424 MR. RENNIE ON THE FRICTION AND RESISTANCE OF FLUIDS. 
and uncertain. Accordingly we find that the subject of fluids attracted the 
attention of some of the most distinguished mathematicians and philosophers 
of Europe for the last two centuries; that is, from the year 1628, when Castelli 
first published his Treatise on the Measure of running Water, down to the 
hydraulic investigations of Eytelwein and Young. Between these periods, 
Italy, France, Germany and England, added their contributions to the science. 
But it is to the Italians principally that we owe the foundation of it, in their 
numerous investigations and controversies on the rivers of Italy ; hence the 
writings of Castelli, Viviani, Zendrini, Manfredi, Polini, Frisi, Gulielmini, 
Lechi, Michellotti, and of many others *. 
Each of them has endeavoured to establish a theory applicable to rivers and 
torrents, but in general with indifferent success. The science again received 
fresh accessions from the more valuable investigations of Bossut, Bubuat, 
Venturi, Funck, Brunning, Bidone, Coulomb, Prony, Eytelwein and Girard; 
and among our own countrymen, of M’Claurin, Vince, Matthew Young, 
Dr. Jurin, Professor Robinson, and the late Dr. Thomas Young. Sir Isaac 
Newton had already demonstrated, in his celebrated propositions 51, 52, and 
53, of the Principia, (in the case of a cylinder in motion immersed in a fluid,) 
that the resistance arising from the want of a perfect lubricity in fluids is 
(cseteris paribus) proportional to the velocity with which the parts of a fluid 
separated from each other ; and that, if a solid cylinder of infinite length 
revolves with a uniform motion round a fixed axis, in a uniform and infinite 
fluid, the periodical times of the parts of the fluid thus put in motion will be 
proportional to their distances from the axis. This theory (although conform- 
able to experiment) was objected to by Bernoulli and D’Alembert, on the 
ground that Sir Isaac Newton had not taken into consideration the centrifugal 
force or friction arising from the pressure of the concentric rings or filaments 
round the cylinder, the fluid being supposed in a state of permanence, and the 
friction of the rings equal throughout. 
Pitot (1728), in his experiments on the water-works at Marly and Versailles, 
was the first to demonstrate that with equal velocities, and in the ratio of the 
volume of water, the friction of water in pipes was in the inverse ratio of their 
* Raccotta d’ Autori che trattano del Moto dell’Acque. 
