RESISTANCE. 



resistance would be hereby ascertain- 

 ed. 



In this kind of discontinued fluid, the 

 particles being 1 detached from each 

 other, every one of them can pursue its 

 own motion in any direction, at least for 

 some time, independently of the neigh- 

 bouring ones; wherefore, if instead of a 

 cylinder moving in the direction of its 

 axis, a body, with a surface oblique to its 

 direction, be supposed to move in such 

 a fluid, the motion the parts of the -fluid 

 will hereby acquire, will not be in the 

 direction of the resisted body, but per- 

 pendicular to its oblique surface ; whence 

 the resistance to such u body will not be 

 estimated from the whole "motion com- 

 municated to the particles of the fluid, 

 but from that part of it only which is in 

 the direction of the resisted body. In 

 fluids then, where the parts are thus dis- 

 continued in eacli other, the different 

 obliquities of that surface, which goes 

 foremost, will occasion considerable 

 changes in the resistance ; although the 

 section of the solid, by a plain perpen- 

 dicular to its direction, should in all cases 

 be the same. And Sir Isaac Xewton lias 

 particularly determined, that in a fluid 

 thus constituted the resistance of a globe 

 is but half the resistance of a cylinder of 

 the same diameter, moving in the direc- 

 tion of its axis with the same velocity. 



But though the hypothesis of a fluid, 

 thus constituted, be of great use in ex- 

 plaining the nature of resistances, yet in 

 reality no such fluid does exist within 

 our knowledge : all the fluids with 

 which we are conversant are so formed, 

 that their particles cither lie contiguous 

 to each other, or at least act on each 

 other in the same manner as if they did ; 

 consequently, in these fluids, no one par- 

 ticle, contiguous to the resisted body, 

 can be moved, without moving at the 

 same time a great number of others, some 

 of which will be distant from it ; and the 

 motion thus communicated to a mass of 

 the fluid will not be in any one deter- 

 mined direction, but will in each particle 

 be different, according to the different 

 manners in which it lies in contact with 

 those from which it receives its impulse ; 

 whence great numbers of the particles 

 being diverted into oblique directions, 

 the resistance of the moving body, which 

 will depend on the quantity of motion 

 communicated to the fluid in its own di- 

 rection, will be hereby different in 

 quantity from what it would be in the 

 preceding supposition, and its estimation 

 becomes much more complicated and 

 operose. Sir Isaac Xewton, however, 



has determined, that the resistance to a 

 cylinder, moving in the direction of its 

 axis in such a compressed fluid as we 

 have here treated of, is but one-fourth 

 part of the resistance, wjuch the same 

 cylinder would undergo if it moved with 

 the same velocity in a fluid constituted 

 in the manner we have described in our 

 first hypothesis, each fluid being sup- 

 posed to be of the same density. But 

 again, it is not only in the quantity of their 

 resistance that these fluids differ, but 

 likewise in the different manner in which 

 they act on solids of different forms mov- 

 ing in them. 



We have shown, that in the discontinu- 

 ed fluid, which we first described, the ob- 

 liquity of the foremost surface of the 

 moving body would diminish the re.sist- 

 ance ; but in compressed fluids this 

 holds not true, at least not in any con- 

 siderable degree ; for the principal resist- 

 ance in compressed fluids arises from the 

 greater or lesser facility with which the 

 fluid, impelled by the forepart of the body, 

 can circulate towards its (undermost part ; 

 and this being little, if at all, affected by 

 the form of the moving body, whether it 

 be cylindrical, conical, or spherical, it fol- 

 lows, that while the transverse section of 

 the body, and consequently the quantity 

 of impelling fluid, is the same, the change 

 of figure in the body will scarcely affect 

 the quantity of its resistance. 



The resistance of bodies of different 

 figures, moving in one and the same me- 

 dium, lias been considered by M. J. Ber- 

 noulli, and the rules lie lays down on this 

 subject are the following : 1. If an isosceles 

 triangle be moved in tiie fluid according 

 to the direction of a line which is normal 

 to its base ; first with the vertex foremost, 

 and then with its base ; the resistances 

 will be as the legs, and as the square of 

 the base, and as the sum of the legs. 2. 

 The resistance of a square moved accord- 

 ing to the direction of its side, and of its di- 

 agonal, is as the diagonal to the side. 3- 

 The resistance of a circular segment (less 

 than a semicircle) carried in a direction 

 perpendicular to its basis, when it goes 

 with the base foremost, and when with 

 its vertex foremost (the same direction 

 and celerity continuing, which is all along 

 supposed) is as the square of the diameter 

 to the same, less one-third of the square 

 of the base of the segment. Hence the 

 resistances of a semicircle, when its base, 

 and when its vertex go foremost, are to 

 one another in a sesquialterate ratio. 4. 

 A parabola moving in the direction of its 

 axis, with its basis, and then its vertex 



