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Nov. 24, 1870 | 
NATURE 
79 
iu 
proceeded to speak of the paper, Avwmer (1), which discusses 
the cases in which a quartic.surface has upon it a system of 
conics ; or what is the same thing, in what cases there is a 
system of planes each intersecting the surface in two conics. 
It is, in the first place, remarked that there is no proper quartic 
surface cut by every plane in a pair of conics or even a 
proper quartic surface cut in a pair of conics by every plane 
through afixed point. Thecases considered are :—(I.) where the 
planes are non-tangent planes ; (II.) where they are singletangent 
planes; and (III.) where they are double tangent planes (Steiner's 
surface, where every tangent plane meets the surface in a pair of 
conics, comes under II.). It was then pointed out that several of 
the papers by C/ebsch and others, refer in their titles to the ‘‘ Ab- 
bildung” of a surface, viz. they show that a (1,1) correspond- 
ence exists between the points of a surface and the points of a 
plane. For surfaces of the higher orders it is only ‘certain 
surfaces which admit of an “ Abbildung,” or (1,1) correspondence 
of the points thereof with the points of a plane; viz. a surface, 
in order that it may thus correspond with the plane, (or say in 
order that it may be unicursal), must have a sufficient singularity 
in the way of a nodal or cuspidal curve. In the memoir Clebsch 
(3), after explaining the above method of the transformation of a 
cubic surface by means of two of the lines thereof, the author 
goes on to notice that the like method is applicable to certain 
quartic and quintic surfaces, viz. (1) quartic surfaces with a 
nodal conic ; (2) quartic surfaces with a nodal line ; (3) quintic 
surfaces having a nodal skew cubic (the nodal skew cubic may 
break up into a conic and line which meets it, or into three 
lines, two of them not meeting each other, but each met 
by the third line; and the like theory applies to these quintic 
surfaces). The memoir by Korndorfer relates to the ‘‘ abbildung ” 
of a quartic surface having a nodal conic, and one, two, three, or 
four cnicnodes. CZebsch (4) relates to the ‘‘abbildung ” ofa quartic 
scroll. ‘* As regards quintic surfaces (not being scrolls), we have, 
so faras Iam aware, only the paper C/ebsch (3) relating to quintic 
surfaces with a nodel Skew Cubic ; the paper C/ebsch (5), which 
relates to the ‘abbildung’ of a quintic surface having a nodal 
quadriquadric. It only remains to speak of Schwars’s memoirs 
on Quintic Scrolls : itis to be remarked that the theory of scrolls 
is allied more closely with that of plane curves than with that of 
surfaces, viz. considering any plane section of the scroll the lines 
of the scroll have in general a (1, 1) correspondence with the points 
of the plane section, and the scrolls of any given order are properly 
arranged according to the deficiency of the plane section. This is 
what is done in the memoirs by Cvemona, and this is the principle 
of classification in Schwarz’s memoir. A model of Steimer’s sur- 
face was exhibited, and many of its properties pointed out. The 
following list of memoirs will indicate the sources whence the 
sketch was principally drawn. Memoirs by the author: (1) Sur 
Ja Surface des Ondes. Liouville, tom. xi. 1846. (2) Sur un cas 
particulier de la Surface du quatrieme ordre avec seize points 
singuliers. Crelle, tom. Ixv. pp. 284—290.  (3.) Second 
memoir on Skew Surfaces otherwise Scrolls. Phil. Trans. vol. 
cliy. (1864), pp. 559—577. (4.) Third memoir. Phil. Trans. 
vol. clix. (1869), pp. 111—126. (5.) A memoir on Quartic 
Surfaces. Proc. of London Math. Society (1870), vol. iii. pp. 19 
—69. (6.) On the Quartic Surfaces (* %*, U, V, W)?=0, 
Quarterly Journal of Math. tom. x. (1868), pp. 24—34. (7) Do. 
tom. xi. pp. 15—25 (1870). (8.) Memoir on Cubic Surfaces. 
Phil. Trans. vol. clix. (1869), pp. 231—326. Cvemona: Sulle 
superficie gobbe di quarto grado. Mem di Bologna, tom, 
vill. (1868). Schwarz: Ueber die geradlinigen Flachen 
fiinften Grades. Crelle, tom. Ixvii. (1867), pp. 23—57. Clebsch 
(1) Ueber die Flachen vierter Ordnung welche eine Doppelcurve 
zweiten Grades besitzen. Crelle, tom. Ixix. (2.) Intorno 
alla rappresentazione di superficie algebriche sopra un piano, 
Atti di R. Ist. Lomb. (1868), 13 pages. (3.) Ueber die 
Abbildung algebraischer Flachen insbesondere der vierten 
und fiinften Ordnung. Ann. Clebsch und Neumann, vol. i. 
(1868), pp. 253—316. (4.) Ueber die ebene Abbildung der 
geradlinigen Flachen vierter Ordnung welche eine Doppelcurve 
dritten Grades besitzen. Ann. Clebsch und Neumann (1870), 
pp: 445—466.{(5.) Ueber die Abbildung einer Classe von Flachen, 
5 Ordnung. Gott. abh. tom. xv. 64 pages. Geisser: Ueber 
die Flachen vierten Grades welche eine Doppelcurve weiten 
Grades haben. Crelle, tom. Ixx. (1868), pp. 249—257. Korn- 
dorfer: Ueber die ebene Abbildung Clebsch und Neumann, tom. ii. 
