PRESIDENTIAL AOnRESS, 595 



On examining sections of the two forms, megalospheric and microspheric, in 

 the three species, a further point of interest presented itself, namely, that the 

 megalosphere, the initial chamber of the megalospheric form of N. lisvigatus, was 

 much larger in proportion to the size of the megalospheric shell than the megalo- 

 spheres of N. variolarius or N. Orbigyiyi. I was, therefore, led to examine the 

 proportion in a larger number of forms, and the fine series of nummulites contained 

 in the collection presented by Dr. H. B. Brady to the University of Cambrido-e 

 gave me the opportunity of doing so on ten species or varieties.* 



In N. com2ilanatus the microspheric form attains a diameter of about 2 inches 

 (61 mm.), the megalospheric form a diameter of 5-9 mm. In N. variolarius the 

 microspheric form has a diameter of about 1'92 mm. and the megalospheric form 

 of about 1'8 mm. 



The result of careful measurement was to sliow that the volume of the megalo- 

 sphere is, within narrow limits, proportional to the volume of protoplasm con- 

 tained, not in the whole megalospheric, but in the whole microspheric test. In 

 other words and in the light of our knowledge of the life-history of the dimorphic 

 Foraminifera, the volume of each of the individual members of a brood of megalo- 

 spheric young is in Nummulites proportional to the bulk of the protoplasm of the 

 microspheric parent out of which they are formed. In Hertwig's essay, above 

 quoted, it is pointed out (p. 30) that in functional cells (not eggs) there is a definite 

 proportion between the mass of a protoplasmic body and the mass of nuclear sub- 

 stance contained in it. If we apply this to the result attained for Nummulites it 

 ■would appear that the mass both of the protoplasm and its contained nuclear 

 material are in this asexual mode of reproduction proportional to the whole bulk of 

 the protoplasm out of which they are formed. It would appear to follow that 

 among Nummulites the number of the members of the brood in the asexual mode 

 of reproduction ought to be approximately the same in all species. 



In the sexual mode of reproduction no such relation holds, for the microsphere 

 in N. gizehensis,'^ the microspheric form of which attains a diameter of 237 mm., 

 is hardly larger than that of N. variolarius, in which the diameter of this form is, 

 as we have seen, 1'92 mm. 



In addition to the structural and other characters, binding the members of ' a 

 pair ' of Nummulites togetiier, which led de la Harpe to conclude that they belono- 

 to the same zoological group, we may now therefore add another — the ratio in 

 volume between the megalosphere of one and the protoplasmic contents of the 

 whole shell of the other. 



It would be interesting to find how far this proportion holds good in other 

 genera of Foraminifera. I do not know of any phenomenon precisely comparable 

 with it elsewhere, but the result is so definite that it would appear to be the 

 expression of a general principle. 



In conclusion, I may call attention to the difference presented by the species of 



' The species (or, on the old view, pairs of species) thus examined are : — 



N. complanatug, Lamk., megalospheric form, ^ N. Tchihatelieffi., d'Arch.' 



N.perforatusiA&Tsloniii.') „ „ ' N. Zvcasa>ius, Befi.' 



N. &izehensis(FoTBk.) „ „ ' N. curvispirvs {Menegh.)' 



N.perforatus, var. obesus „ „ ' N. Lncasamts, var. obsoletus, 



d. 1. H.' 



N. lavigatus (Brug.) „ „ ' ZamarcM, d'Aich.' 



Assiliiia expone7is (Sow.) „ „ ' A. mamillata (d'Arch.) ' 



N. biarritzensis, d'Arch. „ „ ' N. Guettardi, d'Arch.' 



N. discorbimis (8chlot.) „ „ ' N. sub-discorbinvs, d. 1. H.' 



N. Orbignyi (Gal.), var. elegans (Sow.) „ „ ' N. Wemmelensis, d. 1. H. and 



and v. d. Br., var. elegans, Sow.' 



N. variolarins (Lz,mk.) microspheric „ 'iV. ZTeierii.d' Arch. and J/rtm^.' 



' I have been unable to measure the microsphere in the larger species owing to 

 the cavities of the chambers in my specimens being filled with calcite, and their 

 outlines obliterated. 



QQ2 



