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locality about the time of the winter awakening, and we should par- 
ticularly consider the temperature that follows after the thermometer 
has passed the freezing point, as well as the quantity of light radiated 
by the sun. 
It must therefore be admitted that cold, as long as it does not 
destroy the life of the plant, may be more or less severe or more or less 
prolonged, and thus lower the average yearly temperature, without 
causing any marked difference in the epochs of vegetation. This 
reflection explains, independent of all hypothesis, that for any equable 
mean annual temperature the acceleration in vegetation should be 
in favor of localities where the annual variation is the greatest, par- 
ticularly in northern countries, where the frost prevails during many 
wonths of the year and where duing many of the following months 
the sunlight never ceases to fill the sky. Admitting the hypothesis 
that the action is proportional to the sum of the squares of the tem- - 
peratures, the results are still more positive; for, other things being 
equal, the greater the annual variation the greater will be the sum of 
the square of the positive ordinates in the curves of temperatures. 
I will now present some conclusions that one can deduce from all 
that precedes. I must first of all warn my readers that this work 
must be considered only as an attempt to solve a problem as difficult 
as it is interesting, the principal elements for the solution of which 
are still wanting. 
1. A great number of factors combine to produce variations in the 
periodic phenomena of vegetation, the most important of which 
in our climate is temperature. 
2. It may be estimated that the progress of vegetation is in pro- 
portion to the sum of the temperatures, or, better, to the sum of the 
squares of temperatures, calculated above the freezing point, starting 
with the epoch of the awakening of vegetation after the winter sleep. 
3. The cold of winter, if it does not injure the vitality of the plant, 
does not cause any perceptible retardation in its future development, 
particularly if the ground has been covered with snow. 
The effects that can be produced by the cold of winter must, how- 
ever, be considered, and especially the condition of the plant when 
it entered upon its winter sleep, a condition which should correspond 
to a certain sum of acquired temperatures (or heat stored up). As 
to the ripening of the harvest and because plants develop under the 
influence of the sun, we must consult a thermometer exposed to its 
direct action, and not a thermometer exposed to its direct action, and 
not a thermometer placed in the shade, as is commonly done. 
4. The temperatures at night are not comparable with those of the 
day as to their effects on vegetation. The quantity of light received 
by the plants must also be taken into consideration. 
5. An increase of 1° in latitude produces about the same retarda- 
tion in vegetation as an increase in elevation of 100 meters; that is to 
say, in our climate, a retardation of about four days. 
This result should be looked upon as only a kind of average of 
quantities that vary during the year, the differences of latitude and 
elevation having scarcely any real influence further than as they 
produce differences of temperature. 
6. The variations of temperature, other things being equal, are 
