RESISTANCE, or RESISTING force, in philosophy, denotes, in general, any power which acts in an opposite direc tion to another, so as to destroy or dimi nish its effect. Hence the force where with bodies, moving in fluid mediums, are impeded or retarded, is the resistance of those fluids. Authors have established it as a certain rule, that, whilst the same body moves in the same medium, it is al ways resisted in the duplicate proportion of its velocity ; that is, if the resisted body move in one part of its track with three times the velocity with which it moved in some other part, then its re sistance to the greater velocity will be 'nine times the resistance to the lesser : if the velocity in one place be four times the velocity in another, the resistance to the greater velocity will he sixteen times the resistance to the lesser, and so on. This rule, though very erroneous, when taken in a general sense, is yet undoubt edly very near the truth, when confined within certain limits.
In order to conceive the resistance of fluids to a body moving in them, Mr. Ro bins distinguishes between those fluids, which being compressed by some incum bent weight, perpetually close up the space instant, deserted by the body in motion, without permitting, for an nstant, any vacuity to remain behind it ; and those fluids in which, they being not sufficient ly compressed, the space left behind the moving body remains for some time empty. These differences inthe resist ing fluids will occasion very remarkable varieties in the laws of their resistance, and are absolutely necessary to he con sidered in the determination of the action of the air in shot and shells; for the air partakes of both these afections, accord ing to the different velocities of the pro jected body. If a fluid were so con stituted, that all the particles composing it were at some distance from each other, and there was no action between them, then the resistance of a body moving therein would be easily computed from the quantity of motion communicated to these particles : for instance, if a cylinder moved in such a fluid in the direction of its axis, it would communicate to the particles it met with a velocity equal to its own, and in its own direction, sup posing that neither the cylinder nor the parts of the fluid were elastic ; whence, if the velocity and diameter of the cylin der be known, and also the density of the fluid, there would thence be determined the quantity of motion communicated to the fluid, which (action and re-action be ing equal) is the same with the quantity lost by the cylinder ; consequently the 4.! resistance would be hereby ascertain .
ed. • • In this kind of discontinued fluid, the particles being detached from each other, every one of them can pursue its own motion iu 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 a 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 each 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 Newton has 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 either 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 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 Newton, 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, which 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.