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PROCEEDINGS

OF THE

ROYAL IRISH ACADEMY,

FOR THE YEAR 1841-2.

PART VI.

DUBLIN:

PRINTED BY M. H. GILL,
PRINTER TO THE ACADEMY.
MDCCCXLIIL.

1}

e YWTCLON HOR

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1840. ~ No. 25.

November 9.
SIR Ws. R. HAMILTON, LL.D., President, in the Chair.

The President read a letter from the Secretary of State
for the Home Department, informing him that her Majesty
had been pleased to receive very graciously the address of
the President, Council, and Members of the Royal Irish
Academy, congratulating her Majesty on the recent provi-
dential deliverance of herself and her illustrious Consort.

The decease of the Very Rev. the Dean of St. Patrick’s,
V.P., having been announced to the Academy, it was re-
solved—

That we have heard with deep regret of the death of
our valued Vice-President, the Dean of St. Patrick’s; and
that while we sympathize with all classes of our fellow-
citizens, in lamenting the removal of one so universally be-
loved and esteemed, we would desire to record our sense of
the peculiar loss sustained by the Academy, in being de-
prived of the assistance of one who could estimate the value
of our Institution, and give to it his most cordial coopera-
tion; one who found leisure from the multifarious duties of

VOL. II. B

2

his station, to cultivate successfully the researches connected
with the antiquities of Ireland, and had earned for himself a
high place among those who labour to illustrate her ancient
records, or to save from destruction the perishing relics of
her former civilization.

Samuel Ferguson, Esq., was elected to the vacant place
in the Council; and the Rev. J. H. Todd, D.D., was ap-
pointed by the President, under his hand and seal, to suc-
ceed the Dean of St. Patrick’s in the office of Vice-Presi-
dent.

The Rev. T.R. Robinson, D.D., M.R.I.A., gave the Aca-
demy an account of a large reflecting telescope, lately con-
structed by Lord Oxmantown, and of the processes em-
ployed in forming its specula.

After explaining the relative importance of magnifying
and illuminating power, Dr. R. proceeded to give a brief
sketch of the history of the reflecting telescope, which
seemed to have been forgotten for many years after its in-
vention, till it was revived by Hadley. The labours of
Short soon gave it celebrity ; yet even this artist limited
himself in almost every instance to sizes which were not
more powerful than the achromatics of his day, and _ his
large instruments appear to have been failures.* It was
not till a full century after the publication of Newton’s
paper, that Sir William Herschel gave this telescope the
gigantic development which has crowned him with imperish-
able fame; and by the construction of telescopes of nineteen

* A Newtonian of six feet focus, and 9-4 inches aperture, is said by Maskelyne
to have shewr the first satellite of Jupiter 13” longer than a triple achromatic of
3-6 inches aperture. The telescope of twelve feet focus, and eighteen inches aper-
lure, now at Oxford, shewed tnultiple rings of Saturn.

Yo
Vv

and forty-eightinches aperture, placed regions almost beyond
the scope of measurement within the reach of human intel-
lect. But as Short, in a spirit unworthy of his talents, took
care that his knowledge should die with himself, and Her-
schel published nothing of the means to which his success
was owing, the construction of a large reflector is still as
much as ever a perilous adventure, in which each individual
must grope his way. Accordingly, the London opticians
themselves do not like to attempt a mirror even of nine
inches diameter, and demand a price for it which shews the
uncertainty and difficulty of its execution. In Ireland we
are more fortunate, for a member of our Academy, Mr.
Grubb, finds no difficulty in making them of admirable
quality up to this size, or even fifteen inches; but with all
his distinguished mechanical talent, he is believed to be
doubtful of the possibility of more than doubling this last
magnitude in perfect speculum metal.

Under these circumstances, too much praise cannot be
given to Lord Oxmantown, who, in the midst of other pur-
suits, has found leisure for such researches; and by a rare
combination of optical science, chemical knowlege, and prac-
tical mechanics, has given us the power of overcoming the
difficulties which arrested our predecessors, and of carrying
to an extent which even Herschel himself did not venture to
contemplate, the illuminating power of this telescope, along
with a sharpness of definition scarcely inferior to that of the
achromatic.

The chief difficulties which are to be overcome in the
construction of reflectors, arise from the excessive brittleness
of the composition of which specula are made, and from the
necessity of giving them figures which shall be free from
aberration. The great mirror in the Newtonian form is
(if the eyepiece and plane mirror be correct) the conical

paraboloid.
B 2

4

It is necessary that speculum metal should possess, in
the highest attainable degree, the qualities of whiteness,
brilliancy, and resistance to tarnish. Lord Oxmantown has
found that these conditions are best satisfied in the definite
combinations of four equivalents of copper to one of tin; or
by weight, 32 and 14-7 nearly. Metals differing from this
by a slight excess of either component, are, when first
polished, scarcely less brilliant, but are dimmed so rapidly
that the lapse of a few days produces a sensible difference.
On the other hand, some large specula of the atomic com-
pound have been lying uncovered for years, without ma-
terial injury to their polish.

But this compound is brittle almost beyond belief; a
slight blow, or even the application of partial warmth, will
shiver a large mass of it; though harder than steel, its sur-
face is broken up with the utmost facility, and it has a
most energetic tendency to crystallize. The common pro-
cess of the founder fails with it, except for masses of very
limited magnitude, as the cast cracks in the mould, and the
subsequent difficulties of the annealing are such, that it has
been a very general practice to use an alloy lower (contain-
ing more copper) than the atomic standard. Even Sir
William Herschel was obliged to yield to this necessity. It
appears froma letter of Smeaton, (Rees’ Cyclopedia, Art. Tele-
scope,) that for his 20 feet mirror of 19 inches aperture, the
composition was 32 copper to 12:4 tin; and that for the 40
feet it was even lower. Yet two out of three attempts to cast
this huge speculum failed.

Lord Oxmantown at first endeavoured to evade the diffi-
culty, by constructing a speculum in pieces, soldering plates
of fine metal to a back ofa peculiar brass, ascertained to
have the same expansion; and has completed one of thirty-
six inches aperture and twenty-seven feet focal length,
which performs very well on stars below the fifth magnitude,

5

but above that exhibits a cross formed by the diffraction at
the joints; and in unsteady states of the air exhibits the six-
teen divisions of the great mirror on the star’s disk, By dimi-
nishing the number and size of the joints it is found, that
these inconveniences can be diminished, so as to be scarcely
perceptible; and in all probability this is the process by
which the remotest limits of telescopic vision will ultimately
be attained. It is, however, not necessary for instruments
of even greater dimensions than this, since Lord Oxmantown
has succeeded, by a contrivance as simple as ingenious, in
casting at the first attempt a solid mirror of the same size ;
and there is no reason to suppose that it will be less effec-
tive on a much larger scale.

But however difficult it may be to obtain the rough spe-
culum of large dimensions, it is still more so to give it a
proper figure, combined with that brilliant polish which is
technically called black, because it reflects no light out of
the plane of incidence. In such mirrors as can be wrought
by hand, they are worked by short cross strokes on the
polisher, and at the same time have a slow rotation relative
toit. This might be expected to produce merely a spherical
figure; but by varying the length of the stroke, by circular
movement, elliptic figure of the polisher, or removing por-
tions of its pitch covering, a parabolic figure is obtained.
For sizes above nine inches diameter, the work must be per-
formed by machinery; but in all which Dr. R. has seen,
(the most remarkable of which are those of Sir William
Herschel* and Mr. Grubb,) the cross stroke is given by a
lever moved by hand; and it is supposed that perfect results
cannot be obtained but by the feeling of the polisher’s”
action. Sir John Herschel is believed to have made important

* Dr. R. had the good fortune to see this at Slough, in 1830, while at work
on a twenty-feet mirror.

6

additions to his father’s apparatus; and it is t» be hoped he
will soon redeem his promise (Mem. R. Ast. Soc. vol. vi.)
of publishing his improvements.

Lord Oxmantown has in many respects deviated from
the usual process. His polisher, of the mirror’s diameter,
intersected by transverse and circular grooves, into por-
tions not exceeding half an inch of surface, is coated, first,
with a thin layer of the common optical pitch, and then with
a much harder compound. It is worked on the mirror, and
counterpoised so that but little of its weight bears; but the
want of pressure is compensated by a long and rapid stroke.
The mirror revolves slowly in a cistern of water, maintained
at a uniform temperature, to prevent the extrication of heat
by friction, The polisher moves slowly in the same direc-
tion, while it is also impelled with two rectangular move-
ments. The machine is driven by steam, and requires no
superintendence, except to supply occasionally a little water
to the polisher, and to watch when the polish is complete.
By an induction from experiments on mirrors from six to
thirty-six inches aperture it was found, that if the magni-
tudes of the transverse movements be } and +2, of the aper-
ture, and their times be to its period of rotation as } and
18 to 37, the figure will be parabolic: but to combine with
this the highest degree of lustre, it is found necessary to
apply, towards the close, a solution of soap in liquid ammonia,
which seems to exert a specific action.

The certainty of the process is such, that the solid
mirror of thirty-six inches aperture, after being scratched all
all over its surface with coarse putty, was, in Dr. R.’s pre-
sence, perfectly polished in about six hours, and was placed
in its tube for examination, without any previous trial as to
quality.

Lord Oxmantown has preferred the Newtonian to the
Herschelian form, and, in Dr. R.’s opinion, with good

~
é

reason. In the latter, the inclination of the great mirror to
the incident rays must deform the image,* and it is now
known, that even with faint objects sharp definition is of
high importance. It should, in fact, be a segment of a
paraboloid, exterior to the axis; and though a theorem of
Sir William Hamilton (Trans. R. Irish Acad., vol. xv. p.
97,) might seem to indicate mechanical means of approxi-
mating to the figure, yet Dr. R. fears there would be greater
difficulty in applying them than in enlarging the aperture of
the Newtonian, so as to make up for the loss of light.
Another serious objection is, that in the Herschelian the
observer’s position at the mouth of the tube, must cause
currents of heated air, which will materially interfere with
sharpness of definition.

As to the loss of light by the second reflexion, Dr. R.
thinks it has been much overrated, and expresses a wish that
a careful set of experiments were made on reflexion by plane
specula at various incidences, on prisms of total reflexion,
and the achromatic prism, proposed as a substitute by Sir
David Brewster.

As to the rest of the instrument, it may suffice to say,
that it bears a general resemblance to that of Ramage, but
that the tube, gallery, and vertical axis of the stand are
counterpoised, so that one man can easily work it, notwith-
standing its enormous bulk. The specula, when not in use,
are preserved from moisture or acid vapours, by connecting
their boxes with chambers containing quicklime, which is
occasionally renewed. This arrangement, (which also oc-
curred to Dr. R., and has been for several years applied by

* Any one who has a Newtonian telescope can verify this, by inclining a little
the great mirror, so however as not to pass the edge of the plave mirror by the
pencil. In Lord O.’s instrument, an inclination of 11’ sensibly injures it ; were it

Herschelian, the inclination must be 3° 11’.

8

him to the Armagh reflector,) appears to be very effective in
preserving the polish.

In trying the performance of the telescope, Dr. R. had
the advantage of the assistance of one of the most celebrated
of British astronomers, Sir James South; but they were un-
fortunate in respect to weather, as the air was unsteady in
almost every instance; the moonlight was also powerful on
most of the nights when they were using it. After mid-
night, too, (when large reflectors act best,) the sky, in
general, became overcast. The time was from October 29th
to November 8th.

Both specula, the divided and the solid, seem exactly
parabolic, there being no sensible difference in the focal
adjustment of the eyepiece with the whole aperture of
thirty-six inches, or one of twelve; in the former case there
is more flutter, but apparently no difference in definition,
and the eyepiece comes to its place of adjustment very
sharply.

The solid speculum showed a Lyre round and well de-
fined, with powers up to 1000 inclusive, and at moments
even with 1600; but the air was not fit for so high a power
on any telescope. Rigel, two hours from the meridian, with
600, was round, the field quite dark, the companion separated
by more than a diameter of the star from its light, and so
brilliant that it would certainly be visible long before sunset.

é Orionis, well defined, with all the powers from 200 to
1000, with the latter a wide black separation between the
stars ; 32 Orionis and 31 Canis minoris were also well sepa-
rated.

It is scarcely possible to preserve the necessary sobriety
of language, in speaking of the moon’s appearance with this
instrument, which discovers a multitude of new objects at
every point of its surface. Among these may be named a
mountainous tract near Ptolemy, every ridge of which is

9

dotted with extremely minute craters, and two black parallel
stripes in the bottom of Aristarchus.

The Georgian was the only planet visible; its disc did
not show any trace of aring. As to its satellites, it is diffi-
cult to pronounce whether the luminous points seen near it
are satellites or stars, without micrometer measures. On
October 29, three such points were seen within a few
seconds of the planet, which were not visible on November
5; but then two others were to be traced, one of which could
not have been overlooked in the first instance, had it been
in the same position. If these were satellites, as is not im-
probable, there would be no great difficulty in taking good
measurement both of their distance and position.

There could be little doubt of the high illuminating
power of such a telescope, yet an example or two may be
desirable. Between «<' and « Lyre, there are two faint
stars, which Sir J. Herschel (Phil. Trans. 1824) calls ‘‘ de-
bilissima,” and which seem to have been, at that time, the
only set visible in the twenty-feet reflector. These, at the
altitude of 18° were visible without an eye-glass, and also
when the aperture was contracted to twelve inches. With
an aperture of eighteen inches, power 600, they and two
other stars (seen in Mr. Cooper’s achromatic of 13°2 aper-
ture, and the Armagh reflector of 15) are easily seen.
With the whole aperture, a fifth is visible, which Dr. R.
had not before noticed. Nov. 5th, strong moonlight.

In the nebula of Orion, the fifth star of the trapezium
is easily seen with either speculum, even when the aperture
is contracted to eighteen inches. The divided speculum
will not shew the sixth with the whole aperture, on account
of that sort of disintegration of large stars already noticed,
but does, in favourable moments, when contracted to
eighteen inches. With the solid mirror and whole aperture,
it stands out conspicuously under all the powers up to 1000,

10

and even with eighteen inches is not likely to be over-
looked.

Comparatively little attention was paid to nebula and
clusters, from the moonlight, and the superior importance of
ascertaining the telescope’s defining power. Of the few
examined were 13 Messier, in which the central mass of
stars was more distinctly separated, and the stars themselves
larger than had been anticipated ; the great nebula of Orion
and that of Andromeda shewed no appearance of resolution,
but the small nebula near the latter is clearly resolvable.
This is also the case with the ring nebula of Lyra; indeed,
Dr. R. thought it was resolved at its minor axis; the fainter
nebulous matter which fills it is irregularly distributed,
having several stripes or wisps in it, and there are four stars
near it, besides the one figured by Sir John Herschel, in his
catalogue of nebule. It is also worthy of notice, that this
nebula, instead of that regular outline which he has there
given it, is fringed with appendages, branching out into the
surrounding space, like those of 13 Messier, and in parti-
cular, having prolongations brighter than the others in the
direction of the major axis, longer than the ring’s breadth.
A still greater difference is found in 1 Messier, described by
Sir John Herschel, as “‘a barely resolvable cluster,” and
drawn, fig. 81, with a fair elliptic boundary. This telescope,
however, shews the stars, as in his figure 89, and some more
plainly, while the general outline, besides being irregular
and fringed with appendages, has a deep bifurcation to the
south.

From these and some other discrepancies, Dr. R. thinks
it of great importance that the globular nebule and clusters
should be all carefully reviewed, as it is chiefly from their
supposed regularity that the hypothesis of the condensation
of nebulous matter into suns and planets has arisen, an
hypothesis which he thinks has, in some instances, been car-
ried to an unwarrantable extent.

11

On the whole, he is of opinion that this is the most
powerful telescope that has ever been constructed. So
little has been published respecting the performance of Sir
W. Herschel’s forty-foot telescope, that it is not easy to
institute a comparison with that, the only one that can fairly
be made to compete with it. But there are two facts on
record which lead to the inference that it was deficient in
defining power; one, the low power used, which Dr. R.
thinks was not above 370; the other, the circumstance that
neither the fifth nor sixth stars of the trapezium of the
nebula of Orion were shewn by it. As to light, there is no
reason to believe that the composition of the forty-foot
mirror was as reflective as that of the twenty-foot; and if
Dr. R. be correct in the opinion, that the latter* did not
shew the fifth star easily, or the sixth at all, and that it only
exhibited the ‘ debilissima” and one star near the ring-ne-
bula, then i has decidedly less illuminating power than
eighteen, perhaps not more than fourteen inches aperture of
Lord Oxmantown’s mirror, notwithstanding the loss of
light in that by the reflexion at the second speculum.

However, any question about this optical pre-eminence
is likely soon to be decided, for Lord Oxmantown is about
to construct a telescope of unequalled dimensions. He in-
tends it to be six feet aperture, and fifty feet focus, mounted
in the meridian, but with a range of about half an hour on
each side of it. If he succeeds in giving it the same degree
of perfection as that which he has attained in the present
instance, which is exceedingly probable, it will be, indeed, a
proud achievement; his character is an assurance that it
will be devoted, in the most unreserved manner, to the ser-
vice of astronomy, while the energy that could accomplish

* In its original state, not as improved by the more perfeet means latterly
employed by Sir John Herschel.

12

such a triumph, and the liberality that has placed his disco-
veries in this difficult art within reach of all, may justly be
reckoned among the highest distinctions of Ireland.

DONATIONS.

Eleven Quern Stones of different Kinds.

Eight Methers of different Sizes and Patterns.

A round wooden Goblet.

An ancient Horn Vessel. Presented by Captain Portlock,
M.R.I.A.

An ancient Spur found in the Grave-yard at Ferns. Pre-
sented by Stephen Radcliffe, Esq., per Haliday Bruce,
Esq., M.R.LA.

A Papal Bulla, found near the Foundation of the Cathe-
dral of Cloyne, (Clemens PP. IIII.) Presented by R. J.
Graves, M.D.

Fisica di Corpi ponderabili. 2 vols. 8vo. By the Che-
valier Amadeo Avogadro. Presented by the Author.

Third Annual Report of the Proceedings of the Botanical
Society of Edinburgh. Presented by the Society.

Sixth Report of the Poor Law Commissioners in Ireland.
Presented by George Nicholls, Esq.

Ancient Laws and Institutes of England. Presented by
the Commissioners of the Public Records of the Kingdom.

A Geological Map of England and Wales. By G. B.
Greenough, Esq. Presented by the Geological Society.

Transactions of the Geological Society of London. Vol.V.
(1840.) Presented by the Society.

Quarterly Journal of the Statistical Society of London.
July, 1840. Presented by the Society.

Address of the General Secretaries of the British Associ-
ation. Presented by the Authors.

Journal of the Franklin Institute. Vol. XXV. (1840.)
Presented by the Institute.

13

Transactions of the Royal Society of Gottingen, from
1828 to 1831. Vol. VII. Presented by the Society.

Proceedings of the American Philosophical Society, to
July, 1840. (No. 12.) Presented by the Society.

Directions for using Philosophical Apparatus. By E.
M. Clarke, Esq. Presented by the Author.

Manuscript Notices relating to the Cathedral of St.
Patrick, Armagh. By John Davidson, Esq., M.R.I.A.
Presented by the Author.

Ordnance Survey of the King’s County. In 49 Sheets,
including Title and Index. Also,

Ordnance Survey of Carlow. In 28 Sheets, including

Title and Index. Presented by His Excellency the Lord
Lieutenant.

November 30, (Stated Meeting.)
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Dr. Kane read a Paper “‘ On the Production of Audible
Sounds,” of which the following is an abstract.

The sensation of sound is produced upon the ear by the
tympanum being thrown into vibratory motion, isochro-
nous with the vibrations transmitted from the sounding
body.

Any body which vibrates as a single mass gives origin at
the same moment to two waves, whose motions are in opposite
directions, and of which one is rarefied and the other con-
densed.

If these two arrive at the tympanum at the same mo-
ment and with equal power, perfect neutralization should
result, and no sound be heard: hence, where a vibratory
body produces upon the ear the sensation of sound, it arises

14:

from one wave of the two being either totally intercepted
or, at least, diminished in force, and the loudness of the
sound is proportional to the difference of the intensity of the
two waves when they affect the ear.

All instruments for increasing sound, and producing re-
sonance, act upon this principle.

The following pie will illustrate these principles in de-

tail. tuning fork is a centre of four
waves, two + and two —, but unless it be
- a close to the ear, no soci is heard from
; because the centre of all the four waves
ie very close, all act on the ear with
equal force, and the difference is 0, (approximatively.)

Now, if an open tube, of the same length as a one-phase
wave from the fork, be approached to one centre, as A, in
the adjoining figure, the air in it commences to vibrate in
unison with the fork, from being set in motion by the first

lai wave which passes into it:

Das the vibration of the tube is,

A ee ee AL|||"° however, a phase behind

that of the fork, and hence,

when a — wave passes from

the centre a, it meets a + wave from the end of the tube E:

and both are destroyed. The — centre, c, destroys also a

+ centre, as D, and there remain only the centres of +

waves, B from the fork, and F from the tube, and these acting

in concert on the tympanum produce the sound that we
hear.

If the tube be closed, and of only one-half the length,
the + wave, which emanates from the centre A, passes in,
and being reflected from the bottom, issues again at the
moment when the next — wave from a is about to enter; E
and a then destroy each other, and c and p_also inter fering,
there results only the + wave B, which acts unimpeded on

15

gs. the ear. The sound of an open

:
ri tube is, therefore, ceteris paribus,

a [ -¢ much stronger than that of a

/ a NE, closed tube, as there are two
* waves in place of one.

That the office of closed tubes, when resonant, is to de-
stroy a portion of the sound of the original vibrating body,
and of the open tubes to afford, in addition to that, a new
centre of a wave of the same phase as that which remains,
may be exhibited in many ways. Thus, Mr. Adams shewed
long since, that when two closed tubes are placed at right
angles to each other, they interfere when made to speak to
a tuning fork, and for this effect no explanation has hitherto
been given. But it is evident that the tubes being at right
angles to each other, the waves destroyed are in opposite
phases, and those which remain are in opposite phases also,
so that the effect is the same as if no tubes were present at

all. The same effect may be produced
by a single tube, bent so that its aper-
tures may be at right angles to cach other;

A B
SS x
x CAy~r© the — and + waves, p and c, meeting in
D O10:
the tube, produce neutralization, and the
waves A and B, also + and —, which re-

main, interfere also, and hence no sound

results.. In an open tube bent into a circle,

as in the figure, the two waves destroyed (a c) are of the
same phase, and also those which

k remain, (B D,) and hence, such a
tube sounds with nearly double the
A rot power of an ordinary open tube.

That it is the sound of the waves
which do not go into the tube,
and not that of the waves in the
tube, we hear, may be shewn by applying two closed tubes, as
in the next figure. When the two — waves are absorbed

+
D

16

-by the circular open tube, each
closed tube absorbes a + wave,
and hence, notwithstanding that
there is so much vibrating mate-
rial, no sound is heard. But if
the tubes a and B were open, then
the vibrating centres should
have been simply transferred to
their farther extremities, and the
tubes would emit sound as the
fork had done without them in

the preceding figure.

If the open tube be double the length of a phase, then
the neutralization oc-
curs as in the figure,
+ the residual waves
5 ama aes i cp lee being 8 and Fr, in op-
posite phases; but
as their centres are
separated so far, they interfere only in hyperboloidal planes,
which are not detected unless when carefully sought for, but
have been noticed to exist by Savart, although he did not
suspect their cause.

All these principles have received very full verification
from an instrument constructed for the purpose, and termed
a Chorizophone. It consists of a square glass plate, which
is placed above a set of closed tubes of such size, that when
the plate vibrates in four pieces, with diagonal nodal lines,
the length of each tube is half the length of the phase of the
wave produced, and their form is triangular, of the magnitude
of one of the four vibrating portions of the plate; when one
of these tubes is presented to the plate, and this brought to
vibrate by a violin bow applied to the centre of one of the
sides, the tube resounds, and more loudly in proportion as the
plate is brought nearer to its orifice. Nowhere the entire

17

wave from the plate is caught by the tube, and the more per-
fectly its escape into the air is prevented, the louder is the
sound produced, the sound must arise therefore from the
waves which do not pass into the tube. Any one or more
waves may thus be absorbed by the closed tubes, and a range
of loudness of sound produced from the same plate with one
or more of the four tubes, according as they are disposed as
follows :

The vibrating plate gives eight waves, four above and
four below, 4 being + and 4 minus.

With one tube, one wave is absorbed, and 3 + and 3 —
destroying each other, a wave remains opposite in phase to
that which is absorbed, and produces an audible sound.

With two tubes, the waves absorbed may be either of op-
posite or of the same phases. If opposite, then, the remain-
ing waves are 3 + and3 —, and no sound is produced; but
if the waves absorbed be of the same phase as +, then there
remains 4 — and 2+, and hence the ear is doubly affected

,by 2—. The two tubes may be either both above or both
below, or one above and one below the plate.

With three tubes, the absorbed waves may be either all

‘of the same phase, or two of one and one of the other. Inthe
first instance, 3 + being absorbed, there remains 4 — and
1 —, and the ear receives the impulse of 3—. In the other
case 2 +- and 1 — being absorbed, there remains 2 + and 3—
and the impulse on the ear is only 1—. The position of the
tubes may vary in this as in the former case.

With four tubes, the absorption may be either all of the
same phase, or 2-4-and 2—. In the former case, the re-
maining waves will be either 4 + or 4—, in which case the
greatest sound the plate can produce is heard, or else there
remain 2 + and 2 —, in which case the plate gives no sound.
These results prove fully that it is the residual sound that is
heard, and not that which passes into the tube.

VOL. II. c

18

A vibrating plate gives some sound always, even without
the tubes, for since there are at least eight waves, some one
will always be more favourably disposed for acting on the ear
than another, this difference will increase with the number
of waves; and hence, the independent sound of a plate in-
creases in proportion as the vibrating portions into which it
divides, become more numerous.

A string vibrating in free space, produces little or no
sound; but if it be strung over, or in connexion with, an
elastic board or box, a great resonance is produced. ‘This
arises from two sources ; first, the string when by itself is the
centre of two waves excessively close, and the action of which
is therefore interfering. But ifthe string as, vibrate near a
plane surface c, the wave —1, which passes
towards it is reflected back, and meeting
the wave + 2, which follows, it neutralizes
it partly, and enables the wave — 2, to
reach the ear without diminution. It is
probable, however, that the great portion
of the sound arises from the board or plate
itself vibrating in parts, or as a whole. If
in parts, these parts are variously situated, as regards the
ear, and hence produce an effect upon it. Or if, as a whole,
the plate c is so broad, or bounded, if a box, that one wave
is lost by internal reflexion, and only the wave emanating from
the outer surface can arrive at the ear.

When a tuning fork is placed on a table, one wave is lost
by internal transmission and reflexions, whilst that directed
from the outer surface reaches to the ear.

In the case of reed instruments, the reed produces two
waves, which, if it vibrated freely, should neutralize each
other on the ear ; but in practice whilst an open passage is al-
lowed to one by the mouth-piece, the other wave is lost
within the cavities of the lips and mouth. In mouth-piece
instruments, as bugles and trumpets, the cavity of the mouth

19

serves also for the absorption of the one wave, leaving the
other free to act.

The following note, “ On the Course ofthe diurnal Fluc-
tuations of the Barometer,” by James P. Espy. A.M., of Phi-
ladelphia, was communicated by Dr. Apjohn.

* Tt isa law of inertia, that if a body is forced upwards,
it will react and press on its support, more than its natural
gravity ; and if itis permitted to descend, it will press on its
support less than its natural gravity, and the increase and
diminution of pressure will be proportional to its velocity.

** Moreover, if a body is permitted to descend with a cer-
tain velocity, and then retarded, it will, when retarded, press
more on its support than its natural gravity, and that in pro-
portion to the rapidity of its retardation.

“This principle will explain the four fluctuations of the
barometer which occur every day.

‘‘ Just before sunrise, when the atmosphere is neither
becoming hotter nor colder, the barometer will indicate the
natural weight of the air, which we may call a mean; as the
sun rises the air will begin to expand by heat, andthe whole
atmosphere will be lifted up by this expansion, and by its
reaction will cause the barometer to rise; and this will be
the greatest, at the time when the air is receiving the most
rapid accessions of heat, which must take place before the
hottest time of the day, when the air is becoming neither
hotter nor colder. On this principle, then, the maximum
day fluctuation will take place between daylight in the morn-
ing and the hottest time of the day, and this corresponds with
the fact; for this maximum, which amounts to more than
the tenth of an inch, takes place about nine or ten o'clock,
A. M.

‘¢ At the hottest part of the day, when the air is neither
expanding nor contracting, it is manifest that the barometer
will stand again at a mean. Soon after this, however, the air

20

will begin to contract from diminishing temperature, and at
the moment of the most rapid acceleration of contraction, the
barometer will stand at its day minimum, which will probably
be late in the afternoon; and it is found in fact to be from
four to five o’clock. From this time the rapidity of the down-
ward motion of the air from contraction begins to diminish,
and the barometer of course begins to rise; and at the mo-
ment when it is most rapidly retarded in its contraction, the
barometer will be at its maximum night fluctuation, and will
again be above the mean, but not so much as the day max.

“‘ This max. is found to occur about ten or eleven o'clock,
p.m. The air will now go on contracting more and more
slowly, until about daylight, when it will be at rest, and the ba-
rometer will again be at a mean.

«This theory was given by me to the Journal of the
Franklin Institute, and published ten or twelve years ago.

“ IT ventured in that paper to predict, notwithstanding
some alleged observations at St. Bernard’s Hospital to the
contrary, that it would be found by more careful observations
that the morning max. fluctuation would be greater in lofty
situations on the sides of mountains, provided they were not
very lofty, than on the plain below.

** For it is manifest, that there will be not only a reaction
at these lofty situations, (a little less, it is true, than below,)
but some ofthe air will be lifted up, by the expansion of the
air below, above the upper place of observation ; which would
in all probability more than compensate the diminished re-
action at moderate elevations.

“ This prediction has been entirely verified by Lieute-
nant-Colonel Sykes’s observations in India, and this verifica-
tion may be considered as a strong proof of the correctness
of the theory. It is quite probable, that max. day fluctua-
tion occurs later at considerable elevations than on the plain
below.

“‘ The theory would lead us also to suppose, that at very

|

great elevations, where the reaction is very minute, only two
fluctuations would be found in the day: the maximum at
about two o'clock, Pp. M., when most air would be above the
barometer; and the minimum at daylight in the morning,
when least air would be above it ; but I know of no observa-
tions to confirm or refute these deductions.”

Mr. Ball brought under the notice of the Academy the
fact, that the ordinary sturgeon of the Dublin markets is an
undescribed species. He stated that Mr. Thompson of Bel-
fast, and Professor Agassiz, concurred with him in this opi-
nion, and he proposed to call it Accipenser Thompsoni, pur-
posing, if permitted, to give figures and full descriptions in a
future number of the Proceedings.

A notice of an unpublished Irish coin of Edward IV. was
read by A. Smith, M.D., M.R.1.A.

‘* Within the last month some workmen were employed
in cleaning one of the city drains in the Cross Poddle, and a
few coins werefound. Among them was one of no intrinsic
value, and apparently of nointerest whatever. It is made of
brass, and was originally plated with silver, traces of which
still remain. On one side it has a crown within a circle of
pellets, outside which, in place of a legend, are crosses and
roses alternately ; on the other side it has the common type—
a cross, with three pellets in each quarter; the legend is de-
faced. It weighs nearly five grains, and is now in the cabinet
of Lieutenant-Colonel Weld Hartstonge.

‘This little coin bears no evidence in itself which would
enable us to say towhat king’s reign it should be appropriated,
or even to what country. But on referring to an Act passed
in the second year of Edward IV., at a parliament held in
Dublin, we find it enacted, ‘ that a coyne of copper mixed
with silver, be made within the Castle of Dublin, having on
one side the print of a cross, and on the other part a crown, of
which four shall be taken for a penny; and that the said

22

coyne shall havegraven within the circumference of the said
cross, the name of the place where it was made; and on the
other part suns and roses in the circumference of the said
crowne.’*

“It is to be regretted, that this little coin, the only one of
the kind which has been found, is not in better preservation ;
but such as it is, it corresponds in every particular with the
description in the Act; and, therefore, we do not hesitate to
assert that it is one of the farthings of mixed metal ordered
to be madein 1462.

‘It may be objected, that this coin has crosses instead of
sunsround the crown, and itwould be difficult indeed to give
a more accurate symbol of the sun, in so many places, within
so limited a space; but we should recollect, that similar
crosses occur on some of the silver groats of Edward IV.,
coined in Dublin, in the beginning of his reign. On these
groats, immediately over the crown, on the obverse, are placed
three small crosses, which have usually been considered as
privy marks.t

“ Now taking for granted, that these crosses on the groats
were intended to represent suns, as they evidently were on
the farthing, we suspect we can account for them, not only
as privy marks, indicating that the coins on which they are
found belong to Edward IV., but also assign a probable rea-
son why three only should appear.

“The sun was first introduced by Edward IV. upon the
coins, ‘ in commemoration ofan extraordinary appearance in
the heavens, immediately before the battle of Mortimer’s
Cross, in Herefordshire, (in 1461,) where three suns were seen
which shone for a time, and then were suddenly conjoined
in one.’

“Tt matters little whether the extraordinary phenomenon

* Simon’s Essay on Irish Coins, Appendix, No. VII.
+ Simon, pl. 4, fig. 71.
¢ Ruding’s Annals of the Coinage, vol. ii. p. 359, 2nd Edition, 8vo.

23

just alluded to be explained or not ; it is sufficient for our
purpose to know, that it gave rise to the introduction of the
sun as a privy mark on the coins of Edward; and we may be
permitted to hazard the conjecture, that the three crosses on
his Irish groats, coined shortly after the battle of Mortimer’s
Cross, were intended to represent the three suns.

‘We could refer to many instances in which dates and
other matters were determined with certainty, by studying
with attention minute particulars in the type of coins, con-
cerning which the records were unsatisfactory, or altogether
wanting ; and there are still in existence authentic records of
more than one Irish coinage, specimens of which have not
yet been discovered ; and within the last few years numerous
coins, whose existence had not been suspected, have come to
light, for the preservation of many of which we are indebted
to the indefatigable zeal and research of a highly esteemed
and deeply lamented individual, whose memory will long be
regarded with respect and admiration, and the recollection
of whose labours in preserving the proud memorials of our
country, will, we trust, be perpetuated by depositing within
these walls his collection of Irish antiquities, in accordance
with his well known intention, and thus constituting a monu-
ment worthy of the late Dean of St. Patrick’s.”

The Archbishop of Dublin made some observations on a
remarkable meteor, lately seen in different parts of Britain.

Resolved—That the Committee of Antiquities be re-
quested to take immediate steps towards opening a subscrip-
tion for the purchase of the collection of Irish antiquities
which belonged to the late Dean of St. Patrick’s.

DONATIONS.

Memoires de ? Academie Imperiale des Sciences de St.
Petersbourg. ‘Tome I.—XI.

24

Sciences Mathematiques, §c. Tome IV. 3rd and 4th
Livraisons, and Tome IV. Sciences Politiques, Histoire, §c.
4th and 5th Livraisons.

Novi Commentarii Academie Scientiarum Imperialis. Pe-
tropolitane. 'Tom. I.—XX.

Nova Acta Academie Scientiarum Imperialis Petropoli-
tane. Tom. VI. VII. VIII. and XV.

Recueil des Actes del Académie Impériale des Sciences de
St. Petersbourg. An. 1838 and 1839. Nos. 13 and 14.
Presented bythe Academy.

The Polytechnic Journal. Vol, III. Part 5. Presented
by W. Farran, Esq.

Quarterly Journal of Statistical Society. Vol. III. Part 3.
Oct. 1840. Presented by the Society.

An Inquiry into the Causes of popular Discontents in
Freland. By an Irish Gentleman. 1804. Presented by
Joseph Hone, Esq.

Descriptive Catalogue of the Museum of the Royal Col-
lege of Surgeons in Ireland. Vol. II. By John Houston,
M.D., M.R.I.A., &c. Presented by the College of Sur-
geons.

On the Diminution of Temperature with Height of the
Atmosphere.

Researches on Heat. Fourth Series.

Additional Experiments on terrestrial Magnetism in
1837. By James D. Forbes, Esq. Presented by the Author.

Memorie della Reale Academia delle Scienze di Torino.
Second Series. Vol. II. Presented by the Academy.

Transactions of the American Philosophical Society. New
Series. Vol. VII. Part 1. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1840. No. 26.

December 14, 1840.

Rey. J. H. TODD, D.D., Vice-President, in the Chair.

Dr. Apjohn read the following notice, by George J.
Knox, Esq., of “‘ some Improvements in the Voltaic Pile.”

“ The chief imperfection in the voltaic pile, its want of a
constant uniform power of long duration, by which itisrendered
almost useless as an instrument of research, having been
overcome by the ability of Professor Daniell, the only thing
that remained to render it efficient seemed to be, to increase
its power; a desideratum accomplished by Mr.Grove, by sub-
stituting for copper and sulphate of copper, platinum and ni-
tric acid. To give to Grove’s battery a constancy of action
equal to that of Professor Daniell’s, would require an increase
in the quantity of acids, (particularly the sulphuric,) into
which the metals are immersed; but inasmuch as in galvanic
batteries of the ordinary construction an increase of acid so-
lution would require an increased distance of the metals
from each other, producing a diminution of intensity, I endea-
voured to obviate these disadvantages by the following con-
trivance. Porous vessels are fixed half an inch apart in lateral
wooden supports, in which grooves are cut, to retain the zinc
plates from touching ; the porous vessels are filled with ni-
tric acid, from a long glass tube, sealed at one end, and bent

VOL II. D

26

at the otherat right angles. Along the side of the tube also
holes are bored at distances corresponding to the distances
of the porous vessels from each other ; so that, upon pour-
ing nitric acid into the tube, the vessels are all filled at the
same moment; when filled, the entire apparatus is placed in
a vessel containing sulphuric acid. ‘The advantages of this
arrangement were, that I had only two solutions to pour in,
whatever number of alternations were employed ; a sufficient
supply of acid solutions to keep up a constant action for a
length of time; and a distance between the plates scarcely
exceeding the thickness of the porous vessel employed.

« The following experiments were undertaken with the
intention of estimating the relative values of the different con-
structions of Grove’s battery, recommended by Mr. Knight
of Foster Lane, as far as respects the arrangement of the
zinc and platina plates, when, to my surprise, I found the
same quantity of electricity to be evolved when the zinc is
bent so as to expose an opposing surface to each surface of
a platinum plate, as when a platinum plate, of the size of
the former zinc, is similarly placed with respect to a plate of
zinc of the same size as the former platinum, affording an
economical method of arranging a Wollaston’s battery, the
zincs being bent round the coppers, in place of the coppers
round the zincs.

“< Experiments with Grove’s Battery.

‘The acid solutions were those recommended by Mr.
Grove, i. e. pure nitric acid, in contact with the platina ; sul-.
phuric acid + 4-5 water by measure, in contact with the
zinc. Thesurfaces of zincs immersed were 3 by 2°5 inches ;
those of the platina, bent round the porous vessel holding
the zines, were 6 by 2°5 inches. The glasses containing the
acid, &c., were 3°2 inches long, 1°5 broad, 3:5 deep. The
length of the porous vessel of pipeclay was 2°5 inches, the

20

breadth 0:3, the depth 3:5. ‘The number of alternations was
five.

Cubic Inches.

Time, 2 minutes, .. . seu 5 80
The battery-being at rest for 10 saitaten, otwal © 180
” it) Po ae BLED MS Vy od) Dies eae
* 5 1 hour, Sv wows: 40
” » 19 hours, . . . + .none

“The porous vessel was found filled with sulphate of zinc,
which stopped the action of the battery.

** Second Experiment.

* The zinc plates being of the same size as the former pla-
tina, and the platina of the same size as the former zincs,
the zincs bent round the platina, all other things being as

before.
Cubic Inches.

faite, 2 masetes, 9. Shad tur ig ee, 6 8 8
Peter, Inititesy 4) te re ee oa 2 Re Oe
9) 95 33 ° . e e . . e es . . . . 8:

“ Third Experiment.

‘* Another battery, the diameter ofthe cells of which was
23 inches, gave a diminution of only one-half of the quantity
of gas after the lapse of forty-eight hours, shewing the advan-
tage of having a large supply of sulphuric acid.*

_ “ Experiments with Smee’s Battery of Platinized Silver.

“The acid solution was of the same strength as before,
and the sizes of the zincs and platinized silver the same as

* «The porous vessels were of pipeclay. The same expertments repeated with
unglazed porcelain gave 10 cubic inehes in two minutes ; with very porous pipe-
clay, they gave as much as 15 cubic inches in two minutes, shewing the import-
ance of attending to the nature of the porous vessel employed.”

p 2

28

of the zines and platina formerly employed. The zincs were

bent round the platina.*
Cubic Inches.

Time, 2 minutes, .... ... .s <> >) eeaaeemren ee
After 5 minutes, tui; ©! «i* eee ie -deteatley bie

“ Second Experiment.

* The zincs being raised out of the acid, cut in two, and

re-immersed.
Cubic Inches.

Time, 2 minutes’...; 2: ©-sin ae en
After. 5 ‘minutes, .\s0se<iqs- A wetaee -) 2. esoeelee

“ Third Experiment.

“‘ The zincs and platinized silver being removed, the acid
remaining untouched ; the platinized silver plates were bent

round the. zincs.
Cubic Inches.

Time, 2 mintites;. V's. Beak. oe ee
After ‘5: minutes;:". "se tees ee. oe eee

“ Fourth Experiment.

“The platinized silver cut in two.
Cubic Inches.
Time, 2minutes, . "sec. cote) are eee eee

After ‘Simninutes, “S\ sieee Weel ere a eee

“Supposing from these experiments the same quan-
tity of electricity to be developed, whichever of the opposed
surfaces of the two metals be the greater, I placed in sepa-
rate glasses five zinc cylinders, one-inch diameter, immerged

*, “The most advantageous. method of arranging a Smee’s battery is, packing
the zincs and platinized. silvers in the manner, recommended. by Dr. Faraday in
his 10th series, (also. by Mr. Young, Phil. Mag, vol. x, p.241,) placing the
package on supports so as to.allow the sulphate of zinc to fall to the bottom of
the vessel, while the fresh acid rises to the surface.”

29

eight-tenths of an inch in the acid ; platina foil, connected by
binding screws with the zincs, was rolled into cylinders two-
tenths of an inch in diameter, and then immersed in pipeclay
tubes one inch deep.
Cubic Inches.
Pime,,2 minutes, §, .Virsiuiesanee Apa.’ .s. +. eda 0
matertO miniites, io...) apse Select. 26 ts oO

** Second Experiment.

‘« Platina foil of the same size as the zincs, and zinc rods
of the same diameter as the platina cylinders being employed,

the effects were precisely the same.
Cubic Inches.

Mine WMMULES, i. a wae co els gt ge woe EO
PerorlO mintites;; .° -) ay ust. sts ee le el EU

** Third Experiment.

“ The zinc cylinders being made twice the diameter of the
former; the quantity of gas generated in two minutes was
the same as before; the increased number of lines of elec-
trical force compensating the increased resistance offered by
the acid solution.

“ Fourth Experiment.

** With cylinders twice the diameter of these, a very fee-
ble current passed, the obstacle being too great to be over-
come ; by increasing the diameter of the porous vessels,
and thereby of the nitric acid solution, which is a good con-
ductor, the impediment is diminished, as shewn in experi-
ment fifth. Thus Mr. Binks (Phil. Mag. vol. xi. p. 68)
finds, that in dilute sulphuric acid, the size of the copper
compared to a given surface of zinc, to produce a maximum
effect, should be 16, that of the zinc to a given surface of
copper being 7; while in a galvanic arrangement, in which the
zinc is immersed in dilute sulphuric acid, inclosed in a mem-

30

branous bag, and the copper ina surrounding solution of sul-
phate of copper, the proportion of zinc to copper was as one
to eight, the impediment to the passage of the current being
double in the latter case what it was in the former.

“ Fifth Experiment.

“ Five cylinders of zinc, 10 inches high, 3 diameter, were
placed in glass vessels, containing sulphuric acid, as before.
Into these were placed cylindrical earthenware vessels, 13
inches diameter, containing pure nitric acid ; slips of platina

foil were rolled into cylinders as before.
Cubic Inches.

Time, 2 miniites,) 2 249 - ae one Wileer gee eee
After 10 ___,, ree Sara ah pain meme 2
Prune * TE IIE ok eens. 0) 3 Sema

“From these data may be calculated the heights of the
zinc pipes, and the weight of platina foil required to obtain
any given decomposition, to be employed, as shewn by
Jacobi, either as a motive power, or applied to light-houses,
to the polariscope, or to the fusion of refractory substances.
For the latter purposes, I had fixed to a strong, shallow
woolf bottle, two tubes with glass cocks, and to them tubes
containing chloride of calcium, applied to a Daniell’s jet,
playing upon a cylinder of lime, rotated by clock work.
A third tube was inserted in the bottle, intended as a regu-
lation of the pressure, or a safety valve, in case of explosion.”

Dr. Apjohn then made a brief verbal communication on
the subject of the Composition of Pyrope. This mineral, long

* “The dilute acid in the voltameter began to boil ; the cause of the increase
of decomposition, compared to what took place in the small cylinder, was the small
stratum of sulphuric acid between the porous vessel and the zinc. For a continu-
ous action the zinc pipes, sealed at one end and amalgamated, should be connected
by pipes at top and bottom, with an earthenware vessel, containing the sulphuric
acid.”

3l

confounded with garnet, is known to be distinguished from
it by containing chrome, and by exhibiting, not the dodeca-
hedral, but the hexahedral form. The best analyses of it,
however, which are by Kobel and Wachtmiester, are ob-
viously imperfect, of which no better proof can be given than
that Gustavus Rose, in his Crystallography, does not attempt
to give the formula of the mineral, but contents himself with
enumerating the different oxides of which it is composed.
Under these circumstances, Dr. Apjohn conceived that a
re-examination of the constitution of pyrope would not be
without interest. He, therefore, undertook its analysis ; and
the result has been that he has detected in it yttria, one of
the rarest of the earths; one, in fact, which had previously
been known to exist only in a few minerals of exceeding
scarcity. ‘The yttria was insulated in the following manner.

The mineral being fused with carbonate of potash, and
the silex separated in the usual way, the peroxide of iron,
alumina, and yttria were precipitated together by a mixed
solution of ammonia and sal-ammoniac. The alumina was
taken up by caustic potash; and to the iron and yttria, dis-
solved in a minimum of muriatic acid, such a quantity of
tartaric acid was added, that upon subsequently pouring in
ammonia in excess there was no precipitate produced. The
iron was now removed by sulphuretted hydrogen; and the
solution evaporated to dryness, and ignited in a large pla-
tinum crucible, so as to volatilize the ammoniacal salts, and
burn away the carbon of the tartaric acid, left the yttria
slightly coloured by oxide of chrome. From this latter sub-
stance it is separated, but not perfectly, by the action ofa
dilute acid, and by the addition of ammonia, or caustic potash,
to the solution the yttria is again recovered. That the sub-
stance thus obtained is yttria seems proved by the following
considerations.

It is separated, though not completely, from acids by

32

ammonia largely diluted with sal-ammoniac, and hence cannot
be one of the alkaline earths.

It is insoluble in potash, and is, therefore, not alumina or
glucina. After ignition it dissolves readily in dilute acids, and
is hence not zirconia or thorina. From zirconia it is further
distinguished by its saline solutions, being aiencai os by
ferrocyanide of potassium.

It is not oxide of cerium, for it does not redden in the
exterior flame of the blow-pipe, and because its salts are not
precipitated by the sulphate of potash. The quantity of the
yttria amounts to at least 3 per cent.

Dr. A. is still engaged in investigating the composition
of pyrope; and expressed his intention of bringing his re-
sults on a future occasion in a more detailed form under the
notice of the Academy, when he hoped also to be able to
assign the true formula of the mineral.

Mr. J. Huband Smith exhibited to the Academy an an-
cient monastic seal, from an impression of which the annexed
wood engraving is taken.

This seal has been for some time supposed to have been
that of the Dean and Chapter of Lismore, and it was recently
found among the effects of the late Rey. Sir George Bisshopp,
formerly Dean of Lismore; but the legend around the seal
shews this supposition to be totally groundless.

Itreads thus: “SIGILLVM : CAPITYLI: PRIORIS : ET: CONVEN-
TVS: DE: BVLLYNGIONA. It surrounds the figures of the Vir-
gin and Child. She appears seated, and wearing a highly
ornamented crown; her robe, which falls in gracefully ar-
ranged folds, displays no inconsiderable degree of skill and
tastefulness of design. In her right hand is a star of five
rays, intended possibly to represent the star of Bethlehem,
to which the infant Saviour points. It is observable that
his head displays the ecclesiastical tonsure. The seal is of

33

a pointed oval form, and measures two inches and seven-
eighths in length, and one inch and three-quarters in its
greatest breadth.

Wi
U
i ys
7 5tw

iit indhha

It has been surmised, with considerable appearance of
probability, that this seal (which, if an inference were drawn
solely from the style of the characters, might be pretty con-
fidently referred to the close of the fourteenth, or the
beginning of the fifteenth century) belonged to a monastic
establishment dedicated to the Virgin, as Archdall states,
[Monast. Hibern, 626,] at Ballindown, on Lough Garagh, in
the county of Sligo, of which but inconsiderable remains
now exist. It is said to have been founded by M‘Donogh,
lord of Corran and Tirreril, A.D. 1427, for nuns of the order
of Saint Dominick, about the very period to which the cha-
racters of the legend may he attributed.

Like other names of places in Ireland, that of Ballindown
is variously written. In a tract entitled, “Valor beneficiorum
ecclesiasticorum in Hibernia,” we find “V.de Ballendowne

34

in the ‘‘ Dicecesis Tuamensis,” of which the ‘‘ Extenta et
taxatio facta fuit, 28mo. Eliz.” So that it seems highly pro-
bable that “ Bullyngiona” may have been but an arbitrary
Latinization of the same name by the artificer by whom the
seal was made, possibly a monk of the religious house to
which it belonged.

Mr. Clibborn made the following communication on the
subject of the Leyden Jar.

“In Brand’s Manual of Chemistry, vol. i., 3rd Edition,
p- 76, I find it stated, that, ‘if one Leyden jar be insu-
lated, with its internal surface connected with the positive
conductor, another jar may be charged from its exterior
coating ; and if this second jar be insulated, a third may be
charged from its exterior coating, and so on for any number
of jars, provided always that the exterior coating of the last
jar be connected with the ground.’

‘As my electrifying machine was but small,it occurred to
me that I might economise both time and labour by con-
structing a battery of jars so arranged that I should be able
to take advantage of this principle, aud make one jar charge
another, instead of my being obliged to charge the whole
series; for, though they are all connected together, and
charged by the same operation in the common electric bat-
tery, yet the time and labour consumed in charging the
battery is exactly the same as if each jar were charged sepa-
rately and then added to the series. A great saving of labour
and time would have been effected had the arrangement of
jars answered, for it was exactly the same as that described
by Brand, so far as the charging part of the apparatus was
concerned ; but when the jars were loaded, or rather should
have been loaded, they were made to turn through a qua-
drant, and form a new arrangement, by which all their out-
side coatings were connected together by a common con-
ductor. A similar arrangement connected all their inside

35

coatings, which made all the conditions necessary to the
perfection of the common battery; and I found it capable of
being charged by the electrifying machine in this form, but
it could not be charged to any extent in the other. It ap-
peared, that but few sparks would pass from the conductor
to the first jar. If the last one was removed, and its chain
fastened to the next, the first jar would take a few more
sparks, and so on; for it was found that whenever the last
jar in the series at any time was removed, the same results
followed; and this was the case when the last but one was
removed, clearly proving, that the capacity or aptitude of
the first jar to take a charge was influenced and diminished
by the second, more so by the third, fourth, &c. Its apti-
tude was greatest when it was by itself, and not connected,
as described, with the others.

“‘ This result disappointed my expectations, so far as my
intended improvement on the electric battery was concerned;
and it also appeared to point out the existence of a principle
influencing the charge of the electric jar, which was not
recognized in the popular treatises on electricity. I procured
a number of glass plates with fixed and moveable coatings.
These plates were insulated and arranged with and without
coatings in every way that Brand’s rule required, but the
general result was the same as that given above.

«‘ From numerous experiments made with these plates, I
came to the following general conclusions :

‘1. That the actual quantity of the positive and negative
electricities which we can accumulate in the opposite sur-
faces of an electric or non-conductor, as a plate of glass or
dry ice, depends upon the distance of these surfaces.

«©Q, Every case of charge of one jar or plate may be assimi-
lated to that of any number of jars or plates in a series, such
as Brand’s, by supposing the one jar or plate to be divided
into the greater number, its thickness being the sum of the
thicknesses of all the segments or plates. 'The inside of the

36

first jar or surface of first plate, in contact with conductor,
and outside of last jar or plate in contact with the ground,
being considered as the proper opposite surfaces of the pro-
per plate, and those on which the electricities evolved by the
friction of the cylinder and rubber of the electrifying machine
are accumulated or heaped.

“Ifwe make a pile of the plates coated or not, and charge
the outside surfaces by coating them, and connecting one
with the cylinder and the other with the rubber of the ma-
chine, we find all the conditions of the experiment complied
with. There is nonecessity for any connexion with the ground,
which in Brand’s can act merely as the conductor to convey
the negative charge of the rubber to the extreme surface.

*‘ Let us now unpack the pile, and we find that the charge
of the intermediate plates diminishes, as we approximate
towards the centre of the pile, being greatest near the ex-
tremes. At equal distances the charges are equal; for the
charges of the first plate but one, and the last but one, will
as perfectly neutralize each other as the charges of the sur-
faces of the first and last. The same is found to be the case
with the surfaces of the third plates from each extreme, and
so on of the others; but it is not the case with a second and
a third, a first and a fourth plate, and so on, o two unequals
as to place exactly neutralizing each other. Hence we
may conclude, that the charge of the intermediate jars
in a series, such as described by Brand, though it really de-
pends on inductive agency, is altogether different from that
kind he alludes to, which may be inferred from his erroneous
representation of the actual fact; and the charge of the
extreme surfaces is immediately the result of that action
only, which several electricians have called conduction,
arising from the connexion of these surfaces with the sources
of the free electric forces.

“The fact here described appears capable of throwing
much light on the corpuscular arrangement of the atoms of

37

bodies, which retain an electric charge on their surfaces, or
which, by a change of form from mechanical pressure or dif-
ference of temperature, exhibit differences of electric state.
In speaking of a charged electric, we may consider it a pile
of an infinite number of plates, each of which, except the
extreme surfaces, is composed of a surface of atoms, which
are acted on by two sets of induced electric forces, whose
differences, arising from their distances from the extremes,
we discover when we split the plate, or if it be a pile, when
we separate the plates from each other.”

January 11, 1841.

His Grace the ARCHBISHOP OF DUBLIN, V.P.,
in the Chair.

Rév. Henry Barry Knox, Rev. John West, Thomas
Fortescue, Esq., M. P., Chichester Bolton, Esq., and Henry
Coulson Beauchamp, M. D., were elected Members of the
Academy.

The Rev. Thomas H. Porter, D.D., read a paper ‘“‘ On the
Deposits of Gravel in the Neighbourhood of Dublin.”

After detailing the facts commonly known as to the stra-
tified beds and ridges of limestone gravel, lying over the
great central limestone region of Ireland, and the continu-
ance of deposits containing a large proportion of rounded
pebbles and stones of the same material, over the granite’
and other primitive rocks to the eastward of the limestone
country ; it was argued that there were clear indications of
a great diluvial action from west to east, by which the sur-
face of the limestone was reduced to its present level, and
the remains of its upper portions spread over the limestone

38

region itself, and carried eastward to the sea. The occur-
rence of similar calcareous deposits in the seaward glens
and valleys of the Dublin and Wicklow mountains for some
miles south, and on their sides to a considerable height,
was ascribed to the current of the same deluge, sweeping
the transported substances over the lower parts of the moun-
tain range, and then turning southwards along the sea coast,
after passing the north flank of the mountains. Similar
facts, but in an inverted order, from south to north, have
been observed towards the southern flank, in the County
Wexford.

It was urged, that the subsiding waters of this inunda-
tion, rushing down the valleys, and meeting below with the
main current on the plains, would throw up those ridges
along the sides of the hills, and on the flats beneath; of
which a remarkable example is presented in the glen of
Ballynascorney, (through which the Dodder descends from
the Dublin mountains,) and in the gravel hills in front of
that, from Tallaght to Crumlin.

The direction assumed in this paper for the diluvial cur-
rent agrees remarkably with that assigned by Professor
Phillips, as the cause of the distribution of the Shapfell
boulders over the north-east of England. A conjecture
was proposed as to the possible occasion of such a move-
ment of water over the country. The limestone tract was
evidently formed under the sea. Its elevation may have
been connected with the last great convulsion, which deter-
mined nearly the present form of the surface. Great
disturbances are seen at Killiney, the Scalp, &c., to have
attended the appearance of the granite, and even to have
followed that period, affecting the granite itself. Many
parts of the Irish coasts present such abrupt terminations
towards the sea, as to indicate either a violent raising of the
island from a continuous tract at the bottom, or a sudden
sinking of an extent of dry land around the present surface.

39

Either of these events would create immense commotions in
the waters,

Reference was made, in the course of this argument, to
the theory of Professor Agassiz, respecting the supposed
evidence, that glaciers once existed in the mountains of this
island, and produced, as moraines, some of the accumula-
tions of mountain debris commonly attributed to the agency
of water. This theory having been pushed so far by some
eminent British geologists as to have almost every ridge of
gravel and stones unhesitatingly called a moraine, it was
urged, that their principle could not be applied here at least,
since the limestone abounding in the deposits of the glens
could never have been brought down by ice from mountains
in which no limestone rocks exist. It is but justice to Pro-
fessor Agassiz to state, that he did not ascribe the limestone
gravel ridges at Ballynascorney to a glacier; but professed
to find the traces of one higher up the course of the stream.

Against the glacier theory, in general, it was maintained,

that evidences of a glacier having existed in any locality
must be derived from the existing form of the ground; and
that, therefore, no considerable change of the surface could
be admitted, since the time when the moraines were
imagined to have been thrown up. More especially, no
deluge could have taken place since their formation; for in
that case, the moraines must have been swept away. Hence
they must be supposed to have existed between Noah’s flood
and the commencement of the historical periods. This inter-
val, it was contended, would not allow time for their forma-
tion and disappearance.
_ A gradual change of the temperature of the whole nor-
thern hemisphere would be at variance with the fact esta-
blished by geologists, that the heat of the earth’s surface had
been formerly much greater than now.

Had the degree of cold necessary for the formation of
glaciers, been owing to a greaterelevation of this entire coun-

40

try, its sinking to its present level must have been. attended
with convulsions and floods, which could scarcely have failed
to obliterate all vestiges of moraines.

An objection, brought from the known change of tempera-
ture in Greenland within modern times, was met by observ-
ing, that Greenland in its best days was. always a land of
glaciers ; in the extent of which it is easy to suppose an oc-
casional increase or diminution,

Mr.J. Huband Smith gave an account of the discovery,
in the month of November last, of a human skeleton, accom-
panied with weapons, ornaments, &c., interred on the sea
shore, in the vicinity of Larne, in the county of Antrim.

He suggested, that a timely effort to preserve a record of
such interesting discoveries, can hardly fail to rescue from
destruction some valuable “‘ scattered leaves belonging to the
lost books of history.”

The locality in which these remains were found is one of
considerable historical interest; it was within less than a mile
of Olderflete Castle, where it will be remembered that Ed-
ward Bruce landed with a considerable force for the invasion
of this country, in the beginning of the fourteenth century.
A very cursory inspection, however, suffices to shew that these
weapons and ornaments could not have belonged to one of his
followers, but must be referred to a period considerably more
remote. They consist of a sword of very characteristic form,
double edged, and rounded at the point; measuring two feet
eight inches and nearly a quarter in its extreme length; a
small portion, said to have been about six inches in length,
was broken off and lost at the time of its discovery ; the blade
varies from two inches to two inches and a quarter in
breadth;—the head of a lance (both this and the sword are of
iron or steel, much corroded) ;—a small and very elegantly
formed bronze pin, which measures five inches and_a half in

41

length, thickly encrusted with verd antique, and of the shape
usually supposed to have been used in fastening the cloak or
mantle ;—and lastly, four fragments of bone; three of them be-
ing portions of a comb, the
back of which (attached to
the serrated part by rivets)
is slightly but not untaste-
fully carved-on both sides ;
and the fourth is so minute
and indistinct, as to render
its original use and form
uncertain.

The manner in which
the skeleton was discovered
was thus : some lime quar-
ries having been lately open-
ed along the shore, at a dis-
tance from the jetty, or
wooden pier, at which small
coasting vessels, trading be-
tween Larne and the op-
posite ports of Scotland,
usually take in their car-
goes, it became necessary,
for the greater convenience
of transporting limestone
from the newly opened
quarries, to construct a
rail or tramway. In level-

ing the line marked out

for the purposes of such construction, in the afternoon of

the 7th of last November, the workmen discovered these re-

mains at a spot three quarters ofa mile distant from the town
VOL, II. E

42

of Larne, about seventy yards from the sea shore, and about
five feet above the level of high water mark. ‘The skeleton,
when uncovered, lay obliquely, the head pointing towards the
N. W. The soil about it, consisting of sand, without almost
any admixture of clay, may have, in the lapse of time, shifted
its depth; but there scarcely appeared to have been more
than from eighteen inches to two feet of sand or soil above
these remains.

There was no appearance of stone kist, or hollow space
formed by flags set edgeways, which appear to belong ex-
clusively to the more ancient interments preceded by crema-
tion; fragments of the skeleton alone being found in such,
with indications of the action of fire, and usually accompanied
by one or more cinerary urns. Yet although there was in
the present instance no trace of coffin, either of stone or
wood, there appeared no reason to doubt that the inter-
ment was effected in aregular and orderly manner. Across
the breast was found the sword, its handle disposed towards
the right hand. On the same side, but beneath the sword,
was the lance head. The position of the remaining articles
was not noticed at the time by the workmen, and therefore
cannot now be ascertained.

Mr. Smith placed beside these weapons a sword and lance
from his collection, selected from some found in the remark-
able heap of bones in the townland of Lagore, near Dun-
shaughlin, in the County of Meath; a paper descriptive of
which was read before the Academy by Doctor Wilde, on the
27th of April last. The straight shape and uniform breadth
of the blade of this last mentioned sword, and the form of the
lance head, appeared remarkably similar, though on a reduced
scale, to those of the weapons found near Larne. The comb
' and bronze pin are nearly identical with several of those dis-
covered at Dunshaughlin, where, it is observable, no brazen
weapon of any description occurred.

43

From a consideration of all these circumstances, Mr. Smith
ventured to express an opinion thatthe remains found at Larne,
as wellas those at Dunshaughlin, are to be referred to that re-
mote period when the use of brass or bronze was superseded
by iron and steel inthe manufacture of offensive weapons, while
it was yet retained in the lighter works of ornament.. From
the invariable shortness of the Dunshaughlin swords, he was
disposed to infer, that the remains there discovered were of a
period not far removed from the age of the bronze swords of
similar length, still not unfrequently found in Ireland ; while
he suggested, that the articles to which the present paper re-
ferred might be considered as furnishing a closely following,
though later link in the chain.

- The sword bears no slight resemblance. to one which has
been engraved in Walker’s Essay on the Costume and Arms
of the Ancient Irish, and which, attributing it to the Knights
Templars, he states to have been found about forty years
before, near the site of the old priory of Kilmainham. It
was accordingly objected, that the weapons found at Larne
belonged to some one of that Order, and were therefore of a
much later date than that assigned to them as above men-
tioned. In reply to this, Mr. Smith urged the remarkable
circumstance of the bronze pin, of unquestionable antiquity,
having been found in connexion with the sword, a fact of
which he was able to give the most decisive assurance, upon
the testimony of the overseer of the works, a person of strict-
est integrity, and who, not having any antiquarian predilec-
tions, could not be aware of the force or nature of the evi-
dence he was furnishing. It was also to be recollected, that
long antecedent to the establishment of the priory of Knights
Templars by Richard Earl Strongbow, in 1174, a monastic
institution had been founded there by St. Magnen, from
whom Kilmainham (which in many ancient documents is writ-
ten Kilmaynan) took its name so early as the sixth or se-
venth century of our era; and that the adjoining burial

44

ground was used by the Irish, we learn from the Munster
book of battles, attributed to Mac Liag, a poet who died in
the year 1015, where it is recorded, that several of the chiefs
who fell at the battle of Clontarf were interred at Kilmain-
ham.

In the hall of the Commander of the Forces is suspended
a sword of the same shape and character found in the old
burial ground, vulgarly known by the name of “ Bully’s Acre,”
about forty years ago. In some adjacent fields, between the
immediate grounds of the Royal Hospital and the brink of
the river Liffey, about four years ago, some labourers, em-
ployed in raising gravel, discovered a skeleton, around which
were disposed a variety of weapons and ornaments; they are
now in the possession of the Commander of the Forces, and
Mr. Smith had the advantage of inspecting them. They con-
sist of a sword, lance head, and brass or bronze pin, all of pre-
cisely the same form and character as that now exhibited to
the Academy. The total length of the sword is 3 feet 2
inches, the blade being 2 feet 8, and the handle 6 inches
in length; the pin measures about 6 inches. There was
also found along with these a hatchet head, and some frag-
ments of iron, so much shattered and corroded as to occa-
sion some difficulty in coming to the conclusion, which how-
ever may be just, that they once formed an iron skull cap.
Common rumour asserts, that the labourer, by whom these re-
mains were discovered, had also the good fortune to find with
them some ornaments of gold of considerable value; which
fact, for prudential reasons, he kept profoundly secret; but
its effects became speedily apparent, in a well-stocked shop,
which he soon afterwards opened in a village not ten miles
distant from Dublin.

In the Memoirs of the French National Institute,* a me-
moir is given, furnished by M. Mongez, concerning a Gaulish
sword, as he denominates one found in the bed of the river

* Literature et Beaux Arts, tom. V.

45

Somme, near Abbeville. A comparison of his description,
as well as of the engraving appended, shews this sword to
have been nearly identical in form and size with those found
in Ireland. This description, which applies in a remarkable
manner to the sword exhibited to the Academy, is as follows :

‘*Sa lame et sa poignée ne font qu’un tout solidement af-
fermi; elle a deux tranchans, et, loin d’étre terminée en
pointe, elle est obtuse et arrondie a son extremité, .... II
n’y manque que losier tressé, ou la corde, ou le bois, ouenfin
la substance qui entouroit la soie pour former une poignée
solide... .. La lame prolongée forme la soie sur laquelle
est fixée la traverse de la poignée par le moyen de deux
clous rivés; et la masse imparfaitement arrondie qui la ter
mine est traversée et maintenue par cette méme soie. . . . .
Longueur totale, 33 pouces 10 lignes; lame seule, 28 pouces
10 lignes ;_poignée, 5 pouces ; largeur de la lame a la poig-
née, 2 pouces 3 lignes.”

Ifit be kept in recollection, that the French inch is some-
what greater than the English, these measurements will be
seen to correspond surprisingly with those of the sword found
at Larne. M. Mongez’s paper exhibits great research and
learning. He quotes passages at length, from Polybius, Plu-
tarch’s Life of Camillus, Dion Cassius, and Strabo, which
describe with considerable minuteness the swords which the
Gauls used in their engagements with the Romans; and he
rests his argument not only on the identity he alleges of these
descriptions with that of the sword found near Abbeville, but
also on the fact of bronze and brazen ornaments having been
found with skeletons having similar iron or steel weapons
about them, discovered in 1788 at Velu, near Bapaume, in
Artois. He adds, “ Je puis donc assurer que l’épée qui est
sous les yeux de la classe est ’épée gauloise décrite par les
auteurs anciens. J’ajouterai que c’est la seule A ma con-
naissance qui soit conservée. On jugera d’apres cela com-
bien elle est précieuse pour l’etude des costumes anciens.”

46

Mr. Smith, in conclusion, drew the attention of the Aca-
demy to the circumstance that those and many other venera-
ble and most interesting remains of remote antiquity, which
are but rarely, and at distant intervals of time, discovered in
Great Britain, and on the Continent, literally abound in Ire-
land; and hence inferred, the incalculable advantage which
will be attained, in the study.of the ancient history not only of
this country but of the world, by the formation of a great
National Museum of Irish Antiquities, such as is at present
projected to be formed under the auspices of the Academy.

