232 JOURNAT. OK CONCMOI.Or.Y, VOL. l6. NO. 7, SICI' IKMKKK, I921. 



for the fust specimen so treated are given in Table IV, the corre- 

 sponding curve being shewn in fig. 5. Tluis it appears that the 

 ontogeny is in complete agreement with the growth curve based on 

 the whole series of shells. 









Table IV. 













Length, mm. 



iii 



14 



35 



19 24 



22^^ 



24 



27 



3oi 



35 

 81 



Width, mm. 



25 



31 



43 48^ 



51 



56 



63 



71 



It was not found practicable to follow the growth of an individual 

 in the case of the relation between thickness and length. 



However, it appears legitimate to assume that here again the onto- 

 genetic curve will agree with that given by the series ; in Unio 

 pictoruni, as in other bivalves — Anodonta cygtiea Linne, SphcBrium 

 corneum Linne, etc. — the young shells are always slender, and this 

 fact, coupled with the proof above given in the case of the width : 

 length relation, seems to justify the assumption. 



Over the range between lengths 23 and 35 mm., the curve shewing 

 the variation of thickness with length agrees almost perfectly with the 

 expression : — 



i'55-(-o'o44 L 



T = e 



where L ■= length in mm., T = thickness in mm. ; the curve corre- 

 sponding with this equation is given in fig. 4 (broken curve). 



This is particularly interesting in view of a recent investigation of 

 Petersen.' From the mathematical analysis of data obtained by 

 measurement of individual Clausilia lamhiata Mont., he establishes 

 an exponential law of the type : — 



a-l-bx-|-c.\- - 



for the growth of the species. He then shews that measurements of 

 the height and of the chest in man, of the number of rays in the 

 caudal fin of plaice, of the weight of Clausilia lamitiata, of the length 

 of beans {Fhaseoljis muliiflorus), of the ratio of the width of the head 

 to the length of the body in crabs, of the number of florets of 

 Chrysanthemum segetu7n, and of the weight of beans, give distribution 

 curves which are in agreement with this law. In the particular case 

 where c = o, the equation reduces to : — 



a + bx 



which Petersen designates the " law of quotients." It is of interest to 

 note that the curve connecting thickness and length in U. pictoru?n 

 agrees with an equation of this simpler type. 



