
March 2, 1871 | 
NATURE 
359 

each positive, and x, > +,). 
gives 
The ordinary method of solution 
jy? =x +A, for 
where (x, + A) me (@ + a)®=2C. 
So long asc is not less than (x, — x,) 3, there is a real value 
of A, but for a smaller value of c there is no real value. The 
difficulty arising in this last case is somewhat illustrated by re- 
placing the original problem by a like problem of ordinary 
maxima and minima ; viz., x), %, x" being given posi- 
tive values of «x, in the order of increasing magnitude—and if in 
general 
% = 3 (34 — HW) In 
then the problem is to find y, a function of x, such that 
=z, = max. or min., subject to the condition Zvi =c. We 
have here y,2 =x; + A, where A is then to be determined by 
the condition Sy; = c; the remainder of the investigation tums 
on the question of the sign 
He= + A/a trory, =—A/ Ki +A 
to be taken for the several values of 7 respectively.—Prof. 
Henrici exhibited a plaster model of a tubular surface of 
the 6th order, which may be generated in either of the two fol- 
lowing modes. Either a sphere of constant radius moves with 
its centre on a parabola, or it rolls along the same parabola 
always touching both its branches. The two envelopes thus 
produced differ in position only. The second mode of generation 
shows that the surface has a nodal curve, which is a parabola 
congruent to that on which the centre of the sphere moves ; but 
ina plane perpendicular to it. Through a part of it only do real 
sheets of the surface pass. There is also a cuspidal curve of the 
6th order, which has two cusps. The nodal curve passes through 
them, and has at these cusps the same tangents. The equation 
to the surface is 
(27 py? + 9 x K-23)? = («2 + 3K)8 
where 
K=( + Pt+yt+ 2-7 
r= radius of the sphere and 4/ is the parameter of the parabola, 
The equations to the parabola, on which the centre of the sphere 
moves, are 
Y= 4p (x + 2h), 2 = 03 
those of the nodal curve, 
— 4px +7 — 4p; 
the equations to the cuspidal curve are 
27py? -— 43 = 0, 2? + 34 = 0; 
the first is a cylinder, which cuts the plane z = 0 in the evolute 
of the parabola, the second represents an ellipsoid of revolution. 
The model was constructed to the scale 
Bp = dy, * = 2 inches. 
It was agreed, on the suggestion of Dr. Hirst, that Prof. 
Henrici should order a second model to be cast for the use of the 
society. Mr. Merrifield, F.R.S. laid the following statement 
before the society. ‘‘ If the equation of a surface be 
Z= F(x y) (1) 
it is very well known that the condition that it should be a ruled 
surface is{that 
y= 0, — 
d dasa (2) 
Sgt —)2 
(x ax i ) 
and q TEN (3) 
( ax hea dy 
should have a common factor of the form AA + Bu; andalso that 
the condition of its being developable is that (2) should have two 
equal factors of that form. I have found upon actual trial that 
for a conical surface (3) will have two equal factors, and for a 
cylindrical surface, three equal factors ; that is to say, if we 

write, _ @2 , n= az &c., we have for a 
ax dx*dy 
conical surface : 
(a5 — By)? = (ay — B’) (Bd — 7’) 
and for a cylindrical surface we have separately 
(a5 — By) =9, (ay = B*) =0, BS - 7? =O 
Jf, following Monge, we regard the surface as traced out by a 
right line moving on three director curves, the condition of two 
or three equal roots is evidently the same as that, out of the 



