HYDRODYNAMICS. 



547 



MM 



Fluid*. 



Rt- :r < - 



r< , 



pi'.: I h 

 r . -. y 



In the preceding Table, column 1st contains the 

 angles of inclination at which the plane surface struck 

 the fluid. Column d shews the resistance by experi- 

 ment in the direction of their motion in Troy ounces. 

 Column 3d shews the resi.-tance by theory, the per- 

 pendicular resistance being supposed the same as that 

 which is deduced from experiment. Column 4th 

 contains the exponent of the power of the sine of 

 the angle to which the resistance is proportional. 

 This column was computed in the following man- 

 ner : Calling s the sine of the inclination, and r the 

 corresponding resistance; then, if r is proportional 

 to the with power of *, or to ** , we have sin. 90*, or 1 * 



J- = 2321 : rand*- = 



and, consequently, 



According to theory, the 



Log. r Log. 0.2321 

 vi = ^ 



Log.* 



resistance in the direction of the motion of the plane 

 should vary as the cube of the sine (Prop. II. Cor. 

 p. .3 12) ; but it appears from the Table, that it varies in 

 a much less ratio, but not as any constant power, or as 

 any function of the sine and cosine. The actual resist- 

 ance, therefore, must always exceed the theoretical resist- 

 ance, which Mr Vince attributes partly to the part of the 

 force parallel to the plane being neglected in the theory, 

 but which appears to be really a pan of the force which 

 acts upon the plane. 



When the plane surface was struck by the fluid in mo- 

 tion, Mr Vince obtained th results contained in the 

 following Table. 



TABLE thriving the Resistance of a Plane Surface tlrmci 

 by a Fluid in Motion, and inclined at different Angle* 

 to the line of ilt Motion. 



The coincidence between the experimental and the 

 theoretical results is very surprising, the difference be- 

 ing nothing more than might have been expected from 

 the ordinary inaccuracy of experiments. It follow*, 

 therefore, from Mr Vince's experiments, that when the 

 rtuid i.t in motion, the resistance varies as the sine of 

 the angle of the plane's inclination. 



The difference between the resistances in the two 

 cases confirm the results obtained by Du Boat, and 

 prove, that the resistance when the plane moves is to 

 the resistance when the fluid moves as 5 to 6, a result 

 which Mr Vince ancribes to the action of the fluid be- 

 bind the body when in motion. 



*. Account of Cmlomb't Experiment! on tkt Resistance 

 of Flu id t in Slo Motion*. 



NOTWITHSTANDING the great value of the expert. 



mcnts of Bossut and Du Buat, yet none of these au- Resistance 

 thors succeeded in determining; the true law of the of Muid^ 

 resistance of fluids. This honour vv;n reserved for A '^ u j lto f 

 the late M. Coulomb, who first entertained the hap; y Cnulmob'i 

 idea of ascertaining the laws of the resistance of fluids experiments 

 in slow motions, by the oscillation of horizontal discs on the re- 

 in consequence of the torsion, or the twisting and un- a' st ', nce ^ 

 twisting of the wire by which they were suspended. ul 

 In the present Section we shall endeavour to lay before 

 our readers as distinct an account as possible of the in* 

 vestigations of this celebrated philosopher. 



When a body in motion strikes a fluid at rest, it ex- 

 periences two kinds of resistance. One of these arises 

 from the cohesion of the fluid particles, which are se- 

 parated from each other by the moving body ; and as 

 the number of molecules thus separated is proportional 

 to the velocity of the body, this part of the resistance 

 depending upon the cohesion, will likewise be propor- 

 tional to the simple velocity. 



The other part of the resistance arises from the in- 

 ertia of the fluid particles, which being struck by 

 the body, acquire a degree of velocity proportional to 

 the velocity of the body ; but as the number of these 

 parts is proportional to the velocity, there ought to 

 anse a resistance proportional to the square of the ve- 

 locity. Hence the theory seems to inform us, that 

 the reiitlance nf fluids thould be represented by the sum 

 ot (nx> ifuaiilitiet, one oj which it proportional to the tint' 

 fte arlocily, and the other to the square of the velocity. 

 This theoretical result was completely verified by 

 Coulomb's experiments. 



In order to submit these views to the test of experi- 

 ence, the ordinary methods of measuring the resist- 

 ance of fluid* are of no avail. When the moving body 

 has a velocity about eight or nine inches per second, 

 the resistance is always proportion.il to the square of 

 the velocity ; but when the velocity does not exceed 

 four-tenths of an inch per second, the part propor- 

 tional to the simple velocity becomes sensible ; but as 

 the velocity is extremely small, the resistance it also 

 very small, and therefore the ordinary means cannot be 

 used either in measuring the resistance, or in separating 

 the parts due to the different terms of the formula. 

 Coulomb therefore found it necessary, 1. To employ 

 measure, by which he could determine with great 

 exactneM very small forces. And, 2. To have it in hit 

 power to give to toe moving body a degree of velocity 

 so small, that the part of the resistance proportional to 

 the square of the velocity might be compared with the 

 other terms of the function which represent the retut- 

 ance ; or to be able to make the part of the resistance 

 proportional to the square of the velocity so small 

 compared with the other terms, that it might be safely 

 myl.-ctid. 



These object* were completely gained, by employing Appirattu 

 the apparatus represented in Plate CCCXIX. Fig. 11 .""ployed 

 where ABC is a stand, having a horizontal arm BC, to j^ " 

 which is fixed the small circle ef, perforated in the PI.ATB 

 centre for the purpose of admitting the cylindrical pin rccxix. 

 b a. Into a slit in the extremity of this pin is fas- <''* It. 

 tened, by means ofa screw, the bras* wire a g, whose 

 force of torsion is to be compared with the resistance of 

 the fluid ; and its lower extremity is fixed in the same 

 way into a cylinder of copper g d, whose diameter is 

 about four-tenths of an inch. The cylinder g d is per- 

 pendicular to the disc DS, whose circumference if di- 

 vided into 480 equal part*. When this horizontal disc 

 is at rest, which happen* when the tor-ion of the 

 Iras* wire U nothing, the index RS if placed upon 



