178 
NATURE 
[Dec. 29, 1870 


of the fittest,” adopted by Mr. Wallace from Mr. Herbert 
Spencer. The subject of individual variation was discussed at 
some length, and the laws of divergence commented on. The 
author expressed his dissent from Mr. Wallace’s interpretation of 
Darwin’s theory. 
Mathematical Society, Dec. 8.—Mr. W. Spottiswoode, 
F.R.S., president, in the chair. Mr. J. Hamblin Smith, 
M.A., of Caius College, Cambridge, was elected a member.— 
Prof. H. J. S. Smith made a communication on the subject of 
Elliptic Integrals.—Prof. Cayley read a note on his former 
paper, ‘*On the Theory of the Rational Transformation between 
two Planes, and on Special Systems of Points,” followed by 
an account of an addendum to his recent memoir on ‘‘ Quartic 
Surfaces.” In this latter communication he stated the following 
theorem :—Take any seven points ; an eighth point at pleasure 
on the dianodal surface of the seven points ; a ninth point at 
pleasure on the dianodal curve of the eight points. In the 
system of nine points so determined take any one as vertex, 
and joining it with the remaining eight, construct the ninth line 
of the ‘‘ennead”: we have thus nine lines passing through the 
nine points respectively. These nine lines meet in a point which 
is the ‘‘enneadic centre” of the nine points; and further, the 
ten points form acompletely symmetrical system, so that each 
one of them is the enneadic centre of the remaining nine. [The 
name ‘*ennead” is given to any nine pomts zz plano, which are 
the intersections of two cubic curves, or to any nine lines through 
a point which are the intersections of two cubic curves; the ten 
points in space are such that taking any one whatsoever as 
vertex, and joining it with the remaining points, the nine lines 
form an ennead.] The author stated the following system of 
correspondence as a subject for investigation—viz., given any 
eight points in space ; then to every point in space corresponds 
a line through this point, viz., the ninth line of the ennead ob- 
tained by joining the point with the eight given points respec- 
tively ; and to each line in space a point or points on the line, 
viz., the point or points for each of which the line is the ninth 
line of the ennead obtained by joining the point with the eight 
given points respectively. —Dr. Hirst entered at some length into 
an explanation of the methods employed in his paper ‘‘on the 
Polar Correlation of two planes, and its connection with their 
Quadric correspondence.” Profs. Cayley, Smith, Mr. Cotterill, 
and the author took part in a discussion on the paper.—Prof. 
Henrici exhibited a large model of Dr. Sylvester’s amphigenous 
surface, which has for its equation 
JK‘ + 8LK3 — 2J?LK? - 72JL°K — 4321 + J? L?=0 
a Deal’ 
aig: 128 
The equation of the surface is obtained by substituting 
x = 1024L, y =$D, zs =6J and taking x, 7, z as rectangular 
cordinates. The unit was taken = % of an inch. The sections 
parallel to the axes of cérdinates are unicursal curves. Thus 
the cordinates x, y, may be expressed and terms of z and a para- 
meter ¢ :— 
where 



ee gS 
“38 OF (p+ 1) 
2137/9 b2V b= Big 
cf # ( r ic ae 
The surface is of the ninth order, and has two cusp lines. The 
one is a common parabola in the plane L = 0, and has the equa- 
tion K = oor D = J?. It is of the second species, that is to 
say, any plane section of the surface possesses a cusp of the 
second species where it cuts it. The second is a common cusp 
line. Itisa curve of double curvature of the third order, and 
has the equations 
a7L =-J®; 3D =- 125]? 
thus the projections on the three axes are a common parabola, a 
semi-cubic and a cubic parabola respectively. Both cusp lines 
ouch one another at the origin, where the axis of J is a common 
tangent ; thus the origin is a triple point, as appears also from 
the equation. The surface divides the whole space into two 
congruent parts. If we turn the surface through an angle of 
180” about the axis of D, which is altogether on the surface, one 
half will take the original position of the other. The plane 
D =0 touches the surface along a curve 2048 L = J%, and divides 
each half of the space, separated by the surface, into three dis- 
tinct parts, Itis this property, which connects the surface in 


