XI 



OF BIVALVE SHELLS 



827 



Chords of an ellipse, whose major and minor axes {a, b) 

 are in certain given ratios 



0° 

 10 

 20 

 30 

 40 

 50 

 60 

 70 

 80 

 90 



a/6 = 1/3 



10 



101 



105 



1115 



1-21 



1-34 



1-50 



1-59 



1-235 



00 



1/2 



10 



101 



103 



1065 



Ml 



1145 



1142 



101^ 



0-635 



0-0 



2/3 



10 



1-002 



1005 



1-005 



0-995 



0-952 



0-857 



0-670 



0-375 



0-0 



1/1 



1-0 



0-985 



0-940 



0-866 



0-766 



0-643 



0-500 



0-342 



0-174 



0-0 



3/2 



10 



0-948 



0-820 



0-666 



0-505 



0-372 



0-258 



0-163 



0-078 



0-0 



2/1 



1-0 



0-902 



0-695 



0-495 



0-342 



0-232 



0-152 



0-092 



0-045 



0-0 



3/1 



1-0 



0-793 



0-485 



0-289 



0-178 



0-113 



0-071 



0-042 



0-020 



0-0 



The ellipses whicli we then draw, from the values given in the 

 table, are such as are shewn in Fig. 401 for the ratio a/6 = f, and 

 in Fig. 402 for the ratio a/6 = J ; these are 

 fair approximations to the actual outlines, and 

 to the actual arrangement of the lines of growth, 

 in such forms as Solecurtus or Cultellus, and in 

 Tellina or Psammobia. It is not difficult to in- 

 troduce a constant into our equation to meet the 

 case of a shell which is somewhat unsymmetrical 

 on either side of the median axis. It is a some- 

 what more troublesome matter, however, to 

 bring these configurations into relation with a 

 "law of growth," as was so easily done in the 

 case of the circular figure: in other words, to °° 



formulate a law of acceleration according to which ^^^' ^^^ • 



points starting from the origin 0, and moving along radial lines, 

 would all lie, at any future epoch, on an ellipse passing through ; 

 and this calculation we n^ed not enter into. 



All that we are immediately concerned with is the simple fact 

 that where a velocity, such as our rate of growth, varies with its 

 direction — varies that is to say as a function of the angular divergfence 

 from a certain axis — then, in a certain simple case, we get lines of 

 growth laid down as a system of coaxial circles, and, in some- 

 what less simple cases, we obtain a system of ellipses or of 

 other more complicated coaxial figures, which may or may not 

 be symmetrical on either side of the axis. Among our bivalve 

 mollusca we shall find the Unes of growth to be approximately circular 

 in, for instance, Anomia] in Lima (e.g. L. subauriculata) we have 



