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 accurac}^ not only for any given station, but still 

 more when Ave consider the temperatures belonging to a giA^en stage 

 of A^egetation of the same plant in localities that differ much in lat- 

 itude or longitude. 



The third hypothesis is that Avhich Avas favored by Quetelet, and 

 the second is .that which had for a hundred years been generally 

 adopted by botanists. Both of these tAvo latter hypotheses Avere 

 most thoroughlA' investigated by Erman in his memoir, published in 

 1845 and 1819.^' 



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 iuA'estigation consists in finding a method 

 of computing the sums of the temperatures or the sums of the 

 squares of the temperatures aboA^e freezing when the aA^erage 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 obserA^ations.'' 



The summation of the squares of the mean daily temperatures Ava:-; 

 computed by Linsser by the method knoAvn as mechanical quadra- 

 tures. The folloAving table illustrates his results for scA^en groups of 



o I very much regret that I have not been able to examine these memoirs, 

 which are published in the Archiv fiir Wissenschaftliche Kentnisse Russlantl, 

 A'ols. IV and VIII.— C. A. 



6 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 diffei*- 

 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. 



