April 12, 1894J 



NA TURE 



57« 



the chart. As a consequence of this straightness, the swiis 

 of the ages of the ])arents to which each point in the 

 straight portion of the same isogen refers is constant. The 

 difference between their ages is of no account whatever in eight 

 nr nine tenths of (lie total number of marriages ; it is only when 

 the wife is older than the husband, or when she approaches the 

 limit of the child bearing age, that this curious law ceases to 

 hold true. 



Again, through a coincidence between the increasing age of 

 either parent and the decrease of fertility, it happens that the 

 sum of the three elements of (l) father's age, (2) mother's age, 

 (3) percental birth rate in a year has a value that is itself appro- 

 priately constant. 



From this follows the curious law that if we wish to calculate 

 the percental hiith rate per annum for a married couple within 

 the limits of the chart where the isogens run straight and 

 parallel, we have only to add the ages of the father and mother 

 and subtract the total from 93 or 94, in order to obtain it with 

 considerable precision. The approximate limits within which 

 this law obtains are: (l) the wife is not to be older than her 

 husband ; (2) she is not to be less than twenty-three years of 

 age, nor (3) more than forty. 



Example. — In any large number of husbands and wives living 

 under like conditions to the inhabitants of Budapest, whose re- 

 spective ages at their nearest birthdays, to 2 1st June, 1892, 

 were : that of the father, thirty-five, that of the mother, twenty- 

 seven : then the number of children born to them during the 

 year 1892 would be at the rate of 93 -(35 + 27) per cent. = 31 

 per cent ; the is )gen makes it about 32 per cent. 



Entomological Society, March 28. — Captain H J. Elwes, 

 President, in the chair. — Mr. McLachlan, F.R.S., announced 

 the sudden death, on the 23rd inst., of Mr. J. Jenner-Weir, 

 who joined the Society in 1845, and had been one of its most 

 regular attendants. He also commented on the scientific attain- 

 ments of the deceased, and his social qualities and virtues. Mr. 

 Goss and Mr. Merrifield also spoke of their long friendship 

 with the deceased, and of the resp;ct and esteem which they 

 entertained for him. — Mr. W. Borrer, jun., exhibited a wasp's 

 nest which had been built in such a way as to conceal the entrance 

 thereto and to protect the whole nest from observation. He 

 believed the nest to be that of Vespa vulgaris. Mr. McLachlan 

 and Mr. Blandford made some remarks on the subject, — Mr. 

 G. F. Hampson exhibited a specimen of Gaudaritis flavata, 

 Moore, from the Khari Hills, and called attention to the exist- 

 ence in the males of this species, in the closely allied British 

 species Cidaria dotata, Linn., and a'so in two Japanese species, 

 of an organ on the under-side of the fore wing, which he 

 suggf-sted might be for stridulation ; this organ consisting of a 

 small scar of hyaline membranes situated just below the middle 

 of vein 2, which is much curved ; this scar is fringed with long 

 hair, and has running doA'u its middle a row of sharp spines 

 situated on the aborted remains of vein i, and which is curved 

 up close to vein 2 ; the spines would naturally rub against part 

 of the costa of the hind wing, but no spines or unusual roughen- 

 ing seems to exist 011 that or on any of the veins on the upper 

 side of hind wing against which they could strike ; below the 

 scar is situated a large shallow fjvea or pit in the membrane, 

 slightly developed in C. dotata and C. flavata, but much more 

 prominently in the t^vo Japanese species, and, should the organ 

 prove to be for stridulati )n, would probably act as a sounding 

 board. Mr. Ham,)Son said that in the Japanese species closely 

 allied to flavata, the males have no trace of this curious 

 organ. Prof. E. R. Poulton, F.R.S., Lord Walsingham, 

 F. R. S. , and Mr. Hampson took part in the discussion which 

 ensued. — The Rev. T. A. Marshall communicated a paper 

 entitled "A Monoi;raph of the British Braconidce, part v." — 

 Mons. Louis Peringuey communicated a paper entitled " De- 

 scriptions of new Cicindelidse from Mashunaland." — Prof. 

 Poulton gave an' account of his recent tour in the United 

 Statc^, and commented on the entomological and other 

 collections contained in the American museums. Lord Walsing- 

 ham, Mr. Hampson, and the President also made some remarks 

 on the subject. 



Edinburgh. 

 Royal Society, ALarch 5.— Prof. Sir W. Turner, Vice- 

 President, in the chair. — Prof. Crum Brown read the fiist part 

 of a paper on the division of a parallelepiped into tetrahedra. 

