50 Mr. D. Thoday. Experimental Researches on [June 11, 



too laborious, the time of experiment must he increased, or the average degree of 

 asymmetry for individual leaves reduced by avoiding veins. 



Thus if the average degree of asymmetry were for Helianthus annuus reduced to 

 1*5 per cent., that is by f, and the time of experiment increased to 10 hours, the number 

 of leaves required, for the same degree of accuracy which demanded 16 leaves under the 

 conditions originally assumed, would be reduced to 16 x (|x that is, to two or 



three. 



The number of leaves of Helianthus annuus used by Sachs for each experiment was 

 seven or eight, and the same number gave Brown and Morris's difference of I'l percent., 

 which for a 10 hours' experiment works out to 0'4 milligramme per hour, and thus 

 within the ± 0"5 milligramme error for which we have been calculating. 



It will be convenient in this place to examine Brown and Escombe's experi- 

 ments, in which they compared the apparent increase of dry weight, given by 

 the simple half-leaf method, with the weight of carbohydrate corresponding 

 to the carbon dioxide actually absorbed. 



Considerations will be adduced in favour of the conclusion that the great 

 discrepancies which tliey found are adequately explained by the asymmetry 

 of leaves of Catalpa bignonioides, and their shrinkage under the experimental 

 conditions. 



Changes in ash content and inadequacy of tlie " carbohydrate factor " could 

 account for a small part, but their effect may be ignored for the present 

 purpose. 



Before considering the results of the experiments themselves, it is necessary 

 to estimate the probable magnitude of the errors. Unfortunately, this can 

 only be done in a general way, as Brown and Escombe give neither the 

 conditions under which the individual experiments were performed nor the 

 time during wliich each lasted. 



An instance of the possible error from asymmetry can' be derived from the 

 results of their own asymmetry test.* In each of tlieir dry weight experi- 

 ments they used four leaves, taking as control half-leaves the left and right, 

 halves alternately. Treating in tliis way the first four examples of Catalpa 

 bignonioides from their asymmetry table, a difference is obtained, when the 

 four leaves are taken together, of 2'1 per cent. The average dry weight per 

 square decimetre of their Catalpa leaves is about 0'45 gramme, so that 

 lliis error would have meant an under- or over-estimate of the total increase 

 of dry weiglit by !)'4 milligramiiies per square decimetre. 



Tlie ])0SHible errors from shrinkage must be deduced from the one expcri- 

 mentf in which Brown and Escombe measured the changes of area taking 

 place in the exi)erimontal ch!iiii])er used in tlieir tests. Tliey found the 



* Quoted on j). l.'J. 

 t /ax: rlt., ]). 60. 



