162 THIRD REPORT — 1833. 



sagacity his observations on the different kinds of resistance 

 experienced in the motion of fluids, and which might have led 

 him to express the sum of the resistances by a rational function 

 of the velocity composed of two or three terms only. Yet the 

 merit of this determination was reserved to M. Coulomb, who, 

 in a beautiful paper, entitled " Experiences destinees a deter- 

 miner la Coherence des Fluides et les Lois de leurs Resistances 

 dans les Mouvemens tres lents," proves, by reasoning and facts, 



1st, That in extremely slow motions the part of the resist- 

 ance is proportional to the square of the velocity. 



2ndly, That the resistance is not sensibly increased by in- 

 creasing the height of the fluid above the resisting body. 



3rdly, That the resistance arises solely from the mutual co- 

 hesion of the fluid particles, and not from their adhesion to the 

 body upon which they act. 



4thly, That the resistance in clarified oil, at the temperature 

 of 69° Fahrenheit, is to that of water as 17*5 : 1 ; a proportion 

 which expresses the ratio of the mutual cohesion of the par- 

 ticles of oil to the mutual cohesion of the particles of water. 



M. Coulomb concludes his experiments by ascertaining the 

 resistance experienced by cylinders that move very slowly and 

 perpendicularly to their axes, &c. 



This eminent philosopher, who had applied the doctrine of 

 torsion with such distinguished success in investigating the 

 phasnomena of electricity and magnetism, entertained the idea 

 of examining in a similar manner the resistance of fluids, con- 

 trary to the doctrines of resistance previously laid down. 

 M. Coulomb proved, that in the resistance of fluids against 

 solids, there was no constant quantity of sufficient magnitude 

 to be detected ; and that the pressure sustained by a moving 

 body is represented by two terms, one which varies as the 

 simple velocity, and the other with its square. 



The apparatus with which these results were obtained con- 

 sisted of discs of various sizes, which were fixed to the lower 

 extremity of a brass wire, and were made to oscillate under a 

 fluid by the force of torsion of the wire. By observing the 

 successive diminution of the oscillations, the law of resistance 

 was easily found. The oscillations which were best suited to 

 these experiments continued for twenty or thirty seconds, and 

 the amplitude of the oscillation (that gave the most regular re- 

 sults) was between 480 the entire division of the disc, and 8 or 

 10 divisions from zero. 



The first who had the happy idea of applying the law of 

 Coulomb to the case of the velocities of water running in na- 

 tural or artificial channels was M. Girard, Ingenieur en chef 



