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; ¢ is the num- 
ber of days from sprouting to flowering; ¢ is the mean daily tempera- 
ture from sprouting to flowering; ¢ ¢ is the total sum of mean daily 
temperatures from sprouting to flowering; as this temperature is 
principally active during the daytime, therefore one-twelfth of ¢ ¢ 
represents the efficient heat during an hour; / is the duration in 
hours of an average growing day, viz, from sunrise to sunset; there- 
fore one-twelfth of the product ¢ h ¢ 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 mits, 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 temperature 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 dailystemperatures 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 bright bulb in vacuo. 
Hervé Mangon (1879) modifies Gasparin’s method shghtly 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 
ob 
