CONDITIONS OF EXISTENCE 15 



following figures apply to the development of the cod {Gadus 

 callarias) , 15 



Temperature, C -1° +3° 4° 5° 6° 8° 10° 12° 14° 



Period of development 



in days 42 23 20.5 17.5 15.5 12.75 10.5 9.7 8.5 



The eggs of the herring develop equally well at +0.5° and at 16°, 

 but require 40-50 days at the lower temperature and 6-8 at the higher. 

 The eggs of the rotifer Notomma hatch in 4 days at 15°, in 2 days 

 at 28°. The rate of reproduction for protozoans follows a similar 

 rule: Paramecium aurelia, for example, divides once in 24 hours at 

 14°-16°, twice at 18-20°. 1C The period of pupation in insects similarly 

 depends on temperature. According to Krogh, the meal worm, Tenebrio 

 molitor, requires the following periods from pupation to transforma- 

 tion: 



AtC 13.5° 17° 21° 27° 33° 



Hours 1116 593 320 172 134 



The rate of animal metabolism, measured by the consumption of 

 oxygen and the production of carbon dioxide, also increases with in- 

 creasing temperature. The meal worm pupa uses, per kilogram and 

 hour, 104 cc. of oxygen at 15°C, 300 cc. at 25°, 529 cc. at 32.5°. The 

 carp, per kilogram and day, uses 661 cc. at 9°C, 1692 cc. at 18.2°. 



Three formulae have been devised to interpret these temperature 

 effects. The most widely known is that of Van't Hoff, which is based 

 on the observation that chemical and biological processes, within 

 favorable temperature limits, are increased by an approximate con- 

 stant (two to three times usually) for each 10° rise in temperature. 

 Ludwig 17 reviews the literature and cites original observations on the 

 rate of development of the egg and of pupa of the Japanese beetle 

 {Popillia japonica) which show that the temperature coefficient tends 

 to decrease regularly as the temperature increases. The Arrhenius 

 formula, based upon changes in absolute temperature, better fits the 

 facts in many cases which show such a variation in the Van't Hoff 

 coefficient. 18 Krogh 19 advanced a formula to express the relation be- 

 tween temperature and the rate of development in which the constant 

 is added to the rate at one temperature to obtain the rate at a higher 

 one rather than multiplying the slower rate by a constant as required 

 by Van't Hoff. Krogh 's formula is based on the observation that 

 within normal temperature limits an increase of 1° has as great effect 

 upon metabolic processes at one temperature as at another. The time- 

 temperature curve is, within these limits, an hyperbola, and the rate- 

 temperature curve is a straight line which crosses the temperature axis 