** Without claiming any undue importance for the pursuit
of antiquarian research, it nevertheless has its office, and
that by no means an ignoble one, as the handmaid of history—
‘ Principatum non habet; ancillari debet.’ It furnishes the
critical student not only with curious information and the
most valuable commentary on minute points, but summons
up for him a host of most important witnesses, whom, though
silent, he can subject to the most scrutinizing examination
again and again; on whose testimony, carefully weighed as to
its true value, history ever rests as on its securest basis.”

The reading ofa paper by the Rev. T. R. Robinson,
D. D., “ On the Constant of Refraction, determined by Ob-
servations with the Mural Circle of the Armagh Observa-
tory,” was commenced.

A paper by Dr. Andrews of Belfast, “ on the Heat deve-
loped during the Combination of Acids and Bases,” was read.

The general conclusions at which the author arrives are
contained in the two following Laws.

Law |. “ The heat developed during the union of acids
and bases is determined by the base, and not by the acid;
the same base producing, when combined with an equivalent
of different acids, nearly the same quantity of heat, but dif-
ferent bases a different quantity.”

47

Law 2. “ When a neutral is converted into an acid salt,
no change of temperature occurs.”

In the commencement of the paper a preliminary experi-
ment is described, the object of which is, to determine the ex-
act quantity of heat evolved during the combination of nitric
acid and potash. The solutions, both acid and alkaline, were
taken so weak in this and all the other experiments detailed
in the communication, that subsequent dilution with water did
not produce any change of temperature. On neutralizing the
solution of caustic potash, containing 0°353 grammes of pure
alcali, with nitric acid, the temperature of the resulting solu-
tion of nitrate of potash, whose weight amounted to 30 gr.,
was found (after all corrections had been made) to rise 6°75°,F,

To illustrate law first, the author adduces tables which
shew, ata glance, the heat produced when an eqnivalent of
each base is neutralized by different acids. Thus, when the
same proportion of pure potash is combined under similar
circumstances with the arsenic, phosphoric, nitric, boracic,
hydrochloric, hydriodic, and oxalic acids, the elevations of
temperature, indicated by the thermometer, vary only
from 6°&° to 66°. Sulphuric acid produces rather a
higher temperature than any other acid (7°3°), and the
acetic, formic, tartaric, citric, and succinic acids, give ra-
ther less heat than those before mentioned (from 6-4° to 61°)
In like manner, ammonia produces an increase of tempera-
ture varying from 5-7° to 5°5°, when neutralized by the nitric,
hydrochloric, hydriodic, arsenic, oxalic, and acetic acids ;
the greatest divergence from these numbers occurring, on the
one hand, with the sulphuric acid (6°3°), and on the other,
with the citric, tartaric, and succinic acids (5°1°). Analogous
results are described as having been obtained with other
bases, such as soda, barytes, magnesia, lime, and the oxides
of zinc and lead. On the contrary, the heat developed by
each base is peculiar to itself; and, consequently, the same
acid gives different elevations of temperature, with equiva-

48

lents of different bases. To take, as an example, the nitric
acid, which also produces very nearly the mean quantity
of heat given by all the acids, the following numbers ex-
press the increments of temperature obtained on combining
the same quantity of it with each base: magnesia, 8°1° ; lime,
7°'2°; barytes, 6:9°; potash, 6°8° ; soda, 6°5° ; ammonia, 5°6° ;
oxide of zinc, 4°8°; oxide of lead, 4°2° ; oxide of silver, 3°2°.
The numbers for barytes, potash, soda, and ammonia, are
strictly comparable with one another (except a slight correc-
tion for differences in the specific heats of the solutions ;) but
in the case of the other bases, an absorption of heat, unknown
in amount, takes place in consequence of their conversion
from the solid to the fluid state. Hence the numbers for
these bases are all below the truth.

Two singular anomalies are described as occurring in the
combinations of the peroxide of mercury with the hydracids,
and in those of the hydrocyanic acid with the bases.

In confirmation of the second law the author adduces a
series of experiments, which prove, that during the conver-
sion of a neutral into a supersalt no heat is produced. “Thus
while the normal development of heat occurs when a solution
of caustic potash is neutralized by oxalic acid, the subsequent
additions, first of one, and afterwards of two more atoms of
the same acid, so as to convert the neutral oxalate into the
binoxalate, and the latter again into the quadroxalate of
potash, is not accompanied by any change of temperature in
the solutions. In testing the accuracy of this law, it is neces-
sary to select examples where all the compounds are soluble
in water, otherwise the heat arising from the formation of
precipitates would interfere with and complicate the result.

The second law does not extend to the case of the conver-
sion of neutral into basic compounds,—a part of the subject
which the author has carefully investigated.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY,

1841. * No. 27.

January 25, 1841.
SIR Ws. R. HAMILTON, LL.D., President, in the Chair.

The Rev. Dr. Todd, V.P., made some remarks on two
large medallion busts, with Greek inscriptions, which are
preserved in the Manuscript Room of the Library of Trinity
College. These busts have been in the possession of the
College for upwards of a century, but there is no record in
the archives of the University stating how or from whom
they were obtained. In the Appendix to the Preface of
‘Gudius’s Inscriptiones Antique,* the editors of that work
have given a list of inscriptions, which they state to have
been furnished by Herman Van der Hoorst, Chaplain, to
the Dutch in Smyrna; and, in this list, the very busts now
in Dublin are thus described, (No. XIII.):

* No. XIII. Smyrnez in domo cujusdam Greeci Zachariz

* The full title of this work is as follows :—‘ Antique Inscriptiones olim a
Marquardo Gudio collect, nuper a Toanne Koolio digeste, hortatu consilioque
Joannis Georgii Greevii; nunc a Francisco Hesselio edite, cum annotationibus
eorum.””, -Leovard.. 1731, Fol.

VOL. II. F

50

nomine, duz muliebres imagines sculptz adfabre, et incor-
rupte ; altera cum hac inscriptione,

KAS. AYSIMAXHN THN ®IAANAPON
O OPEVAS OHAYMITPHS

altera cum hac inscriptione

————— THN NEAN MYHZION TIOAIN
TIAS ATTIKOS.”

Dr. Todd stated that he had met with a letter in the
Bodleian Library, in which these busts are mentioned, and the
interpretation of the inscriptions discussed. It is preserved.
in the valuable correspondence of Dr. Thomas Smith, who _
was Fellow of Magdalen College at the Revolution, and
whose lot it was to have been twice deprived of his Fellow-
ship by the opposite parties of that period ; first, by King
James II., when the attempt was made by that monarch to
alter the constitution of the College; and secondly, by King
William III., when Dr. Smith resigned his preferment rather
than take the oath to the new dynasty. The letteris addressed.
by Dr. Smith to Dr. Narcissus Marsh, then Lord Primate of
Ireland, who had. been Principal of St. Alban’ Hall, Oxford,
and subsequently Provost of Trinity College, Dublin. ‘The
portion of the letter which relates to the busts is as follows :—

“The two busts sent to Dublin from Legorne,I suppose
came from Smyrna, or the country thereabout, where old
monuments are continually discovered.

“The first erected to the honour (for so I will favourably
interpretit) of Clodia Lysimache (whoisstyled there ¢iAavdpoe,
1. €. vire sive maritt amans ; tho’ oftentimes ¢idavdpoc yuri is
taken in an ill sense for a lascivious and. incontinent woman)
by one who bred her up and maintained her, viz., Thelymi-
tres, if that be his proper name, which is not unlikely, tho’
the appellative OnAvprpoc is used of an effeminate man
abandoned to the excessive love of the other sex, and there-

51

fore explained by Suidas by the word répvoc. But bee that
as it will, hee was desirous to preserve the memory of his
Operrn or Alumna by this representation, as some of the
Operipes or of Opélavrec used to do frequently enough, as
is evident from undoubted inscriptions.

“Tis pity, that the other inscription is imperfect and
erased. Stephanus Byzantinus, in his booke wepi méAcwvs
mentions: Ming a city of Ionia, its 2Ovcov or Gentilitiwm
nomen Muiowoc, w™ is the name in the inscription; but
whether Myes bee here meant by véa wéArc then newly
erected into a city, or some other city built by the inhabi-
tants of the former, forced to remove to a more convenient
and healthier place, the defect in the beginning, owing to the
injury of time after so many ages, will not suffer us to know

now who it was that did honour to this new city by setting
up this monument, who I suppose was a Greeke of Attica,

and the word preceding it may be the name of the tribe or
djpoc to which hee belonged. If it be the same with Myis,
Mvove, as is very likely, then it is certaine that it was a mari-
time city of Ionia, not farre from the river Maander, w® I
passed over in my travells to take a view of the once famous
churches of Asia, on a rotten wooden bridge going thence,
leaving Caria on the other side into Ionia, of we wee have
several accounts given by Strabo, Pausanias, and Pliny, not
to mention other authors both Greek and Latine. Pliny now
lying upon my table I think fit to transcribe his words, Nat.
Histor. lib. v. cap. 29—Mytis, quod primo condidisse Tones
narrantur, Athenis profecti. But I do not pretend to writea
commentary on these marbles, but leave that to be done by
those learned men, who are in possession of them.”

In a P.S. he adds :

“Reviewing those hasty notes upon the two Greek in-
scriptions, | began soone to doubt of my conjecture about
Atticus, as if it had beene a patronymic, and the name of the
tribe or Ojo of Attica prefixed : but now I am prone to be-

F2

52

lieve that this Atticus reckoned among the most famous
orators of Greece, who flourished in the times of Hadrian
and Antoninus Pius, and who had been sent upon several em-
bassyes mpeoeiac to Smyrna, and other free cityes of the
lesser Asia, where hee presided with great honour, as appears
from Philostratus in the life of Scopelianus, and was'the
father of Herodes Atticus, as hee is commonly called by the
Roman writers, as if it were the name of the familye : whereas’
it should bee more properly Herodes Aitici, viz., filius, as in
the inscription on his monument at Athens preserved by
Philostratus in his life.

~ € id
’Arrixov ‘Hewenc, Mapabervioc, ov rade Tava
Keira: mde Tagy, wavro0ev evddKioc.

This Herodes succeeded his father in the same honours at
home, and in the like governments abroad, and was magnifi-
cent in his buildings and public works, in Greece and Italy,
having been preceptor to Marcus Aurelius in the studyes of
oratory (of which he was universally esteemed. a most cele-
brated Master) as Julius Capitolinus has observed in the life
of that Emperour, and Consul A.U.C. 896. A. Ch. 143. But
I thinke to the father, rather than the son, the Atticus in
the inscription is to bee ascribed, and if so, how hee comes
to bee called Hippitias or Hippotias if that bee his pre-
nomen, and the right reading, or whether Hippatias, or
whatever it should bee, bee the proper name of the person,
who put up the monument, and Atticus of his country, I
have not time nor leisure to enquire; and. in the whole am
no way fond of my conjertares w I look upon as altogether
uncertaine.”
‘* 4 Nov. 1707.”* ‘
t

* Collect, Smith, vol. 58, p. 257.

53

The following are exact representations of the inscrip-
tions reduced to one-fifth of the original size:

\AN M ¥HSIMNMMcAIN
TIAZ<AT TIKoO&

Dr. Todd stated that one of the busts appears to have
suffered some injury since they were described by the editors

54

of Gudius, and by Dr. Smith. The second inscription has
lost some letters; instead of THN NEAN, the words with
which its first line then commenced, the last two letters of
these words only are now discernible. He also exhibited to
the Academy fac-similes of the inscriptions, and made some
remarks on the differences observable in the characters in
which they are written.

The Rev. Charles Graves, F.T.C.D., read a paper On
certain general Properties of the Cones of the Second De-
gree.

Let a sphere be described whose centre is at the vertex
of a cone of the second degree, and through the vertex let
two planes be drawn parallel to the planes of the circular
sections of the cone; the curve formed by the intersection
of the cone and sphere is called a spherical conic, and the
two planes meet the surface of the sphere in two great circles
which are called the cyclic arcs of the conic. ‘These arcs,
as M. Chasles has observed, possess properties relative to
the conic exactly analogous to those of the asymptotes of
a hyperbola. Moreover, many of their properties depend
on the most elementary ones of the circle; but, as all the
properties of cones, and therefore of spherical conics, are
double, each theorem relative to the cyclic arcs furnishes a
corresponding one relative to the foci of the supplementary
conic, formed by the intersection of the sphere with a cone
whose generatrices are perpendicular to the tangent planes
of the cone on which the proposed conic is traced. And
further, the theorems relating to spherical conics become
applicable in general to the plane conic sections, by suppo-
sing the radius of the sphere to become infinite.

These considerations, for which we are indebted to M.
Chasles, are calculated to direct the attention of geometers
to the cyclic ares of the spherical conics. In following this
track, Mr. Graves has been led to many, new and general

55

properties of the cones of the second degree, amongst which
the following deserve to be noticed :

1. If two fixed tangent arcs be drawn to a spherical
conic, and any third tangent arc be drawn meeting them in
two points, the arcs passing through these two points and
through the pole of a cyclic are will intercept on that cyclic
are a portion of a constant length.

2. If from two fixed points in a spherical conic, arcs be
drawn to any third point onthe curve, and produced to meet
one of the director arcs, they will intercept between them on
that director arc a portion which will subtend a constant
angle at the corresponding focus.

3. A spherical conic and one of its cyclic arcs being
given, if, round the pole of this cyclic arc, as vertex, a spheri-
cal angle of variable magnitude be made to turn, whose sides
intercept between them on the cyclic arc a portion of a con-
stant length, the arc joining the points in which the sides of
the moveable angle meet the given conic will envelope a
second spherical conic: the given cyclic arc will be a cyclic
arc of the new conic, and this arc will have the same pole
with relation to the two curves.

4, A spherical conic and one of its foci being given, if
round that focus, as vertex, a constant spherical angle be
made to turn, and from the points in which its sides meet the
director arc corresponding to the given focus, two arcs be
drawn touching the given conic, their point of concourse will
generate a second spherical conic: the given focus will be a
focus of the new conic, and the corresponding director arc
will be the same in the two curves.

5. Ifa variable spherical angle turn round a fixed point
on the surface of a sphere soas to intercept between its sides
a constant segment on a fixed arc, the arc joining the points
in which its sides meet two other fixed arcs will envelope a
spherical conic touching these two fixed arcs.

6. If aconstant spherical angle turn round a fixed point

56

on the surface of a sphere, the arcs joining the points in
which its sides meet a fixed arc with two other fixed points
will intersect in a point, the locus of which will be a sphe-
rical conic passing through these two last mentioned. fixed
points.

If two tangents to a parabola intersect ata donstat
angle, the radii vectores drawn from the focus to the two
points of contact will also contain between them‘a constant
angle. But, as is well known, in any conic: section, the
point of concourse of the tangents at the extremities of two
focal radii vectores, which contain between them a constant
angle, will generate a conic section. Hence we deduce the
following very general properties of spherical conics.

7. If two tangent arcs to a spherical conic intercept be-
tween them a segment of a constant length on’a fixed tan-
gent arc to the curve, their point of concourse will generate
a second spherical conic,

8. Ifa constant spherical angle turn round a fixed point
on a spherical conic, the arc joining the points, in which
its sides meet the curve, will envelope a second spherical
conic.

9. In theorem 7, if the segment intercepted on the fixed
tangent arc be a quadrant, the point of concourse of the
tangent arcs will move along an arc of a great circle.

10. In theorem 8, if the constant angle be right, the arc
which it subtends in the spherical conic will pass’through a
fixed point.

The two following theorems may be obtained‘by the aid
of the equation of a spherical conic, expressed in spherical
coordinates:

11. From two fixed points on the surface’ of'a sphere,
the distance between which is 90°, let arcs p, p’; be drawn
perpendicular to a moveable arc, and let a, 3, be arcs of a

sin P sin *p’
aagee +328 = 3g = 1, the moveable arc will

given length ; if

57

envelope a spherical conic whose principal diametral arcs
are 2a, and 23; they will pass through the fixed points, and
the:centre of the conic will be the pole of the great circle
passing through the two fixed points.

12. The base of a spherical triangle being a quadrant, if
cot*a _ cot?
tan *a i tan
a and 3 are given arcs, the locus of the vertex will be a
spherical conic, whose principal diametral arcs are 2a, and
28; they will pass through the extremities of the given qua-

drant, and the centre of the conic will be the pole of the

= 1, where

its base angles a, b, be such that

quadrant.

Some of the preceding theorems lead to new and very
general properties of the conic sections: and one (No. 6)
gives rise to a new and remarkably simple organic de-
scription of them. It should be observed that the arcs here
spoken of are all arcs of great circles,

His Grace the Archbishop of Dublin having taken the
Chair, the President continued the reading of Dr. Robin-
son’s Paper ‘‘ On the Determination of the Constant of
Refraction by Observations with the Mural Circle of the
Armagh Observatory.”

The author remarks, that the problem of astronomical
refraction is embarrassed by two causes of error. The dif-
ferential of the refraction is obtained by supposing the at-
mosphere to consist of spherical shells concentric with the
earth; and the integral of this, by assuming some mathe-
matical relation between the height above the earth and the
corresponding density of the air. He shews that the first
of these cannot be rigorously true; and that the relation
between density and height, besides being unknown in ge-
neral, may be expected to vary. with the latitude. He
therefore considers all existing refraction tables as approxi-

58

mations which require correction for each individual ob-
servatory.

For about 74° from the zenith, the refraction is inde-
pendent of the law of density, and requires only an exact
knowledge of the air’s refractive power; this, however, has
not been yet obtained with sufficient accuracy by direct
experiment, and, therefore, must be deduced from astrono-
mical observations. At greater zenith distances ‘some 'con-
stitution of the atmosphere must be assumed, and if its
expression contain a sufficient number of arbitrary constants,
the resulting refraction can always be made to represent
with sufficient exactness what is actually observed. As,
however, neither the formula of Bessel, nor that of Ivory,
very readily admits such modifications, Dr. R, used the
method given by the late Bishop of Cloyne, in the twelfth
volume of the Royal Irish Academy’s Transactions, which,
however, he has extended to 85° zenith distance.

If the atmosphere be supposed of uniform temperature
the refraction has been computed by Kramp; it is found
greater than the truth. If the density be supposed to de-
crease uniformly as the height above the surface increases,
the refraction is given by Simson; it is nearly as much in
defect as the other in excess, and it is found that their mean
is very near the truth. If then the differential equation of
refraction be developed in terms of the tangent of the appa-
rent zenith distance, it is found, on integrating, that the first
term belongs to an-atmosphere bounded by parallel planes ;
the second depends on the equilibrium’ of the strata,
and the others alone are affected by the assumed hypo-
theses. Their geometrical means are found to satisfy the
Armagh observations as far as 85° zenith distance, below
which the series ceases to converge, and the mean changes
its relation to the true refraction according to the tempera-
ture and pressure. The expression thus obtained for re-

59

fraction admits of being tabulated with the corrections for
the thermometer and barometer in a couple of pages; and
he thinks this form of tables more convenient than any other
with which he is acquainted.

To compute them are required the expansion of air by
heat; the ratio of the height of the homogeneous atmos-
phere to the radius of curvature of the meridian at the place
of observation, and the refractive power of air at a given
temperature and pressure. For the first he has used the
value given by Rudberg, namely, that 1 of air at 32° be-
comes 1°365 at 212°. This differs from Gay Lussac, but is
identical with that deduced by Bessel from astronomical ob-
servations. The second is derived from the researches of
Arago and Biot, corrected for the change of gravity from
Paris to Armagh.

Of the refractive power of air there are different values
of high authority. Denoting by the symbol » the quantity
‘iota a for 50° Fahrenheit and 29°60 inches pres-
sin R X sin 1”
sure, the experiments of Arago and Biot give it 57°82. The
observations of Delambre with a repeating circle give 57-72,
which is also adopted by Brinkley. But the barometer used
by this great astronomer is shewn by Dr. R. to require the
. correction + 0-078, which would change the constant ‘to
57°567; and as he also used the internal thermometer, per-
haps a further diminution might be necessary. That of
Bessel is 57-524, and that deduced by Dr. R. from his own
observations is 57°546 ; but they cannot be exactly compared
without a knowledge of the length of the pendulum at each
station, as the measure of density given by the barometer
depends on local gravity.

It was determined as follows by circumpolar stars.». The
refraction is obtained by subtracting from the subpolar dis-
tance 270° plus the declination observed above the pole. If
the constant of refraction require a correction, it affects this

60

declination both at the star and at the polar point, and the
latter also affects the subpolar observation; hence, calling
the tabular refraction nv, and the difference between it and
the observed dr, we have for each observation the equation
of condition
dr=du {v—v—2P} =duxk;

combining which by minimum squares, the value of du for that
star is obtained. If the values of it at different zenith dis-
tances are equal, or differ only by what may reasonably be
considered error of observation, then it may be also inferred,
that the formula correctly assigns the refraction through
the range of zenith distance included by the observations. °'

Dr. R. then gives details respecting the mural circle
which he used, the permanence of its microscopes as to run,
and the mode of obtaining its index correction, and the cor-
rection of its divisions. When the stars are spectra, he
bisects the yellow near the green, and remarks that the flue-
tuations of irregular refraction are often of considerable
duration. The hygrometric state of the air does not seem to
produce any effect, and he shews that the external thermo-
meter is to be used at his observatory. The details of ob-
servation are then given for seventeen stars, from 77° 10/ to
84° 56’ zen. dist., of which there are 317 subpolar obser-
vations.

If a southern star be determined at a place when it
passes near the zenith, so that its place may be assumed
as free from error of refraction, the value of du is multiplied
by a much larger factor. This advantage, however, is more
than balanced by the uncertainty caused by the difference of
instruments and local circumstances at the two observatories;
but Dr. R. has given the result of such a trial. He used
the declinations of Mr. Johnson, (St. Helena Catalogue, ) and,
in many instances, those of Mr. Henderson at the Cape, and
by 241 observations from 77° 53/ to 84° 40’ he found for pu
57°586; but conceives the result obtained from the northern

61

stars decidedly preferable, and has used it alone in computing
the tables which are given at the end of the paper.

DONATIONS.

Proceedings of the Royal Academy of Berlin. July,1838—
January, 1840, with Index from 1836-39. Presented by the
Academy.

Observations of the Magnetic Intensity in Europe. By
A. D. Bache, LL.D., &c. Presented by the Author.

The Seventh Annual Report of the Royal Cornwall Poly-
technic Society for 1839. Presented by the Society.

Natural History asa Branch of General Education. Pre-
sented by the Natural History Society of Belfast.

Proceedings of the Numismatic Society of London. 1838,
1839. Presented by the Society.

Proceedings of the American Philosophical Society. No.
13. Presented by the Society.

Flora Batava. By Jan Kops. Nos. 120 and 121. Pre-
sented by the Author. .

Memoirs of the Royal Astronomical Society. Vol. XI.
Presented by the Society.

Edinburgh Astronomical Observations. Vol. III. 1837.
Presented by the Royal Astronomical Society.

On Paralytic, Neuralgic, and other Nervous Diseases of
the Eye. By Arthur Jacob, M.D. Presented by the
Author.

Quarterly Journal of the Statistical Society of London.
Vol. III; Part 4. Presented by the Society.

An. ancient Silver Ring foundnear Drogheda. Presented
by Lieut. W. Persse Newenham, R.N.

Model of Thumb Screws lately found in the Priory of St.
James, Drogheda. Presented by the same.

A large Collection of Miscellaneous Antiquities, consisting
of Stone, Flint, Bronze, and Iron Instruments, Coins, Se. Se.
Presented by Captain Portlock, M.R.I.A.

62

The special thanks of the Academy were voted to’ Cap-
tain Portlock for his large donation of Irish Antiquities.

February 8, 1841.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Mr. J. Huband Smith submitted to the inspection of the
Academy the swordand otheriron weapons, brass mantle-pin,
&c., with which he had been favoured by the Commander of the
Forces, and which were discovered, with a human skeleton,
at Kilmainham some years since. He further produced a
still more perfect iron sword, which was also most obligingly
lent to him by Captain Hort of the Royal Hospital. This,
too, had been found about eight years ago in the same vici-
nity, and under similar circumstances with the weapons
above mentioned.

The remarkable similarity of these, and all the incidents
of the interments which they appear to have accompanied,
with the remains found in the county of Antrim, described
in the paper which Mr. Smith read before the Academy, on
the 25th of January, as well as with the engraving and de-
scription of the Gaulish (Celtic) weapons, the account of
which by M. Mongez, Keeper of the Museum of St.
Genevieve at Paris, he had also on that occasion alluded to,
together with the invariable discovery of bronze, or brass
ornaments, unquestionably Celtic, in connexion with them,
induced Mr. Smith to adhere to his opinion, that all
these various remains were to be referred to people of Celtic
race.

If this conclusion be just, the inference would seem to
follow, that in the skeletons accompanying these weapons,
&c., an opportunity is offered to the student of ethnography

63

and the natural history of the human family, of investigating
the characteristics of the pure Celtic type of a considerable
branch of the Caucasian variety of man.

His Grace the Archbishop of Dublin communicated some
observations ‘ On the Leafing of Plants.”

It is well known that there is a diversity in the times of
leafing and shedding in individual trees of the same species ;
e. g. hawthorn, sycamore, horse-chesnut, beech, &c., some-
times as much as a fortnight ; and the earliest in leaf are also
theearliest shed, the same individuals keeping their time every
year. Hence the question, whether this diversity arises from
the “ separable accidents” of soil, situation, &c., or whether
from “inseparable accidents” which constitute what physio-
logists call varieties ?

An experiment was tried by grafting an early hawthorn on
a late, and vice versa. The scions kept their times (abouta
fortnight’s difference) as if on their own stocks ; thus proving
that it was a case of “seedling variety.”

Many other such varieties are known, not only of apples,
peaches, &c., but of wild trees also, differing in shape of leaf,
form of growth, colour and size of fruit, &c., and also time of
ripening. It was, therefore, to be expected that there should
be the like, in respect of times of leafing.

This may throw some light on the question respecting
* acclimating.” It may be, that species may be brought to
bear climates originally ill-suited,—not by any especial virtue
in the seeds ripened in any particular climate, but—by multi-
plying seedlings, a few of which, out of multitudes, may have
qualities suited to this or that country, e.g. some to cold,
some to drought, some to wet, &c.

In some cases, a plant’s beginning to vegetate later may
secure it from spring frosts, which would destroy a preco-
cious variety ; in others, earlier flowering may enable a tree to
ripen fruit in a climate in which a later would be useless, &c.

64

Further, the experiment shews that the common opinion
respecting the commencement of spring vegetation,—the rise
of the sap from the roots, through, the trunk and’ branches
to the twigs,—is groundless; since ascion of an early variety,
ona late stock, will be im leaf while the stock is torpid. |

REsOLVED,—(on the recommendation of Council,) ‘that
the sum of £200 be placed at the disposal of the Committee
of Antiquities, to employ such portion of it as they may deem
necessary in increasing the present collection of Irish. Anti-
quities in the possession of the Academy.”

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1841. No. 28.

February 22, 1841.
. Rev. H. LLOYD, D.D., Vice-President, in the Chair.

Mr. Charles T. Webber presented to the Academy an
ancient stone, on which is carved a rude bass-relief, supposed
to be the representation of a dog killing a wolf. Mr. Webber
accompanied the present with a communication to the effect,
that the stone was taken from the Castle of Ardnaglass, in
the barony of Tireragh and county of Sligo, and was
said. to commemorate the destruction of the last wolf in
Ireland. The current tradition in the place from whence
it came was, that some years after it was supposed that
the race. of wolves was. extinct, the flocks in the county
of Leitrim were attacked by a wild animal which turned
out to be a wolf; that thereupon the. chieftains of Lei-
trim applied to O’Dowd, the chieftain of Tireragh, (who
possessed a. celebrated dog of the breed of the ancient
Irish wolf dog), to come and hunt the wolf; which appli-
cation being complied with by O’Dowd, there ensued a
chase, which forms the subject of an ancient Irish legend,
detailing the various districts through which it was pursued,
until at length the wolf was overtaken and killed in a
small wood of pine trees, at the foot of one of the mountains
in Tireragh. The quarter of land on which the wolf was
killed, is to this day called Carrow na Madhoo, which means

G

66
the dogs’ quarter. In commemoration of the event, O'Dowd

had the annexed representation of it carved on the stone, and
placed in the wall of his baronial residence.

came

cn

ggg

MIU
oA
"y |

SS

La

|

TASTE THAT TTA EA MTL
Hl HH i hi

i I |

The Secretary read the following “Collection of Notes on
the early History of Science in Ireland.” By James Orchard
Halliwell, Esq., F.R.S., F.S. A., F.R. A. S., &e.

“* The following scraps on a subject which has never yet
been treated of by any writer with whose works I am ac-
quainted, although unfolding no views of any great impor-
tance, will, it is believed, form a subject of discussion inte-
resting to all natives of Ireland, who would think favourably
of the intellectual character and resources of their country-
men.

“ The earliest remnant of Irish science that I have met
with, is contained in MS. Arundel, 333, in the British
Museum, which contains several medical and astrological
tracts in the Irish language of the thirteenth century,
together with similar tracts of the fourteenth and fifteenth
centuries. These tracts are of a similar nature with contem-
porary manuscripts written in England and on the continent.

67

For instance, at fol. 27, is an extract translated from the
treatise of the venerable Bede, ‘De Divisionibus Temporis ;”
at fol. 35, is a short tract on the months of the year and
their several durations; at fol. 76, is a scrap on the four
seasons of the year, and on the planets which govern them.

«‘ The whole volume contains astrology, mixed with the
sciences of medicine and astronomy: Medical manuscripts
in Irish of this early period are more numerous than others ;
and the Egerton collection in the British Museum con-
tains several; one dated in the year 1303, and written on the
continent.*

“* Some-writers say, that Johannes de Sacro Bosco, the
contemporary of Roger Bacon, and who shines so con-
spicuously in the history of the mathematical sciences of the
thirteenth century, was a native of Ireland ; but, whatever
obscurity may hang over the actual place of his birth, it is
certain that he resided nearly the whole of his life in Eng-
land and France, and there is nothing to show that his
writings were ever circulated in that country.

“ Be this as it may, yet it appears from MS. Egerton,
No. 90, that the Arabic numerals usually, though erro-
neously,{ ascribed to Roger Bacon, were well known and
understood in Ireland at the commencement of the four-
teenth century. The document contained in this volume is
very valuable evidence, in the absence of any other as early.
The MS. referred to contains an astronomical and eccle-
siastical calendar, together with a table of ecclesiastical
computation, all in the Irish character, and the numerals are
written in identically the same form as they appear in foreign
documents of the same period :—

2253 XH EABGO-

‘¢ The introduction of the zero isa proof, that the Arabic

* MS. Egerton, No. 89. +See my Rara Mathematica, p. 114.

G2

68

notation was fully understood by the writer of the manu-
script. It may be added, that there follows, immediately after
the documents just mentioned, a table of the twelve signs of
the zodiac, with their different astrological influences, viz. :
Aries = good ; Taurus = evil; Gemini = evil ; Leo = evil ;
Virgo = evil; Libra = good; Sagittarius = good; Capricor-
nus = evil; Aquarius = good.‘ The others are said to neu-
tralize their influences.

«In the Philosophical Transactions of the Royal Society of
London,* Dr. Ward has given an account of a date in Arabic
numerals found on a stone in Ireland, which he considered
to belong to the twelfth century. Professor Peacock, how-
ever, in his History of Arithmetic, has ably confuted this
conjecture.

“* The Liber Niger of Christ Church, Dublin, is said to
contain ‘a curious treatise on arithmetic, exhibiting the
state of that science before the introduction of Arabic nu-
merals.’| I much question the accuracy of this statement,
and should be rather inclined to think, that it is merely an
account of the numbers of algorism, so common in manuscripts
of this class. The same volume also contains, a transcript
of the French poetical treatise entitled ‘ Imago Mundi, one
of the most curious unpublished scientific tracts of the middle
ages. This latter treatise is now in the progress of publica-
tion, by the Historical Society of Science.

‘* But by far the most curious document that I have met
with relating to the early science of Ireland, is a manuscript
in the possession of C. Wright, Esq., of Cambridge, who
has kindly allowed me to make use of it, and has also fur-
nished me with a translation of the greater part, which has
been of great assistance to me. This MS. consists of six
folio leaves on vellum, slightly injured by damp, apparently

* For the yearl745, p. 283.
+ Report on the Public Records of Ireland, p. 307.

69

belonging to the early part of the fifteenth century, and
containing the following articles:

“1, A brief treatise on arithmetic.

“This unfortunately commences imperfectly in the ac-
count of the rule of duplation; ‘ In duplation only one order
of figures is necessary : in the three preceding kinds, we com-
menced from the right and from a smaller figure; but in this
this, and the following kinds, we commence from the left and
from:a larger figure. For if you. wish to double from the
first figure, it happens that you must double it twice. And
if you can in any other manner commence from the right
hand; the operation and construction will be much more diffi-
cult. If, therefore, you. wish to double any number, that
number must be written by its differences, and the last
number must be doubled. From that duplation, therefore,
either results a digit, an article, or a composite. Ifa digit,
it must be written in the place of the other blotted out. If
an article, a 0 must be written in the place of the other
blotted out, and the article must be removed towards the
left hand. Ifa composite number, the digit which is a part
of that composite must be written in the place of the other
blotted ‘out, and the article be removed to the Jeft hand.
This being done, the last figure must be doubled, and what-
ever thence arises must be dealt with as before ; but if a
cipher turns up, it must be left untouched. We prove du-
plation by means of mediation.’

‘“‘ This extract willbe sufficient to give an idea of the whole
tract. After this rule, follow those of multiplication, division,
and progression in their proper order. For the comprehen-
sion of the uninitiated in the old arithmetic, it may be neces-
sary to state, that a digit is any number below ten, an article
is ten, or any multiple of ten, and that all other numbers are
composites, or composed of an article and some digit. My
friend Mr. Wright, gives it as his opinion, that this tract is
a translation from the Latin or French.

70

“2. * Tractatus de Geometria.’

‘‘ This is an Irish tract with a Latin title, and consists of
only one page, containing the simplest rules of geometrical
measurement, applied to one example of finding the height
of a tower. No mention occurs of any of the old geome-
ters.

“‘ 3. A treatise on the signs of the zodiac.

** An astrological tract with very curious drawings of the
various signs. Messabalah, the famous Arabic astronomer,
is mentioned at the commencement, and this tract is very
probably translated from one of that author’s works. »

‘* 4, A treatise on the length of the days, in the year.

** 5. A fragment (one half page).

«« This terminates the contents of this manuscript, and is
written in Latin. It appears to relate to abacal arithmetic,
but as I confess myself unable to understand its meaning, I
give it here entire, in the hopes that some other may be
more fortunate in attempting to decipher its meaning.

“‘ Intervalla autem in quibus distribuuntur. dicimus sedes
horum numerorum. qui in abaci regula secundum geometri-
cam habitudinem sie proportionaliter ordinati continentur.
ut juxta numerum novem caracterum nonis termis alternati
distinctis terminis. secundum propor. .* * *?

“Thave pointed this exactly asin the original manuscript,
but the fragment appears to be altogether unconnected.

“In addition to the above, I may mention, that in the
library of Trinity College, Cambridge, under the pressmark
R. xiv. 48, is preserved a short poem in the Irish language on
astronomy, of the early part of the thirteenth century.*
And in the the Bodleian Library, MS. Rawlinson, B. 490, is
a translation of the ‘ Secreta Secretorum, of Aristotle, by
James Yonge, on vellum, of the early part of the fifteenth

* This I learn from Mr. Wright. In the printed catalogue, it is said to be in

Saxon characters.

71

century. This work, of Young is not, mentioned by Sir
James Ware, nor does it appear to’ be at all known to Irish
writers. Itis almost unnecessary to observe, that this latter
work has no relation with science, but its rarity is a suffi-
cient excuse for mentioning it here.

«‘ It will now be necessary to pass over nearly two cen-
turies before we meet with any traces of scientific progress.
Some time about the year 1600, William Farmer, ‘ Chirur-
gian and Practitioner in the Mathematicall Artes,’ dwelt at
Dublin ; and among the manuscripts of Archbishop Tenison,
at Lambeth Palace, No. 816, is an autograph MS. by him,
entitled, ‘ A Prognosticall Almanack for this Bissextile yere,
1612, composed with a three fould Kallender generally cal-
culated for this Kingdom of Ireland, and will also serve very
well for alle the Northe and Northweste partes of England.’
William Bourne also, who flourished at the same time, and
greatly distinguished himself by his mechanical inventions,
was anative of Ireland. To these two we may add, Nathaniel
Carpenter, an Englishman _ by birth, but who resided: in
Dublin early in the seventeenth century, and left behind him
treatises on geography and optics.| A copy of this latter
work is still preserved in MS. in the Library of University
College, Oxford.*

«With Molyneux, in more recent times, the science of
Ireland rose to a level with that of surrounding nations, and
the names Ponce, Boyle, Petty, and Ashe,{ serve to fill the
complement of the seventeenth century. In January, 1684,
Molyneux succeeded in forming a Philosophical Society at
Dublin, on the plan of the Royal Society of London. The
first meeting of the Society took place on the 28th of Ja-
nuary, 1684, when Sir William Petty was chosen President,

* Under the press mark L..14. See Bernard’s Catalogue, 1697, p. 5.
+ Archbishop Ussher was the author of some treatises on sciences and. their

history, more especially astronomy.

72

Dr. Charles Willoughby, Director, and) Molyneux. under-
took the combined offices of Secretary and Treasurer.
November Ist, All Saints’ day, was chosen for the anniver-
sary of the Society. On the Ist of November, 1684, Sir
William Petty was re-elected President, Molyneux as Secre-
tary, and William Pleydell, Esq., Treasurer. On the 2nd of
November, 1685, Lord Viscount Meuntjoy was elected Pre-
sident, George Tollet, Esq., Treasurer, and St. George Ashe
Secretary. Inthis year, Molyneux retired from actual office,
but retained his place on the council of the Society. On the
Ist of November, 1686, Lord. Viscount Mountjoy was. re-
elected President, George Tollet. Esq., Treasurer, and
Edward Smyth, Secretary.

‘“ The preceding particulars are taken from the original
Minute-book of the Society preserved in the British Museum,
MS. Addit. 4811.* ‘The last entry in this book is, the
account of the General Meeting of 1686, and this would lead
us to suppose that the Society was dissolved at this period,
although Dr. Hutton assures us, that it was not broken up
till 1688.7

«From MS. Addit. 4812, it appears that in the year 1707,
an attempt was made to reestablish the Society, but its suc-
cess was not of any long duration, and this MS. contains a
register of the philosophical papers read before the Society,
- from August 15th, 1707, to March 11th, 1708. The Earl of
Pembroke, then Lord Lieutenant of Ireland, presided over
the Society at this revival.

_ “In 1686, Molyneux printed at Dublin, his ‘ Sciothericum
Telescopium,’ containing a description of the structure and
use of a telescopic dial invented by him. In the British
Museum is preserved the author’s own copy of this volume,

* The same volume likewise contains copies of numerous letters and papers on
scientific subjects, addressed for the most part to Molyneux.
+ Mathematical Dictionary, vol. ii. p. 117.

73

enriched with numerous MS. notes, and observations, and
what is particularly worthy of being noticed, an analysis of
its history.”

March 16, (Stated Meeting).

SIR Wm. R. HAMILTON, LL.D. President, in the Chair.

- On the recommendation of Council, the following gentle-
men were elected Honorary Members of the Academy :
Professor Adrian, Giessen.
Jean B. Dumas, Paris.
A. Quetelet, Brussells.
J. O. Halliwell, Esq., Cambridge.

The Secretary of Council read the following Report :

In conformity with the precedent lately established, the Coun-
cil, at the expiration of their year of office, beg to offer the Aca-
demy a general account of its history and progress during that
interval.

The Council have to report, in the first place, that the publica-
tions of the Academy have proceeded with considerable vigour.
The first Part of Vol. XIX. of the Transactions has been. lately
issued, and the second Part, for which many papers are in readiness,
is now beginning to be printed. The first Volume also of the
Proceedings, containing, along with other ordinary business, an
account of the communications made to the Academy during the
last four sessions, has just been published. As the quantity re-
maining on hands of the fourth Number of the Proceedings was
remarkably small, the Council, on the recommendation of the
Committee of Publication, have ordered 250 copies of that Num-
ber to be reprinted, by which means a large stock of complete
copies of the first Volume has been made up for the supply of
future demands, and for sale to Members and others at a fixed
price.

74

The Council are gratified to observe the increasing interest
which is every day felt in the publication of the Proceedings. _ Not
being confined to the mere analysis of elaborate memoirs intended
for the Transactions, but giving free admission, and occasionally
complete insertion, to smaller papers of various kinds, the Pro-
ceedings serve as a repository for scattered facts, and important no-
tices, which would otherwise be lost. Speedy publication is an ad-
ditional inducement to authors to communicate such notices; and
by the adoption, of woodcuts for antiquarian and scientific objects,
of which the mere verbal description would be vague and unsatis-
factory, the value of the communications is very much enhanced.

The expenses of printing and engraving continue, as might be
expected, to press very heavily on the funds of the Academy.
With the view, therefore, of practising every possible economy,
the Council have entered into an arrangement with Mr. Petrie, by
which that gentleman has bound himself to print, at his own risk,
his Essay on the Round Towers of Ireland, as the twentieth Volume
of the Transactions, engaging to supply the Academy with 450
copies of the work at a settled price, the sum which they have al-
ready expended for engraving to be deducted therefrom. The
Academy will thus be furnished with as many copies as they want,
and will be saved the additional outlay which would be requisite if
they were themselves to defray the charge of the whole edition.
After the great and unusual delays which have attended the publi-
cation of this Essay, the Council are gratified in being able to
state that it has been actually put to press, and that the author
confidently expects it will make its appearance soon after the second
part of the nineteenth Volume of the Transactions.

Notwithstanding the limited extent of the resources of the
Academy, the Council are of opinion that the formation of a Na-
tional Museum of Antiquities is an object which the Academy
should continue steadily to pursue, as far as these resources will
reasonably permit ; and since many articles of great value to the
antiquarian are disposed of from time to time by public and by
private sale, and may never again be met with, if such opportunities
of procuring them are lost, they have thought it advisable to
recommend to the Academy that a sum of money should be en-

75

trusted to the Committee of Antiquities to enable them to profit by
such chances. The Academy have accordingly, by a recent vote,
placed at the disposal of the Committee the sum of £200, which
will probably serve the purpose for a considerable period. In the
meantime, from the liberality of members and other gentlemen,
the Museum is receiving constant accessions, which are regularly
recorded in the Proceedings, and among which the large donation
lately made by Captain Portlock is deserving of especial mention.

In touching on this subject, the Council are reminded of the
severe loss which the Academy have sustained by the decease of
their late respected Vice-President, the Very Rev. Henry Richard
Dawson, Dean of St. Patrick’s, a gentleman universally lamented
by those who had the pleasure of knowing him in private life, but
whom the lovers of Irish antiquities have peculiar reasons to re-
gret ; for he was a zealous preserver and collector of the old me-
morials of his country, and the treasures of this kind which he had
accumulated in a period of many years, would have been bequeathed
to the Museum now begun withinth ese walls, had not his’ well-
known intentions been. frustrated by the suddenness of the stroke
which removed him from amongst us. The Dean having died in-
testate, his collections will of course be sold; but as they will
fetch a price far above what the Academy could afford, a sub-
scription, which it is to. be hoped may be successful, has. been set
on foot, under the management of the Committee of Antiquities,
for the purpose of depositing these valuable remains in the place
for which they were intended by their generous collector.

The past year has also deprived us of some other distinguished
Members, among whom was Thomas Drummond, Esq., Captain in
the Corps of Royal Engineers, and Under-Secretary of State for
Treland. In his professional character, Mr. Drummond. was re-
markable for combined energy and talent, and for the singular
power which he possessed of making the truths of science available
for important purposes in practice. Though this was not the
country of his birth, yet it was here that he spent the most active
period of his life. Engaged in the Ordnance Survey, at its com-
mencement in this kingdom, he enriched the practice of geodetical
operations with some of its most useful instruments, which have

76

now become indispensable in the observation of distant stations ;
and it deserves to be remembered, that it was from the summit of
Slieve Snaght, in Donegal, to a party stationed on the hill of Divis,
near Belfast, that he first exhibited, across the haze of Lough Neagh,
the celebrated Light which bears his name, and which will serve,
better than any monument, to perpetuate his memory.

In the person of Nicholas Aylward Vigors, Esq., late Member
of Parliament for the county of Carlow, the Academy and the sci-
entific world have lost'one of the best zoologists of his day. His
papers, in the department of ornithology more especially, are highly
esteemed by naturalists; and the zeal which he felt for the advance-
ment of his favourite science was manifested in the active part
which he took, along with some other eminent men, in the founda-
tion of the Zoological Society of London.

But a very few days have elapsed since the hand of death has
blotted from’ our roll the honoured name of Laurence Earl of
Rosse, one of the original Members of this Academy, and one of
the ablest vindicators of the ancient literature of Ireland. Of the
illustrious noblemen and gentlemen who founded our Society, who
watched over its infancy, and powerfully promoted its early pro- _
gress, his Lordship ‘was the last survivor. Hitherto, for more than
half a century of our corporate existence, our meetings have been
cheered by the presence of some—though a constantly decreasing
number—of those who witnessed their beginning, and who felt, as
it were, a paternal interest in our welfare. But now they have
all disappeared from amongst'us. Let us endeavour to show that
we are worthy to succeed them ; for so we shall best do honour to
their memory.

The other Members whom the Academy has lost by death
within the year are:

The Earl of Ranfurly.

Right Honourable Lord Garvagh.
Rev. Sir Francis Lynch Blosse, Bart.
Arthur Hamilton, Esq., L.L.D.

Rev. Hosea Guinness.

John Crampton, Esq., M.D.

77

And the new Members added to the body since the 16th of
March, 1840, are:

J. Davidson, Esq. Rev. Henry Barry Knox.
Abraham Abell, Esq. Rev. J. West.

J. H. Blake, Esq., Q. C. Thomas Fortescue, Esq., M.P.
G. Wilkinson, Esq. Chichester Bolton, Esq.

George Willoughby Hemans, Esq. Henry Coulson Beauchamp,M.D.

In accordance with the suggestion of the Council of last year,
the Council have ordered the compositions received in lieu of annual
subscriptions to be henceforth invested in the Government Funds.

The following have been added to the list of Societies with
whom the Academy interchange Transactions:

_ The Bavarian Academy of Sciences.
The Institute of Sciences of Milan.
The Rotterdam Society of Sciences.

In connexion with the subject of Mr. Webber’s remarks
at the last meeting, Sir W. Betham communicated the follow-
ing document, giving an account of an order made by King
James I. for the destruction of wolves in Ireland.

Patent Roll, 12 Jac. 1.d.R. 17. “ The King being given
to understand the great loss and hindrance which arose in
Ireland by the multitude of wolves, in all parts of the king-
dom, did by letters from Newmarket, 26th November, 1614,
direct a grant to be made by patent to Henrie Tuttesham,
who by petition had made offer to repair into Ireland, and
there use his best skill and endeavour to destroy the said
wolves, providing at his own charge men, dogs, traps, and
engines, and requiring no other allowance, save only four
nobles sterling, for the head of every wolf, young or old,
out of every county, and to be authorized to keep four men
and twelve couple of hounds in every county, for seven years
next after the date of these letters.” 12 Jac. s. L. R. 27.

The Rev. C. Otway read a letter from Mr. Blacker, on
the origin of the emblem of the shamrock.

78

Mr. J. M. Ferrall drew the attention of the Academy to
several drawings, and a preparation, exhibiting a new and
beautiful mechanism belonging to the human eye, and
discovered by him in April last, while engaged in researches
on certain diseases of the orbit, which the received anatomy
of those parts did not appear to him to explain.

The new structures consisted of a distinct fibrous tunic,
investing the globe of the eye, facilitating its movements,
and separating it from all the surrounding tissues.

The anatomy of the schools, and of the best authors,
from the earliest time to the present, teaches that the ball of
the eye is in contact with its muscles, and, between them,
with a quantity of adipose substance on which it was sup-
posed to be cushioned. It was difficult to conceive, how-
ever, why the eye did not manifest any of the symptoms
incidental to pressure suddenly endured, whenever those
muscles were brought into action, since there appeared to
be no provision for its protection. That pressure, sud-
denly made on the globe of the eye, produces the sensation
of a spark or flash of light, is familiarly known as the con-
sequence of a slight blow on the eye.

The act of sneezing is frequently followed by a similar
phenomenon, and Sir Charles Bell has shown, in a paper
published in the Philosophical Transactions, that it is occa-
sioned by the sudden pressure on the ball of the eye, by the
orbicularis palpebrarum or principal muscle of the eyelids,
which is suddenly brought into action by the respiratory
nerves. The four recti muscles, which move the eye in dif-
ferent directions, being favourably placed, (according to the
received anatomy), for exercising such a pressure, it might
have been expected that a similar phenomenon would have re-
sulted ; but no such coruscations have ever been observed
to follow their most rapid actions.

The discovery of this tunic, which Mr. Ferrall has ven-
tured to term the TUNICA VAGINALIs OCULI, at once explains

79

the absence of those phenomena, by showing that a pro-
tective provision has always existed to prevent them.

Mr. Ferrall went on to state, that the most beautiful por-
tion of this mechanism remained to be described. It was
one of those exquisite manifestations of design which abound
in the animal frame.

In the anterior portion of this tunic were to be found
six different well defined openings, through which the ten-
dons of the muscles pass to their insertion in the sclerotic
coat of the eye, and over which they play as over pulleys in
their progress. ‘

The annexed engravings, executed from original draw-
ings made in April, 1840, for Mr. Ferrall’s clinical lectures
in St. Vincent’s Hospital, display this conformation faith-
fully.

Fig.1, shows the tendon of the internal rectus, emerging
from behind the tunic, and passing through its pulley to be
inserted in the eyeball.

Fig. 2, represents the eyeball drawn downwards, in
order to expose the exit of the tendons of the superior

80

rectus and superior oblique muscles; the superior rectus
plays over its pulley, and the superior oblique passes beneath
the former to reach its insertion in the sclerotic coat.

The presence of some such contrivance as is here ex-
hibited might have been inferred from its necessity, and yet
it has never been suspected to exist. ‘The four recti muscles
running from the bottom or apex of the orbit, forward to grasp
the eye, must, without it, have had the power of retracting the
ball of the eye, and yet no such retraction has ever been ob-
served in the human eye. Retraction is certainly performed
in some of the lower classes of animals; but they are provided
with a strong retractor muscle, independent of the four recti
muscles. Again, the rotatory movements of the human eye,
which enlarge the sphere of vision, and contribute to ex-
pression, are not easily accounted for by the received ana-
tomy of the orbit, because the course of the muscles from
the bottom of the orbit forwards, manifestly gives them a
power of retracting rather than of rotating the eye upon its
centre. Thus, then, there appeared to be no provision for

81

the rotatory movements of the ball of the eye, which are of
constant occurrence, and nothing to prevent retraction, which
we knew did not take place. A knowledge of the existence
of this new and beautiful mechanism reconciles and explains
these anatomical and physiological contradictions.

Mr. Ferrall said, he had found these structures in several
of the lower animals, in whom they appear to enable the
recti to antagonize the proper retractor muscles.

Several phenomena in diseases of those parts, formerly
obscure, are now easily understood; but Mr. Ferrall re-
frained, on this occasion, from discussing questions of a
- practical nature.

The Auditors appointed by Council to examine the Trea-
surer’s Account, for the year ending December 31, 1840, re-
ported as follows:

‘© We have examined the above account,* with the vouchers pro-
duced, and have found it to be correct; and we find that there is a
balance in Bank of £100 7s. and in the Treasurer’s hands, of
£110 9s. 4d. making a total balance of 210 16s. 4d.

«« (Signed,)
‘‘ FRANC SADLEIR.

“© SAMUEL LITTON.
“ March, 13th 1841.”

«« The Treasurer reports that there is £1390 17s. 4d. in three per
cent. consols, and £1526 6s, 1d. in three and a-half per cent. Govern-
ment Stock, to the credit of the Academy, in the Bank of Ireland ;
the latter being the Cunningham Fund.

‘¢ (Signed, )
‘¢ Toomas HERBERT ORPEN.
“ March 18th, 1841.”

The ballot for the annual election having closed, the
scrutineers reported that the following gentlemen were duly
elected Officers and Council for the ensuing year :

* Entered in the Treasurer’s book.

H

82

President.

Sir Wm. Rowan Hamilton, LL.D.

Committee of Science.

Rev. France Sadleir, D.D., Provost; Rev. Humphrey
Lloyd, D.D.; James Apjohn, M.D.; James Mac Cullagh,
Esq., LL.D. ; Rev. William D. Sadleir, A.M. ; Robert Ball,
Esq.; Robert Kane, M.D.

Committee of Polite Literature.

His Grace the Archbishop of Dublin; Rev. Joseph H.
Singer, D.D.; Samuel Litton, M.D.; Rev. William H.
Drummond, D.D.; Rev. Charles R. Elrington, D.D.; Rev.
Charles W. Wall, D.D.; Rev. Thomas H. Porter, D.D.

Committee of Antiquities.

Thomas H. Orpen, M.D.; George Petrie, Esq., R.H.A.;
Rev. Caesar Otway ; Rev. James H. Todd, D.D.; Henry J.
Monk Mason, Esq., LL.D.; Aquilla Smith, M.D.; Samuel
Ferguson, Esq.

Officers.

Treasurer.—Thomas H. Orpen, M.D.

Secretary to the Academy.—Rev. Joseph H. Singer, D.D.

Secretary to the Council.—J. Mac Cullagh, Esq., LL.D.

Secretary of Foreign Correspondence.—Rev. Humphrey
Lloyd, D.D.

Librarian.—Rev. William H. Drummond, D.D.

Clerk and Assistant Librarian.—Edward Clibborn.

The President appointed under his hand and seal the
following Vice-Presidents :
His Grace the Archbishop of Dublin; the Provost of

83

Trinity College; the Rev. Humphrey Lloyd, D.D.; the
Rey. J.H. Todd, D. D.

DONATIONS.

Résumé des Observations Météorologiques faites en 1839,
a UV Observatoire Royal de Bruxelles, par A. Quetelet.

Second Mémoire sur le Magnétisme Terrestre en Italie,
par A. Quetelet.

Deuxiéme Mémoire sur les Variations Annuelles de la
Température de la Terre a différentes profondeurs, par A.
Quetelet.

Extraits du Tom. VII. No. 2, des Bulletins de lA. R. de
Bruxelles. No.2. Température dela Terre. No. 3. Mag-
nelisme Terrestre. No. 4. Magnetisme Terrestre. Par A.
Quetelet. Presented by the Author.

Bulletin de l’ Academie Royale de Bruxelles. Nos. 1—8
An. 1840. Presented by the Academy.

American Almanack for 1841. Presented by the American
Philosophical Society.

_ Nautical Observations on the Port of Cardiff. By Cap-
tain W. H. Smith, R. N., &c. Presented by the Author.

Ninth Report of the British Association. Presented by
the Association.

A Catalogue of the Miscellaneous Manuscripts in the Li-
brary of the RoyalSociety. By J. O. Halliwell, Esq., F.R.S.,
&e. Presented by the Royal Society.

A Collection of Letters illustrative of the Progress of
Science in England. Edited by J. O. Halliwell, Esq., F.R.S.,
&c. Presented by the Editor.

Proceedings of the Royal Society of Lordon, 1839—40.
Nos. 41—44. List of Members of the Royal Society of
London, (30th November, 1840).

Philosophical Transactions of the Royal Society of London
for 1840. Parts I. and II. Catalogue of the Miscellaneous

84

Manuscripts in the Possession of the Royal Society. Pre-
sented by the Society.

Remarks on the Classification of Human Knowledge. An
Elementary Treatise on the Tides. On the Theory of the
Moon. On Currency. By J. W. Lubbock, Esq. Presented
by the Author.

An Examination of the ancient Orthography of the Jews.
Vol. III. By Rev. C. W. Wall, D.D. Presented by the
Author.

The Negroland of the Arabs. By W. Desborough
Cooley, Esq. Presented by the Author.

Constitution and By-Laws of the National Institution for
the Promotion of Science at Washington.

Discourse on the Objects and Importance of the National
Institution for the Promotion of Science. By Joel R. Poin-
sett, Esq. &c. Presented by order of the Directors.

Memoires de la Société Géologique de France. Tome
4me. lre partie. Pesented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1841. No. 29.

April 12.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The following gentlemen were elected Members of the
Academy:

William Monsell, Esq., Robert Tighe, Esq., W. E. Hud-
son, Esq., G. Fitzgibbon, Esq., William Phibbs, Esq., Rev.
James Reid, William Lee, Esq., F.T.C.D., Robert Jones,
Esq, Thomas Wilson, Esq., Beriah Botfield, Esq., M.P.,
W. T. Mulvany, Esq.

Mr. Ferguson made a communication on the Classification
of ancient Military Weapons found in Ireland.

DONATIONS.

Transactions of the Cambridge Philosophical Society.
Vol. II. Part 2; Vol. III. Parts 1, 2,3; Vol. IV. Part 1;
Vol. V. Part 3. Presented by the Society.

On the Geological Structure of the Northern and Central
Regions of Russia in Europe. ByR.J. Murchison, F.R.S., &c.
Presented by the Author.

Proceedings of the Geological Society of London. Nos. 74
and 75. Presented by the Society.

Journal of the Franklin Institute. Vol. XXVI. (1840).
Presented by the Institute.

The Numismatic Chronicle. No. 12. Presented by the
Numismatic Society of London.

VOL. II. I

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87

April 26.
Rev. H. LLOYD, D.D., V.P., in the Chair.

Mr. George Downes read a paper “ On the Norse Geo-
graphy of Ancient Ireland.” The earlier part consisted
of remarks on an “Essay on the earliest Expeditions from
the North to Ireland,” and on a small Map of Ireland accom-
panying it, as published in the Annals and Memoirs of the
Royal Society of Northern Antiquaries.

The author began by adverting to the two provincial
names on the map— Ulaxtir (Ulster), and Kunnaktir (Con-
naught),—and to twonames ofdistricts in Leinster— Dyflinar-
skirt, or Dublinshire, and Kunnjdttaborg (a part of Meath),
He argued that the local name in Johnstone’s edition of
Lodbroe’s Death-Song, translated “ Leinster’s,” more pro-
bably belongs to Lambay, the Amvoc of Ptolemy, support-
ing his argument also by a geographical consideration.—He
next proceeded to the estuaries—Jéllduhlaup, supposed to
be Lough Swilly ; and U/freksfjérSr, or Ulf kelsfjérSr, sup-
posed to be either Lough Foyle or Carlingford Bay, but
perhaps an English locality, and, if so, that arm of More-
cambe Bay which runs up to Ulverstone—The town ;
Dyflin he stated to be evidently a Norse adaptation of the
Irish name of Dublin; Ve$rafjérdr, or Waterford, to be
undoubtedly Norse, adducing its various derivations, and
giving the preference to vedr “ weather,” and fjér%r “ bay ;”
and Hlimrék, or Limerick, to be probably a Norse adaptation
of the Irish name Luimneach,—notwithstanding its consisting
of two Norse words, meaning “ branch” and “ district,” and
the resemblance between the Lower Shannon and'the Lim-
Jiord, or “ branching bay,” in Denmark. Kunnjattaborg, or
Kantaraborg, given in the Antiquitates Celto-Scandicx as
Kunnaktirborg, and (in the genitive form) Kantaraborgar—
the place of Brian Boru’s nuptials with Kormléda, or Gorm-

12

88

liath—he concluded to be Cancora ; and then adverted to the
minor localities of Iniskillen (perhaps Inisclothran, in Lough
Ree), Themar (Tara), and Glendelaga (Glendalogh).

The name Smerwick, laid down as Smjorvik on the map,
but left unexplained in the essay, was traced by the author
to two sources. The first derivation—from smjér ‘ butter,’
and vik “ bay,” or ‘‘ town”—was supported by the frequency
of the former word as an element of Norse local nomencla-
ture, and the probability that some trade in butter was car-
ried on between the Northmen and the south-western Irish.
A curious tradition, connected with the fortunes of Leif,
the son of Hrodmar, was adduced, in which the name mynn-
thak occurs—that is, meal and butter blended together—a
word apparently identical with the Irish méinzeaé “ boggy,”
and somehow connected with the discovery of butter, or an
adipocere resembling it, in the Irish bogs. The second deri-.
vation was founded on a tradition current in Munster, that
Smerwick is a contraction of St. Mary’s Wick; and a tradi-
tion from Olave Tryggvason’s Saga was adduced, showing
the probability that, if it be so, the name is due to him.

Kaupmannaey, laid down on the map at the entrance of
Belfast Lough, and also left unexplained in the essay, was

shown to be Copeland Island.
, Mr. Downes prefaced the latter part of his subject by
briefly adverting to the principal countries, in which the
Northmen have left topographical traces of their invasions—
namely, Normandy, Eastland (extending from Mecklen-
burgh to the White Sea), and the British Islands—alluding to_
various classes of Norse names occurring in Normandy, a few
solitary instances inEastland,and dwelling at some length on
those found in Ireland. A minute analysis of the Irish loca-
lities, ending in ford, was closed by the inference; that as
Odin's Ford, in the county of Carlow, is certainly a. Norse
locality, so Urlingford, Freshford, and Erke, in the adjacent
county of Kilkenny, are Norse likewise. A less minute ana-

89

lysis was undertaken with several similar names; after which
the author proceeded to a rapid scrutiny of names of baro-
nies, townlands, and towns—noticing in particular, as wholly
or partly of Norse derivation, Rathgorman, Slaghtmanus,
and, Ballyvedra, alias Weatherstown, near Waterford.—The
last class of Irish names analysed was that of islands. Se-
veral instances were adduced of insular localities derivable
from some one of the three, Norse words for island—ey,
holm, and kalfr—the. distinctive meanings of which were
explained. The name of a locality, in particular, off the
south coast of Iceland, called ‘‘ Irishman’s Islands,” was
explained from the sequel of the tradition of Leif, before
cited.

The author closed his paper by recommending to the
antiquary some attention to the neglected literature of the
North, as a means not only of accumulating information, but
of correcting error ; and concluded by adducing the follow-
ing examples of error, corrected by a comparison of speci-
mens found in different countries :—‘‘ ‘The short sword,
or dagger,’ with which King, in his account of Richborough,
has equipped a Roman bagpiper, would still maintain its
belligerent masquerade, had not the discovery of a more per-
fect specimen in Scandinavia proved it to be the more appro-
priate appendage of a pipe; and certain figures, published
by Pennant, which were deified in Sweden, might have long
enjoyed their sanctity, had not the subsequent discovery of

more perfect specimens in Denmark desecrated them into—
knife-handles.”

Dr. Anster, on the part of Dr. Luby, F.T.C.D., read a
letter of the late Rev. Charles Wolfe, author of the lines on
the burial of Sir John Moore. The letter, or rather frag-
ment of a letter, had been found by Dr. Luby among the
papers of a deceased brother, who was a college friend of
Wolfe and of Mr. Taylor, to whom the letter was addressed.

90

The part found had the appearance of having been torn off
from the rest of the letter. It contains the address ; ‘a com-
plete copy of the ode; a sentence mentioning to Mr. Taylor
that his praise of the stanzas first written led him to com-
plete the poem ; a few words of a private nature at the end of
the letter; and the signature. There is no date on the part
preserved ; but the post-mark of September 6, 1816, fixes
the time at which it was sent. Dr. Anster read passages
from Captain Medwin’s “‘ Conversations of Lord Byron” and
Archdeacon Russell’s ‘‘ Remains of Wolfe,” in which men-
tion is made of the various guesses as to the author, when the
poem first appeared, without the author’s name, in the news-
papers and magazines. It was attributed to Moore, to Camp-
bell, to Wilson, to Byron, and now and then to a writer in
many respects equal to the highest of these names, whose
poems have been published under the name of Barry Cornwall.
Shelley thought the poem likely to be Campbell’s ;and Med-
win believed Byron to be the author. When Medwin’s book
appeared in which this was stated, several friends of Wolfe’s,
among others Mr. Taylor, to whom was addressed the letter,
of which an important part has been fortunately found, stated
their knowledge of Wolfe’s having written the ode. One
gratifying result of the controversy was the publication, by
Archdeacon Russell, of the Remains of Charles Wolfe, with a
memoir written with great beauty, and, what constitutes the
rare charm of the work, describing with entire fidelity the
character, and habits, and feelings of one of the most
pureminded, generous, and affectionate natures that ever
existed.

The question as to the authorship ofthe ode was for ever
set at rest to any one who had seen either the letters of Mr.
Wolfe's friends, at the time of Captain Medwin’s publication,
or Archdeacon Russell’s book. Were there any doubt on the
subject of authorship, the documentnow produced would com-
pletely remove it ; but for this purpose it would really not be

91

worth while to trouble the Academy with the communication,
as it would be treating the insane pretensions, now and then
put forward in the newspapers for this person or the other,
with too much respect to discuss them seriously, or at all;
but another:and avery important purpose would be answered
by the publication of this authentic copy of the poem, from
Wolfe’s: autograph, in their Proceedings. The poem has
been more frequently reprinted than almost any other in the
language ; and, an almost necessary consequence of such fre-
quent reprints, it is now seldom printed as it was originally
written. Every person who has had occasion to compare
the common editions of Milton,.or Cowper, or any of our
poets, with those printed in the life-time of the authors, is
aware thatno dependence whatever can be placed on the text
of the books in common use. Every successive reprint from
a ‘volume, carelessly edited, adds its own stock of blunders
to the general mass. Wolfe’s ode has been, in this way, quite
spoiled in many of its best passages. The Academy had
now the opportunity of correcting these mistakes by publish-
ing an authentic copy of the poem. Dr. Anster stated the
fitness of this being done by the Academy, not only from its
being the natural and proper guardian of every thing relating
to' the literature of Ireland,—which alone would seem to him
asufficient reason, —but even yet more, from the circumstance,
that the Academy’s Proceedings must command a circulation
over the Continent, which it would be in vain to expect for
any private publication. ‘The poem has been often trans-
lated; and the strange blunders which have got into our
copies are faithfully preserved in the translations. In a Ger-
man translation of the ode, three stanzas of a poem, consist-
ing of but eight, are spoiled by the translator’s manifestly
having read an imperfect copy of the original. In one. itis
quiteplain that the stanza, which closes with the lines—
«And we heard the distant and random gun
That the foe was sullenly firing,”

92

and in which the word “ suddenly” is often substituted for
‘‘sullenly,” was printed falsely in the copy before the German
translator. In the second stanza, “‘ The struggling moon-
beam’s misty light,” is lost probably from some similar reason:
The general effect of Wolfe’s poem is exceedingly well pre-
served in the translation ; but there are several mistakes in
detail, most of which, perhaps all, arise from the translator’s
having used an incorrect copy of the original. The trans-
lation is printed in the octavo edition of ‘‘ Hayward’s Faust,”
p- 304.

The Rey. Dr. Todd, V.P., having taken the Chair, Pro-
fessor Lloyd read a supplement to his paper, ‘‘ On the Mu-
tual Action of Permanent Magnets in an Observatory,”
printed in the Transactions, Vol. XIX. p. 159.

This supplement was immediately printed in the same
volume of the Transactions.

May 10.
Sir Wu. R. HAMILTON, LL.D., President, in the Chair.

Oliver Sproule, Esq., and James Thompson, Esq., were
elected Members of the Academy.

A note on some new Properties of Surfaces of the second
Order, by John H. Jellett, Esq., F.T.C.D., was read.

I. Let the points on the focal conic, at which the tangent
is parallel to the trace of the tangent plane, be considered
analogous to foci.

II. Let the axis of the surface, perpendicular to the plane
of the conic, be considered analogous to the conjugate axis ;
then, since the square of the distance from focus to centre, in
a conic, is equal to the difference between the squares of the
transverse and conjugate semi-axis, we may consider, as ana-
Jogous to the transverse semi-axis, the line drawn to the ex-

93

tremity of the perpendicular axis from the point analogous
to the focus.

III. Since the square of the semiconjugate diameter is
equal to the sum of squares of semiaxes minus the square of
central radius vector, let the same be supposed true of the
line analogous; i. e. if s be the line analogous to the trans-
verse, and B to the conjugate semi-axis, let

B= Vat B?— a”.
Assuming these definitions, we shall have the following theo-
rems analogous to those én plano.

1. The sum or difference (according as the focal conic is
perpendicular to a real or imaginary axis) of the distances
from the points analogous to the foci, to the corresponding
point on the surface, is equal to 2a.

