1864<.] On the Structure and Affinities o/Eozoon Canadense. 545 



addition of 2, 4, 6, 8, 10, «&c., which must be added alternately to each ; 2, 

 6, 10, 14, &c. to b, b, and 4, 8, 12, 16, &c. to « + 1 ; but the effect of this 

 alternate addition of 2, 6, 10, &c. to b, 5, by increasing one of them by 1 

 and diminishing the other, and of 4,8, 12, &c. to a,a + l by decreasing 

 each time by 1 and increasing « + 1 by 1, is to make the algebraic sum 

 of the four roots at all times equal to 1, as is distinctly shown in the paper ; 

 and if 2«^ + 2a-|- 1 + 25^ + c^ + c will represent any odd number, then 

 2a2 + 2«+l4-26HcHc=27i+l, deducting 1 and dividing by 2. 



a^-\-a-{-b^-\-—-^=n, and as a^-\-a + b^ equals the sum of 2 triangular 



^ is a triangular number j, therefore every number is 

 composed of not exceeding three triangular Qumbers. 



IV. ^' On the Structure and Affinities of Eozoon CanadenseJ' In a 

 Letter to the President. By W. B. Carpenter, M.D., F.R.S. 

 Received December 14, 1864. 



I cannot doubt that your attention has been drawn to the discovery 

 announced by Sir Charles Lyell in his Presidential Address at the late 

 Meeting of the British Association, of large masses of a fossil organism re- 

 ferable to the Foraminiferous type, near the base of the Laurentian series 

 of rocks in Canada. The geological position of this fossil (almost 40,000 

 feet beneath the base of the Silurian system) is scarcely more remarkable 

 than its zoological relations ; for there is found in it the evidence of a most 

 extraordinary development of that Rhizopod type of animal life which at 

 the present time presents itself only in forms of comparative insignificance 

 — a development which enabled it to separate carbonate of lime from the 

 ocean-waters in quantity sufficient to produce masses rivalling in bulk and 

 solidity those of the stony corals of later epochs, and thus to furnish (as 

 there seems good reason to believe) the materials of those calcareous strata 

 which occur in the higher parts of the Laurentian series. 



Although a detailed account of this discovery, including the results of 

 the microscopic examinations into the structure of the fossil which have 

 been made by Dr. Dawson and myself, has been already communicated to 

 the Geological Society by Sir William E. Logan, I venture to beheve that 

 the Fellows of the Royal Society may be glad to be more directly made ac- 

 quainted with my view of its relations to the types of Foraminifera which I 

 have already described in the Philosophical Transactions. 



The massive skeletons of the Rhizopod to which the name Eozoon Cana- ' 

 dense has been given, seem to have extended themselves over the surface of 

 submarine rocks, their base frequently reaching a diameter of 12 inches, and 

 their thickness being usually from 4 to 6 inches. A vertical section of one 

 of these masses exhibits a more or less regular alternation of calcareous and 



