SECT. 2] 



AND WEIGHT 



531 



B^lehradek interprets b as being a measure of protoplasmic viscosity, 

 so tliat in his opinion all temperature effects on growth can be 

 regarded as primarily effects upon viscosity, and only acting in- 

 directly upon the rapidity of the growth-process. Whether this point 

 of view will prove to be either more fruitful or more correct than 

 that of Crozier and his collaborators cannot at present be decided. 

 Crozier & Stier have, however, shown that the fit of B^lehradek's 

 formula in one case, at any rate, is not at all good, while Belehradek 

 has strengthened his case by studying the time factor in cooling and 

 heating protoplasm. But it is interesting that the constant b should 

 increase with age, for protoplasmic viscosity almost certainly does, 

 and this has an obvious importance in view of the gradual loading up 



Exponential curve 



Catenary 

 Fig. 85. 



Hyperbola 



of the cells of the body with paraplasmatic substances. Belehradek 

 has answered Crozier's criticisms and the papers must be consulted 

 for the details of the argument. 



Janisch represents the time/temperature relation not by a simple 

 exponential curve, nor by a hyperbola, but by a " Kettenlinie " or 

 catenary curve. The reciprocal of this is not a straight line or a 

 sigmoid curve rising most rapidly at the point of inflection; it is a 

 sigmoid curve rising most slowly at the point of inflection. Such a 

 complex exponential curve should therefore be produced when the 

 velocity/temperature graph is drawn, and Janisch actually showed 

 that Krogh's straight lines turn into curves of this character when 

 the points which Krogh neglected at the upper and lower ends are 

 taken into consideration. Just the same can be shown for the figures 

 of Sanderson and Peairs. Fig. 85, which is taken from Janisch, shows 

 the relations between these curves. Fig. 86, also taken from Janisch, 

 shows a replotting of the data of Sanderson for Margaropus annulatus. 

 The time of development is shortest at 28°, and, just as Faure- 



34-2 