2. The rectangle under them = 8B”.
3. The sine of the angle, made by either with the tangent

. &B
plane, is mo

4. The rectangle under the perpendiculars from these

points on tangent plane = B’.
5. The sine of the angle between the central radius

AB , 5
vector and tangent plane = ap” (a’ being the central radius

vector).
6. The portion of the normal intercepted between the sur-

cant Eat
face and the plane of the focal conic is pee

7. If aplane be drawn perpendicular to the line joining

points analogous to the foci, and at a distance from the centre
2
A : : ;
equal to mar (c being the distance of one of the focal points

from the centre), the distance of a point in the surface from
the corresponding focus will be to its distance from this plane
351Gb als

8. Hence, given a focal conic and the perpendicular axis,

94

wecan find points and tangent planesad libitum, by the follow-
ing construction :—Take in the focal conic two. diametrically
opposite points ; with one as centre, and twice the distance
from it to the extremity of the perpendicular axis as radius,
describe a sphere. Through the other point draw a plane,
normal to the focal conic ; it will cut the sphere in a certain
circle. Connect any point in this circle with the two points.on
the focal conic, and at the middle point of the line connecting
it with the second point draw to it a perpendicular plane.
This is a tangent plane to the surface, and the point where
it cuts the first connecting line isa point on the surface.

Another mode of generating the surface is easily derivable
from (7).

Mr. Petrie gave an account of some ancient Irish inserip-
tions of the sixth century, found in the island of Arran.

Dr. Kane made some remarks on the Theory of Types.

DONATIONS.

Transactions of the Literary and Historical Society of
Quebec. Vols. 1. and II.; and Parts 1—4 of Vol. III. Pre-
sented by the Society.

Report of the Directors of the Chamber of Commerce at
Manchester on Import Duties. 11th March, 1841.

Report of the Select Committee of the House of Commons
on the Import Duties.

Proceedings of a Meeting of Members of the House of
Commons, held at the Thatched House Tavern, St. James’s-
street, on the 20th February, 1841. Presented by Joseph
Hume, Esq., M.P.

95

May 24.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Mr. Robert Mallet read a paper ‘‘ On the Physical Pro-
perties and Electro-Chemical and other Relations of the Al-
loys of Copper with Tin and Zinc.”

These experiments are collateral to the researches on the
action of air and water on iron, upon which the author has
been engaged at the desire of the British Association. In
the progress of these inquiries, it became necessary to deter-
mine the action of solvents on iron in presence of various
definite alloys of copper and tin and of copper and zinc.
Hence it was requisite to form many such alloys in rigidly
assigned proportions as to their constituents, a matter known
to experimenters to be one of difficulty, especially in the case
of so oxidable and volatile a metal as zinc. The difficulties
were overcome by a peculiar arrangement of apparatus, per-
mitting the metals to be fused and combined in close vessels.
The results were verified by assay. Having these alloys
which belong to the classes of brass or gun metal, of which
most of our instruments of precision are made, and their con-
stitution being atomic and certain, it seemed useful to de-
termine some of their properties for practical purposes. The
results are given in the two annexed tables,

The author has also determined the numerical conditions
governing the rate of solution, or amount of loss sustained
in a given time by equal surfaces of iron in solvent menstrua,
when in presence of all these alloys, and of the alloys them-
selves. ‘Tables of these were presented : the results do not
seem to coincide with the law of volta equivalents, which is
explained by showing gaivanometrically that the «— and
<-+ metals of the alloy are often not acted on equally by a
solvent ; thus, that an alloy of Zn, + Cu, may assume a cop-

per surface after a certain time of reaction. This circumstance,

96

the author has shown, suggests a method of determining the
molecular arrangement of an alloy ; and, in general, whether
any alloy be a chemical compound or a mixture.

The author also enters into several details as to peculiar,
and, in some cases, singular reaction of these and other
alloys upon solutions of the salts of their own metals: thus,
certain alloys of lead and zine decompose solutions of lead
as rapidly as pure zinc; while others, containing much zinc,
act as lead towards the salts of lead.

In the case of three metals, A, B, C, whereof A is e +,and
C ise —to B, the author investigates the question as to what
will be the electro-chemical relation of the atomic alloys of
A, + C, towards B, in solvent menstrua; and inthe class
of alloys of copper and zinc, has determined the alloy of no
action, with reference to iron; and has also found alloys
which protect iron in solvents electro-chemically as fully as
pure zinc, and yet are not themselves acted on by the sol-
vent.

He enters into the subject of the specific gravities of the
alloys of Zn + Cu and Sn + Cu minutely, and shows reason
to doubt the accuracy of the published specific gravities of
most alloys of these and some other classes.

Professor Mac Cullagh read a supplement to his paper
** On the dynamical Theory of Crystalline Reflexion and Re-
fraction.”

In his former paper on that subject (see Proceedings,
9th December, 1839) the author had given the general prin-
ciples for solving all questions relative to the propagation of
light in a given medium, or its reflexion and refraction at
the separating surface of two media; but he had applied
them only to the common case of waves, which suffer no
diminution of intensity in their progress, and in which the
vibration may be represented by the sine or cosine of an are
multiplied by a constant quantity. Some months after that

97

paper was read, it occurred to him that he might obtain new
and important results by substituting in his differential
equations of motion a more general expression for the inte-
gral, that is, (as usual in such problems), by making the
displacements proportional to the sine or cosine of an are,
multiplied by a negative exponential, of which the exponent
should be a linear function of the coordinates. Such vibra-
tions would become very rapidly insensible, and would,
therefore, be fitted to represent the disturbance which, in
the case of total reflexion, takes place immediately behind
the reflecting surface ; and the laws of this disturbance being
thus discovered, the laws of polarization in the totally re-
flected light would also become known, by means of the
general formule which the author had established for all
cases of reflexion at the common surface of two media.

The present supplement is the fruit of these considera-
tions. It contains the complete theory of the new kind of
vibrations, not only in ordinary media, but in doubly refract-
ing crystals; and also the complete discussion of the laws of
total reflexion at the first or second surface of a crystal, in-
cluding, as a particular case, the well known empirical for-
mule of Fresnel for total reflexion at the surface of an ordi-
nary medium.

The existence of vibrations represented by an expression
containing a negative exponential as a factor, had been re-
cognized by other writers, and was indeed sufficiently indi-
cated by the phenomenon of total reflexion; but it was
impossible to obtain the laws of such vibrations, so long as
the general equations for the propagation of light were un-
known.

The method of deducing these equations was given in
the abstract of the author’s former paper, (see Proceedings,
as above) ; but as they were not there stated, it may be well
to transcribe them here. If then we put

dy dZ dZ dé dé dy
mee coal ae ae Cn ele (1)

98
and suppose the axes of coordinates to be the principal axes
of the crystal, the equations, in question may, be thus written:

a ghee dz 2 dy 7

dE =C dy —b Py |

) |

dn .ax in diz |
dein te ae i

a dv. dx |

de —° de © dy’ |

i x y |

and if we further put
fom, te ia ey to Ey es _ am (3)
Y, de ay” y de. de" dy” dat

they will take the following simple form:

2 2
a == ax, - = — by, a =—cz, (4)

in which it is remarkable that the auxiliary quantities
£1, m, 1, are exactly, for an ordinary medium, the compo-
nents of the displacement in the theory of Fresnel. Ina
doubly defracting crystal, the resultant of %,, n, Z, is per-
pendicular to the ray, and comprised in a plane passing
through the ray and the wave normal. Its amplitude, or
greatest magnitude, is proportional to the amplitude of the
vibration itself, multiplied by the velocity of the ray.

The conditions to be fulfilled at the separating surface of
two media were given in the abstract already referred to.
From these it follows, that the resultant of the quantities
£1. m, €1, projected on that surface, is the same in both
media; but the part perpendicular to the surface is not the
same; whereas the quantities £, n, Z, are identical in both.
These assertions, analytically expressed, would give five
equations, though four are sufficient; but it can be shown
that any one of the equations is implied in the other four,
not only in the case of common, but of total reflexion ; which

99

is a very remarkable circumstance, and a very strong con-
firmation of the theory.

The laws of double refraction, discovered by Fresnel,
but not legitimately deduced from a consistent hypothesis,
either by himself or any intermediate writer, may be very
easily obtained, as the author has already shown, from equa-
tions (2), by assuming
E=peosasing, n= peosP sing, C=pcosysing, (5)

where
6 = e+ my +02 — st);

but the new laws, which are the object of the present sup-
plement, are to be obtained from the same equations by
making

= «(pcosa sind + gcosa'cos @), |

n = «(pcos sing + g.cos 3’ cos.¢), (6)
= «(pcos y sin @ + g cos y' cos 9), |

where ¢ has the same signification as before, and

2ur
peor x teh,
the vibrations being now elliptical, whereas in the former
case they were rectilinear. In these elliptic vibrations the
motion depends not only on the distance of the vibrating
particle from the plane whose equation is

le + my +nz = 0, (7)
but also on its distance from the plane expressed by the
equation

fetgythz=0; (8)
and if the constants in the equation of each plane denote the
- cosines of the angles which it makes with the coordinate

planes, we shall have A for the length of the wave, and s for
the velocity of propagation; while the rapidity with which

100

the motion is extinguished, in receding from the second plane,
will depend upon the constant 7. The constants p and qg may
be any two conjugate semidiameters of the ellipse in which
the vibration is performed ; the former making, with the axes
of coordinates, the angles a, 8, y, the latter the angles a’,
B’, y’:

As vibrations of this kind cannot exist in any medium,
unless they are maintained by total reflexion at its surface,
we shall suppose, in order to contemplate their laws in their
utmost generality, that a crystal is in contact with a fluid
of greater refractive power than itself, and that a ray is
incident at their common surface, at such an angle as to pro-
duce total reflexion. 'The question then is, the angle of in-
cidence being given, to determine the laws of the disturbance
within the crystal.

The author finds that the refraction is still double, and
that two distinct and separable systems of vibration are trans-
mitted into the crystal. He shows that the surface of the
crystal itself (the origin of coordinates being upon it at the
point of incidence) must coincide with the plane expressed
by equation (8), a circumstance which determines the three
constants f, g, 4. The plane expressed by (7) is parallel to
the plane of the refracted wave; and a normal, drawn to it
through the origin, lies in the plane of incidence, making
with a perpendicular to the face of the crystal an angle w
which may be called the angle of refraction, so that, if 7 be
the angle of incidence, we have

sin w= s sin 2,
the velocity of propagation in the fluid being regarded as
unity.

To each refracted wave, or system of vibration, corres-
ponds a particular system of values for 7, 5, w. These the
author shows how to determine by means of the ¢ndex-sur-
face (the reciprocal of Fresnel’s wave surface) which he has
employed on other occasions, (‘Transactions of the Academy,

101

vol. xvii. and xviii.), and the rule which he gives for this
purpose affords a remarkable example of the use of the
imaginary roots of equations, without the theory of which,
indeed, it would have been difficult to prove, in the present
instance, that there are two, and only two, refracted waves.
Taking a new system of coordinates x’, y’, 2’, of which 2’ is
perpendicular to the surface of the crystal, and 7’ to the plane
of incidence, while 2’ lies in the intersection of these two
planes, put y’=0 in the equation of the index-surface re-
ferred to those coordinates, the origin being at its centre ;
we shall then have an equation of the fourth degree between
_#’ and 2', which will be the equation of the section made in
the index surface by the plane of incidence. In this equation
put «’ = sin z, and then‘solve it for 2’. When i exceeds a
certain angle 2’, the four values of 2’ will be imaginary, and
if they be denoted by

utv aly wbyy 1,
each pair will correspond toa refracted system, and we shall
have, for the first,

; sinz sin w (9)
anw = — sa r= sv;

nu” sin?” é
and for the second,

sin 2 sin w!
tan oS 101 ss } te ‘y, (10)
u sin 2

When 2 lies between 7’ and a certain smaller angle @”, two
of the roots will be real, and two imaginary. The real roots
correspond to waves which follow the law of Fresnel; the
imaginary roots give a single wave, following the other laws
just mentioned.

Lastly, when z is less than 2”, all the roots are real, the
refraction is entirely regulated by Fresnel’s law, and the
reflexion by the laws already discovered and published by
the author.

VOL. II. K

102

If the crystal be uniaxal, and all the values of z’ imaginary,
the ordinary wave normal will coincide with the axis of x’;
whilst the extraordinary wave normal and the axis of z’ will
be. conjugate diameters of the ellipse in which the index
surface is cut by the plane of incidence.

When a = 6 = c, the crystal becomes an ordinary me-
dium ; there is then only single refraction, and the refracted
wave is always perpendicular to the axis of x’.

With regard, to the ellipse in which the vibrations ‘are
performed, it may be worth while to observe, that if it be
projected. perpendicularly on the plane of incidence, the pro-
jected. diameters which are parallel to the surface of the
erystal and to the wave plane will, in all cases, be conjugate
to each other, and their respective lengths will be in the
proportion of r to unity. The vibrations, it is obvious, are
not performed in the plane of the wave, though they take
place without changing the density of the ether.

The new laws here announced are, properly speaking,
laws of double refraction, and are necessary to complete our
knowledge of that subject. Between them and theilaws of
_ Fresnel a curious analogy exists, founded on the change of
real into imaginary constants.

The laws ofthe total reflexion, which accompanies thenew
kind of refraction, need not be dwelt upon in this abstract, as
nothing is now more easy than to form the equations which
contain them. In fact, the difficulties which formerly sur-
rounded the problem of reflexion,.evem in the simplest cases,
have completely disappeared, since the author made known
the conditions which must be fulfilled at the sepa ‘sur-
face of two media.

In what precedes, it has been supposed that the reflexion
and refraction take; place at the jist surface of the crystal,
because this is the more difficult.and: complicated of the two
cases into which the question resolves itself. But it will
usually happen in practice that a ray which has entered’ the

103

erystal will, suffer total reflexion at the second surface, while
the new kind. of vibration is propagated into the air without.
The refracted wave will then. be always) perpendicular to
the axis of x’; the two reflected rays, within the crystal,
will be plane-polarized, according to the common law, but
they will each undergo a change of phase; and the vis
viva of the two rays together will be equal to that of the
incident ray, the vis viva being measured by the square
of the amplitude multiplied by the proportional mass.

In conclusion, the author states a mathematical hy-
pothesis by which both the laws of dispersion, and those of the
elliptic polarization of rock crystal, may be connected with
the laws already developed.

The Rev. Dr. Todd communicated the following particu-
lars concerning an ancient inkstand, contained in a letter from
Joseph H. Monck Mason, Esq., dated Rome, May 4th, 1841:

‘© This relic (described by Mrs. Hamilton Gray, in her
Tour in Etruria, p. 334) is of coarse ¢erra-cotta, black and
ill-formed; it is a truncated cone, about eight inches long,
about four or five inches round the mouth, and about twelve
(not more, I think) round the base; there are about twelve
lines of letters written round the upper three-fourths, and
one round the very base; they are written from left to right.
I repeat it, that, being cramped by the rules and restrictions,
I was not entirely particular; and the upper part was dirty,
and not very legible without close inspection. I could see
of the last line (I do not mean that round the base, which has
some Greek capitals,) about three-fifths ; this contained four-
teen letters. I saw no omicron or omega. ‘This line might
have had twenty-four letters ; and allowing about twelve, or
say fifteen lines in all, gradually diminishing as on the out-
side of a cone, there was scarcely room for ba, be, in a se-
cond language. I believe them all to be Greek. About
three or four lines up, I remember, there was P (ro,) and

K2

104

a little higher, mu, with vowels in order. So much for this
wonder, if it be the right one; and it was shown to me as
such by one who knew it to be so.”

The following Note ‘‘ On the Force of aqueous Vapour
within the Range of atmospheric Temperature,” was read
by James Apjohn, M.D., M.R.I.A., Professor of Chemistry
in the Royal College of Surgeons.

Having had it in contemplation some time since to inves-
tigate by means of an indirect, but I believe a very accurate
process, the caloric of elasticity of the vapours of several
liquids, I found myself stopped on the threshold of the in-
quiry by a want of knowledge of the tension of such vapours
at different temperatures; for, with the exception of the
vapours of water, alcohol, ether, and oil of turpentine, the
tension of no others had been made the subject of experi-
ment; and even in the case of the fluids just named, the
results recorded in the books appeared to me very far from
being of such a nature as to preclude the necessity of further
research.

The method which I intended to employ, in order to ar-
rive at the latent heats of vapours, not requiring a knowledge
of their tensions beyond the range of atmospheric tempera-
ture, it occurred to me, that the necessary data for the solu-
tion of the preliminary problem might be obtained with faci-
lity, and, at the same time, with much precision, in the
following manner :

Let a known volume of dry air be charged with moisture
at any given temperature, and let the expansion produced
by the moisture be accurately noted. The pressure being
also measured by an accurate barometer, we have the means
of calculating the force of the vapour which has produced
the expansion. For if v be the volume of the dry air, and
v’ that of same air when charged with moisture, f the force

105

of the vapour, and p the existing atmospheric pressure, we
shall have

from which we deduce
/
s= (C52) xp
It was not my original intention to make any experi-
ments upon the force of aqueous vapour, believing the table
which I have hitherto employed, and which was calculated
by the author of the article ‘‘ Hygrometry,” in Brewster’s
Encyclopedia, from the experiments of Dalton, to have been
sufficiently exact. But the correctness of this table having
been indirectly called in question by so high an authority as
Mr. Kupffer, who has come to the conclusion, that the table
of the force of aqueous vapour, given by a German meteoro-
logist, of the name of Kamtz, is alone to be relied upon, I
resolved to commence with the vapour of water, in the hope
that I might be able, by the results of direct experiment, to
corroborate a conclusion previously drawn by Professor
Lloyd, from a discussion of some hygrometrical observations
of mine, viz., that for temperatures within the atmospheric
range, the table of Kamtz is less accurate than. that of
Dalton, the values given in the former being all too low.
The apparatus I have employed in my experiments is
composed of a glass ball prolonged on the one side into a
short tube, furnished with a cap and stopcock, and, on the
other, into a long tube of somewhat smaller diameter, di-
vided into 100 equal parts, each being .042 of a cubic inch,
or the .001 of the total capacity of ball and tubes down as
far as the division marked 1000.
The first step consisted in filling this vessel with dry air,
which was done in the following manner : into the extremity

106

of the graduated tubular portion, a cork pierced by a small
tube, open at both ends, was inserted, and this tube was
then connected with the orifice of a table air-pump usually
occupied by a syphon gauge. The stop-cock was now con-
nected with one end of a long tube, packed with fragments
of fused caustic potash, while the other end of this tube was
attached by means of a slip of caoutchouc to a second tube
passing through an air-tight cork fixed in one of the mouths
of the bottle, at present used for the inhalation of chlorine.
This bottle being charged with oil of vitriol, and the orifice
of the plate of the pump being closed, the pump was worked,
and a current of air was thus drawn through the glass vessel
for about fifteen minutes, which in passing through the oil
of vitriol, and over the fused potash, was deprived of all hy-
grometric moisture. ‘The included air being now absolutely
dry, the stopcock was closed, and the small tube connecting
the air vessel with the pump having been drawn out in the
middle, and sealed hermetically by means of a spirit lamp,
the air apparatus was separated from the potash tube, and
transferred to a tall jar containing mercury, after which the
sealed end of the small glass tube was broken beneath the
surface of the quicksilver. The apparatus, however, being
now completely filled, it became necessary to remove some
of the air, and this was done by opening the stopcock very
gradually, care being taken that during this manipulation the
external mercury should be higher than its level within the
tubular portion. The entire was then placed in a small
room, the temperature of which was found not to vary more
than one degree Fahrenheit during the twenty-four hours,
the stopcock having been first attached to one extremity of
a string, which was carried over a fixed pulley placed in
the ceiling, and whose other end carried a counterpoise by
which the air vessel was kept in a vertical position, and the
observer was enabled readily to bring the mercury within

107

and without to the same level, before he registered the vo-
lume of the included air.

On the next day, after the apparatus was mounted, and
the four following ones, the volume of the dry air, its tem-
perature, and the existing pressure were accurately noted.
This pressure, which was measured by a portable barometer
of Newman’s, having undergone a variety of corrections, for
the capacity of the cistern compared to that of the tube, for
the excess of the temperature of the quicksilver over 32°, for
eapillarity, and for a constant error by which I found my
barometer affected, when compared with the standard instru.
ment in the Observatory of Trinity College, I reduced by
calculation in each instance the observed volume of air to
what it would be at 32°, and under a pressure of 30, using
for the expansion of air the corrected coefficient 433, which
has resulted from the experiments of Rudberg, and thus
obtained the following numbers, which, it will be observed,
differ very little from each other.

1 cele age oh aad LA tk
2 911°85
3 910°21
AyD ees gl ee OS 30
Be ees be med Bee

911-64, therefore, the mean of the five observations, may
be assumed as the true volume of the included dry air, at
32°, and under a pressure of 30.

The volume of the dry air being determined, the next
step was to charge it with moisture. In order to accom-
plish this, the air vessel was lifted by means of the string,
so as that the mercury within should be about an inch
higher than the external mercury, and distilled water was
then poured into the upper cavity of the stopcock, so as
completely to fill it. The stopcock was now cautiously
turned, so as to admit the entrance of the moisture guttatim ;

108

and more water being occasionally poured on, this manipu-
lation was repeated until the mercury within came to be co-
vered by a film of water of about one-tenth of an inch in
thickness. The stopcock was now closed, and the appa-
ratus being lowered, the whole was left to itself until the
following day, when the first of a series of observations, con-
tinued for twenty successive days, was made, each compre-
hending the volume of the moist air, the pressure, and the
temperature both of the air and of the mercury in the baro-

v’—v uv,
ov! Ps

meter. To deduce from these by the formula f=

the force of vapour, it was necessary, in the first instance, to
apply to p all the corrections already explained, and in ad-
dition to raise 911:64, the volume of the dry air, to what it
would be at the temperature and pressure of the moist air,
as noted in each observation. But, as this involved tedious
arithmetical computations, and as the thermometer during
the performance of the twenty experiments varied only
about 15°, I came to the resolution, being at the time upon
the eve of leaving town for a couple of months, to postpone
the calculations until 1 should be possessed of data applica-
ble to the solution of the problem I had undertaken, through-
out a more extended range of temperature.

Accordingly, in November last, I resumed the subject
with the very same apparatus, which had been left statu quo
in the interval, and succeeded in completing a series of forty-
five additional observations, extending nearly as low as 32°,
and which I had every reason to expect would lead to satis-
factory results. Upon, however, submitting the whole to
calculation, Ihave been led to the mortifying conviction,
that in consequence either of the absorption of the oxygen
by the mercury and brass-work, or some accident which
befel the apparatus during my absence from town, the
entire of the latter series of observations is of no value, as
they lead to results for the force of aqueous vapour, which

109

are certainly greatly below the truth. Upon the present
occasion, therefore, I can direct attention only to the obser-
vations made in July and August last. ‘These are contained
in the following table, and, as has been already stated, they
amount to twenty in number, the highest temperature
having been 65°, and the lowest 49°°6. The numbers in the
last column represent the bulks which the 911°64 volumes
of dry air would have, if reduced to the temperature /, and
the corrected pressure p.

TaB_e I.
Tempera- 911-64 reduced
p observed ture of |p corrected.| to¢andp
Barometer. corrected.

29-450 29-430 982-82
29-364 29-338 984-77
29-548 29-524 978-94
29-822 29-807 967-97
29-980 29-971 961-38
29-780 29-767 967-97
29-624 29-607 974-33
29-862 29-847 967-23
30-100 30-086 962-69
30-132 30-165 960-35
30-05 30 037 965°18
30-230 30-212 960-69
30-214 30-197 960-06
30-156 30131 964-93
30-130 30-104 968-01
30:032 30-005 970-83
29-989 29-961 973-55
29-972 | 29-940 974-6]

30-120 969-12
29-306 978-62

30-152
29-834

From the first, last, and second last columns of the pre-
ceding table, the force of aqueous vapour has been calcu-
lated in the manner already explained. The values thus
obtained are exhibited in the second column of Table IT.

110

Column 1 ‘contains the temperatures ; column 3 the ten-
sions, as deduced from Dalton’s experiments ; and column
4 the same as given by Kamtz.

Tasxe II.
1 2 3 4

Dalton. Kamtz.
60°°4 5345 +5302 “5125
59 +2 ‘4908 5197 "5023
60° +5348 +5232 *5061
59 +1 4855 “5077 “4893
58 °4 “4917 -4960 ‘4768
58 °4 “4849 “4960 “4768
59 - -4980 -5060 “4875
59 °4 4937 5128 *4949
60 -2 -5169 *5265 °5093
61 -2 *5292 *5444 *5261
61 -6 “5445 “5517 "5343
62 -2 4120-06 -5628 -5458
61 °6 *5660 5517 *5343
63-1 *5689 5798 5615
64 °3 *59AI 6033 *5860
64 +1 -6107 *5993 “5824
64 °8 ‘6311 °6133 “5949
65° *5988 6173 *5985
65 +2 6054 6214 -6029
64 °8 6372 *6133 *5949

When the corresponding numbers in the three columns
are compared, it will be at once observed, that the values of
J; investigated by the method just explained, are somewhat
less than those extracted from the table I have been hitherto
in the habit of using; but that they are considerably greater
than the values of Kamtz, the differences being generally
better than twice as great in the latter instance as in the
former. This will be more manifest by taking a mean of the
different results in column 2, and comparing it with the force

111

of vapour corresponding to the same temperature as given in
the two other tables. Now, the mean of the temperatures is
61°63, the quotient got by dividing their sum by twenty.
But the corresponding mean value of f, in column 2,
must be differently calculated, seeing that the temperature
and the corresponding tensions of the vapour augment at a
very different rate. For temperatures, in fact, in arithmetic
progression, the corresponding tensions are in geometric
progression; and, although this is well known to be but an
approximate law, it may be considered as rigorously true
for the limited range of temperature within which my expe-
riments have been made. To calculate, therefore, the mean
force of vapour, as deducible from the numbers in column
2, and which mustcorrespond to the temperature 61°'63,
it is only necessary to add together the logarithms of the
numbers in this column, and divide their sum by twenty, and
the quotient will be the logarithm of the mean. When this
proeess is gone through, the mean logarithm is found to be
73699, and the corresponding number *54575. ‘The follow-
ing, therefore, are the tensions of aqueous vapour at 61°-63,
as deduced from my experiments, and as extracted from the
tables of Dalton and Kamtz.

My Experiments. Dalton. Kamtz.

B63 a 3, i (DADT), oe ei ACL OOZS ee Ke 849

Difference between Dalton’s number and mine, = + .0066.

Difference between Dalton’s number and that of Kamtz,
= + .0174,

It thus appears, that the result at which I have arrived
is somewhat less than the Daltonian number, but consider-
ably greater than that given by Kamtz ; and that, therefore,
my experiments, as far as they have been discussed, give at
least a prima facie countenance to the opinion, that the
values of the elastic force of aqueous vapour, as given by
the latter philosopher, are, at and about 61°63, below the
truth.

112

Before, however, this conclusion can be considered as
fully established, and before we can judge correctly of the
amount of the errors by which his table is affected, it will be
necessary to inquire whether the thermometer I have em-
ployed be a true one. This essential inquiry I have been
enabled to institute by my friend, Professor Lloyd, who has
put into my possession, for the purpose, a thermometer given
him by Professor John Phillips, together with a table of
differences between it and the standard thermometer belong-
ing to the Royal Society. Upon a comparison of the two
instruments, I find, that at and about 60°, the thermometer
I have employed stands ‘6 of a degree higher than that lent
me by Professor Lloyd, while the latter stands ‘3 of a
degree higher than the standard in possession of the Royal
Society ; so that the indications of my instrument are at 60°
9-10ths of a degree higher than the truth. If such be the
case, °5457, instead of being the force of vapour at 61°.63, is
the force at 61°63 — 0°9 = 60°73; and to compare the result
of my experiments with the tables of Dalton and Kamtz, it
is only necessary to extract from these the values of the force
of vapour corresponding to the temperature 60°73.

My Experiments. Dalton. Kamtz.

602-73. « $5457 |. ets hw . (2 olay

Difference between Dalton’s number and mine — :0096.

Difference between Dalton’s number and that of Kamtz
+ -0184.

The consideration, therefore, of the error of my thermo-
meter, and the allowance made for it, only strengthens the
conclusion already arrived at ; and I do not now feel any dif-
ficulty in giving it as my deliberate opinion, that the table
of the force of vapour given by Kamtz is, within the atmos-
pheric range of temperature, erroneous, his values being all
too low.

113

Dr. Anster, on the part of the Rev. Dr. Luby, F.T.C.D.,
presented to the Academy the original letter of the Rev. C.
Wolfe, which he had read at a former Meeting, and of which
a fac-simile is published in the present Number of the Pro-
ceedings. (See p. 90.)

The special thanks of the Academy were voted to Doctor
Luby for the donation of this very interesting document.

Professor Mac Cullagh presented to the Academy three
additional ornamented plates belonging to the cross of Cong.
When the cross came into his possession, these plates were
missing; but they were lately recovered for him by the exer-
tions of a friend. The front of the cross is now complete,
and only one plate is left wanting at the back.

DONATIONS.

Astronomical Observations made at the Honourable the
East India Company’s Observatory at Madras, for the Years
1831—89. Vols. I.—V. Presented by the Court of Direc-
tors.

Journal of the Statistical Society. Vol.1V. Part 1. Pre-
sented by the Society.

Contributions towards the History of Swansea. By Lewis
W. Dillwyn, F.R.S., &c. Presented by the Author.

Mémoires préséntes par divers savants a T Académie
Royale des Sciences de 0 Institut de France ; Science Mathé-
matiques et Physiques. Tome V.

Mémoires de l'Institut Royal de France, Académie des
Inscriptions et Belles Lettres. Tomes XI., XU., XIIL., and
XIV. ; Part 2.

Mémoires de U Institut de France, Académie Royale des
Sciences. Tome XIV.—XVII.

Séance Publique Annuelle de Académie Royale des In-
scriptions et Belles Lettres, du Vendredi 25th Septembre,
1840.

°

114

Comptes Rendus Hebdomadaires des Seances del Academie
des Sciences. Premiere Semestre, 1840. Nos. 20—26;
Deuxieme Semestre, 1840. Nos. 1—26; Premiere Semestre,
1841, Nos. 1—10. Presented by the Academy.

Catalogue des Manuscrits de la Bibliotheque de Chartres.
Presented by J. O. Halliwell, Esq., M. R. 1. A.

Greenwich Astronomical Observations for the Year 18389.
Presented by the Royal Astronomical Society.

Report of the Tenth. Meeting of the British Association for
the Advancement of Science. 1840. Presented:by the As-
sociation.

Transactions of the American Philosophical Society. Vol.
VIL... New series. Part 2. .

Proceedings of the: American. Philosophical Society.
Nos. 14—16. (1841). Presented by the Society.

On the Composition of Chalk Rocks and Chalk Marl by
invisible organic Bodies; with an Appendix. By Thomas

Weaver, Esq., M.R.I.A, Presented by the Author.

aes 182P a
Fra 45

Mia

Sei ie Pramod the See

te PROCEEDINGS
P OF

THE ROYAL IRISH ACADEMY.

1841, No. 30.

Beiter; June 14.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

- James Patten, M.D., was elected a member of the Aca-
demy.

Dr. Aquilla Smith read a paper ‘‘ On the Irish Coins of
Henry VII.” .

- In the preliminary remarks, the author entered at some
lengthinto the history ofthe Irish coinage during the reignsof
Henry V. and Henry VI., with the view of facilitating his
inquiries in the subsequent part of his essay. And from the,
evidence of several Acts of Parliament, which were not
known to previous writers on the coinage of Ireland, he in-
ferred that no legal money was coined in this country by
Henry V., and that very few coins are known which can be
appropriated to his immediate successor.

The coins of Henry VII., which are very numerous,
were divided into three sections, each distinguished by the
form of thecrosson the reverse; and in the last section the au-
thor supported Mr. Lindsay’s appropriation to Henry VII. of
the untressured groats which Simon had given to Henry V.

Rev. H. Lloyd, V. P. read a “‘ Note on the Mode of ob-
serving the vibrating Magnet, so as to eliminate the Effect
of the Vibration.”

VOL. Il, z

116

The following modification of one of the methods pro-
posed by Gauss, for the attainment of this end, appears to
combine the greatest number of advantages ; namely, to take
three readings, at the times

i—T, t, t€+7;
t being the epoch for which the position of the magnet ts de-
sired, and Tt its time of vibration.* In order to show that
this method is adequate, it is necessary to deduce the
equation of motion of a vibrating magnet ih a retarding
medium.

Let x denote the horizontal part of the earth’s magnetic
force; g the quantity of free magnetism in the unit of vo-
lume of the suspended magnet, at the distance 7 from the
centre of rotation; and @ the deviation of the magnet from
its mean position. The moment of the force exerted by the
earth on the element of the mass, dm, is

xqrdm sin 0;
and the sum of the moments of the forces exerted upon the
entire magnet is i

xu sin 6;
where « denotes the value of the integral § grdm, taken
between the limits r = = /, 2/7 being the length of the
magnet.

Again, the velocity being small, the resistance may be
assumed to be proportional to the velocity. Accordingly, if
w denote the angular velocity, the retarding force due to
resistance, upon any element of the surface, ds, at the dis-
tance x from the centre of motion, is

— Kds rw;

and the entire moment of this force upon. the whole mag-
net is

* In practice, it is sufficient to take the nearest whole number of seconds,
for the value of 7. :

117

r2>dm

— Kw §r%ds= — Kw f mek:

dm : é .
where H = Ws" The ratio, H, is constant for all bodies of
prismatic form; and for these, therefore, the moment of

resistance is

MK
— —w;3

m denoting the moment of inertia §7°dm
The differential equation of motion is, therefore,

dw xe ~ K
dis. we si seh
dé ‘ :
But w= — di’ and, @ being small, we may substitute 0 for
sn@. The ne thus becomes
Kd) xu
a ata dt Tig Peal

<“ ‘ K x : .
Making, for abridgment, — = 2a, ce at B’, the integral is
H M

6 =(c cos B?— a2. t +e’ sine’ — v2. Weare
But, a being small, we have approximately
e“*=1—at;
aa, if r denote the time of vibration,
A Bets Na D = ie

Hence the preceding equation may be put under the form
t Be t
0 =(1—at) (ccosr—+ ec sin).
, ry ao

Now, let 0, and 6’ denote the values of 0, when ¢ becomes
2

118

é—Tandt+r. It will be seen at once, on substitution,
that
6,+ 20+ 6 =0.

Hence by combining the three readings according to the
preceding formula, the deviation of the magnet from its
mean position, arising from the vibratory movement, is com-
pletely eliminated ; and it will readily appear that the same
result may be attained by any greater number of readings,
taken and combined according to the same law.

Now, let the value of # contain an additional term, + pt,
proportional to the time: or, in other words, let us suppose
that there is a progressive change of the declination, which
may be regarded as uniform during the whole interval of
observation. - It is then manifest that 0, + 20 + 0’ = 4pt;
and accordingly that the quantity

4(0,+ 2040) *
will give the mean place of the magnet corresponding to the
epoch 7.

The supposition of a uniform change can, however, be
regarded as an approximation to the truth, only when the
interval of time between the first and last reading is very
small, in comparison with the interval between the successive
maxima and minima, in the fluctuations of the irregular
movement. Hence, we may conclude, that it is important,
in the first place, to employ three readingsin preference to
any greater number ; and, secondly, that it is desirable that
the time of vibration of the magnet itself should be as small
as possible, consistently with the accuracy of its indications
in other respects.

Professor Lloyd read the following extract of a letter
from the Rev. George 8. Smith, containing some facts rela-
tive to the storm ‘of May 26th and 27th.

119

It appears that the thunder storm commenced on Wed-
nesday night in Tipperary, Clare, Limerick, and Waterford,
reaching its greatest violence on Thursday morning at about
six. It was on Thursday evening that it was most severe in
Carlow and Queen’s County, from nine till twelve p.m.,
having, however, been felt in the morning of the same day.
On Thursday evening it began in Dublin; but the thunder
was loudest at half-past three a.m. on Friday morning. On
Friday morning, at ten o’clock, a.m., it raged in the county
Mayo.

“In Windsor forest and the neighbouring country it was
amore furious tempest, and took place on the evening of
Thursday the 27th, as in the county Carlow.

“It was reported to me, that there were some remark-
able phenomena of the tide in Dublin Bay during the storm ;
and I accordingly inquired from a variety of persons on the
quays and elsewhere, and they concurred in stating, that
about half-past three the tide, which was then flowing and
approaching to high water, suddenly retired in half an hour
to low water mark, and that it rapidly returned and rose
two feet higher than high water mark, and so quickly that
boats were knocked violently against each other. The coal-
porters, and dockyard keepers, and various sailors both in
the river and Kingstown, agreed in this statement.

** Further, in the River Foyle, in the North of Ireland,
there is an embankment in the course of being formed by
Thomas Hutton, Esq., and he states that the tide on Thurs-
day night, or Friday morning, retired so suddenly, that con-
siderable damage was done to his embankment.

** The concurrence of these phenomena with the storm is
a point of some interest; and I write these few lines to in-
vite inquiry, and to ascertain, if possible, whether this extra-
ordinary tide-wave was generally observed, and on what day
and hour, and whether it coincided or not with the storm.

120

The newspapers report the occurrence of the storm, as
mentioned above; but say nothing of the tide.
“The course of the storm seems to have been from
south to north; but I think a north-east wind was blow-
ing.

”

A communication by Francis Crawford, Esq., A.B.,
“ On the Utility of the Irish Language in Classical Studies,”
was read.

The object of the writer was to show, that, notwith-
standing the contempt and ridicule into which the subject
had fallen in consequence of the rash and unphilosophic
views of injudicious advocates, still there existed reasonable
grounds for believing that a careful and sober analysis of
Heathen mythological names would resolve them into Celtic
elements through the medium of Jrish ; accordingly he pro-
ceeded to give numerous instances of such analysis, at the
same time declaring, that unless supported by such analogies,
or other external evidence, as he offered, investigations of
this sort were by no means to be relied upon.

After interpreting, in this manner, the names of some ah
the Syrian deities mentioned by Selden, in his learned
work ‘ De Dis Syris,” the writer went on. to set the whole
subject in a more interesting point of view, by attempting.
to show, that even the Bible might receive illustration and
confirmation from such inquiries; to effect this, he under-
took to identify the Melchizedek of Scripture with the famous
Tyrian Hercules; he shewed at some length, that they
were contemporaries in history, that they agreed in cha-
racter, that tithes were paid to both, and finally that the
name of Malcarth, by which the Tyrian Hercules was best
known, when resolved into its Celtic components Mat-ceanz,
literally signified “ Righteous King,” or “ King of Righ-
teousness.”

The writer, after some further proofs of their identity,

121

concluded by giving a description of the rites and ceremo-
nies used in the worship of Hercules at Gades, intimating
that they denoted a purer mode of religious culture than
generally obtained in the heathen world.

DONATIONS.

Notes on the United States of North America in 1838,
1839, 1840. 3 Vols. By George Combe, Esq.,Hon. M.R.I.A.,
&c. Presented by the Author.

The Silurian System. By William H. Fitton, Esq.
Presented by the Author.

Dublin Metropolitan Police Returns of Persons taken into
Custody in 1840. Presented by the Commissioners.

Ordnance Survey of the County of Galway, in 139 sheets,
Presented by his Excellency the Lord Lieutenant.

Verhandelingen van het Bataafsch Genootschap der Proe-
fondervindelyke Wysbegeerte te Rotterdam, Vols. 1.—XIL.,
and New Series, Vols. I.—VIII. Part I.

A Collection of Temperance Medals. Engraved by J.C.
Parkes. Presented by the Artist.

June 28.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Mr. Mallet read a paper “ On a new Method of raising
Ships of War out of Water for the Purpose of Repair.”

Although the author conceived that the objects of the
Royal Irish Academy were rather to investigate principles
than to apply them in detail, still as any application of these,
which proposes to add to our naval power, is of importance,
and as on a like subject the Royal Society conferred on
Sir R. Seppings their highest reward for his application of
diagonal framing to ships, he did not deem it altogether out
of place to bring hismethod of raising ships out of water be-

122

fore the Academy, with models and drawings to illustrate;
it. The inventor first gave a rapid description of the
several methods of taking ships ont of water for repair,
which have been in use from the earliest times to the present
day, viz., by—

1. Stranding on bilge ways.

2. Careening.
. The machine called the Camel, invented about 1680.
. The graving dock.
- Morton’s patent slip.

Ry ey ere:
Spans iabel. cm comparatively recent Ame

YID co HW

FRE li deaclindseks rican inventions, and only used
there.

8. The floating dock of the River Tyne, used at New-
castle.

He then pointed out the several disadvantages to which
each of these is severally liable.

These are briefly, in the first case, costliness, tedious-
hess, straining of the ship, and imperfect access to the hull.
In the second, great danger and imperfect access to the hull.
The Royal George was sunk by careening her. In the
third case, want of access to the ship—impossibility of ex-
posing the whole hull—straining of the framing, and danger.
In the fourth or graving dock, great original outlay ; great
labour and loss of time in pumping out water where rise of
tide is small; loss of two or three hours of daylight every
day by the sunken position of the ship, and awkwardness in
handling long spars or timber ; difficulty of inspection, and
unhealthiness of situation to workmen; and, lastly, rotting
of timbers, from the constant damp atmosphere of a sunk
or graving dock.

Morton’s slip overcomes most of these evils, but has
some peculiar to itself. Ships can only come on and go
off the slip at high and low water; hence, in large ves-
sels, the loss of one tide is often the loss of a fortnight;

123

it cannot be used in foul weather, or with the tail of the slip
in a tideway ; the average length of the inclined plane being
about five hundred feet, and the rate of elevation of a ship
from three to five feet per minute, the time of taking a
ship out of water, including the removal of the cradle, oc-
cupies from four to six hours ; and hence, thoughnominally
cheap, this is by loss of time really adear mode of repair to
the ship-owner—the ship lies on an inclined plane, which is
inconvenient in hoisting or lowering heavy parts, particularly
in steam-ships. The hull is always strained, and new cop-
pering is often found wrinkled, by the ship running off the
slip, and receiving unequal support from the water meeting
her at an angle to her plane of stable floatation. The vibra-
tion of the numerous rollers is also injurious in the same
way.

The American screw and hydraulic docks have the ad-
vantage, in point of speed, when in use; but are unsafe for
large ships, and awkward in the posture of the ship’s
hull.

The Newcastle-on-Tyne floating dock possesses all the
disadvantages (except original costliness) of the graving
dock, and is without the safety of the latter.

The author then explained the nature of his own method,
and exhibited it in action by means of a large working
model; without plates it is difficult to describe this com-
bination. The vessel to be raised, floats in over a timber
platform of a suitable size laying at the bottom, and by
means of two very powerful cabstern cranes, actuated by a
small steam engine, and acting on two large flat linked
chains, the platform is raised above the surface of the water,
bringing up the vessel along with it, and placing her upon
a suitable level for the convenience of workmen to get under
andround the hull, for which the platform isspecially adapted.
The two chains spoken of lay horizontally at either side
of the platform, and above it, and are armed with rollers at

124

equal intervals, resting on a hollow iron railway; and from
these points of the chains anumber of suspending rods pro-
ceed to the platform; at each side below the latter, are an
equal number of jointed struts or supports; and the nature
of the motion is such, that, when the platform is at the
bottom, these struts are nearly horizontal, and the suspend-
ing rods vertical, and vice versa when the platform is at its
greatest elevation ; hence, the latter is at all times fully and
firmly supported.

The combination is such, that power isto the utmost
economized, the ratio of the power to the weight increasing
as the hull of the vessel leaves the water, and advantage
being taken of her own floatage power as long as possible.

The inventor stated, that a fifty gun frigate, with her
standing rigging up, could be taken out of water, and- laid
dry and ready for workmen, insixteen minutes from the
time she came over the platform, by his arrangement, which
is equally applicable where there is no tide, (as at Malta,
&c.,) as where the rise and fall are considerable. The objects _
also held in view, and he conceives attained, by his method,
are equal strain, and wear and tear (by principle) on all the
parts—and hence freedom from risk of accident—durability
and facility of repair in the machine itself.

A paper by the Rev. Dr. Hincks, “On the pein
Stéle, or Tablet,” was read.

Among the Egyptian monuments in museums, there is
none more likely to afford information than the stéles, or fu-
neral tablets, which resemble in form the head-stones in our
grave-yards, and which appear to have been set up in similar
positions. The object of this paper is to describe the parts
of which the inscriptions that these tablets contain usually
consist, with such observations as may enable a person, who
should meet with one of them, to form a judgment as to its
age, and as to the importance of its contents. —--

It commences with some details respecting two tablets

125

each of which records the dates of the birth and death of
the deceased person, and also the length of his life. A dili+
gent search should be made for similar tablets, which would
evidently be of the greatest value in settling the chronology
of the Egyptian sovereigns. One of these, which is at Flo-
rence, records that a person named Psammetich was born in
the third year of Necho, the tenth month and first day ; that
he died in the thirty-fifth year of Amasis, the second month
and sixth day; and that he lived seventy-one years, four
months, and six days. From this it appears, that the inter-
val between the first year of Necho and the first of Amasis
was forty years; and it follows that the reigns of these kings
must have commenced in 611 and 571 before our era. The
other tablet, which belongs to Mr. Harris of Alexandria, is
that of a priest named Psherinphthah, who died, aged forty-
nine years, in the eleventh year of Cleopatra, the eleventh
month and twentieth day. The chronology of this period
being well known from other sources, the dates of the tablet
would be of no value, did not that of the birth contain a royal
cartouche, which does not occur elsewhere, and an unknown
numeral character. The cartouche is shown to be that of
Ptolemy Alexander, though it does not contain his usual sur-
name ; and the unknown character, a bird’s head, is proved
to stand for teventy. ‘The tablet of Te-imothph, the wife of
this priest, who was also his half-sister, is in the British
Museum ; and several circumstances in their family history,
taken from the two tablets, are collected together. The
birth of their son Imothph, in the sixth year of Cleopatra,
and when the father was turned of forty-three, is recorded
on both of them.

The most usual form of the inscription on a stéle is tran-
lated as follows:—‘‘ An act of homage to A; he has (or as
the case may be) given B unto C; who says D.” The blank
at A is filled up with the names and titles of deities ; that at
B with an enumeration of gifts ; that at C with the name and
description of the deceased person; and at D is the speech

126

attributed to him, in which he sometimes records the leading
events of his life. Sometimes the tablet is without a speech,
the inscription closing at the end of C; and sometimes it
begins with C, containing only the name and description of
the deceased person and his speech. In a few tablets the
prefatory matter is somewhat different from the above; but
the form given above is much the most usual.

No record of facts is to be expected in a tablet till we
come to C; the preceding part of the inscription is only va-
luable, as it may aid usin the study of the language, and as
it may lead us to know the age of the tablet, supposing it to
be without a regular date. For this last purpose, a number
of criteria of antiquity are proposed, the result of a careful
examination ofa great many tablets of known ages. The
most remarkable of these is, that in the most ancient tablets
the sculptured figures are exclusively those of the deceased
person and his relatives ; never these of deities, as in the ta-
blets of the eighteenth dynasty and subsequent ages.

At the close of the paper some remarks are made on the
chronology of the early Egyptian kings, who are mentioned
in the course of it. It is demonstrated that the predecessor
of Amenemhe II., the first king in the series of Abydos, was
Osortasen I. ; the latter being the successor of Amenemhe I.,
and not his predecessor, as he has been stated to be by Major
Felix and others, on the supposed authority of an inscription
at Beni-Hassan. This completely overturns the hypothesis
of Mr. Cullimore, respecting the connexion of a pretended
royal series at Karnac with the series of Abydos.

The phonetic hieroglyphics are represented in this paper
by Hebrew characters, in preference to Roman. This has
been done on account of the author’s peculiar views respect-
ing the extended arm, the crux ansata, and some other cha-
racters, which he considers to be equivalent to the Hebrew
Ayin, and by no means “vague vowels,” as Champollion
supposed. He regards these characters as essentially dis-

127

tinct from the feather, the eagle, and others, with which they
have been hitherto confounded, and which he represents by
the Hebrew Aleph.

The Rev. Charles Graves, F.T.C.D., read a paper “On
the Application of Analysis to spherical Geometry.”

The object of this paper is to investigate and apply to
the geometry of the sphere, a method strictly analogous to
that of rectilinear coordinates employed in plane geometry.

Through a point 0 on the surface of the sphere, which is
called the origin, \et two fixed quadrantal arcs of great circles
ox, oy, be drawn; then if arcs be drawn from y and x
through any point P on the sphere, and respectively meeting
ox and oy in M and QW, the trigonometric tangents of the arcs
OM, ON, are to be considered as the coordinates of the point
p, and denoted by z and y. ‘The fixed arcs may be called
arcs of reference. An equation of the first degree between
x“ and y represents a great circle; an equation of the second
degree, a spherical conic; and, in general, an equation of
the n‘ degree, between the spherical coordinates x and y,
represents a curve formed by the intersection of the sphere
with a cone of the x degree, having its vertex at the centre
of the sphere.

Though it is not easy to establish the general formulz
for the transformation of spherical coordinates, they are
found to be simple.

Let x and y be the coordinates of a point referred to two
given arcs, and let 2’, y’, be the coordinates of the same
point referred to two new arcs, whose equations as referred
to the given arcs are

y—y’ =m(ae— x”),

y —'y” = m! (a at a”),
els ale being the coordinates of the new origin; then the
values of x and y to be used in the transformation of coordi-
nates would be

125

2" (ax' + by'—1)
— px er qy —1 3
y"” (ex' + dy’—1)

pe’ + qy'—1 —
In which a, 0, c, d, p, and g, are functions of m, m’, x’,
and y’’.. It is evident that the degree of the transformed
equation in 2’, y’, will be the same as that of the original

one in # and y.
The great circle represented by the equation

Y=

ax + By=1,

meets the arcs of reference in two points, the cotangents of
whose distances from the origin are a and (3; and, if the
arcs of reference meet at right angles, the coordinates of the
pole of this great circle are — a, and — 3. It appears from
this, that if a and (3, instead of being fixed, are connected by
an equation of the first degree, the great circle will turn round
a fixed point.. And, in general, if a and (9 be connected by
an equation of the n™ degree, the great circle will envelope
a spherical curve to which m tangent arcs may be drawn from
the same point. Thus, the fundamental principles. of the
theory of polar reciprocals present themselves to us in the
most obvious manner as we enter upon the analytic geometry
of the sphere.

A spherical curve being represented by an equation be-
tween rectangular coordinates, the equation of the great
circle touching it at the point wv’, 9’, is

(y — y’) dx’ — («— x’) dy’ =0;
the equation of the normal are at the same point is

(y — y') [dy! + a! (a/dy’ — y/dx')]
+ (@ — 2') [de' + y' (y/dax! —a/dy’)] = 0.

Now, if we differentiate this last equation with respect to

129

x and y’, supposing x and y to be constant, we should find
another equation, which, taken along with that of the normal
arc, would furnish the values of « and y, the coordinates of
the point in which two consecutive normal arcs intersect :
and thus, as in plane geometry, we find the evolute of a
spherical curve.

Let 2y be the diametral arc of the circle of the sphere
which osculates a spherical curve at the point 2’, y’, Mr.
Graves finds that

(da? + dy? + (a/dy' — 3 y'da’)}3_ ii

Sh ee a we EN
tany = a a? + ys (da'd?y’ — 7 — dy’ Pa’) ni

For the rectification and quadrature of a spherical curve
given by an equation between rectangular coordinates, the
following formulz are to be employed :—

ds = Sage ee aT = eae

and
d {area) = ti-edous Er od bonus
(+2?) Vl4+ a+ 9?

In the preceding equations the radius of the sphere has
been supposed = 1.

The method of coordinates here eeiaployed by Mr. Graves
is entirely. distinct. from that which is developed by Mr.
Davies in a-paper in the 12th Vol. of the Transactions of the
Royal Society of Edinburgh. Mr. Graves apprehends, how-
ever, that he has been anticipated in the choice of these
coordinates by M. Gudermann of Cleves, who is the author
of an “ Outline of Analytic Spherics,” which Mr. Graves
has been unable to procure.

The President communicated a new demonstration of
Fourier’s theorem.

130

A letter was read from Professor Holmboe, accompany-
ing his memoir, “ De Priscd re Monetariéd Norvegiz,” &c.,
and requesting to know from the Academy whether any of
the coins described in that work are found in Ireland.*

July 12.
SIR Wan. R. HAMILTON, LL.D., President, in the Chair.

Part I. of a ‘‘ Memoir on the Dialytic Method of Elimi-
nation,” by J. J. Sylvester, Esq. A. M., of Trinity College,
Dublin, and Professor of Natural Philosophy in University
College, London, was read.

The Author confines himself in this part to the treatment
of two equations, the final and other derivees of which form
the subject of investigation.

The Author was led to reconsider his former labours in
this department of the general theory by finding certain
results announced by M. Cauchy in L’Institut, March Num-
ber, of the present year, which flow as obvious and imme-
diate consequences from Mr. Sylvester’s own previously pub-
lished principles and method.

Let there be two equations in zx,

U= aa" + ba" + cx" + ex"? + &e. = 0,
V= aa™ + Ba" + ra" + &e. = 0;
and let n = m +1, where « is zero or any positive value (as
may be).
Let any such quantities as 2” U, «°V, be termed aug-
mentatives of U or V.
To obtain the derivee of a degree s units lower than V,
we must join s augmentatives of U withs +.0f V. Then
out of 25 + . equations

* The Committee of Antiquities, having been consulted on this point, reported
in the negative.

13L

Peo 0; ek bh 0,- iat SOy ec. tO = 0,
TiO, 30) ak Os eh a VEO,

we may eliminate linearly 2s +. .—1 quantities.

Now these equations contain no power of z higher than
m-+.1+s—1; accordingly, all powers of x, superior to
m —s, may be eliminated, and the derivee of the degree
(m —s) obtained in its prime form.

Thus to obtain the final derivee (which is the derivee of
the degree zero), we take m augmentatives of U with n of V,
and eliminate (m + —1) quantities, namely, ;

ie RG ek ae aN tg up to apres"

This process, founded upon the dialytic principle, admits
of a very simple modification. Jet us begin with the case
where. = 0, orm=n. Let the augmentatives of U, be
termed U,, U,, U., U3, ..... and of V, Vo, Vi, Vo, V3
the equations themselves being written

y,°°

U = ax” + ba"—' + ca"-? + &e.
V=- a‘a” th b/a"—" 4 c'a"—? 4. &e,

It will readily be seen that

a’.U,—a.V,,

(b' U, — bV,) + (aU, — aP,),

(c.Uy—c.V,) + (b'U, — bV,) + (a’Us—aP),
&e.

will be each linearly independent functions of 2, x7, ......
2”, no higher power of remaining. Whence it follows,
that to obtain a derivee of the degree (m—s) in its prime
form, we have only to employ the s of those which occur
first in order, and amongst them eliminate z”—', 7-2, ...
z™—-s+!l. Thus, to obtain the final derivee, we must make use
of n, that is, the entire number of them.

Now, let us suppose that cis not zero, but m=n—1.

VOL. Ul. M

132

The equation V may be conceived to be of n instead of m
dimensions, if we write it under the form

0.2% + 0.2%! + 0.277 +..... 4+.0,a7t! 4
az” + Ba™—! + &e. = 0.
and we are able to apply the same method as above ;

but as the first « of the coefficients in the equation above
written are zero, the first 7 of the quantities

(a’U5 = aV,), (b'U, = bV,) + (aU, = aV,), &c.
may be read simply
= GeWVes —b.V,—an,, —cVi.— bV, — aV2, &c.

and evidently their office can be supplied by the simple
augmentatives themselves

Vo = 0 =O | 0. V "pe

and thus « letters, which otherwise would be érrelevant, fall
out of the several derivees.

The Author then proceeds with remarks upon the gene-
ral theory of simple equations, and shows how by virtue of
that theory his method contains a solution of the identity

KO Wee = Dx

where D, is a derivee of the 7‘ degree of U and JV, and,
accordingly, X, of the form

A we + va? .... 4 Oa",
and Y,. of the form
US mnt et eee

and accounts a priori for the fact of not more than (nm — 1)
simple equations being required for the determination of the
(m + n—2r) quantities A, uw, v, &c. 2, m, n, &e., by exhibit-
ing these latter as known linear functions of no more than
_(m—1r) unknown quantities left to be determined.

133

Upon this remarkable relation may be constructed a me-
thod well adapted for the expeditious computation of nume-
rical values of the different derivees.

He next, as a point of curiosity, exhibits the values of
the secondary functions

a’.U,— aV,

b.U,— bV, +a'.U,—alN,

ce .U,—¢.4Y+4.0,— bY, +a’.U,—ahy,

&e.
under the form of symmetric functions of the roots of the
equations U = 0, Y= 0, by aid of the theorems developed
in the “ London and Edinburgh Philosophical Magazine,”
December, 1839, and afterwards proceeds to a more close
examination of the final derivee resulting from two equations
each of the same (any given) degree.

He conceives a number of cubic blocks each of which
has two numbers, termed its characteristics, inscribed upon
one of its faces, upon which the value of such a block (itself
called an element) depends.

For instance, the value of the element, whose character-
istics are r, S, is the difference between two products: the
one of the coefficient r” in order occurring in the polyno-
mial U, by that which comes s“ in order in V; the other
product is that of the coefficient s” in order of the polyno-
mial V, by that 7” in order of U; so that if the degree of

each equation be n, there will be altogether (oad such

elements.
The blocks are formed into squares or flats (plafonds) of

Lae ue) n+l 3 2
which the number is 5 or —,— according as n is even or

odd. ‘The first of these contains x blanks in a side, the
next (2 — 2), the next (n— 4), till finally we reach a square
of four blocks or of one, according as » is even or odd.
These flats are laid upon one another so as to form a regu-

134

larly ascending pyramid, of which the two diagonal planes are
termed the planes of separation and symmetry respectively.
The former divides the pyramid into two halves, such that
no element on the one side of it is the same as that of any
block in the other. The plane of symmetry, as the name
denotes, divides the pyramid into two exactly szmdar parts ;
it being a rule, that all elements lying in any given line of
a square (plafond) parallel to the plane of separation are
identical; moreover, the sum of the characteristics is the
same, for all elements lying any where in a plane parallel
to that of separation.

All the terms in the final derivee are made up by multi-
plying z elements of the pile together, under the sole restric-
tion, that no two or more terms of the said product shall
lie in any one plane out of the two sets of planes perpendi-
cular to the sides of the squares. The sign of any such pro-
duct is determined by the places of either set of planes
parallel to a side of the squares and to one another, in
which the elements composing it may be conceived to lie.

The Author then enters into a disquisition relating to
the number of terms which will appear in the final derivee,
and concludes this first part with the statement of two
general canons, each of which affords as many tests for de-
termining whether a prepared combination of coefficients
can enter into the final derivee of any number of equations
as there are units in that number, but so connected as
together only to afford double that number, Jess one of in-
dependent conditions.

The first of these canons refers simply to the number of
letters drawn out of each of the given equations, (supposed
homogeneous); the second to what he proposes to call the
weight of every term in the derivee in respect to each of the
variables which are to be eliminated.

The Author subjoins, for the purpose of conveying a more

135

accurate conception of his Pyramid of derivation, examples
of the mode in which it is constructed.

When xz=1 there is one flat, When n = 2 there is one flat,

V1Z. V1Z.
2,3 | 2,4
1,2
Fh | 34

Let » = 3, there willbe two Let x = 4, there will still be

flats: two flats only:
2,3 | 2,4
2, 3
Road 3 4

by 2s eae alec ag nd

Meee eles: 1 14

BS 1, ae (he, 5

ho} 4 | 2.4
Le la ae i tes at a

fed | 204 FS
oper fi ars Oe sn

136

Let » = 5, there will be three flats :

3, 4

Poe |) shy

2,5 | 3,5 | 4,5

LOTT Ee 3h) eae: 1; oe akG

137, 2 leleoa 6 2G

1.4) teSaleiel! 2.651346

1,5 | 1,6 15236 | 3,6 | 4,6

1,°6 |) 226 qmsue | 4,6 | w56

137

Let » = 6, there will be three flats :

~ ~
= ot
© ™
= rail

Ne}
at aap
= tle)
= aa
of a
=) =
N ine)
cap i

~ ~ ~
ooh ~~ iD
~ ~ ~
ot oo st
~ ~ ~
ite) MX X
ey = ot
Yo) (too) ~
Bal eo)
ES = =)

Thus the work of computation reduces itself merely to

- elements, or the n (x + 1) cross-products

n+1
z

calculating n.

138

out of which they are constituted, and combining them fac-
torially after that law of the pyramid, to which allusion has
been already made.

DONATIONS.

First Principles of Medicine. 4th Edition. By Archi-
bald Billing, M.D., &c. Presented by the Author.

Bulletin de la Société Geologique de France. Tome XI.
(1839 4 1840.) Presented by the Society.

O’Halloran on the Air; a Manuscript, presented by
Major-General Sir Joseph O’Halloran, M.R.LA., &c.

Mémoires de la Société de Physique et d’ Histoire Natu-
rvelle de Genéve. Tome IX., lere Partie. Presented by the
Society.

Caicul de la Densité de la Terre, suivi d'un Memoire sur
an cas special du Mouvement d'un Pendule. Par L. F. Me-
nabrea. Presented by the Author.

Proceedings of the Royal Society of Edinburgh. Nos.
16—i8.

Transactions of the Royal Society of Edinburgh. Vol.
XIV. Part 2; Vol. XV. Part 1. Presented by the So-
ciety.

Transactions of the American Philosophical Society. Vol.
VII. Part 3. (New Series.) Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1841. No. 31.

November 8.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

John H. Jellett, Esq., F. T.C.D., was elected a member
of the Academy.

A letter was read from Dr. Orpen, stating that increas-
ing ill health would not allow him to continue to discharge
his duties to the Academy, and tendering the resignation
of his office of Treasurer, and of his place as a member of
Council.

ResoLtveD,—That the Academy have heard Dr. Orpen’s
communication with much regret, and that they deeply la-
ment the cause which deprives them of his valuable services.

Professor Mac Cullagh read the following notes on some
points in the Theory of Light.
I.

On a Mechanical Theory which has been proposed for the
Explanation of the Phenomena of Circular Polarization
in Liquids, and of Circular and Elliptic Polarization in
Quartz or Rock-crystal ; with Remarks on the correspond-
ing Theory of Rectilinear Polarization.

Thetheory of elliptic polarization, which I feel myselfcalled
upon to notice, was first stated by M. Cauchy, and has been
VOL. II. N

140

made the subject of elaborate investigation by other writers.
That celebrated analyst, conceiving (though without suffi-
cient reason, as will presently appear) that he had fully ex-
plained the known laws of the propagation of rectilinear vibra-
tions by the hypothesis that the luminiferous ether, in media
transmitting such vibrations, consists of separate molecules
symmetrically arranged with respect to each ofthree rectangu-
lar planes, and acting on each other by forces which are some
function of the distance, was led very naturally to imagine
that he would find the laws of cércular and elliptic vibrations,
in other media, to be included in the more general hypothesis
of an unsymmetrical arrangement. Accordingly, in a letter
read to the French Academy on the 22nd of February, 1836,
a letter to which he attached so much importance that he
desired it might not only be published in the Proceedings,
but also ‘“‘ deposited in the Archives” of that body (see the
Comptes rendus des Séances de 1 Académie des Sciences, tom.
li. p. 182), he gave a precise statement of his more extended
views, informing the Academy that he had submitted his new
theory to calculation, and that, among other remarkable re-
sults, he had obtained (with a slight variation or correction)
the laws of circular polarization, discovered by Arago, Biot,
and Fresnel. Referring to his Memoir on Dispersion, pub-
lished at Prague, under the title of Nouveaux Exercices de
Mathématiques, he observes, that the results therein con-
tained may be generalised, by “ceasing to neglect” in the
equations of motion [the equations marked (24) in § 2 of
that memoir], certain terms which vanish in the case ofa
symmetrical distribution of the ether. He then goes on to
say—

‘‘ Nos formules ainsi généralisées représentent les phé-
noménes de l’absorption de Ja lumiére ou de certains rayons,
produite par les verres colorés, la tourmaline, &c., le phe-
noméne de la polarisation circulaire produite par le cristal
de roche, l’huile de térébenthine, &c. (Voir les expériences

141

de MM. Arago, Biot, Fresnel). Illes servent méme a dé-
terminer les conditions et les lois de ces phénoménes ; elles
montrent que généralement, dans un rayon de lumiére po-
lariseé, une molecule d’éther décrit une ellipse. Mais dans
certains cas particuliers, cette ellipse se change en une droite,
et alors on obtient la polarisation rectiligne.” ‘‘ Enfin le calcul
prouve que, dans le cristal de roche, l’huile de térébenthine,
&c., la polarisation des rayons transmis parallélement a l’axe
(s'il s’agit du cristal de roche) n’est pas rigoureusement cir-
eulaire, mais qu’alors ellipse différe trés peu du cercle.”
Thus, to say nothing for the present of the questions of
dispersion and absorption, it appears that M. Cauchy con-
ceived he had completely accounted for the facts of circular
and elliptic polarization, and that he had deduced the for-
mulas “ which serve to determine the conditions and laws of
these phenomena.” But neither in this letter, nor in any
subsequent version* of his theory, has he given the formulas
themselves. Nor has he told us the nature of the calculations
by which he was enabled to correct the received opinion,
and to prove that the vibrations in a ray transmitted along
the axis of quartz, or through oil of turpentine, are not ri-
gorously circular, as Fresnel and others have supposed, but
slightly elliptical. Now—to take the case of quartz—if we
‘consider that the vibrations of a ray passing along the axis
are in a plane perpendicular to it, and if we admit, as M.
Cauchy always does in the case of other uniaxal crystals, that
there is a perfect optical symmetry all round the axis, we
shall find it hard to conceive on what grounds he could have

* From some statements that have been made within the last few days by Pro-
fessor Powell (Phil. Mag. vol. xix. p. 374), at the request of M. Cauchy himself,
it appears that the latter republished his views about circular and elliptic polariza-
tion, in alithographed memoir of the date of August, 1836. But I do not find that
he published, either then or since, the detailed calculations which he seems to have
made.

N&

142

come to the conclusion that the vibrations of such a ray are
performed in an ellipse. For if all planes passing through
the axis of the crystal be alike in their optical properties,
there will be absolutely nothing to determine the position and
ratio of the axes of the ellipse; there will be no reason why its
major axis, for example, should lie in one of these planes,
rather than in any other. But, whatever may be thought of
this case independently of observation, it is manifestly ab-
surd to suppose that the vibrations are elliptical in the case
of a ray passing through oil of turpentine, or any other lgued
possessing the property of rotatory polarization; for, in a
liquid, all planes drawn through the ray itself are circum-

stanced alike. From these simple considerations it is evident .

that the theory of M. Cauchy is unsound; but a closer exa-
mination will show that it is entirely without foundation, and
that it is directly opposed to the very phenomena which it
professes to explain. To make this appear, however, in
the easiest way that the abstruseness of the subject will
allow, it will be necessary to advert to some former re-
searches of my own, which have a direct bearing on the
question.

The same day on which M. Cauchy’s letter was read to
the French Academy, I had the honour of reading to the
Royal Irish Academy, a paper ‘‘ On the Laws of Double Re-
fraction in Quartz” (see Transactions R. I. A., vol. xvii.
p- 461), wherein I showed that every thing which we know
respecting the action of that crystal upon light is comprised
mathematically in the following equations :

Pe PE bn
dé = *aat + aa”
dyn dn ae

— —_ —_ C—-

di — ° az dz”

which differ from the common equations of vibratory motion
by the two additional terms containing third differential co-

(1)

143

efficients multiplied by the same constant c, this constant
having opposite signs in the two equations. The quantities
€ and » are, at any time ¢, the displacements parallel to the
axes of z and y, which are supposed to be the principal di-
rections in the plane of the wave, one of them being there-
fore perpendicular to the axis of the crystal. The constants
A and B are given by the expressions
Aza’, Boa’— (a?—0D?) sin),

where a and 6 are the principal velocities of propagation,
ordinary and extraordinary, and yj is the angle made by the
wave-normal (or the direction of z) with the axis of the crys-
tal. The only new constant introduced is c, which, though
the peculiar phenomena of quartz depend entirely on its ex-
istence, isalmost inconceivably small; its value is determined
in the paper just referred to. The equations are there proved
to afford a strict geometrical representation of the facts ; not
only connecting together all the Jaws discovered by the dis-
tinguished observers to whom M. Cauchy refers, and in-
cluding the subsequent additions for which we are indebted
to Mr. Airy, but leading to new results, one of which esta-
blishes a relation between two different classes of pheno-
mena, and is verified by the experiments of M. Biot and Mr.
Airy. Having, therefore, such conclusive proofs of the truth
of these equations, we are entitled to assume them as a
standard whereby to judge of any theory; so that any me-
chanical hypothesis which leads to results inconsistent with
them may be at once rejected.

