_ ceilings of rooms in opposition to the force of 
_ gravity, and to hold the mechanism of the joints 
together with a force proportional to their respec- 
_ tive areas. 
_ The air being elastic, its density decreases as 
the elevations above the earth’s surface increase, 
and when the heights increase in an arithme- 
tical progression the densities decrease in a 
geometrical progression ; hence, in the flight 
of birds, the weight of air which they displace, 
and the effective force of their wings must 
oo vary with every change of eleva- 
on. 
_ Animals moving in water at various depths 
are not subjected to the same variations of den- 
sity that are experienced in air, since water, being 
nea So suffers no sensible change 
of volume at the greatest depths of the ocean ; 
but although the density remains nearly con- 
st the pressure increases with the depth, 
being equivalent to about one pound on the 
‘Square inch for every two feet. The specific 
‘Btavity of water being from 800 to 1000 times 
greater than air, its pressure becomes very great 
at the known depths to which many fishes and 
Cetaceous animals descend. 
Resistance of fluids—Animals moving in 
air and water experience in those media a 
sensible resistance, which is greater or less 
“proportion to the density and tenacity of 
fluid, and the figure, superficies, and ve- 
city of the animal. 
An inquiry into the amount and nature of the 
Stance of air and water to the progression of 
mals will also furnish the data for estimating 
; proportional values of those fluids acting as 
fulera to their lcsomotive organs, whether they 
be fins, wings, or other forms of lever. 
The motions of air and water, and their direc- 
exercise very important influences over 
ty resulting from muscular action. 
_ The resistance of a plane moving perpendi- 
eularly to itself in a fluid, equals the weight of a 
column of the fluid of which the base is equal to 
the plane, and the altitude to the depth through 
which a body would fall to acquire by gravity 
_ the velocity of the plane.* 
__ If the direction} of the motion, instead of 
_ being perpendicular to the plane, as before 
_ Supposed, be inclined to it at any angle, the 
__ * Leta represent the area of the plane, v the 
_ velocity, p the specific gravity of the fluid, then 
ae 2 
the height due to the velocity being, the whole 
Betis” 
resistance is . 
e 2 
a2 a p—. weet ceccccccccee( Me) 
___ hence, ceteris paribus, the resistance is as the 
_ square of the velocity. 
: <al Let 4B (fig. 215) be the plane, and x p the 
__ direction of its motion, a 8 pv the angle whose sine 
__ iss, the number of particles which strike the plane, 
_ as well as the force of each particle, will be dimi- 
__ hished in the ratio of 1 to s, therefore the whole 
_ Fesistance will be diminished in the ratio of 1 : s?, 
_ but the effective part of the resistance being per- 
_ pendicular to the plane, the whole resistance in 
_ the direction a £ is to the effective part in the 
on 8 Eperpendicular to a zB, as A £ and B g, 
ins 
f. 
MOTION. 
415 
resistance will be diminished in the triplicate 
ratio of the sine of the angle of inclination. 
When a body is termi- 
nated by a curved surface 
generated by the revolu- 
tion of a plane round its 
axis, and moves parallel 
to that axis, the amount 
of resistance may be ob- 
tained by the formule 
and analysis subjoined.* 
Fig. 215. 
b d 
Fig. 216. 
e 
d 
But the forms of animals, though symme- 
trical, can rarely be considered as mathemati- 
cally regular figures, and consequently many 
of the data for calculating the resistance to 
their movements must be derived from experi- 
ment. 
Passive organs of locomotion. Bones.—The 
solid framework, or skeleton of animals which 
supports and protects their more delicate tissues, 
whether chemically composed of entomoline, 
carbonate, or phosphate of lime; whether 
placed internally or externally; or whatever 
may be its form or dimensions, presents levers 
and fulcra for the action of the muscular system, 
in all animals furnished with earthy solids 
for their support, and possessing locomotive 
power. 
The form, strength, density, and elasticity 
of skeletons vary in relation to the bulk 
and locomotive power of the animal, and to 
the media in which it is destined to move. 
oras 1tos, Hence the whole resistance in the 
direction of the motion will be diminished in the 
ratio of 1 : s8, and will therefore be 
apy s eccccvecceces+(10.) 
2g. 
* Letbead (fig.216) be the section through the 
axis ca of the body whose motion is in the direction 
of ca, draw the tangent e g to any point of 
the curve meeting the axis produced in g, draw the 
ordinates e f and e’ f’ indefinitely near each other, 
also draw e’ a’ parallel to gc, then lete f= zx, 
e f=y,be=z, and s the sine of the angle g 
to the radius 1; then 2 w y is the circumference of 
the circle whose radius is ef and2@ yx ee’ or 
2 yd z is the surface described by e’ ¢ in its re- 
volution about the axis c a, which is the quantity 
represented by (a) in the preceding note, therefore 
ae a oles SEE PROT 5 
will be the resistance on that ring or the differen- 
tial of the resistance to the body whatever 
its figure may be.—(See Gregory’s Mechanics, 
chap. v. p- 521.) 
2uyd z, or 
