Note 92 — Chapter V

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 Hors eContr. force of Bee = sect. area of muscles (Horse )sect. area of muscles (Bee) = R²r² .

But since Ww = R³r³ , R²r² = Ww × rR .

Therefore Contr. force of Horse Contr. force of Bee = WrwR

But, by definition,

Rel. m.f. of HorseRel. m.f. of Bee = Contr. f. of HorseWContr. f. of Beew = Contr. f. of HorseContr. f. of Bee × wW =

WrwR × wW = rR = r³R^{3 13} = wW ¹³ .

The weight of a horse is about 270,000 grammes, that of a bee ·09 gramme; so that

wW ¹³ = ·09270,000 ¹³ = ·000,000,3̅ ¹³ = ·0015 (nearly) =

Calculated Ratio of Relative Muscular Force of Horse to that of Bee. The Observed Ratio (Plateau) is ·523·5 = ·02128; 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.