Now [I assert that the mechanical hypothesis of M.
Cauchy contradicts these equations, and therefore contra-
dicts all the phenomena and experiments which he supposed
it to represent. But before we proceed to the proof of this
assertion, it may perhaps be proper to remark, that pre-
viously to the date of M. Cauchy’s communication, and of my
own paper, I had actually tried and rejected this identical

144

hypothesis, and had even gone so far as to reject along with it
the whole of M. Cauchy’s views about the mechanism of light.
For though, in my paper, I have said nothing of any mecha-
nical investigations, yet, as a matter of course, before it was
read to the Academy, I made every effort to connect my
equations in some way with mechanical principles; and it
was because I had failed in doing so to my own satisfaction,
that I chose to publish the equations without comment,* as
bare geometrical assumptions, and contented myself with
stating orally to the Academy, as I did some months after to
the Physical Section of the British Association in Bristol
(see Transactions of the Sections, p. 18), that a mechanical
account of the phenomena still remained a desideratum which
no attempts of mine had been able tosupply. I am not sure
that on the first occasion I stated the precise nature of these
attempts, though I incline to think I did; but I have a dis-
tinct recollection of having done so on the second occasion,
in reply to questions that were asked me by some Members
of the Association.f Now, my first attempt to explain those
equations, which was made almost as soon as I| discovered
them, actually turned upon the very idea which about the
same time found entrance into the mind of M. Cauchy—
I mean the idea of an unsymmetrical arrangement of the
ether. For as it was generally believed, at that period,

* The circumstances here related will account for what Mr. Whewell (History of
the Inductive Sciences, vol. ii. p. 449) calls the “obscure and oracular form” in
which those equations were published. Having, at that time, no good explanation
of them to give, I thought it better to attempt none. But in thegeneral view which
I have since taken (see p. 103 of this volume), they do not offer any peculiar diffi-
culty.

+ At the period of this meeting, M. Cauchy’s letter on Elliptic Polarization
had been published for some months; but I was not then aware of its existence.
Indeed the letter appears not to have attracted any general notice; for the theory
which it contains was afterwards advanced in England as a new one, and M.
Cauchy has been lately obliged to assert his prior claim to it, through the medium
of Professor Powell.—See notes, pp. 144, 149.

145

that the hypothesis of ethereal molecules symmetrically
distributed had led, in the hands of M. Cauchy, to a
complete theory of rectilinear polarization in crystals (see
his Exercices de Mathématiques, Cinquiéme Année, Paris,
1830, and the Mémoires de l'Institut, tom x. p. 293), the
notion of endeavouring to account for the phenomena of
elliptic polarization, by freeing the hypothesis from any re-
striction as to the distribution of the ether, would naturally
occur to any one who was thinking on the subject, no less
than to M. Cauchy himself. And though, for my own part,
I never was satisfied with that theory, which seemed to me to
possess no other merit than that of following out in detail
the extremely curious, but (as I thought) very imperfect,
analogy which had been perceived to exist between the vi-
brations of the luminiferous medium and those of a common
elastic* solid (for it is usual to regard such a solid as a rigid

* The analogy was suggested by the hypothesis of transversal vibrations, which,
when viewed in its physical bearing, was considered by Dr. Young to be “perfectly
appalling in its consequences,” as it was only to solids that a “lateral resistance”
tending to produce such vibrations had ever been attributed. (Supplement to the
Encyclopedia Britannica, vol. vi. p. 862: Edinburgh, 1824). He, admits, how-
ever, that the question whether fluids may not “ transmit impressions by lateral ad-
hesion, remains completely open for discussion, notwithstanding the apparent diffi-
culties attending it.”’ As far as I am aware, Fresnel always regarded the ether asa
fluid. M. Poisson affirms that it must be so regarded, and attributes its apparent
peculiarities to the immense rapidity of its vibrations, which does not allow the law
of equal pressure to hold good in the state of motion (Annales de Chimie, tom. xliv.
p- 432). M. Cauchy calls the ether a fluid, though he treats it as a solid. My.own
impression is, that the ether is a medium ofa peculiar kind, differing from all ponder-
able bodies, whether solid or fluid, in this respect, that it absolutely refuses, in any
case, to change its density, and therefore propagates to a distance transversal vibra-
tions only ; while ordinary elastic fluids transmit only normal vibrations, and ordi-
nary solids admit vibrations of both kinds. This hypothesis also includes the
supposition that the density of the ether is unchanged by the presence of pondera-
ble matter. As to M. Cauchy’s third ray, with vibrations nearly normal to the wave,
there isno reason to believe that it has even the faintest existence; but it is neces-
sarily introduced by his identification of the vibrations of light with those of an in-
definitely extended elastic solid.

1:6

system of attracting or repelling molecules, and M. Cauchy
has really done nothing more than transfer to the luminife-
rous ether both the constitution of the solid and differential
formulas of its vibration), still I should have been glad, in
the absence of anything better, to find my equations sup-
ported by a similar theory, and their form at least counte-
nanced by the like mechanical analogy. Besides, I recol-
lected that Fresnel himself, in his Memoir on Double Re-
fraction, had indicated a ‘‘ helicoidal arrangement,” or some-
thing of that sort, as a probable cause of circular polariza-
tion (Mémoires de l'Institut, tom. vil. p. 73); and as this
was an hypothesis of the same kind as the other, only not
so general, I was prepared to find that the supposition of
an arbitrary arrangement, whatever might be thought of its
physical reality, would lead to equations of the same form
as those which I had assumed. Upon trial, however, the
very contrary proved to be the case, for though it was pos-
sible to obtain additional terms, containing differential co-
efficients of the third order, multiplied by the same constant
C, yet this constant always came out with the same sign in
both equations, whereas a difference of sign was essential
for the expression of the phenomena. I had no sooner ar-
rived at this result, than I perceived it to be fatal to the
theory of M. Cauchy, and to afford a demonstration of its
insufficiency, not only in the particular application which I
had made of it, but in all its applications. For the hypo-
thesis which I used was, in fact, identical with that theory,
in the most general form of which it is susceptible, when un-
restricted by any particular supposition as to the arrange-
ment of the ethereal molecules; and therefore the funda-
mental conception of the theory could not be true, as it not
merely failed to explain a large and most remarkable class of
phenomena—those of circular and elliptical polarization—but
absolutely excluded them, and left no room for their exist-
ence. It followed from this, that the mechanical explanation,

a

147

which the same theory was supposed to have given, of the
phenomena of rectilinear polarization and double refraction
in erystals, could not be well founded; indeed, as I have
said, I had always distrusted it, and that for various rea-
sons, of which one has been already mentioned, and another
was suggested by the forced relations which M. Cauchy had
found it necessary to establish among the constants of his
theory, and by which he had compelled, as it were, his com-
plicated formulas to assume the appearance of an agreement
(though, after all, a very imperfect one) with the simple laws
of Fresnel.

Such were the conclusions at which I arrived, and the
reflections which they forced upon me, nearly six years ago.
They have been frequently mentioned in conversation to
those who took an interest in such matters, and their general
tenor may be gathered from what I have elsewhere written
(Transactions of the Academy, vol. xviii. p. 68); but I did not
think it worth while to publish themin detail, because it seemed
probable that juster notions would prevail in the course of a
few years, and that the ingenious speculations to which I
have alluded would gradually come to be estimated at their
proper value. But from whatever cause it has arisen—whe-
ther from the real difficulties of the subject, or the extreme
vagueness of the ideas that most persons are content to form
of it, or from deference to the authority of a distinguished
mathematician—certain it is that the doctrines in question
have not only been received without any expression of dissent,
but have been eagerly adopted, both inthis country and abroad,
by a host of followers; and even the extraordinary error, which
it is my more immediate object to expose, has been continually
gaining ground up to the very moment at which I write, and
has at last begun to be ranked among the elementary truths of
the undulatory theory of light. Notwithstanding my unwilling-
ness, therefore, to be at all concerned in such discussions,
I do not think myself at liberty to remain silent any longer,

148

There are occasions on which every consideration of this kind
must give way to a regard for the interests of science.

To show that the principles of M. Cauchy contradict, in-
stead of explaining, the phenomenon of elliptic polarization,
let us take the axes of coordinates as before; and let us sup-
pose, for the sake of simplicity, and to avoid his third ray,
that the normal displacements vanish. Then his fundamental
equations take the form

2
a = afAg + ShAn,
di*
ee (2)
ae = DgAn + SAAE,

where f, g, # are quantities depending on the law of force
and the mutual distances of the molecules.* If, therefore,

* | have not thought it necessary to transcribe the original equations of M.
Cauchy, which are rather long. He has presented them in different forms; but the
system marked (16) at the end of § 1 of his Memoir on Dispersion, already quoted,
is the most convenient, and it is the one which I have here used.
of the coordinates being arbitrary,

The directions
I have supposed the axis of z to be perpendicu-
lar to the wave-plane. Then, on putting = 0, A = 0, in order to get rid of
the normal vibration, the last equation of the system becomes useless,

two are reduced to the equations (2), given above; the letters f,

and the other
&, h, being writ-
ten in place of certain functions depending on the mutual actions of the molecules.
It will be proved, further on, that this simplification does not at all affect the argu-
ment. As the directions of x and y still remain arbitrary, I have made them pa-
rallel to the axes of the supposed elliptic vibration.

It may be right to observe, for the sake of clearness,

that, when the medium is
arranged symmetrically, it is always

possible to take the directions of x and y such
that the two sums depending on the quantity # may disa
(2), and then the vibrations are rectilinear.

metrical, this is no longer possible.

Ppear from the equations
But when the arrangement is unsym-

The equations (2) are precisely the same as those which have been employed
by Mr. Tovey and by Professor Powell, the latter of whom, in his lately published
work, entitled, ‘4 General and Elementary View of the Undulatory Theory, as ap-

plied to the Dispersion of Light, and other Subjects,” has dwelt at great length on

the theory of elliptic polarization, which they have been supposed to afford, and

which he regards as a most important accession to the Science of Light. Professor

Powell has also made some communications on the subject to the British Asso-

oF

149

we assume that each molecule describes an ellipse, the axes
of which are parallel to those of # and y; that is to say, if we
make
E=pceos¢, n= qsin9g,
On (3)
e= z (4 a7 ®),
and consequently

AE = p(sin 26 sin ¢ — 2 sin 70 cos 9),

An= — q(sin 20 cos ¢ + 2sin 76 sin ¢),
where 0 = uae , we shall find, by substituting these values in
the equations (2), which must hold good independently of 4,
Si Ae Oks sae wile: (4)

Sfsin 20 — 2kSh sind = 0,
; 2 Dg
Sg sin 26 + k Dh sin 70 = 0,

ei

wherein £ = 4 expresses the ratio of the semiaxes of the el-

liptic vibration, and
2 2

5=/fsin 76 B/ igatadersies 4 °6,

= oF? D7?

4

ciation, and has written two papers about it in the Philosophical Transactions (1838,
p. 253; and 1840, p. 157), besides several others in the Philosophical Magazine.
He, however, always attributed this theory of elliptic polarization to Mr. Tovey,
until his attention was directed, by a letter from M. Cauchy, to some investiga-
tions of the latter which he had not previously seen (Phil. Mag. vol. xix. p. 374).
Mr. Tovey set out with the principles of M. Cauchy, and therefore naturally struck
into the same track, in pursuit of the same object, apparently quite unconscious that
any one had preceded him. It was, indeed, an obvious reflection, that these prin-
ciples, when generalised to the utmost, ought toinclude, not only the laws of
elliptic polarization, but (as really has been thought by M. Cauchy and his fol-

lowers) of dispersion and absorption, and, in short, of all the phenomena of optics.

150

Equating the two values of s’, we get, for the determination
of k, the following quadratic :

42S k+1=0. (5)
Now making the substitutions (3) in equations (1), page 142,
we have
jae 27 Seis 2m
ya ao hig Se i Ge (6)
and thence
5 r
#— (4 — 2) k—1=0, (1)

a result which is perfectly inconsistent with the former, since
the two roots of (5) have the same sign, if they are not imagi-
nary, while those of (7) have opposite signs, and cannot be
imaginary. If, therefore, one equation agrees with the phe-
nomena, the other must contradict them. The last equation
indicates that, in the double refraction of quartz, the two
elliptic vibrations are always possible, and performed in op-
posite directions, which is in accordance with the facts ;
whereas the equation (5), deduced from M. Cauchy’s theory,
would inform us that the vibrations of the two rays are
either ¢mpossible or in the same direction.*

To apply the results to a particular instance, let us con-
ceive a circularly polarized ray passing along the axis of
quartz, or through one of the rotatory liquids, such as oil of
turpentine; the position of the coordinates x and y, in the
plane of the wave, being now, of course, arbitrary. In each
of these cases we have f = + 1, anda = 8 = a’, so that the
value of s* in equation (6) is expressed by the constant a2,
plus or minus a term which is inversely proportional to the

* This conclusion, which shows that M. Cauchy’s Theory is in direct Opposition
to the phenomena, might have been obtained without any reference to the equa-

tions (1). But these equations are necessary in what follows.

151

wave-length); the sign of this term depending on the direc-
tion of the circular vibration. Now it will not be possible
to obtain a similar value of s? from the formulas (4), unless
we suppose a’ = 8’ = a”, since it is only in the expansion
of c’ that a term inversely proportional to A can be found;
but on this supposition the formulas are inconsistent with
each other, nor can they be reconciled by any value of 4.
Indeed, when a’ = B’, the equation (5) gives k= + ees.
Thus it appears that circular vibrations, such as are known
to be propagated along the axis of quartz, and through cer-
tain fluids, cannot possibly exist on the hypothesis of M.
Cauchy. It was probably some partial perception of this
fact that caused M. Cauchy to assert that the vibrations,
in these cases, are not exactly circular, but in some degree
elliptical ; a supposition which, if it were at all conceivable,
which we have seen it is not (p. 142), would be at once set
aside by what has just been proved; for no assumed value
of &, whether small or great, will in any way help to remove
the difficulty.

But this is not all. Rectilinear vibrations are excluded
as well as circular; for we cannot suppose / = 0 in the equa-
tions (4), so long as the quantity c’, resulting from the hypo-
thesis of unsymmetrical arrangement, has any existence.
Thus the inconsistency of that hypothesis is complete, and the
equations to which it leads are utterly devoid of mean-
ing.

The foregoing investigation does not differ materially
from that which I had recourse to in the beginning of the
year 1836. To render the proof more easily intelligible,
and to get rid of M. Cauchy’s “third ray,” which has no
existence n the nature of things, I have suppressed the
normal vibrations; a procedure which is not, in general, al-
lowable on the principles of M. Cauchy. It will readily ap-
pear, however, that this simplification still leaves the demon-
stration perfectly rigorous in the case of circular vibrations,

152

and does not affect its force when the vibrations are ellipti-
eal. For in the rotatory fluids it is obvious that the normal
vibrations, supposing such to exist, must, by reason of the
symmetry which the fluid constitution requires, be indepen-
dent of the transversal vibrations, and separable from them,
so that the one kind of vibrations may be supposed to vanish
when we wish merely to determine the laws of the other.
The equations (2) are, therefore, quite exact in this case;
and they are also exact in the case of a ray passing along
the axis of quartz, since such a ray is not experimentally dis-
tinguishable from one transmitted by a rotatory fluid, and
its vibrations must consequently be subject to the same kind
of symmetry. In these two cases, therefore, it is rigorously
proved that the values of £4, which ought to be equal to plus
and minus unity, are imaginary, and equal to + y¥ — 1.
And if we now take the most general case with regard to
quartz, and suppose that the ray, which was at first coinci-
dent with the axis of the crystal, becomes gradually inclined
to it, the values of £ must evidently continue to be imaginary,
until such an inclination has been attained that the two roots
of equation (5) become possible and equal, in consequence of
the increased magnitude of the co-efficient of the second
term. Supposing the last term of that equation to remain
unchanged, this would take place when the co-efficient of &
(without regarding its sign) became equal to the number 2,
and the values of & each equal to unity, both values being
positive or both negative. The vibrations which before were
impossible, would, at this inclination, suddenly become pos-
sible; they would be ctreular, which is the exclusive pro-
perty of vibrations transmitted along the axis; and they
would have the same direction in both rays, which is not a
property ofany vibrations that are known to exist. At greater
inclinations the vibrations would be elliptical, but they would
still have the same direction in the two rays. These re-
sults would not be sensibly altered by regarding the equa-

153

tion (5) as only approximate in the case of rays inclined to
the axis; for the last term of that equation, if it does not re-
main the same, can never differ much from unity ; since it must
become exactly equal to unity, whatever be the direction of
the ray, when the crystalline structure is supposed to disap-
pear, and the medium to become a rotatory fluid.

That a theory involving so many inconsistencies should
have been advanced by a person of M. Cauchy’s reputation,
would, perhaps, appear very extraordinary, if we did not re-
collect that it was unavoidably suggested by the general
principles which he had previously adopted, and which were
supposed, not merely by himself, but by the scientific world
generally, to have already afforded the only satisfactory ex-
planation of the laws of double refraction in the common
and well-known case where the vibrations are rectilinear.
This supposed explanation was obtained, as has been said,
by restricting the application of M. Cauchy’s principles to
the hypothesis of a vibrating medium arranged symmetrically,
in which case it was shown that the vibrations were neces-
sarily rectilinear; and of course the removal of this restric-
tion was the only way in which it was possible, on those
principles, to account for the existence of circular and ellip-
tical vibrations. Accordingly, when M. Cauchy perceived
that, on the hypothesis of unsymmetrical arrangement, the ex-
istence of rectilinear vibrations became impossible, and that -
of elliptic vibrations, generally speaking, possible, he found
it very easy to persuade himself that he had obtained a
new proof of the correctness of his views, and a new and
most important application of the fundamental equations
by which his general principles were analytically expressed.
To have supposed otherwise would have been to admit
that his general principles were false. If the elliptical or
quasi-circular vibrations which he was now contemplating
were not capable of being identified with those which had
been recognized in the phenomena presented by quartz and

154

the rotatory fluids—if their laws were essentially or very
considerably different—his theory would be inconsistent
with a wide range of well known facts, and, notwith-
standing its so-called explanations of other laws, should be
finally abandoned. Under these circumstances, therefore,
he very naturally supposed that his new results must be
in complete harmony with the phenomena discovered by
M. Arago, and analysed so successfully by MM. Biot and
Fresnel; although, had he taken the precaution of acquiring
such a clear notion of the phenomena as would have enabled
him to translate them into analytical language, he must have
perceived that they were entirely opposed to his results, and
that this opposition furnished an argument which swept away
the very foundations of his theory. For, if the constitution
of the luminiferous medium were such as M. Cauchy (sup-
poses, the well-known phenomena of circular and elliptic po-
larization would, as we have seen, be absolutely impos-
sible.

Thus the argument which overturns the particular theory
of elliptical polarization destroys at the same time all the
other optical theories of M. Cauchy, because they are all
built on the principles which we have now demonstrated to be
false. But though the principles of M. Cauchy are now, for
the first time, formally refuted, they were objected to, on
‘general grounds, so long ago as the year 1830, by a person
whose opinion, on a question of mechanics, ought to have had
considerable weight. This was M. Poisson, who, having de-
duced from the equations of motion of an elastic solid the con-
sequence that such a body admitted vibrations perpendicu-
lar to the direction of their propagation, thought it right to
remark that this conclusion could not be supposed toaccount
for transversal vibrations in the theory of light, because (as
he expressed himself) ‘‘the same equations of motion could
not possibly apply to two systems [of molecules] so essen-
tially different from each other” as the ethereal fluid and

155

an elastic solid.*—(See the Annales de Chimie, tom. xliv.
p- 432). The remark, however, did not meet with much
attention from mathematicians, who were, perhaps, not dis-
posed to scrutinize too closely any hypothesis which gave
transversal vibrations as a result. Besides, the hypothesis
appeared to go much further, as it offered primd facie
explanations of a great variety of phenomena; it was one
to which calculation could be readily applied, and there-
fore it naturally found favour with the calculator; and as
to M. Poisson’s objection, it was easily removed by a change
of terms, for when the elastic solid was called an “ elastic
system,” there was no longer anything startling in the an-
nouncement that the motions of the ether are those of such
asystem. The hypothesis was therefore embraced by a great
number of writers in every part of Europe, who reproduced,
each in his own way, the results of M. Cauchy, though some-
times with considerable modifications. Every day saw some
new investigation purely analytical—some new mathematical
research uncontrolled by a single physical conception—put
forward as a “mechanical theory” of double refraction, of
circular polarization, of dispersion, of absorption; until at
length the Journals of Science and Transactions of Societies
were filled with a great mass of unmeaning formulas. This
state of things was partly occasioned by the great number of
** disposable” constants entering into the differential equations
of M. Cauchy and their integrals; for it was easy to introduce,
among the constants, such relations as would lead to any de-
sired conclusion ; and this method was frequently adopted by
M. Cauchy himself. Thus, in his theory of double (or rather
triple) refraction, given in the works already cited (p. 145), he
supposes three out of his nineconstants to vanish, and assumes,

* As the theory of M. Cauchy (Mem. de I’ Institut, tom. x.) had been communi-
cated to the Academy of Sciences some months before the period (October, 1830)
at which M. Poisson wrote, there can be no doubt that M. Poisson’s remark was

directed against that theory, though he did not expressly mention it.
VOL. Il. c@)

156

among the other six, three very strange and improbable re-
lations, by means of which each of the principal sections of
his wave-surface (considering only two out ofits three sheets)
is reduced to the circle and ellipse of Fresnel’s law; and
the three principal sections being thus forced to coincide, it
would not be very surprising if the two sheets were found
to coincide in every part with the wave-surface of Fresnel.
The coincidence, however, is only approximate ; but M.
Cauchy is so far from being embarrassed by this circumstance,
that he does not hesitate to regard his own theory as rigo-
rously true, and that of Fresnel as bearing to it, in point of
accuracy, the same relation which the elliptical theory of the
planets, in the system of the world, bears to that of gravita-
tion (Mémoires de (Institut, tom. x. p. 313). Nor is he at
all embarrassed by the supernumerary ray belonging to the
third sheet of his wave-surface ; he assumes at once that
such a ray exists, though it was never seen, and promises,
for the satisfaction of philosophers, to make known the means
of ascertaining its existence (Ibid. p. 305). But he afterwards
contented himself with observing that as its vibrations are in
the direction of propagation they probably make no impres-
sion on the eye, and he then gave it the name of the “ invisible
ray.” (Nouveaux Exercices, p. 40).

In these investigations, the suppositions which M. Cauchy
had made respecting the constants led to the result that the
vibrations of a polarized ray are parallel to its plane of pola-
rization; but in the year 1836 he changed his opinion on this
point, and then, by reinstating the constants that he had be-
fore supposed to vanish, and establishing proper relations
amongst them and the rest, he arrived at the conclusion that
the vibrations are perpendicular to the plane of polarization
(Comptes Rendus, Tom. ii. p. 242). All his other results, of
course, underwent some corresponding change ; and it is this
new theory which must now be regarded as rigorous, while
that of Fresnel is to be looked on as approximate. But itis

157

needless to say, that if the accuracy of Fresnel’s law of
double refraction is to be disputed, it must be on much better
grounds than these; and the results of M. Cauchy are cer-
tainly too far removed from that law to have any chance of
being consonant with truth. Although, for example, his new
views respecting the direction of the vibrations agree, in a
general way, with those of Fresnel, there is yet, in one par-
ticular, an important difference between them; for accord-
ing to Fresnel, the vibrations are always exactly in the sur-
face of the wave, while, according to M. Cauchy (in his old
theory as well as the new), they are only so in ordinary media.
In a biaxal crystal he finds—and this is one of the ways in
which the “invisible ray” manifests its influence—that the
direction of vibration, in each of the two rays that are visible,
is inclined at a certain angle to the wave-plane; but this
angle, though small, is by no means inconsiderable, as M.
Cauchy seems to intimate, overlooking the fact, which appears
from his own equations, that it is of the same order of mag-
nitude as the quantities on which the double refraction de-
pends. It is true, the deviation measured by this angle can-
not, if it exists, be directly observed in the refracted light ;
but its indirect effects on reflected light ought to be very
great, since the action of the crystal on a ray reflected at its
surface differs from that of an ordinary medium by a quantity
of the same order merely as the aforesaid angle; and as the
problem of crystalline reflexion has been already solved
(Trans. R. I. A. vol. xviii., p. 31) on the supposition (which
is an essential one in the solution) that the vibrations are ex-
actly in the plane of the wave, it is highly improbable, con-
sidering the complex nature of the question, that it will be
solved, in any satisfactory way, on a supposition so different
as that which is required by the theory of M. Cauchy. How-
ever, as the laws of such reflexion are now well known, by
means of the solution alluded to, it is possible that M. Cauchy
may, as in the case of double refraction, succeed in deducing
02

158

the same laws, or, if not the same, what may seem to be more
exact laws, from certain principles* of his own, helped out,
if need be, by proper relations among his constants; espe-
cially if, to allow greater scope for such relations, the number
of constants be increased by the hypothesis of two coexist-

* In applying these principles to the question of reflexion and refraction at the
surface of an ordinary medium (Comptes Rendus, Tom. ii. p. 348), M. Cauchy has
arrived at the singular conclusion, that light may be greatly increased by refraction
through a prism, at the same time that it is almost totally reflected within it. Sup-
posing the refracting angle of the prism to be very little less than the angle of to-
tal reflexion for the substance of which it is composed, a ray incident perpendicu-
larly on one of the faces will emerge making a very small angle wita the other
face; and as the reflexion at the latter face is nearly total, it is self-evident that
the intensity of the emergent light, as compared with that of the incident, must be
very smal]. M. Cauchy, however, finds, by an elaborate analysis, that a prodigious
multiplication of light [‘‘ wane prodigieuse multiplication de la lumiére”’| takes place,
the emergent ray being nearly six times more intense than the incident when the
prism is made of glass, and nearly nine times when the prism is of diamond. This
result was, in a general way, actually verified experimentally by himself and ano-
ther person; soeasy it is, in some cases, to see anything that we expect to see. Had
the result been true, it would have been a very brilliant discovery indeed; for then
we should have been able, by a simple series of refractions, to convert the feeblest
light into one of any intensity we pleased; but the very absurdity of such a sup-
position should have taught M. Cauchy to distrust both his theory and his experi-
ment. Far from doing so, however, he considers the fact to be perfectly esta-
blished, and to afford a new argument against the system of emission. “Ici,” says
he, ‘un rayon, réféchi en totalité, est de plus transmis avec accroissement de
lumiére ; ce qui est un nouvel argument contre le systéme d’émission.” The sys-
tem of emission has at least this advantage, that by no possible error could such a
conclusion be deduced from it. For if all the particles of light be reflected, cer-
tainly none of them can be refracted.

The truth is, that M. Cauchy mistook the measure of intensity in the hypothe-
sis of undulations, supposing it to be proportional simply to the square of the
amplitude of vibration; whereas it is really measured by the vis viva, or by that
square multiplied by the quantity of ether put in motion, a quantity which in the
present case is evanescent, since the corresponding volumes of ether, moved by the
ray within in the prism and by the emergent ray, are to each other as the sine of
twice the angle of the prism to the sine of twice the very small angle which the
emergent ray makes with the second face of the prism. The intensity of the emer-
gent light is therefore very small, as it ought to be, though the amplitude of its
vibrations is considerable. ;

159

ing systems of molecules, an hypothesis which M. Cauchy has
already considered with his usual generality, but without
making any precise application of it. (Hzercices d’ Analyse
et de Physique Mathématique, Tom. i. p. 33.)

Perhaps one cause why M. Cauchy’s views on the subject
of double refraction have met with such general acceptance,
may be found in the fact, that a theory setting out from the
same principles, and leading, by the same relations among
constants, to formulas identical in every respect with his
earlier results, was advanced independently, and nearly at the
same time, by M. Neumann of Konigsberg (Poggendorff’s
Annals, vol. xxv. p. 418). A coincidence so remarkable
would be looked upon, not unreasonably, as a strong argu-
ment in favour of the theory ; though it must be allowed that,
in the effort to extend the knowledge of any subject, there is
a tendency in different minds to adopt the same errors re-
specting it, as well as the same truths; a fact of which we
have seen other examples in the course of the present
article.

According to M. Neumann (bid. p. 454), the ‘ third
ray,” not being perceived as light, must manifest its existence
as radiant heat, or as a chemical power, or as some other
agent [‘‘als strahlende Warme, oder chemisch wirkend, oder
als irgend ein anderes Agens”], and he thinks that the nature
of this ray will be more easily investigated, if the laws of re-
flexion shall be deduced from the aforesaid theory. But we
have seen that the laws of reflexion are, to all appearance, at
variance with the theory, and they take no account whatever
of the third ray. Besides, the discoveries which have been
made of late years respecting the polarization of radiant heat,
and the strong analogies that have been traced between it
and light, amount to a demonstration that its vibrations are
transversal, and of course essentially different from those
of the supposed third ray, which are normal, or nearly so.
There is every reason to believe that the vibrations of the

160

chemical rays are also transversal; and we may confidently
assert, that the three species of rays—those of light and
heat, and the chemical rays,—are produced not only by vi-
brations of the same medium, but by the same kind of vibra-
tions, propagated with nearly the same velocities. If, there-
fore, the third ray of MM. Cauchy and Neumann has any
existence, it must be referred to ‘‘ some other agent,” the
nature of which it is impossible to conjecture.

Enough has now been said to show that the optical theory
which we have examined, and which has passed current in
the scientific world for a considerable period, is quite inade-
quate to explain the leading phenomena of light, and that it
is based upon principles which are altogether inapplicable to
the subject. M. Cauchy states, in the memoir so often
quoted (Mem. de l'Institut, Tom. x. p. 294), that the first ap-
plication which he had made of his principles was to the
theory of sound, and that the formulas which he had deduced
from them agreed remarkably well with the experiments of
Savart and others on the vibrations of elastic solids. As I
have already intimated, it is in the solution of such ques-
tions (which, however, have long been familiar to mathemati-
cians) that the fundamental equations of M. Cauchy may be
most advantageously employed ; and had he pursued his re-
searches in this direction, his labours would doubtless have
been attended with more success, and with greater benefit
to science.

II.
On Fresnel’s Formula for the Intensity of Reflected
Light, with Remarks on Metallic Reflexion.

When Mr. Potter discovered, by experiment, that more
light is reflected by a metal at a perpendicular incidence
than at any oblique incidence (at least as far as 70°), the fact
was looked upon, by himself and others, as contrary to all re-
ceived theories ; and certainly the universal opinion, up to
that time, was, that the intensity of reflexion always increases

161

with the incidence. It may therefore be worth while to re-
mark, that the formula given by Fresnel for reflexion at the
surface of a transparent body, though not of course appli-
cable, except in a very rude way, to the case of metals, would
yet lead us to expect, for highly refracting bodies as the
metals are supposed to be, precisely such a result as that
obtained by Mr. Potter. For when the index of refraction
exceeds the number 2 + V3, or the tangent of 75°, the ex-
pression for the intensity of reflected light will be found to
have a minimum value at a certain angle of incidence; while
for all less values of the refractive index the intensity will be
least at the perpendicular incidence.

Let é and #’ be the angles of incidence and refraction,
and put

sin 2 cos2
im

=> ray ae
sin 2” cos 2’

then if 1 be the intensity of the reflected light, when common
light is incident, Fresnel’s expression

il pane — 7’) tan*(i _ a ;
7 Asin? (zg + ¢/) © tan?(¢ +7)
in which the intensity of the incident light is taken for unity,
may be put under the form

1 2 1 M\ 2
Cees)
(ooh Ay y
pert t sast 3)
which has a minimum value when
1 8
Hoy SoS
the value of 1 being in that case

(1 - =) 4 (1+- us

1
e+-=M+
rT

162

and the corresponding angle of incidence being given by the
formula
_ vw e—l ]
sing = ral vet 1’ where «= a(n eal

: 1 Ms
Since « + — cannot be less than 2, it is easy to see that, when
be

. Se 1
there is a minimum, m + — cannot be less than 4, and there-
M

fore m cannot be less than 2 + V/ 3, or 3.732.
As an example, let m + 2 =6. Then, at a perpendicu-

lar incidence, one-half the incident light will be reflected.
The minimum will be when i = 65° 36’, and at this angle
only 5% of the incident light will be reflected. The value
here assumed for the refractive index is that which Sir J.
Herschel (Treatise on Light, Art. 594), assigns to mercury ;
but if my ideas be correct, it is far too low for that metal.

The only person who supposes that the refractive index
of a metal is not a large number, is M. Cauchy. It has always
been held as a maxim in optics, that the higher the reflective
power of any substance, the higher also is its refractive index.
But M. Cauchy completely reverses this maxim; for, as I
have elsewhere shown (Comptes Rendus, tom. vili. p. 964), it
follows from his theory that the most reflective metals are the
least refractive, and even that the index of refraction, which
for transparent bodies is always greater than unity, may for
metals descend far below unity. Thus, according to his for-
mula, the index of refraction for pure silver is the fraction 4,
so that the dense body of the silver actually plays the part
of a very rare medium with respect toa vacuum. It appears
to me that such a result as this is quite sufficient to overturn
the theory from which it is derived. The formulas, however,
which he gives for the intensity of the reflected light, are
identical with the empirical expressions which I had given
long before, and are at least approximately true.

In framing my own empirical theory (see Proceedings,

163

vol. i. p. 2), two suppositions relative to the value of the
refractive index presented themselves. Putting m for the
modulus, and x for the characteristic, I had to choose be-

M ; :
tween the values Mcosy and an The latter value is that
SX

which I adopted; the former, whichis M. Cauchy’s, was re-
jected because I saw that it would lead to the result above
mentioned.

Another result of M. Cauchy’s, which he has given twice
in the Comptes Rendus (tom. ii. p. 428, and tom. viii. p. 965)
requires to be noticed. When a polarized ray is reflected
by a metal, the phase of its vibration is altered, and if the in-
cidence be oblique, the change of phase is different, accord-
ing as the light is polarized in the plane of incidence, or in
the perpendicular plane. But when the ray is reflected at a
perpendicular incidence, it is manifest that the change is a
constant quantity, whatever be the plane of polarization. In
fact, the distinction between the plane of incidence and the
perpendicular plane no longer exists, and the phenomena
must be the same in all planes passing through the ray.
Yet M. Cauchy, in the two places above quoted, asserts it to
be a consequence of his theory, that in this case the altera-
tions of phase are different for two planes of polarization at
right angles to each other, and that the difference of the al-
terations amounts to half an undulation. The same singular
hypothesis had been previously made by M. Neumann (Pog-
gendorff’s Annals, vol. xxvi. p. 90), whom M. Cauchy appears
to have followed; but M. Neumann has since admitted it to
be erroneous (Jbzd. vol. xl. p. 513).

Mr. J. Huband Smith communicated to the Academy some
particulars connected with the recent discovery of a cairn
containing cinerary urns, which appears to have been accom-
panied by some circumstances not unworthy of notice.

It took place at Loughanmore, in the county of Antrim,

164

the seat of Mr. Thomas Adair, in a field which was being
ploughed, in the spring of 1840. After a few urns had been
found, there being some difficulty in preserving them en-
tire, Mr. Adair, with a commendable desire to avoid the de-
struction of remains so full of interest, caused the cairn, in
which these urns were found, to be closed carefully, and re-
stored the ground to its former state as nearly as might be, in
order to leave it to some skilful and experienced antiquary to
explore the entire ina more deliberate and scientific manner.

The discovery was occasioned by one of the horses which
were in the plough suddenly stumbling, one of his legs
having sunk nearly up to the knee in adeep hole. On exa-
mination it was found he had put his foot into a fine sepul-
chral urn, which, it need hardly be stated, was broken into
shivers.

On a slight further search a second urn was discovered.
Every effort was made to preserve this one entire, but in
vain; it fell to pieces in the hands of the person who took it
up. A third urn was then exposed, when Mr. Adair finding
it impossible to save them, put a stop for the time to the fur-
ther opening of the cairn.

The cairn in which these urns were found is situated
in the townland of Loughanmore, and not far from the
Loughan or lake (now drained) from which the townland de-
rives its name. It lies within a field called the cove-park,
there being one or more artificial caves, or coves (as they
are termed by the Antrim peasantry), within it. And from
a hollow sound which the ground gives, other caves, as yet
unopened, are confidently supposed to exist near where the
urns were found.

The cairn in question is indicated by so very slight an
elevation of thesurface, thatit was in course of being ploughed
over without any particular notice, till the finding of the urns
drew Mr. Adair’s attention to it. This elevation was then
observed to have a circumference of some twelve or fourteen

165

feet, perhaps a little more ; and on closer examination proved
to be composed of loose field-stones mixed with earth, ap-
parently laid in, upon, and around the urns, with just so
much care as not to break them.

It will not fail to be noticed, that in this latter circum-
stance this cairn seems to differ remarkably from most others,
for instance Deveril Barrow in Dorsetshire, which has been
thought worthy of an elegant descriptive work, and many
other of the Wiltshire Barrows, so carefully and scientifically
opened by an eminent and accomplished English antiquary,
the late Sir Richard Colt Hoare; and also from the very
important cairn opened at Mount Stewart, near Grey-Abbey,
in the county of Down, about the year 1807. In these the
urns have almost invariably been protected by a kist or stone
chest formed of flags, enclosing a considerable space. We
have the authority of our distinguished Irish antiquary,
Mr. George Petrie, for saying that ‘‘ the sepulchral urns of
Ireland are superior in ornament to any found in England.
The ornaments of gold frequently found in them are richer
and more numerous.” And he does not hesitate to infer
from these and other facts, that ‘‘the pagan Irish were supe-
rior in the arts of civilized life to their British neighbours.”

These urns found at Loughanmore were found to have
been all placed with the mouth downwards. They lay rather
closely together, scarce eighteen inches apart from each ,
other, the smaller urns appearing to surround the larger one,
which was that broken by the horse.

The two smaller sized urns were of the same size, and
would hold probably eight or nine quarts of liquid each.

No metallic remains of brass or bronze; no flint arrow-
heads, stone adzes, or any other remains were found. Every
probability exists of future discoveries of a most interesting
description being made on a stricter examination of this
cairn.

Opportunities such as this daily offer themselves in this

166

country, of pursuing an inquiry of deep historical interest ;
which if they were to occur at the other side of the Irish
channel, would be grasped at with avidity by the untiring
zeal of many an English antiquary, who, while he cultivates
assiduously, and under circumstances of extreme difficulty,
the meagre opportunities which England affords to the
study of ancient British and Celtic remains, cannot but look
with a feeling of astonishment (akin perhaps to contempt),
on the apathy with which in Ireland we suffer daily the tan-
gible and unquestionable proofs of the early civilization of
our country, to which we have long proudly laid claim, ac-
tually to perish before our eyes, from the most disgraceful

negligence.

The Chair having been taken, pro tempore, by the Rey.
J. H. Todd, D. D., V. P., the President communicated the
following proof of the known law of Composition of Forces.

Two rectangular forces, x and y, being supposed to be
equivalent to a single resultant force p, inclined at an angle
v to the force x, it is required to determine the law of the
dependence of this angle on the ratio of the two component
forces x and y.

Denoting by p’ any other single force, intermediate be-
tween « and y, and inclined to w at an angle v’, which we
shall suppose to be greater thanv; and denoting by 2’ and
7 the rectangular components of this new force p’, in the
directions of x and y, we may, by easy decompositions and
‘recompositions, obtain a new pair of rectangular forces, 2”
and y", which are together equivalent to p’, and have for

components
al! —2y4ty,;
P ie
y= y — 2 a,

167

the direction of 2” coinciding with that of p’, but the direc-
tion of y” being perpendicular thereto. Hence,

that is,

or, finally,

Se — ve) =f) —f (2); (a)
at least for values of v, v’, and v/— v, which are each greater
than 0, and less than = if f be a function so chosen that the
equation :

< = tan f(v)

expresses the sought law of connexion between the ratio

= and the angle v. The functional equation (a) gives

J (mv) = mf(v) = =f ( (nv),

m and » being any whole numbers; and the case of equal
components gives evidently

hence

Mm T Mm iT
f(2O) = 2h

fe) = 2, (8)

because it is evident, by the nature of the question, that

and ultimately,

. . Tv
while v increases from 0 to a?
therewith, and therefore could not be equal thereto for all

the function f(v) increases

values of v commensurable with = 7 unless it had the same

property also for all intermediate incommensurable values.
We find, therefore, that for all values of the component
forces x and y, the equation

168

Y — tanv (c)
x

holds good; that is, the resultant force coincides én direction
with the diagonal of the rectangle constructed with lines re-
presenting x and y as sides.

The other part of the known law of the composition of
forces, namely, that this resultant is represented also in mag-
nitude by the same diagonal, may easily be proved by the
process of the Mécanique Céleste, which, in the present no-
tation, corresponds to making

Gre Toye = JEN Hee oy
and therefore gives
p= =e, p = 2? hs 7.
But the demonstration above assigned for the law of the

direction of the resultant, appears to Sir William Hamilton
to be new.

It was resolved, on the recommendation of the Council,
to present a congratulatory address to His Excellency the
Lord Lieutenant ; whereupon, the Academy having adjourn-
ed for a short interval, an address was prepared, which was
afterwards agreed to.

A letter was read from M. Moreau de Jonnés, present-
ing to the Academy two volumes of the Agricultural Statistics
of France.

DONATIONS.

Comptes Rendus Hebdomadaires des Seances de l Acade-
mite des Sciences. Premier Semestre. 1841. Nos. 17—24.

Ordnance Map of the Queen’s County, in 39 sheets, in-
cluding Title and Index. Presented by His Excellency the
Lord Lieutenant.

Journal of the Franklin Institute. Vol. 1. Third Series.
(1841).

169

Det Kongelige Danske Videnskabernes Selskabs Natur-
videnskabelige og Mathematiske Afhandlinger. 8 Deel.
(1841). .

Commentationes Societatis Regie Scientiarum Gottingensis
recentiores. Vol. VIII. (1832-1837).

Esop’s Fables in Chinese. Presented by the Rev. David
Thom.

An Account of the Magnetic Observations made at Har-
vard University. (U. S.) Presented by the American
Academy.

Résumé des Observations sur la Meteorologie, sur le Mag-
netisme, &c., faites a 0 Observatoire Royal de Bruxelles en
1840. Par le Directeur A. Quetelet. Presented by the
Author.

Memoire sur la Diathermansie Electrique des Couples
Metalliques :

Des Travaux et des Opinions des Allemands sur la Pile
Voltaique :

Essai Historique sur les Phénoménes et les Doctrines de
lV’ Electro-Chimie. Par Professeur C. F. Wartmann. Pre-
sented by the Author.

Oversigt over det Kongelige Danske Videnskabernes Sel-
skabs Forhandlinger og dets Medlemmers Arbeider. 1 Aaret,
1839-40.

Report of the Council of the Zoological Society of Lon-
don. April 29, 1841.

Report on the Observations by the self-registering Ane-
mometer, in 1837-40. By A. F. Osler, Esq. Presented by
the British Association.

Abstract of the Magnetic Observations made at the Tra-
vandrum Observatory in May, 1841. By John Caldecott,
Esq. Presented by the Author.

Extrait du Tom. VIII. No. 6, des Bulletins de ? Academie
Royale de Bruxelles. (‘ Physique du Globe.”) Presented
by M. Gudele.

170

Rapport Decennal des Travaux de l’ Academie Royale
de Bruxelles depuis 1830. Par M. A. Quetelet, Hon. M.
R.I.A., &c. &e.

Annuaire de 1 Academie Royal de Bruxelles. 1 année.

Annuaire de l Observatoire Royale de Bruxelles, pour
V’An 1841. Par M. Quetelet. Presented by the Author.

Des Moyens de soustraire ( Exploitation des Mines de
Houille aux Chances @ Explosion. Recueil de Memoires et
de Rapports publié par ? Academie Royale de Brucelles.
Presented by the Academy.

Traité élémentaire des Fonctions Elliptiques. Par P. F.
Verhulst. Presented by the Author.

Statisque dela France (Agriculture). Tom. 1. I. Par
M. De Jonnés. Presented by the Author.

First Publication of the Irish Archeological Society.
Presented by the Society.

Memoires couronnes de ! Academie Royale de Bruxelles.
Tome XIV. 2™° Partie (1839-40).

Nouveaux Memoires de 0 Academie Royale de Bruxelles.
Tome XIII. (1841).

Bulletins de ! Academie Royale de Bruxelles. Nos. 9, 12
(1840). Nos. 1, 6 (1841).

Transactions of the Zoological Society of London. Vol.
II. Part 5.

Meteorological Observations made in Dublin. By Thomas
H. Orpen, M.D., M.R.I.A. Presented by the Author.

Journal of the Statistical Society of London. Vol. IV.
Part 3.

Seventh Annual Report of the Poor-Law Commissioners
(1841).

Report of the Poor-Law Commissioners on Medical Chari-
ties in Ireland. (1841). Presented by George Nicholls,
Esq.

Abhandlungen der Kéniglichen Akademie der Wissens-
chaften zu Berlin, (1839).

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1841. No. 32.

November 30. (Stated Meeting.)
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The following communication “on the Compound Na-
ture of Nitrogen,” by George J. Knox, Esq., was read by
Dr. Kane.

Soon after the discovery of the bases of the alcalies and
earths by Sir Humphrey Davy, the compound nature of ni-
trogen began to be a subject of discussion amongst chemists ;
but the arguments in favour of this supposition, deduced
principally from the nature of the ammoniacal amalgam, led
to no satisfactory physical results.

The experiments of Sir Humphrey Davy on the ammo-
niacal nitruret of potassium, and those of Despretz and
Grove on the compounds of nitrogen with iron, copper, &c.,
have shown that the metals singly (even when aided by the
most powerful electrical induction) have not the power of de-
composing nitrogen. ‘There is one experiment, however, by
Sir Humphrey Davy, from which one might deduce its com-
pound nature.

Upon heating ammonia-nitruret of potassium in an iron
tube, he obtained more hydrogen, and less nitrogen, than
the ammonia ought to have given.

Again: on mixing this substance with a greater pro-
portion of potassium, he obtained still more hydrogen, and

VOL. Il. P

172

less nitrogen; whereas, on heating the same substance in a
tube of platinum, the potassium alloyed with the platinum, and
the ammonia was given off almost entirely undecomposed.

How can these experiments be explained except upon
the supposition that the potassium and the iron had con-
jointly decomposed the nitrogen? ‘The latest experiments
which bear upon this subject, and from which I received the
idea which led me to this investigation, are those of Doctor
Brown, “upon the conversion of Carbon into Silicon,” an
explanation of phenomena which appears to me most un-
reasonable, and contrary to all chemical analogy; whilst the
supposition of the carbon having reduced the nitrogen is not
only a simple but an unavoidable conclusion to arrive at, if
nitrogen be a compound substance. To determine, by ex-
periment, the correctness or incorrectness of this idea, it were
only necessary to reduce nitrogen by some other substance
than charcoal; and should silica result from its decomposition,
the problem might be considered to be solved.

Exp. I.—A considerable quantity of ammonia-nitruret of
potassium was formed, by passing ammonia over potassium
heated in an iron tube; the part which had not been in con-
tact with the tube, having been examined for silica, contained
none.

Exp. II.—Ammonia was passed for several hours over
pure iron, heated to a dull red heat; examined for silica, it
contained none.

Exp. I1].—Ammonia-nitruret of potassium was heated
with pure iron in an iron crucible, for one half hour, over a
large Rose’s lamp; the contents of the crucible, on examina-
tion, gave silicon and silica, the weight of which was not re-
gistered, as it might have been said to have derived a portion
of silica from the inner surface of the crucible.

Exp. [V.—Twenty grains of ammonia-nitruret of potas-
sium were heated with twenty grains of pure iron in the
same iron vessel for one half hour; when treated with nitric

173

and muriatic acids there remained insoluble a small quantity
of a brownish colour, which, when fused with carbonate of
potash, gave of silica 0.10. The solution, supersaturated
with potash, filtered, neutralized, evaporated to dryness,
gave of silica 1.450; sum total of silica 1.550.

From these experiments, together with those of Sir Hum-
phrey Davy mentioned above, one might infer that nitrogen
is either a compound of silicon and hydrogen, or of silicon,
hydrogen, and oxygen; to determine which, synthetically, a
current of dry muriatic acid gas was passed over siliciuret
of potassium (formed by heating silica with potassium),
placed in a bent tube of Bohemian glass, the extremity of
which dipped into a cup of mercury, lying on the bottom of
a vessel filled with water. The atmospheric air had been
previously expelled from the apparatus by a current of
hydrogen.

The gases insoluble in water having been collected, were
found, on examination, to be hydrogen and nitrogen, the
relative proportions of which varied in different experiments.

In two experiments the proportions of hydrogen to ni-
trogen were four of the former to one of the latter.

In a third experiment, as six of hydrogen to one of
nitrogen.

In a fourth, as five of hydrogen to four of nitrogen.

Observation.— White fumes appeared occasionally in the
tube, indicating the presence of muriate of ammonia.

Professor Lloyd exhibited a specimen of Rock from Terr
Adele. ,

Professor Mac Cullagh communicated to the Academy a
very simple geometrical rule, which gives the solution of the
problem of total reflexion, for ordinary media and for uni-
axal crystals.

P 2

174:

First, let the total reflexion take place at the common
surface of two ordinary media, as between glass and air, and
let it be proposed to determine the incident and reflected
vibrations, when the refracted vibration is known, It is to
be observed, that the refracted vibration (which is in general
elliptical) cannot be arbitrarily assumed; for, as may be
inferred from what has been already stated (Proceedings of
the Academy, vol. ii. p. 102), it must be always similar to the
section of a certain cylinder, the sides of which are perpen-
dicular to the plane of incidence, and the base of which is
an ellipse lying in that plane and having its major axis per-
pendicular to the reflecting surface, the ratio of the major to
_ the minor axis being that of unity to the constant r. The
value of 7, as determined by the general rule in p, 101, is

1
p= VA _- =
1 n?sin22’

where 7 is the angle of incidence, and the index of refrac-
tion out of the rarer into the denser medium. ‘The ellipse is
greatest for a particle at the common surface of the media;
and for a particle situated in the rarer medium, at the
distance z from that surface, its linear dimensions are pro-

Qnre

portional to the quantity & * ; so that for a very small value
of z the refracted vibration becomes insensible.

Now, taking any plane section of the aforesaid cylinder
to represent the refracted vibration for a particle situated at
the common surface of the two media, let op and 0@ be the
semiaxes of the section, and let them be drawn, with their
proper lengths and directions, from the point of incidence 0;
through which point also let two planes be drawn to repre-
sent the incident and reflected waves. ‘Then conceive a
plane passing through the semiaxis op, and intersecting the
two wave-planes, to revolve until it comes into the position
where the semiaxis makes equal angles with the two inter-
sections; and in this position let the intersections be made
the sides of a parallelogram, of which the. semiaxis op is the

175

diagonal. Let oa and 0a’, which are of course equal in length,
denote these two sides. Make a similar construction for the
other semiaxis 0Q, and let os, ox’, which are also equal, denote
the two sides of the corresponding parallelogram. Then will
the incident vibration be represented by the ellipse of which
OA and oB are conjugate semidiameters, and the reflected vi-
bration by the ellipse of which 0a’ and op’ are conjugate semi-
diameters. And the correspondence of phase in describing
the three ellipses will be such that the points a, a’, P will be
simultaneous positions, as also the points B, B’, @.

The same construction precisely will answer for the case
of total reflexion at the surface of a uniaxal crystal, which is
covered with a fluid of greater refractive power than itself.
It is to be applied successively to the ordinary and extraordi-
nary refracted vibrations, and we thus get the uniradial inci-
dent and reflected vibrations, or rather the ellipses which are
similar to them. And as any incident vibration may be re-
solved into two which shall be similar to the uniradial ones,
we can find the reflected vibration which corresponds to it,
by compounding the uniradial reflected vibrations.

It may be well to mention that, in a uniaxal crystal, the
plane of the extraordinary refracted vibration is always per-
pendicular to the axis, and therefore the ellipse in which the
vibration is performed may be easily determined by the re-
mark in p. 102. The plane of the ordinary vibration has no
fixed position in the crystal; but if we conceive the auxi-
liary quantities &, m, Ci, (p. 98) to be compounded into an el-
lipse (as if they were displacements), the plane of this auxi-
liary ellipse will be perpendicular to the axis of the crystal.

Whether the preceding very simple construction, for find-
ing the incident and reflected vibrations by means of the re-
fracted vibration, extends also to the case of biaxal crystals,
is a point which has not yet been determined, on account of
the complicated operations to which the investigation leads,
at least when attempted in any way that obviously suggests
itself.

176

Joseph Huband Smith, Esq. was elected a Member of the
Committee of Antiquities, and Dr. Aquilla Smith was elected
Treasurer of the Academy, in the room of Dr. Orpen, re-
signed.

The following Address was presented on the 13th No-
vember to the Lord Lieutenant :

“© To His Excellency the Right Hon. Thomas Philip Earl De
Grey, Lord Lieutenant-General and General-Governor of
Ireland.

‘© May IT PLEASE YOUR EXCELLLENCY,

“* We, the President and Members of the Royal Irish
Academy, have the honour to present to your Excellency our
very sincere congratulations on your arrival in our metropo-
litan city, as the representative of our most gracious So-
vereign.

‘«* It has been the pleasure of her Majesty to declare her-
self the Patron of the Institution of which we are members ;
and, in virtue of the charter which was granted to us by one
of her royal predecessors, King George the III., the office of
Visitor of the Academy has become vested in your Excel-
lency, as Lord Lieutenant of Ireland.

«* We cannot but think ourselves fortunate in an official
connexion with a nobleman who, in his private career, has
shown himself so much attached to arts and letters as your
Excellency is known to be.

“ The objects of the Royal Irish Academy are Science,
Polite Literature, and Antiquities ; and in the tranquil pursuit
of these objects, the importance of which is appreciated by
your Excellency, we have had the pleasure of seeing fos-
tered within our body those feelings of mutual good-will,
which are, perhaps, scarcely less highly to be prized than the
pursuit of knowledge itself.

(Signed)
“© Witt1am Rowan Hamitton, President.”

177

To which His Excellency was pleased to return the fellow-
ing answer :

* Mr. PresipENT, AND Members or THE Roya
Irish AcADEMyY,

** I thank you for your congratulations on my arrival in
Treland.

“ Tt is a source of pleasure to me to feel that a part of my
public duty, as the Representative of her Majesty, will bring
me into such immediate connexion with the body of scienti-
fic and learned gentlemen forming the Royal Irish Academy.

“« The duties of a visitor lose the austerity of official cha-
racter, and merge into those of friendship and association,
when the person who is invested with them has the honour of
being received with the warmth which has distinguished your
reception of myself.

** You are pleased to estimate my fitness and talents be-
yond their value; but I can assure you that you cannot attach
more importance than I do to the welfare and prosperity of
such institutions as yours. As you justly observe, the pur-
suit of the objects principally cultivated by the Royal Irish
Academy enables you to foster within your body feelings of
mutual good-will; and when I see enrolled amongst your
members those who conscientiously entertain a difference of
opinion upon points ofthe very highest importance, I cannot
withhold my conviction of the public utility of a society which
affords them a point of union, and holds out to them an ob-
ject upon which they can honestly coincide.”

DONATIONS.

Bericht tiber die zur Bekanntmachung geeigneten Ver-
handlungen der Kénigl. Preuss. Akademie der Wissenschaf-
ten zu Berlin. VomJuli 1840 bis Juni 1841.

Transactions of the Cambridge Philosophical Society.
Vol. VII. Part. 2.

178

Astronomische Nachrichten. Nos. 413-432.

Magnétisme terrestre. Par M.Quetelet. Extrait du tom.
VIII. No. 9, des Bulletins de ’ Academie Royale du Brux-
elles. Presented by the Author.

Nouveaux Memoires de ? Academie Royale des Sciences
et Belles-Letires de Bruxelles. 'Tome. XIV.

Memoires Couronnés par l Academie Royale des Sciences
et Belles-Lettres de Bruxelles. ‘Tome XV. 1 partie
1840-41.

Memoire sur différens Procédes d Integration, par lesquels
on obtient l'attraction d’un ellipsoide homogene dont les trois
axes sont inégaux, sur un point extérieur. Par M. J. Plana.
Presented by the Author.

The Fishes of the Dukhun. By Lieut.-Col. W. H. Sykes,
F.R.S. Presented by the Author.

Notes on India before the Mahommedan Invasion. By
Lieut.-Col. W. H. Sykes, F. R.S. Presented by the Author.

Proceedings of the Royal Society. Nos. 44-48. 1840-41.

Supplemental Instructions for the Use of the Magnetical
Observatories. Presented by the Royal Society.

On the Character of Sir John Falstaff. By James O. Hal-
liwell, Esq. Presented by the Author.

A Plan of Medical Reform and Reorganization of the Pro-
fession. By Richard Carmichael, Esq. Presented by the
Author.

December 13.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The President read the following letter from the Right.
Hon. Sir John Newport, Bart., presenting to the Academy

a manuscript containing an account of the Loans of Money
to King Charles I.

‘“ New Park,
‘¢ 12th November, 1841.

*‘ T desire, Sir, to offer for acceptance of the Royal Irish
Academy, of which I have, during many years, had the
honour of being a member, a volume, which, as it respects a
most interesting period of British history, and materially
tends to elucidate transactions which had a powerful influ-
ence in producing the calamitous results, in the reign of
Charles the First, that immediately succeeded, may be
deemed not unworthy of admission into the Library of the
Institution.

‘«¢ The volume contains correct copies of the orders of the
Lords of the Council, and letters addressed to the Lord
Lieutenants of the counties of England, and others, directing
the assessment and collection of what was called a voluntary
loan, according to the annexed lists, from the several land-
holders, merchants, and merchant strangers of England, and
the citizens of the cities and towns therein, including the
judges and law officers, but specially excluding all members
of the peerage, ‘ with whom it was not purposed to deal for
the present.’

“ The original documents, of which this volume is a tran-
script, were found during the period whilst I held the office
of Comptroller-General of the Exchequer, amongst a large
collection of papers deposited in the Pells Office; and as I
considered them to afford interesting materials to elucidate
the history of that eventful period, I directed two copies to
be made of them; one of these I sent to the British Museum,
and now offer the other to the acceptance of the Royal Irish
Academy.

** The great inequality of the extent of the demand onthe
several parties thus assessed, varying in a great degree with
their capacity of resistance to its enforcement, will be quite
apparent on examining the lists; as will also the urgency of
the measure, from the repetition of the letters from the Lords

180

of the Council, at a short interval of time, deprecating further
delay, and censuring what had already occurred.

One name in the list of contributors from the town of
Cambridge, that of Hobson the carrier, celebrated by some
lines of Milton, has, from that circumstance, attracted atten-
tion, from the sum demanded and the nature of his occupa-
tion.

“‘ The original papers have been injured by damp, and
rendered in some degree, but not materially, defective.

“In order to render the papers more accessible for
perusal, I have sketched out a table of reference which I
enclose, and avail myself of the kindness of my valued
friend, the Lord Bishop of Cashel, for their transmission to
Dublin.

‘* T am, Sir,
** Your obedient Servant,

‘© Joun Newport.
* Str William R. Hamilton,

President R. I. Academy,
Sc. Se. Fe.”
The special thanks of the Academy were voted to Sir
J. Newport.

A paper was read by William Roberts, Esq., F.T.C. D.,
“on the Rectification of Lemniscates and other Curves.”

Let a curve be traced out by the feet of perpendiculars
dropped from a fixed origin upon the tangents to a given
curve: and from this new curve, let another be derived by a
similar construction, and soon. Also let acurve be imagined
which is constantly touched by perpendiculars to the radii
vectores of the given curve, drawn at the points where it is
met by these radii, and from this let another be derived by a
similar mode of generation, and so on.

Then if s, denote the are of the curve which is n in
order in the former series, and s_, that of the n” in the lat-
ter, we shall have

181

dw dw dw®*
5 alae ie f Sy) ae a | vate a
dr Cal dr) ae ( i i
———_ |r — rdr,

d 2 tn +1
ee lie

F (r, w) = 0 being the polar equation of the given curve.

ds, ——

It is convenient to distinguish the curves of the two series
by calling those of the former positive, and those of the lat-
ter negative; we may also generally denote their polar co-
ordinates by the symbols 71,, w1,.

If the given curve, which may be denominated the base
of either system, be an ellipse whose centre is the origin, it
will be found, by applying the above formula, that the nega-
tive curves will in general have their arcs expressible by
elliptic integrals of the first and second kinds, whose modulus
is the eccentricity of the base-ellipse. The arc of the first
will involve only a function of the first kind: a result which
has been given by Mr. Talbot in a letter addressed to M.
Gergonne, and inserted in the Annales des Mathematiques,
tom. xiv. p. 380.

A function of the third kind, with a circular parameter
— 1 + 0+, where is the semiaxis minor of the ellipse, its
semiaxis major being unity, and the modulus of which is the
eccentricity, enters into the arcs of all the positive curves ;
and their general rectification depends only on that of the
ellipse, and of the first derived, both positive and negative.

The quadrants of the ellipse, and of the first two curves,
positive and negative, are connected by the following rela-
tion :

(s_; + si) s_1 = (88 — S_g) (2s — 59).
V5—1
y) — Ss
the functions of the third kind disappear, and the rectifica-
tion of both series depends only on that of the ellipse and of
the first negative curve.

It is worthy of notice, that if the eccentricity be

182

If the base curve be a hyperbola, whose centre is the
origin, the arcs of all the curves of the negative series will
depend only on elliptic functions of the first and second kinds.
But the general expression for the arc in the positive series
contains a function of the third kind, the parameter of which
is alternately circular and logarithmic: the curves of an odd
order involving the same function of the circular kind, and
those of an even order the same of the logarithmic kind, if
the real axis of the base-hyperbola be greater than the ima-
ginary, and vice versa.

Mr. Roberts also shows, that besides the case of the
equilateral hyperbola, in which the first positive curve is the
lemniscate of Bernouilli, and which has been the only one
hitherto noticed, at least as far as he is aware, there are two
others, in which the arc of the first positive curve can be ex-
pressed by a function of the first kind, with the addition of
a circular arc in one case, and of a logarithm in the other.

The first of these occurs when the imaginary semiaxis is
V5—1

2

equal to (the distance between the centre and focus

being unity), and this fraction is the modulus of the function.
The other case is furnished by the conjugate hyperbola, and
the modulus is complementary. In both these cases func-
tions of the third kind disappear from the arcs of the positive
curves.

If the hyperbola be equilateral, and its semiaxis be sup-
posed equal to unity, the general equation of the derived
curves of both series may be presented under the form

2

+on—1 Qw
Hie = cos ee
a = 2n—1

The successive curves represented by this equation are very
curiously related to each other. The following property ap-
pears worthy of remark :

Let Pri, Pn; Pn4i be corresponding points on the

183

(n—1)", n', and (n+ 1)" curves of the positive series respec-

tively, and v their common vertex, which is also that of the

hyperbola, then will

2n—1

2n +
Mr. Roberts states that he has demonstrated the property

in a manner purely geometrical.

arc VPn_, + right line P,_; Px = arc VPnit

This equation shows that the arcs of all the curves of an
odd order will depend only on that of Bernouilli’s lemniscate,

or the function F { 2, ¢}, and those of an even order only
on the arc of the second of the series. This latter arc is
three times the difference between the corresponding hyper-
bolic arc and the portion of the tangent applied at its extre-
mity, which is intercepted between the point of contact and
the perpendicular dropped upon it from the centre: and the
entire quadrant is three times the difference between the
infinite hyperbolic are and its asymptot.

Also, Sn, Sn41, denoting the quadrants of the x, and
(n+ 1)" curves, the following very remarkable relation exists
between them,

Sn Sn = (Qn+ 1) Z:

The curves of the negative series enjoy analogous pro-
perties.

Lastly, let the base curve be a circle, the origin being
within it: and it appears that the rectification of the curves
of both series, which are of an even order, can be effected
by the arcs of circles ; and that those ofan odd order, which
belong to the positive series, will involve elliptic integrals of
the first and second kinds in their arcs. The negative curves
of an odd order contain a term depending on a function of
the third kind, which is however reducible to a function of
the first kind and a logarithm.

By the particular consideration of the first negative curve
in this case, Mr. Roberts was led to a very simple demon-

184

stration of the equation which results from the application of
Lagrange’s celebrated scale of reduction to elliptic functions
of the second kind, and which is nothing more than the
analytical expression of Landen’s theorem.

Professor Mac Cullagh exhibited to the Academy some
Roman Denarii, from the collection of Mrs. Alexander of
Blackheath (Coleraine).

These coins (twenty-eight in number) were found in
the year 1831, along with an immense quantity of others
of the same kind, weighing altogether about eight pounds,
by a labourer who was digging in a field on the Faugh
Mountain, near Pleaskin, one of the headlands of the
Giant’s Causeway. According to an account published
at the time in the Belfast News’ Letter (June, 1831), and
communicated to the Academy by the Rev. Dr. Drummond,
they were found under a flat stone which was turned up by
the spade. Nearly 200 of them (says this account) were sold
for a trifling sum to an English gentleman at Coleraine, and
some of the remainder were bought by the Rev. R. Alexander.
Of the twenty-eight coins that were exhibited, only seventeen
have their legends legible, and these are of the times of the
emperors, from Vespasian to the Antonines. The following
list of them has been supplied by Dr. Aquilla Smith, with
references to the catalogue of the University Cabinet, pub-
lished by the Rev. J. Malet, F.T.C.D.

1. Vespasian, . . . Malet, 384.

2. Vespasian, . . . Reverse, a winged Caduceus.
3. Domitian, . . - Malet, 452.

4. Domitian, . . . Reverse, Minerva.

5. Nerva, . . . . Malet, 467.

pees Malet, 513.

8. Trajan, . .- . . Reverse, Minerva.

9. Trajan, . . . . Reverse, a Female seated.

—
Oo

. Hadrian, . . . . Malet, 548.

185

11. Hadrian, . . . Malet, 552,
12. Antoninus Pius, . Malet, 615.
13. Antoninus Pius, . Malet, 621.
14. Antoninus Pius, . Malet, 623.
15. Antoninus Pius, Re. a Female holding a Cornucopia.
16. Faustina the Elder, Malet, 670.
17. Faustinathe Younger, Malet, 723.

Dr. Smith remarks, that the coin of Hadrian, No. 11, is
interesting, as having on the reverse a star and crescent,
resembling those on the Lrish coins of King John.

The Rev. Dr. Drummond then gave an account of other
Roman coins that had been found in Ireland; and in some
preliminary observations he dwelt on the utility of preserving
a knowledge even of such an insulated fact as the discovery
of a coin, for though of little importance in itself, it might
prompt to farther research, and lead both the historian and
antiquary to consequences which could scarcely have been
anticipated.

In England, almost every year is bringing to light various
monuments of Roman antiquity, but in Ireland they are ex-
ceedingly rare; though, perhaps, of more frequent occurrence
than is generally known. Ancient coins and other articles
have been repeatedly found by persons ignorant of their real
value, and sold as mere metal by their weight, without re-
gard to their age and character. Thus, we read in Mason’s
Parochial Survey, that in the parish of Dunaghy were found
a number of silver coins, which were sold at Ballymena be-
fore any one had an opportunity of examining or describing
them. Again, the Rev. Alexander Ross informs us, that
a person on whose veracity he could depend, assured him,
that about thirty years prior to the time of his writing, two
or three men, in digging an old fort near Cashel, found an
earthen pot, which might contain four or five quarts, filled
with gold coins of different sizes (Par. Survey, II. p. 304).

186

The same writer states that “a fine copper coin of the Em-
peror Nero was found some years ago, and is now in Mr. A.
Ogilby’s collection, the head finely relieved, and in perfect
preservation.” In the collection of the Royal Dublin Society
are three Roman copper coins of the Cesars, dug up in Fer-
managh, and presented by Sir C. Coote. But the most cu-
rious fact in connexion with the coins exhibited by Mr. Mac
Cullagh, is that of a Roman gold coin being found many
years previous, nearly in the same locality. The Rev. Robert
Trail, in his statistical account of Ballintoy (Mason’s Par.
Survey), says, “within these few days a gold coin of Valen-
tinian was brought to me in perfect preservation, and is now
in my custody. It is about the size of half a guinea, and on
the head side is the following inscription D. N. VALENTI-
NIANUS, P. F. AUG. On the reverse RESTITUTOR REIPUBLICE.
As Valentinian succeeded Jovian in 364, and died in 375,
this money must have been struck during that period, but
how it came into this parish I cannot conjecture.”—(II.
p. 155).