so remarkable a manner with the theory of binary quintics, 
and by aid of which Dr. Sylvester has shown (Phil. Trans. 
Part iii. 1864) how to decide whether the roots of an equation 
of the fifth degree are real or imaginary. 
BERLIN 
German Chemical Society, November 14.—Alex. Miiller 
reported on the determination of very minute quantities of sul- 
phuric acid in water. His method requires but small quantities 
of water, and consists in adding to it a weighed quantity of 
chloride of barium and an equivalent proportion of chromic acid. 
For every equivalent of sulphuric acid present in the water, one 
equivalent of chromic acid remains free, and can be determined 
by colorimetric comparison. He was thus enabled to determine 
one milligramme of sulphuric acid in fifty grammes of water.— 
Messrs. Emmerling and Engler have prepared phenyl-methyl- 
aceton: Cz H;-CO-CHy, by distilling together benzoate and 
acetate of lime. Nitric acid converts this body into two isomeric 
nitro-compounds of the formula C,; H, (NO,)-CO-CH~s,, one ot 
which is crystalline and the other a liquid. These compounds 
have acquired an unusual interest in the hands of Emmerling and 
Engler, serving as they have done for the first artificial formation 
of indigo blue. Indigo blue having the composition Cg H, NO, 
the nitro-compound mentioned Cy H, NO, has to lose H, O and 
O to yield C; H; NO. This it does under the influence of soda 
and powdered zinc. The transformation is somewhat analogous 
to the reaction lately described by Baeyer, by which nitrocin- 
namic acid, C, H, NO,, submitted to the action of powdered 
zinc, loses CO, and O, and forms indol, Cg H,; N. It appears 
that two molecules of nitro-phenyl-methyl-aceton enter into the 
reaction, and that the formula of indigo blue ought to be doubled, 
thus : 
C, H,.CO.CH [H,] = [H,] HC. CO. H, €, 
N[0,] [0.] 
The elements put in brackets are those eliminated in the re- 
action, by which apparently the nitro-groups are conyerted into 
azo-groups. Nascent hydrogen transforms the azo-groups into the 
hydrazo-groups, that is to say, the artificial indigo-blue into 
indigo-white. The latter reaction has been employed to identify 
the artificial with the natural product.—L. Henry indicated a 
practical way of forming iodate of potassium, by treating the corre- 
sponding chlorate with protochloride of iodine: K Cl O, + ICl 
gives K I O; + Cl,.—Dittmar and Kékulé have prepared a 
glycolic acid of the aromatic series. Cymol from camphor was 
converted into toluylic acid, then into bromotoluylic acid, and by 
the action of baryta water into oxytoluylic acid C,; H, u ao Z 
—E. Erlenmeyer has studied the action of cyanamide on the 
hydrochlorides, of compound ammonias, particularly of methyl- 
amine. He has thus produced methyl-guanidine, hitherto called 
methyluramine, and obtained by oxydising kreatine. It appears 
that crystallographic differences exist between the platinum 
salts of the artificial and of the natural compound. The same 
chemist has found that ordinary butylic alcohol yields isobutylic 
and acetic, but not propionic acid. He likewise communicated 
researches on the differences of the various valerianic acids. — 
A. Lieben communicated his views on the formation of chloral- 
alcoholate, thinking that trichlorinated acetal precedes the 
formation of the above compound.—A. Bunge reported on the 
electrolysis of some sulphur compounds. —C, Lieberman has 
investigated the substance described some years ago by Roussin 
under the incorrect name of artificial alizarine. It is formed by 
gradually adding nitro-naphthaline and zine to sulphuric acid 
previously heated to 200°. Brown crystals are thus separated, 
giving colours with alkalies of a different hue from those pro- 
duced by alizarine, and showing the composition C,,H,O,. It 
appears to be binoxynaphthochinone, and to stand in the same 
relation to naphthaline in which alizarine stands to anthracene, 
He calls the substance naphthazarine ; the colours itgives are of no 
practical interest.—C. Vogel reported on the practical production 
of oxygen and of hydrogen by the New York Oxygen Gas Com- 
pany. This company prepared inthe month of August 20, 000 cubic 
feet of oxygen a day at the price of five cents a cubic foot. The 
gas is pressed into copper reservoirs under a pressure of ten 
atmospheres, and largely used for laboratory and medical pur- 
poses, but chiefly for hydro-oxygen lamps in bridge-building 
under the surface of rivers. In lecture rooms also this kind of 
illumination is largely used to procure enlarged views of small 
photographs or drawings made on gelatine. The process for 
making oxygen is that first used by Jessie du Mothay. Iron 
‘ 
