MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 441 
the particles of the fluid vein are not reflected in the same angle, and as a 
considerable portion of the velocity is destroyed by the first angle or bend the 
fluid meets with in the pipe, M. Dubuat’s theory is fundamentally erroneous, 
the more especially as he has rejected more than one half of the twenty-five 
experiments mentioned by him. Dr. Young’s suppositions, of the resistance 
being as the angular flexure and the power of the radius, of which the index is 
f, are equally erroneous, as is evinced by the foregoing experiments. 
In conclusion, it is evident that the subject of friction admits of an immense 
variety of applications. To determine the measure of the resistances expe- 
rienced by vessels and floating bodies in their motion through fluids ; the law 
of the retardations of rivers, and the cause of the obstructions presented to the 
waves of the ocean in the slopes assumed by its shores ; the equilibrium of 
earths, and their connection with solids and fluids, — all of them are questions of 
the utmost importance in the economy of nature, and their solution can only 
be attained by an accumulation of facts. 
N.B. Since the foregoing paper was presented to the Royal Society, an abs- 
tract of an extensive series of experiments on the expenditure of water through 
rectangular orifices of large dimensions, has been submitted to the French 
Academy by Messrs. Poncelet and Lesbros, of the Corps de Genie at Metz ; 
and as these experiments were undertaken by order of the French government, 
no expense was spared to have them made as extensive as possible. Their 
objects were principally to ascertain the exact measure of the coefficient of 
contraction and the forms of the fluid veins under different altitudes and areas. 
The results of which are : — 
That with an orifice of 20 centimetres square, the coefficient is 0.600 under 
altitudes of 1 metre 68 centimetres. But when the altitude was reduced to 
four or five times the opening of the orifice, the coefficient increased to 0.605, 
but again diminished rapidly as the altitude diminished, to 0.593. 
That with orifices of smaller dimensions, i. e. from 10 to 5 centimetres 
square, the same law was observed, the coefficients being respectively 0.61 1, 
3 l 2 
