212 
(2) That the same stage of vegetation is attained when in the 
course of any year the sum total of the mean daily temperatures 
above freezing attains the same value. 
(3) That the same stage of vegetation is attained when in the 
course of any year the sum of the squares of these positive tempera- 
tures attains a certain constant value. 
The first of these hypotheses has, he states, long since been given 
up as of insufficient accuracy not only for any given station, but still 
more when we consider the temperatures belonging to a given stage 
of vegetation of the same plant in localities that differ much in lat- 
itude or longitude. 
The third hypothesis is.that which was favored by Quetelet, and 
the second is that which had for a hundred years been generally 
adopted by botanists. Both of these two latter hypotheses were 
most thoroughly investigated by Erman in his memoir, published in 
1845 and 1849.¢ 
Erman demonstrates that both these hypotheses are unsatisfac- 
tory, but Linsser proposes to reinvestigate the question on the basis 
of a much larger collection of material, both phenological and mete- 
orological. ; 
The first step in Linsser’s investigation consists in finding a method 
of computing the sums of the temperatures or the sums of the 
squares of the temperatures above freezing when the average tem- 
perature of any day of the year is expressed by the so-called sine 
and cosine formula of Bessel. He computes the coefficients of Bes- 
sel’s formula, and therefore knows the equations that express the 
mean daily temperature for any day in the year and for each of his 
stations of observations.’ sell 
The summation of the squares of the mean daily temperatures was 
computed by Linsser by the method known as mechanical quadra- 
tures. The following table illustrates his results for seven groups of 
a{ very much regret that I have not been able to examine these memoirs, 
which are published in the Archiv fiir Wissenschaftliche Kentnisse Russland, 
Vols. IV and VIII.—C. A. 
>A similar computation had been made by Erman, but for the benefit of those 
who may in the future have to go through similar labors I would suggest that 
it is not more laborious and is certainly more perspicuous to compute the actual 
daily temperature for every fourth day of the year, beginning with January 0, 
and in the adjoining column make up the continuous summations. The differ- 
ence between the sums for any two dates is then the total mean daily tempera- 
ture to which the plant has been subjected.—C. A. 
