548 



HYDRODYNAMICS. 



of Fluids. 



Account of 

 Coulomb's 

 i xperinients 

 on the re- 



. i-unce of 

 fluids. 



General re- 

 sults. 



the point 0, the zero of the circular scale. The small 

 rule R m may be elevated or depressed at pleasure 

 round its axis n ; and the stand GH which supports it 

 may be brought into any position round the horizon- 

 tal disu. The lower extremity of the cylinder g d is 

 immersed about two inches in the vessel of water 

 MNOP, and to the extremity rf is attached the discs, or 

 the bodies, whose resistance is to be determined when 

 they oscillate in tne fluid by the torsion of the brass 

 wire. 



In order to produce these oscillations, the disc DS, 

 supported by both hands, must be turned gently round 

 to a certain distance from the index, without deranging 

 the vertical position of the suspended wire. The disc 

 !>eing then left to itself, the force of torsion causes it 

 to oscillate, and the successive diminution of these 

 oscillations is carefully observed. A simple formula 

 {jives in weights the force of torsion that produces the 

 oscillations ; and another formula well known to geo- 

 meters, determines (by an approximation sufficiently 

 accurate in practice) by means of the successive dimi- 

 nution of the oscillations, compared with their ampli- 

 tude, what is the law of the resistance, relative to the 

 velocity which produces these diminutions. 



The method employed by Coulomb in reducing his 

 experiments, is nearly the same as that by which Newton 

 and others determined the resistance of fluids from 

 the successive diminution of the oscillations of a pen- 

 dulum vibrating in a fluid ; but Coulomb's apparatus is 

 not liable to any of the objections which attach to the 

 use of the pendulum. It would be impossible, with- 

 out a previous explanation of the principles of torsion, 

 and a discussion too long and minute for the limits of 

 our work, to make our readers acquainted with the 

 various steps of Coulomb's investigation. All that we 

 can pretend to do, is to give an account of the different 

 physical results which he obtained. 



Having attached to the lower extremity of the cy- 

 linder g d a circular white iron plate, about 6.677 

 inches in diameter, he found that when its oscilla- 

 tions were so slow, that the part of the resistance 

 proportional to the square of the velocity was greatly 

 inferior to the other part, the resistance which di- 

 minished the oscillations of the horizontal plate was 

 uniformly proportional to the simple velocity, and that 

 the other part produced no sensible effect upon the 

 motion of the disc. He likewise found, in conformity 

 with theory, that the momenta of resistance in different 

 circular plates oscillating in a fluid, are as the fourth 

 power of the diameters of these circles, when the re- 

 sistance is proportional to the simple velocity ; and 

 that when a circle, 6.677 inches in diameter, oscil- 

 lated with the velocity of 5.512 inches per second in 

 its circumference, the momentum of resistance which 

 the fluid opposed to its circular motion, was equal to 

 TS- of a gramme, multiplied by a lever 143 millimetres 

 long, or 1.544 English Troy grains, at the end of a 

 line 5.63 English inches long. Hence it follows, that 

 the resistance of the two circular surfaces of the disc, is 

 rqual to a weight of 0.587 grammes. 



If the plane or disc had only a velocity of ten milli- 

 metres, or one centimetre, the resistance would be only 

 0.04.2 grammes. In like manner it follows, that the 

 resistance experienced by a surface of one square metre, 

 moving with a velocity of one centimetre per second, 

 is 0.703 grammes. 



In order to determine comparatively with water the 

 cohesion of different fluids, he filled a large vessel with 



c larified oil, such as is used in commerce for the lamps 

 called Quinquet ; and he i'ound its temperature to be 

 16" of Reaumur's scale, which he marked, because the 



,..,. . . 



cohesion of oil varies with the temperature, though this 



variation is not sensible in water by small change* of 

 temperature. By causing discs of different diameters to 

 oscillate in the oil, he found that the momenta of re- 

 sistance for two circles, moving round their centre in 

 the plane of their superficies, varies as the fourth 

 power of the diameter, a result which is also conforma- 

 ble with theory. The agreement of these results, Cou- 

 lomb considers as leaving no doubt respecting the 

 certainty of the term proportional to the velocity in 

 the resistance of fluids. 



From these experiments, Coulomb likewise conclu- 

 ded that the difficulty which the same disc moving with 

 the same degree of velocity -experienced in separating 

 the particles of oil, was to the difficulty which it expe- 

 rienced in separating the particles of water as 17.5 to 

 1, which will therefore express the ratio between the 

 mutual cohesion of the particles of oil, and the mutual 

 cohesion of the particles of water. 



The next object of our author was to determine two 

 important points. 1st, If the resistance of a body was 

 influenced by the nature of its surface ; and, 2ci, if it 

 was influenced by the pressure of the superincumbent 

 fluid. In order to settle the first of these points, he 

 covered the surface of a circle of white iron with a film 

 of tallow, and wiped it slightly away, that the thick- 

 ness of the plate might not be sensibly increased. He 

 then caused this circle to oscillate as before; and he ob- 

 served that the successive diminution of the oscilla- 

 tions was exactly the same as before the application of 

 the tallow. Upon the coat of tallow he next scattered, 

 by means of a sieve, a quantity of sand, which adhered 

 to the surface ; and he found that the resistance to the 

 oscillations of the plate was not sensibly increased. 

 Hence he concludes, that the part of the resistance pro- 

 portional to the simple velocity arises from the mutual 

 cohesion of the fluid particles, and not from the adhe- 

 sion of these particles to the surface of the body. What- 

 ever, indeed, was the nature of the surface, there was 

 an infinite number of inequalities where the fluid par- 

 ticles were permanently lodged. 



In order to determine the second point, M. Coulomb 

 caused the bodies to oscillate at two different depths ; 

 one at a depth of .787 inches, and another at a depth 

 of 19.6855 inches, and he found no difference in the re- 

 sistances ; but as the surface of the water supported 

 the whole weight of the atmosphere, it was scarcely to 

 be expected that a pressure of 19 inches of fluid would 

 produce a very sensible increase of resistance. In or- 

 der to decide the question, therefore, M. Coulomb em- 

 plo3 r ed another method. 



Having placed a vessel full of water under the recei- 

 ver of an air-pump, the receiver being furnished with 

 a rod and collar of leather at its top, he fixed to the 

 hook at the end of the rod a harpsichord wire number. 

 ed 7 in commerce, and suspended to it a cylinder of 

 copper like gd, Fig. 11. which plunged in the water of 

 the vessel, and under this cylinder he fixed a circular 

 plane, whose diameter was 10! millimetres (3.975 Eng- 

 lish inches). When the oscillations were finished, and . 

 consequently the force of torsion nothing, the zero of 

 torsion was marked by the aid of an index fixed to the 

 cylinder. The rod was then made to turn quickly 

 round through a complete circle, which gave to the 

 wire a complete circle of torsion, and the successh < 



Hesi ' 

 ot Fluids 



Account ot 



c oll i,, 



on the re- 

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flullls - 



Ratio of tiie 

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On the ef- 

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On the ef- 

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