RESISTANCE. 
'®en be moved, without moving at the same 
time a great number of others, some of 
which will be distant, from it; and the mo- 
tion thus communicated to a mass of the 
fluid will not be in any one determined di- 
rection, but will in each particle be dif- 
/erent, according to the different manners 
in w’hich it lies in contact with those from 
which it receives its impulse ; wiience great 
numbers of the particles being diverted into 
oblique directions, the resistance of the 
moving body, which will depend on tlie 
c|uantity of motion communicated to tlie 
fluid in its own direction, will be hereby 
different in quantity from what it would be 
in the preceding supposition, and its esti- 
mation 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 offi is but one-fourth part of the re- 
sistance, which the same cylinder w'ould 
undergo if it moved with the same velocity 
in a fluid constituted in the maimer we liave 
described in our first hypothesis, each fluid 
being supposed 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 moving 
in them. 
We have showm, that in the discontinued 
fluid, which we first described, the obliquity 
of the foremost surface of the moving body 
would diminish the resistance; but in com- 
pressed fluids this holds not true, at least not 
in any considerable degree : for the princi- 
pal resistance in compressed fluids aiises 
flom the greater or lesser facility witii 
which the fluid, impelled by the forepart of 
the body, can circulate towards its hinder- 
most part; and this being little, if at all, 
affected by the form of tlie moving body, 
whether it be cylindrical, conical, or spheri- 
cal, it follows, that while the transverse 
section of the body, and consequently tlie 
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 ' differe.nt 
figures, moving in one and the same me- 
dium, has been considered by M. J. Ber- 
nouli, and the rules he lays down on this 
subject are the following ; 1. If an isosceles 
triangle he moved in the fluid according to 
the direction of a line which is normal to 
its base ; first with the vertex foremost, and 
tiieii with its base; the resistances will he 
as the legs, and as the square of the base, 
and as tlie sum of the legs. g. The resis- 
tance of a square moved according to the 
direction of its side, and of its diagonal, is 
as the diagonal to the side. 3. The resis- 
tance of a circular segment (less than a 
semicircle) carried in a direction perpendi- 
cular to its basis, when it goes with the base 
foremost, and when with its vertex foremost 
(the same direction and ceicrity 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 fore- 
most, lias its resistances, as the tangent to 
an arch of a circle, whose diameter is equal 
to the parameter, and the tangent equal to 
half the basis of the parabola. 5. The re- 
sistances of an hyperbola, or the semi-ellip. 
sis, when the base aud when tlie vertex go 
foremost, may he thus computed ; let it be, 
as the sum, or difference, of the transverse 
axis andiatus rectum is to the transverse 
axis, so is the square of the latus rectum to 
the square of the diameter of a certain 
circle ; in which circle apply a tangent equal 
to half the basis of the liyperbola or ellipsis. 
Then say again, as the sum, or difference, 
of the axis and parameter is to the parame- 
ter, so is the aforesaid tangent to another 
right line. And further, as the sum, or 
difference, of the axis and parameter is to 
the axis, so is the circular arch correspond- 
ing to the aforesaid tangent, to another 
arch. This done, the resistances will be as' 
the tangent to the sum, or difference, of the 
right line thus found, and that arcli last 
mentioned. 6. In general, the resistances 
of any figure whatsoever, going now with its 
base foremost, and tlien with its vertex are 
as the figures of the basis to the sum of all 
the cubes of the elqment of the basis divided 
by the squares of the element of the curve 
line, All which rules, he thinks, may he of 
use in the fabric or construction of ships, 
and in perfecting the art of navigation uni- 
versally. As also for determining the figures 
of the balls of pendulums for clocks. 
As to the resistance of the a7r, Mr. Eo, 
bins, in his new prmciples of gmmery, took 
the following method to determine it: he 
charged a musket-barrel three times suc- 
cessively with a leaden ball | of an inch 
diameter, and took such precaution in 
weighing of the pow’der, and placing it, as 
