432 MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 
Conclusions. 
1. That the resistances are as the square of the velocities. 
2. That the mean resistances of circular discs, square plates, and globes in air, are as the numbers 
25.180, 22.010, 10.627; and in water, 1.18, 1.36, 0.755 ; consequently the proportional resistance of 
air to water, with 
Circular discs, is as 1 to 21.3 
Plates and fans . . 1 to 16.2 
Wooden balls ... 1 to 2.2 
Note . — A portion of the square fans, represented by the letters a, b, c, d, in Plate XII. fig. l,and 
equal to one fourth of the area of each fan, was cut off, when the resistance was found to be the same 
as with the square fans. 
Experiments on the Quantities of Water discharged by Orifices and Tubes of 
different diameters and lengths, and at different altitudes. 
The phenomena incident to spouting fluids are, 
First, The inequality observed in the velocity of the particles comprised in 
every horizontal section parallel to the orifice. 
Secondly, The contraction of the fluid vein beyond the orifice, and conse- 
quent diminution of discharge as compared with theory. 
Thirdly, The inversion and changes in the sections of the fluid vein at dif- 
ferent distances from the orifices. 
All these phenomena have been noticed and recorded by various writers, 
and formulae adapted to the different circumstances of the expenditure have 
been given. But neither Bossut nor Du Buat (the most accurate of writers) 
have recorded a continuous and systematic series of experiments upon the 
comparative expenditure of orifices and tubes under the circumstances of area, 
altitude, and length. 
The apparatus with which these experiments were performed, consisted of a 
wooden cistern very accurately made, two feet square inside, and four feet 
four inches in height. The water was kept at a constant altitude by a regu- 
lating cock ; and a float having an index attached to it enabled the observer 
to ascertain the exact height at which the water stood in the cistern above the 
centre of the orifice. 
The orifices were accurately made by Dollond in brass plates one sixtieth 
of an inch in thickness. The plates were accurately adjusted to a hole in the 