A single coin might be accidentally dropped and lost by
some collector or virtuoso, on his tour to the Giant’s Cause-
way ; but we cannot account in this way for a large collection
of coins of ancient date. ‘They must have been placed
where they were found, by some careful hand, probably in
times of turbulence and danger, as in a place of safety,
whence they might be removed at a more favourable season.

A few years ago, G. Putland, Esq., of Bray, had occasion
to build piers for a gate contiguous to the sea-beach, on the
north side of Bray Head. His workmen, on digging for a
foundation, were surprised to meet with the skeletons of se-
veral human bodies, which, on farther examination, they
found to be placed, not confusedly heaped together, as the
slain on a battle field, but in graves placed regularly side
by side, and separated each from its neighbour, by thin
partitions of flag or of stone. On the exposure to the air,

187

the bones crumbled to atoms; the teeth alone were more
durable, and in tolerable preservation.* The most remarka-
ble circumstance connected with these skeletons was a num-
ber of Roman copper coins, one or two of which lay on or
beside the breast of each. Of these coins, which were about
the size of our penny pieces, some bore the image and super-
scription of Adrian, and others those of Trajan, in clear and
distinct relief. Several were greatly corroded, and rendered
altogether illegible. A few of the best of these coins were
for a short time in Dr. Drummond’s possession, He shewed
them to the late lamented Dean of St. Patrick’s, who said
that he had seen a coin precisely similar, which was found
in the island of Lambay.

As the Romans never formed any settlement in Ireland,
the question naturally arises, how came these coins to be
placed in this locality, and under such circumstances? The
ready reply is, that the bodies here interred were probably
those of mariners, the crew of some Roman galley that had
been stranded and lost on the shores of Bray, and that some
of the survivors who had escaped, performed the funeral
rites. Among the Romans it was deemed an act of great im-
piety to leave a corpse unburied; and hence Horace intro-
duces the shade of the drowned Archytas, imploring the
passer by to sprinkle a little dust on his body, which had
been cast on the shores of Tarentum. Palinurus, in Virgil,
makes a similar request.

The coins, it is presumed, were the fee designed for the
grim ferryman; a part of the funeral rites of the greatest im-
portance, and by no means to be neglected, for the shades of
those who had not the proper fee, as well as of those whose

* Sir William Hamilton, in a paper in the Archzologia (vol. iv. p.161), observes
that the teeth of some skeletons of soldiers, found at Pompeii, were remarkably
sound. “ Perhaps,” says he, “ among the ancients, who did not use sugar, they

might not be so subject to decay as ours.”

VOL. Il. Q

188

bodies remained unburied, were condemned to wander a
hundred years-on the banks of the Styx.

Thus may we account for the Roman coins found at Bray;
but how shall we account for those dug up at Fermanagh, or
discovered at Dungiven, Ballintoy, and the neighbourhood of
the Giants’ Causeway ?

Though the Romans never had any permanent station in
Ireland, they were well acquainted with its geographical po-
sition, its passages, and its harbours, as we learn from the
unquestionable testimony of Tacitus; and though this and
other testimonies were wanting, it might be fairly presumed
that the Roman fleets which encompassed Great Britain,
sailed beyond the Orkneys, and boasted that they had ar-
rived at the Ultima Thule, could not be ignorant of Ireland
and its coasts, though not induced by the spirit of commerce
or adventure. ‘The mariners would sometimes be tempted to
land, if not to repair their shattered vessels, to procure wood,
water, and provisions.

Tacitus informs us that Agricola obtained information
concerning the state of Ireland, from one of its chiefs, who,
for disaffection or rebellion, had been driven into exile, and
sought refuge from the Roman commander. It is to be la-
mented that our native Irish historians, as far as the writer
has been able to ascertain, are completely dark on this sub-
ject. Though an eminent Irish scholar, profoundly versed
in our ancient MSS.,can produce one passage—but it is the
only one he ever met with—which seems to countenance
the idea that the Romans had subjected any sept of the
Irish to their yoke. He states that in discussing the means
bywhich Conor Mac Nesa, King of Ulster, and cotemporary
with Christ, discovered the crucifixion of the Saviour, a
writer, in an old Irish MS., in the library of T.C.D., says
that “ he learned it from the Druid Bachrach, or from Altus
the Consul, who came from Octavin to ask the tribute from
the Gaels.”

——

189

Roman coins might find their way to Ireland in the com-
mon intercourse of trade. ‘They may have been brought by
the early Christian missionaries, or by men who fled hither,
as to an asylum, from persecution. It is universally admit-
ted, says Lanigan, that there were Christian congregations in
Ireland before the mission of Palladius in 431, though it is
impossible to determine who first introduced Christianity.—
It is reasonably conjectured, that during the persecution of
Diocletian and Maximian, the only one recorded as having
extended to Britain, some Christians, and particularly those
of the clerical order, sought refuge in Ireland ; and it is a fair
presumption that they would bring with them such articles as
were most precious and most easily carried, among which ~
coins and jewels are the chief. There is yet another mode of
accounting for these remains of antiquity, not less plausible.
The early Irish, like the neighbouring nations, were fond of
making predatory excursions. ‘They often landed on the
shores of England and Wales, and carried off whatever spoil
fell into their hands. They also assisted their friends, the
Albanian Scots, whose country they colonized under Carbre
Riada, in their wars with the Romans, and may have
sometimes returned enriched with treasure, obtained by the
sword.

Of the spoils, by which they were sometimes enriched, it
may suffice to mention an instance, extracted from O’Fla-
herty’s Ogygia. Crimthan Nianair, the 111th Monarch of
Ireland, towards the end of the first century, returned
from a “ foreign expedition, in which he obtained a very
rich booty; among which was a golden chariot ; a pair of
tables, studded with 300 brilliant gems; a quilt, of va-
rious colours; a cloak, interwoven with threads of gold; a
sword, engraved with various figures of serpents, which were
of the purest gold; a shield, embossed with refulgent silver
studs; a spear, which always gave an incurable wound; a
sling, so unerring, that it never missed ; two hounds coupled

Q2

190

with a chain, which, being made of silver, was worth 300 cows,
with other valuable rarities.’— Ogygia, II. pp. 182-183.

The same author informs us that about the middle of the
third century, Cormac, the 126th Monarch of Ireland,
“equipped a large fleet, which he sent to the North of
Britain, where he was committing depredations for three
years.”"—p. 238.

He also states, on the authority of Ammianus Marcellinus
and Claudian, that the Saxons, in conjunction with our coun-
trymen the Scots and Picts, made frequent excursions to
Britain a long time before they made settlements in that
country. Ammianus, he says, writes that “the Scots (i.e. the
Irish) and Picts, not only invaded those places in Britain that
were adjacent to the Roman boundaries, but that in the first
year of the Emperor Valentinian, A.D. 364, a combined army
ofthe Picts, Saxons, Scots, and Attacots, reduced the Britains
to the utmost distress.” Hence, he concludes, there was a
common league between them, with intermarriages and com-
mercial intercourse.

According to Dr. Drummond, when we consider the va-
rious modes in which Roman coins may have found their way
into Ireland, the wonder perhaps should be, not that so many,
but that so few, have been discovered.

The Rev. G. Sidney Smith, D.D., M.R.I. A., read “an
Account of some Characters found on Stones on the top of
Knockmany Hill, county Tyrone.”

On the top of Knockmany hill, in the parish of Clogher,
and demesne of the Rev. Francis Gervais, there are some
interesting remains of ancient times. Besides two moats, one
internal to the other, there is an ancient chamber or kyst-
vaen, consisting of upright flag-stones, about six feet high.
It includes a space fourteen feet long by seven wide. Its po-
sition with respect to the moats is represented in the ground
plan, fig. 1. The stones marked by a darker shade are

i ANN
hig,
a RA NTA eG
f a
|
7 CS
| Fig:6 .
-| || | | | Fig:4

“Aliens Tata: J5 Gratin 3? Proceedings RL. AVol: 2. PI9O

191

standing, and those in dotted lines have been thrown down.
On five of the stones characters are found, which seemed to
be well worth copying, which I have accordingly done, and
represented them in the accompanying figures. The most
remarkable of these characters occur on the stone marked
No. 1, inthe ground plan. Those represented in fig. 2, are
on the lower part of the stone, and those in fig. 3, on the up-
per; there may have been other intermediate characters, but
they are effaced. The spiral in fig. 2, is about nine inches
in diameter, and that in fig. 3, about twelve inches. Fig. 4
represents the characters on stone No. 2, and fig. 6, those
on No. 5, on the same scale as in figs. 2 and 3; and fig. 5
represents the stones marked 3 and 4, which are six feet high.
It will be observed that in the spirals and other marks, there
is some resemblance to the New Grange characters, and in
fig. 4, we have a close approach to the Ogham. The copies
were made with great pains, and are I believe exact in the
small details.

On the difficult subject of these ancient characters little
can be done until a greater mass of facts shall have been col-
lected ; and hitherto few have been observed in the North
of Ireland. Mr.Windele and other zealous antiquarians have
prosecuted the subject in Munster with great zeal and suc-
cess.

Mr.8. Ferguson exhibited some gold beads found in the
county of Donegal.

January 10.

Rev. HUMPHREY LLOYD, D.D., Vice-President, in
the Chair.

William Andrews, Esq., John Thomas Banks, Esq., Robert
Bateson, Esq., John Burrowes, Esq., Rev. Samuel Butcher,
F. T. C. D., Fleetwood Churchill, M.D., Alexander Clendin-

192

ning, Esq., Rev. Reginald Courtenay, Durham Dunlop, Esq.,
Alexander Ferrier, Esq., Wrigley Grimshaw, M.D., Wil-
liam Hogan, Esq., William John Hughes, Esq., and William
Roberts, Esq., F. T. C. D., were elected members of the
Academy.

REso.LvED,—-On the recommendation of Council,—‘* That
henceforth, at every annual election of officers, the President
for the expiring year be considered as eligible to any one of
the Committees of Council.”

Mr. Ball, referring to his paper read before the Academy
in November, 1839, relative to a Loligo, to which he gave
the specific name of Eblane, exhibited the following Aceta-
buliferous Cephalopoda, with the view of showing the increased
knowledge of species of the Irish seas, and of placing on re-
cord the very interesting discovery of two of the genus Rossia,
which he had reason to believe had not before been noticed.
He then exhibited specimens of

1. Sepia officinalis. Dublin bay.

2. Sepia Rupellaria.? A dorsal plate, being one of three
specimens found by G. Hyndman, Esq., at Magilligan. See
Ferussac and D’Orbigny’s Cephalopoda, plate 3 of sas

3. Loligo vulgaris. Dublin, &c.

4. Loligo sagittata. Leith. Obtained by W. Bicccack
Ksq., of Belfast.

5. Loligo sagittata, var.? This was in the former pa-
per considered as a variety, but on comparison with the true
sagittata, No. 3, it seems to be a distinct species. It was
obtained by G. Allman, Esq., on the coast of Cork.

6. Loligo subulata,var.? Was obtained by John Montgo-
mery, Esq., of Locust Lodge, on the coast ofthe County Down.

7. Loligo subulata, var. No. 2. Somewhat shorter than
No. 5. Youghal, 1832.

8. Loligo media. Youghal, 1819.

193

9. Loligo media, var. - It approaches the form of sagit-
tata in the termination of its visceral sac.

10. Loligo Eblanze. Of the former paper. Obtained byT.W.
Warren, Esq., in 1836; and other specimens of greater beauty
and larger size obtained in the bays of Belfast and Dublin by
W. Thompson, Esq., and Mr. Ball. As it now appears that
the animal possesses both eyelids and a lacrymal sinus, cha-
racters not ascribed to the genus Loligo, it may require to
be placed in another genus.

11. Eledone ventricosa. Youghal, 1820, and Dublin. A
very fine specimen was found by Mrs. Lyle at Kingstown.

12. Octopus vulgaris. Plymouth, 1841. Mr. Ball.

13. Sepiola Rondeletii. Youghal, 1819. Dublin, 1829.
Mr. Ball.

14. Rossia Owenii. Was obtained in 1839 by Mr. Ball,
from a fishwoman who had found it ina Dublin bay fishing
boat. It is remarkable for the great size and distinctness
of its acetabula, which are placed on long peduncles, and may
be compared to the pearls in a diadem: they are ranged in
three rows, those of the centre row being not more than half
the diamater of those on each side; on the first pair of arms
the acetabula are more numerous, more equal in size, and
smaller than onthe others. The specific name has been given
in honour of R. Owen, Esq., the founder of the genus Rossia.

15. Rossia Jacobii. Was obtained from the same woman
as the foregoing, in 1840, by A. Jacob, Esq:, M.D., who
kindly sent it to Mr. Ball. It is much larger, but differs
considerably in its proportions from Rossia Owenii; its ace-
tabula are smaller; its arms proportionably shorter; the
membrane round the mouth forms a hexagonal figure, from
each angle of which a ridge runs, which is decurrent in six
cases ; on the second, third, and fourth pair of arms, and in
the seventh the ridge passes upon the web between the first
pair of arms, where it bifurcates, and runs out on each side.
Its specific name is given in honour of Dr. Jacob, from

194

whom Mr. Ball has in many instances received valuable aid
in zoological pursuits. The fins of both these species of Ros-
sie are like in form and position to those of Sepiola Ronde-
letii.

16. Spirula australis. Shell found at Youghal, 1820.

The following are the Measurements of the Rossic in Inches :

Rossia Rossia

4 Owenii. Jacobii.
length of bodys)... s+. “sei sucsrie sethirike ae eee
Breadth Gver; finse2 | siadcuexeh. -asosixarn 2 Ooh at
Lengthvofifin,y ola tus ai tinedisos (OM som aah ie

Extreme! breadth,iaj.disciaal&l © each pOAS math Bese
Breadth betweeneyes, . . . . . . OD . . 1:2
Extreme breadth ofhead,. . . . . Itl . . 14

Lenethyof heady): a; jnsanha wei). stoswOgeuath anole
“Length of tentacule, .. . » ye ARO: cue eames
Portion of tentacule ee is Maas.

Bula calpains. 0'9.\...7o seagules
Length of first pair ae arms, canine

from top,ofhead,.. } As genicnsel) 20 Sid) eee
Ditto, second ditto, OittO snes (2A. hose eee
Ditto, third ditto, GittOs i. ssl settee sO

Ditto, fourth ditto, Gittoiss, 2:3), xobteaahoee

Depth of fin between first pair ofarms, 0-2 . . 0-4
Ditto, first and second do. 033 . . 0°53
Ditto, second and third do. 0-42 . . O6
Ditto, third and fourth do. O4 . . O8
Ditto, fourth do. 0°04 . . 0:03

William Roberts, Esq., F.T.C.D., read a paper on a class
of spherical curves, the arcs of which represent the three
species of elliptic transcendents.

A cone of the second order, whose vertex is upon the
surface of a sphere, and one of whose principal axes is a
diameter, will intersect the sphere along a curve which ad-

195

mits of several varieties, according to the nature of the sec-
tions of the cone parallel to its principal planes, and the
position of its internal axis. This curve may be made to
furnish, by means of its arc, a geometrical representation of
the three species of elliptic trancendents, including the two
cases of the third.

In the course of the investigations alluded to, Mr. Roberts
was also led to consider two species of the curve called the
spherical conic, which appear to possess many remarkable
analogies to the properties of the equilateral hyperbola.
These cases occur when the axis minor is a quadrant, and
when the semi-axes a and bare connected by the relation

sin a = tan 6.

The following extract of a letter from Andrew Dur-
ham, Esq., to the Marquess of Downshire, was read to the
Academy by Sir William Betham, with his Lordship’s per-
mission :

‘* Belvedere, Lisburn,

** 29th December, 1841.
“* My Lorp,

“* As your Lordship and party were prevented from at
tending the interesting search at Drumboe Tower, I beg
to inform your Lordship that about seven feet below where
we commenced excavating, we found a skeleton, in situ, lying
by compass N. W. by W.., wanting both legs and feet from
the knees, and also the right arm. The earth we removed
was of a blackish colour, as if composed of decomposed vege-
table matter, full of stones, many of which, from the mortar
on them, must have fallen from the top and the entrance,
which is about five feet from the external level; and on the
eastern side, it also abounded in bones of different animals,
and a few bones seemingly of black cattle. Under this earth
we came to a surface of mortar; this induced us to proceed
still more cautiously ; and immediately under this mortar we

196

first discovered the skull, in good preservation, together with
the teeth ; we then laid bare the whole body, a work of no
little difficulty, from the wetness and adhesiveness of the soil.
We were much inclined to leave the body as we found it, but
were obliged to raise it to continue our search. We excava-
ted to the very foundation of the Tower, without finding any-
thing else, with the exception of many pieces of charcoal.
The skull was lying on the right side, and the dorsal and cer-
vical vertebrae were considerably decomposed.

** The diameter of the Tower inside is nine feet. The
skeleton was not placed exactly in the centre, but the head
was so near the side that there would have been room suffi-
cient for the body with its legs and feet, had it been placed
in the centre. The mystery seems increased by the want of
the arm. None of the bones found had been acted on by fire.

“ There was no flag-stone, nor floor either above or below
the body. The layer of mortar seems intended as a substi-
tute for a floor.

“« There were several jawbones, apparently pigs’, from the
size of the tusks; but no skulls, with the exception of one of
a bird.

“‘ The external circumference of the Tower is fifty-one
feet; the wall being four feet thick.

“ T believe I have mentioned every thing of importance;
I leave others to draw conclusions.”’

Sir W. Betham stated that he considered this tower had
been opened before, and that the skeleton was then dislocated.
The propensity of searching for treasure may have led to the
violation of this tomb, asit had to that ofothers, as Cashel, from
which the bones had all been removed; but at Ardmore and
Cloyne the skeletons were found really én situ; the floor of mor-
tar, both above and below, being perfect. The Tower of Aber-
nethy in Scotland has also been examined with the same re-
sults as at Ardmore and Cloyne. The stones, with mortar
attached to them, found in Drumboe, were certainly part of

197

the concrete course of mortar covering the earth in which the

body reposed, which was broken up by the violaters of the
tomb.

A notice of the occurrence of a Metallic Alloy in an un-
usual state of aggregation and molecular arrangement, was
read by Robert Mallet, Esq., M.R.I. A.

Amongst the several classes of substances which chemistry
at present considers as simple, the metals stand preeminently
marked by their almost invariable possession of a nearly fixed
and striking group of sensible qualities, which together con-
stitute the well known “ metallic character.” Some of these,
such as lustre and fusibility, are common to every metallic
body; but by the occasional variation of nearly every other
sensible quality of the metals, the law of continuity remains
unbroken, which unites them in different directions with the
other classes of material bodies. Thus opacity, which is pro-
bably mechanically destroyed in gold leaf, is lost in selenium;
and so, in this most prevalent of their properties, the metals,
through tellurium, selenium and sulphur, become translucent,
and mingle with the nonmetallicelements. Soalso their solidity,
at common temperature, is lost in mercury; their great den-
sity, in sodium and potassium ; their malleability, in bismuth,
antimony, and arsenic; while in tellurium, the power to con-
duct electricity is nearly wanting; and, lastly, hydrogen, to
all intents a metal in its chemical relations, yet possesses not
a single physical quality in common with these, but exists as
an invisible and scarcely ponderable gas.

But although differen¢ metals thus vary in sensible quali-
ties, those which collectively belong to the same individual
metal are as remarkable for their permanence.

Unless selenium be admitted to be a metal, no approach
to dimorphism has hitherto been recognized in any body of
the class ; the only case recorded, that by Dufresnoy, of the
occurrence of cast iron in cubes and rhomboids, not having

198

been given by him with certainty, nor since verified by other
observers. Hence any instance of such acharacter, or tendency
towards it, is worthy of attentive consideration ; andit was with
this view that the author brought before the Academy the
following notice of the occurrence of an alloy of copper, in
two states, having totally different sensible and physical
qualities, while identical in chemical constitution. The alloy
in question, in its original or normal condition, was in fact a
species of brass; and the particular specimen presented to
the Academy was a portion of one of the brass bearings, or
beds, in which the principal shaft of a large steam engine re-
volved.

The bearing, or bed of a shaft (as is generally known),
consists of a hollow cylinder, generally of brass, divided in
two by a plane passing through the axis; its inner surface is
finely polished, and sustains the shaft, during its revolution,
which is also polished; the cavity of the brass being com-
pletely filled by the shaft, which, in the present instance, was
of cast iron, and about nine inches in diameter.

It frequently happens, notwithstanding the polish of both
metallic surfaces, and the application of oil, that the friction
due to their rapid passage over each other, while exposed to
undue or irregular pressure, produces a considerable rise of
temperature, and the brass becomes abraded. Its particles
have no coherence, and much resemble the “‘ bronze powder”
used by painters.

In an instance, however, which some time since came
under the author’s notice, a different result took place. The
minute particles of abraded brass were by the motion of the
shaft, during a few hours, impacted into a cavity, at the junc-
tion of the two semicylinders of the bearing, where they be-
came again a coherent mass, and when removed presented all
the external appearance of an ingot or piece of brass, which
had been poured in a state of fusion into the cavity. On
more minute examination, however, the mass was found to

199

differ much in properties from the original brass, out of which
it was formed.

The mass or ingot of brass, thus formed by the union of
particles at a temperature which had never reached that of
boiling water, and a fragment of which was presented, pos-
sessed on that side which had been in contact with the shaft,
a bright polished metallic surface, like that of the original
metal from which it had been formed: its other surfaces bore
the impress of the cavity in which it was found. It was hard,
coherent, and could be filed or polished like ordinary brass.
It was, however, perfectly brétt/e; and when broken, the frac-
ture, in place of possessing asub-crystalline structure, and me-
tallic lustre, like that of the normal brass or alloy, was nearly
black, and ofa fine grained earthy character, and without any
trace of metallic lustre or appearance.

Examined with a lens, some very minute pores or cavities
are found throughout its substance, which is uniformly of a
very dark brown or nearly black colour, and devoid of all me-
tallic character, except when cut or filed—that is, in mine-
ralogical language, its colour is earthy black, and its streak
metallic.

The author remarked that the observed cases of aggrega-
tion in solid particles, without the intervention either of a sol-
vent or of fusion, are extremely rare, and as bearing upon the
little understood subject of cohesive attraction, are of much
interest.

The property of welding, which is possessed by all bodies,
whether metallic or not, which pass through an intermediate
stage of softness or pastyness previous to fusion, and is not
found in any substance which readily crystallizes, and hence
passes ‘‘ per saltum” from the solid to the liquid state by
heat, forms a “ frontier instance” of cohesive forces, being
enabled to act in the aggregation of bodies, by only an
approach to liquidity, or by a very small degree of intermo-
bility.

200

Aggregation may also take place between portions of a
body merely softened by a solvent, which is afterwards with-
drawn, as in the familiar instance of Indian Rubber, softened
by naptha for the manufacture of waterproof cloths; where
the former, after being moulded or united in any way re-
quired, is left in its pristine condition by the evaporation of
the naptha from amongst its particles. But the cases of
aggregation of solids, without such elevation of temperature,
or the presence of solvents, are so rare, that but two or three
have as yet been observed. Of these the most remarkable
is that recorded by Pouillet, of the gradual, but complete,
adhesion of surfaces of clean plate-glass, when left to re-
pose on each other for a considerable time. It has also been
stated, that clean plates of lead or of tin, if pressed together
by a considerable force when cold, require a proportionably
great force to separate them. The case presented to the
Academy, therefore,is another added to these rare instances
of molecular aggregation in solids, independent of solution
or fusion: the author therefore thought it worth while to
examine with a little care the properties both of the original
brass, and of the mass thus curiously formed from it, or, as
he thenceforth called them, of the normal and the anomalous
alloy.

The normal alloy is of a bright gold colour, and sub-cryscal-
line in structure, and of great toughness; its cohesive force is
equal to 21.8 tons per square inch, which is above the average
strength of any of the alloys of copper and zinc, or copper
and tin, as found by my experiments on the cohesive power
of these alloys, published in the Proceedings of the Academy,
and elsewhere. The cohesive force of the anomalous alloy
is only 1.43 tons per square inch, or only about one-fifteenth
that of the former.

The specific gravity of the normal alloy is = 8.600; that
of the anomalous only = 7.581.

201

On submitting both alloys to analysis, their constitution
proved identical; it is as follows:

Copper’... 9: : « . 83,523
pine ee ARSENE! 1B. BSS
RTE OP ta ee ETB LO
Merde MELO hie Lee OOa4
Hass Peale Sk ONO

100.000

Uniting the small amount of lead with the tin, and dividing
by the atomic weights, the nearest approach to atomic con-
stitution is,

Copper = 26.3 atoms.
Zinc = 2.3
Tin = 1.5

These alloys have therefore not a strictly definite constitution,
but one more nearly so than is usually found in commerce.
Both alloys are equally good conductors of electricity.
The author examined their relative powers of conducting heat
by the method which Despretz has employed with so much
accuracy, and found that of the normal to that of the anoma-
lous alloy as 36: 35, numbers which are so nearly equal as
to render it likely the difference is only error of experiment.
He also endeavoured to determine their relative specific
heats, using the method of mixture, which was the only one
which the small size of the metals permitted, and eliminating
the errors incident to this mode by first plunging the alloy
hot into cold water, and then cold into hot water. In this
way, if
wand ¢ = the weight and temperature of the water,
m and ¢’ = the weight and temperature of the metallic alloy,
m... . = the mean temperature of both,
s.... = the specific heat of the alloy,

there are two values, one where the metal is the hotter,

202

_wi(m—t)
~ M (é’/—m)’

and another where the water is the hotter body,

ea (¢{ — m)
~ M(m—t)’

the mean of which is the specific heat of the alloy pretty
exactly. The result gave the specific heat of the normal
alloy = .0879, water as unity, and that of the anomalous
alloy = .0848; both of which are below the specific heat as-
signed by Dalton to brass.

The normal alloy is malleable, flexible, ductile, and la-
minable. In the anomalous alloy there is an absolute negation
of all these properties.

The normal alloy readily amalgamates with mercury, at
common temperatures ; the anomalous alloy will not amalga-
mate with mercury even at 400° Fahr.

When the anomalous alloy is heated to incipient redness
in a glass tube, a minute trace of water, and of a burned or-
ganic substance, probably adherent oil, are discoverable; it
suffers no change, however, but a slight increase of density.
The normal alloy suffers no change when so treated. The
normal alloy, treated on charcoal with the blow-pipe, fuses
at once into a bead. On treating the anomalous alloy so,
the fragment swells rapidly to more than twice its original
bulk, on becoming bright red hot; it then glows, or becomes
spontaneously incandescent, in the way that hydrated oxide
of chrome and some others do, and instantly contracts to less
than its original bulk, and becomes a fluid bead, which, on
cooling, differs in no respect from the original alloy.

The anomalous alloy, when pulverized in an agate mor-
tar, forms a black powder, devoid of all appearance of a
metal; its filings also are quite black; while those of the
normal alloy, produced by the same file, possess the usual
metallic lustre. ‘These facts, in connexion with the black

Se ee

203

colour and fine earthy appearance of the fracture, bring to
mind the case recorded by Sir David Brewster, of a piece
of smoky quartz, the fracture of which was absolutely
black, and yet was quite transparent to transmitted light,
and whose blackness, he found, arose from the surfaces
of fracture, consisting of a fine down of short and slen-
der filaments of transparent and colourless quartz, the dia-
meter of which was so small (not exceeding the one-third
of the millionth part ofan inch), that they were incapable
of reflecting a single ray of the strongest light. In describing
this, Sir David Brewster predicted, that “ fractures of quartz
and other minerals would yet be found which should exhibit
a fine down of different colours depending on their size.”

It seems, therefore, extremely probable, that the cause of
the near approach to blackness in the fracture and filings of
this alloy, arises from the excessive minuteness of its parti-
cles, and thus fulfils the foregoing prediction; the brownish
tinge being produced by the reflexion of a little red light.*

The polish and power of reflecting light of the anomalous
alloy are not quite so great as those of the normal, but are
still remarkable ; and, as it seemed a matter of some interest
to determine whether both reflected the same quantity or in-
tensity of light at equal angles, the author endeavoured to
ascertain this point as respects heat, by means of Melloni’s
pile for the galvanometrical determination of temperature,
assuming, as suggested to him by Professor Mac Cullagh,
that what would be true of heat in this respect, would also be
so of light; but from the small size of the reflecting surfaces
he had at his command, he found it impossible to arrive at

* Since this paper was read, Professor Lloyd suggested to the author, the ana-
logy between the appearance of the powder and filings of the anomalous alloy and
Platina Mohr, and those powders obtained by reduction of other metals by hydro-
gen. None of these, however, are coherent, which constitutes the peculiarity in
the present case.

VOL. IT. R

204
any trustworthy result. He is, however, inclined to believe,
that both metals reflect most at a perpendicular incidence.

From the foregoing detail of the properties, in several
respects so different, of this substance in its normal and ano-
malous states, the author thinks he is warranted in pro-
nouncing it the first observed instance of an approach to
dimorphism in a metallic alloy; and one, the mode of pro-
duction and characteristics of which present several points
of interest.

The conditions under which the alloy was aggregated,
involved extremely minute division of the metal, great pres-
sure in forcing the divided particles into contact, and nearly
the exclusion of air. Considerable electrical disturbance
may have also co-operated; such, together with induced mag-
netism, being the constant accompaniments of motion in
heavy machinery. By re-establishing these conditions, under
suitable arrangements, the author hopes to repeat the re-
sults thus accidentally first obtained, and so produce possibly
dimorphous states of other metals or their definite combina-
tions.

There is but one body which occurred to the author,
presenting an analogy to this anomalous alloy, namely, indigo ;
whose fracture, it is well known, is fine earthy, and of the
usual blue colour, but becomes coppery, or assumes the me-~
tallic lustre on being rubbed or burnished.

DONATIONS.

Uber den Galvanismus gegen ortliche Krankheiten, von
Dr. Gustav Crusell.

Recueil des Acts de la Seance Publique de l Académie Im-
periale des Sciences de St.Petersbourg, tenue le 29 Decembre,
1840.

Memoires de ? Academie Imperiale des Sciences de St.
Petersbourg. 6™° Série. Sciences Politiques, §c. TomelY.
Livraison 6, and Tome V. Livraisons 1-4.

205

Sciences Mathematiques, §c. Tome lV. Premiere par-
tie, Livraisons 5° et 6°™°; Tome VI. Seconde partie,
Livraisons 1-5.

Proceedings of the Committee of Commerce and Agricul-
ture of Royal Asiatic Society, 1841.

Journal of the Royal Asiatie Society. No. 12.

Prelection on the Studies connected with the School of
Engineering in Trinity College, Dublin. By the Rev. Hum-
phrey Lloyd, D.D. Presented by the Author.

The Chronicle of William de Rishanger. By Richard
O. Halliwell, Esq., Hon. M.R.I.A., &c. Presented by the
Editor.

Ordnance Survey of Wexford, in eighty-six sheets. Pre-
sented by the Lord Lieutenant.

Sketch of the Loan Fund System in Ireland. By Charles
Piesse, Esq. Presented by the Author.

Catalogue of the Miscellaneous Literature in the Library
of the Royal Society. (1841).

Proceedings of the Royal Society, 1841. Nos. 46-50.

Supplemental Instructions for the use of Magnetical Ob-
servatories. 1841.

Phil. Transactions for 1841. Parts 1 and 2.

Edinburgh Astronomical Observations. Vol. 1V: 1838.

Memoires de l Académie Royale des Sciences de U Institut
de France. Tome XII.

Memoires présentés par divers savans a l Academie des
Sciences Mathematiques et Physiques. Tome IV.

The American Almanack for 1842.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1842. No. 33:

January 24.

Rev. HUMPHREY LLOYD, D. D., Vice-President, in
the Chair.

ReEsotveD,—On the recommendation of Council,—That
it shall be the duty of the Committee of Publication to report
on Papers intended for publication in the Transactions.

ReEsoLtvED,—On the recommendation of Council,—That
the Treasurer be authorized to sell stock of the Academy to
the amount of £300, for payment of the Printer’s bill and
other arrears.

The Rev. Charles Graves, F.T.C.D., read a paper “on
the Motion of a Point upon the Surface of a Sphere.”

When the motion of a material point is limited to a given
plane, the circumstances of its motion are commonly investi-
gated by means of the equations,

ROP sas) Nei = ay;

x and y being rectangular coordinates in the given plane.
Mr. Graves shows that, in like manner, the motion of a ma-
terial point, constrained to move on the surface of a sphere,
whose radius = 1, may be discussed by means of the similar
equations,

VOL, Il. s

208

a =) (1) ere ae (2)

in which x and y are used to denote the rectangular spheri-
cal coordinates of the moving point (vid. page 127), and x, y,
the moments, in the planes of the a and y arcs of reference,
of the resultant of the forces acting upon the point. The re-
action of the surface being taken into account, this resultant
is tangential to the sphere, and so may be conceived to act
along a great circle passing through the point.
From equations (1) and (2) we derive a third,

ae
1+ a? + y?

which leads to important consequences.

(xy —yx) dP =d ( (3)

It appears from the second formula in p. 129 that, if the
equations (1) (2) and (3) be multiplied respectively by

2dx 2dy {1 2(ydx—ady)
lHarty? l4a?ty” La? +y?’

they will give for the velocity, v, of the moving point,

pele xdy)| ai A i —yda)] (4)
l+27+y°

Now, if the resultant tangential force r act always along
a great circle which passes through the origin, that is, if we
consider the case analogous to that of a central force in the
dynamics of the plane,

a @appP and y =

vant filinor
eG 7 “@+y)
In this case, therefore, which for simplicity we may call that
of a central force, equation (3) gives

ydx — xdi
ee - = hdt, (5)

and equation (4) is reduced to

209

9 xdx Hh ay sige (6)
ea

It is easy to show that these two latter equations are equiva-

lent to the two following,

sin’pdw = hdt, (7)
2hrdp =e’, (8)

in which p is the vector arc drawn from the origin to the
moving point, and w is the angle between it and the 2 arc of
reference. Let us now describe the circle of the sphere
which osculates the trajectory along which the point Pp moves,
and let c be the arc of the great circle passing through P
and the origin, and intercepted within the osculating circle;
then it may be shown that

v
R = ——. 9
tan3c )
If p denote the arc of the great circle drawn from the origin
perpendicular to the arc touching the trajectory at Pp, we may

deduce from (7) that
‘Sapa ts (10)

sin? p’

By the help of equation (9) it may be proved that “A
material point may be made to describe a spherical conic if it
be urged by a force, acting along the arc of a great circle
drawn from the focus to the point, and varying inversely as
the square of the sine of the vector arc p.”

Also: ‘‘ A material point may be made to describe a
spherical conic by the agency of a force, acting along the arc
of a great circle drawn from the centre to the point, and vary-
ing as tanp sec’p.”

In the dynamics of a point constrained to move on the
surface of a sphere, we have, for the discussion of the inverse
problem of central forces, the following equation,

s2

210

R = W?(1 4+?) («4 55),

in which zw is the cotangent of p.

The analogy between the formula given in this paper and
those usually employed in discussing the motion of a point
on a plane is very striking. The former too become identical
with the latter when the portion of the sphere on which the
trajectory is described becomes infinitely small in comparison
with the radius.

The Rev. H. Lloyd V. P. read the following paper “ ona
New Magnetical Instrument, for the Measurement of the In-
clination, and its Changes.”

In order to know all that relates to the earth’s magnetic
force, at a given place, observation must furnish the values of
three elements. Those which naturally present themselves
for immediate determination are, the intensity of the force
itself, and the two angles (the declination and inclination)
which determine its direction. We may substitute for these,
however, any other system of elements which are connected
with them by known relations. Thus, we have hitherto pre-
ferred to observe the declination, and the two components
(horizontal and vertical) of ihe intensity; and, in general,
the main considerations which should guide us in our choice
are, the exactness of the observed results, and the facility of
their determination.

In this point of view, the declination and the horizontal
component of the intensity leave us nothing to desire, their
determination being now reduced to a degree of precision,
hardly (if at all) inferior to that of astronomical measure-
ments. The same thing, however, cannot be said respecting
the third element, as hitherto observed. In the Dublin
Magnetical Observatory, and in the Observatories since es-
tablished by order of the Government and of the East India
Company upon the same plan, the third element chosen for

ae ee

211

observation has been the vertical component of the intensity,
the instrument for the measurement of which has been al-
ready submitted to the notice of the Academy. The prin-
ciple of this instrument, it will be remembered, is to balance
the vertical component of the magnetic force by a fixed
weight, and to observe the changes of the position of equili-
brium, under the action of the changing force. Unexcep-
tionable as this principle is in theory, the accuracy of the
results has not been commensurate with that of the other
two instruments. ‘This inferiority is to be traced to the
large influence which the unavoidable errors of workman-
ship must necessarily have on the position of equilibrium of
a magnet supported on a fixed axle. It has been shown that
the effect of magnetizing a bar, under the most advantageous
circumstances of form, and at the part of the globe where
the vertical component of the magnetic force is greatest, is
the same (as to its position of equilibrium) as if its centre of
gravity had been transferred about the ,,th of an inch to-
wards the north end; so that the moment of the force,
exerted by the vertical component of the earth’s magne-
tism, can never exceed this small quantity multiplied by the
weight of the bar. Now, in order to render the results of
this instrument comparable to those of the horizontal-force
magnetometer, it should enable us to measure changes of
the vertical force, amounting to the +5;4555dth part of the
whole; i. e. we have to measure effects, such as would be
produced by shifting the centre of gravity through the one-
millionth of an inch. It will be easily understood, from this
statement, how great must be the effect of a minute distur-
bance of the relative parts of the instrument, or of inequalities
in the bearing points of the axle; and experience has ac-
cordingly shown that it is altogether unavailable for the de-
termination of changes of long period.

_ The same difficulties, and from the same source, have
been found to attach to the usual method of observing the

212

magnetic inclination, and its changes, however refined the
construction of the instrument. ‘The sources of error seem,
in fact, to be inherent in every direct process of determining
the third element; and it is only by an indirect method that
we can hope to evade them.* Of this characteris the method
now proposed.

If a soft iron bar, perfectly devoid of magnetic polarity,
be held in a vertical position, it immediately becomes a tem-
porary magnet under the inducing action of the earth’s mag-
netic force, the lower extremity becoming a north pole, and
the upper a south pole. Accordingly, if a freely-suspended
horizontal magnet, whose dimensions are small in comparison
with those of the bar, be situated near, in a plane passing
through one of these poles, it will be deflected from the
magnetic meridian. The deflecting force is the induced
force of the bar, which may be regarded as proportional to
the energy of the inducing cause, i. e. to the vertical compo-
nent of the earth’s force; while the counteracting force is
the horizontal component of the same force, acting directly
on the magnet itself, to bring it back to the magnetic meri-
dian. Thus the magnet will take up a position of equili-
brium, under the action of these opposing forces; and this
position will serve to determine the ratio which subsists be-
tween them. When the right line connecting the centre of
the horizontal magnet, and the acting pole of the bar, is
perpendicular to the magnetic meridian, the tangent of the
angle of deflection will measure the ratio of the two forces,
and will therefore be proportional to the tangent of the mag-
netic inclination. Accordingly, by observing the changes of

* Two such indirect methods of determining the inclination have been pro-
posed in Germany, one by Professors Gauss and Weber, the other by Dr. Sar-
torius von Walterhausen. That now suggested bears a close analogy, in principle,
to the former of these: it differs from it, however, not only in the means em-
ployed, but also in the end in view,—the main object of the present method

being the determination of the inclination-changes.

213

position of the horizontal magnet, so circumstanced, we can
infer those of the inclination itself.

But the iron bar may have (and generally will have) a
certain portion of permanent magnetism, which will concur
with the induced magnetism in producing the deflection;
and it becomes necessary to institute the observations in
such a manner, as to be able to eliminate the effects of
this extraneous cause. For this purpose we have only to
invert the bar, so that the acting pole, which was uppermost
in one part of the observation, shall be lowermost in the
other. The induced polarity will, under these circumstances,
be opposite in the two cases; and the acting force will in one
case be the sum of the tnduced and permanent forces, and
in the other their difference.

Let x and y denote the horizontal and vertical compo-
nents of the earth’s magnetic force, m the intensity of the
permanent magnetism in the acting pole, and m the magnetic
moment of the suspended magnet. The intensity of the in-
duced magnetism is, by hypothesis, equal to

ky,
i being an unknown constant; and when this is of the same

name as the permanent magnetism, the intensity of the act-
ing force, at the unit of distance, is

Ay + M.

Accordingly, the moment of this force to turn the suspended
magnet is (ky + m) mr cosu, u being the angle of deflection,
and 7 a constant depending on the distance; or, making, for
abridgment, kr = p, mr = q,

(py + q) mcosu.

But this deflecting force is resisted by the earth’s horizontal
force, the moment of which to turn the magnet is

Xm sin u ;

214

and the magnet will rest when these moments are equal.
Hence the equation of equilibrium is

pyr + q=xtanu. (1)

By the same reasoning it will appear, that when the induced
and permanent magnetisms are of contrary names, there is

py —g=xtanw; (2)
in which w’ is the new angle of deflection when the bar is

inverted. And adding these equations together, and ob-
serving that y = x tan@, 6 being the inclination, we have

2p tan = tanu + tanw’. (3)

This equation would furnish at once the inclination sought,
provided we knew the value of the constant £. In order to
determine it, we have only to place the iron bar horizon-
tally in the magnetic meridian, its acting pole remaining in
the same place as before, but pointing alternately to the north
and south. The inducing force is, in this case, the horz-
zontal component of the earth’s magnetic force; and it will
be readily seen that the equations of equilibrium are similar
to (1) and (2), substituting x for y. If therefore v and v’
denote the angles of deflection in these positions, we have

2p = tanv + tanv’; (4)
and dividing (3) by this,
tanw + tan w’

tan? = :
tanv + tanv’

(5)

Thus, from the deflections produced in these four positions
of the bar, we obtain the inclination. |

In order to determine the changes of the inclination, it is
not necessary to observe the deflections in the horizontal po-
sition of the bar. Let equation (1) be differentiated, x, y,
and w being all variable, and-let the resulting equation be
divided by (3). We thus obtain the following equation, from
which p and q are both eliminated :

215

ANe sc 2 Au 2 tanu Ax
¥ cos’u(tanu-+tanw) tanu+tanw’” x”

But from the relation y = x tan@, we have

Ay» AX AO}
SE sin @ cos @”’
and substituting,
AB oi) peosm Au 41 sin (wz — wu’) Ax
sin20 7” cosusin(u+u') © *sin(u+u’) x”

(6)

The second term of the right-hand member of this equation
contains a correction required for the simultaneous changes
of the horizontal intensity ; but this correction will be gene-
rally small, and, when the bar has no permanent magnetism,
will vanish altogether. In this latter case, in fact, it appears
from (1) and (2) that wu’ = «3; so that the preceding equation
is reduced to

sin 20
hance Qu a

(7)

We must remember that the angle w in the preceding
formule, being the deviation of the suspended magnet from
the position which it would assume under the action of the
earth alone, its changes are the differences between the ob-
served changes of position of the suspended magnet, and the
corresponding changes of declination. Let a denote the de-
viation of the suspended magnet, measured from some fixed
line, and a’ the corresponding angle when the iron bar is
removed; then

u=a—a, Au= Aa— Ad’.

But Aa = kn, Aa’ = k’n’; in which x denotes the number of
divisions of the scale of the instrument corresponding to the
angle Aa, n’ the number corresponding to the angle Aa’, as
shown by the declinometer, and & and #’ the arc-values of a
single division in each instrument. Hence

Au = kn — k’n’'. (8)

216

I now proceed to the construction of the apparatus em-
ployed in these measurements.

The magnet is cylindrical; its length is three inches,
and diameter one-fourth of an inch. A mirror is attached to
the stirrup by which it is suspended, by means of which the
varying position of the magnet may be observed with a
telescope at a distance, after the method of Gauss. This
mirror is of course vertical; and it has a motion round a ver-
tical axis, by means of which it may be adjusted to any de-
sired position of the observing telescope. The mirror ‘is
circular, and is three-fourths of an inch in diameter. The
moveable part of the stirrup to which it is attached has the
form of a cross; and it is rendered vertical by means of three
screws, near the extremities of three of the arms of the
cross, the heads of which project and hold it. The mirror
is maintained in contact with these heads by springs at the
back.

The box is octagonal; the interval between the opposite
sides is four inches, and that between the top and bottom
twoinches. The top and bottom, and the connecting pillars,
are formed of gun-metal; the eight sides are closed by
moveable pieces, three of which are of glass, and the rest of
ebony. To the top of the box is attached an upright tube
of glass, eight inches in length, which encloses the suspen-
sion thread. The suspension apparatus at the top of the
tube is of the usual construction; the circular piece to which
it is attached has a movement of rotation, and its outer sur-
face is graduated to 5°, for the purpose of determining the
effect of torsion of the suspension thread.

The base of the instrument is a circle of gun-metal, six
inches in diameter, graduated on the edge. ‘The box is
connected with this circle by a short conical stem, forming
the axis of a second plate, which revolves upon the fixed
one. This moveable plate carries two verniers, by which
the angle of rotation may be read off to minutes. Two

217

tubular arms, slightly inclined to one another, are attached
to this plate; and their other extremities are connected by a
cross-piece, which carries a short scale at a distance of
eighteen inches from the mirror. This part of the apparatus
is employed in determining the total angles of deflection.

The soft iron bar is a cylinder, twelve inches long, and
three-fourths of an inch in diameter. One of its extremities
is enclosed in a hollow cylinder of brass, connected with a
horizontal pivot which revolves in a fixed socket. The axis
of this pivot being in the line passing through the centre of
the suspended magnet, and perpendicular to the magnetic
meridian, it is obvious that the bar has a movement of rota-
tion in the plane of the magnetic meridian itself. The dis-
tance of the axis of the bar from the centre of the magnet is
about five inches; and it is so placed that. the induced pole
is in the direction of the axis of the pivot, and thus remains
fixed during the movement of the bar.

The changes of position of the suspended magnet are
observed at a distance by means of a fixed telescope and
scale. The scale, whose divisions are reflected by the mir-
ror, is attached above the telescope to the support near the

eye-end.

Dr. Fulton made some observations on Grecian and Ro-

man Architecture.

February 14.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Captain Stirling, 73rd Regt., Rev. Thomas Stack, F.T.C.D.,
Joseph Nelson, Esq., Q-C., and Rev. Robert Chatto, were
elected members of the Academy.

Dr. Anster read a paper, by the Rev. J. Wills, upon
Mr. Stewart’s attempt to explain certain processes of the

218

Human Understanding, on the supposition that it acquires,
by habit, an acceleration in the succession of ideas, so
great as to escape the consciousness.

After having observed that Mr. Stewart’s error consisted,
not in his reasoning, but in having failed to observe that his
facts are themselves complex results which demand a minute
analysis, and having also dwelt upon some elementary errors
to which he mainly attributed the entire of Mr. Stewart's the-
ory, the author proceeded to a detailed investigation of the
several examples brought forward in its support.

He first stated the case of a player on the harpsichord,
whose rapidity of execution is adduced to illustrate the pro-
position that so many separate acts of will and attention, as it
seems to involve, are so accelerated as to take place without
any consciousness of their separate occurrence. On this
he observed, that, to a very great extent, the separate acts
assumed could have no existence, by reason of the absolute
coincidence, in point of time, of the rapid and complex move-
ment of the musician’s hand; from which he inferred, that
some other law must be sought for to explain the phenomena.
To discover this law, the author proceeded to examine the
process of the mind in the acquisition of the art by which
the complex and simultaneous movements are effected. These
are, he observed, first separately attended to and separately
executed; but so long as this separateness continues, it is
evident that the required result is not attained. Slowly,
however, and by frequent repetition of the same set of ideas
presented in combination, this combination itself becomes the
object of perception; and from being separate ideas and
movements, they become simultaneous, and assume the new
form of a single complex conception, executed by a complex
movement. In confirmation of this inference, he observed,
that the slightest attempt to attend to any of the component
parts would disconcert the best skill. He also observed,
that Mr. Stewart had been in some degree misled by having

219

generally fixed his attention on examples in which the com-
ponent ideas are successive in the order of occurrence. He
observed upon a considerable class of cases which are deci-
sive against Mr. Stewart, being composed of very complex
acts, of which the separate parts are never recognized, such
as the class of movements called ‘‘ mechanical.”

The author next entered on a detailed view of Mr.
Stewart’s example of a person reading, and showed that the
same reasoning is applicable. He noticed the complica-
tion of trains of thought, which, according to Mr. Stewart’s
theory, must be simultaneously proceeding; and alsoobserved,
that his theory could not stop short at any point of these;
and that wherever he might attempt to stop, an explanation
should be given, which ought to supersede his whole theory.
He then pursued the inquiry as in the previous example, by
investigating the mind’s progress in learning to read, and de-
duced similar conclusions. These he also confirmed, by
noticing the various errors which occur in reading and print-
ing; of these he showed, that they illustrate the effect of the
combinations or complex conceptions previously formed to
supply even the want of many of the component parts; so
that the letter is inferred from the general form of the sylla-
ble, and the syllable from that .of the word, rather than the
contrary process. From this example he concluded, that the
mind, by repeated acts of attention, acquires a stock of syl-
labic and vocal associations, of which the act of reading is a
combined result; that by a further extension, written. sen-
tences may become combined with a process of thought, and
that every reader possesses some range of thought thus
symbolized by habit; and finally, that the general inference
to be drawn from this and other similar examples is, that by
means of habit, groups of signs, of movements, facts, thoughts,
sensations or phenomena, may acquire varied relations to each
other; and that these being acquired, the combination alone
becomes the object of notice. He then pursued the applica-

220

tion of the same reasoning to some other examples, not no-
ticed by Mr. Stewart, which he observed were better adapted
for illustration ; and then proceeded to notice briefly the ap-
plication of the same principles to the other examples adduced
by Mr. Stewart.

He then reverted to an explanation of Mr. Stewart’s and
of other writers, concerning the perception of the distance of
visible objects; and after noticing the fallacy which it: in-
volved, he showed it to be explicable by the same general
process as in the former cases.

He next observed that the numerous errors arising from
the same law of habit might be made use of to illustrate or
prove the same conclusions ; and explained, at some length,
the illusion of faces and other visual phenomena framed by
the imagination.

After several observations on the comparative difficulties
of Mr. Stewart’s method and his own, the author noticed the
distinction between the previous cases, in which there is an
apparent character of combination, and others in which a
difficulty must seem to arise from continuity. He then went
at considerable length to apply the same reasoning to the case
of the orator, as adduced by Mr. Stewart, and more fully de-
scribed by Lord Brougham. He lastly adverted to Mr.
Stewart’s explanation of dreams, and showed that it involved
some important contradictions and inconsistencies ; and that,
contrary to Mr. Stewart’s assertion, it implies a new law of
mind. He then showed that it could be explained by the
same method which he had already applied to the other ex-
amples. And after some explanations of the manner in which
the law of suggestion operated in dreams, he observed, in
conclusion, that Mr. Stewart had set out with a notion adapted
to lead him astray ; which he thought to be a subject of re-
gret, as the line of investigation which he had selected would
otherwise have offered a clearer and better evidenced founda-

221

tion for metaphysical science than any which had been pre-
viously adopted.

DONATIONS.

Catalogue of the Works of Art in the Possession of Sir
Peier P. Rubens, atthe Time of his Decease. Presented by
Dawson Turner, Esq.

Ueber die Himjaritische Sprache und Schrift. Von Dr.
W. Gesenius. Presented by the Author. .

A Descriptive Vocabulary of the Language of the Abo-
rigines of Western Australia. By G. Fletcher Moore, Esq.
Presented by the Author.

Magnetische und Meteorologische Beobachtungen zu Prag.
Vom 1 Juli 1839, bis 31 Juli 1840. By Karl Kreil. Pre-
sented by the Author.

Proceedings of the American Philosophical Society. Vol.
II. No. 19.

A Record of the Case of Mary Jobson. By W. R.
Clanny, M.D., &c. Presented by the Author.

February 28.

Rev. HUMPHREY LLOYD, D. D., Vice-President,
in the Chair.

Dr. Evory Kennedy read a paper on the peculiar Sys-
tem of Generation, and Habits, observed by him to prevail in
certain Acephalocysts, parasitical animals inhabiting the
human body, and belonging to the class of hydatid entozoa.

Having considered their animal nature, and their primary
formation, as involving the question of spontaneous genera-
tion, he described generally the methods of reproduction
adopted in this class of animals, and adduced the explana-
tions and opinions offered by the best authorities on the

222

subject, but particularly those of Bremner, Lannec, and
Owen, by which acephalocystic reproduction is referred to
imperfect ovation or generation. Dr. Kennedy went on to
show that the uterine hydatid or hydrometra hydatica of
Wiesmantel, which should more correctly be termed the
“ Acephalocystis Hysterobiavel uterina,”’ multiplies by fissipa-
rous generation, and that the creatures still continue adherent
to, or connected with each other by filiform bands or elon-
gations of the strictured parts of their bodies. Dr. Kennedy
exhibited several preparations and drawings in which this
mode of reproduction by subdivision was perceptible in dif-
ferent stages of progress, and having alluded to an imperfect
division, observed also to occur in infusorial animalcules, re-
commended that the system of reproduction which he de-
scribed should be termed ‘‘ fissiparo-coherent.”

A paper “on the colouring Matters of the Persian Berries”
was read by Dr. Kane.

These berries, the fruit of the dyer’s buckthorn, Rhamnus
Tinctoria, are imported from the Levant, and from the south
of France, for the use of dyers, to whom they furnish a yel-
low colour of great brilliancy, though not so permanent as
some others. ‘The appearance of the berries, as found in
commerce, varies considerably ; some samples, and those the
most valuable, being larger, fuller, and of a light greenish
olive colour, whilst others are smaller, as if shrivelled, and
dark brown in tint. The former Dr. Kane considers to have
the appearance of being gathered before complete ripening,
whilst the latter owe their altered character to being allowed
to remain longer on the stem, or to having been incautiously
dried.

The colouring matter in these two kinds is essentially
different. The unripe berries yield but little colour to pure
water, and when digested in ether give abundance of a rich

225

golden yellow substance, to which Dr. Kane has given the
name of chrysorhamnine. The dark coloured berries contain
little of the substance soluble in ether, but give out to boil-
ing water an olive yellow material, to which, in its pure form,
Dr. Kane gives the name of xanthorhamnine. This sub-
stance is produced, however, only by the decomposition of
the former; thus, if the unripe berries be boiled for a few
minutes in water, they, when dried, yield to ether scarcely
traces of chrysorhamnine, this principle being, by contact
of air and hot water, changed into xanthorhamnine.

Omitting the details of methods of purification, and of
analysis, the properties and composition of these bodies may
be expressed as follows :

Chrysorhamnine is of a rich golden yellow colour, of a
crystalline aspect, and may be obtained in brilliant stellated
tufts of short silky needles. It is but very sparingly soluble
in cold water, and when boiled with water the portion which
dissolves does not separate on cooling, but is found to be
changed into xanthorhamnine. It dissolves in alcohol, but
is not obtained by its evaporation, without being much al-
tered. In ether, however, it dissolves abundantly, and by
the spontaneous evaporation of its solution is deposited in a
pure form. It has no acid reaction, but dissolves in alkaline
solutions, in which, however, it appears also to be mostly
altered.

Dried at 212° Fahr. it consisted of
r Il.
Carbon... . 58.23 57.81
Hydrogen . . . 4.77 4,64
Oxypeni! 9S 49 S700 © (63756

100.00 100.00

These numbers give the formula C,; Hy, Oy, by which there
should be

VOL. Il. T

224

€., “= (138 58.23
Hig AL 4.64
Oj, = 6-88 ae

237 100.00

On adding an alcoholic solution of chrysorhamnine to a
solution of acetate of lead, a rich yellow precipitate is
formed, which, when dried at 212°, was found to be expressed
by the formula C,; Hy On + 2 PbO, the numbers being as
follow :

Theory. Experiment.
Carbon... 43) 2.1380 N29. 98 n5 ecu
Hydrogen 2.0.) TNO | (2339.2) +) Heel
Oxygen... 6 6 Spe S8i0) Qs ies. i aleledeea

Oxide oflead. . 223.4 48.52 . . . 48.60

460.4 100.00 100.00

A little water appears to have been lost in the analysis,
which, however, does not affect the formula deduced.

By the decomposition of a more basic acetate of lead, a
yellow precipitate is obtained, which consisted of one equi-
valent of chrysorhamnine united to three equivalents of oxide
of lead.

The chrysorhamnine may be easily observed in its na-
tural state of deposition in the berry; it lines the interior of
the capsule-cells, with a brilliant resinous-looking pale yel-
low, and semitransparent coating.

Xanthorhamnine is formed by boiling chrysorhamnine in
water, in a capsule, so as to admit of free access of air. It
dissolves with an olive, yellow colour, and on evaporating to
dryness, remains as a dark, extractive looking mass, quite in-
soluble in ether, but abundantly soluble in alcohol and water.
It may be procured also from the berries, without previous
separation of the chrysorhamnine, by similar treatment, but
it is then rendered impure by a gummy substance being

225

mixed with it. It is very difficult to determine when this
substance can be considered anhydrous. Prepared by eva-
poration over sulphuric acid in vacuo, it is quite dry, and
may be powdered, but if heated it liquefies below 212°, and
continues giving out watery vapour until the temperature is
raised to 350°, beyond which the organic matter itself cannot
be heated without decomposition. On cooling it reassumes
its perfectly dry aspect, and may be easily powdered.

It was hence analyzed in all these stages of desiccation,
with the following results. It contained :

Dried in vacuo. Formula deduced.
Carbon .. . . 34.74 Cae) =k 38 34.78
Hydrogen . . . 6.93 H, = 27 6.80
Oxygen . . . . 58.33 (SO eee SRN 1 58.42
100.00 397 ~=—-: 100.00

Dried at 212°. Formula deduced.
Carbon. . 49.97 51.20 CF elas 50.92
Hydrogen. 5.18 5.28 hee = 13 4.80
Oxygen . 44.85 43.52 = 120 44.28
100.00 100.00 271 100.00

Dried in an oil bath at 320°. Formula deduced.

Carbon . .: . 52.55 C3 = 138 52.67
Hydrogen . . . 5,15 yy 12 4.58
Oxygen . . . . 42.30 On = 112 42.75
100.00 262 100.00

By adding a solution of xanthorhamnine to solutions of
acetate of lead, two combinations may be formed, one by
neutral acetate of lead, the other by using the tribasic salt.
But it is difficult to obtain either unmixed with some traces
of the other, and thence the analysis of both vary a little
from the true atomic constitution. Thus the tribasic salt

gives
T2

226

Dried at 212°. Formula deduced.
Carbon . . 26.58 Cos eel 350 26.93
Hydrogen . 2.86 Heep allo 2.93
Oxygen. . 25.97 Oj =.) 136.0 26.54
Oxide of lead 45.36 44.59 2.PbhO = 223.4 43.60
100.00 512.4 100.00

The tribasic salt gives

Dried at 212°, Formula deduced.
Carbon .- . 21.89' 22.07 Ciuc 11880 21.20
Hydrogen . 3.06 2.82 Bysshe 2.76
Oxygen . 23.75 23.73 Oz, = . 160.0 24.57

Oxide of lead 52.30 51.38 3.PbO= 335.1 51.47

100.00 100.00 651.1 100.00

If we consider the xanthorhamnine, as dried in the oil-
bath, to be then anhydrous, the bodies analyzed become

Xanthorhamnine, dry = Cy3 Hig Oy.
do. dried at 212°. = C.3 Hy Ou + Aq.
do. dried in vacuo = C23 Hy, O14. + 15 Aq.
Ist lead salt, Cz Hy. Ou. + D3 PbO + 3 Aq.
2nd lead salt, cc Hy, Or. + 3 PbO + 6 Aq.

The xanthorhamnine is thus formed by the addition of
one equivalent of water and two of oxygen to the chry-
sorhamnine, as C,; H,, O,, + HO + O, = C.;Hjy.O 4. And
if we were to consider the substance dried in the oil-bath at
320° still to retain an atom of water, it should be simply
oxidated chrysorhamnine, being, when dry,

C.; Hy, On + 20.

The Rev. H. Lloyd, V. P., read a supplement to a former
communication “on a New Magnetical Instrument, for the
measurement of the Inclination and its Changes.”

227

Having, on a former occasion, explained the principle of
this instrument, and given the details of its construction, it re-
mains only that I should now describe the observations made
for the purpose of testing its performance. I shall pass over
for the present those which relate to the absolute inclination,
because they have yielded results which can be regarded only
as approximations to the truth, and I have not succeeded as
yet in tracing the errors to their source. It is manifest, how-
ever, that an instrument may be a good differential instru-
ment, while it is incapable of yielding absolute results ; and
there are special reasons why this should be the case with
the apparatus now under consideration. Accordingly its
failure in the latter respect, even though established, would
furnish no ground for despairing of its success in the former.

It is obvious that the apparatus is wholly free from the
sources of error already noticed, belonging to magnetical in-
struments moving on a fixed axle; and the only doubt of its
performance must relate to the changes of induced mag-
netism in the iron bar. Thus it might be questioned, before
trial, whether such a bar receives in all cases an amount of
free magnetism proportional to the inducing force ;—whe-
ther, again, the minutest changes in the latter are accompa-
nied by corresponding changes in the former ;—and whether,
lastly, the changes thus produced are instantaneous, or, at
least, demand no appreciable time for their development.

In the first experiments which I made, for the purpose of
determining these questions, the induced magnetism of the
iron bar was altered by means of a permanent magnet, placed
in the same right line with the bar, and at a known distance
from it. The etfect produced upon the position of the sus-
pended magnet being observed, the distance was altered by
a known amount, and a new observation taken; and so on,
at many different distances. ‘Then, the law of action of the
inducing magnet being known, we may calculate the changes
of deflection of the suspended magnet, on the supposition

228

that the changes of the induced force of the bar are propor-
tional to those of the inducing action, and then compare them
with the changes of deflection observed. The calculated and
observed results of many series of observations, taken in this
manner, were found to accord as nearly as the accuracy of
the observations themselves allowed.

In making this comparison, however, it is necessary to
take into account the effect of the direct action of the fixed
magnet upon the suspended one. The axis of the former
magnet being not far from the vertical passing through the
centre of the latter, its action upon it and upon the iron bar
follow, nearly, the same law; so that its direct effects upon
the position of the suspended magnet are, very nearly, pro-
portional to those which it produces through the medium
of the induced force of the bar. On this principle the ob-
served results may be cleared, approximately, of those parts
of the changes which are foreign to the question. Still it
must be admitted that such a complication of the results
tends to weaken their evidence; and it was therefore de-
sirable to obtain further proof, in a manner less exception-
able.

The object being to alter the inducing action according
to a known law, and to observe the changes of the induced
force, as shown by the position of the suspended magnet, it
is manifest that it may be attained by simply varying the
angle which the iron bar makes with the direction of the
earth’s magnetic force, the distance of its pole from the sus-
pended magnet remaining unchanged. In fact, it will be
seen, by pursuing the same reasoning as before, that if Rr
denote the total force of the earth, and y the angle which
the bar makes with its direction, the equation of equilibrium
of the suspended magnet is

pReosy + q=Xtanu;

the line connecting the pole of the bar with the centre of the

229

suspended magnet being, as before, perpendicular to the
magnetic meridian. Hence, if the bar be devoid of perma-
nent magnetism (or g=0), and ifthe forces R and x remain
unchanged during the experiments, we have

tanw = acosy,
a being a constant.

In order to observe whether the deflections of the sus-
pended magnet obeyed this law, a small divided circle was
attached to the piece upon which the iron bar moved, in such
a manner that the axis of the pivot passed through its centre.
The circle being fixed, and the bar connected with the
moveable arm carrying the vernier, we have the means of
determining the angle through which it is moved. The
plane of the motion coinciding with the magnetic meridian,
the inclination of the bar to the vertical was altered by 5°
between the successive observations of the position of the
suspended magnet. The following Tables contain the re-
sults of two such series of observations. The first column of
each gives the inclination of the bar to the vertical; the se-
cond, its inclination (J) to the direction of the magnetic
force, i. e. the former angle increased by the complement of
the magnetic inclination (19° 10’). The third column con-
tains the observed readings of the scale, corresponding to
the positions of the suspended magnet ; the fourth, the dif-
ferences between each of these readings and the reading
belonging to the vertical position of the bar, converted into
angular measure ; the fifth, the actual deflections; the sixth,
the calculated deflections, as deduced by the formula given
above; and the seventh, the differences.

In order to derive the numbers of the fifth column from
those of the fourth, it is necessary to know the deflection cor-
responding to the vertical position of the bar. This angle
is determined by placing the bar vertically, with its acting
pole above and below successively, and noting the readings
of the horizontal circle, when the same division of the move-

230

able scale, reflected by the mirror, was brought to coincide
with the fixed wire of the telescope. The differences be-
tween each of these readings, and the similar reading when
the bar is removed, are double the deflections corresponding
to the two positions of the bar; and, when they are nearly
equal, the mean of these deflections may be taken as that due
to the induced force.

_ FIRST OBSERVATION.

Acting end of bar asouth pole, reading = 14° 8’, deflection = 17° 0’
9 north pole, : 82 51, a =17 22
Bar removed, . 48 7, mean =17 11

Inclination Reading} Angular u u :

to vertical. wy. lof Scale. ogee tes! Observed. | Calculated. Direc.
+ 14° 30’) 33° 40/ 2-2 |—1°56/.2/}15°14/-8 | 15° 14"5| + 073
+10 0; 29 10 13-2 |—1 12:4/15 586/15 57-2) 4+ 1-4
+ 5 0; 24 10 23:1 |— 33:0)16 38:0)16 37-8| + 0-2

0 O;} 19 10 31-4 0:0;17 11-0

— 5 0} 1410 37-5 | 24-3/17 35:3/17 36:7| — 1-4
—10 O;|} 910 42:8 | 45:4/17 56-4/17 54-7) + 1-7
—13 30} 5 40 45-8 |+ 57:3/18 83/18 2-7| + 56

SECOND OBSERVATION.

Acting end of bar asouth pole, reading = 14° 23/, deflection = 16°36’

a north pole, 5 82 15, i = 17 20
Bar removed, . 47 35, mean = 16 58

Inclination Reading} Angular u u :
to vertical. ba of Scale.|Differences.| Observed. |Calculated. DCE aee:

+ 15° 0/, 34° 10! 2:6 |— 2° 18) 14° 56/-2| 149 57/-8| — 1/6
+10 0; 29 10 | 144 |—1 148 15 43:2/15 45-0; — 1-8

+ 5 0; 24 10 | 248 |— 33-4 16 24-6 | 16 25:2) — 0-6
0 0| 19 10 | 33-2 0.0) 16 58-0
— 5 0) 14 10 | 40:0 |4+ 27-1) 17 25-1|17 23:3} + 1-8

In the preceding observations a telescope of low power
was employed, and the arc-value of a single division of the

a $

231

scale: (which was at the distance of eighteen inches from the
mirror) was 3’.98. The differences of the observed and
calculated results, therefore, do not in general exceed the
amount which may be fairly ascribed to errors of observa-
tion; and the accordance is sufficient to establish the fact,
that the changes of the induced force of the bar are, within
the observed limits, proportional to those of the inducing
action. It is important to observe also that the changes of
the induced force, produced artificially in these experiments,
are much greater than any which are likely to arise from the
variations of the vertical component of the earth’s magnetic
force, and therefore that the experiments may be regarded
as severe tests of the performance of the instrument.

The preceding observations further showed, that the
changes in the inducing force were instantly followed by their
effects upon the suspended magnet; so that the changes of
induced force required no appreciable time for their develop-
ment. It remained only to ascertain, in a somewhat fuller
manner, how far the bar was susceptible of minute magnetic
changes, from very small variations of the acting force. For
this purpose, a series of readings of the scale was taken, the
inclination of the bar to the vertical being altered by half a
degree between the consecutive readings. ‘The mean diffe-
rence of the successive readings was found to agree, very
exactly, with the calculated difference; while the partial dif-
ferences deviated from the mean by an amount not exceeding
the limits of error of observation. It may be presumed there-
fore, that the changes of the induced force in the iron bar
are continuous; and, accordingly, that the sensibility of the
instrument is only limited by the optical power, which is ap-
plied to observe the changes of position of the suspended
magnet.* In the experiments above described, the arc-value

* Against this conclusion is the fact, that considerable changes in the induced
force of the bar seem to be attended with some permanent changes of polarity ;
and it may be presumed that the same thing will take place, in a proportionate

232

of the divisions of the scale was 3/.98; with the modifications
since introduced into the reading part of the apparatus, the
scale divisions have nearly the same value as in the instrument
for the measurement of the declination, so that the readings
may be made with certainty to less than the tenth of a minute.
The present value of the inclination in Dublin is about
70° 50’; and the mean deflection produced by the iron bar
in its actual position being about 19°, it follows from (7) that
the changes of inclination are inferred with the same degree
of precision, very nearly, as the observed changes of angle.
The last test to which the instrument was subjected, was,
to employ it for some time in the regular observation of in-
clination changes, for which it is destined; and to ascertain
how far the mean results of the observations of successive
weeks agreed in exhibiting the law of the diurnal variation.
The instrument was accordingly observed for five successive
weeks, every second hour during the day and night, and the
means calculated, omitting those days in which the series
was broken by changes of adjustment during experiment.
The curves now laid before the Academy represent the pro-
jected results of the observations of each of these weeks,
together with that of the mean ofthe whole. An inspection
of them is sufficient to show that the curves of the separate
weeks accord with one another, and with the mean, as nearly
as can be expected in the results of such limited series, the
discordances being only such as are due to the known irre-
gularities in the direction of the earth’s magnetic force.

