238 
NATURE 
[Fuly 9, 1885 
and a pair of such points lying at the extremities of a side are 
undistinguishable from the three other like pairs, but are dis- 
tinguishable from the two pairs formed by taking angular points 
at the extremities of a diagonal, which pairs again are undis- 
tinguishable from each other. Further, a pair, ad, may some- 
times be distinguished from a pair, da, though the units @ and 0 
are undistinguished. Thus if a, 6,¢ be the angular points of 
an equilateral triangle, and barbs be drawn on the sides pointing 
from a to 4, from é to c, and from ¢ to a respectively, the angu- 
lar points a, 4, ¢ will be undistinguished from each other; each 
has an arrow proceeding from it and to it, but the pair ad is 
distinguished from the pair a, for an arrow proceeds from a to 4, 
but none from @ to a. 
In the same way we have distinguished and undistinguished 
triads, tetrads, &c. 
Every collection of units has a definite forvz, due—(1) to the 
number of its component units, and (2) to the way in which the 
distinguished and undistinguished units, pairs, triads, &e., are 
distributed through the collection. Two collections of the same 
number of units, but having diiferent distrzbutzons, will be of 
different forms. The angular points of a cube and of a regular 
plane octagon furnish examples of two systems of eight units, 
having different distributions. In the former case there are 
three sorts of pairs, in the latter four. 
Each of the forms which a system of units can assume 
owing to varieties of distribution is one of a definite number of 
possible forms, and the peculiarities and properties of the col- 
lection depend, as far as the processes of reasoning are con- 
cerned, upon the particular form it assumes, and are independent 
of the dress—geometrical, logical, algebraical, &c.—in which 
it is presented ; so that two systems which are of the same form 
have precisely the same properties, although the garbs in which 
they are severally clothed may by their dissimilarity lead us 
to place the systems under very different categories, and even to 
regard them as belonging to ‘‘ different branches of science.” 
It may seem in some cases that other considerations are in- 
volved besides ‘‘ form,” but it will be found on investigation 
that the introduction of such considerations involves also the 
introduction of fresh units, and then we have merely to consider 
the form of the enlarged collection. 
Taking these principles as a basis, the memoir, which is a 
lengthy one of 426 sections arranged under 42 heads, discusses 
the various forms which systems can assume, and gives some 
general modes, graphical and literal, of representing them. The 
genesis of algebras is considered, and the nature of the particular 
forms dealt with in geometry, ordinary algebra, formal logic, 
and other cases, is specified. 
Zoological Society, June 16.—Prof. W. H. Flower, 
President, in the chair.—The Secretary read some extracts from 
a letter addressed to him by Mr. J. Buttikofer, of the Leyden 
Museum, calling attention to a paper published in 1857 by the late 
Dr. Bernstein, concerning the material of which the edible birds’ 
nests of Collocalia esculenta aré composed.—A letter was read 
from Major-General Sir Peter Lumsden, K.C.B., giving details 
of the place and time of capture of two young Snow-Leopards 
sent down from the Afghan frontier to Quettah, and intended 
for the Society’s collection.—Mr. Oldfield Thomas exhibited 
and remarked ona specimen of a rare burrowing Rodent (Herero- 
cephalus glaber) procured by Mr. E. Lort Phillips during his 
recent expedition in Somaliland, remarkable for having an 
almost completely naked skin, and for its extraordinary habits. 
—Dr. Guillemard exhibited a series of eight skulis of the Kam- 
tschatkan Wild Sheep (Ovés zivzcola), pointing out the difference 
existing between it and-O. canadensis.—Mr. W. T. Blanford 
exhibited the skull and an imperfect skin of a supposed new 
species of Paradoxurus from the Pulnai Hills, Southern India. 
—A communication was read from Dr. G. Hartlaub, F.M.Z.S., 
giving an account of a new species of Parrot of the genus 
Psittacula recently received from Barranquilla, U.S. of Colombia, 
which he proposed to describe as Psittacula spengeli.—Dr. 
Guillemard, F.Z.S., read the sixth part of his report on the col- 
lection of birds formed during the voyage of the yacht Marchesa. 
