412 



MOTION. 



From this table it appears conclusive that no 

 muscular force is employed or required to pro- 

 pel the leg forwards after it has been raised and 

 bent by the flexor muscles, and that the force 

 of the earth's gravity alone on the leg is suffi- 

 cient to accomplish that purpose. The diffe- 

 rence found between the oscillation of the legs 

 in the living and the dead body is very small, 

 and is attributed by those authors to the elas- 

 ticity of the ligaments connecting the leg to the 

 trunk, and some trifling differences in the 

 length of the legs, but decidedly not to muscu- 

 lar action. An application of the principles 

 of the pendulum to the legs of animals mov- 

 ing in a vertical plane shows that the durations 

 of their periodic oscillations must be respec- 

 tively as the square roots of their lengths,* 

 estimated by the distance of the centre of 

 oscillation ; or the time of a complete oscillation 

 of any leg from behind forwards when in- 

 fluenced only by gravity is to the time in 

 which a heavy body would fall through half 

 the length of the leg, considered as a com- 

 pound pendulum, as the circumference of a 

 circle is to its diameter. 



It further results from the periodic move- 

 ments of the legs being subordinate to the 

 force of gravity, that the same individual 

 would necessarily walk slower as he ap- 

 proached the equator, and quicker as he ap- 

 proached the poles, all other circumstances 

 being equal. For example, let us suppose 

 any two persons to be walking in different 

 latitudes, whose legs are of unequal length, and 

 acted on by unequal gravitating forces, then by 

 the theory of the pendulum the time of the 

 swinging forward of their legs respectively will 

 be as the square roots of their lengths directly 

 and as the square roots of the gravitating forces 

 in those latitudes inversely .f 



Mechanical effects of fluids on animals im- 

 mersed in them. When a body is immersed in 

 any fluid whatever, it will lose as much of its 

 weight relatively as is equal to the weight of 

 the fluid it displaces. In order to ascertain 

 whether an animal will sink or swim, or be sus- 

 tained without the aid of muscular force, or to 

 estimate the amount of force required that the 

 animal may either sink or float in water, or fly 

 in the air, it will be necessary to have recourse 

 to the specific gravities both of the animal 

 and of the fluid in which it is placed. 



The specific gravities or comparative weights 

 of different substances are the respective weights 



* Let I and I' equal the lengths of any two 

 pendulums, 1 1' the times of vibrations, g the force 

 of gravity, it to i the ratio of the circumference of 

 a circle to its diameter, then 



(5.) 



.-. t : t' : : <J I : J I' 



t For as t = ir A /_, and t' it A / , 



V g V g' 



of equal volumes of those substances.* When 

 any solid body is immersed in a fluid and left 

 to itself, it will sink if its specific gravity is 

 greater than that of the fluid; but if its specific 

 gravity be less than that of the fluid, it will rise 

 to the surface and be sustained there; and when 

 the specific gravity of the solid and fluid are 

 equal, the body will remain stationary wherever 

 it is placed. When the weight of any body 

 taken in a fluid is subtracted from its weight 

 out of the fluid, the difference is the weight of 

 a volume of the fluid equal to that of the solid; 

 this is to its weight in air, as the specific gravity 

 of the fluid to that of the solid ; so that generally 

 the specific gravities of solid bodies are as their 

 weights in the air directly, and their losses in 

 water or any other fluid inversely .f 



The specific gravity of air, water, and mer- 

 cury, when tha barometer stands at 30 in. and 

 the thermometer at 55, being to each other as 

 If, 1000, 13600, it results that all those ani- 

 mals whose specific gravities approximate to 

 that of water are nearly 1000 times heavier 

 than air, and more than thirteen times lighter 

 than mercury, and consequently animals that 

 would sink and perish in water could walk on 

 the surface of mercury. 



The human body in a healthy state, with 

 the chest filled with air, is specifically lighter 

 than water, and its sinking generally depends 

 upon the air in the lungs escaping under 

 the pressure of water upon its immersion. Dr. 

 Arnott remarks that if this truth were generally 

 and familiarly understood, it would lead to the 

 saving of more lives than all the mechanical 

 life-preservers which man's ingenuity will ever 

 contrive. 



Atmospheric pressure produces a great va- 

 riety of mechanical effects on animal structures. 

 If we estimate the surface of a man to be equal 

 to 2000 square inches, the pressure of the atmo- 

 sphere on his body with the barometer at 

 30 in. will amount to 30,000lbs., or about 15 

 tons ; when the barometer falls from 30 to 27 

 inches, the pressure is reduced from 15 to 13| 

 tons ; we need not, therefore, be surprised that 

 variations of atmospheric pressure should be 

 attended with corresponding sensations in living 

 animals. 



The pressure of the atmosphere enables some 

 animals (as we shall subsequently prove) to fix 

 themselves to rocks with great force, to walk 

 up the surfaces of glass windows, to sustain 

 themselves in an inverted position on the 



* If W, w are the weights of two substances, 

 V, v their volumes, S, s their specific gravities, 



then S : s : : 



V v 



t Let W the weight of the body in air, W 

 its weight in water or any other fluid, S the 

 specific gravity of the solid, s ~ the specific gra- 

 vity of the fluid, then we shall have the following 

 proportions ; 



W W': W : : S : S; 



W W 

 hence s rr? S (7.) 



hence t : t' : : L : L. 



(6.) 



and 



c __ 



W 



W 



W W 



-, s 



(8) 



