT^S propositions, in the case of a river or 

 open cut ; D the diameter, in the case of a pipe ; h 

 the height of the water in the reservoir above the up- 

 per orifice of the pipe, and h' the height above the 

 lower orifice, at which the water stands in the cis-, 

 tern into which it is emptied, through that orifice. 



Let -, or the sine of the inclination I ; and 



295. The denominations above being supposed, 

 we have for pipes, 



V ^ * 1541131 + \/- 023751 + 32806 . 6 x r DK, 



4 



and 



