A later series of experiments[93] brings out this difference in a precise form. Plateau has determined by ingenious methods what he calls the Absolute Muscular Force [94] of a number of Invertebrate animals (Lamellibranch Mollusca, and Crustacea), comparing them with man and other Vertebrates. His general conclusions may be shortly given as follows:—The absolute muscular force of the muscles closing the pincers of Crabs is low in comparison with that of Vertebrate muscles. The absolute force of the adductor muscles closing a bivalve shell may, in certain Lamellibranchs, equal that of the most powerful Mammalian muscles; in others it falls below that of the least powerful muscles of the frog, which are greatly inferior in contractile force to Mammalian muscles. We find, therefore, that the low contractile force of Insect muscles is in harmony, and not in contrast, with common observation of their physical properties, and that the high relative muscular force, correctly enough attributed to them, is explicable by considerations which apply equally well to models or other artificial structures.
The comparison between the muscular force of Insects and large animals is sometimes made in another way. For example, in Carpenter’s Zoology[95] the spring of the Cheese-hopper is described, and we are told that “the height of the leap is often from twenty to thirty times the length of the body; exhibiting an energy of motion which is particularly remarkable in the soft larva of an Insect. A Viper, if endowed with similar powers, would throw itself nearly a hundred feet from the ground.” It is here implied that the equation
Height of Insect’s leapLength of Insect = Supposed ht. of Viper’s leap (100 ft.)Length of Viper
should hold if the two animals were “endowed with similar powers.”
But it is known that the work done by contraction of muscles of the same kind is proportional to the volume of the muscles (“Borelli’s Law”),[96] and in similar animals the muscular volumes are as the weights. Therefore the equation
Work of InsectWeight of Insect = Work of ViperWeight of Viper
will more truly represent the imaginary case of equal leaping power. But the work = weight raised × height, and the weight raised is in both cases the weight of the animal itself. Therefore
Wt. × Ht.Wt. (Insect) = Wt. × Ht.Wt. (Viper),
and Ht. (Insect) = Ht. (Viper). The Viper’s efficiency as a leaping animal would, therefore, equal that of a Cheese-hopper if it leaped the same vertical height. Therefore, if the two animals were “endowed with similar powers,” the heights to which they could leap would be equal, and not proportional to their lengths, as is assumed in the passage quoted.