Hypothesis of Contraction of Striated Muscle. 141 



the calculations are made for ellipsoids 0*9 fi long and 0'4, 0-3, 0-2, and 

 0-1 fi in diameter ; that is with half-axes, a and b, 0-45 /a and 0-20, 0-15, 010, 

 and - 05 fi respectively. 



We can assume that the ellipsoid swells to become a sphere of the same 

 surface area, that the ellipsoid is really an extended sphere with the walls 

 thrown into folds, or that it has inextensible longitudinal fibres and extensible 

 circular fibres. The first assumption is not valid, as one cannot imagine a 

 surface area of constant magnitude which would be so mobile as to change 

 from the surface of an ellipsoid to that of a sphere. The other two 

 assumptions give the same results and they form the mechanical basis of the 

 ensuing calculations. 



We can simplify the description by dealing with one dim band and an 

 adjacent light band, since the result is the same even if one dim band is 

 associated with the two adjacent half light bands. 



Extent of Contraction. 



The quotation given above refers specifically to Macdougall's hypothesis (13), 

 but the same criticism seems to be tacitly applied to all osmotic hypotheses. 



Assuming that the ellipsoid becomes a sphere, the longitudinal perimeter 

 of the ellipsoid (Table, p. 146, column 3) will be the circumference of the 

 sphere. The dim band, therefore, shortens in the ratio of the length of 

 ellipsoid to diameter of sphere, that is as 2a is to 2r. 



Not only does the dim band shorten but the area of the dim band 

 increases. The fibrils being closely packed together, the increase in area of 

 dim band will be proportional to the squares of the radii of the ellipsoid and 

 sphere respectively, or as b 2 is to r 2 . The relative volumes of the dim band 

 in the two conditions are given by this ratio multiplied by the corresponding 

 length of the band. These relative volumes, 2a x b 2 , and 2r x r 2 , are given in 

 the Table (columns 4 and 8). 



The volume of the dim band is more than doubled as the result of 

 contraction (column 9). The extent of contraction can be estimated by 

 assuming — (a) that, as measured above, the light band is exactly the same 

 length as the dim band, or (b) that the length of the light band is such 

 that, during contraction, the whole of the muscle can be just absorbed by 

 the dim band. These figures are given in the Table (columns 10, 11, and 12). 

 The length of the muscle fibre which can be absorbed by the dim band is 

 easy to calculate, as the area of the light band is exactly the same as that of 

 the dim band before contraction, hence the relative length is the number 

 of times that the volume of the contracted dim band contains the volume of 

 the dim band before contraction. 



M 2 