A communication from the President was read, contain-
ing some remarks supplementary to the account which he
had given at a former meeting, of his Researches respecting
Fluctuating Functions, (see Proceedings, June 22nd, 1840).

*

degree, with the minute changes induced by the variations of the earth’s force.
It remains for future examination to determine how far such permanent changes,

if they occur, may impair the accuracy of the results.

233

The following general observations are extracted, on the
nature and history of this branch of analysis :—

Lagrange appears to have been the first who was led (in
connexion with the celebrated problem of vibrating cords) to
assign, as the result of a species of interpolation, an expres-
sion for an arbitrary function, continuous or discontinuous in
form, between any finite limits, by a series of sines of multi-
ples, in which the coefficients are definite integrals. Analo-
gous expressions, for a particular class of rational and inte-
gral functions, were derived by Daniel Bernouilli, through
successive integrations, from the results of certain trigono-
metric summations, which he had characterized in a former
memoir as being éncongruously true. No further step of im-
portance towards the improvement of this theory seems to
have been made, till Fourier, in his researches on Heat, was
led to the discovery of his well known theorem, by which any
arbitrary function of any real variable is expressed, between
finite or infinite limits, by a double definite integral. Poisson
and Cauchy have treated the same subject since, and en-
riched it with new views and applications ; and through the
labours of these and, perhaps, of other writers, the theory of
the development or transformation of arbitrary functions,
through functions of determined forms, has become one of
the most important and interesting departments of modern
algebra.

It must, however, be owned that some obscurity seems
still to hang over the subject, and that a further examination
of its principles may not be useless or unnecessary. The
very existence of such transformations as in this theory are
sought for and obtained, appears at first sight paradoxical ;
it is difficult at first to conceive the possibility of expressing
a perfectly arbitrary function through any series of sines or
cosines; the variable being thus made the subject of known
and determined operations, whereas it had offered itself
originally as the subject of operations unknown and undeter-

23-4

mined. And even after this first feeling of paradox is re-
moved, or relieved, by the consideration that the number of
the operations of known form is infinite, and that the opera-
tion of arbitrary form reappears in another part of the ex-
pression, as performed on an auxiliary variable; it still
requires attentive consideration to see clearly how it is pos-
sible that none of the values of this new variable should have
any influence on the final result, except those which are
extremely nearly equal to the variable originally proposed.
This latter difficulty has not, perhaps, been removed to the
complete satisfaction of those who desire to examine the
question with all the diligence its importance deserves, by
any of the published works upon the subject, A conviction,
doubtless, may be attained, that the results are true, but
something is, perhaps, felt to be still wanting for the full
rigour of mathematical demonstration. Such has, at least,
been the impression left on the mind of the present writer,
after an attentive study of the reasonings usually employed,
respecting the transformations of arbitrary functions.
Poisson, for example, in treating this subject, sets out,
most commonly, with a series of cosines of multiple arcs ; and
because the sum is generally indeterminate, when continued
to infinity, he alters the series by multiplying each term by
the corresponding power of an auxiliary quantity which he
assumes to be less than unity, in order that its powers may
diminish, and at last vanish ; but, in order that the new series
may tend indefinitely to coincide with the old one, he con-
ceives, after effecting its summation, that the auxiliary quan-
tity tends to become unity. The limit thus obtained is
generally zero, but becomes on the contrary infinite when the
arc and its multiples vanish; from which it is inferred by
Poisson, that if this are be the difference of two variables, an
_ original and an auxiliary, and if the series be multiplied by
any arbitrary function of the latter variable, and integrated
with respect thereto, the effect of all the values of that

235

variable will disappear from the result, except the effect of
those which are extremely nearly equal to the variable origi-
nally proposed.

Poisson has made, with consummate skill, a great number
of applications of this method; yet it appears to present, on
close consideration, some difficulties of the kind above alluded
to. In fact, the introduction of the system of factors, which
tend to vanish before the integration, as their indices increase,
but tend to unity, after the integration, for all finite values of
those indices, seems somewhat to change the nature of the
question, by the introduction of a foreignelement. Nor is it
perhaps manifest that the original series, of which the sum is
indeterminate, may be replaced by the convergent series with
determined sum, which results from multiplying its terms by
the powers of a factor infinitely little less than unity; while
it is held that to multiply by the powers of a factor infinitely
little greater than unity would give an useless or even false
result. Besides there is something unsatisfactory in employ-
ing an apparently arbitrary contrivance for annulling the
effect of those terms of the proposed series which are situated
at a great distance from the origin, but which do not them-
selves originally tend to vanish as they become more distant
therefrom. Nor is this difficulty entirely removed, when
integration by parts is had recourse to, in order to show that
the effect of these distant terms is insensible in the ultimate
result ; because it then becomes necessary to differentiate the
arbitrary function; but to treat its differential coefficient as
always finite is to diminish the generality of the inquiry.

Many other processes and proofs are subject to similar or
different difficulties; but there is one method of demonstra-
tion employed by Fourier, in his separate Treatise on Heat,
which has, in the opinion of the present writer, received less
notice than it deserves, and of which it is proper here to
speak. The principle of the method here alluded to may be
called the Principle of Fluctuation, and is the same which

236

was enunciated under that title in the remarks prefixed to
this paper. In virtue of this principle (which may thus be
considered as having been indicated by Fourier, although
not expressly stated by him), if any function, such as the
sine or cosine of an infinite multiple of an arc, changes sign
infinitely often within a finite extent of the variable on which
it depends, and has for its mean value zero; and if this,
which may be called a fluctuating function, be multiplied by
any arbitrary but finite function of the same variable, and
afterwards integrated between any finite limits; the integral
of the product will be zero, on account of the mutual destruc-
tion or neutralization of all its elements.

It follows immediately from this principle, that if the
factor by which the fluctuating function is multiplied, instead
of remaining always finite, becomes infinite between the limits
of integration, for one or more particular values of the vari-
able on which it depends; it is then only necessary to attend
to values in the immediate neighbourhood of these, in order
to obtain the value of the integral. And in this way Fourier
has given what seems to be the most satisfactory published
proof, and (so to speak) the most natural explanation of the
theorem called by his name; since it exhibits the actual pro-
cess, one might almost say the interior mechanism, which, in
the expression assigned by him, destroys the effect of all
those values of the auxiliary variable which are not required
for the result. So clear, indeed, is this conception, that it
admits of being easily translated into geometrical construc-
tions, which have accordingly been used by Fourier for that
purpose.

There are, however, some remaining difficulties connected
with this mode of demonstration, which may perhaps account
for the circumstance that it seems never to be mentioned,
nor alluded to, in any of the historical notices which Poisson
las given on the subject of these transformations. For ex-
ample, although Fourier, in the proof just referred to, of the

237

theorem called by his name, shows clearly that in integrating
the product of an arbitrary but finite function, and the sine
or cosine of an infinite multiple, each successive positive
portion of the integral is destroyed by the negative portion
which follows it, if infinitely small quantities be neglected,
yet he omits to show that the infinitely small outstanding dif-
ference of values of these positive and negative portions, cor-
responding to a single period of the trigonometric function
introduced, is of the second order; and, therefore, a doubt
may arise whether the infinite number of such infinitely small
periods, contained in any finite interval, may not produce, by
their accumulation, a finite result. It it also desirable to be
able to state the argument in the language of limits, rather
than in that of infinitesimals; and to exhibit, by appropriate
definitions and notations, what was evidently foreseen by
Fourier, that the result depends rather on the fluctuating
than on the trigonometric character of the auxiliary function
employed.

_ The same view of the question had occurred to the pre-
sent writer, before he was aware that indications of it were to
be found among the published works of Fourier ; and he still
conceives that the details of the demonstration to which he
was thus led may be not devoid of interest and utility, as
tending to give greater rigour and clearness to the proofand
the conception of a widely applicable and highly remarkable
theorem.

Yet, if he did not suppose that the present paper contains
something more than a mere expansion or improvement of a
known proof of a known result, the Author would scarcely
have ventured to offer it to the Transactions* of the Royal
Irish Academy. It aims not merely to give a more perfectly
satisfactory demonstration of Fourier’s celebrated theorem

* Sir William Hamilton’s Essay on Fluctuating Functions, will be found in

the Second Part of volume xix. of the Transactions of the Academy.

238

than any which the writer has elsewhere seen, but also to
present that theorem, and many others analogous thereto,
under a greatly generalized form, deduced from the principle
of fluctuation. Functions more general than sines or cosines,
yet having some correspondent properties, are introduced
throughout ; and constants, distinct from the ratio of the cir-
cumference to the diameter of a circle, present themselves in
connexion therewith. And thus, ifthe intention of the writer
have been in any degree accomplished, it will have been
shown, according to the opinion expressed in the remarks
prefixed to this paper, that the development of the impor-
tant principle above referred to gives not only a new clear-
ness, but also (in some respects) a new extension, to this de-
partment of science.

DONATIONS.

Memorie dell? Imperiale Regio Instituto del Regno Lom-
bardo-Veneto. Vols. 1-5.

Memorie dell’ Instituto Nazionale Italiano. Vol. 1, 4 Parts,
vol. 2, 2 Parts.

Maxwell's Narrative of the Prince’s Expedition. (1745).
Published by the Maitland Club. Presented by John Smith,
Ksq., Secretary M. C. :

Bibliotheca Scoto-Celtica. By John Reid, Esq. Pre-
sented by the Author.

Hints for the better Construction of Dwellings for small
Farmers, §c. By W. J. Hughes, M.R.I. A. Presented
by the Author.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1842. No. 34.

March 16. (Stated Meeting).

SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

On the recommendation of Council, Charles Wheatstone,
Ksq., was elected an honorary member of the Academy.

The Secretary of Council read the following Report,
which was ordered to be entered on the Minutes:

“ The affairs of the Academy during the past year will require but
a brief review, as the interval has not been very fertile in results. The
second part of the nineteenth volume of our Transactions has not yet
been published ; and the Essay on the Round Towers (which is to
make the twentieth volume) is still advancing slowly through the
press, its progress being necessarily retarded by the great number of
illustrations which are required from the nature of the work.

‘¢ The subscription which was opened last year, under the manage-
ment of the Committee of Antiquities, for the purchase of the collec-
tion of the late Dean of St. Patrick’s, has not hitherto answered the
expectations that were formed of it. Of the sum of one thousand
pounds, which the Dean’s representatives agreed to accept for the
collection, little more than one-half has been raised. Notwithstand-
ing this circumstance, however, the Council are persuaded that. public
feeling is in favour of the project, and that a little more energy, on
our part, is all that is required to ensure success. It would indeed
be a disgrace to us, if, for want of proper exertions, this fine collection
should be lost to the country.

VOL. II. U

240

« Meanwhile, the small cabinet in the possession of the Academy
has been augmented by some valuable articles, from the fund of two
hundred pounds set apart for that purpose. Among these are a
gold torquis, weighing upwards of twelve ounces; and a gold collar
of the most elegant form and workmanship, weighing four and a-half
ounces. The latter beautiful specimen of ancient art was lately dug
up in a bog, by a common labourer, and but for the existence of the
fund above mentioned, which allowed it to be secured at once for the
Academy, it would probably have been condemned to the crucible;
the usual fate of such old ornaments as possess a high intrinsic
value.

«: As this fund, however, is but small, and in the present state of
our finances cannot be expected to be permanent, while the re-
sources of private subscription, to which we have so often had occa-
sion to resort, must be considered as now almost exhausted, the
Council have thought it advisable to try whether it might not be pos-
sible to obtain some public assistance towards carrying out an object
which is admitted to be one of great public interest. They have
therefore presented a memorial to the Lord Lieutenant, praying his
Excellency to recommend to her Majesty’s Government the addition
of £100 a year to our usual grant, for the sole purpose of purchasing
antiquities; this additional sum to be strictly accounted for every
year. Should the proposal be favourably received by the Government,
the Academy will be in a position to accomplish its designs in this de-
partment, at a very trifling expense to the public.

«Tn order that a greater number of the members of the Academy
may be induced to take a lively interest in its affairs, by enjoying a
share of its honours, the Council have thought it expedient to re-
commend that there should in future be an annual change in the list
of Vice-Presidents, the senior Vice-President going out of office
after the stated meeting in March, and they hope that every future
President will consent to act upon this suggestion in the appointment
of Vice-Presidents. But as it is proposed, by this arrangement, that
no person should be appointed as Vice-President more than four times
successively, so it is not intended to recommend that any Vice-Pre-
sident should be displaced, who may have been appointed less than
four times successively.

«« Among the deaths that have occurred in our body, during the

4

241

past year, we have had to regret that of the Very Rev. Robert
Burrowes, D. D., Dean of Cork, and formerly Fellow of Trinity Col-
lege. Though not an original member, Dr. Burrowes was among the
very first members of the Academy. He filled the office of Secretary
for several years, and contributed some very elegant papers, in the
department of Polite Literature, to the early volumes of our Trans-
actions.

‘‘ Within the last few days we have had to lament the death of
another distinguished member of the Academy and Council, the Rev.
Czsar Otway, the author of several well-known works illustrative of
the history and antiquities of his native country, and abounding in
graphic sketches of Irish scenery, and vigorous delineations of Irish
character and manners.

«In the list of honorary members, we have lost an eminent
Botanist, Aylmer Burke Lambert, Esq. He was the author of a
magnificent work on Pines, in three volumes, the last of which, more
recently published than the rest, contains some fine contributions
from the Californian collections of our countryman and fellow-acade-
mician, Dr. Coulter.

«« The other members deceased within the year are :

Peter Burrowes, Esq., Q.C. Isaac D’Olier, LL. D.
J. H. Blake, Esq., Q. C.

« And the new members elected within the year are:

William Monsell, Esq. J. H. Jellett, Esq., F.T.C.D.
Robert Tighe, Esq. William Andrews, Esq.

W. E. Hudson, Esq. J. T. Banks, Esq.

G. Fitzgibbon, Esq. Robert Bateson, Esq.

William Phibbs, Esq. John Burrowes, Esq.

Rev. James Reid. Rey. Samuel Butcher, F. T.C.D.
William Lee, Esq., F.T.C.D. | Fleetwood Churchill, M.D.
Robert Jones, Esq. Alexander Clendinning, Esq.
Thomas Wilson, Esq. Rev. Reg. Courtenay.

Beriah Botfield, Esq. Durham Dunlop, Esgq., Jun.
W. T. Mulyany, Esq. Alexander Ferrier, Esq.
Oliver Sproule, Esq. Wrigley Grimshaw, M.D.
James Thompson, Esq. William Hogan, Esq.

James Patten, M.D. W. J. Hughes, Esq.

u 2

242

William Roberts, Esq., F.T.C.D. Joseph Nelson, Esq.
Captain A. C. Sterling. Rev. Robert Chatto.”
Rey. Thomas Stack, F. T.C. D.

Resoivep,—That we have heard, with deep regret, of the
death of our fellow Academician, the Rev. Caesar Otway, and
that, while we wish to record our sense of the value of his ser-
vices to the Academy, and our opinion of his merits as an
author, who, possessing in his own person many of the best
traits in the Irish character, has by his lively and interesting
sketches powerfully assisted in drawing public attention to
the history, scenery, and antiquities of his native land; we de-
sire also to convey to his afflicted family the assurances of our
sincere sympathy in their sorrow for one whose private vir-
tues rendered him the delight of the domestic circle, as his
talents and information made him valuable as a member ofour
Institution.

ReEsoLveD,—That the Academy have heard, with regret,
that Dr. Aquilla Smith, having found his attendance on the
Council inconsistent with his professional pursuits, has ten-
dered the resignation of his place as a member of Council;
and they desire to express their sense of the valuable assis-
tance they received from him during the time they had his
cooperation in advancing their objects.

The ballot for the Annual Election having closed, the
scrutineers reported that the following gentlemen were elected
Officers and Council for the ensuing year:

President—Sir William Rowan Hamilton, LL.D.

Treasurer—James Pim, Jun., Esq.

Secretary to the Academy—Rev. Joseph H. Singer, D.D.

Secretary to the Council—J. Mac Cullagh, Esq. LL.D.

Secretary of Foreign Correspondence—Rev. Humphrey
Lloyd, D.D.

Librarian—Rev. William H. Drummond, D.D.

Clerk and Assistant Librarian—Edward Clibborn.

ee a ae

243

Committee of Science.

Rev. Franc Sadleir, D.D., Provost of ‘Trinity College ;
Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D. ; James
Mace Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.;
Robert Ball, Esq.; Robert Kane, M.D.

Committee of Polite Literature.

His Grace the Archbishop of Dublin ; Rev. Joseph Hen-
derson Singer, D.D.; Samuel Litton, M.D.; Rev. William
Hamilton Drummond, D.D.; Rev. Charles Richard Elring-
ton, D.D.; Rev. Charles William Wall, D.D.; Rev. Thomas
H. Porter, D.D.

Committee of Antiquities.

George Petrie, Esq.; Rev. James Henthorn Todd, D.D.;
Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq. ;
Joseph Huband Smith, Esq.; James Pim, Jun. Esq.; Cap-
tain Larcom, R.E.

The President then appointed, under his hand and seal,
the following Vice-Presidents :

His Grace the Archbishop of Dublin; the Rev. Hum-
phrey Lloyd, D.D.; the Rev. James Henthorn Todd, D.D.;
the Rev. Joseph Henderson Singer, D.D.

The auditors appointed by Council to examine the Trea-
surer’s accounts reported as follows :

«We have examined the above accounts,* with the vouchers pro-
duced, and have found it to be correct; and we find that there is a
balance in bank, amounting to £169 17s. 1d. sterling.

«< (Signed,)
“ Tuomas Hotton,

« JosEPH CARSON.
“ March 16, 1842,”

* Entered in Treasurer’s book.

244:

“ The Treasurer reports, that there is £1052 6s. 8d. in 3 per
Cent. Consols, and £1609 4s. 9d., in 34 per Cent. Stock, the latter
being the Cunningham Fund.

“ (Signed, )
, “ AQUILLA SMITH.
* March 16, 1842.”

April 11.
SIR Ws. R. HAMILTON, LL.D., President, in the Chair.

Rev. Richard Butler, Robert Law, M.D., and John
Toleken, M. D., F.T. C.D., were elected members of the
Academy.

Mr. Ferguson read a paper by the Rev. Arthur B.
Rowan, A. M., M.R.I.A., on the ancient Church of Kil-
melchedor.

This church stands in a small hamlet and parish of the
same name, in the barony of Corkaguiny, county of Kerry,
at the foot of Brandon mountain, and near the harbour of
Smerwick. At the top of the. neighbouring mountain is a
small ruined oratory, and a well of great reputed sanctity,
which are dedicated to St. Brandon, or Brendan, the founder

‘of the Diocesan Cathedral of Ardfert; and the neighbour-
hood is further remarkable for some of those small stone-
roofed cells or chapelries which are supposed to belong to
a very remote age, and of which one that has been described
and engraved by Smith, in his History of Kerry, still remains
in complete preservation. The church derives its name from
St. Melchedor, who is mentioned in a catalogue of saints in
the book of Ballimote; also ina MS. calendar in the Library
of the Academy, where, under the date May 14, he is com-
memorated as ‘‘ Melchedar, son of Ronan, son of the King
of Ulster, of Kilmeilche[dor?], on the sea shore, at Knock-

245

Brennaun in the west.” For this information the author ac-
knowledges himself indebted to Mr. Owen Connellan. He
then proceeds to the description of the church, of which
plans and drawings are given. ‘The building,” he says,
‘*‘ stands due east and west, and consists of two parts, the
nave and choir, separated by a richly carved semicircular
archway. The former is twenty-six feet long, by sixteen
feet wide, and thirteen feet high to the springing of the
stone roof. The choir is, as usual, much smaller, being but
sixteen feet long, by twelve wide, and eleven feet high to the
roof, which was also of stone. There are five windows, one
in the eastern gable, and one at each side in the nave and
choir; all of them having the round arch of the same style of
architecture as the ornamented doorways. The entrance to
the church is at the western end, through a richly orna-
mented doorway of the Anglo-Norman, or, as it is more cor-
rectly called, the Lombardic style of architecture. Making
allowance for the greater size and profusion of ornament, I
find in the arches of the western door and nave of Rochester
Cathedral, the nearest model for the doorways of Kilmelche-
dor church. In Ireland, the account given by Grose, in his
Antiquities, of Cormac’s Chapel or Crypt at Cashel, may,
pro tanto, be copied asa description of Kilmelchedor. Thus
he tells us, ‘it is a stone-roofed chapel,’ with ‘a nave and
choir, with ‘columns supporting the grand arch leading into
the choir; the columns short and thick; the portal semécir-
cular, with nail-head and chevron mouldings; the windows
also round.’ So far the descriptions of both buildings exactly
agree.”

The roof of Kilmelchedor seems to have been constructed
on the same principle as the roofs of the ancient and curious
stone hermitages in its neighbourhood; one stone overlap-
ping the other, with sufficient bearing to sustain the weight
as the work advanced. But the chief peculiarity of this
church is the elaborate ornament of the interior nave,

246

which is of a kind to attract attention even if found in one
of our most richly adorned churches, but much more so
in a building in this remote situation. At the height of about
four feet from the floor, the nave shows, on each side through
its whole length, a series of square pannelled compartments,
separated by short massive pilasters projecting from the
wall. These compartments, twelve in number, are in per-
fect preservation, and appear to have been originally exe-
cuted in polished stone. The nave windows occupy a com-
partment at each side, and are surmounted by plain round
arches.

Within the choir, and springing directly from each side
of the doorway, there are small arched apertures, the use of
which the author is at a loss to conjecture. The semicir-
cular head of the western doorway is filled with a single
stone, on the inner side of which is a projecting effigy, now
too much defaced to admit more than a conjecture as to what
it represented. In the church-yard stands a rude gigantic
cross, formed of a single stone; another, less rude, lies half
prostrate, and has been built into the wallofa tomb. Ogham
stones are found at several places in the neighbourhood ;
there is one, much effaced, in the churchyard.

Having noticed the vulgar tradition that the church
‘‘ was built long ago by the Spaniards,” the author offers some
conjectures as to the probable date of its erection, which he
concludes to have been in the eighth or ninth century, ‘“‘when
the Danes had intercourse with this and with other parts of
Treland;” but he supposes that it was ornamented and finished
in its present style at a subsequent period.

The following notice of an ancient Boat, found near
Drogheda, was read by W. I. Hughes, Esq.

During the progress of the works carried on by the Cor-
poration of Drogheda for the improvement of the port and
harbour, it was found necessary to deepen the bed of the River

24:7

Boyne below the bridge, towards the sea, which left that
part of the river above the bridge, towards Oldbridge, quite
dry. At this part (in the Summer of 1837), the boat, the
subject of the present notice, was found by some workmen
who were engaged taking gravel from the river, close by the
obelisk erected to commemorate the battle fought between
James the Second and William the Third, about two miles
from the town of Drogheda.

Its extreme length is eighteen feet nine inches, and
breadth two feet eight inches, tapering to a breadth of four-
teen inches at the back, and to nine inches in the front, being
flattened at either end; no oars seem to have been used in
propelling it, there being no marks on the sides, or places for
dowells used in modern boats to secure the oars, but at either
end a groove is perceptible where oars were placed to steer
or scull with. Paddles may have been used in the same
manner as the Indians manage their canoes. Some of the
paddles have been found, but they are of a very rough kind,
having the appearance of the branch of a tree, feathered at
one end, without any attempt at shape.

Along with this cott was found what I shall call an
anchor ; it is four feet in length, and three feet across, having
two arms, to one of which a rope was attached to secure the
boat.

The Royal Dublin Society have one of those ancient cotts
in their possession, which differs from that now described in
shape and size; the cott found at Drogheda being flattened
at both ends, whilst that belonging to the Dublin Society has
one end flat and the other pointed, being of the shape of a
modern boat. Its length is twenty-one feet twoinches, breadth
one foot, and depth ten inches; being scarcely sufficient
for a person to sit in. ‘There is no keel to either of the
boats.

Another was found lately in a bog, on the estate of Sir
Charles Kennedy, in the county of Waterford ; it is only

248

eight feet six inches long, and two feet ten inches broad, and
is round at the bottom, having a keel.

Ware, in his work on the Antiquities of Ireland, states
it as his opinion, that the Phoenicians were the original colo-
nisers of this country, and that they used boats made of osiers
or wicker work, and covered with skins, in which they navi-
gated the bays and the mouths of the rivers. The ancient
Irish, he says, made use of another kind of boat in the
rivers and lakes, formed out of an oak wrought hollow,
which is called by the Irish coétz, and by the English cott, a
vessel well known to antiquity under other names. Pliny
calls boats hollowed out of a single beam, Monoxyle, from a
Greek word of that import, and describes them to be—
lintres ex uno ligno excavate, i. e. boats formed out of one
piece of timber wrought hollow. And in another place
Pliny relates that the German pirates sailed in boats hol-
lowed out of single trees, each of which they made so large
as to contain thirty men.

April 265.
SIR Wu. R. HAMILTON, LUL.D., President, in the Chair.

The Rev. Dr. Kennedy Bailie commenced the reading of
a paper containing an Account of his Researches in certain
parts of Asia Minor.

The Rev. Dr. Robinson gave an account of the casting
of the great six-foot Speculum by the Earl of Rosse.

The publication of this account i§ deferred, for the pre-
sent, by Dr. Robinson. On a future occasion he expects to
lay before the Academy a statement of the performance of
the telescope when it shall be turned, for the first time, to
the heavens. The history of the casting of the specu-

a 249

lum, of the performance of the telescope, and of the ma-
ehinery by which it is moved, will then appear in the Pro-
ceedings.

May 9.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

William Blacker, Esq. and the Rev. James Booth were
elected members of the Academy.

James Mac Cullagh, Esq. was elected Secretary of the
Academy, in the room of the Rev. Dr. Singer, resigned ;
and Dr. Kane was elected Secretary of Council.

A paper, by the Rev. Dr. Hincks, ‘‘ On the True Date
of the Rosetta Stone,” was read.

The date usually assigned to this monument, on the au-
thority of Dr. Young, is the 27th March, 196 B. c., according
to the proleptic Julian reckoning ; the true date, as deter-
mined by Dr. Hincks, is the 27th March, 197 8. c. Taking
the former date for granted, M. Letronne has drawn from it
a great many inferences, which the error of a single year en-
tirely vitiates. These inferences relate to the history of
Ptolemy Epiphanes, and to the mode of computing the years
of his reign and of the reigns of other Egyptian kings; as
also to the various priesthoods of royal personages that are
mentioned on the Ptolemaic monuments. The conclusions
of M. Letronne, and those which are to be deduced from
the corrected date, are exhibited by the author in parallel
columns.

The President made some remarks on the day of the
Vernal Equinox at the time of the Council of Nice.

It has been stated by some eminent writers on astronomy,
for example by Brinkley and Biot, and seems to be gene-
rally supposed, that the vernal equinox in the year 325, a. D.

250

fell on the 21st of March. But Sir W. Hamilton finds that
Vince’s Solar Tables (or Delambre’s, from which those are
formed) conduct to about 2} hours before the Greenwich
mean noon of the 20th of March, as the true date of the
equinox in that year; which thus appears to have been as-
signed to a wrong day, by some erroneous computation or
report, perhaps as long ago as the time of the phenomenon
in question.

As this result is curious, Sir W. Hamilton conceives that
it may not be uninteresting to confirm it by a very simple
process of calculation, derived from the Gregorian Calendar.
According to that calendar, 400 years contain 146097 days,
being a number less by 3 than that of the days in four Julian
centuries; and if the farther refinement be adopted, which
some have suggested, of suppressing the intercalary day in
each of the years, 4000, 8000, &c., then, in the calendar
thus improved, 4000 civil years will contain 1460969 solar
days. Assuming then, as a sufficiently near approximation,
that such is the real length of 4000 tropical years; multiply-
ing by 3, and dividing by 8, we find that 1500 tropical years
are equivalent to 547863 days and a fraction; which fraction
of a day, according to this simple arithmetic, would be equi-
valent to 9 hours. But 1500 Julian years contain 547875
days, that is, 12 more than the number last determined ; and
these 12 days are precisely the difference of new and old
styles in the present century. If, then, we neglect the frac-
tion, the new-style date of an equinox in any year of the
nineteenth century ought to be the same with the old-style
date of the same equinox in the corresponding year of the
fourth century; and in particular the vernal equinox of 325
ought to have fallen on the 20th of March, because that of
1825 fell on the day so named: while the fraction of a day
above referred to, though not entirely to be relied on, ren-
ders this result a little more exact, by throwing back the
equinox from the evening to a time more near to noon.

251

The following communication from the Rev. Thomas
Knox was read:

** River Glebe, Toomavara,
** April 27, 1842.

** An application of the Daguerreotype process to astro-
nomical purposes occurred to me last autumn. It is well
known that an inscription on a building which it would re-
quire a telescope to read, from its smallness or distance, can
(if a view of that building be taken in the camera on one of
Daguerre’s plates) be read by a microscope, though invisible
on the plate to the naked eye; also, that the internal struc-
ture of some insects can be as well studied by examining the
image of the object on the plate by a microscope (that image
having been formed from the oxyhydrogen microscope).

“From these known facts it is extremely probable that
were an image of a double star, or of one of the nebula, taken
on a Daguerre plate in the focus of a telescope of moderate
power, but which of itself could not divide the star or resolve
the nebula; that by then examining the plate by a strong
microscope, the state of that star, &c. might be ascertained,
as well as if it had in the first place been examined by a
telescope of very high power.

“That the light of the fixed stars possesses chemical
rays, and would therefore affect Daguerre’s plates, there can
be little doubt; and I feel certain in my own mind that the
image thus formed would reveal to the microscope as much
as a telescope of equal power could in the first instance have
ascertained.

‘“‘T am aware that theorising this way is very unprofit-
able, but I do not possess instrumental means for trying the
experiment myself, my equatorial not having any clock mo-
tion adapted to it. On the accuracy and steadiness of the
clock movement al/ would depend; any small telescope, or
perhaps even a single lens, equatorially mounted, would do

252

the rest. The plates need not exceed in size the pencil of
rays, and may be very small.

‘“‘ If this succeed, we might gain great advantages by thus
mapping the stars and nebule, and examining their state at
our leisure, in our study, and being able to take advantage
of what every practical astronomer knows to occur so seldom
in our climate, namely, a state of the atmosphere favourable
for delicate observation.

“To try it, some easily divided star, such as Z Urs,
might be first used, and, if the plate registered it as a double
star, we might then proceed to other more difficult objects.”

DONATIONS.

A Letter on the State of Schools of Chemistry in the United
Kingdom. By Wm. Gregory, M.D., M.R.I.A., &e. &c.
Presented by the Author.

A volume of Tracts relating to the Historical Society of
Dublin. Presented by G. A. Kennedy, M.D., M.R.I. A.
&c. &e.

Journal of the Franklin Institute. Third Series. Vol. II.

Eleventh Report of the British Association for 1841.
(Plymouth). Presented by the Association.

Account of the Magnetical Observatory of Dublin. By
the Rev. H. Lloyd, D. D., &c. Presented by the Author.

A View of the Coinage of the Heptarchy. By John Lind-
say, Esq. Presented by the Author.

Mémoires de la Societe Géologique de France. Tome IV.
Second Part.

Transactions of the Royal Society of Copenhagen. Vol. V1.
(1841).

On the Use and Study of History. By W. Torrens M‘Cul-
lagh, LL.B. Presented by the Author.

293

May 23.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The Rev. Dr. Kennedy Bailie, late F. T. C. D., concluded
a paper which he had commenced on the last meeting but
one of the Academy, the subject of which was a general
statement of his researches in certain parts of Asia Minor,
relative to Inscriptions of the Graeco-Roman era. The fol-
lowing is an outline of his communication.

He commenced with some brief notices of what has been
done by scholars in this department of classical literature,
and with remarking on its importance, as illustrative of the
language, the history, and the institutions of the people who
have bequeathed these monuments to after-ages. In this
section, the labours of Chandler, Pococke, Spon, Clarke, and
Professor Boeckh, were particularly commemorated.

Next followed an account of the rules by which he was
guided, in forming his collection of inscriptions, during a
tour which he had recently made in the countries bordering
on the Mediterranean.

The third section embraced notices of the inscriptions
which he copied in six of the Apocalyptic sites, namely,
Ephesus, Philadelphia, Sardes, Thyatira, Pergamus, and
Smyrna, and of a few others which he found in some neigh-
bouring localities, viz. two sepulchral, from the sites of the
ancient Cotyaion, and three from the Turkish town of Kir-
kagatch, situated on the road from Thyatira to Pergamus.

The Ephesian monuments related chiefly to circumstances
connected with the Artemisiac festivals. They were three in
number; one, a psephisma, or decree of the senate and
people of Ephesus; the two remaining, honorary tituli.

Of the four inscriptions found at Philadelphia, the most
remarkable was a fragment of a titulus, which, in all proba-
bility, had been inscribed on the pedestal of a statue of the

254

eunuch Eutropius, after the downfall of the power of that
favourite of Arcadius.

In support of this opinion, Dr. Kennedy Bailie entered at
some length into that part of the history of the period which
concerns the expedition against Trigibild the Ostrogoth,
under the auspices of Eutropius, which terminated in the dis-
comfiture and death of the general whom he had selected.

This inscription was found in an extremely mutilated
state ; and an attempt has been made by the author of the
paper to restore it, on the basis of the historical notices de-
rivable from Claudian’s two books against Eutropius.

It was metrical: the lines alternately hexameter and pen-
tameter.

The inscriptions found at Thyatira were nine in number,
of which four at least were entaphial. The others were
chiefly honorary tituli, and of these, the most perfect which
Dr. Kennedy Bailie found, was one which had been inscribed
on the pedestal of a statue erected in memory of the skill and
prowess ofa distinguished Thyatirene athlete, Menander the
son of Paullus, by the youths of the first Heraclean Gym-
nasia.

The most perfect amongst the sepulchral epigraphs was
found on a soros which had been the property of a distin-
guished citizen of Thyatira, named Fabius Zosimus. In this
are recited, at full length, the intentions of the owner, the

legal sanction under which they were to be carried into

effect, the names of the Proconsul and Registrar, as also the
date.

It contains, moreover, some interesting notices relating to
the astyography of the ancient site amongst the ruins of
which it was found.

Of the Sardian monuments, the most remarkable was one
which appeared to have been destined to commemorate the
munificence of Tiberius, Trajan, and, most probably, of Ha-
drian also, to the citizens of Sardes.

255

This record was found by the author in a most mutilated
state ; but sufficient of it fortunately remained, to enable him
to connect its notices with the accounts given by Tacitus,
Spartianus, and Dio, of the liberality of those emperors to
the distressed States of the Proconsular Asia, which had been
devastated by a succession of earthquakes in the region of
the Katakekaumene.

The most remarkable of the Pergamenian incriptions
were those in honour of Hadrian, both after his assumption
of the purple, and during the life-time of Trajan. One of
these may be regarded as peculiarly valuable, the great pro-
bability being, that it still exists amongst the inedited monu-
ments of the Greco-Roman era, and that it bears most
strongly on the historical doubt originated by the above-
mentioned Dio, on the subject of Hadrian’s adoption.

Two other inscriptions, which were copied at Pergamos,
appear evidently to belong to the period of the Lower Em-
pire. They have, however, been allowed a place in this
collection, as tending to illustrate the taste and style of the
age in such matters. Both are honorary, and one en-
taphial.

The Smyrnzan Tituli are five in number, viz. a fragment
of a decree, or treaty ; a notice of the officers of the customs
of the port of the ancient city; a votive epigraph, ona stele;
a fragment of an inscription from the frieze of a temple;
lastly, an epitaph.

On these the author of the essay dwelt at considerable
length, more especially on the third, in which he pointed out
a circumstance which appeared to have escaped the notice
of former writers: amongst these, of Mr. Arundell, whose
work on the Apocalyptic Churches appeared in 1828. This
yemark concerned the metre, and led to a conversation with
a gentleman present, who expressed an interest in Mr.
Arundell’s discoveries, and a wish to be informed on the sub-
ject of the accuracy of that traveller’s statements.

VOL. II. Mn

256

Dr. Kennedy Bailie’s reply was: that his sole concern, at
present, was the literature of inscriptions; that therefore he
felt not at liberty to venture any observation on either the
style or the accuracy of the reverend gentleman’s volumes,
excepting so far as related to that subject ; and that he was
bound in candour to confess, that the form in which his col-
lection of inscriptions has been offered to the public is not
one on which any reader could rely as a scholar-like repre-
sentation of the original monuments.

The inscriptions of the Turkish town of Kirgagatch and
Cotyaion, next occupied the author’s attention. The first
of these, three in number, comprised an honorary titulus, in
favour of Hadrian, inscribed on a block of marble, which was
most probably brought from Stratonicea. Secondly, a de-
cree of the senate and people of that city in honour of Dio-
dorus Philometor, son of Nicander, in consideration of his
public services. Thirdly, a dedication of a church, in the
age of the Lower Empire, or what appears to have been
such, for the characters had been very much effaced.

Of these the author read a detailed account, and stated
his reasons for supposing that the more ancient tituli had
been brought from Stratonicea in Caria, thus establishing
some connexion between that site and the Turkish town.
This is the more remarkable, inasmuch as there exist no
architectural remains in Kirkagatch to lead to the supposition
that it occupied any known ancient site.

Two inscriptions from Kdataiah (Cotyaion) concluded the
series, both of which were copied from grave-stones in the
Armenian cemetery. They were sepulchral tituli, and the
stones themselves, on which they were engraved, most pro-
bably fragments of Sarkophagi.

The Secretary read a letter from Dr. Hunter, presenting
to the Academy three mathematical works, by the Nuwab ~
Shums-ool-oomrah of Hyderabad.

257

** Dublin, Royal Barracks,
, *“ May 23, 1842.
** Sir,
‘I beg to present to the Library of the Royal
Irish Academy the three accompanying works on scientific
subjects, printed in the Persian language and character, and
the composition of a native prince.

«They were brought home by me three years ago, on
my return from India, where I was serving with my regiment,
and were given me by the Prince for the purpose of being
presented to some scientific Institution.

«‘ They are the composition of Nuwab Shums-ool-oomrah
of Hyderabad, in the Nizam’s Country; a prince who has
distinguished himself much by his scientific acquirements,
his original genius, and general love of literature. He has
great curiosity about every European invention, and his
house is set round with every sort of mechanical contrivance.
These works were printed by himself in his lithographic
printing press. The large work is on geometry and trigo-
nometry; the two smaller are on spherical trigonometry and
logarithms.

‘*T remain, Sir, &c.
«Tuomas Hunter, M.D.,
“ Assistant-Surgeon, 12th Royal Lancers.

* To the Secretary of the
* Royal Irish Academy.”

DONATIONS.

Three Lithographed Manuscripts in Persian, on Geo-
metry, Trigonometry, and Logarithms. By the Prince Shums-
ool-oomrah, of Hyderabad. Presented by Thomas Hunter,
M. D., &c.

Ordnance Survey of Kilkenny, in 49 Sheets. Presented
by His Excellency the Lord Lieutenant.

258

Statistical Returns of the Dublin Metropolitan Police for
1841. Presented by the Commissioners.

Nouveau Catalogue des principales Apparitions d’ Etoiles
Filantes. Par M. Quetelet. Presented by the Author.

Annuaire de V Academie Royale de Bruxelles (1842).

Bulletins de lv Academie Royale de Bruxelles (1841).

The Manuscript Rarities of the University of Cambridge.
By James Orchard Halliwell, Esq. Presented by the Author.

Notes on the United States of North America in 1838-9-
40. By George Combe, Esq.,Hon. M.R.1I. A. Presented by
the Author.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1842. No. 85.
June 13.

REV. HUMPHREY LLOYD, D.D., Vice-President, in
the Chair.

Maria Edgeworth was elected (by acclamation) an Ho-
norary Member of the Academy.

Arthur B. Cane, Esq., B. J. Chapman, Esq., Francis M.
Jennings, Esq., and Sir Thomas Staples, Bart., were elected
Ordinary Members.

Mr. J. Huband Smith read a paper descriptive of the
recent discovery of a vast number of Cinerary Urns at the
Hill of Rath, within a few miles of Drogheda, on the road to
Collon.

At the foot of the hill a quarry had been opened to pro-
cure stones for the repair of the road. In the beginning of
spring the tenant in the occupation of the farm proceeded
to level this quarry, by carrying down the earth from the
brow of the hill; and in the progress of his work he disco-
vered from 150 to 200 urns of unbaked clay, of various sizes,
almost all placed in an inverted position, and covering, each
of them, a considerable quantity of human bones. ;

As it seemed probable that a more careful examination
of the portion of this interesting rath or tumulus which yet
remained undisturbed might be productive of some discovery

VOL, Il. ¥

260

calculated to throw light upon the still unsettled question of
the date of this mode of interment, as well as “ the authors
of these sepulchral memorials,” Mr. Smith was induced to
undertake it, and accordingly proceeded to the spot for that
purpose on the 30th of November last.

The rath appears to have occupied the declivity of a
hill, sloping gently to the west, and was originally enclosed
by a breastwork of earth, of inconsiderable elevation, all
trace of which had nearly disappeared, but which, according
to report, may have once enclosed a space of five or six
acres. The soil upon the surface having been found to con-
sist of rich clay, had been from time to time spread over the
poorer land adjoining. It was not, however, till the process
of levelling was begun that urns were discovered; they were
then found at a depth of from four to five feet beneath the
original surface, resting upon the till, or gravelly subsoil.

Mr. Smith proceeded to a part of the hill pointed out to
him as not having been yet disturbed, and, with the assistance
of a few labourers, very soon had the satisfaction of laying
bare four or five, or more urns. They were placed appa-
rently without any regularity, about two or three feet asun-
der, and having been imbedded in yellow clay, without any.
flags or other stones to protect them, had in most cases been
pressed in, and broken to pieces, by the superincumbent
earth. One, however, which remained whole, Mr. Smith,
by the utmost care in freeing it from the moist clay which
surrounded it, and by allowing it to dry for two or three
hours before he ventured to move it, was enabled to carry
away entire, and he now presented it, with its contents, to the
Academy.

These urns varied in size, and were in general from about
eight to fifteen inches in height. Closely adjoining one of
the larger ones, in fact crushed against it, lay two smaller,
measuring probably but two or three inches each in diameter;
these latter ones did not appear to have held bones. In

261

another instance a group of three or more urns, of a larger
size, appeared pressed together. On removing the broken
pieces of each urn the bones appeared in a little conical heap
within, in very small fragments, the larger ones having fallen
to the sides, mixed at bottom with black unctuous earth, and
occasionally small morsels of charred wood. In the very
large and fine iurn which had been found previous to Mr.
Smith’s visit to the tumulus, and which he now presented to
the Academy in the name of Mr. Kelly of Drogheda, by
whom it had been disinterred, some very interesting matters
had been found mixed up with a very considerable quantity
of human remains which it contained. ‘These consisted of a
flint arrow head, a curious curved needle of bone, one end
of which was flattened and perforated, and some small stone
tools, one of which seemed likely to have been used in
making the indentations or rudely sculptured patterns by
which this urn, in common with all the others, was orna-
mented; and lastly, a small, thin scale of copper, pierced with
asmall hole. No other metallic remains of any kind were dis-
covered, nor upon the closest inquiry does there seem any
ground for supposing that any ornaments, either of silver or
gold, such as have been so frequently obtained in barrows
and other sepulchral tumuli, both here and in England, were
found in this rath. This last mentioned urn, which was the
largest discovered here, measures seventeen inches in height,
and the same in extreme breadth; and would probably con-
tain about eight gallons of liquid.

The most remarkable differences between this tumulus
and most other repositories of the ashes of our pagan pre-
decessors, both in this country and in England, appear to be
the vast number of urns which were found here, in one vast
cemetery, and the total absence of any kist of flags, or other
cavity formed to receive and protect the urns from the pres-
sure of the earth either laterally or from above.

Ye

262

A paper entitled, ‘‘ An Inquiry as to the Coefficient of
Labouring Force in Overshot Water-Wheels, whose diameter
is equal to, or exceeds the total descent due to the fall; and
of Water-Wheels moving in Circular Channels,” was read
by Robert Mallet, Esq., Mem. Ins. C. E., M. R.I. A.

This paper is partly mathematical and partly experimen-
tal. The investigation which it describes, the results of
which are given in ten tables, had in view principally to ob-
tain definite experimental answers to the following ques-
tions :

Ist. With a given height of fall and head of water, or in
other words, with a given descent and depth of water in the
pentrongh, will any diameter of wheel greater than that equal
to the fall give an increase of labouring force (i. e. a better
effect than the latter), or will a loss of labouring force result
from such increase of diameter ?

2nd. When the head of water is necessarily variable, un-
der what conditions will an advantage be obtained by the
use of the larger wheel, and what will be the maximum ad-
vantage ?

ord. Is any increase of labouring force obtained by causing
the loaded are of an overshot wheel to revolve in a closely
fitting circular race or conduit, and if so, what is the amount
of advantage, and what the conditions of maximum effect ?

The author briefly reviews the history of our knowledge
of this branch of hydrodynamics, the experimental researches
of Da Borda, Smeaton, &c., and the more recent improve-
ments in the theory of water-wheels, due to the analytic
investigations of German and French engineers, and the
admirably conducted experiments of Poncelet, Morin, and
the Franklin Institute.

Smeaton, in his paper on water-wheels, read to the Royal
Society in May, 1759, and Dr. Robison of Edinburgh, in his
treatise on water-power, lay downas a fixed principle, that no
advantage can be obtained by making the diameter of an over-

263

shot wheel greater than that of the total descent, minus so much
asis necessary to give the water a proper velocity on reaching
the wheel. The author, however, contends that the reasoning
by which the latter writer upholds this is inconclusive,—that
there are some circumstances which he points out necessarily
in favour of the larger wheel, and that conditions may occur
in practice in which it is desirable to use the larger wheel,
even at some sacrifice of power; and that hence it is of im-
portance to ascertain its value in use, as compared with
Smeaton’s size for maximum effect.

The author states the general proposition, ‘ that the la-
bouring force (travail of French authors, or mechanical power
of Smeaton) of any machine, transferring the motive power
of water, is equal to that of the whole moving power em-
ployed, minus one-half of the vés viva lost by the water on
entering the machine, and minus one-half of the vis viva due
to the velocity of the water on quitting it.” He then obtains
general equations expressing the relations between the fall,
the velocity, the weight of fluid, the power, &c. in overshot
water-wheels, at whatever point the water may first reach
the wheel, and whether the latter move naked, or in a cir-
cular channel or course. From these he deduces, that—

Ist. If the portion of the total descent passed through by
the water, before reaching the wheel, be given, the velocity of
the circumference should be one-half that due to this height.

2nd. If the velocity of the circumference be given, the
water must descend through such a fraction of the whole fall,
before reaching the wheel, as will generate this velocity.

ord. The maximum of labouring force is greater as the
velocity of the wheel is less, and its limit theoretically ap-
proaches that due to the whole fall; general equations are
then given, expressing the amount of labouring force in all
the conditions considered by the author, and their maxima.

One of the principal advantages of using an overshot
wheel greater in diameter than the height of the fall, is the

264

capability thus given of making any additional head of water
occurring at intervals, by freshes or any other cause, -avail-
able, by letting the water on the wheel at higher and higher
levels.

The first course of experiments is devoted to the deter-
mination of the comparative value of two water-wheels, the
one whose diameter is equal to the whole fall; the other to
the head and fall, or to the total descent. By the head, the
author always means the efficient head, or that due to the
actual velocity of efflux at the sluice or shuttle, as determined
by Smeaton’s experimental method,—this was equal to six
inches in all cases.

The apparatus employed in these researches consisted of
two accurately made models of these wheels, with curved
buckets, made of tin plate, the arms, &c. of brass, and the
axes of cast iron, working on brass. Special contrivances
were adopted to measure the weight of water passed through
each wheel in each experiment, which was in every case
1000 lbs. avoirdupoise; and others, to preserve the head of
water quite constant,—to determine the number of revolu-
tions made per minute, and thence the speed of the wheels.
One wheel was 25.5 inches diameter, the other 33 inches
diameter. The value of the labouring force was determined
directly by the elevation of known weights to a recorded
height by a silken cord over a pulley; the altitude was read
off, on a fixed rule placed vertically against a lofty chimney.
The relative power of the wheels was determined by the
speed of rotation of a regulating fly or vane.

All the principal results given in the ten tables are the
average of five good experiments. Yrom the accurate work-
manship and large size of these models, the peculiar con-
trivances for ensuring accuracy of observation, and the care
taken in the experiments, the author reposes considerable
confidence in his results as practical data.

The velocity, in reference to maximum effect, isdetermined,

265

and found to be lower than that deduced by Smeaton from
his experiments, which the author presumes arises from the
better construction of apparatus, and better form of bucket
used in the present case.

The author then ascertains, by another train of experi-
ments on both wheels, the value of the circular conduit or
race, and finds, in round numbers, that there is an economy
of labouring force, amounting to from eight to eleven per cent.
of the power of the fall, obtained by its use. This conduit
acts by retaining the water in the buckets at the lower por-
tion of the loaded arc. The velocity of a water-wheel work-
ing thus, he finds may vary through a greater range without
a material loss of power than when working naked, and that
a steady motion is also continued to a much lower velocity.

The author arrives at the following practical conclusions :

Ist. When the depth of water in the reservoir is inva-
riable, the diameter of the water-wheel should never be
greater than the entire height of the fall, less so much of it
as may be requisite to give the water a proper velocity on
entering the buckets.

2nd. When the depth of water in the reservoir varies
considerably and unavoidably in depth, an advantage may
be obtained by applying a larger wheel dependent upon the
extent of fluctuation and the ratio in time that the water is at
its highest and lowest levels during a given prolonged period ;
if this be a ratio of equality in time there will be no advan-
tage, and hence in practice the cases will be rare where any
advantage will be obtained.

3rd. If the level of the water in the reservoir never fall
below the mean depth of the reservoir, when at the highest
and lowest, and the average depth be between an eighth and
a tenth of the height of the fall, then the average labour-
ing force of the large wheel will be greater than that of the
small one, and it will of course increase this advantage at
periods of increased depth of reservoir.

266

Hence the author affirms that Dr. Robison’s conclusions
must henceforth receive a limitation.

Having shown that a positive advantage is obtained by
the use of the circular conduit, amounting to about eleven
per cent. of the total power, and that this value increases
with an increase in the velocity of the wheel up to six feet
per second, or more in large wheels, the author contends,
that it is practicable to increase the efficiency of the best
overshot wheels as now usually made, at least ten per cent. by
this application. The only objections ever urged against the
conduit were of a merely practical character, and the author
shows that improved workmanship, and the modern use of
cast iron, of which the conduit may be constructed, and
provided with adjustments, render these no longer tenable.

Drawings of the apparatus used in these researches, and
the tabulated results, were exhibited to the Academy.

Professor Lloyd read a paper ‘‘ on the Phenomena of Thin
Plates in Polarized Light.”

The author stated, that his attention had been drawn to
this subject by a letter which he had received from Sir David
Brewster, describing a large class of hitherto unobserved
phenomena. Sir David Brewster having expressed his de-
sire, in this letter, to know whether the wave-theory could
furnish an explanation of the facts which he had observed,
Professor Lloyd was thus led to undertake the investigation
which formed the subject of the present communication.*

Mr. Airy had long since inferred, from a consideration of
the form of Fresnel’s expression for the intensity of reflected
light, that when light, polarized perpendicularly to the plane

* The present paper was read in the Mathematical Section of the British
Association, last year; anda summary of the results was published in the dthe-
neum, of August, 1841. The author deferred submitting it to the Academy, in the
hope of being able to add an experimental confirmation of some of the conclusions
not noticed by Sir D. Brewster. He has, however, been compelled, by the pressure
of other duties, to postpone still further this branch of the investigation,

267

of incidence, was incident upon a thin plate bounded by
media of unequal refractive powers, a remarkable change in
the reflected light should take place, when the angle of inci-
dence was intermediate to the polarizing angles of the two
surfaces of the plate. This theoretical anticipation was fully
verified by experiment. When a lens of low refracting power
was laid upon a plate of high refracting power, the rings
which were formed appeared with a black centre, when the
angle of incidence was less than the polarizing angle of the low
refracting substance, or greater than the polarizing angle of the
high refracting substance ; while, when the incidence was in-
termediate to these two angles, the rings were white-centred,
and the whole system was complementary to what it had been
before. At the polarizing angle itself the rings disappeared,
there being no light reflected from one of the surfaces of the
plate, and therefore no interference.

The examination of this subject has since been re-
sumed by Sir David Brewster; and he has repeated the ex-
periments of Mr. Airy in a more general form, the incident
light being polarized in any plane. He has thus been led to
many new results. The rings are found to disappear under
circumstances in which light is reflected from both surfaces
of the plate; and there are many remarkable peculiarities in
the transition of the rings into the complementary system.*

It was to the theoretical explanation of these phenomena
that Professor Lloyd now invited the attention of the Aca-
demy. In the conduct of the investigation he has generalized
the methods followed by M. Poisson and Mr. Airy on the
same subject. The incident vibration being resolved into
two, one in the plane of incidence, and the other in the per-
pendicular plane, each portion will give rise to an infinite
series of reflected vibrations, into which it is subdivided at
the bounding surfaces of the plate. The expression of the
resultant intensity, for each portion, being then deduced, the

* The researches of Sir David Brewster are now published in the Philosophical
Transactions for 1841,

268

actual intensity of the reflected beam is the sum of these in-
tensities. Its value is found to be expressed by the formula
u’+2 uu! cos a . 5 w+2ww’ cos aw!
I = cos” Y ies 2 bist + sin’y is SNS
1+2uu'cosa+ u7? 1+ 2ww’cosa +ww
in which w and w’ denote the ratios of the reflected to the in-
cident vibration at the two surfaces of the plate, when the
light is polarized in the plane of incidence; w and w’ the
corresponding quantities for light polarized in the perpen-
dicular plane; anda the difference of phase of the successive
portions of the reflected beam. The values of w, wu’, w’, w, are,

_sin(9—6’) gibt sin(@’— oe __ tan(0— an(8— 6") guia tan(0’—@”)

~ sin(0+0)’ ~~ sin(@+ Q”) ~ tan(0+0)’~ ~ tan(@/+0”)
where 0 denotes the angle of incidence on the first surface of
the plate; 6’ the corresponding angle of refraction, or the
angle of incidence on the second surface; and @” the angle
of refraction at the second. The value of a is

4
a= = T cos’;
t being the thickness of the plate, and X the length of the
wave.

When the obliquity of the incident pencil is not very
great, the squares and higher powers of u, w’, w, w’, may be
neglected in comparison with unity, and the expression of
the intensity has the approximate value,

I= cos’y(u? + 2uu'cosa + wu”) +'sin®y(w? 4+ 2ww'cosa + w”)
This quantity will be independent of the phase a, and there-
fore the intensity will be constani, and the rings désappear,
when

uu cosy + ww’'sin’y = 0;
that is, when the azimuth of the plane of polarization has the
value given by the formula,
till si cos (0@— 0’) cos (#’— 6”)
ww cos(0-+ 8’) cos (0 + 0’)

In this formula cos(@—8’) and cos (0’—0”) are always positive ;

tan?y = —

269

and accordingly the resulting value of tany will be real, and
therefore the disappearance of the rings possible, only when
cos(#+ 6) and cos(@ + 0”) are of opposite signs; i.e. when
the angles of incidence on the two surfaces are, in the one
case greater, and in the other less, than the polarizing angle.
The media at the two sides of the plate, therefore, must
have different refractive powers.

Again, the phases of the two portions of the reflected
beam, and which are polarized respectively in the plane of
incidence and in the perpendicular plane, are given by the

formulas,
HA TAOR w’(1—wu?) sina
oe u(1+w’) + w/(1+ uv?) cosa’
fain w'(1—w?) sina
ana’ =

w(1+ w”) +w’(l+w’) cosa

The phases, a’ and a", are consequently in general different,
and therefore the resulting light will be, in general, ellipti-
cally polarized. The author entered into some developments
connected with this part of the subject, which does not ap-
pear to have been noticed by Sir D. Brewster in the course
of his experimental inquiries; and he concluded by stating
the important bearings which it may possibly have upon the
phenomena of elliptical polarization by metals.

Professor Lloyd having, in the preceding commmnication,
thrown out the idea that the elliptical polarization of metals
might possibly be identified with that which is produced
by a thin film on the surface of a reflecting body, Pro-
fessor Mac Cullagh took occasion to observe that an analo-
gous, but far more general, hypothesis had occurred to
himself some years ago, among the various conjectures by
which he had sought to account for the remarkable dif-
ference between the action of metals and that of trans-
parent media in reflecting light. In his theory of crystalline
reflexion he had found it allowable to suppose that the
change in the elasticity of the ether, in passing out of

270

one medium into the other, takes place abruplly at their
common surface; and he had thought it not unlikely that the
supposition of agradual change of elasticity, taking place with-
in a very small space at one or both sides of the surface of a
metal, might afford an explanation of the peculiar phenomena
of metallic reflexion. Such a supposition would be mathe-
matically equivalent to the hypothesis that an immense num-
ber of films, of which the refractive powers vary between
given limits according to some law, compose a very thin
stratum at the surface of a polished metal; and it would
be in accordance with the inference drawn by Professor
Mac Cullagh from certain formulas (Transactions R.I. A.,
vol. xviii. p. 70) that the law of equivalent vibrations is not
observed in metals; an inference which, indeed, originally
suggested to him the hypothesis in question. He had not
yet compared the hypothesis with his formulas, but it was
easy to see that it would explain the non-existence of an
angle of complete polarization for metals, as well as the ge-
neral fact of elliptical polarization; and perhaps the metallic
brilliancy, difference of colour, &c. might be occasioned by
the great number of reflexions in the variable stratum at
the surface, and the endless variety of interferences pro-
duced by them.

The above was only one of the conjectures which had
been formerly made by Professor Mac Cullagh in relation to
this subject, and it was mentioned on this occasion chiefly on
account of its analogy with the view taken by Professor Lloyd.
Another and very different hypothesis, which was the first
that had occurred to him, as being immediately suggested by
the imaginary form which he had assumed for the velocity
of propagation in a metal, will be found stated in the Comptes
Rendus of the French Academy, tom. viii., p. 962, in a letter
to M. Arago, dated May 11,1839. It consisted in supposing
the amplitude of the vibration within the metal to be propor-
tional to acertain exponential of which the value is there given,
accompanied with the remark that this expression for the vibra-

271

tion, if introduced into the differential equations (at that time
unknown) which subsist at the confines of two media, would
probably explain the peculiar phenomena of metallic re-
flexion, such as change of phase, &c. Very soon after that
date the equations were discovered which hold good at the
common surface of two transparent media (see Proceedings
R.LA. vol.i., p.378); and it is certainly nota little singular that
these equations, with the help of the aforesaid expression for
the vibration, not only explain the change of phase, but lead
to the precise formulas which had been previously given for
the case of metallic reflexion (Transactions R. I. A. vol. xviii.
p- 71). The application of the equations, however, to this
case, cannot be regarded as legitimate without further proof;
and the hypothesis is attended by another difficulty, the na-
ture of which may be seen in the letter alluded to.

On the whole, Professor Mac Cullagh did not consider him-
self warranted, as yet, in choosing between his two hypo-
theses, nor even in concluding that one or other of them must
be the right one. Before constructing any refined theory, he
thought it necessary that the formulas to which he had re-
ferred, and which, if they are correct, must be the foundation
of the theory, should be tested by experiments more accu-
rate than any that had yet been made, and this was a task to
which he hoped he should soon have leisure to devote him-
self.

Professor Lloyd explained, that the hypothesis which he
had suggested had not been offered by him as an exact
physical representation of the optical constitution of metals ;
but rather as one which lent itself, with tolerable facility, to
mathematical expression, and the results of which might
possibly, by a suitable determination of the constants of the
formulas, be found to coincide with the phenomena, and
therefore with the results of a more rigid theory.

Resotvep,—T hat, in future, when the office of Secretary
of the Academy is vacant, the vacancy shall be filled up by
express election.

June 27.
REV. J. H. TODD, D. D., Vice-President, in the Chair.

H. J. Monck Mason, Esq., LL.D., read an account of
a visit which he had paid to the Tomb of the Volumnii at

Perugia.

Mr. Mason then presented a gold fibula found in Ireland,
as a contribution to the Museum of Antiquities, now in pro-
cess of formation by the Academy.

The thanks of the Academy were voted to Mr. Mason for
the donation.

A paper was read by Dr. Macartney ‘ on the minute
Structure of the Brain in the Chimpanzee and the human
Idiot, compared with that of the perfect Brain of Man, with
some reflections on the Cerebral Functions.”

The author commenced by stating, that he had disco-
vered the brain of all animals to be composed of a plexiform
arrangement of white (or, as he termed them, senéient) fila-
ments, the most delicate of which he found to pervade all the
coloured substances of the brain. He attributed the higher
sensorial powers of the cerebral organ to the disposition and
intercommunication of these filaments, more especially where
they exist in the coloured substances. The mode he em-
ploys for rendering the finer filaments evident is to moisten
the different substances during the dissection with a solution
of alum in water, which, causing a slight coagulation, makes
the filaments opaque and visible. ‘The author accounted for
the fact that the existence of the most delicate plexuses had
hitherto escaped observation, from the circumstance that
other anatomists had not used any fluid to coagulate them.
He considers the shape and magnitude of the different parts
of the brain as merely subservient to the proper arrange-
ment and number of the plexuses of the sentient substance.

273

The principal object of the paper was to point out the
first gradations from the perfect structure of the brain in
man, and for this purpose the author related the dissection
of the brain of the chimpanzee (simia troglodytes, Lin.) and of
two human idiots, from which he was led to conclude that the
primary deviations in the anatomy of the brain were to be
found in the essential structure of the locus niger, of the cor-
pus fimbriatum, and of the corpora olivaria,—in the existence
of the white strig in the fourth ventricle, of the corpora can-
dicantia, and of calcareous granules in the pineal gland,—in
the degree of intermixture of the white filaments of the arbor
vite, the distinction of the anterior crura of the fornix, and
lastly the decussations of the pyramids. By the dissections
it was evident that the brain of the chimpanzee possessed a
superior structure to that of the natural human idiot.

As the author had previously ascertained that all the
plexuses in the brain are conjoined, and all the cerebral and
spinal nerves are incorporated with the parts from which
they are said to arise, he was led to infer that the functions
of the brain are not confined to particular parts of the surface,
but that all the parts exercise a mutual influence on each
other, that its powers and operation are systematic and har-
monious, instead of the effect of different parts of the brain
acting independently and often in opposition to each other.
He stated a number of facts contradicting the opinion of the
cerebellum being designed to produce the sexual instinct, as
taught by Gall and his followers. He ascribed the origin of all
instincts to the organs to the operations of which the instincts
are subservient. He argued that if instinctive impulses were
to originate in the brain, they would interfere with all its
higher functions. The author further considered the per-
fect continuity and incorporation of the nerves with central
parts of the system, as sufficient to account for the functions
of sensation and voluntary motion, without the interposition
of nervous fluid.

274

Dr. Macartney exhibited a drawing of the base of the
brain of an idiot, in which there was a singular deficiency of
the cerebellum; and also a cast of the brain of the chim-
panzee, and one of the human brain. These two, making
allowance for the size, almost perfectly agreed with regard to
external appearances.

J. Huband Smith, Esq., by command of His Excellency
the Lord Lieutenant, presented to the Academy an ancient
gold semilunar ornament of considerable value, found in the
county of Roscommon.

The thanks of the Academy were voted to His Excel-
lency for this donation.

A considerable number of ancient bronze articles, con-
sisting of portions of chain armour, a spear head, a lance
blade, with some coins, found near Headfort, County Gal-
way, were presented to the Museum on the part of Richard
J. Mansergh St. George, Esq.

Mr. St. George received the thanks of the Academy.

The collection of Antiquities of the late Dean of St. Pa-
trick’s was presented to the Academy in the name of the
Subscribers.

ReEsoLtveD,—That the List of Subscribers be printed as
an Appendix to the Proceedings.*

* See Appendix, No. I.

275

August 4.
REV. C. W. WALL, D. D., in the Chair.

The President made a communication respecting a me-
thod which had been lately proposed by Professor Badano
of Genoa, for the solution of algebraical equations of the
fifth and higher degrees.*

Lagrange has shown that the function

P= (ae +r! +0? av” + wal! + wx’)?
receives only twenty-four different values, for all possible

changes of arrangement of the five quantities, v’,... 2x7, if
w be an imaginary root of unity, so that

vw + wo +o +v+1=0
Professor Badano has proposed to express these twenty-
four values by certain combinations of quadratic and cubic

radicals, suggested by the theory of biquadratic equations,
and having the following for their type:

= ay + V Hot A/a + V Ba + / Hs — ean,
+7 {H,+V H+ A A/ Ho V Bio + / Hu — V Hig
Ae §t3+V But 0 6/tis + Vv Bie + O'4/ Br — Vane
A fig + Hoy + 0? 4/ Har V Hoo + 8 A/ Hos— V Hod 5

6 being here an imaginary cube root of unity. He contends
that the twenty-four quantities, H,,...Ho,, are all symme-
tric functions of the five quantities x’,...a”; and that they
are connected among themselves by the sixteen relations
H3=H;, U4= He, H7 = Hi3 = Hig, Hg — Hi4 = Ho9, Ho = His— Hai,
Hyp = Hig= Ho, Hy) = Hi7 = Ho3, Hig—Hig—Hos, Ho=H1, Hio=Hi2-
EE SEERA SENSE eh EET aE

* Nuove Ricerche sulla Risoluzione Generale delle Equazioni Algebriche del
P. GeRotaAMo BaDANo, Carmelitano scalzo, Professore di Matematica nella R.

Universita di Genova. Genova, Tipografia Ponthenier, 1840. See also an “ Ap-
pendice” to the same work.

VOL. Il. Z

276

Sir W. Hamilton examines, in great detail, the composition of
the two conjugate quantities H,, He, which are each of the
thirtieth dimension relatively to the five original quantities
a’,...a"; and arrives at the conclusion that neither nH, nor
Hg is a symmetric function of those five quantities 2’,... 2”,
though each is symmetric relatively to four of them. He
finds also that these two quantities H, and Hg are not gene-
rally equal to each other, but differ by the sign of an imagi-
nary radical, namely,

(0— 6?) (ow—w’?— wv? + 0) = V —15,

when they are fully developed, in consistency with Professor
Badano’s definitions. Analogous results are obtained for
the two quantities H3, H;; and these general results are veri-
fied by applying them to a particular system of numerical
values of the five quantities 2’,...a”. It is shown also that
the three quantities H7, H)3, Hig, are neither independent of
the arrangement of those five quantities 2, nor (generally)
equal to each other. And thus, although 4, is symmetric,
and Hy vanishes, Sir W.H. conceives it to be proved that
Professor Badano’s expressions, for the twenty-four values
of Lagrange’s function ¢°, give no assistance towards the
solution of the general equation of the fifth degree, and
therefore that the same method could not be expected to
resolve equations still more elevated, even if we were not in
possession of an @ priori proof that no root of any general
equation above the fourth degree can be expressed as a func-
tion of its coefficients, by any finite combination of radicals
and rational functions.

DONATIONS.
Three Silver Coins, found at Rockingham, the seat of Vis-

count Lorton. Presented by C. T. Webber, Esq.
Copper Medal, “‘ The glorious attempt of LXIV. to pre-

+

277

serve the Constitution.” MDCCXLIX. Dublin. Presented
by Miss A. Clibborn.

The past and present Statistical State of Ireland exhibited
ina Series of Tables. By Cesar Moreu, Esq., F.R.S. Pre-
sented by James Hardiman, Esq.

Proceedings of the Royal Society of Edinburgh, Nos. 19,
20, for 1841-2.

