174 



where the notation is as follows : C is the total heat from the date of 

 sowing up to the date of sprouting ; x is the thermal constant from one 

 phase to the next, such as from sprouting to flowering ; t is the num- 

 ber of days from sprouting to flowering; c is the mean daily tempera- 

 ture from sjjrouting to flowering ; t c is the total sum of mean daily 

 temperatures from sprouting to flowering; as this temperatvire is 

 principally active during the daytime, therefore one-twelfth of ^ c 

 represents the efficient heat during an hour; h is the duration in. 

 hours of an average growing day, viz, from sunrise to sunset; there- 

 fore one-twelfth of the product e h t represents the total heat that 

 has been utilized by the plant. 



The method of reasoning by which Kabsch arrives at the above 

 formula, which I have quoted from Fritsch, is not known to me. 



Sachs, by direct experiment, finds that for each plant there is a 

 temperature most favorable to its growth and two other limits, mini- 

 mum and maximum, beyond which it will not grow. 



Deblanchis finds that the temperature on which vegetation depends 

 is not the ordinary temperature of the air as given by a sheltered 

 thermometer; he prefers to approximate to the temperature of the 

 leaf of the plant by the use of his " vegetation-thermoscope," which 

 is an ordinary minimum thermometer covered with green muslin and 

 kept moist, as in the ordinary wet-bulb thermometer. He places 

 his thermometer at one and a half meters above the soil and in full 

 exposure to sun and sky. Evidently the sum total of his tempera- 

 tures will be between the sums of the ordinary wet-bulb and the 

 ordinary dry-bulb thermometers, but must differ greatly from the 

 temperature of the roots on which the growth of the plant primarily 

 depends. 



Hoffmann prefers to take for the daily temj^erature the excess above 

 freezing of the maximum thermometer exposed to full sunshine and 

 free air. Hoffmann's temperatures approach more nearly the tem- 

 perature of the roots within a few inches of the surface of the ground. 

 Besides taking the sums of the average daily temperatures of the 

 shaded air thermometer, omitting all negative values or all those 

 below freezing point, Hoffmann also took the sum of the bright bulb 

 in vacuo and of the black bulb in vacuo, both in full sunshine ; these 

 latter temperatures are generally higher than those of the roots and 

 much higher than those of the leaves. Hoffmann prefers to use the 

 readings of the l)right bulb in vacuo. 



Herve Mangon (1870) modifies Gasparin's method slightly in that 

 he takes account of the shade temperatures of the air from the date 

 of sowing up to the date of harvest, rejecting all cases where the 

 mean daily temperature in the shade is less than 6° C. ; he had been 

 led to think that the vegetation of cereals and other important crops 

 ceases below this temperature. Thus he determines the sum total 



