OF TUE PEDIASTKE^. 27 



cells; or 6 cells are enclosed by 11 and 15, or by 10 and 16 ; or, lastly, the 

 distribution is partly or completely iiTegular. In the case of 64 cells, no 

 regular aggregation frequently is observable : sometimes 2 or 3 external con- 

 centric series are perceptible, where the position of the inner cells follows 

 no rule ; less fi^equently, the concentric arrangement can be followed to the 

 centre ; when this is the case, one central cell may be enclosed by four 

 series respectively of 6, 13, 19, 25, or of 7, 13, 19, 24 cells; or again, 2 

 middle cells have around them 8, 13, 18, 23, or 7, 12, 19, 24, or 7, 13, 19, 

 23 ceUs in four rows ; or fui'ther, 3 central ceUs have 8, 13, 18, 22 ceUs 

 around, and so forth. 



" The form of the genus PecUastrum has in general a decided tendency to 

 a concentiic disposition of the ceUs. Thus 4 cells combine in 1, 8 in 2, 

 16 in 3, 32 in 4, and 64 in 5 circles. A\Tien this concentric arrangement is 

 distui^bed, it occui's more frequently in larger than in small fi'onds, and more 

 frequently among the central than the peripheral ceUs." 



Braun {Gen. Nov. p. 71) has entered much in detail respecting the number 

 ajjd disposition of the cells, and arrived at the same general results as Nageli. 

 He observes that " the same numerical law is common to all the species [of 

 PecUastrum'], but the number may vary more or less within the legitimate 

 series, even indeed in one and the same species : the disposition also is liable 

 to variation where there is the like number of cells in the same multifarious 

 species ; and this so much the more the greater the number of cells. . , .The 

 legitimate (normal) series, viz. 1, 2, 4, 8, 16, 32, 64, 128, is explained by the 

 binary division which takes place in the formation of gonidia, and which is 

 quicldy arrested or continued for a longer period. 



" I have no dii-ect observations to show whether specimens consisting of a 

 single cell are generated singly from the parent cell, or, after being developed 

 in company with others, they have become dispersed by some accident, which 

 is very probable. Such specimens, belonging pretty clearly to PecUastrum 

 Ehrenbergii, occur eveiyw'here in company with the multicellular fi'onds of 

 this species. Unicellular examples of other species are, it would seem, very 

 rare. I have seen one such of P. Motida ; of some which I think should be 

 assigned to P. Boryanum. Bi-cellular specimens I have only observed in the 

 case of P. Ehrenbergii : instances of 128 cells have frequently occurred to me 

 with P. valgum, and twice with P. Boryanum. The other numbers are common, 

 and occur in very many or in all species, or in the majority ; certain of them 

 indeed much more frequently than others. 



" Numbers divergent fi^om the normal series, whether incomplete or more 

 than complete (supra- complete), are rare, whilst veiy divergent ones are 

 very rare. The former have their origin in the process of fission and the 

 formation of gonidia, when one or other segment in the penultimate division 

 remains undivided, or divides once too often. Thus in P. Boryanum, specimens 

 are occasionally found ha\dng 15 instead of 16, 31 for 32, 63 for 64 cells, or 

 on the contrary, 17 for 16. Examples of 65 in lieu of 64 cells have occuiTed 

 to me in P. asperum. The latter, i. e. those numbers widely divergent, may 

 originate, if in the earlier division of the cytioplasm [protoplasm] some seg- 

 ment is, as it were, passed by, and subsequently enters again in the series of 

 segmentation. In this way the numbers entering into the series 3, 6, 12, 

 24, 48, examples of which are at hand, may be explained. Three cells have 

 been met mth by me in P. Ehrenbergii, and more frequently 6, both in this 

 species and in P. Rotula ; . . . .24 cells, once, in P. asperum.^' 



Braun adds that, if any person should doubt that the number of cells differs 

 in the same species, he has only to inspect collections made in the same place 

 and li\ing imder like conditions, and to note the unequal fonns produced 