Transactions of the Royal Society of Edinburgh. Vol.
XV. Part 2 (pp. 265-334).

Memoirs of the Literary and Philosophical Society of
Manchester. Vol. VI. New Series.

Statistical Returns of the Dublin Metropolitan Police for
the year 1841. Presented by the Commissioners.

Lecture on the Application of Science to Agriculture. By
Charles Daubeny, M.D. Presented by the Author.

Proceedings of the American Philosophical Society. From
November, 1841, to April, 1842.

The New County Book of Tipperary. By Jeffries Kings-
ley, M.R. I. A. Presented by the Author.

Proceedings of the Geological Society of London. Vol. III.
Part II. 1841-42. Nos. 77 to 83.

Fourth Annual Report of the Commissioners of the Central
Loan Fund Board of Ireland. (Act 1& 2 Vict. c. 78.) Pre-
sented by Mr. Piessé.

Transactions of the Ameriean Philosophical Society held
at Philadelphia.

Flora Batava, door Jan Kops. Nos. 123 and 124.

Niewe Verhandelingen Van het Bataafsch Genootschap der
Proefondervindelijke Wijsbegeerte te Rotterdam. Achtste
Deel. Tweede Stuk.

Copy of an Inscription found in Babylon by Harford
Jones, Esq. Presented by Professor H. H. Wilson.

Abhandlungen der Philosophisch-Philolog. Classe der
Keniglich Bayerischen Akademie der Wissenschaften, Drit-

278

ten Bandes Zweite Abtheilung, in der Reihe der denkschriften
der XVIII, Band.

Philosophical Transactions of the Royal Society of Lon-
don for the Year 1842. Part I.

Abhandlungen der Mathematisch-Physikalischen Classe der
Keeniglich Bayerischen Akademie der Wissens-chaften, Drit-
ten Bandes Zweite Abtheilung, in der rethe der denkschriften
der XVI. Band.

Ueber das Magnetische Observatorium der Kénigl. Stern-
warte bet Miinchen. Von Dr. J. Lamont. Presented by the
Author.

A Piece of Leather, found in taking up Part of the old
City of Dublin Wall, adjoining the old Tower in the lower
Castle Yard, by Mr. Johnson, and which is supposed to have
lain there since the Year 1202, Presented by W. Farren, Esq.

Memoires de l’ Institut de France. Academie des Sciences
Morales et Politiques. Savans Etrangers, Tome I.

Academie des Sciences Morales et Politiques. 'Tome III.

Memoires preseniés par divers Savans al Academie Royale
des Sciences de U Institut de France. Sciences Mathema-
tiques et Physiques. ‘Tome VII.

Memoires de l'Institut de France, Academie Royale des
Sciences. Tome XVIII.

Notices et Extraits des Manuscrits. Tome XIV. 2nd
Partie.

Archeologia. Vol. XXIX.

Journal of the Statistical Society of London. Vol. V.
Part 2. July to September, 1842.

Archives du Musée d'Histoire Naturelle. Tome lI. Liv.
1,2, 3,4; and Tome II. Liv. 1 and 2.

The South Australian Almanack for 1842. By James F.
Bennett. Presented by George Davies, Esq., T. C. D.

Proceedings of the Zoological Society of London. Part
IX. 1841.

Pe eee a

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1842. No. 36.

November 14.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The Secretary read a paper by Sir David Brewster, “on
the Compensations of Polarized Light, with a description of
a Polarimeter for measuring Degrees of Polarization.”

The author first directed attention to the difference of
opinion between him and most other philosophers, as to the
constitution of partially polarized light; it being generally
supposed that such light is a mixture of common light and
perfectly polarized light, whilst he considers that the entire
quantity of light undergoes a physical change by approxima-
ting more or less to the condition of light completely pola-
rized. Upon this view he had long since explained the laws
of polarization discovered by himself, but he had been
anxious to obtain experimental evidence capable of deciding
between the two ideas, and in this he considers that he is
now successful.

By means of experiments,—described in the paper,—-the
author points out that when two portions of light oppositely
polarized compensate each other, the proportions and con-
ditions necessary are not those which could result from mix-

_ tures of common light with fully polarized light, and hence
infers that the pencils must be wholly in different physical
conditions. These experiments led him to the invention of

VOL. II. Dee IN

280

an instrument termed the Compensating Rhomb, by means of
which he considers decisive evidence of the correctness of
his views has been obtained.

Tn order to determine if this principle be general, and to
ascertain the laws of the compensation of polarized light,
Sir David Brewster constructed an instrument for measuring
the degrees of polarization. This he calls a Polarimeter. It
consists of two parts, one of which is intended to produce a
ray of compensation, having a physical character susceptible
of numerical expression, and the other to produce polarized
bands, or rectilinear isochromatic lines, the extinction of
which indicates that the compensation is effected. ‘The de-
tails of the construction of the instrument are fully given in
the memoir, and numerous experiments made with it, and
confirmatory of the author’s views, are described.

In conclusion, Sir D. Brewster points out as the general
results of his inquiries, as follows:

“1, The first and most important result of this inquiry
is, that it affords a new and independent demonstration of the
laws of the polarization of light by reflexion and refraction,
given in my papers of 1830. As this result has been already
referred to, I shall merely mention the following general
proposition.

‘© When a ray of common light is incident at any angle
upon the polished surface of a transparent body, the whole
of the reflected pencil suffers a physical change, bringing it
more or less into a state of complete polarization; inwirtue
of which change, its planes of polarization are more or less
turned into the plane of reflexion, while the whole of the re-
fracted pencil has suffered a similar, but opposite change, in
virtue of which, its planes of polarization are turned more or
less into a plane perpendicular to the plane of reflexion.

2, Asthe light of the sky and the clouds is more or less
polarized, the employment of the light which they reflect
may, in delicate experiments, be a serious source of error, if

vl

251

we are not aware of its properties. By the principle of com-
pensation, however, we may convert this partially polarized
light into common light, and thus make experiments with as
great accuracy in the day-time, as we can do with the direct
light of a flame. If the light from a particular part of the
sky be admitted into a dark room, or otherwise employed, we
have only to compensate its polarization either by reflexion
or refraction, and employ, as unpolarized or common light,
that part of the light which corresponds with the neutral
line.

«3. The laws of the compensation of polarized light enable
us to investigate the polarizing structure of the atmosphere,
and to ascertain the nature and extent of the two opposite
polarizing influences, which I have found to exist in it, and
by the compensation of which the neutral points are pro-
duced. But, as I shall soon submit to the Society the results
of my observations on this subject, I shall not add any thing
further at present.

“4. Inevery case where reflected or refracted light reaches
the eye of the observer, whether it comes from bodies near
us, or from the primary or secondary planets of our system,
the doctrine of compensation enables us to obtain important
information respecting the phenomena presented by light
thus polarized. The nature of the reflecting or refracting
surface, the angles of reflexion or refraction, and the nature
of the source of illumination, may, in certain cases, be ap-
proximately ascertained.

“5. When the light of the sun, or any self-luminous body,
is reflected from the surface of standing water, such as the
sea or a lake, it is polarized according to laws which are well
known; but when the partially polarized light of the sky
(light polarized in every possible plane, passing through the
sun and the observer) is reflected, a variety of curious com-
pensations take place, which, when the position of the ob-
server is fixed, vary with the season of the year, and the hour

2A2

282

of the day. In some cases, there is a perfect compensation,
the partially polarized light of the sky being restored to
common light by the reflection of the water. In other cases
the light of the sky has its polarization increased by re-
flexion from the water in the same. plane in which it was
itself polarized; and in other cases, the compensation is:
effected only in particular planes. At sunset, for example,
the light reflected from the sea at a great obliquity in two
vertical planes inclined 45° to a vertical plane passing through
- the sun and the observer, is compensated in these two planes,
or the plane of its polarization is inclined about 45° to the
reflecting surface. The same observations apply to the light
of the two rainbows when reflected from the surface of
water.

“6. When the light of the sky, or of the rainbow, is re-
flected from surfaces not horizontal, such as the roofs of
houses, sheets of falling water, or surfaces of smoke and va-
pour, the compensations are more varied, and a perfect
neutralization of the light by the second reflexion is more
frequently obtained.”

Professor Lloyd mentioned some circumstances which
appeared to be opposed to Sir David Brewster’s views.

Professor Kane commenced the reading of a paper “ on
the Tannin of Catechu, and the chemical Substances derived

from it.”
The abstract of this paper will be printed when the con-

clusion has been read.

DONATIONS.

Transactions of the Zoological Society of London, Vol.
III. Partl. 1842.

Reports of the Auditors and Council of the Zoological
Society of London, April 29th, 1842, and List of Members.’

oI ye a ale ii a

283

Proceedings of the Royal Society. Nos. 52, 53.

Supplementary Appendix to the Report of the Poor Law
Commissioners of the Medical Charities in Ireland, with In-
dexes. 1841. Presented by the Commissioners.

A pamphlet entitled, “ Is Selenium a true Element?” Pre-
sented by Septimus Piesse.

November 30. (Stated Meeting.)
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

John Anster, LL. D., was elected a member of the Com-
mittee of Polite Literature, in the room of the Rev. Dr.
Porter, who had resigned.

ReEso_vep,—On the recommendation of Council,—That
Mr. E. Curry be employed to make a Catalogue of the Irish
MSS. in the Library of the Academy, for the sum of £100.

The Secretary read a letter from George Birch, Esq.,
presenting to the Academy an ancient tombstone, from the
Abbey of Monahinchy, with an inscription in the Irish cha-
racter.

Resotvep,—That the thanks of the Academy be given
to Mr. Birch for his donation.

Rev. Dr. Todd, V.P., gave the following account of the
Proceedings of the Committee for the purchase of the late
Dean of St. Patrick’s collection of Irish Antiquities, which
had been recently presented to the Academy.

“It has been thought fitting that some record should appear in
the Proceedings of the Academy of the successful efforts that have
been made under the direction of the Committee of Antiquities, for
raising the subscription, which has preserved from dispersion, and

284

placed in the safe keeping of this Society the invaluable Collection
of Irish antiquities belonging to our late lamented Vice-President,
the Dean of St. Patrick’s.

“‘ Tt was well known to all his intimate friends that one of the
principal motives that influenced him in the formation of his Mu-
seum, next to the zeal for the preservation and study of antiquities
which characterized him, was a wish to have his collection pre-
served for public use, under the care of the Royal Irish Academy.

“«« As soon as it was ascertained, therefore, that he had died intes-
tate, and consequently without making any provision for carrying these
his often expressed wishes into effect, many of his personal friends,
knowing how deeply he would have deprecated the dispersion of his
Collection, felt anxious, were it only as a testimony of respect to his
memory, that the Irish part at least of the Museum should be ob-
tained for the Academy; and in this they were warmly seconded by
all who were aware of the value of the Collection, and who felt the
great importance of a National Museum of Antiquities to the study
of our ancient history.

“‘ Accordingly, at the Stated Meeting of the Academy in No-
vember; 1840, soon after the lamented death of the Dean, the sub-
ject was brought forward, and the Committee of Antiquities were
requested to take immediate steps towards opening a subscription
for the purchase of the Irish part of the collection.

“The Committee met immediately after, and their first act was
to publish in the principal newspapers of Dublin a short address,
for the purpose of ascertaining the state of public feeling on the
subject. A circular was also prepared, and sent to the principal
nobility and gentry of Ireland, to all in short, as far as they could
be ascertained, who were thought likely to take an interest in the
design.

‘¢ This was all that could be done at that time. The absence of
Mrs. Dawson on the Continent, and the consequent difficulty of as-
certaining the wishes of the Dean’s family, rendered it impossible
to discover what sum they were likely to accept for that portion of
the Museum which the Committee were commissioned to purchase,
or indeed whether they would consent at all to separate the —
part of the Collection from the rest.

285

“From this unavoidable delay, the zeal of many appeared to
cool, and the subscription for a time proceeded but slowly; but at
length, on the 27th of March, 1841, the Committee took the bold
step of authorizing Mr. Petrie and Dr. Aquilla Smith to offer £1000
for the Collection.

“«T should have mentioned that this sum was decided upon after
an exact valuation of the whole. The coins were valued by Dr.
Aquilla Smith, and the other antiquities, at Mrs. Dawson’s special
request, by Mr. Petrie; and the sum at which these gentlemen fixed
the value of the Collection was £1060. The Committee were of
opinion, therefore, that in offering the sum of £1000, they were
dealing fairly with the public fund entrusted to them; while by
striking off about six per cent. from the amount of the valuation,
they were only allowing for the necessary expenses which would
have attended the sale of the Museum had it been submitted to a
public auction.

“* It was not, however, until the 26th of June following that a
final answer was obtained from the Dean’s family to the proposal of
the Committee. On that day Dr. Smith reported that Mrs. Dawson
had consented to accept the offered sum, and also that she was will-
ing to allow three months from that date for its collection.

“* New efforts were then made by the Committee: circulars were
again sent out, and an address to the public was inserted in the
newspapers ; a deputation was appointed to wait on His Excellency
the Lord Lieutenant, who contributed £20 to the fund; and in
short every exertion was made to rouse the friends of Ireland to the
importance of the great national object that was in view.

“< The success that has crowned these efforts is mainly owing to
the zealous manner in which the exertions of the Committee were
seconded by some other members of the Academy, who aided them
by their advice and counsel, and also by their invaluable and inde-
fatigable labours. Of these it is impossible to avoid naming Mr.
Carr and Mr. Hutton, as the individuals to whose cooperation the
Committee were most deeply indebted for the success of their un-
dertaking ; and although it is obviously improper to allude to any
individual of those who were members of the Committee itself, yet
I feel sure I shall be pardoned in departing from strict propriety so

286

far as to say, that to the exertions of Dr. Aquilla Smith and Mr. Petrie,
their intimate knowledge of the contents and value of the Collection,
and their good offices with the family of the Dean, the Academy
and the country are mainly indebted for the possession of the trea-
sures which have been added to our Museum.

“« Still, ‘however, the subscriptions for some time came in so
slowly, that it became necessary to solicit more time for collecting
the money than was originally agreed upon; and this request was
acceded to by Mrs. Dawson, with a liberality for which she deserves
the gratitude and the thanks of the Academy.

‘« At length on the 9th of April of the present year, the first in-
stalment of £500 was paid to Mrs. Dawson, and the Collection was
soon after removed to the Academy House, under the superinten-
dence of Dr. Aquilla Smith.

‘A guarantee for the payment of the remaining half of the
purchase money having been given to Mrs. Dawson by certain sub-
scribers to the fund, the Antiquities were at first placed under the
custody of those gentlemen; who bound themselves to hand over
the Collection to the Committee as soon as the debt for which they
had made themselves responsible was discharged.

“* On the 31st May the whole remainder of the purchase money
was paid to Mrs. Dawson, and the gentlemen who had so liberally
come forward to guarantee its discharge were released from their
obligation. It was found also, that after the payment of all the
incidental expenses, a balance remained at that time in favour of the
fund to the amount of £24 17s. 6d. This balance was subsequently
increased by some subscriptions that afterwards came in, and the
whole overplus has been applied, under the direction of the Com-
mittee, to the purchase of some valuable antiquities, which have been
added to the Collection.

“In recording this last stage of the proceedings of the Com-
mittee it is necessary to remark, that but for the public spirit of the
individuals who came forward to give their personal security to
Mrs. Dawson for the payment of the purchase money, all would
have been lost, and the Museum would necessarily have been sent
for public sale to London. For although at that time the stipulated
sum had been very nearly promised, yet many of those who had put

—pS es

287

down their names had not paid their subscriptions, and the time ne-
cessary for collecting the money would have exceeded the limit to
which the Committee had bound themselves to Mrs. Dawson; and
thus she would have been left at liberty to take other means for
disposing of the Museum. It is necessary, therefore, that the Aca-
demy should know that the gentlemen who came forward to rescue
the Committee from a dilemma which would have made vain all
their previous exertions, and to whom we are therefore so particu-
larly indebted for the great step that has been made towards the
formation of a National Museum, are George Carr, Esq., Dr. Aquilla
Smith, Professor Mac Cullagh, Thomas Hutton, Esq., and Robert
Callwell, Esq.

‘¢ The thanks of the Academy are also due to Mr. Clibborn for
his invaluable services throughout the whole of these transactions,
and particularly in the last stage of them, when it became necessary
to make exertions to call in the subscriptions that had been pro-
mised, and to take steps, after the Museum had come into our pos-
session, for the arrangement and safe keeping of its contents. To
him also we are indebted for the ingenious plan for a new Board

Room, which has received the approval of the Council, and is sub-

mitted to your consideration this evening: a plan which will enable
us to convert the room in which we are now assembled into a Mu-
seum, where the treasures of which we are now the guardians, may
be displayed in a manner useful to the public, and their permanent
security duly provided for.

“‘The special thanks of the Academy are also due to Messrs.
Boyle, Low, Pim, and Co., who kindly permitted subscriptions to
be paid at their house, without any charge whatsoever to the fund ;
and whoalso offered to advance to the Committee any sum that might

‘be required as a temporary accommodation, during the necessary

delay that attended the collection of the subscriptions. This liberal
offer the Committee were compelled to avail themselves of, by
drawing upon Messrs. Boyle and Co. for a sum of £53 15s. 5d. on
the Ist of June last, a sum which was not entirely repaid for up-
wards of two months afterwards.

““It is proper to mention here, that His Excellency Earl De
Grey, in addition to his subscription to the fund for the purchase of

288

the Dawson Collection, has also been pleased to present to the
Academy a valuable Aision of gold, which was recently found in
the county of Roscommon, and of which His Excellency became the
purchaser, for the express purpose of placing it in our Museum. Mr.
H. J. Monck Mason also, in addition to his subscription, presented a
very beautiful gold Fibula, of considerable weight and value.

‘< Tt should be distinctly understood, that the subscriptions re-
ceived have enabled the Committee to pay all the expenses attendant
upon these transactions, without any charge whatsoever to the funds
of the Academy.

“The Academy, as a body, have had nothing whatsoever to do
with the purchase of the Museum, and there will be found among
the subscribers very many names of gentlemen who are not mem-
bers of, or in any way connected with our Society. The Museum,
therefore, strictly speaking, is the property of the subscribers, and
is by them presented to the Academy, to be kept by us in trust, for
the benefit of the public. The Academy, as a Corporation, have
contributed nothing to the purchase, except so far as their consent-
ing to take the charge of so valuable a gift, and to provide a room
for its exhibition, may be considered, as it doubtless is, a most im-
portant contribution to the great end which the subscribers have
had in view.

“‘ The accounts of the Committee have been audited by Messrs.
Callwell and Hutton; they are in the hands of Mr. Clibborn, and
are open, of course, to the inspection of any of the contributors.

“It may be well now to say a few words on the value and con-
tents of the Museum of which we are thus become the guardians.

“ The Museum contains no less than ninety-seven ornaments of
solid gold, whose total weight amounts to 98 oz. 144. dwt. It pos-
sesses also 252 articles of pure silver, and 1674 bronzes and other
antiques, composed of pottery, amber, glass, and the baser metals.

‘« This enumeration does not include the coins and medals, which
are of singular interest and value, and of which a catalogue, in the
handwriting of Dean Dawson, is now on the table.

‘* To specify the various articles of value and interest more par-
ticularly, so far at least as to give any detailed account of them,
would be too great a trespass on your time, even if I could feel my-

289

self fully competent to the task; but it is impossible to close this
Report without endeavouring to give you some rough and general
view at least of the treasure which we have now obtained.

“* Among the gold ornaments are twenty-seven fibula, one of
them of considerable size; three perfect torques, and fragments of

-some others; two gorgets; two singular hollow balls or beads of
gold, which were found with eleven others in the County of Ros-
common, and which the Dean saved from the crucible of the gold-
smith; a most interesting collection of ancient finger rings, and
sixteen specimens of the small solid rings of gold, which are be-
lieved to have been the current money of the ancient inhabitants of
Treland.

“‘ The collection of silver finger rings and of ancient seals, is of
great interest and value. Among them will be found the matrices
of the seals of the O’Neills and other Irish chiefs, with several ec-
clesiastical seals of various periods.

«There is a remarkable collection of the ancient Irish bells,
whose uses and history our friend Mr. Petrie has so ably discussed ;
some of these are the large bells, which once, perhaps, were sus-
pended in the Round Towers ; others are the small altar bells, many
of them exhibiting proofs of great antiquity. One of the large bells
contains an Irish inscription, which proves it to be as old as the
ninth century.

“The collection of military weapons and other antiques con-
nected with the warfare of our ancestors is of great extent and
value. It contains a great variety of specimens, in excellent preser-
vation, of the flint arrow heads and spear heads, which are supposed
to have been the most ancient weapons in use in Ireland; a large
number of the peculiar weapon, in stone and bronze, called celts, of
all the sizes and forms in which they are found; and a magnificent
collection of swords and spear heads, from many of the remarkable
fields of battle recorded in the history of Ireland.

“It would be drawing too much on your patience to enter
more particularly into a description of particular objects of interest
in this Collection ; at some future time it might perhaps be an enter-
taining, as well as an instructive task (if some of our antiquaries
would undertake it), to exhibit to the Academy, from time to time,

290

the more remarkable and important articles of our Museum, with
remarks on their history, and use. But a more fitting occasion for
this will perhaps be found, when Tuz Dawson Coxuzction is pro-
perly arranged and displayed, as I hope it soon will be, in a room
fitted for its reception.

“‘T must say a few words of the coins and medals before I can
conclude this Report.

‘« They may be divided into three classes :

“1. The Danish Irish coins of thé ninth and tenth centuries.

‘‘ This series comprehends the coins of Domnald and some of
the sovereigns unknown; a coin of Ivar, A. D. 872, and a large
collection of the Dublin coins of Sitric, A. D. 980 and 989. Also
the Dublin coins of Aithelred, and some of great singularity and
rarity, which bear the impress of the Dublin mint, and which the
Dean, on grounds however admitted by himself to be doubtful, was
at one time disposed to refer to the reign of A‘thelstan.

‘© 2. The coins struck in and for Ireland by British sove-

reigns. .
“Among these are a magnificent series of the coins of John,
minted in Dublin, Waterford, and Limerick, between the years 1177
and 1199; and a singularly perfect series of the coins struck in Ire-
land from the reign of John to that of George IV., containing many
varieties of great rarity and value.

“<3, A series of medals struck in Ireland.

«The most complete that has ever been collected. This series
is particularly interesting to the Academy, because the late Dean, a
very short time before his decease, contributed to our Transactions
a valuable paper on the subject of Irish Medals, in which the most
remarkable of these very medals are noticed and described.

“« On the whole, I would congratulate the Academy, and not the
Academy only, but the country, on the possession of this important
and invaluable Collection. As one of those who enjoyed the pri-
vilege of an intimate acquaintance with its late lamented owner, I
cannot help expressing the gratification which I feel in the reflection
that this, the national part of his Museum, is saved from dispersion,
secured to Ireland, and presented to the Academy, for which he
had destined it. I feel a melancholy satisfaction, in which his

291

friends will sympathize with me, in having (in however humble a
degree) taken a part in bringing about the fulfilment of the wish
I have often heard him utter, that his Museum might be here; and
in the assurance that here his name will live as a benefactor to his
country, and an example to our gentry, by whom the study and
preservation of our antiquities have been (I must say) disgracefully
neglected.

“* But on public grounds, most of all, I would congratulate the
Academy on having now laid the foundation of a National Museum,
which will doubtless be the means of preserving many articles of
value and interest from destruction—of bringing together the many
curious relics of the past, which are now in the hands of private
families or individuals, and perhaps also of awakening the attention
of the Government of the country, to the importance (too long for-
gotten or overlooked) of forming, upon a liberal and extensive basis,
a really National Museum of the Antiquities of Ireland.”

ResotvepD,—That this Report be entered on the Minutes,
and published in the Proceedings.

Resotvep,—That the special thanks of the Academy be
given to those subscribers to the Dawson Fund who are not
members of the Academy.*

ReEsoLtvep,—On the recommendation of Council,—That
the plan of the new Board Room proposed by Mr. Murray
and Mr. Owen, be approved of by the Academy.

December 12. |
SIR Wu. R. HAMILTON, LL.D., President, in the Chair.

Rev. Dr. Todd, V. P. on the part of the Knight of Glin, pre-
sented to the Academy a gold coin, with an Arabic inscrip-
tion, found in the wall of a house in the townland of Killeny,
near Glin.

* See List of Subscribers in Appendix No. I.

292

The thanks of the Academy were presented to the Knight
of Glin for his donation.

Dr. Apjohn read a paper by Dr. Andrews, “ on the Heat
developed during the Formation of the Metallic Compounds
of Chlorine, Bromine, and Iodine.”

The author confines his attention in the present paper
to the combinations of zinc and iron, which metals, he shows,
will not combine at ordinary temperatures with chlorine,
bromine, or iodine, unless water is also present. The re-
actions which take place when an excess of iron in a state of
fine subdivision is agitated with any of the three elements
just mentioned, are rather complicated,—a sesqui-compound
(Fe, Cl;, Fe. Br3, Fe, 1;) being first formed, which afterwards
combines with an additional atom of iron, and becomes con-
verted into a proto-compound (Fe; Cl;, &c.) The heat de-
veloped during this process consequently arises from three
distinct causes:—first, the union of Fe, with Cl;; secondly,
the solution of the compound so formed in water ; and thirdly,
its conversion into Fe; Cl; by its combination with Fe. The
heat arising from the two latter causes being determined by
separate experiments, and taken from that obtained during
the original reaction, the remainder will be evidently the heat
due to the union of Fe, and Cl;; and by a similar method,
the heat developed during the union of Fe, with Br3, and of
Fe, with I;, may also be determined. Referred to the num-
ber of degrees of Fahrenheit’s scale, through which one grain
of water would be heated by the combination of one grain of
iron in each case, the heat evolved during the formation of
Fe, + Cl, is 3246°; during that of Fe, + Br3, 2302°; and of
Fe, + I;, 834°. The reaction which occurs when zine is
treated in a similar manner is much simpler, and the heat
developed, referred to the zine as unit, is 2766° for Zn + Cl;
2284° for Zn + Br; and 1474° for Zn + I.

The author also proves, by direct experiments, that when

TE ee ee ee ee ee ee

293

solutions of the sesqui-chloride, sesqui-bromide, or sesqui-
iodide of iron are converted into the corresponding proto-
compounds of iron, by combining with iron, the heat in all
cases is the same for the same quantity of iron dissolved.

The method by which these numerical results were ob-
tained, and the apparatus employed, are minutely described
in the original communication.

Dr. Kane inquired how far he considered the final results
obtained by Dr. Andrews to affect the ideas of thermo-che-
mical combination, founded on the experiments of Despretz
and Dulong?

Dr. Apjohn stated that the results of Dr. Andrews were
quite opposed to their experiments, as he found the quanti-
ties of heat not to bear any relation to the atomic weight of
the combining bodies.

The Secretary read a paper by the Rev. Edward Hincks
* on the Chronology of the Eighteenth Dynasty of Manetho.”

The object of this paper is to determine the period at
which the eighteenth dynasty of Manetho flourished, by the
recorded dates, in months of the wandering year, of facts,
which must, from their nature, have occurred at known sea-
sons of the solar year. Three such dates are brought for-
ward: two of them relating to the time of the commencement
of campaigns ; and the third, to that of the inundation: and
they all concur in depressing the epochs of the eighteenth
dynasty about 350 years below those, which the Cham-
pollions and Rosellini have adopted. An approximation to
the dates of the accession of many monarchs of the dynasty is
attempted. For example, the year B. C. 1278 is fixed upon
as very nearly, if not exactly, that of the accession of Ame-
nothph III.

Mr. Mallet having become acquainted with the recent
improvements effected by Mr. Bessemer in the art of glass-

294

making, for optical and other purposes, gave a short account
of them to the Academy.

The improvements consist chiefly in—

Ist. The use of platina bottoms to earthen melting pots,
and heating these in improved furnaces from below, so as to
produce circulation in the fluid glass.

2nd. In preserving the liquid glass from all contamina-
tion from without by “tears,” &c. and from the dome of
the furnace, as well as from deoxidation of the lead salts by
contact of carbon.

3rd. In an improved mode of cutting off, by a platina
blade, the upper portion of the fluid glass, without distur-
bance of the remainder; thus separating the whole of the
impure dross at top, which was heretofore stirred down into
the mass just previous to casting.

4th. In a beautiful and effective mode of removing the
air bubbles, or “ seeds,” as they are called, from the liquid
glass, by placing the ignited glass pot of liquid metal within
an exhausted receiver, so contrived that it can be rapidly
placed within, and withdrawn from the vacuum vessel.

Mr. Mallet was not aware that as yet any specimen of
glass prepared by these improved processes had been wrought
for any optical purpose, the inventor’s efforts having been as
yet principally directed to the manufacture of plate glass;
but he considered that the practical nature of these improve-
ments, and their capability of being applied upon a large
scale, gave good hope of their extension to the making of
optical glasses also.

Rev. Dr. Robinson made some remarks with reference to
Mr. Faraday’s experiments on the manufacture of glass for
optical purposes, and described the processes adopted at
Munich in selecting the portions of glass of which lenses are
formed.

ee rT

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1843. No. 37.

January 9.
SIR Ws. R. HAMILTON, LL.D., President, in the Chair.

Stewart Blacker, Esq., Thomas Cather, Esq., William V.
Drury, M. D., William Gore, M. D., Thomas Hodder, Esq.
R. N., Rev. John Homan, Henry Hutton, Esq., Robert Leslie
Ogilby, Esq., the Hon. Frederick Ponsonby, and George Sal-
mon, Esq., F.T.C.D., were elected members of the Academy.

Rev. H. Lloyd, V. P., read a paper “ on the Determina-
tion of the Intensity of the Earth’s Magnetic Force in abso-
lute Measure.”

The means of determining the intensity of the earth’s mag-
netic force in absolute measure consist, it is well known, in
observing the time of vibration of a freely-suspended hori-
zontal magnet, under the influence of the earth alone, and
then employing the same magnet to act upon another, which
is also freely-suspended, and noting the effects of its action
combined with that of the earth. From the former of these
observations we deduce the product of the horizontal com-
ponent of the earth’s magnetic force into the moment of free
magnetism of the first magnet,—from the latter, the ratio of
the same quantities; and, the product and the ratio being
thus known, the two factors are absolutely determined. ‘The
former part of this process involving no difficulty which may

VOL. Il. 2B

296

not be overcome by due care in observing, we shall confine
our attention, in the present communication, to the latter.

Two methods have been proposed for this second obser-
vation, one by Poisson, and the other by Gauss. The me-
thod of Poisson consisted in observing the time of vibration
of the second magnet, under the combined action of the first
and of the earth, the acting magnet having its axis in the
magnetic meridian passing through the centre of the sus-
pended magnet. In the method of Gauss, which is now
universally adopted, we observe the position of equilibrium
of the second magnet, resulting from the action of the same
forces. The acting magnet being placed transversely with
respect to the suspended one, the latter is deflected from the
meridian, and the amount of this deflection serves to deter-
mine the ratio of the deflecting force to the earth’s force.
The position chosen by Gauss for the deflecting magnet is
that in which its axis is in the right line passing through the
centre of the suspended magnet, and perpendicular to the
magnetic meridian, in which case the tangent of the angle of
deflection is equal to the ratio of the two forces. From this
ratio it remains to deduce that of the magnetic moment of
the deflecting bar to the earth’s force.

The difficulty of this process arises from the form of the
expression of the force of the deflecting bar. This force
being expressed by a series descending according to the
negative odd powers of the distance, with unknown co-
efficients, it is evident that observation must furnish as
many equations of condition, corresponding to different
distances, as there are terms of sensible magnitude in the
series; and from these equations the unknown quantities are
to be deduced by elimination. Now, the greater the num-
ber of unknown quantities thus eliminated, the greater will
be the influence of the errors of observation on the final re-
sult; and if, on the other hand, the distance between the
magnets be taken so great, that all the terms of the series

——

* 0 et ee ="

297

after the first may be insensible, the angle of deflection be-
comes very small, and the errors in its observed value beara
large proportion to the whole.

It fortunately happens, that at moderate distances (dis-
tances not less than four times the length of the magnets) all
the terms beyond the second may be neglected. The ex-
pression for the tangent of the angle of deflection is thus
reduced to two terms, one of which contains the inverse cube
of the distance, and the other the inverse fifth power; that
is, if « denote the angle of deflection, and p the distance,

,

Q Q
tanu =— + =;
D? De

in which @ and @’ are unknown coefficients, the former of
which is double of the ratio sought. Accordingly, the me-
thod recommended by Gauss consists in observing the angles
of deflection, u and wu’, at two different distances, p and D’,
and inferring the coefficient @ by elimination between the
two resulting equations of condition.

It is evident, however, that if the coefficient of the in-
verse fifth power of the distance be evanescent,—or, more
generally, if the ratio of the two coefficients be known @
priort,—the quantity sought may be obtained, without elimi-
nation, from the results of observation at one distance only.
For if a’ = ha, h being a known quantity, the preceding ex-
pression becomes

Q h
tanw=2 (145);

and accordingly the value of @ is obtained, from the result of
observation at a single distance, by the formula
D* tana
64 SS =
l+hv
And, not only is the labour of observation thus diminished,
but (which is of more importance) the accuracy of the re-
2B2

298

sult is increased. In order to show this, the author en-
tered into an examination of the amount of the probable
error in the two methods, from which it appeared that the
probable error of @, arising from an error in the observed
deflection, will be less than in the usual method in the ratio
of 1 to 5.563, even when the latter is employed in the man-
ner most conducive to accuracy. In fact, the ratio of the
probable error to the entire quantity is found to be ex-
pressed, in the two cases, by the formulz

Ae Aw Aa Vg? +I Au

2) ce ae = 6gf—l b
where q denotes the ratio of the two distances; and the least

Varet

value of the factor — is 5.563, and corresponds to the

ratio g = 1.32.

In order to know the ratio /, it is necessary to de-
termine the moment of the force exerted by the deflecting
magnet upon the suspended magnet, extending the approxi-
mation to the terms involving the fifth power of the distance.
The axis of the deflecting magnet being supposed to lie in
the right line joining the centres of the two magnets, and
the axis of the suspended magnet forming the angle = with
that line, this moment is found to be

Qu’
Dp?

simp $14 (252 +.3(5cos*y—1) = aS

in which m and m’, M; and w’3, denote certain integrals de-
pending on the distribution of free magnetism, in the deflect-
ing and suspended magnets, whose values are

+1 1
M=\ mrdr, M3; = ." mrdr,
1 ae

m being the quantity of free magnetism in any transverse
section of the magnet, r its distance from the centre, and J
half the length of the bar. The form of this result exhibits

INS en, ae a

299

the advantage of the method of deflection recently proposed
by Professor Lamont, in which ~ = 90°, or the deflecting bar
perpendicular to the suspended bar.

In the ordinary method, £ =$0° — uw; and, the moment
of the force exerted by the earth being xm’ sinw, where x de-
notes the horizontal component of the earth’s magnetic force,
the equation of equilibrium is

on 1 Ms o Ma’ ae. he | :
=—)j5 —— 3— + l5sin? ~) reiki
tanu ey + (25 af, + 1l5sin Zaher,
The angle of deflection, ~, being small, the term involving
the square of its sine may be neglected, in comparison with
the others; and the equation assumes the form already ad-
verted to, namely,

Q h
in which we have made, for abridgment,

/
M3 M3

PAN
—= 2——3—=h.
M M

x a. !

In order to apply this result, we must know, at least ap-
proximately, the law of magnetic distribution, or the function
of by which m is represented. Almost the only knowledge
which we possess on this subject is that derived from the
researches of Coulomb. From these researches M. Biot has
inferred, that the quantity of free magnetism, in each point
of a bar magnetized by the method of double touch, may be

represented by the formula

m= Aq pix /1ak8 ie
p being a quantity independent of the length of the magnet,
and a a function of » and/. M. Biot has further shown, that

when the length of the magnet is small, the relation between
m and r is approximately expressed by the simple formula

300

the curve of intensities becoming, in that case, very nearly a
right line passing through the centre of the magnet.
Employing then this approximate formula, we have

mM=2m'?; mjs= 2m.

. e,s - M :
The ratio of these quantities is a = 37, a value indepen-

dent of m’; and substituting in the expression of # above
given, and designating the half lengths of the deflecting and
of the suspended magnets by / and /’, respectively,

h=iQP—31);

an expression whose value may be exactly known, indepen-
dently of experiment. This value vanishes, when 7? = 30”, or
b= 12241;
and in this case, therefore, the quantity sought is given by
the simple formula
Q = D* tan.

The author concluded his paper with an account ofa
series of deflection experiments, instituted for the purpose
of confirming these results. The magnets employed were
cylindrical, their lengths being 3 inches and 33 inches, and.
their diameter 3-10ths of aninch. ‘The observations were
made with every precaution necessary to insure exactness,
and at times when the fluctuations in the direction and in-
tensity of the magnetic force were very small; and their re-
sults verify the conclusions above obtained, as applied to the
case of small magnets.

Dr. Apjohn next read the following letter, which he had
received from Captain Boileau, superintendent of the Mag-
netic Observatory at Simla, in India.

** Simla, March, 7, 1842.
“* My pear Sir,

‘* T have the pleasure of forwarding to you, through the

Government of India, a complete set of hygrometric tables,

301

computed by my assistant, from your last formula, to which
I have added a vapour table, computed by Biot’s formula,
from Dalton’s experiments, which is the same that Pouillet
has used in the last edition of his Traité de Physique, that
I have seen. Every one of the numerical values in this
table (No. 3) has been computed directly from the formula
to seven places of decimals, five of which only have been
retained. In like manner, in part 1, each of the numerical
values for depressions to one-tenth of a degree Fahrenheit,
has been directly computed for twenty and for thirty inches of
pressure, and the intermediate values obtained by addition.
All the work has been checked by differences, and examined
by three separate computors.

** Accompanying, are also sent the separate observations
of the wet and dry bulb thermometers, of Daniell’s hygro-
meter, and of the standard barometer, -with notice of the
weather for the twelve term days of 1841, which have been
taken specially for your own use, and which you will, I think,
find to confirm the views you had already taken upon the
subject. There is one point which strikes at first sight, viz.,
that with very few exceptions, the dew-point, by the hygro-
meter, is too high. It is a difficult instrument to use. It
requires the observer to approach near to it; and, even with
the utmost care, it is difficult to prevent an effect sensible at
times to a prejudicial extent, upon the hygrometric condition
of the surrounding air. None of these difficulties occur with
the wet and dry thermometers, which have one still greater
advantage, viz., the ease with which the wet ball can, under
almost any circumstances, be moistened.

** During several months, we observed the hygrometer
hourly on term days, but finding that this gave much trouble,
and was likely to prejudice the readings of the magnetome-
ter, I discontinued the practice, and had since but one ob-
servation every two hours.

During this year, I regret to say, that a failure in ether

302

has prevented any readings on either January or February

term days, and of a supply of five pints just had up under

order of Government, nearly three and a-half pints have

evaporated on the journey. So much for an Indian climate,

and bottles not hermetically sealed. You will oblige me by

acknowledging the receipt of this packet, either through our

-mutual friend Professor Lloyd, or through the Military Se-

cretary at the East India House, Philip Melvill, Esq.; and

if you wish me to alter the system adopted, you have only to

say so, and I will endeavour to meet your views. I hope to

continue the regular series from this month again without
interruption.

“ Believe me to remain, with kind regards,

“ My dear Sir,
“Yours very truly,
* S. Bomeavu.

“ P. S.—You can make any use of the accompanying do-
cument you may please to do.”

Dr. Apjohnthen observed, that availing himself of the per-
mission given him by Captain Boileau, he would make a few
remarks upon the hygrometric observations made on the mag-
netic term days for 1841. These observations were highly in-
teresting to meteorologists, having been made by an officer of
great scientific attainments, of extensive experience as an
observer, and with the aid of first-rate instruments: but his
(Dr. Apjohn’s) reason for considering them particularly im-
portant was, that they furnished the means of estimating the
relative merits of the two hygrometric processes at present
in use, viz., that according to which, the dewpoint is directly
got by the aid of Mr. Daniell’s instrument, and that which
conducts to the same conclusion through the application of
the well known formula,

Sf! =f’ — 0l47 (t-#/) x PS =

* In this expression 7” is the force of vapour at dew-point, f’ the force of

303

to the temperatures indicated by a wet and dry thermo-
meter.

The observations for the April term day, were those
to which it was his intention to advert, as they exhibited
higher values for ¢—d’, than those made in any other month.
Now upon looking through these which amount to 24, the
first fact which at once presents itself is, that in every in-
stance but two, the observed dew-points are higher than ob-
tained by the formula, and in some instances, by as many as
nine degrees Fahrenheit. One or other series, therefore,
must be erroneous. That the observed dew-points are inac-
curate, Dr. Apjohn inferred, on the ground of their being in-
consistent with each other ; for he held it as quite certain, whe-
ther the hygrometric expression be correct or not, that when
in the case of any two distinct observations, ¢ and ¢’ have the
same values, that upon both such occasions the air includes
the same amount of moisture, or has the same dew-point.
Tried by such a criterion, the results obtained with Daniell’s
instrument are defective, as is well illustrated by the follow-
ing extract from the April observations.

t t! t' ob. = t" cale.

10 § 70 51 43.5 elt
aie 51 34 39.3 PB ialat

Teas. 47 Bl 31.6
ae 47 36.6 sag¢ O8 Ly

2 § 55 42.5 30.5 28.9 é
5 -
24 pe 42.2 33 28 . wi

From what has been just said, it is obvious, that observa-
tions 10 and 11 should give nearly the same dew-point. This
is true of the dew points got by the formula, but not at all
of the direct determinations by the hygrometer, as those

vapour at ¢’, the temperature by the wet thermometer, and ¢ the temperature of

the air,

304

differ 9°.5. In 7 and 17, the dew-points are necessarily nearly
the same. The results got by the formula differ by only
1°.2, while the instrumental ones differ by 6°.6. Again,
2and 24 should give g.p. the same dew-point. This is true of
the formula, but not at all of the hygrometer, as the tem-
peratures it yields differ by 2°.5. The preceding instances,
the number of which might be greatly augmented, were, Dr.
Apjohn conceived, quite sufficient to show, that even in the
hands of Captain Boileau, Daniell’s instrument has not given
correct conclusions; and that, therefore, generally it cannot
be relied upon for determining, accurately, the hygrometric
relations of the atmosphere.

With respect to the column of results obtained by Cap-
tain Boileau, from the wet bulb process, Dr. Apjohn could
not entertain the slightest doubt of their exactness, having
found that his formula stood the severest experimental tests
to which he could subject it. ‘These experiments, however,
(see Transactions Royal Irish Academy, vol. vi.) were, he
admitted, all made under pressures, at or about 30: and
hence it always appeared to him desirable, that they should
be repeated at such diminished pressures, as are met with
at elevated points on the earth’s surface. In this point of
view, the Simla observations appeared at first highly impor-
tant, the pressure there being but little over 23; but as no
reliance ean be placed on the dew-points directly got, they
cannot be used to test the accuracy of the hygrometric ex-
pression.

Dr. Apjohn then expressed a hope, that no one who
heard him would misunderstand him to assert, that the dew-
point could not be accurately got by Daniell’s instrument.
He knew it could, and he had explained elsewhere how to
use it, so as to arrive at a correct result. What he had,
however, asserted before, and would again repeat, was, first,
that it was an instrument very difficult to observe accurately
with; and second, that when Mr. Daniell’s rule is attended

305

to, namely, to take asdew-point, the mean of the temperatures
indicated by the inner thermometer at the instant of the de-
position of the dew, and at that of its disappearance, the
result is necessarily higher than the truth.

Dr. Apjohn concluded, by drawing attention to the great
value of the other tables alluded to in Captain Boileau’s
letter, the construction of which, must have been a work of
immense labour. Two of these greatly simplify the calcula-
tions necessary in applying the hygrometric formula, as the
arithmetical operations are thereby reduced to mere addition
and subtraction.

The third table gives the force of vapour to tenths of a
degree Fahrenheit, throughout the entire range included
between —3° and + 146, Fahrenheit, calculated de novo by
the well known method of Biot, from the experiments of
Dalton and Ure. It does not materially-differ, except in its
greater extent and minuteness, from the table of the tension of
aqueous vapour which Dr. Apjohn has hitherto used, and
the superior accuracy of which, as compared with the table
of Kaemtz, and that not long since published by the Meteor-
ological Committee of the Royal Society, has been rendered
highly probable by Professor Lloyd.

Professor Mac Cullagh read a paper on the Catalogue of
Egyptian Kings, which is usually known by the name of the
Laterculum of Eratosthenes.

This Catalogue, which the distinguished mathematician
and philosopher whose name it bears drew up by com-
mand of Ptolemy Euergetes, contains a long series of kings
who reigned at Thebes in Upper Egypt; and has been pre-
served to us in the Chronographia of Georgius Syncellus, a
Greek monk of the eighth century. It is a document which
has been made much use of by chronologers; by some of
whom, as by Sir John Marsham for example, who calls it
“ venerandissimum antiquitatis monumentum,” it has been
reckoned of the very highest authority; but it is extremely

306

corrupt in the latter part, owing to the carelessness with
which it was transcribed either by Syncellus himself or his
immediate copyists. The writers on Egyptian antiquities
have in consequence been much perplexed in settling the
chronology of the reigns in which the errors exist, and the
attempts that have been made to remove the confusion have
only served to increase it. It was the object of the author
to restore the document to its original state, and he showed
that this might be effected, with complete certainty, by a pro-
per attention to the manuscripts of Syncellus. Of these only
two are known; one has been used by Father Goar, the first
editor of the Chronographia (Paris, 1652); the other, which
is a much better one, has been collated by Dindorf, the se-
cond and latest editor. Dindorf’s edition was published at
Bonn, in the year 1829, as part of the Corpus Scripto-
rum Historie Byzantine, and on its first appearance Mr.
Mac Cullagh had satisfied himself as to the original readings
of the Catalogue, and had seen how to account for the errors
which, probably from Syncellus’s own negligence, had crept
into it; but he did not publish his conclusions at the time,
thinking that similar considerations could not fail to occur to
some of the numerous writers who were then giving their
especial attention to such subjects. ‘This, however, has not
been the case. Chronologers have continued to follow in the
footsteps of Goar, a man of little learning, and of no critical
sagacity, who corrected the Catalogue most injudiciously,
and whose corrections, strange to say, are left without any
remark by Dindorf. Thus Mr. Cory, in his Ancient Frag-
ments, a work much referred to, merely transcribes Goar’s
list; and Mr. Cullimore, in attempting to reconcile ancient
authors with each other and with the monuments, has adopted
an hypothesis respecting the identity of two sovereigns, which
is not tenable when the true version of the Catalogue is
known. Even in Goar’s edition, however, there was quite
enough to have led a person of ordinary judgment to the

307

correct readings of the Catalogue, though perhaps they could
not be said to be absolutely certain without the additional
light obtained from that of Dindorf.

The Catalogue in question professes to contain the names
of thirty-eight sovereigns, with the years of their reigns; the
whole succession occupying, as is stated, a period of 1076
years; but it is only in the last eight reigns that the errors
and inconsistencies occur. The thirty-second prince is called
Stamenemes (3, that is, Stamenemes the Second, though
there is, at present, no other of that name in the list; and
the beginning of his reign—as appears from the years of the
world, which Syncellus has annexed according to the Con-
stantinopolitan reckoning—follows the termination of the
preceding one by an interval of twenty-six years. Jackson,
in his Chronological Antiquities, is positive that this prince is
called the Second by a mistake, and adds the years that are
wanting to the reign of his predecessor, as Goar had pre-
viously done. In the first part of this view all authors, with-
out exception, are agreed, though they do not explain howa
mistake, so very odd, could have originated; but the learned
Marsham,—who, having adopted the short chronology of the
Hebrew Bible, is so hard pressed to find room for the Egyp-
tian dynasties that he is obliged to begin the reign of
Menes the very year after the Deluge,—is glad to omit the
twenty-six years altogether, thus reducing the sum of all the
reigns to 1050 years, contrary to what is expressly stated by
Syncellus. The natural inference from the state of the MSS.
is, however, simply this: that the thirty-second king was
Stamenemes I., that he reigned twenty-six years, and was
succeeded by Stamenemes II. We may easily conceive that
the eye of the transcriber, deceived by the identity of names,
passed over the first, and rested on the second, thus occa-
sioning the error. Indeed there can now be no doubt that this
was the fact; because, in the MS. marked (B) by Dindorf,
the next king is numbered as the thirty-fourth, the next but

308

one as the thirty-fifth, and so on; which shows that a name
had dropped out, and this name could be no other than that
of Stamenemes I., who must have filled the vacant interval,
and must consequently have reigned the number of years that
has been assigned to him.

As neither Goar nor any other writer perceived this omis-
sion, the successor of Stamenemes II. has always been ‘rec-
koned as the thirty-third in the list; and the next following as
the thirty-fourth, &c. Butas one error begets another, the
omission was compensated by the insertion of an anonymous
king, who is placed thirty-sixth in the list, with a reign of
fourteen years; the insertion being: necessary to complete
the number (thirty-eight) which the Catalogue ought tocon-
tain. And, by a further error, these fourteen years are taken
out of the reign of the thirty-seventh sovereign, who ought
to have nineteen years instead of the five that have been
hitherto assigned to him. This last error was occasioned by
an ignorant correction of a mistake which is found in both
the MSS., and which therefore probably arose from the care-
lessness of Syncellus himself. The thirty-seventh king and
his predecessor are stated to have begun to reign in the
same year of the world, and to have reigned the same num-
ber of years (five). Now from what goes before it is plain
that both these numbers belong to the thirty-sixth king; and
from the year of the world in which the thirty-eighth and
last king began to reign, it is clear that the thirty-seventh
reigned nineteen years. ‘The mistake in the MSS. is one
which might easily be made by a thoughtless writer; for
the Catalogue is given in detached portions—a few reigns at
a time—separated by a great quantity of other matter, and
the name of the thirty-sixth king ends one of these portions,
while that of the thirty-seventh begins another; so that, not
having both before his eyes at the same moment, a person so
careless as Syncellus might, without being conscious of it,
attach the same reign and date to the two names, by tran-

309

scribing twice over the same line of numbers in the Catalogue
which he was copying; the whole of which Catalogue, in all
likelihood, he had previously drawn up ina tabular form, with
the years of the world annexed according to his own chro-
nology, that it might be ready, as any portion of it was wanted,
for immediate transference to his pages. Such seems to be the
natural account of the matter; but, as usual, it does not occur
to Goar, who takes the opportunity, which the confusion
affords him, of foisting in his supplementary king between
the two last mentioned, giving each of these five years, as in
the MS., by which means he obtains room for him, while on
the other hand he alters the year of the world attached to
the thirty-seventh king, so as to make it suit his hypothesis.

The following is a view of the last eight reigns, as they
appear to have stood in the original document, compared
with the erroneous list of Goar, The years of the world
are omitted, as being of no importance, except so far as they
are useful in the preceding argument.

I. Goar’s List. II. Correctep List.
Years. Years.
31. Peteathyres reigned 42 dl. Peteathyres reigned 16
32. Stamenemes ee 32. Stamenemes I. ,, 26

30. Sistosichermes ,, 55 33. Stamenemes II. ,, 23
34, Maris » 43 34. Ststosichermes ,, 55
35. Siphoas bn 9) 35. Maris » 43
36. Anonymous ,, 14 36. Siphoas e. 5
37. Phruoro x 5 37. Phruoro Zorneg

38. Amutharteus ,, 63 388. Amutharteus ,, 63

The interval of time which has been shown to belong to
the first Stamenemes, and which was added by Goar to the
reign of Peteathyres, is differently disposed of by Mr. Cul-
limore,-in a chronological table which he has given in the
second volume of the Transactions of the Royal Society of
Literature. His object being to compare the lists of Eratos-

310

thenes, Manetho, &c., with the supposed hieroglyphical
series, he makes Saophis, the fifteenth in Eratosthenes’ Ca-
talogue, the same as a king whose name is read Phrathek
Osirtesen; but the forty-third year of the latter is mentioned
on the monuments, whereas Saophis has only twenty-nine
years in the Catalogue. To escape from this difficulty,
therefore, Mr. Cullimore adds the unappropriated interval to
the reign of Saophis, thus giving him fifty-five years instead
of twenty-nine. But it now appears that such a supposition
is altogether inadmissible, and consequently the two per-
sonages in question cannot be identified; a circumstance
which proves that there is some fault in Mr. Cullimore’s
assumptions, and that his other conclusions, at least in this
part of his table, cannot be relied on.

The corrections here given do not interfere with the in-
ferences drawn by Professor Mac Cullagh from the Cata-
logue of Eratosthenes ina former paper on Egyptian Chrono-
logy (Proceedings of the Royal Irish Academy, vol. i. p. 66),
because the portion of the Catalogue with which he was there
concerned terminates with the reign of Queen Nitocris, the
twenty-second in the list. The corrections, indeed, though
not hitherto published, were made long before the date
(April, 1837) of that paper, but not before he had adopted
the hypothesis therein proposed, as an answer to the old
and ever-recurring question—Who were the Egyptian sove-
reigns that were contemporary with Moses? For it was in
consequence of this hypothesis, which had suggested itself
to him at a very early period, that he was led to examine the
Catalogue minutely, in order to discover whether his chro-
nology was affected by its errors.

Having been led to refer to his hypothesis, Mr. Mac Cul-
lagh took occasion to observe that, in the interval which had
elapsed since it was published, he had not met with any
facts that were opposed to it: on the contrary, the more
he considered it, the more he was inclined to believe in its

— a or

0 a

3il

reality ; though it was entirely different from every other that
had been proposed, either by modern chronologers or by the
early Fathers of the Church, in their manifold attempts to
connect the narrative of Moses with the remaining fragments
of Egyptian history. The hypothesis, indeed, is the only
one which, while it gives a probable date for the Exodus,
also satisfies what Mr. Mac Cullagh conceives to be the ne-
cessary conditions of the question; namely, a very long reign
—of at least eighty years—during which the Israelites were
persecuted, succeeded by a very short one—apparently not
more than a year—during which their deliverance was
wrought; and it is interesting in itself, on account of the
remarkable connexion which it establishes between sacred
and profane history, and the highly dramatic character of the
events which are thus, for the first time, brought into view.

ee

Mr. Petrie exhibited a drawing, on a large scale, of an
ancient inscribed grave stone at Clonmacnoise, which he con-
sidered as interesting, not only as a characteristic example
of the usual sepulchral memorials of the Irish, from the sixth
to the twelfth century,—and of which Mr. Petrie has col-
lected upwards of three hundred examples,—but also as a
monumental record of a person very eminently distinguished
for his learning in Ireland in the ninth century.

This stone, which is about four feet in length, and three
in breadth, though never squared or dressed, exhibits a very
richly carved cross, and the following simple inscription :

ce
SVIOINGE. M MAICAE hvmMdt-:
SUIBHNE, THE SON oF MAIL@HUMAI.

Of the celebrity, in his day, of the person who is thus
recorded, the Irish Annals, as weil as those of England and
Wales, bear abundant evidence.

In the Chronicon Scotorum his death is thus recorded

VOL, Il. 2

312

at the year 890: Suibne mc Maoithuma, ancomiza Cluana mac
nowy, oes.

Thus also in the Annals of Ulster at the same year, or
more correctly 891: Suibne mac Maele humai, Clncopica, et
pemba opzimup Cluana mac noip, vopmiuie.

To the latter entry, Doctor O’Conor, in his Rerum Hib.
Scriptores, appends the following note:

“ Suibneum hune Annales Anglosaxonici Suifnethum ap-
pellant— Vide Chron. Saxon. ad ann. 891, ‘ Tres Scoti de
Hibernia, ad Alfredum regem Anglorum venerunt, Dubsla-
nus, Maccebethus, et Melinmunus, Swifneth etiam, preecipuus
doctor qui inter Scotos fuit, decessit,—concordat Fabius
Aithelwerdus, qui tertium appellat—‘ Magilmumenum artibus
frondentem, littera doctum, magistrum insignem Scotorum.’—
Chron. |. 4, ¢. 3. Eadem habet Wigorniensis ad ann, 892, et
Matheus Florilegus,ad ann. 891. Huc etiam referenda sunt
que habet Caradocus ad ann. 889, ‘ Suibnion Cubin Doc-
torum Scotize maximus obiit.’”

Sir James Ware, in his Irish Writers, tells us, that ‘ his
works, and the titles of them, are lost.”

Mr. Griffith presented, on the part of the Shannon Com-
missioners, a collection of antiquities discovered in the Shan-
non, and gave the following account of the locality and other
circumstances attending the discovery.

The object of my present communication is to notice the
discovery of certain ancient arms in an excavation made in
the bed of the river Shannon at the ford of Keelogue, four
miles below Banagher, in the King’s County.

The ford at Keelogue, and that of Meelick, which is im-
mediately below it, is the first point of the river Shannon
which was anciently passable except by boat, above the falls
at Killaloe, a distance of thirty British, or nearly twenty-five
Irish miles; and consequently, previously to the construction
of roads, and the erection of bridges at Portumna and Ba-

——

313

nagher, this ford must have been the main pass between the
northern portion of the county of Clare, and the southern
portion of the county of Galway, with the counties of Tip-
perary, King’s County, &c. &c. Hence it is probable that at
a former period the ford at Keelogue, which is the shal-
lowest on the river, and much better than that of Banagher,
was the principal point of communication between the dis-
tricts above enumerated; and even in modern times, in com-
mon with the passes by the bridges of Banagher, Shannon
Bridge, and Athlone, the defence of the pass at Keelogue
and Meelick was considered of sufficient importance to induce
the British Government to erect two towers, mounted with
cannon, on the King’s County side, to guard the passes of
the river from the west.

The fall of the river Shannon at Keelogue and Meelick
amounts to ten feet; and to render the river navigable, the
commissioners appointed to direct the improvements of the
navigation of the Shannon, have agreed with contractors for
the construction of a lock of very large dimensions, a stone
weir to regulate the discharge and the level of the water,
and for the deepening of the river at Keelogue ford, by ex-
cavating the bed to the depth of six feet below the present
bottom, so as to give a depth of full seven feet six inches for
navigation when the works shall have been completed.

Towards deepening this ford the contractors dammed off
a portion of the river 100 feet in width, and 700 feet in length,
and have commenced an excavation of nearly six feet in
depth ; the material to be excavated consisted at the top of
two feet of gravel, loose stone, and sand, and at the bottom
of four feet of a mass, composed of clay and rolled limestone,
which in some parts was found to be so solid and compact,
that it became necessary to blast it with gunpowder, in
preference to excavating, according to the ordinary system,
through detrital matter.

This compound of clay and rolled limestone, and lime-

314

stone gravel, is similar to that which forms the bed of the
Shannon at all the other fords over which bridges have
been erected, as at Banagher, Shannon Bridge, Athlone, &c.,
and these gravel banks in most cases are in connexion with,
and in fact form a part of those low, but steep, ridges or
hills, composed of clay and rolled limestone, which occur so
abundantly in the King’s, Queen’s County, and the counties
of Westmeath and Longford, on the east side of the river, and
in the counties of Clare, Galway, and Roscommon, on the west.
These gravel ridges, or eskers, as they are generally called,
usually affect an east and west, or north-west and south-east
direction, and consequently cross the river Shannon, whose
direction between Athlone and Killaloe is north-east, south-
west, nearly at right angles; hence the fords, which, particu-
larly at Athlone, Shannon Bridge, &c., are merely gaps cut
through the eskers by the action of the water, run directly
~across the river, and present shallow, having deep ponds of
water on either side, so that when the falls are not consider-
able, as at the fords of Banagher, Shannon Bridge, &c.,
the excavation of the bed of the river at the ford will bring
the water on both sides to a level, and there will still remain
ample depth above for the purposes of navigation.

But to return to Keelogue, I have already mentioned
that the upper part of the excavation consisted of two feet
of loose stones, gravel, and sand, and the lower part of four
feet of a very compact mass, composed of indurated clay and
rolled limestone. In excavating in the loose material of
which the upper two feet was composed, the labourers found
in the shallowest part of the ford, a considerable number of
ancient arms, consisting of bronze swords, spears, &c., in
excellent preservation, which are similar to those which have
been frequently discovered in other parts of Ireland; and to-
wards the lower part of the upper two feet they discovered a
great number of stone hatchets, also similar in many respects
to those which have been so frequently met with in different

way
ig

ald

parts of this country. In regard to the stone hatchets, I
would merely observe, that the greater number, which are
black, are composed of the siliceous rock called Lydean
Stone, which occurs in thin beds, interstratified with the
dark gray, impure limestone called Calp, which is abun-
dant in the neighbourhood of Keelogue and Banagher; but
the others, some of which present a bluish gray, and some a
yellowish colour, are composed of a subcrystalline, and ap-
parently igneous porphyritic rock, none of which occurs in
the neighbourhood, or possibly in the south of Ireland.
Hence it is probable that the latter, which are much more
perfectly executed than the black, or those composed of
Lydean Stone, were brought from a distance, and probably
from a foreign country.

The important and interesting subject for consideration
in the antiquities before us is, that they are evidently the
relics of very different, and probably distant periods. Owing
to the rapidity of the current at Keelogue ford, it is extra-
ordinary that any comparatively recent deposit should have
been formed, and at all events the annual increase must have
been inconsiderable; hence, though not more than one foot
of silty matter may be found between the stone weapons of
a very remote age, and the swords and spears of another
period still remote from us, yet under the circumstances de-
scribed centuries may have intervened between the periods
of mortal strife which must have taken place in the river
probably between the Leinster men and Connaught men of
old, disputing the passage of the river at two distinct and no
doubt very distant periods.

I am not sufficiently versed in the ancient Irish history to
say whether any records are in existence of a battle having
been fought at the fords of Meelick and Keelogue; but if
any such exist I have no doubt that many members of the
Academy, and lovers of ancient lore, will be enabled to en-
lighten us on the subject. Ihave only further to mention,

316

that I have been deputed by my brother Commissioners for
the improvement of the Shannon Navigation to present these
ancient relics to the Royal Irish Academy, for the purpose
of being added to their already important and valuable col-
lection of Irish antiquities.

DONATIONS.

Supplementary Appendix to the Report of the Poor Law
Commissioners of the Medical Charities in Ireland, with In-
dexes. 1841. Presented by the Commissioners.

A pamphlet entitled, “ Is Selenium a true Element?” Pre-
sented by Septimus Piesse.

Transactions of the Zoological Society of London. Vol.
III. Part l. 1842.

Reports of the Auditors and Council of the Zoological
Society of London, April 29th, 1842, and List of Members.

Su la Falsita dell’ Origine Scandinava di Jacopo Graberg
di Hemso.

Sunto della Letteratura Svezzese.

Degli Ultimi Progressi della Geografia (two copies).

Saggio Istorico su Gli Scaldi 0 Antichi Poeti Scandinavi.

Occhiata Sullo stato della Geografia nei Tempi Antichi e
Moderni.

Specchio Geografico, e Statistico del! _Impero di Marocco.
Presented by the Author.

A copy of the Ordnance Survey of the County of Water-

Jord, in forty-two sheets, including the Title and Index. Pre-
sented by His Excellency the Lord Lieutenant.

Extraits du Tome XV. et XVI. des Memoires de l Academie
Royal de Bruxelles, with Notes. Presented by the Academy.

Examinations at the University of London for M.D.,
B. M., B. L., M. A., and B. A.,(six pamphlets). Presented
by the University.

Memoires de 0 Institut Royal de France. 'Tome Quinzieme.
Presented by the Institute.

ss

317

Specimen de I Imprimerie de Bachelier. Presented by
the Author.

Memoirs of the Royal Astronomical Society. Vol. XIV.
Presented by the Society.

Memoire sur la Chaleur des Gas Permanens. Par Jean
Plana. Presented by the Author.

Proceedings of the Royal Society, §c. 30th Nov. 1842.
Presented by the Society.

Revista de Espana y del Estrangero. B. Fezuier Gon-
zalo Moror. TomolI. Presented by the Author.

Geological Report of Londonderry. By Captain Port-
lock, M.R.I.A., &c. Presented by the Master General and
Board of Ordnance.

Archives du Muséum @ Histoire Naturelle de Paris. 'Tome
IJ. Liv. 1 and2. Presented by the Museum.

Address to the Geological Society of London. By Rode-
rick Impey Murchison, F.R.S., &c. Presented by the Au-
thor.

Report of the Twelfth Meeting of the Brilish Association,
held at Manchester in 1842. Presented by the Association.

Statutes relating to the Admiralty, to the eighth Year of
George III. Presented by Captain Portlock.

Ancient Irish Pavement Tiles, with Introductory Remarks.
By Thomas Oldham, Esq. Presented by the Author.

Proceedings of the Glasgow Philosophical Society, 1841,
1842. Presented by the Society.

Memoires publies parla Société Hollandaise des Sciences.
Second Serie. Tome II. Presented by the Society.

Proceedings of the American Philosophical Society. Vol.
II. Nos. 24 and 25.

Transactions of the American Philosophical Society. Vol.
VIII. Newseries. Parts 2 and 3. Presented by the Society.

Fifth Annual Report of the Loan Fund Board of Ireland.
1843. Presented by the Commissioners.

Communication to the Right Hon. Sir Robert Peel, Bart.

318

By Jeffries Kingsley, Esq., M.R.L.A. Presented by the
Author.

Bulletin des Séances de la Société Vaudoise des Sciences
Naturelles. Nos. 1-4. Presented by the Society.

Sur les Figures Roriques et les Bandes Colorées produites
par VElectricité. Par M. P. Riess. Presented by the Author.

Expériences sur la non caloricité propre de l Electricité.

Sur les relations qui lient la lumiere a l’ Electricité.

Sur les travaux récents qui ont eu pour objet Vetude de la
vitesse de propagation de l’Electricité. Par M. le Prof. Elie
Wartmann. Presented by the Author.

Journal of the Franklin Institute. Vols. II. and IV.
Third Series. Presented by the Institute.

Proceedings of the Zoological Society of London. Part
10. 1843. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.
1842. No. 88.

January 23.

Rev. JAMES H. TODD, D. D., Vice-President, in the
Chair.

Mr. G. J. Allman, read the following paper on the Mus-
cular System of certain fresh water ascidian Zoophytes, being
the first of a series of memoirs which he proposed present-
ing to the Academy on the physiological and zoological his-
tory of the zoophytes of fresh water.

“The subject on which I have now the honour of ad-
dressing the Academy, belongs to a hitherto but little inves-
tigated department of zoology, the structure of the ascidian
zoophytes* of fresh water. Our present knowledge of these
minute creatures is chiefly due to Raspail, the distinguished
French naturalist and chemist, whose researches into the
structure of Alcyonella Stagnorum, are characterized by
much patient observation,} while in these countries the sub-
ject has been totally neglected. Not so, however, with the
ascidian zoophytes of the ocean; these interesting animals
have had both here and on the continent some able investi-
gators, among whom none deserve to be mentioned before

* The zoophyta ascidioida of Johnston are synonymous with the bryozoa of
Ehrenberg, and the ciliobrachiata of Farre, and include all those zoophytes whose
organization is referrible to the molluscan type.

+ Compte rendu des seances de l’Academie des Sciences. 4 Fevrier, 1839.
VOL. Il. 2D

320

Milne Edwards, and Farre, and it is especially to the latter
indefatigable and accurate observer that we are indebted for
a knowledge of the minute anatomy of these most curious
and highly organized polypes. Though in my own investi-
gations into the anatomy of the fresh water zoophytes of this
order, I have not restricted myself to any particular struc-
tures, I yet intend, in the following remarks, confining my
observations to their muscular system; reserving for some
other occasion the pleasure of directing the attention of the
Academy to those points of their anatomy not dwelt upon in
the present paper.

“In the remarks which I am about to offer, it will be
seen how closely the ascidian zoophytes of our fresh waters
correspond in organization with the marine species; and
though in minute anatomical detail certain differences will
be observed, yet these differences are far from invalidating
the unity of the type of structure,—a unity which will be
found from the following observations to pervade, in a re-
markable degree, the entire order. I would wish it to be
understood too, that if I should in any respect differ from
the statements of Dr. Farre, I offer no opposition whatever
to his observed facts, but solely to one or two of the conclu-
sions to which they have induced him to arrive.

