376 
NATURE 

tides was about 4 to 1. After reading the report, Sir William 
said that one chief object which the originators of this investiga- 
tion had in view was the determination of long period tides, 
and particularly the lunar declinational fortnightiy tide, and 
the solar declinational semi-annual tide. Tne reason for 
desiring the determination of such tides with great accuracy was 
that this » ould give a mea: sofestimating withabsolute certainty the 
degree of elastic yielding which the solid earth experienced under 
thetide-generating influences ofsun and moon. It was quite certain 
_ that the solid earth did yield to some degree, as it must do so 
unless they were infinitely rigid. It had long been a favourite 
assumption of geologists that the ea:th consis‘ed of a thin shell 
of solid sock twenty to fifty miles thick, according to various 
estimates, inclosiny an interior filled with melted material, lava, 
metals, &:. This hypothesis was, however, absolutely unt nable, 
because, were i true, the solid crust would yield with almost as 
perfect freedom (on account of its tninvess aud great area) as if 
it were perfectly liqud Thus the boundary of the solid earth 
wou d mise and fall under the tide-genera ng influences so much 
as to leave no sensible difference tv be shown by the water rising 
and falling relatively to the solid, showing that if the earth, asa 
whole, had an average degree of rapidity, equal to t at of yla s, 
the tides would be very much diminished from the maym ude 
corresponding to a perfectly rigid globe with water like that o! 
our seas upon it. ‘I his consideration, he had shown, :endcred it 
probable that the earth had consiverably mre average rigidity 
than a globe of glass of the same size. The mathematical cal- 
culation showed a somewhat startling resulr, to the effect that a 
globe of glass of the same size as the earih, it through ut of 
exactly the same rigidity as glass on a similar scale, wouid yield, 
like an indiarubber b. 1], with remark-ble freecoum to the tide- 
generating influenc-s, thus leavinga very much smalier difference 
to be shown by water if placed on the surface of such a glube, 
and estimat:d inits rise and fall relatively }o the solid bottom on 
which i: rested. The preci-e agreement of precession and nuta- 
tion with dynamical estimates, founded ou the supposition of 
the earth being perfe.tly rigid, made it probable that the earth 
was in reality vastly more rigid as a whole than any specimen 
of surface rock in the condition in which it was when expert- 
mented on in our laborator es. In speaking on this subject about 
ten yearsago .\o Dr. Joule, that gentieman suggested that pro- 
bably the great pre-sure in the intertor produces in the material— 
which might be of the same substance as surface r. cks—a greatly- 
increased ngidity im its actual position at any great depth below 
the surface ; but the prop sd tidal observation and calculation 
was the only method which gave directly, and without any pos- 
sibly doubttul suppositions regarding iierior arrangement of 
density on the earth, a n easurement ot its elastic yielding to the 
tide generating influences. Now that observations from so lowa 
latitu e as that of Cat Island were available for c mparison with 
those of the tides on our own coast, ‘he committee might advance 
hopefully to this part of their inquiry, which, accordingly, they 
proposed ro make a prima:y object in the calculations to be next 
undertaken, 
The other papers read were almost entirely confined to pure 
mathematical subjects. They were as follows :— 
Report on Hyper-elliptic Functions by W. H. L. Russell, 
RES 
Note on a Question in Partitions, by Prof. Sylvester, F.R.S. 
On the Number of Invariants of a Binary Quantic, by Prof. 
Cayley, F.R S. 
On Linear Differential Equations, and On Focal Properties of 
Surfaces of the second Order, by W. H. L. Russell, FL RLS. 
On Certain Familirs of Surfaces, by C. W. Merrifield, F.R.S. 
If 2 = # (xy) bea surface, then writing 
dz dz ; 
=—_, B= ——_, &. 
*~ das dx2dy ; 
If the surface be a cone (a5 — By)? = (ay — B2) (88 — y2);and 
if a cylinder a5 - By = 0, ay — B2=0,B6—y2=0. In the 
present paper it is in estigated whether solid surfaces, fulfilling 
these conditions, are neces-arily cones or cylinders. 
Description of a Model of a Ruled Cubic Surface, by Prof. 
Bail. The cutic surface was 2 (x2 + 7") — 2axy=0. 
On Vortex Rings, by Prof. Ball. 
On the Mathematical Theory of Atmospheric Tides, by Prof. 
Challis, F.R.S. 


