204 THE QUANTITATIVE METHOD IN BIOLOGY 



Comparing the four curves in Fig. 27, it may be concluded 

 that the gradation of each primordium is independent of the 

 gradation of the others. The study of several examples of 

 gradation in other Phanerogamia (internodes and leaves in 

 Ilex, Ulmus, etc.) and in animals (shells of Molluscs, etc.) has 

 brought me to the same conclusion. In my paper on Mnium 

 referred to above I have given the gradation curves of a dozen 

 of primordia of the leaves along the axis of the fertile stem in 

 ten British species of that genus : here, also, the curves were 

 found to be in general independent of each other, although 

 in certain cases two curves have the same form or thereabout. 



The independence of the gradation curves of different 

 primordia along a given axis seems, therefore, to be a general 

 rule. 



THIRD EXAMPLE: GRADATION IN A LEAF.— The 

 blade of a leaf (in preference an entire oblong, lanceolate, oval 

 or obo val leaf) is an individual (unit) of a certain order (order x) , 

 the longitudinal axis (axis NS) of which is indicated by the mid- 

 nerve. We know that the successive parts (I do not use here 

 the term segments) which follow one another along the axis 

 have been developed successively, ordinarily in basipetal order. 

 If we measure the breadth of the blade at a certain number of 

 equidistant places from the base to the summit of the leaf we 

 obtain a series of figures which represent a gradation curve. 



The margin of a leaf is, on each side, a curve of the gradation 

 of the primordium breadth'^ drawn by nature itself. Very 

 often, even in leaves which seem to be exactly symmetrical, a 

 difference between both margins (right and left) is discovered 

 by measurement. 



In certain leaves (or other phylloms), which are narrowed 

 about their middle, two periods (waves) of gradation exist 

 (marginal curve two-humped). (See my paper on Mnium, 



p. 33.) 



The margm of a leaf is curved ; it consists of a series of 

 successive, straight, simple axes. The curvature is a secondary 

 form brought about by gradation (§ 84) . 



§ 141.— COMPARISON BETWEEN GRADATION CURVES 

 AND EMBRYOLOGICAL CURVES. INDEPENDENCE 

 OF THE PRIMORDIA.— When we compare the different 

 values of a given primordium along a given axis, each value 

 coincides with a certain state of development in which the 

 growth of the primordium has been stopped. (See length of a 

 petal, § 45.) For instance, in the first stem of Poa trivialis, 

 mentioned p. 200, internode V. has been stopped in its growth 



1 The dimension of one-half of the leaf in the direction of the transversal 

 axis (axis EW). 