Kummer: (1) Ueber die Flachen vierten Grades auf welchen 
Schaaren von Kegelschnitten liegen. Berl. Monatsber. Jul. 
1863. Crelle, tom. Ixiv. (1864), pp. 66—76. (2) Ueber die 
algebraischen Strahlensysteme ins besondere iiber die der ersten 
| by Mr. Baxendell, and 6 Lyre by Prof. Argelander. 

und zweiten Ordnung. Berl. abh, (1866), . I—I120, 4 
(Surfaces of the 4th order with sixteen conical points). Be 
Monatsber, (1864), pp. 246—260, and 495— 99. 
Meteorological Society, November 16.—Mr. C. V. Walker 
President, in the chair. Mr. J. H. Gilbert, Mr. C. R. Marten, 
Mr. F. E. Sawyer, and Mr. T. H. Wilson were elected Fellows. 
A paper was read by Mr. G. Dines, ‘‘On Evaporation and 
Evaporation Gauges, with some remarks upon the Formation 
of Dew,” in which, after referring to Dr. Dalton’s investigations, 
he explained the experiments in which he has been engaged 
during the past eighteen months with gauges of different sizes, 
the experiments being made sometimes with water of ordinary 
temperature, and at other times with heated water and also with 
water artificially cooled, in the open air and in a closed room. 
Mr. Dines then gave the results of these experiments, one of 
which confirmed the statement of Mr. Glaisher in 1847, viz. 
that “the formation of dew was found to depend solely on the 
temperature of the bodies upon which it was deposited, and 
that it never appeared upon them till their temperature had 
descended below that of the dew-point in their locality.” 
Finally, he stated that the conclusions which he had arrived at 
were, Ist. The greatest cause of evaporation is the movement 
of the air. 2nd. Whatever tends to increase the temperature of 
the air increases evaporation, and vice versé ; and 3rd, That 
which tends to lessen the temperature of the dew-point, increases 
evaporation, and wice vers@. Mr. Glaisher then made a com- 
munication respecting the November meteors, giving the results 
of the watches which were kept during the nights of the 
12th-13th, 13th-r4th, and r4th-15th. On the latter evening 
fifty-three meteors were observed. He also made some remarks 
on the great magnetic disturbances which occurred during the 
brilliant display of Aurora Borealis on the nights of October 
24th and 25th. The President then adjourned the meeting till 
January 18, 1871. 
MANCHESTER 
Literary and Philosophical Society, October 4.—Rev. 
Wm. Gaskell, Vice-president, in the chair, Mr. Boyd Daw- 
kins gave a short account of the work done in the Victoria Cave, 
near Settle, since the last notice brought before the Society. 
The two layers containing traces of man were separated at 
the entrance by a talus of fallen stones, seven feet thick, that 
gradually coalesced as the excavation passed into the cave, and 
at last became so confused together as not to be easily dis- 
tinguished at afew feet from the entrance. The remains of a 
gigantic bear which had been eaten may probably be assigned to 
the lower horizon, which furnished flint-flakes, and a bone har- 
poon in form resembling that used by the natives of Nootka 
Sound ; the upper or Romano-Celtic stratum continued to supply 
evidence of the comparatively late date of its accumulation in 
barbarous imitations of coins of Tetricus (A.D. 267-273.) A por- 
tion of the ivory handle of a Roman sword and a coin of Trajan 
have also been found, along with large quantities of the bones of 
animals that had been used as food. Several spurs of cocks proved 
that the inhabitants ate the domestic fowl, which was probably 
imported into this country either directly or indirectly by the 
Romans. The most striking object, however, is a beautiful sig- 
moid fibula made of bronze, and ornamented with a beautiful 
pattern in red, yellow, green, and blue enamel. It is an admir- 
able example of the art of enamelling (“Britannicum opus ” ?) 
which the Celtic inhabitants of Britain probably taught their 
Roman conquerors. 
October 18.—Mr. E. W. Binney, President, in the chair. 
Prof, Balfour Stewart, F.R.S., exhibited a series of sun-spot 
curves projected from results obtained by himself and Mr, De 
La Rue, from observations of Schwabe, Carrington, and the Kew 
series of photographs of the sun. These extend over a term o 
about forty years, and exhibit a principal and secondary maxi- 
mum and minimum in each solar spot period of eleven years, 
thus corresponding with the light curves of R Sagittee observed 
Hence it 
may possibly be that notwithstanding the darkening of the sun’s 
surface during the maximum spot period, the total light and heat 
emitted by the sun at this period is really greater than at the 
times of minimum spot frequency. —Mr. Lockyer, F.R.S., gave 
an account of his recent spectroscopic investigations ot the solar 
atmosphere, and pointed out that the conclusions arrived at by 
De La Rue, Stewart, and Loewy, confirmed the views to whieh 
he himself had been led by spectroscopic observations of the 
