THE MUSCLES J THE FAT-BODY AND CCELOM. 81 



Ratio of weight drawn to weight of body (Plateau). 



Horse -5 to -83 



Man '86 



Crab 5-37 



Insects 14*3 to 23*5 



The inference commonly drawn from, such data is that the 



muscles of small animals possess a force which greatly exceeds 



that of large quadrupeds or man, allowance being made for size, 



and that the explanation of this superior force is to be looked for 



in some peculiarity of composition or texture. Gerstaecker,* for 



example, suggests that the higher muscular force of Arthropoda 



may be due to the tender and yielding nature of their muscles. 



An explanation so desperate as this may well lead us to inquire 



whether we have understood the facts aright. Plateau's figures 



give us the ratio of the weight drawn or raised to the weight 



of the animal. This we may, with him, take as a measure of 



the relative muscular force. In reality, it is a datum of very 



little physiological value. By general reasoning of a quite 



simple kind it can be shown that, for muscles possessing the 



same physical properties, the relative muscular force necessarily 



increases very rapidly as the size of the animal decreases. For 



the contractile force of muscles of the same kind depends simply 



upon the number and thickness of the fibres, i.e., upon the 



sectional area of the muscles. If the size of the animal and of 



its muscles be increased according to any uniform scale, the 



O ' 



sectional area of a given muscle will increase as the square of 

 any linear dimension. But the weight increases in a higher 

 proportion, according to the increase in length, breadth, and 

 depth jointly, or as the cube of any linear dirnension.f The 



* Klassen und Ordnungen des Thierreiclis, Bd. V., pp. 61-2. 



t This change in the relation of weight to strength, according to the size of the 

 structure, has long been familiar to engineers. (See, for example, "Comparisons of 

 Similar Structures as to Elasticity, Strength, and Stability," by Prof. James 

 Thomson, Trans. Inst. Engineers, &c., Scotland, 1876.) The application to animal 

 structures has been made by Herbert Spencer (Principles of Biology, Pt. II., ch. i.). 

 The principle can be readily explained by models. Place a cubical block upon a 

 square column. Double all the dimensions in a second model, which may be done 

 by fitting together eight cubes like the first, and four columns, also the same as before 

 except in length. Each column, though no stronger than before, has now to bear 

 twice the weight. 



G 



