454 W. F. LANCHESTER. 



found to be Discontinuous, which I would modify by saying that in some (probably most) 

 cases of this kind, the variation will be found to be of a nature of the above kind, but 

 that in others it may be Continuous. This fact is of some importance. For, though the 

 number of specimens before us is comparatively small, and though certainty of the presence 

 of Continuous Variations must depend primarily on the examination of a very large series 

 of specimens, yet the e\'idence before me hardly lets me doubt that, in such a character, 

 for example, as the relative definition of the carinae, we are dealing with a Continuous Varia- 

 tion. Structurally the different degrees of this variation lead insensibly into one another and, 

 statistically, it is not possible to separate the series into two groups, right and left, and 

 say, " Here end the sharply-carinate, here begin the swollen " ; the proportion of intermediates 

 is too large for this, their number being greater than that of the two extremes. And, while 

 making due allowance for the deficiency of the evidence owing to the relatively small number 

 of specimens, I cannot but feel that we have here a Continuous Variation either presenting 

 itself along with other Discontinuous Variations or, as in some cases, appearing without 

 them. Now I have drawn attention above to the fairly close correlation between the definition 

 of the carinae and the strength of the spines, the latter variation showing evident signs of 

 discontinuity, so that we arrive finally at the idea of the coincidence, not only of Discon- 

 tinuous Variations, as suggested by Borradaile, but also of Discontinuous and Continuous 

 (Specific and Normal in Bateson's later phraseology) Variations. As far as the present instance 

 informs us, it appears that, within the species, the Discontinuous is always coincident with the 

 Continuous Variation (e.g. var. sndthii and var. segregatus a) while the Continuous may appear 

 without the Discontinuous {e.g. var. acutus); from the nature of the case this is only what 

 might have been expected. 



Third heading. Certain of the varieties of G. chiragra do not fall within the transitional 

 scheme given above, nor can I relate them, with any preciseness, to any particular form 

 among those I have described ; they are the following : 



I. Var. B. of Borradaile = anancyrus, Borradaile. 



In the tumidity of the carinae and absence of ' anchor ' this form resembles var. tumidus, 

 but diflfers from it verj' notably in the presence of (1) well-developed lateral marginal teeth, 

 and (2) a small tubercular spine on the distal end of the median carina. 



II. Var. C. of Borradaile = acatirostris de Man. 



Carinae not much swollen, without anchor, lateral marginals developed, carinae on sub- 

 median teeth converging forwards, angles of rostrum sharp. 



I am a little dubious as to the value of the convergence of the carinae on the sub- 

 median teeth as a distinctive character: I have never seen this appearance in the numerous 

 examples of the other varieties of G. chiragra, which I have examined both here and in the 

 Natural History Museum at S. Kensington, and, as Dr de Man was dealing \vith a single 

 specimen, it is possible that this very unusual feature represents an individual abnormality. 

 The other characters are, no doubt, distinctive. 



III. Var. IsL = spinosus Bigelow. PI. XXIII. fig. 14. 



The three carinae are exceedingly swollen so as to touch each other along their sides, 

 the carinae of the submedian and intermediate teeth are also swollen, and all the surface 

 of the telson, except the bottom of the grooves, is covered with minute spinules. In one 



