8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 95 



sent approximately the amount of photosynthesis contributed by an 

 element of spectrum of width a which is transmitted by that Christian- 

 sen filter which predominantly transmits wave length Wo. The sum 

 total of these products 2(^_«iC_n .... eoC^ .... ^+„C+„) repre- 

 sents the total photosynthesis, originally measured as e^. Of this sum 

 of products only one, CqCq, represents the photosynthesis that is pro- 

 duced by radiation lying between the wave lengths \Wo—\a\ and 

 [f^o + io]- But this interval contains the fraction Co of the total 

 amount of energy of radiation which was employed in the experiment 

 at wave length Wo. 



We find, then, that in the experiment, as actually performed, C^q 

 of energy produced 



^ epCo 



i;(c_„,C^,„ .... eoCo .... e^nC^n) 

 of photosynthesis. Had the full unit quantity, q, of radiation of wave 

 length Wo been used, then the amount of photosynthesis would have 

 been (according to the first approximation) : 



gp CqCq __^ 



C-o -^(g-HiC-m .... CqCo .... C+n^+n) 



Performing a similar operation at all wave lengths where photo- 

 synthetic measurements were made, we are now able to plot a new 

 curve in place of curve no. i, somewhat closer to the true form which 

 the photosynthetic curve should take. This new curve may now be 

 used as a new point of departure to obtain a still better approximation. 

 That is to say, starting a second time with the original curve no. i, 

 we employ the corrected form of it, not itself, in determining new 

 and better correction factors by which to multiply the ordinates of 

 the original curve no. i to obtain from it a still better approximation 

 to the true form desired. It has been found desirable to repeat these 

 steps twice in case of curve A obtained with the large Christiansen 

 filters and three times in case of curve B obtained with the small 

 filters. After that no appreciable change in the form occurred and 

 the process was discontinued. 



A numerical example of the first corrected approximation is given 

 in table 2, for wave length above defined as Wo. In the example 

 Wo is 4600 A and the wave-length intervals a are 200 A. 



Using the results given in table 2, 



£l_ ^ eoCo ^ 257 257 X .700 ^2^ 



Co 2(^_mC_m .... CoCo .... e^nC^n) ./GO 249.7 



the first approximation of the amount of photosynthesis produced 

 at 4600 A as originally measured was 257. 



