2 11 Rev. J. F. Blake o/?, the Measurement of the 



and equal in the two valves among the Lamellibranchiata, but 

 greater in the ventral valve among the Brachiopoda. The 

 various forms among the latter class are produced partly by 

 changes of form of the tracing curve, partly by differences in 

 the value of a. Thus such transversely oval forms as Obolus 

 have approximately k> 1, and the inner edge coinciding with 

 the axis, or <r = l ; while elongate ovals, as Siphonotreta, have 

 k<1. Where the hinge-line is straight, as in Spirifera and 

 other genera, the ellipse, in which usually k> 1, overlaps the 

 axis, and consequently X < «, which involves a > 1 ; to ob- 

 tain which the angle of retardation must be imaginary, as it 

 must be therefore in all shells in which we assume a curve 

 cutting the axis. Then also the ratio of growth of the inner 

 edge, which does not, so to speak, exist, is imaginary ; but a, 

 with which we have practically to deal, is real. We can in 

 these cases nevertheless speak of the angle of retardation as 

 being that of the centre over the outer edge, unless the centre 

 itself is on the negative side of the axis, when the phrase be- 

 comes useless and o- is negative and >1. In such conical 

 forms as Discina a. is nearly zero, and y has a moderately 

 small positive or negative value, the latter corresponding to 

 the flat valve. When, as is usually the case, the two valves 

 turn in opposite directions, we must reckon a negative in the 

 dorsal valve ; but when that valve is concave, as in the Pro- 

 ductidce, a. is still positive, but has a different value, less than 

 that of the ventral. 



In the Lamellibranchiata these same differences are com- 

 bined with a very small but not zero value of 7. They all, with 

 few exceptions, principally among the Ostreidce, have the 

 values of a of opposite sign in the two valves, and they pre- 

 sent a greater variety of tracing curves. Their values of a, 

 however, are larger than we find among the Brachiopoda, 

 whose maximum values belong to the Pentameri. Of this we 

 have notable examples, combined with a considerable value of 

 7, in such shells as Isocardia and Dicer as, and with a very low 

 value of 7 in Caprinella. 



Among the Gasteropoda (for a considerable number of 

 which the value of a has been observed by Professor Nau- 

 mann), we have a = for the limpets, while /3 is very small 

 for the Dentaliadce and very large for Haliotis. The suitable 

 values for the other mollusks (the Pteropoda and Cepha- 

 lopoda) will immediately suggest themselves — as we may say 

 generally that the curvature depends on «, the involution on /3, 

 and the elevation on y. 



The direction of the major axis of the generating ellipse in 

 Gasteropoda is generally oblique — being approximately parallel 