three characteristics passing through a point, two or three should 
become coincident. I have not yet had time to look inte the 
question whether the converse of the proposition is true, viz., 
whether the introduction of the condition of developability 
(r¢ = 5s?) necessarily reduces the surface, in which two or 
three of the characteristics coincide, to a cone or cylinder.” 
The president and members present expressed their wish that 
Mr. Merrifield would be able to find time for the consideration 
of this converse proposition. Dr. Hirst then made some remarks 
on the connection between the correlation of two planes, as 
described in his last communication to the Society, and Sturm’s 
solution of the problem of projectivity, as given by him in his 
ae on the subject, published in the Wathematische Annalen, 
ol. 1, Pp. 533. 
Linnean Society, February 16.—Mr. G. Busk, Vice-presi- 
dent, inthe chair. Dr. J. D. Hooker presented to the Society on 
behalf of a committee appointed for the purpose, a half-length 
portrait of the President, Mr. G. Bentham, the expense of which 
had been defrayed by a subscription raised among the fellows of 
the Society. The following papers were then read, the interest 
of which was purely technical :—On Tremellineous Fungi and 
their Analogues, by L. and C. Tulasne ; Bryological Remarks 
by Dr. S, O. Lindberg. 
Entomological Society, February 20.—Mr. A. R. Wallace, 
president, in the chair. Mr. Bond exhibited a hybrid 
between Bombyx Pernyi and 8. yama-mai, two of the larger 
silk-worm moths; this individual was of the colour of the one 
parent with the form of the other. He also exhibited an example 
of Bombyx mori, bred by Dr. Wallace, still retaining the larval 
head. Mr. McLachlan called attention to the first-recorded 
instance of a similar arrest of development, being a paper by 
O. F. Miiller in ‘‘ Der Naturforscher” for 1871. Mr. Smith 
mentioned that a common Egyptian wasp, Riynchium brunneum, 
obliterated, by its nest, the inscriptions on the ancient monu- 
ments in that country ; and he exhibited an example of the same 
wasp which had been found in the folds of the covering of a 
mummy, showing that the same species had inhabited Egypt for 
many ages. Mr, Smith further alluded to a passage in Pepys’s 
Diary, dated May 1665, in which the writer narrated how he 
had seen a glass-hive where the bees could be seen at work, 
proving that observatory hives were not a modern invention. 
Mr. Miiller read a paper ‘‘ On the Dispersion of Non-migratory 
insects by Atmospheric Agencies,” in which he had collected 
together a number of records of showers of insects after violent 
storms, and at sea at long distances from land ; and he was of 
opinion that these agencies played a considerable part in the 
geographical distribution of insect life, though, no doubt, in 
many cases, the species thus involuntarily dispersed died out from 
inability to cope with the pre-existent denizens of the localities 
to which they were driven. Mr. H. Jenner-Fust communicated 
a supplement to his treatise on the geographical distribution in 
these islands of the indigenous Lepidoptera. 
DUBLIN 
Royal Irish Academy, Feb. 13.—Reyv. J. H. Jellett, B.D., 
president, in the chair.—Dr. Ferguson read a paper ‘‘ On the 
Difficulties attendant on the Transcription of Ogham Legends, 
and the Means of Avoiding them.” Leave was given to Mr. 
Charles E. Burton to read notes ‘‘On the Results obtained by 
the Agosta Sicily Expedition to Observe the recent Solar 
Eclipse.”—A paper was read by Profs. W. King and T. H. 
Rowney, ‘‘On the Geological and Microscopical Structure of the 
Serpentine Marble or Ophite of Skye.”—Papers ‘‘On Eozéon 
Canadense,” by Principal Dawson, and on Messrs. King and 
Rowney’s paper ‘On Eozoon Canadense,” by Dr. T. S. Hunt, 
were deferred to the meeting of the 27th inst. when the discussion 
of all the papers on this subject will be taken.—Rey. President 
Henry, D.D., Belfast, H. Dix Hutton, LL.B., and T. W. 
Ellison Macartney were elected members of the Academy, and 
Prof. Traquair was admitted a member.—Sir W. Wilde pre- 
sented on behalf of the Earl of Mayo, a collection of ancient 
Indian Coins, for which the marked thanks of the meeting were 
voted. 
Hosart Town 
Royal Society of Tasmania, October 11, 1870.—His Ex- 
cellency, C. Du Cane, Esq., President, in the chair. The Sec- 
retary read some ‘‘ Notes on an experiment with the fumes of 
sulphur, and of other methods for the destruction of rabbits in 
their burrows,” by W. Archer, Esq., F.L.S. The fumes were 
forced into a burrow by means of bellows, attached to a rece})- 
tecle in which the sulphur was burned ; and that this was effec- 
