410 MR. F. A. BATflER OS PETALOCRINTJS. [Aug. 1 898, 



inference might be justified; but he continues, ' the other speci- 

 men [namelj-, g] does not show any appreciable difference in the 

 different sides.' The measurements tabulated on p. 430 confirm 

 Mr. Weller's second statement more readily than his first. Although 

 there is variation in the width between the arm-bases, in no case 

 can one interradius be selected as conspicuously wider than the 

 others. At the same time, in specimens d, f 1, f 2, and possibly g, 

 one interradius is distinctly narrower than the others, and might 

 plausibly be regarded either as one of the anterolateral interradii, 

 or as the right posterior. This, however, is not the case with a. 



The Arms consist each of two parts : a first primibrach (IBr^), 

 "which rests on the radial facet, and an arm-fan, which rests on 

 the first primibrach. 



The first primibrach is barely '5 mm. high, with its proximal and 

 distal margins parallel, of the same width as the facet of B, and of the 

 arm-fan, and, so far as can be seen, of the same thickness on both 

 dorsal and ventral margins (except perhaps for the slight reentrant 

 angle on the ventral surface, already mentioned as seen in the im- 

 pression of the tegmen in f 1). Pirst primibrachs are seen also in a 

 and d, and less clearly in f 2 and g. They were no doubt always 

 present in P. mirabilis, and probably in other species. Their 

 articular surfaces are unknown, but the structure of the distal one 

 can be inferred from the facet of the arm-fan. 



The Arm-fan, as seen from the ventral surface, roughly resembles 

 a folding fan, opened to a varying extent in different individuals, 

 and still more in different species. Seen from the dorsal surface it 

 is like an oar-blade or paddle. The sides do not meet in a point, 

 but become parallel at a short distance from the proximal end, 

 forming as it were a short handle to the fan or paddle. Also at 

 the distal end the sides usually curve inwards, especially in old 

 iadividuals. 



The angle of any arm-fan is defined as the angle at which lines 

 drawn parallel to the general direction of the diverging sides, ex- 

 clusive of the incurved distal region, meet one another. In 

 P. vishycensis the angle varies from 70° to 93°, the average in ob- 

 served specimens being 82° 24', while in more than half the 

 specimens it falls between 80° and 85° : that is, the mode equals 

 the mean.^ In P. mirabilis the angle varies from 51° to 83°, the 

 average in thirty-one observed specimens being 71°, while in more 

 than half the specimens it falls between 71° and 78° : that is, the 

 mode is a larger angle than the mean. In P. inferior the angle is 

 about 70° ; in P. longus, 38°; in P. angustus, 38°; in P. eicpansus, 

 90° ; in P. vishycensis (senior), about 88°. 



^ G-eologists unfamiliar with the rising flood of zoological literature on Varia- 

 tion may be referred to W. Bateson, ' Materials for the Study of Variation,' 

 London, 1894 ; and Karl Pearson, ' The Chances of Death,' 2 vols., London 

 & New York, 1897. Those works contain explanations of many terms and 

 methods used in the present investigation. 



