366 BOTANICAL GAZETTE [may 



I 



seen that horizontal lines cut the three temperature curves for 

 Xanthium seeds at 5, 7.5, 10, 15, 20, and 25 per cent of intake. 

 The tangents were determined at the points where these horizontal 

 lines of equal intake cut the curves. From the velocity of intake 

 at the three points cut by each horizontal line, the ratios of velocity 

 have been derived, and from these ratios the mean value of Q xo . 



method of measuring 



crude 



of the tangent is high. The English investigators, however, used 

 the method with fair success. Their measured tangents deviate 

 but slightly from tangents calculated accurately for the same points 

 in their curves, but in less skilful hands serious error might occur. 

 In this work all tangents have been calculated from the known 

 algebraic formulae of the curves, and all inaccuracy of measure- 

 ment has been thereby eliminated. 



In some cases data have been discarded, but only when it was 

 entirely justified, and necessary from the mathematical standpoint. 

 Whenever during the course of an experiment any of the seed coats 

 became ruptured, the curve of intake was distorted because the 

 surface of intake was greatly increased. Mathematical analysis 

 of such data is impossible or meaningless. Such series of data have 



have 



many dryi 



Experimental data 



The data presented in table I were obtained with seeds from the 

 first generation of a pure line of Xanthium pennsylvanicutn Wallr.. 

 from the same line as was used for work on soil moisture published 

 previously (4) . The general characters of the type used have been 

 described as type II in a discussion (5) of physiological isolation in 

 the genus. The series of data chosen for mathematical considera- 

 tion were drawn from a large mass of data some time before the 

 analysis was made, solely on the basis of maintenance of satisfactory 

 conditions during the period of observation. Ten lower seeds of 

 X. pennsylvanicum were used in each case. 



The series at any given temperature were fairly uniform with 

 these seeds at the time the work was done. The variability to 



