426 MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 
the expenditure of differently shaped orifices and tubes,, but particularly on the 
lateral communication of motion by the cohesion of fluids. Coulomb first 
approximated to the solution of the question, by a very ingenious apparatus, 
consisting* of discs of different sizes, fixed by their centres to the lower extre- 
mity of a brass wire, and made to oscillate in fluids by the force of torsion 
only; he concluded that the resistance was a function, composed of two terms, 
one proportional to the first, the other to the second powers of the resistance : 
again, that it was not sensibly increased by increasing the height of the fluid, 
but simply by the cohesion of the particles of the fluid which presented greater 
or less resistance, in proportion to the viscidity of the fluid, oil being to water 
in the ratio of 17-5 to 1. But whatever might be the conclusions of Coulomb, 
it is obvious that both the size and construction of his apparatus were ill cal- 
culated to produce results whereon to found a satisfactory theory; and accord- 
ingly both Messrs. Prony and Girard, in expressing their formulae of resist- 
ance, have not admitted that of Coulomb, but have adopted the mean of the 
best of experiments made by other authors : but as these formulae give only 
the mean velocity, which is much greater than the velocity (of the fluid con- 
tiguous to the pipe) which ought alone to enter into the expression of the re- 
tarding force, it follows, that the coefficients deduced from the mean of all the 
experiments adopted by these gentlemen, have a value greatly inferior to the 
motion of the fluid contiguous to the side of the pipe or conduit. To ascer- 
tain correctly the value of this kind of resistance, M. Girard (vide les Memoires 
des Seavans etrangers for 1815), undertook a prodigious number of experi- 
ments on tubes of different diameters and length, from which he deduced that 
the retardation is as the velocity simply. The effects of temperature are very 
remarkable; if the velocity be expressed by 10, when the temperature is 0° 
centigrade thermometer, the velocity will be 42°, or increased four times when 
the temperature is 85°: these values must be deemed approximations only. 
The contributions of British philosophers towards the improvement of this 
science have been, unfortunately, scanty ; for, with the exception of Sir Isaac 
Newton (who led the way), Dr. Jurin, Dr. Matthew Young, Dr. Desagu- 
liers, Dr. Vince, Mr. Smeaton, Mr. Banks, and the late Dr. Thomas Young, 
(see the paper of the latter gentleman in the Philosophical Transactions, and 
his commentaries on Eytelwein’s experiments,) we can scarcely find any 