 The subject of the paper was the question suggested by Lord 

 Kelvin: In ho v many ways can a par.illelepiped be cut into 



N J. ] 276, VOL. 4.9 1 



tetrahedra without introducing newcomers? In the first part 

 the author discusses the division of the cube into tetrahedra, all 

 the corners of the tetrahedra coinciding with the corners of the 

 cube. Noting the corners of the cube A, B, C, D, A, B, C, D, 

 so that A A, &c. are body diagonals of the cub?, and A B» 

 AC, AD, &c. face diagonals, and therefore A B, &o. edges » 

 we_ hav^ the_ following_ five forms of tetrahedra : A B C D, 

 ABC p, AABC, A A BC, and A A C B, and no more, for 

 A B C D and A A B B have all four corners in one plane. These 

 tetrahedra may be designated O, A, I, L, r, respectively. C> 

 has a volume one-third of the cube, has no part of the surface of 

 the cube, and can occur in two positions in the cube, A BC D 

 and A B C D. A has a volume one-sixth of the cube, has three 

 faces coinciding each with half of a face of the cube, and can 

 occur in eight positions. I has a vo'ume one-sixth of that of 

 the cube, has one face coinciding with half a face of the cube, 

 and can occur in twenty-four positions. L and r are enantio- 

 morph, each has a volume one-sixth of thS cube, and each can 

 occur in twelve positions. These give fifty-eight positions in 

 all, which, with the twelve groupings of four corners all four in 

 one plane, make up the seventy groups of four corners. The 

 author then goes on to discuss the number of ways in which 

 these tetrahedra can be built together to form a cube. These 

 are shown to be the following : — 



I O and 4 a's, 



3 a's and 3 I's, 



*2 a's, 2 I's, and 2 L's, 

 *2 a's, 2 I's, I L, and i T, 

 *2 A's, 2 I's, and 2 r's, 

 * I A, I I, 3 L's, and i r, 

 I A, I I, 2 L's, and 2 r's, 



1 A, I I, I L, and 3 r's, 



4 L's and 2 r's. 

 3 L's and 3 r"s, 



2 L's, and 4 r's. 



Of these the three marked * correspond' to two different 

 arrangements each, in one of which the plane separating an I 

 from a A are parallel, in the other inclined to one another. 

 There are therefore fourteen distinct ways in which a cube cm 

 be cut into tetrahedra without making new corners. — Prof. 

 Cossar Ewart read a paper on the second and fourth digits of 

 the horse, their development and subsequent degeneration. He 

 referred to cases in which two or even three digits had been 

 recorded. In some cases the presence of such digits is due to 

 subdivision of the normal middle digit, in others it is due to the 

 restoration of those digits which are always found in the fossil 

 hoise. Prof. Ewart argues that the terminal "buttons" or 

 tubercles of the splint bones of the horse are vestiges of the lost 

 second or fourth digits. He gives a description of the condition 

 of the digits in embryos of different ages. In embryos undtr 

 I inch in length no evidence was found of the phalanges of the 

 second or fourth digits, but in a slightly larger embryo a rudi- 

 ment of the second finger, connected by a complete joint to the 

 second metacarpal, could be made out. The second and fourth 

 phalanges attained their greatest development in embryos about 

 14 inches in length. The second finger then showed a terminal 

 phalanx and an indistinct second phalanx connected to a large 

 first phalanx which was joined by a very complete joint to its 

 metacarpal. The apex of the terminal phalanx was surrounded 

 by a cap corresponding possibly to one of the deeper layers of 

 the normal hoof. In older embryos the joints were never so 

 complete, the second and third joints rapidly disappearing, so 

 that the second and fourth toes of all the limbs consisted of an 

 elongated piece of cartilage connected by more or less distinct 

 joints to the metacarpals. In still older embryos the fused 

 phalanges are ossified and are firmly connected to the splints so 

 as to form the well-known "buttons." 



March 19. — Prof. Geikie, Vice-President, in the chair. — 

 Prof. Crum Brown communicated the second part of his paper 

 on the division of a parallelepiped into tetrahedra. He showed 

 that there are 180 distinct ways in which this may be done with- 

 out introducing a new corner. — A paper, by Mr. Gregg Wilson, 

 on the reproduction of the edible crab, was communicated. — 

 Mr. C. A. Stevenson read a paper on telegraphic communica- 

 tion by induction by means of co Is. Such comnunication has 

 been found possible when two circular coils of 200 yards dia- 

 meter were placed horizontally at a distance of one quarter of a 

 mile apart. 



