MOTION. 



413 



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 

 continually vary with every change of eleva- 

 tion. 



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 

 nearly incompressible, suffers no sensible change 

 of volume at the greatest depths of the ocean; 

 but although the density remains nearly con- 

 stant, the pressure increases with the depth, 

 being equivalent to about one pound on the 

 square inch for every two feet. The specific 

 gravity 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 

 in proportion to the density and tenacity of 

 the fluid, and the figure, superficies, and ve- 

 locity of the animal. 



An inquiry into the amount and nature of the 

 resistance of air and water to the progression of 

 animals will also furnish the data for estimating 

 the proportional values of those fluids acting as 

 fulcra to their locomotive organs, whether they 

 be fins, wings, or other forms of lever. 



The motions of air and water, and their direc- 

 tions, exercise very important influences over 

 velocity resulting from muscular action. 



The resistance of a plane moving perpendi- 

 cularly 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 directionf of the motion, instead of 

 being perpendicular to the plane, as before 

 supposed, be inclined to it at any angle, the 



* Let a represent the area of the plane, v the 

 velocity, p the specific gravity of the fluid, then 



the height due to the velocity being > the whole 



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 formulae 

 and analysis subjoined.* 



Fig. 216. 



resistance is 



<*/> 



(9.) 



hence, cseteris panbus, the resistance is as the 

 square of the velocity. 



t Let A B (fig. 215) he the plane, and B D the 

 direction of its motion, A B D the angle whose sine 

 is s, the number of particles which strike the plane, 

 as well as the force of each particle, will be climi- 

 Tiislied in the ratio of 1 to s, therefore the whole 

 resistance will be diminished in the ratio of 1 : s 2 , 

 but the effective part of the resistance being per- 

 pendicular to the plane, the whole resistance in 

 the direction A E is to the effective part in the 

 direction B E perpendicular to A B, as A E and B E, 



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. 



or as 1 to s. Hence the whole resistance in the 

 direction of the motion will be diminished in the 

 ratio of 1 : s 3 , and will therefore be 



a p ^ ^ (10.) 



* Letbeitd (fig. 2 16) be the section through the 

 axis ca of the body whose motion is in the direction 

 of c a, draw the tangent e g to any point of 

 the curve meeting the axis produced ing-, draw the 

 ordinates e f and e f indefinitely near each other, 

 also draw e' a' parallel to g c, then let c/ x, 

 e f ~ y, b e ~ z, and s the sine of the angle g 

 to the radius 1 ; then 2 it y is the circumference of 

 the circle whose radius is ef and lit y x e e' or 

 2 it y d z is the surface described by e' e in its re- 

 volution about the axis c a, which is the quantity 

 represented by (a) in the preceding note, therefore 



n v 2 S 3 <rr p v 2 S 3 



2 it y d z, or 



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.) 