The present communication treated of the birds collected in New 
Guinea and the Papuan Islands. —Dr. Guillemard also exhibited 
a very fine series of Paradiseidze obtained during the yacht’s 
voyage.—Mr. G. A. Boulenger read a paper containing a de- 
scription of the German River-Frog (Rana esculenta, var. rid?- 
bunda, Pallas).—Mr. P. L. Sclater read the description of a 
new species of /cferus, obtained by Mr. Hauxwell on the Upper 
Amazons, which he proposed to name JZ. hawxwelli,—A second 
paper by Mr. Sclater contained notes on the way in which Lemur 
macaco Carries its young, as obseryed in a specimen living in the 
Society’s Gardens.—Mr. A. D. Bartlett read some notes on the 
female Chimpanzee now living in the Society’s Gardens, which 
he showed to be different from the ordinary Chimpanzee, and to 
be probably the Zroglodytes calvus of Du Chaillu.—Dr. Gadow, 
C.M.Z.S., communicated a memoir by Miss Beatrice Lindsay, 
of Girton College, Cambridge, upon the Avian Sternum. The — 
different theories held as to the origin of the sternum haying 
been reviewed, the author proceeded, after an explanation of the 
various types of structure examined, to give an account of her 
own views. Miss Lindsay came to the conclusion that the keel 
is an apophysis of the two halves of the sternum, and is not pro- 
duced by the clavicles or any other parts belonging to the shoulder- 
girdle ; also that the part of the sternum whereof the keel is an 
outgrowth is itself of secondary origin, and that the various pro- 
cesses of the sternum are produced by addition and not by resorp- 
tion of bony matter.—Col. J. Biddulph read a paper on the Rocky 
Mountain Sheep, in reference to the new geographical race lately 
named by Mr. Nelson Ovis montana dalli, and confirming the 
view that there are two distinct types or races of this sheep in 
North America. 
Geological Society, June 10.—Prof. T. G. Bonney, F.R.S., 
President, in the chair.—Dr. A. G. Nathorst, of Stockholm, 
was proposed asa Foreign Correspondent of this Society. —The 
following communications were read :—Note on the sternal 
apparatus in /ewancdon, by J. W. Hulke, F.R.S., V.P.G.S.— 
The Lower Paleozoic rocks of the neighbourhood of Haverford- 
west, by J. E. Marr, F.G.S., and T. Roberts, F.G.S.—On cer- 
tain fossiliferous nodules and fragments of hematite (sometimes 
magnetite) from the (so-called) Permiezn breccias of Leicester- 
shire and South Derbyshire, by W. 5. Gresley, F.G.S. 
‘SYDNEY 
Linnean Society of New South Wales, April 29.—Dr. 
James C. Cox, F.L.S., Vice-President, in the chair.—The fol- 
lowing papers were read :—Revision of the genus Lamprima, 
with descriptions of new species, by William Macleay, F.L.S.— 
Notes on the zoology of the Maclay Coast, New Guinea, by N. 
de Miklouho-Maclay. This paper consists of a carefully detailed 
account and description of a rare species of Macrapus, to which 
the Baron gives the specific name of 77éo/, the native name for 
the animal. A plate accompanies the paper.—On two new 
species of Dorcofsis from the south coast of New Guinea, by N. 
de Miklouho-Maclay. This contains descriptions and illustra- 
tions of Dercopsis macleayi and D beccari, two new species in the 
Macleay Museum. This brings the number of known species 
of the genus up to five-—The Australian sponges recently de- 
scribed by Carter, by R. von Lendenfeld, Ph.D.—On the fer- 
tilisation of Goodenia hederacea, by Alex. G. Hamilton.—Notes 
on the habits of Hadco subniger and Glareola grallaria, by K. H. 
Bennett.—The geology of Dubbo, by the Rey. J. Milne Curran. 
—Dr. J. C. Cox exhibited a sandstone nodule, the outer crust 
of which to a considerable depth was stained with iron, the 
original colour, as shown by the central portion, having been 
white. Also a large Cephalopod, belonging to the family 
Sepiide and genus Sepia, which had been recently presented to 
the Australian Museum by the Hon. William Macleay. This 
unique specimen is about three feet long from the hinder part to 
the apex of the arms; the body is about eighteen inches long, 
and eighteen inches broad, deeply notched at the lower margin, 
and peaked in the centre at the neck, and arched on each side ; 
the head is about eighteen inches from the body to the apex of 
the arms. It is of a dark brown olive colour, quite smooth, the 
tentacles are about two feet long, the cups on the arms do not 
correspond with any known species, nor do the cups on the 
tentacles ; it is very like Sepia tuberculata of Lamarck, but no 
tubercles exist on the surface, and it is much longer. Sepia 
vermiculata of Quoy and Gaim. is very like it, but is only fifteen 
inches long; most of the species, however, of the genus have 
been described from the shell. 
Paris 
Academy of Sciences, June 29.—M. Bouley, President, 
in the chair—Remarks on Poinsot’s theory, and on two moye- 
ments corresponding to the same polhodie, by M. G. Darboux. 
—On Palmieri’s experiments relative to atmospheric electricity, 
by M. Faye.—Remarks on the same subject by M. Mascart.—- 
Researches on isomery in the aromatic series. Heat of neutral- 
isation of the oxybenzoic acids, by MM. Berthelot and Werner. 
