82 THE COCKROACH : 



ratio of contractile force to weight must therefore become 

 rapidly smaller as the size of the animal increases. Plateau's 

 second table (see above) actually gives a value for the relative 

 muscular force of the Bee, in comparison with the Horse, which 

 is only one-fourteenth of what it ought to turn out, supposing 

 that both animals were of similar construction, and that the 

 muscular fibres in both were equal in contractile force per unit 

 of sectional area.* 



A later series of experimentsf brings out this difference in a 

 precise form. Plateau has determined by ingenious methods 

 what he calls the Absolute Muscular Force^. 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 



* 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) 7? 2 



Contr. force of Bee sect, area of muscles (Bee) r 2 ' 



W R* R* W r 

 But since - - -^-, 5- = x -^-. 

 w r 3 r 2 w R 



Contr. force of Horse Wr 



Therefore ^ ~r~w ~r>- 



Contr. force of Bee wR 



But, by definition, 



Contr. f. of Horse 



Rel. m.f. of Horse W Contr. f. of Horse w 



~ReTnuf."orBee~ Contr. f. of Bee Contr. f. of Bee W 



w 

 Wr w r 



wR W R 



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



wf ~~ ' \270 000 r : ( ' 000 ' 000 '3 r = '0015 (nearly) = = Calculated Eatio of 



Relative Muscular Force of Horse to that of Bee. The Observed Ratio (Plateau) is 



'02128 : so that the relative muscular force of the Horse is more than fourteen 



23'5 



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. 



f Rech. sur la Force Absolue des Muscles des Invertebres. I e Partie. Mollusques 

 Lamellibranches. Bull. Acad. Roy. de Belgique, 3 e Ser., Tom. VI. (1883). 

 Do., H e Partie. Crustaces Decapodes. Ibid., Tom. VII. (1884). 



J Statical muscular force and Specific muscular force are synonymous terms in 

 common use. Contractile force per unit of sectional area gives perhaps the clearest 

 idea of what is meant. 



