HYDRODYNAMICS. 





<* diminution of the oscillation? were carefully obserred. 

 The diminution tor a complete circle of torsion wa 

 ^~! found to be nearly a fourth part of the circle for the 

 ^, first oscillation ; but always the same, whether the ex- 

 Bau periment was made in a vacuum or in the atmosphere. 

 re- A small pallet, 50 millimetres long (l.9(>9 English 

 1 of inches), and 10 millimetres broad (O.S937 English inch- 

 e), which struck the water perpendicular to its plane, 

 furnished a similar result. We may therefore conclude, 

 that when a submerged body moves in a fluid, the 

 pressure which it sustains, measured by the altitude of 

 the superior fluid, does not perceptibly increase the re- 

 sistance; and consequently that the part of this resist- 

 ance proportional to the simple velocity, can in no re- 

 poet be compared with the friction of solid bodies, 

 which is always proportional to the pressure. 



These experiments were twice repeated in the cabi- 

 net of the Institute, in the presence of M. Charles and 

 M. Lsttsuze. 



The attention of M. Coulomb was next directed to 

 the determination of the resistance experienced by cy- 

 linders that moved very slowly, and perpendicular to 

 their axes. When a cylinder, however small be its dia- 

 meter, moves perpendicularly to its axis, the fluid par- 

 ticle* which it strikes partake necessarily of its motion, 

 anil therefore it is not possible in the reduction of the 

 experiments, to neglect the part of the resistance which 

 is proportional to the square of the velocity. Hence 

 be was obliged to perform the experiments in such a 

 manner that both parts of the resistance might be com- 

 puted. The three cylinders, which were successively 

 subjected to trial, had a length of 9.803 inche*. The 

 cylinders were fixed by their middle under the cylinder 

 gd,to that they formed two horizontal radii, the length 



803 

 afMch ofwhioh was ^5-=* 9015 inches. The diitme- 



tenof the cylinder* were determined from tlicir weight. 

 After making the neceumy experiments with cylinders 

 whose diameters were 0.87 millimetre!", 11.2 milliimv 

 tres, and 21.1 millimetres, he found, from a compan- 

 ion of the results, that the part of the resistance pro- 

 portional to the simple velocity, which we -lull call r, 

 M not in different cylinder* in the .nnr rat: > a< the cir- 

 cumference of these cylinders, the ratio of their circum- 

 ferences being aa 24 to 1 , while the values of r were as 

 S to 1. In order to explain this result. Coulomb 'op- 

 poses that the particle* which in mediate!)- touch the 

 cylinder, take the tame velocity a* the r;.' ndcr ; that 

 the panicles a little farther distant talc a* smaller velo- 

 city ; and that at the distance of about one-tenth of an 

 inch, the velocity ceases entirely. I U-nce it is at this 

 last point that the cohesion ceases to have an influence 

 on the resistance. Upon these suppositions, which 

 Coulomb thinks require confirmation, he proposes to 

 augment, by a constant quantity, the circumferences of 

 all the cylinders, hifgn comparing them with their re- 

 sistance. This constant quantity to be added to the 

 circumferences, he found to be <).HH millimetres, or 

 lieail? an addition of three millimetres to thrir diameter; 

 which shews that the portion of the fluid molecules de- 

 .acho-1 from one another by the moving -j lnidiT extends 

 nearly to a distance of 1.5 millimetres from their cir- 



fmntM. 



I.i comparing the part of the resistance proportional 

 o the qiiare of the velocity, which we shall call R, with 

 imcters of the cylinders, it will be seen that these 

 tie in small cylinders are much greater than they 

 ooglrt to be hi relation to their diameters, but in a 



much less ratio than in the preceding case. The aug- 

 mentation of the circumferences is in this case only 1 . 7 T 

 millimetres, which is scarcely one-fifth of the former 

 augmentation. Coulomb explains this difference from 

 the theory in the following manner. All the fluid par- 

 ticles, when they arc detached from one another, op- 

 pose the same resistance, whatever be the velocity 

 which they take ; so that as the quantity r depends only 

 on the cohesion, the resistance due to their cohesion 

 will extend only to the point where the velocity of the 

 molecules of the fluid is nothing. In the comparison 

 of the quantities R, all the particles are supposed to 

 take a velocity equal to that of the cylinder ; but as it 

 is only the molecules in immediate contact with the 

 cylinder that take this velocity, it follows that the aug- 

 mentation of the diameter in determining the value of 

 R, which answers the square of the velocity, should be 

 lew than in determining r, which is due to the cohe- 

 sion. Besides, as Coulomb observes, these different 

 degrees of lateral velocity, from the point of contact 

 with the cylinder, where the velocity is equal to that 

 of the cylinder, to the point where the cohesion ren- 

 ders the velocity nothing, ought to follow laws which 

 new observations may soon determine, and which may 

 throw great light upon tikis interesting branch of ph\ - 

 sica. 



In determining by experiment the part of the mo- 

 mentum of resistance proportional to the velocity in 

 two cylinders of the same diameter but of different 

 lengths, Coulomb found that the momentum of resist- 

 ance was proportional to the cubes of their diameters. 

 The same result is obtained from theory ; for supposing 

 each cylinder to be divided into the same number of 

 parts, the length of each part will be proportional to 

 the total length. The velocity of the corresponding 

 parts will be as the same lengths, and also as the dis- 

 tance of these parts from the centre of rotation. The 

 theory likewise indicates that the part of the momen- 

 tum of resistance depending on the square of the velo- 

 city, in two cylinders of the same diameter, but of dif- 

 ferent lengths, is proportional to the fourth power of 

 the length of the cylinder. 



Coulomb now proceeds to determine the real resist- 

 ance due to the simple velocity which .1 cylinder expe- 

 riences while oscillating parallel to itself, nnd perpen- 

 dicular to its axis. When the cylinder 9-803 inches long, 

 and 0.04409 inches in circumference, was made to os- 

 cillate with a velocity of 5.51 2 inches per srcond, the 

 part of the resistance r was equal to 58 milligramme*, 

 or .8^32 troy grain* ; and when the velocity was 0.3937 

 inches per second, the resistance was 0.001-14 grammes, 

 or 0.637 troy grains. Hence we may conclude, that 

 the resistance of a cylinder of the same diameter, but 

 of a metre in length, or 89.37 inches, will be about 17 

 milligrammes. 



The preceding experiments were repeated in the 

 same oil which was formerly used, and at the same 

 temperature ; and he found as formerly that the cohe- 

 sion of oil was to that of water as 17 to 1. He consi- 

 ders oil as preferable to water fur determining r ; for 

 in the case of small velocities, the part R disappears al- 

 most entirely. 



In these experiment* Coulomb observed an effect 

 which he could not have anticipated. Although the 

 cohesion of the oil is 1 7 times greater than that of wa- 

 ter, yet the augmentation of the diameters of the cylin- 

 ders, which it was necessary to apply, was only 3 mil- 

 limetres, the same as for water. He observed also ano- 

 ther curious fact, which is more easily understood, vi/. 



jnce 



jl Huids. 



Account of 

 Coulomb's 

 experiments 

 on the re- 

 sistance of 

 fluids. 



On the r- 

 sutance of 

 cylinders. 



Real rttirt- 

 nct of* 

 given cylin- 

 der. 



