[92] Contractile force varies as sectional area of muscle. Let _W_ be weight of Horse; _w_, weight of Bee; _R_, a linear dimension of Horse; _r_, a linear dimension of Bee. Then, Contr. force of Horse sect. area of muscles (Horse) _R^2_ --------------------- = ----------------------------- = -----. Contr. force of Bee sect. area of muscles (Bee) _r^2_ _W_ _R^3_ _R^2_ _W_ _r_ But since --- = -----, ----- = --- × ---. _w_ _r^3_ _r^2_ _w_ _R_ Contr. force of Horse _Wr_ Therefore --------------------- = ----. Contr. force of Bee _wR_ But, by definition, Contr. f. of Horse ------------------ Rel. m.f. of Horse _W_ Contr. f. of Horse _w_ ------------------ = ╺━━━━━━━━━━━━━╸ = ------------------ × --- Rel. m.f. of Bee Contr. f. of Bee Contr. f. of Bee _W_ ---------------- _w_ _Wr_ _w_ _r_ _r^3_ _w_ = ---- × --- = --- = (---)^{1/3} = (---)^{1/3}. _wR_ _W_ _R_ _R^3_ _W_ The weight of a horse is about 270,000 grammes, that of a bee ·09 gramme; so that _w_ ·09 (---)^{1/3} = (-----)^{1/3} = (·000,000,3̅)^{1/3} = ·0015 (nearly) = _W_ 270,000 Calculated Ratio of Relative Muscular Force of Horse to that of Bee. ·5 The Observed Ratio (Plateau) is ---- = ·02128; 23·5 so that the relative muscular force of the Horse is more than fourteen times as great in comparison with that of the Bee as it would be if the muscles of both animals were similar in kind, and the proportions of the two animals similar in all respects. 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.