Remarks on Napier’s Original Method of Logarithms, by Prof. | 
Purser. 
On the Calculation of e (the base of the Navierian Logarithms) : 
from a Continued Fraction, by W. L. Glaisher, F.R.A.S. 
The continued fraction from which e was calculated was 
e-I I I I 
20) aati (6h Tages 

A formula far more convergent than the ordinary one fore in a — 
series. The calculation gave eto 137 decimals, and confirmed 
the result given by Mr, Shanks, the value or e given in all the 
editions of Callet’s logarithms being incorrect from the fortieth — 
figure. 
On Certain Definite Integrals, by J. W. L. Glaisher. 
tegrals were [esa (x") dx. [Scos (x") dx. 
° 
On Lamberts Proof of the Irrationality of m, and on the 
Trrationali y of certain other Quantities, by J. W. L. Glaisher. 
The quautities re erred to were chiefly circular and exponential 
jraculuns, 
On Doubly Diametral Quartan Curves, by Prof. F. W. New- 
man, <A large number ot drawings of quartic curves were ex- 
hibited to the S ction. 
On a Canonical Form of Spherical Harmonics, by Prof. W. 
K. Ciiff rd. The canonical torm in question 1s an expression of 
the general harmonic of order, #, as the sum of a certain num- 
ber of sectorial harmonics, the number being when 7 is even, 
5” = 10 and when x is odd, — 
2 
The in- 

SECTION C. 
THE papers to be read on Tuesday numb red twenty-three, so 
that but Jittie tme could be ailowed to cach author, and then 
there was time fur no more than half the papers to be brought 
forward. A report by Prof. Duncan, M B., F.R S., on British 
Fossil Corals was read, wherein he pomted out the relations 
between the neozoic and paizeozoic corals. Then Prof. Geikie 
read his report on the Progress of the Geological Survey of 
Scotland, a notice of which appeared in NATUR»® of August IO. 
Mr. Henry Woodward described anew and near y perfect Arach- 
nide from the Ironstone of the Dudley coal-fiela. The Penny- 
stone Ironstone nodules of the coal measures have long been 
celebrated fur their fossil contents, having yielded King Crabs, 
wings of Orthopterous insects, a supposed beeile, ans 1umerous 
plant remains, both terns and fruits of Lycopodiaceze. The 
specimen described by Mr. Woodward is perh ips the most perfect 
form hitherto described. It is ide: tical with one figured and 
described by Buckland as a Diamond becile (Curcudio) and 
named by him Carculioides Frestvicit. By means, however, of 
the s, ecimen now obtained, the author clearly stowed that it 
was not a Coleopterous imsect, but a true Arachnide, closely 
related to the recent genus /A7yuus. Mr. Woodward proposed, 
therefore, 10 name it Lophrynus Prestvicii, the genus Curculioides 
bei g retained tor C. dm. i, another specimen also figured by 
Buckland, which may bea true Rhynchophorous insect. Dr, 
Bryce called at.ention 10 some fossils from the urine Limestone 
of Sutherland, Prof Harkness extibitea one of the earliest forms 
of Trilobites, snd Mr. John Muler furnished soa e remarks on 
the so-called Hyoid Plate of Asteroiegis, and pointes out that it 
was really the dorsal late. 
Mr. Milne Home brought forward a notice of a scheme for the 
Conservation of Remarkable Boulders in Scotland, and for the 
Incication of their Position on Maps. Mr. Moggridge mentioned 
that in Switzerland a right of property in some of the boulders 
had been acquired by natural history societies and museums with 
a view to their preservation, and that on these a brass plate had 
been fixed with the word *‘ Investable” maiked upon it. 
Prof. Traquair noticed some additions 10 the Fossil Vertebrate 
Fauna of Burdiehouse, near Euinburgh. and also calied atten ion 
to a Labrynthodont skull, seven icies long, irom the same 
limestone quarries (of Lower Carbouiferous aye), probably be- 
longing to Huxley’s genus //ol/doyasier ; Unis was the lowest 
geolozical hernzon from which the remaius of Labyrinthodont 
Amphibia had been as yet described, 
At the meeting of the Brirish Association at Liverpool, the 
Rey. John Gunn, I'.G.S., &c,, expressed the opinion that 

[ Sept. 7, 1871 ; 