*‘ The animal of the present order, to the muscular ana-
tomy of which I have chiefly attended, is one which has not
as yet been recorded as a native of the British Islands.
About two years since I was sent, by Mr. William Thompson
of Belfast, to whose researches into the natural history of
this country we are so much indebted, a small portion of
the dried polypidom of a zoophyte, which he found, in Sep-
tember, 1837, cast upon the shore of Lough Erne. From
the dried condition of the fragment,—a condition in which
the fresh water zoophytes lose all their most interesting
characters,—I was unable at the time to arrive at any-
thing satisfactory in the investigation of the species; I

321

therefore contented myself by sketching in my note-book,
the few imperfect external characters which continued visi-
ble on the dry and shrivelled zoophyte. No farther than
this did my knowledge of Mr. Thompson’s discovery extend,
when an opportunity fortunately occurred in October last,
of obtaining living specimens of the animal. These I dis-
covered in the Grand Canal, near Dublin, and have thus
been enabled to pursue my investigations, from which I
find the species to be one of great interest. I find, more-
over, that although it has been hitherto unnoticed, as a
British animal, it is identical with the alcyonella articulata
of Ehrenberg, for which Gervais, who found the animal near
Paris, subsequently constituted anew genus, under the name
of Paludicella.* It is also noticed by Van Beneden, who
met with it near Louvain, and gives a figure of it, which,
though not very good, will yet be found of use in the iden-
tification of the species. ‘Though Ehrenberg’s appellation
possesses the claim of priority, yet, as it refers the zoophyte
to a genus into which its structure will not admit it, it must
be rejected, and I shall accordingly adopt the name Palludi-
cella, by which it has been designated by Gervais.

** In the following remarks upon the muscular system of
the fresh water ascidian zoophytes, my description of this
system is chiefly derived from observations made upon Palu-
dicella articulata, as there are certain points in the muscular
anatomy of other species, upon which I cannot as yet speak
with certainty, and for completing my observations on which,
I must wait until the approaching Spring shall afford me
fresh objects for investigation.

**In describing the muscles of these animals, I have
availed myself of Dr. Farre’s phraseology, applying to the
several sets of muscles in the fresh water ciliobrachiate zoo-

* Bulletin de l’Acad. Roy. de Bruxelles, an. 1839.
+ Mem. de la Société d’Hist. Nat. de Paris, tom. 4.
2D2

322

phytes, the same terms which Farre has given to the analo-
gous sets in the ciliobrachiates of the sea.

‘© In Paludicella then, three groups of muscles may be
detected. These are strictly analogous to muscles which
have been demonstrated in the salt water zoophytes of the
same order, and for a description of which, we are indebted
to an admirable paper of Dr. Farre, in the Philosophical
Transactions, an. 1837. The first of these groups to which
I shall direct your attention, corresponds with the anterior
set of retractor muscles of Farre. It may be observed (fig. 3
and 4, h, h) to take its origin from the internal surface of the
walls of the cell near the middle, and thence to pass upwards
in order to be inserted into the margin of the tentacular disk,
and upper part of the pharynx. The action of this group is
obvious, it is the true retractor apparatus of the polype, and
it is worthy of remark, that neither in this nor in any other
fresh water zoophyte whose anatomy I have studied, could I
detect muscular fibres analogous to those described by Farre,
as inserted into the remote extremity of the stomach in those
zoophytes of the sea which had come under his observation.

‘The second set of muscles to be described in Paludi-
cella, consists of four bundles of fibres (fig. 3 and 4, 4, 2, 2)
which arise from the inner walls of the cell near the top,
two at each side, having the tubular orifice between them.
From this origin, they pass towards the aperture of the
cell, slightly converging, and are inserted by distinct at-
tachments, which are all placed in the same plane, into
the inner surface of the tube near the margin of the orifice.
These are in every respect analogous to the muscles which
Farre describes under the name of opercular, and to which
he ascribes the office of assisting in the inversion of the
polype tube drawing in its margin after the retreating po-
lype, and by their continued action, closing the orifice of the
cell. Reasons will presently be given for dissenting from
this view of the action of the opercular muscles, and in the

323

meantime I shall proceed to the description of the third
group.

The third groupis analogous to one detected by Dr. Farre,
in the ascidian zoophytes of the sea, and to which he has given
the name parietal. The parietal muscles take a transverse
course, and originate and terminate in the internal membrane
of the cell. In paludicella (fig. 3 and 4, 4, k, &, k) they are
rather numerous, and consist of short fibres of variable length,
which pass transversely round the internal tunic, being
capable of detection through nearly the entire length of the
cell, and sometimes passing one another in their course, they
may be seen to surround the cell with a contractile tissue.
Dr. Farre is of opinion, that these muscles in the zoophytes
which he has examined, are attached by their extremities
only, being free in the intermediate space. In paludicella
however, I saw nothing which would lead me to suspect, that
in this zoophyte such was their disposition. I shall not
here, however, speak positively, as it will require more ex-
tensive observations before any decisive conclusion can be
arrived at.

“ Such are the three great groups of muscles which I have
succeeded in detecting in paludicella, and so far as my obser-
vations have gone, analogous groups are to be found in the
other fresh water ciliobrachiates. It will at once be seen, by
any one acquainted with Dr. Farre’s paper, that while the
muscles just described correspond in all their important
features with those of the ascidian zoophytes of the sea,
thus beautifully demonstrating the unity of type by which
the order is characterized, yet in the details of the several
groups, some remarkable modifications will be found to
exist.

“The first thing which strikes us is the absence, probably
among all the fresh water ascidian zoophytes of that well-
developed fasciculus of muscular fibres, which is observed in
those of the sea, to arise from the bottom of the cell, and

$24

pass upwards to be inserted into the fundus of the stomach.
It is true, that Trembley describes in alcyonella stagnorum, a
certain appendage to the fundus of the stomach, to which he
assigns the office of'a retractor muscle; ‘“ J’ai vu,” says Trem-
bley, ‘‘ distinctement, lorsque les polypes 4 panache etaient
bien au dehors de leur cellules un fil qui tenait d’un coté a
Yextrémité inferieure de l’estomac et de l’autre au fond dela
cellule.”* Raspail supposes this an erroneous observation,
and conceives that Trembley mistook for a distinct organ,
the appearance presented under the microscope, by a fold
of the reflected tunic.+ Notwithstanding, however, the criti-_
cism of Raspail, I believe the observation of the celebrated
historian of the green polype to he perfectly correct, though
his reasoning is erroneous.

** T have myself witnessed in Plumatella repens, an organ
in every respect corresponding to Trembley’s description; I
believe this organ to be an ovary, though from its position
and attachments, Trembley’s opinion might at first appear
correct, and the structure in question might be supposed
analogous to the posterior set of retractor muscles in the
ciliobrachiate zoophytes of the sea. ‘This supposition, how-
ever, is untenable, and I have satisfied myself by repeated
observations, that no such function is performed by it; it is
observed to undergo no contraction, and its motions are en-
tirely passive and dependant on those of the body of the
polype.
‘‘ In the same animal, Trembley also describes as retractor
muscles, filaments attached by one extremity to the base of
the plume of tentacula, and by the other to the bottom of
the cell;{ but this, likewise, is considered by Raspail as an
error, and referrible to the same source as the former. Here
again I must dissent from the French naturalist; the fila-

* Hist. des Polypes d’Eau douce, p. 216.
+ Mem. de la Soc. d’Hist. Nat. de Paris, tom. 4, p. $2.
t Op. cit. p. 216.

329

ments alluded to by Trembley correspond closely with fas-
ciculi described above, as existing in paludicella, and which
I have also witnessed in other fresh water zoophytes; and I
cannot but think, notwithstanding the high authority of
Raspail, that they are really such as Trembley describes
them. It is worth remarking, that Raspail denies the exis-
tence of retractor muscles in alcyonella, believing that, with
the general contractility of the animal, such a contrivance
would be superfluous. I have not yet succeeded in obtaining
any specimens of alcyonella, so that upon this point I cannot
speak from direct observation. Since these muscles, how-
ever, are particularly well marked in all the fresh water
ascidian zoophytes, whose anatomy I have studied, as well
as in those of the ocean, I must still adhere to the original
observation of Trembley ; for it can hardly be supposed, that
a genus so nearly allied to those in which the system in
question is well developed, and which Raspail, by the way,
would consider but as a different grade of evolution, should
be altogether destitute of them.

“ In Plumatella repens I have examined, with much care,
the retractor apparatus. In this species it consists of two
fasciculi of muscular fibres, which arise from the sides of the
cell near the bottom; and thence passing upwards symmetri-
cally, one along each side of the body of the polype, receive
an extensive attachment, being inserted into the wide part of
the tentacular crescent, into the pharynx for its entire length,
and into the upper part of the stomach; a few fibres appear
detached at each side from the main fasciculus, to be inserted
more externally near the base of the tentacular lobes. The
function of these muscles is evident, acting from their more
fixed attachment to the side of the cell, they become power-
ful retractors, by which the body of the polype is drawn
inwards and concealed in the more internal parts of the poly-
pidom.

“In the opercular muscles, paludicella offers no remark-

326

able deviation from the general arrangement of these muscles
in the salt water species. In plumatella repens, however,
and perhaps in most other species of fresh-water ciliobra-
chiates, their arrangement is very peculiar. In this zoo-
phyte, they consist of a series of about twenty-five distinct
delicate fasciculi, which arise from the internal surface of the
cell at regular intervals, and in a plane perpendicular to its
axis, and thence radiating inwards are inserted into the op-
posed surface of the reflected tunic.

“In assigning their proper office to the muscles which have
been already described as the true retractor apparatus of the
polype, no difficulty whatever is met with; neither can we
be at a loss in discovering the true function of the parietal
muscles, for these acting upon the flexible internal tunic of
the polype cell, must necessarily, by their contraction, dimi-
nish transversely the space included between this tunic and
the body of the polype, a function the great importance of
which, in the economy of the little animal, will presently be
apparent. When, however, we attempt to explain the action
of the opercular muscles, the task will perhaps be found not
quite so easy. It has been stated that Dr. Farre assigns to
these muscles the office of drawing in the flexible portion of
the polype tube after the retreating polype, and by their con-
tinued action closing the orifice of the cell. I cannot help
thinking, however, that in ascribing this office to the oper-
cular muscles, Dr. Farre is correct but to a very limited
extent, and that their chief use is directly opposite to that
assigned to them by this excellent observer. The use which
I would assign to the opercular muscles is, first, that of
assisting the polype in its protrusion, an office which they
accomplish by fixing and preserving in the axis of the polype
tube that portion of the reflected tunic (fig. 4, ¢, ¢) which
is included, during the retracted state of the animal, between
the summit of the fasciculus of approximated tentacula, and
the orifice of the cell; and, secondly, what is a still more

327

important function, that of affording to the respiratory sur-
face, when the polype is retracted within the recesses of its
cell, a constant supply of fresh water, of which the little
animal would be deprived, were it not that some means
existed of dilating the tubular reflection of the tunic, an
office to the performance of which these muscles are fully
adequate, acting then in a state of antagonism to the parietal
muscles, which tend to keep the orifice of the tube closely
shut.

«‘ My objections to Dr. Farre’s view of the function per-
formed by the muscles in question are referrible to three
heads: first, want of necessity in ascribing to them the office
for which this anatomist believes them destined; secondly,
their inability to perform the function which he ascribes to
them; and thirdly, the possibility of assigning to them another
office in full accordance with the necessities of the animal.

“‘ That we are not obliged to seek for opercular muscles,
in order to account for the closing of the orifice when the
polype has retired into the recesses of its cell, is evident, if
we give the slightest consideration to the action of the true
retractor muscles. It is quite plain that the retraction of the
polype itself, which is effected by the muscles which act di-
rectly &pon it, is amply sufficient to produce the complete
invagination of the flexible termination of the cell; and, ac-
cordingly, observation will convince us that this invagination
follows exactly the retraction of the polype, and is evidently
related to the latter action as an effect to acause. ‘That the
opercular muscles cannot, except in a very partial manner,
produce the effect ascribed to them by Dr. Farre, is also
evident, when we reflect upon their course and attachments.
Avising from the circumferential portion of the cell, and
thence passing inwards, to be inserted into a point nearer to
the axis, they must, after the invagination of the tunic has
proceeded beyond the plane of their insertion, possess upon
the reflected tunic a decidedly délatable action,—an action

328

which is antagonized, first, by the parietal muscles, as will
be presently explained, and, secondly, by the true retractor
muscles; for these muscles, acting through the medium of the
polype, in most instances nearly centrally, or in the axis of
the tube, will not, in their ordinary action, possess any di-
lating power, but, on the contrary, will tend to close the
aperture by approximating the sides of the tubular reflection
of the cell.

«‘ Since we have thus seen that the opercular muscles are
incapable of producing the closure of the orifice, it becomes
an interesting subject of inquiry to determine by what means
the act in question is performed, and indeed a slight consi-
deration will render manifest the simple yet effective mecha-
nism appropriated to this purpose. The great agents by
which the closure of the cell is effected are to be found in
the parietal muscles, for these fibres, by pressing the fluid of
the cell against the tube of invaginated membrane (fig. 4, ¢; ¢),
will approximate the sides of this tube to one another, at the
same time that the membrane will be thrown upwards against
the aperture of the cell, thus completely closing the orifice,
and enabling the little animal to rest secure fromall intrusion
in the recesses of the polypidom.

«« After this account of the muscular system of the polypes,
the mechanism will now be easily understood by which the
animal is protruded from its cell when hunger calls it
forth to seek its food in the surrounding medium, or when
desirous of exposing its respiratory surface still more per-
fectly to the vivifying influence of the aerated water.

« Previously to the discovery of the parietal muscles no
satisfactory explanation had been given of the protrusive act
of the polype, and even since the detection of these muscles
by Dr. Farre, their share in effecting the protrusion of the
animal would appear to be underrated. Dr. Farre considers
their influence in this respect as of secondary importance,
and would seem to attribute the act in question mainly to the

329

straightening of the oesophagus, which in the ciliobrachiates
of the sea is bent upon itself during the retracted state of
the polype. In none of the fresh water species, however,
which I have examined, with the exception of Paludicella
articulata, does this curvature of the cesophagus appear to
exist; we therefore cannot in these instances have recourse
to its agency in accounting for the phenomenon now under
consideration, and we are consequently driven to the parietal
muscles, or to the general contractibility of the internal tunic,
as the only provision by which this important act can be
effected. I mention the general contractibility of the internal
tunic as a probable agent in protrusion, for I do not think
the existence of the parietal muscles throughout the entire
order as yet sufficiently established.

* We shall now suppose the polype withdrawn into the
recesses of its cell, and that hunger or some other stimulus
impresses on it a desire of protrusion. The parietal muscles,
which appear to me to be the direct agents in effecting the
protrusive act, now begin to contract, and thus exercise a
pressure on the fluid which surrounds the polype, and is in-
cluded between the latter and the internal membrane of the
cell. The compressed fluid in its turn acts upon the polype,
and by its upward pressure against that portion of the flexi-
ble tunic which is carried in by the animal during its re-
treat, will tend to produce an eversion of this membrane,
which, in the completely retracted state, constitutes a tube
of some length between the summit of the fasciculus of ap-
proximated tentacula and the orifice of the cell. ‘The oper-
cular muscles at the same time coming into play will, by their
nicely adjusted action, keep the invaginated tunic exactly
in the axis of the orifice, and thus materially assist in effect-
ing the necessary protrusion, which, by the continued action
of the parietal muscles, will go on increasing till the com-
plete evagination of the reflected membrane has taken place.
This, then, I conceive to be the true account of the protru-

330

sive act, and that the apparatus just mentioned is amply
sufficient for the purpose, without having recourse to the
agency of the bent cesophagus,—an agency which in pluma-
tella repens, and other fresh water zoophytes, which I have
examined, assuredly does not exist, as in these the cesophagus
is straight during the retracted state of the animal. In the
remarks now offered, however, I do not deny that some in-
fluence is exercised by the straightening of the cesophagus
in those species in which this tube is bent upon itself pre-
viously to the commencement of protrusion; I merely wish
to assert that we are not necessarily obliged to have recourse
to this agency, but that in some instances, at least, the pa-
rietal muscles, or, in their absence, the general contractility
of the internal tunic, are agents perfectly effective.

“Such are the observations which I have had an oppor-
tunity of making on the muscular system of the ascidian
polypes of fresh water. Iam fully aware that they are far
from being perfect, but for this my excuse must be found in
the extreme difficulty of such investigations, made, as they
all necessarily are, under a high power of the microscope,
with an illumination most carefully adjusted, and which can
by no means be at all times obtained, in order that structures
of such extreme tenuity and transparency may not entirely
escape detection. The observations have all been made on
the living animals, and no one who has not devoted himself
to such investigations can form any idea of the close and pa-
tient attention which they require,—the constant watching
to obtain the animal in the exact condition or position, in
which alone certain peculiarities of structure are apparent;
and, finally, the mortification of finding the conclusions to
which we had arrived on one day, after hours of painful at-
tention, invalidated by some more favourable observation on
the next.

** In the present communication I have confined myself to
the muscular system; on some other occasion I may perhaps

—————————

331

again entreat the indulgence of the Academy, while I lay
before it my observations upon other not less interesting
parts of the structure of these curious animals.”*

DESCRIPTION OF THE PLATE.

Fig. 1. Paludicella articulata; natural size.
Fig. 2. Portion of the polypidome magnified.
Fig. 3. A cell with the polype exserted,
a,a, a. The polype cell.
b. The orifice of the cell.
c. That portion of the internal tunic which is carried out by
the polype during its egress from the cell.
d. The stomach of the polype.
e. The rectum.
J. The esophagus.
g. The crown of tentacula exserted and expanded.
h, h. The proper retractor muscles of the polype; they are
now relaxed, and carried out by the animal in the act of protrusion.
2,2. Two of the four sets of opercular muscles, also in a state
of relaxation.
k,k, k, k. The parietal muscles, preserving, by their contrac-
tion, the membrane ¢, in a state of tension, and thus maintaining the
exserted condition of the polype.

* After the present account had been written, 1 happened to meet with a
paper by M. Dumortier, in the Bul. Ac. Brx. an. 1835, on the Polype & Panache
of Trembley, a polype belonging to the order now under consideration, and for
which M. Dumortier constitutes a distinct genus under the name Lophopus,
characterized by the tentacula, being destitute of cilia. So remarkable an ex-
ception, however, would this character offer to that of the entire order, that I
cannot but suppose Dumortier in error; an opinion in which I believe myself
fully born out by the phenomena subsequently described by this naturalist, and
which are evidently the result of imperfectly observed cilia.

Dumortier details, at considerable length, the anatomy of the zoophyte, and
has witnessed fibres corresponding with the retractor and opercular muscles
described in the present communication. His paper is well worth perusal, though
some of his statements will require further corroboration.

332

Fig. 4. A cell with the polype retracted.

a, a, a. The polype cell.

6. The orifice of the cell.

c, ec. The inverted membrane, which, in the completely re-
tracted condition of the polype, consists of that portion of the
internal membrane which had been carried out in the act of exser-
tion, together with the more flexible termination of the external
tunic of the cell.

d. The stomach of the polype.

e. The rectum.

J. The cesophagus. Both rectum and cesophagus are here
curved upon themselves, and thus accommodated to the retracted
state of the polype.

9,g. The crown of tentacula retracted, and the tentacula
approximated into a close fasciculus.

h, h. The proper retractor muscles of the polype in a state
of contraction.

i, 2,2. The opercular muscles also contracted.

k, k, k, k. The parietal muscles relaxed.

Dr. Robinson gave a brief account of meteors observed
at Armagh on the 10th of August, 1842, apologizing for the
imperfect nature of the observations, while he felt that it
was desirable that they should be placed on record.

The sky had been overcast, but became clear a little after
ten, of which Dr. R. was availing himself to try an eye-
piece of a peculiar construction, when the appearance of two
large meteors, travelling in nearly the same direction, re-
minded him of the peculiar character of the 10th, and in
conjunction with T. F. Bergin, Esq. and another observer,
he proposed to watch for others. The roof of the dwelling-
house afforded an excellent position. Mr. Bergin looked
south-west; he (Dr. R.) east; and the third north. From
10*.55™. Armagh time, till 12%, seventy-eight were seen; of
which about twenty were in Dr. Robinson’s district, and fifty
in Mr. Bergin’s. With scarcely any exception, their ten-

333
dency was in tracks converging at € Ophiuchi. The greater
part of them were larger than ordinary falling stars, and left
a red train; in some instances a luminous cloud marked
for a few seconds the place of their disappearance, and then
was faint Aurora towards north-west. The night was occa-
sionally cloudy, and after twelve became completely overcast.

DONATIONS.
Report of the Limerick Philosophical and Literary Society.
Presented by Dr. Gore.
Supplementary Appendix to the Report of the Poor Law
Commissioners on the Medical Charities, Ireland. Presented
by the Commissioners.

February 13.
SIR Wma. R. HAMILTON, LL.D., President, in the Chair.

Robert Culley, Esq., James Magee, Esq., and H. L.
Renny, Esq., were elected members of the Academy.

A paper on the Action of certain Salts as Manures, by the
Rev. Thomas Knox, was read by the Secretary of Council.

«¢ A small meadow, containing about an English acre, was
divided into six plots, and in last Spring, were manured as

follows:
Ist. 2nd. 3rd. 4th. 5th. 6th.
Ashes. Stable | Burned | Muriate of ammo- | Guano, | 23 barrels of
manure. | gypsum, | nia, 6 Ibs.; pearl| 2 stone. | lime mixed
4 stone. | ash, 6 lbs. ; 8 lbs. of with earth.

bones, burned and
dissolved in half
a pint of sulphuric
acid, and diluted
largely.

33 b

Plots Ist, 2nd, 3rd, and 6th, were top dressed in March;
plots 4th and 5th in April. Mr. Knox first remarks, about the
composition of No. 4, that the quantity of muriate of ammo-
nia was calculated (according to Liebig) on the supposition
that the decomposition of the ammonia furnished all the
nitrogen required for the plant, and was sufficient to give a
heavy crop with the addition of the ammonia derived from
the rain. The quantity of bones was sufficient to furnish all
the phosphates required, at the rate of from three to four
tons to an acre, and were, as Liebig suggested, first dis-
solved in sulphuric acid, and having been mixed with a
large quantity of water, were sprinkled evenly over the land.
At first, plots Ist and 2nd, those manured with ashes and
stable manure, appeared much the most luxuriant, and even
up to the time of cutting, that top dressed with manure
seemed far a finer and heavier crop, and had a richer colour.
When ripe, the plots were mowed and saved quite separately,
and that there might be no mistake, pegs had been driven
down deep into the ground at the time of laying on the top
dressing. When the hay was quite dry and saved, the pro-
duce of each plot was weighed separately, and I was then
surprised to find, that though the stable manure was to all
appearance the best, yet the plot manured with the mixed
salts and dissolved bones much surpassed it; also that on
which the ashes had been used. This, in case of plot Ist, I
consider to be due to the potash (which the ashes contain),
enabling the plant to take up more silica from the soil; and
in the case of plot 4th, to the potash and phosphates, by
which greater firmness of stalk was acquired by the plant,
and it was prevented from losing weight in drying, as the
one that was top dressed with the stable manure did. I was
prevented at that time from determining this analytically,
which might have been done, simply by weighing the ashes
resulting from burning equal weights of hay. I here give
the weights of hay, the exact quantity of land, which was re-

——'. . 2

309

gularly surveyed, and also the weight of hay calculated at
what it would be per acre.

| |
Ist Plot. 2nd Plot. 3rd Plot. 4th Plot. 6th Plot. | 6th Plot. |

Hay, 5 cwt.
Land,20 perch.

Hay, 8icwt. | Hay, 9}cwt. | Hay, 82cwt. | Hay, 8 ewt. Hay, 6 cwt.
Land, 242 perch| Land, 273 EES ae 253 perch} Land, 22 perch.| Land, 212 perch

Produced at the Rate per Acre,
Ton Cwt. St. } Ton Cwt. St.
2 9 7 Se ree 2

“The results of the above experiments point out the ad-
vantage of the salts of ammonia and potash when combined
with dissolved bones, but the nature of the land and crop to
which it is applied, must be considered, as it might be posi-
tively injurious in some cases. In the instance given above,
the meadow was an old one, which had not been broken up
for many years, and the grass was close and fine in texture,
so that great advantage was gained by the additional silica
and phosphate of lime ; but in the case of a new meadow, the
hay is often, for the first year or so, too strong and wiry. In
such a case, were the same applied, it would be rendered too
coarse for the use of horses or cattle; it might, therefore, be
found better, for the first two seasons, to apply simply the
salts of ammonia, which would increase the sappiness of the

plant and the general growth, without adding to the harsh-
ness of texture.

Ton Ct. St. |
2 0 0 |

Ton Cwt. St.

Ton Cwt. St.
= ld A 1

Ton Cwt. St.
2 °15 6

2 4

“Thope to be able, on some future occasion, to lay before
the Academy the result of further experiments on the sub-
ject, and (should time permit me) accompanied with an
accurate analysis of the ashes of the plant in each case.”

Mr. Webber made an inquiry as to the cost of the ma-
nures mentioned, and suggested that Mr. Knox should be
requested to annex to his paper, a statement of the relative
expenses of the manure employed.

Dr. Kane and Dr. Apjohn made some remarks on the
general subject.

VOL. II. 25

336

Mr. J. Huband Smith gave an account of some ancient
tiles found in the ruins of Bective Abbey, near Trim, and
exhibited specimens of some raised and incaustic tiles, with
drawings of others.

Dr. Todd, V. P., gave an account of an ancient Irish MS.
preserved in the Bodleian Library, Oxford.

This MS., which is a large quarto on vellum, was formerly
in the collection of Archbishop Laud, by whom it was pre-
sented to the Bodleian. It was also once in the posses-
sion of Sir George Carew, as appears from the autograph
** G. Carew” on the margin of the first page. It contains a
large collection of miscellaneous pieces, historical, genealogi-
cal, theological, and poetical, in different hands, and of diffe-
rent dates ; such a collection was called by the ancient Irish
“a Psalter,” and in an entry, which shall be considered
presently, this volume is called ‘ the Psalter of Mac-Richard
Butler.”

Pasted down on the inside of the cover is the following

note:
“ Oxford y° 9" of August 1673.

“ This booke is a famous coppie of a greate part of Salcam
Caipl, the booke of St Mochuda of Rathin & Lismore, and
the chronicles of Conga; wherein is contained many divine
thinges, and y°® most part of y° Antiquities of y® ancientest
houses in Ireland, a Cathologue of their Kings, of the coming
in of y* Romans vnto England, of y* coming of y* Saxons, and
of their lives and raygne; a notable Calender of the Irish
Saints composed in verse eight hundred yeares agoe, w™ the
Saints of ye Romane breviary vntill that tyme; a Cathologue
of y* Popes of Roome; How y° Irish and English were con-
verted to y® Catholique faith; w* many other things as the
reader may finde, and soe understanding what they containe

lett him remember
*“* 'TutLty Conry.

“ Tuileasna o Maolconaine.”

30

This account of the contents of the volume is very in-
adequate, aswell as erroneous. There seems but little reason
to think that the book contains a copy of any part of the
Psalter of Cashel, although that celebrated Collection is
sometimes referred to or quoted; no traces of the book of St.
Mochuda, or the Chronicles of Cong, are now to be found in
the volume; if Tully Conry therefore was not mistaken, there
is ground to suspect that the MS. may have lost something
since the foregoing account of its contents was written.

On the upper and lower margins, in several places, there
are entries and memorandums by various possessors of the
book, which serve to give us its history, and to fix the date
of a great part of the documents of which it consists. The
most remarkable of these entries must now be noticed.

1. On the lower margin of fol. 4, 5, there is the following
note, which is here given in the original, with a translation:

On anopo vo pigpaid m*.
pean, m°. topna, m*% maoilin
moip ui mail-conaine, pil ag
lepugao an libaippe vo muimip
m®°. comaip .1. 1anla oepmujnan,
sup pe an eargeibtmea....
caiz1 na beallcame can eip
veipceant epinn oa planugao
icep gall agup saerorl.

A prayer here for Sighraidh
son of John, son of Torna, son
of Mailin Mor O’Mulconry; who
is restoring this book for Mau-
rice, son of Thomas, i. e. the
Earl of Desmond, who is now
residing at Askeaton..... at
the beginning of May, after the
south of Ireland has submitted
to him both English and Irish.

2. Another entry of a similar kind occurs on the lower

margin of fol. 34, as follows :

Op. npo vom fezip «1. Mumip
m¢ comaip, m* pemaip, nc 0’an
lepugiup an becro cuap Le ono
mpepumencaib.

A prayer hereformy patron (?),
i. e. Maurice, son of Thomas,
son of James, the person for
whom I am restoring the little
portion above, with bad instru-
ments.

The Maurice mentioned in these extracts was the tenth

308

Earl of Desmond, who succeeded his elder brother James in
the Earldom in 1481. He was the son of Thomas, the eighth
Earl, who was beheaded at Drogheda, 5th February, 1467.
He died 1497, according to O’Clery’s book of Pedigrees: and
as the foregoing entries were manifestly made during his
life-time, it is evident that this volume was of some anti-
tiquity, so as to require the ink to be revived and restored, in
the latter end of the fifteenth century. This was a process
very common with Irish scribes, as is evident from the in-
spection of our ancient vellum MSS., many of which have
suffered great damage by ignorant attempts to restore them.

3. A memorandum of peculiar interest oecurs on the Ope
per margin of fol. 110, 6. It is as follows :

Salzaip m¢ purpoepo burzilen This Psalter was the Psalter of

..€monn buizilep, ino c-palzain
peo, no 50 v-cucad marin baile
in ppoill ap iapla upmuman
azsup ap m® puipoeno buizilen
le 1apla vepmuman .1, tomar,
azup oo baiead mleaban po
agup leabap nacappuigi ap pu-
aypglad m* puipoeno, agur If pe
mm M¢ puipoepo pin vo chuip na
leabaip pin oa pepibad vo fem,
no sup bain Tomar [ve a0].

Mae Richard Butler, i. e. Ed-
mond Butler, until after the de-
feat at Bally-in-spoill, of the Earl
of Ormond and of Mae Richard
Butler, by the Earl of Desmond,
i, e. Thomas; and this Book and
the Book of Carrick were given
in ransom of Mac Richard, and
itis this Mac Richard that caused
these books to be transcribed for
himself, until Thomas took them
from him.

Thus it appears that this book, and the book of Carrick,

(now unknown) were in the fifteenth century considered as
a sufficient ransom for the person of a great chieftain,—a re-
markable proof of the preservation of a love of literature
amongst the native Irish nobles, in the midst of all their war
and faction at that period. Nor is this a solitary instance in
Irish history. The Leabhar na h-Uidhri, a manuscript of
the twelfth century, in the collection of Messrs. Hodges and
Smith; contains an entry of a similar kind.

339

The foregoing memorandum, however, shows that this
volume was written originally for Sir Edmund, son of Richard,
Butler, commonly called Mac Richard ; and that on his de-
feat by Thomas, eighth Earl of Desmond, who, as we have
already seen, was beheaded in 1467, it passed into the hands
of the Desmond family.

In the book of Pedigrees of the O’Clerys, an unpublished
work, of which the autograph MS., in the original Irish, is
in the Library of this Academy, the following account of
Thomas, eighth Earl of Desmond is given (p. 247):

‘©The fate of Thomas, son of James, Earl of Desmond,
i.e. the ninth [eighth] Earl. Thus did it happen unto him,
viz. John Tipto [Tiptoft] Earl of Worcester, came into Ireland
as Lord Justice, called by proclamation of the English of
Ireland to the great Council at Drogheda. And bad was the
counsel there agreed upon, viz. to behead Thomas, son of
James, the Earl, without impeachment of crime, right, or
law, but merely from envy and hatred; the man of best mien
and form, wisdom, and intelligence of either English or Irish
of his time. No praise bestowed upon him could be too
high. The sorrow and affliction of that death was felt
equally by the English and the Irish. This Thomas the
Earl invariably overthrew and put down his enemies and op-
ponents on every occasion whenever he fought with them.
Great indeed was the battle in which he overthrew the But-
lers, on the Suir, and innumerable were the hosts of them
that were slain and drowned on that occasion. He likewise
gave several overthrows besides, that are not here enume-
rated. A Lord intellectual and learned in Latin, English,
and ancient Irish writings, was that Thomas. It was he
that gave the great overthrow to the Mac Carthys at Reidh-
an-Eich-bhuidhe. The 5th day of February the Earl was
beheaded, and 42 years was his age at that time. At Tralee
was he buried, 1467.”*

* This is a strictly literal translation of the original Irish.See Grace’s

340

This extract, taken in connexion with the entry in the
Oxford MS., is exceedingly curious, as it notices the fact
that Thomas Earl of Desmond was learned in ancient Irish
writings ; and therefore incidentally confirms the probability
of his accepting ancient MSS. as a ransom for the Mac
Richard. The place called Bally-in-spoill is now unknown ;
but from the record in the Book of Pedigrees it seems pro-
bable that it was a village on the banks of the Suir.

4. Another interesting entry, which enables us to date
one portion of the volume, occurs on fol. 86, a, in the hand-
writing of the original scribe, at the end of a very valuable
fragment of Cormac’s Glossary :

Ip h-e analao in agepna in
uaip vo pepibad m panaran ro
na palcpac, .. mile bliadan
agup ceitm .c. bliavan agup
zm bliabna vec, agup oa .x. in
cuiceo la vo mi Febpa agup n
My
reaan bud o clei: vo pemb,

toccmao la oon erca.

The year of our Lord when
this Glossary of the Psalter was
written, was 1453; on the 5th
day of the month of February,
and the eighth day of the moon.
I am John Boy O’Clery who
wrote it, and for Edmund Butler
Mac Richard was it written.

agup o’emann buizilep m® pip-
zepo vo pepibad.

lt appears therefore that this portion of the volume was
transcribed (doubtless from much more ancient documents,
perhaps from the veritable Psalter of Cashel itself) in the
middle of the fifteenth century for Sir Edmund Butler,
commonly called Mac Richard; and that it subsequently
passed into the family of Desmond, having been received in
ransom of Mac Richard by Thomas Earl of Desmond.

This MS. having been for the last two centuries in Eng-
land, appears to be wholly unknown to our historians. The
rules of the Bodleian Library do not permit its MSS. to be
lent, and as there is no accurate catalogue of the valuable,

Annals, printed by the Irish Archzological Society, p. 165, note °, for a further
mention of Earl Thomas.

b41

but unknown, and, in Oxford, unappreciated collection of Irish
MSS. which it contains, the MSS. there preserved are almost
as inaccessible for the purposes of Irish historical research,
as those of the Vatican or the Escurial.

Dr. Todd did not pretend to give a complete account of
the contents of the “ Psalter of Mac Richard,” as it may per-
haps for convenience be called. He was able only to carry
away a very few memoranda of such articles as appeared, on
a very hasty inspection, likely to prove most interesting.

On fol. 7 is a religious tract, known as the Life of St.
Margaret, a work of no value, except to the philologist.

Fol. 9. The Genealogy of St. Mochoemog.

Fol. 11, &. A religious tract, entitled, in Irish, “The
History of the Image of our Lord,” and also, in Latin, “ In-
cipit Libellus Anastasii [Athanasii] Archiepi Alexandriz
urbis, de passione imaginis Dni. nri. Jhu. X‘.”_ This is pro-
bably an Irish version of the tract attributed to St. Athanasius
at the second Council of Nice, although now admitted to be
spurious. It is published in Greek and Latin in the Bene-
dictine edition of the works of St. Athanasius.

Fol. 14,a. A curious legend of Donogh O’Breen, abbot
of Clonmacnois. The story is, that having gone on a pilgri-
mage to Armagh, he was miraculously detained there until
his death, A. D. 987. He is said to have been the last of
the Irish saints who performed the miracle of raising the
dead.—See Annals of the Four Masters in an. 987.

Fol. 15. An account of the ancient tract called the
Felire, or Festilogium, of Angus the Culdee; being a Mar-
tyrology, or Calendar of the Saints’ days observed in the
ancient Irish Church, compiled in the eighth century.

Fol. 18, 6. ‘* The Destruction of Jerusalem by Titus, son
of Vespasian, in revenge for the Blood of Christ.”

There is a copy of this tract in the Leabhar Breac in the
Library of the Academy, and a fragment of it in the Book of
Lismore.

342

Fol. 23. A legend of the Infancy and Life of Christ, as
revealed by the Virgin Mary to St. Bernard.

Fol. 29. A sermon in Irish on the text, “ Omnia que-
cunque vultis ut faciant vobis homines, et vos facite illis.”

‘Fol, 30, &. A sermon on the text, ‘‘ Cum ergo facies
elimosinam.”

There are copies of these sermons in the Leabhar Breac.

Fol. 33, a. The celebrated Chronological Poem of Giolla
Coemgin, beginning with the Creation, and carried down to
the year 1072, when its author flourished—See O’Reilly’s
Irish Writers (Trans. Hiberno-Celtic Soc. vol. i.), p. Ixxx.

There is a very ancient copy of this poem in the Library
of Trinity College Dublin, MS. H. 2, 18.

Fol. 38 to 42. Genealogies of the Irish Saints.

Fol. 43, a. The three sons of Moses, &c.
b. “ Incipit inventio sanctz crucis.”

Fol. 57, 5. A tract containing the fabulous history of
Ireland before the Deluge, as related by Fintan, one of the

ante-diluvian colonists of Ireland, who, under various trans-
migrations, is supposed to have survived the deluge. This
work ends with an account of a convocation of the states of
Ireland held at Tara, in the sixth century, under Dermot
M‘Cearbhaill (Carroll). There is a fine copy of it in the
Library of Trinity College, MS. H. 2, 16.

Fol. 58. The history of Mac Datho’s hog. Mac Datho
was king of Leinster in the first century. He invited the
kings of Connaught and Ulster to a feast, with a view to sow
dissensions between them for his own political ends. At this
feast there was served up an enormous hog, the cutting up
of which, and the assigning to each chieftain his proper
share, became a matter of fierce contention between the
guests, and produced the effect intended by their crafty en-
tertainer.

There are two copies of this legend in the Library of
Trinity College, MS., H. 2, 18, and H. 3, 18.

—

343

Fol. 59. A very fine and ancient copy of the Felire, or
Festilogium of Angus the Culdee. This part of the volume
is much more ancient than the rest, and was probably written
in the twelfth century. It ends fol. 72, a.

There is a fine copy of this work, with the gloss, in the
Leabhar Breac.

Fol. 72, 6. A poem addressed to Cormac Mac Cuil-
lionan, king and bishop of Cashel, in the ninth and beginning
of the tenth century, on the duties of a king.

There are good copies of it in the Library of Trinity
College, MS., H. 2, 18, and H. 3, 18.

Fol. 73, 6. A poem on the sons of Oillil Olum, king of
Munster in the third century.

There is a good copy of it in the Library of Trinity Col-
lege, MS., H. 2, 18.

Fol. 74, a. A poem on the succession of the kings of
Emania, by Cinaeth O’Hartigan, who died A.D. 975. It
begins Fianna bazap m emam. This poem appears to have
been unknown to O’Reilly.— Irish Writers, p. \xii.

Fol. 75, a. A tract beginning ‘‘ Hibernia insola inter
duos filios principales Militis, i. e. Herimon et Eber, in duas
partes divisa est.” The remainder is in Irish.

Fol. 81, 6. An account of the great plague in A. D. 633,
beginning Clnno oommice incamnaczionip oc.xxm. =Opa mona hi
paxain ctuaipcenz ono anbzhine pucad paulinuy eoilbenca lung
co canzia agurp po haipimed co honopach. ‘* In the year of our
Lord’s incarnation 633, a great mortality in North Saxony,
to avoid which Paulinus Edilberta was carried away in a
ship to Kent, and was there honourably received.”

After this are a number of short poems.

Fol. 83. An imperfect but very ancient copy of Cormac’s
Glossary, beginning with the word Mmoech, which is thus
explained, quar) menoic ab eo quov ere menovicup. It ends
fol. 86, a; after which is the entry already quoted, from

VOL. II. 2F

344

which we learn a very remarkable fact, hitherto I believe
unnoticed by our historians, that Cormac’s Glossary was
compiled from the notes or glosses added by Cormac Mac
Cuilionan, the celebrated king and bishop of Cashel, to the
miscellaneous compilation called the Psalter of Cashel. Cor-
mac was killed in the battle of Belach Mughna, now Ballagh-
moon, in the County of Kildare, near Carlow, A. D. 903.

Fol. 93, b. A tract, with the following Latin title, ‘“‘ De
causis quibus exules aquilonensium ad mumonienses adducti
sunt,” beginning Iped cetamurp pocono cops), &e.

Fol. 94, b. The history of the war between Oilill Olum
and Mac Con. This is a most valuable document. Oilill
Olum was king of Munster in the third century. He de-
prived Mac Con, his stepson, of his lawful inheritance.
Mac Con rebelled, assembled his followers, but was defeated
by Oilill at the battle of Ceannabrat, a place on the borders
of the counties of Cork and Tipperary. The defeated prince
fled to Scotland, where he had influence enough to raise a
large force of foreign adventurers, with whom he returned
to Ireland, and again encountered the troops of his step-
father in the bloody battle of Moy Mocroimhe, in the county
of Galway. In this battle Oilill was aided by Art, son of
Conn of the hundred battles, then monarch of Ireland; but
was defeated. Art was slain, and with him the six sons of
Oilill,with the flower of the Irish chiefs. Mace Conn assumed
the sovereignty of Ireland, and continued to reign until driven
back to Munster by Cormac Mac Art, several years after-
wards, who thus revenged the death of his father.

There is an imperfect copy of this tract (a MS. of the
early part of the twelfth century) in the Library of Trinity
College, Dublin, H. 2, 18.

Fol. 96,a. The history of the battle of Mucruimhe, be-
ginning Cuio eugan mop vo éach mucpuime.

Fo]. 99, 6. The Expulsion of the Decies from Tara by
Cormac Mac Art.

345

Fol. 102, a. Thecoming of St. Finian from abroad into
Ireland with the Gospel.

Fol. 104. The History of Oriell, with the genealogies of
many Irish families.

Fol. 109, a. A poem on the sons of Conor Mac Nessa,
king of Ulster in the first century ; by Mongan, a celebrated
poet.

Fol. 109, b. Pedigrees of the families of Fermoy, County
Cork.

Fol. 111, a. Pedigree of O’Dunlevey.

Fol. 112. Lists of Roman emperors, kings of Egypt,
Assyria, and Israel; bishops of Rome, Armagh, &c.

In the margin of fol. 117, b, there is written in faint red ink,
pale. cal: by which we may infer that the tract there tran-
scribed was preserved also in the Psalterof Cashel. This is
apparently the only reason for supposing that the present
MS. contains extracts from the Psalter of Cashel.

Fol. 118. The actions and deeds of Finn M‘Cumhaill.

Fol. 122. A very important tract, which appears from
the handwriting to be much more ancient than any other
part of the volume, containing the derivation of the names,
local traditions, and other remarkable circumstances of the
hills, mountains, rivers, caves, rocks, carns, and monumental
remains in Ireland: more especially such as relate to the
deeds of Finn Mac Cumhaill and his heroes.

There is an imperfect copy of this tract in the Book of
Lismore, in the possession of His Grace the Duke of Devon-
shire, of which a copy was lately made for the Academy by
Mr. Curry.

Fol. 127, a. A Finian tale, entitled, “ The Elopement of
the Daughter of the King of Munster with Oisin.”

The remainder of the volume is occupied with a series of
these tales, which are of great interest and importance.
Many modern copies of them on paper are preserved, espe-
cially in the valuable collection of Messrs. Hodges and Smith,

345

which is particularly rich in this branch of Irish literature:
but with the exception of the fragment in the book of Lis-
more, the present volume is the only vellum MS. of such tales
whose existence is known.

The special thanks of the Academy were voted to the
Board of Ordnance and to Captain Portlock for the presen-
tation of the Ordnance Geological Survey of Tyrone, Lon-
donderry, and Fermanagh.

DONATIONS.

Abhandlungen der Akademie der Wissenchaften zu Ber-
lin, 1840. Presented by the Academy.

Bericht tiber die zur Bekanntmachung geeigneten Verhand-
lungen der Kénigl. Preuss. Akademie der Wissenschaften zu
Berlin. Presented by the Academy.

Account of the Induction Inclinometer and of its Adjust-
ments. By the Rev. H. Lloyd, D.D., F.R.S., V.P.R.I.A.
Presented by the Author .

Regulations of the School of Engineering in the University °
of Dublin, with a Syllabus of the Course. Presented by Pro-
fessor Lloyd.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1843. No. 39.

February 27.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Sir William Betham exhibited to the Academy an ancient
shoe, found in a bog on the property of Sir Nicholas Fitz-
simon, in the King’s County.

Professor Lloyd read a supplement to a former paper
on the Determination of the Intensity of the Earth’s Mag-
netic Force, in Absolute Measure.”

In a paper recently communicated to the Academy, the
author had shown that the ratio of the coefficients of the first
two terms, in the expression for the moment of the force
exerted by a deflecting upon a suspended magnet, was gene-
rally given by the formula

M M’
h = 2— — —;
M M
in which m and mz; denote certain integrals depending on the
law of distribution of free magnetism in the deflecting mag-
net, and m’ and mw’; the corresponding quantities for the sus-
pended magnet. It was further shown, that when the mag-
nets were small, this formula was reduced to
h=3(2? — 31”);
VOL. Il. 2G

348

Zand U’ denoting the half lengths of the two magnets. This
ratio being thus known @ priori, the two unknown quantities
in the equation of equilibrium of the suspended bar are re-
duced to one; and we are thus enabled not only to dispense
with the observations of deflection at two separate distances,
but also to infer the quantity sought with much greater ac-
curacy than in the received method, by superseding the pro-
cess of elimination.

The preceding value of the ratio, h, has been derived
from an approximate law of magnetic distribution, which can
be regarded as physically exact only in the case of very
small magnets; and the truth of the formula has been veri-
fied, in that case, by direct experiment. It was interesting
to inquire, therefore, how far the same formula represented
the law of action of large magnets, and whether, by any mo-
dification, it might be applied to the results obtained with
such instruments.

For this purpose the following deflection experiments
were made:—The magnets employed were rectangular bars,
12 inches, 9 inches, and 73 inches, in length; % of an inch
in breadth; and + of an inch in thickness. The observations
were made with the aid of the Unifilar Magnetometer of the
Magnetic Observatory, which has been elsewhere described ;
and simultaneous observations were taken with the Declino-
meter, in order to eliminate the changes of declination which
occurred in the interval of the opposite deflections. In the
first and second series, the position of the suspended bar was
observed by means of a collimator attached; in all the rest,
it was observed by the help of a mirror connected with the
stirrup, which reflected the divisions of a scale placed at a
distance of nearly six feet.

The angles of deflection were calculated, in the case of
the collimator bar, by the formula

tan u = 4 (me — Nw) hk;

where , and m, denote the observed readings of the scale,

— ee:

349

with the marked end of the deflecting bar to the East and to
the West respectively. The value of the constant / is given
by the formula

k= (1 +=) tan;
F

6 denoting the angle corresponding to one division of the
scale, and ~ the ratio of the torsion force to the magnetic
force. When the mirror is employed, the formule of re-
duction are similar, if only we substitute 2u and 20 for u
and @. The following Table gives the values of the constants
employed in the reduction:

H
l | 6 z logk
co) (coll.) 49-158 ‘00180 6°37795
‘5 (mirr.) 58/766 “00162 6°75643
<1 ga pe eSB ea 00255 675684
eee ee! AE Na Tar Wet ratie 00292 6°75700

The following Tables contain the calculated results: the
values of 4(-—mw) are corrected for the changes of declination
which occurred in the interval of the two readings m, and my.

Series I.and II. 7=/=°5.

I. Il.

4(me— nw) u 3 (%e—Nw) Le
4.5006 194-78 4 2°39/ 45” 194-22 2° 39/18”
6.0010 82°51 1° 7/43” 82-26 1° 7/305

Series [IL and IV. 2=°5, l’ =°375.

24230 3° 56/ 25” 242°52 3°56’ 38”
5°0015 123°31 2° 0! 53” 123-50 ZOU Av
6-0019 71:40 1°10'4/"5 71:38 MONO FSi

25Gue,

300

Series V. and VI. 2=°5, l’=°315.

a

4:0005 243.58 3°57' 44-5 242-74 3°56! 56”
50008 123-65 2° 1/155 123-36 2° 0/585
6:0010 71°41 1210" G45 71:25 19 Oat

Series VII. and VIII. 2=:°375, ’=°5.

Vil. VIIl.

3°3762 211-18 3° 26/ 105 210:50 3° 25/ 305
4:3754 97°88 1°35’ 55” 97°56 1°35/ 365
5°3757 53°24 0° 52/13” 52°88 0°51'51""5

Series 1X. and X. J=l=:°375.

IX. x.
D.
3 (ne — nw) U $ (Ne = Nw) u
3-3766 212-37 -| 3°27'31” 212°52 3°27/ 40”
4:37 60 97°52 1° 35/ 39/5 97-55 1°35! 41/5

Series Xl.and Xi 2 = 23157 = Als.

xi.

3 (me — Nw) u 3 (Ne — Mw) u

213°83 3°29/ 1”
97-90 1°36) aca
52°82 0°51/52”

3°3766 214-16 ao 20 21”
4-3760 98-05 1°36/13”
5°3765 52°85 0°51/54”

The following Table contains the calculated results of
the foregoing observations. The values of the coefficients,
@ and Q’, are deduced from the formula

tanu = an + a
DD

by the method of least squares.

351

Q/
y — =h

1 l Q Q’ Q

eo sing APBOOs- 2i:\uiy 9 OBC amo Daes

42662 — 0-790 — 085
ethan aee4 + 0:293 + 0-067
5 375 \ 43976 + 0-293 + 0:067
" {43791 + 0 887 _ + 0-202
§ 23830 — 0°823 — 0°345
375 oy) ) 23702 — 0°761 — 0°321
px | §2:3407 — 0-161 spyoeee
375 375 ) 92-3402 — 0:135 — 0:058
§ 23456 + 0:027 + 0012

The values of 4 thus obtained are not adequately re-
presented by the formula which has been already deduced
for the case of small magnets, the differences between the
calculated values and the means of the two observed results
being, in general, greater than the differences of the latter
inter se. It was accordingly natural to inquire whether the
agreement might not be rendered more complete by pushing
farther the approximation in the value of the function which
represents the law of magnetic distribution. This was found
to be the case on trial. But it was also found that the observed
results were represented, with nearly equal exactness, by the
empirical formula,

h=2(l-—cyr—3(— ce);
a formula which agrees with the hypothesis, that the whole
force of each magnet is concentred in two points, or poles, at
given equal distances from the ends. If we expand the pre-
ceding formula, and add together the resulting equations, we
have for the determination of c,

6c? + 23(2I—3l')e + Th—3(22?—3l”) = 0;
or, substituting the numerical values of the coefficients de-
duced from the preceding Table,

352

ce’ — 0°625c¢ + 0°0125 = 0;
from which we deduce c = ‘078.

The following Table contains the values of / thus calcu-
lated, together with the means of the observed results. The
differences barely exceed the probable errors of the latter;
and the corresponding error in the calculated value of @ is
less than the probable error of the same quantity, as deduced
in the ordinary method from the observed deflections at two
distances.

L I | h (obs.)
ao Se |
9) 2) — 0189
5 ‘375 + 0:067
9) 313 + 0-180
“375 5 — 0°333
375 ‘375 — 0-063
"375 “313 + 0:007

It follows from the preceding formula, that the relation
between the half lengths of the two magnets, which will cause
the coefficient of the fifth power of the distance to vanish, is

l—ce = 1:224(/—c);
or, substituting for c its value,
2+ 0175 = 1:2247.

It will appear evidently from the foregoing results, that
on account of the large probable error of f, its value should
be determined in each case from the mean of a much greater
number of observations, before we can obtain thereby a sa-
tisfactory verification of any formula for its calculation. As
far as the comparison has been here carried, the results ap-
pear to indicate that the value of # cannot be obtained a
priori, in the case of large magnets, with that precision
which would justify us in superseding observation, although
we may obtain thereby an approximate value, comparable in
exactness with the result of a single observation.

3od

Mr. T. Oldham read a paper “ on the Tiles found in the
ancient Churches in Ireland.”

Mr. Oldham commenced by drawing attention to speci-
mens of old tiles, from various places, which were on the table;
and having alluded to the fact, that there has hitherto been
no published representation of these tiles from any place in
Ireland, proceeded to show that there were three distinct
varieties :—Ist. Impressed or indented, in which the pattern
is formed by being sunk below the general surface of the
tile. 2nd. Encaustic, in which the pattern is produced by a
differently coloured substance inlaid; and 3rd. Tiles in re-
lief, or embossed, in which the pattern is raised above the
general surface or ground.

(D

De SVEN
= uA ’
ais Gi

uy |

DI
(URIS
be TS {)—

From the great simplicity of the patterns in the indented
tiles, from their interlacing character (Fig. 1), and from the
fact, that several of these patterns occur also in the more
carefully formed encaustic tiles, it was shown that the im-
pressed variety was the earliest in date; and, from a conside-
ration of the history of the establishments where they occur,
probably belonged to the twelfth century ; that the encaustic
variety was a subsequent improvement on this more simple
form, and that the embossed tiles belonged to an era when
the knowledge of the arts had very much declined. This

354

was proved by several from Bective Abbey, the date of which
was fixed by the occurrence of the tudor, or double rose, and
by an heraldic tile from the same place, representing the
arms of the Fitzgeralds, having the motto, “ Crom abo—Si
Dien plet,” and the initials G. E. It was shown, from the
history of this family, that the tile could only be referred to
a date subsequent to 1496 (in which year the Earls of Kil-
dare, previously attainted, were restored to their honours,
and again allowed to use their motto), and to either Gerald
the eighth or Gerald the ninth Earl, both of whom had
wives whose Christian name was Elizabeth, corresponding
to the initials G. E.—Gerald and Elizabeth.

The identity of several of the patterns from different
places in Ireland, and the strong resemblance of many to
those found in England and Normandy were then alluded to,
and several peculiarities in the Irish pattern, which tended
to prove that they were manufactured on the spot, were
pointed out.

Speaking of the comparative cost of these tiles now and
formerly, Mr. Oldham showed from the account of the re-
pairs at Hampton Court in 1536, and allowing for the diffe-

355

rence in the value of money, that the price at present
charged was somewhat less than in the sixteenth century;

and concluded by soliciting the assistance of the members in
bringing together as complete a series as possible of the pat-
terns still remaining in many of the ruined churches of

Treland.

The President read a Supplementary Notice of his Exa-
mination of Signor Badano’s Memoir on the Resolution of
Equations of the Fifth Degree, and described the successful
application to cubic and biquadratic equations of the method
proposed by Badano, but which had been shown to be un-
successful with equations of higher degrees than the fourth.

Rev. Dr. Marks, on the part of the Bishop of Cashel,
presented the seal used by the latter as Dean of St. Patrick’s.

396

March 16. (Stated Meeting).
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

The Secretary of Council read the following Report,
which was ordered to be entered on the Minutes:

‘“‘The affairs of the Academy during the past year have been,
for the most part, of a similar character to those which have formed
the subjects of former Reports. It is, however, satisfactory to the
Council to be able to state, that our proceedings have been distin-
guished by still increasing activity and zeal among our members,
and that some important measures have been entered upon, and
others brought to completion, which it is to be expected will tend
permanently to sustain the reputation of the Academy, and extend
its useful influence.

‘* The second part of the nineteenth volume of the Transactions
of the Academy is now printed, and the Council is enabled to place
before the Academy an early copy. In a few days it will be ready
for distribution among the members.

‘The twentieth volume, which will altogether consist of Mr.
Petrie’s Essay on the Round Towers, is progressing through the
Press; and a portion of the twenty-first volume is in the hands of
the printer.

‘<The Council have with great pleasure to report, that the va-
luable collection of Irish antiquities amassed by the late Dean of
St. Patrick’s, having been purchased by a subscription, has been
presented by the subscribers to the Academy. The amount sub-
scribed having slightly exceeded the cost of the Collection, the
balance was applied to the purchase of some other valuable relics
of antiquity, which were also presented to the Academy, and now
form part of its Museum. The detailed circumstances connected
with the collection and application of this subscription, and the
eminent services rendered to the Academy and to Irish Archeology
by various gentlemen, to whose exertions final success was mainly
due, have already been brought under your notice in the Report
drawn up by the Committee of Antiquities, and presented to the
Academy in November last by Dr. Todd. The Council have there-

357

fore, on the present occasion, only to congratulate the Academy and
the country on the acquisition of this Collection, which it is to be
hoped will prove a centre to which may be attracted the various
objects of antiquarian interest now scattered through the country,
or which may hereafter be discovered, and thus be laid the foun-
dation of a truly national Museum of Antiquities.

“‘ Besides the actual Dawson Collection, our Museum has been
enriched by donations from His Excellency the Lord Lieutenant,
and from various private individuals, to whom on the several occa-
sions of presentation well merited thanks were voted by the Aca-
demy. '

‘The necessity of arranging our Museum in such a form as
should do justice to its intrinsic value, and adapt it for those pur-
poses of reference and exhibition on which much of the influence
it is calculated to exert must depend, has rendered the present ac-
commodation of the Academy House totally inadequate to our
wants, and the Council has consequently directed its attention to
ascertaining how far our accommodation in rooms can be extended.
It has been found that at a moderate cost the present Board Room
may be converted into a Museum Room sufficient for our objects,
and that under the Library and the adjoining spaces, there exists
ground now of little use, on which a Board Room, rather larger than
the present, may be constructed. A model and drawings of the ar-
rangement proposed have been already laid before the Academy,
and met with its approval, but circumstances connected with our te-
nure of this house have induced the Council to postpone for a short
time entering upon any outlay in building.

“In the Report of the last Council, the Academy was informed
that an application had been made to His Excellency the Lord
Lieutenant, that he might recommend to the Government to increase
our Annual Grant by the sum of £100, or to allow that sum per
year, specially for the purchase of Irish antiquities. No decisive
answer has been as yet received to that application, but it is to be
hoped that as we have now made so excellent a beginning to our
Museum, and that the sphere of our public utility has thus been
much extended, so small an increase to our exceedingly scanty
means may not be finally refused.

358

‘“In November last, the Academy authorized the Council to
employ Mr. Curry to draw up a Catalogue Raisonné of the Irish
manuscripts in the Library of the Academy. This work has been
ever since in progress, but will still require some months for its
completion.

‘* Some time ago the Council became aware that it was contem-
plated by Her Majesty’s Government to withdraw from the Irish
branch of the Ordnance Survey those grants of money which have
hitherto been made to the departments of Geology and Natural
History, as well as of Topographical Antiquities and Statistics, so
that the future operations of the Survey should be limited to the
completion of the Maps. Sensible of the great benefit that must
accrue to the country at large by the continuance of those depart-
ments, for which already a vast body of materials have been col-
lected, which, if publication were now abandoned, may be totally
lost, and feeling that independent of its interest, as positively extend-
ing the domain of science, and of which so brilliant an example has
been already presented to the Academy, on the part of the Board of
Ordnance, by Captain Portlock, the Geological branch of the Sur-
vey is of the highest practical importance to Ireland, as making
known the true position and limits of our mineral wealth, and
guarding enterprize from those latent perils on which, from want
of such scientific knowledge, it has been so often wrecked, the
Council did not hesitate to interpose its voice against the relin-
quishing of that undertaking. A deputation of the Council waited
on His Excellency the Lord Lieutenant with a memorial, in which
the more evident reasons in favour of the continuation of this truly
national work were embodied. His Excellency received the depu-
tation with his usual courtesy, and was pleased to express his sym-
pathy with its objects. He undertook to forward the memorial to
the heads of the Government in London, and the Council is not
without: sanguine hopes that the Memoir of the Ordnance Survey
may be finally continued on its original extended scale.

“In obtaining this result, the Council believe that the voice of
the Royal Irish Academy will have afforded some assistance.

“Since the date of the last Report, the Library of the Academy
has been increased by numerous donations of books, for which

359

thanks have been voted to the donors, at the meetings of the Aca-
demy. The Academy continues in communication with the prin-
cipal scientific bodies of Europe and America, with which an inter-
change of Transactions and other publications is kept up.

“‘ During the past year the accession of new members to the
Academy has been such as to show, that notwithstanding the usually
abstract nature of its proceedings, its importance is fully recog-
nized. As honorary members, two have been elected on the recom-
mendation of the Council: the one a philosopher of European
eminence, Professor Wheatstone; the other, an Irish woman, whose
name adorns the roll of the Academy, as her works have long shed
lustre on the literature of her country, Miss Edgeworth. The names
of the gentlemen who have been elected ordinary members of the
Academy are :

Rev. Richard Butler. W. V. Drury, M.D.

Dr. Robert Law. W. R. Gore, M. D.

John Toleken, Esq., F.T.C.D. J. E. Hodder, Esq., R. N.
William Blacker, Esq. Rev. John Homan.

Rev. James Booth. H. Hutton, Esq.

Arthur Cane, Esq. R. Leslie Ogilby, Esq.

B. J. Chapman, Esq. Hon. Frederick Ponsonby.
F. M. Jennings, Esq. George Salmon, Esq., F.T.C.D.
Sir Thomas Staples, Bart. Robert Culley, Esq.
Stewart Blacker, Esq. James Magee, Esq.
Thomas Cather, Esq. H. L. Renny, Esq.

““ In a body so numerous as ours, it could not be expected that
a year should pass away without the loss of some from amongst our
ranks. Unhappily within the last twelve months we have had oc-
casion to deplore the deaths of several valued members.
“ From the list‘of honorary members three have been removed,
Sir James Ivory, Mr. Allan Cunningham, and Professor Heeren.
Of our ordinary members we have lost the Hon. J udge Foster, the
Right Rev. Charles Dickenson, late Lord Bishop of Meath, Dr.
Macartney, Mr. David Aher, and Mr. Bowles. It is fit to notice
briefly their career and their connexion with this Academy,
' “ Str James Ivory was a native of Dundee, and studied in the
University of St. Andrew’s, where he first distinguished himself in

360

those mathematical studies on which the elements of his subsequent
distinction rested. Although intended for the Church, circum-
stances threw him into the totally different career of managing an
extensive flax and spinning concern. But even the engrossing na-
ture of commercial industry could not wean him from scientific
pursuits, and on the dissolution of the company he devoted himself
exclusively to mathematical investigation. He passed to London,
and was appointed Professor in the Military College of Sandhurst,
which he retained until ill health, occasioned by his untiring re-
searches, obliged him to resign. His merits were so well recog-
nized that he received the retiring pension, although he had not
served the time required by the War Office. Subsequently a royal
pension was conferred upon him, and at the same time he received
the honour of Knighthood of the Guelphic Order of Hanover.

‘« Sir James Ivory was elected by this Academy an honorary
member on the score of his eminent mathematical discoveries.
These it is unnecessary to detail. They embraced the solution, in
abstract mathematics and in physical astronomy, of problems of
the greatest difficulty and importance; and the Royal Society of
London sufficiently indicated their opinion of his merits by award-
ing to him at different periods the Royal and the Copley medals.

«Mr. Allan Cunningham, although occupying a totally different
field of intellectual exertion from that trod by Ivory, and cultivating
rather the faculties of imagination and invention than those of
logical thought, is also an example of learning, pursued as an en-
joyment in the first instance to relieve the weary practice of a
mechanical trade, and finally adopted as a profession. Born in
Scotland, he was early apprenticed to a stone-mason, for whom he
worked many years. His mind, imbued with the traditions and
tales of the Border district in which he resided, soon applied its
vigorous though somewhat rugged poetic faculties to their arrange-
ment; and although it is said that many of the traditions he has
rendered popular, had their first origin in his own fertile brain, yet
there is no doubt but that his verses have preserved a great body of
popular Scottish story, that otherwise might have been lost. Would
that the abundant sources of poetical composition which the earlier
chronicles of this country present were similarly utilized. The

361

varied results of Mr. Cunningham’s literary life need not here be
detailed. He subsequently became connected with Sir Francis
Chantrey, in whose workroom he acted as manager and superinten-
dant. Called thus to intimate association with the most elevated in
art, all his subsequent literary works had for object, more or less,
its illustration, and his final labour, concluded but a few days be-
fore his death, was the life of his countryman and friend, Sir David
Wilkie. Mr. Cunningham was elected an honorary member of this
Academy on the score of his various literary merits.

“‘The death of Professor Heeren of Gottingen is felt through
Europe as the removal of one of the brightest luminaries of classical
literature. A reputation, already brilliant, bequeathed to him by
his father, received additional lustre from his elaborate investiga-
tions into the commerce and social condition of the nations of an-
tiquity. He was appointed first Professor of Philosophy, and after-
wards of History, in the University of Gottingen; and his decease
in the past year has added another to the crowd of illustrious dead,
by whose memory that seat of learning is rendered sacred.”

** Our recollection of those members whom we have lost from
the ordinary roll of the Academy during the past year is yet so fresh,
the time that has elapsed since they assisted at our meetings is so
short, that the notice, necessarily so brief, that can be here made of
their career must be imperfect, and may appear unjust. In the in-
stances, however, of two eminent members, whose recent loss we
all deplore, the Right Rev. the Lord Bishop of Meath, and the Hon.
Justice Foster, it may be said, thatalthough numbering them among
its members, this Academy was not the scene of their labours or
their glory; devoted to the pursuit of most important and engross-
ing professions, in which by their varied talents they attained the
highest dignities, time was not available for the prosecution of any
of those objects which this Academy has more especially in view.
Neither contributed to our Transactions, but the purposes of this
Institution, and its progress, were always subjects of their warm
approbation and support.

*“« Mr. Bowles, a young member of the Academy, must be deeply
regretted, as from his extensive knowledge of languages, and the
enlightened assiduity with which he was, up to the period of his

362

death, engaged in acquiring statistical information, much was to be
expected.

‘In Mr. David Aher the country has lost one well conversant,
as a civil engineer, with its physical circumstances, and anxious and
effectual in promoting industry. He was principally engaged in the
working of the coal district of Kilkenny and the Queen’s County, but
was concerned in many other engineering operations in that neighbour-
hood. He supplied a great deal of valuable information embodied
in the Reports onthe Irish Bogs, drawn up by order of Government ;
and recently, I believe his last work, at the time when the plans for
railway intercourse through Ireland were much discussed, he sur-
veyed and proposed a line extending from Dublin to Kilkenny.
Owing to the purely practical nature of Mr. Aher’s labours, he did
not contribute any memoirs to our Transactions, but his career was
not on that account the less valuable. This Academy, necessarily
limited in its scope to the more general and abstract contemplation
of scientific questions, is still most fully cognizant of the merit,
and anxious to express its admiration of those men, who practically
developing the sources of useful employment and industrial wealth
which our country holds, may become important agents in increasing
the comfort and happiness of our people.

«« Dr. James Macartney was born in March, 1770, in Armagh,
where his family had long been resident. He was educated in the
country, where he received the rudiments of an ordinary education,
but was not at college, nor was he intended for a profession.
Forced, however, in 1790, by the death of his father, to decide upon
his future course of life, he chose the profession of surgery, ‘ not,’
as he used to say, ‘ because he had any peculiar aptitude for the
business, but that he thought it would harden his feelings, which
he had found on many occasions painfully acute.’ In 1794 he was
apprenticed to Dr. Hartigan, who was at that time Professor of
Anatomy to the Royal College of Surgeons in Ireland. Passing to
London for the completion of his professional studies, he was ap-
pointed, in 1798, Demonstrator of Anatomy at Bartholomew’s Hos-
pital; and in 1800, having become a member of the Royal College of
Surgeons in London, he began to lecture on Comparative Anatomy
and Physiology, which he continued up to 1810. During the greater

part of this time he was Surgeon to the Radnorshire Militia, which
office, however, was not allowed to interfere with his scientific or
professional pursuits. In 1811 he accompanied that Regiment to
Ireland, and in 1813, the Professorship of Anatomy and Surgery in
Trinity College having become vacant by the death of Dr. Hartigan,
he presented himself as a candidate, and was elected.

“Por twenty-four years Dr. Macartney discharged the duties of
that important office with unexampled zeal and industry, and used
his utmost exertions to improve medical education. He endea-
voured to establish a course of lectures on Comparative Anatomy,
but circumstances prevented his plan being at the time carried out.
He was, however, successful in arranging a separate course on Pa-
thology, and in conjunction with Dr. Jacob, then his Demonstrator,
he instituted a dispensary for the special treatment of diseases of
the eye andear. As a lecturer, his manner, though unadorned by
the arts of verbal eloquence, became highly popular from the sound
ideas which he imparted, and the distinct and logical language in
which they were clothed. His classes were always very large, and
by his means the reputation of the Medical School of the University
of Dublin was materially elevated.

“« He resigned his Professorship in 1837, but still continued his
application to scientific pursuits. On the 5th of the present month
(March) he was seized with apoplexy, and died on the following
morning.

“‘ Tn a literary point of view, Dr. Macartney’s contributions to
medical and zoological science were numerous and important. In
1803 he commenced writing for Rees’ Cyclopedia, to which he
supplied the articles—‘ Comparative Anatomy. Vegetable Ana-
tomy. Bezoar. Anatomy of Birds. