Dlatomaceous Frusttde, and its Genetic Cycle. ■ 5 



eight somewliat larger, and so on in a geometrical ratio, which 

 will soon present us with an innumerable multitude contain- 

 ing individuals in every stage, but in which the larger sizes 

 predominate over the smaller ; and such are the circumstances 

 ordinarily found to attend the presence of large numbers of 

 these organisms." I am afraid that this doctrine of a geome- 

 trical increase in the size of the frustules will not stand the test 

 either of fair theoretical induction or comparison with natural 

 fact J for although there is in truth a gradual diminution, even 

 this does not take place in a geometrical ratio, which, in the 

 nature of the case, can only apply to number, not to size, as 

 will be clearly seen on inspecting fig. 5, pm-jiorting to trace 

 the history of a single frustule through five grades of self- 

 division, in which the numbers accurately express the relative 

 sizes of all the half-frustules, new and old. 



It is now full time to elucidate my own views by illustra- 

 tive facts, which I hope will be considered satisfactory, as 

 supporting all the observations previously made, and by in- 

 ference affording a guide to the study of those forms which, 

 from their extreme delicacy and minuteness, might be for ever 

 problematical and difficult of analysis, both as to structure and 

 physiology. 



As each perfect frustule consists of an older and a younger 

 valve, never of two valves of the same age, Kiitzing's names, 

 primary as applied to the former, and secondary to designate 

 the latter or the invaginated valve, can be open to no possible 

 objection. But to these it is absolutely necessary to add two 

 tertiary valves of the same age, resulting from the process of 

 fission, viz. the first tertiary, developed in connexion wnth the 

 primary valve, and the second tertiary, forming a new frustule 

 with the secondary valve. 



Of all these valves the primary or most external is the 

 largest, the secondary and first tertiary are intermediate, while 

 the second tertiary is the smallest. 



Fig. 1 (PI. III.) is a diagrammatic section of a perfect frustule 

 previously to the transverse fission of its primordial utricle 

 and contents. 



b. Secondary or invaginated valve. 

 b 1. Body of the valve. 

 b 2. Secondary hoop. 



a. Primary valve. 



a 1. Body of the valve. 

 a 2. Primary hoop. 



Fig. 2 represents a perfect frustule after the fission of the 

 primordial utricle and contents and the formation of c and 

 d, the first and second tertiary valves of the same age, and 

 consisting of c 1 and t?l, the body of the valves, and c2 and 

 d 2, the incipient tertiary hoops. The remaining references are 

 the same as in fig. 1. 



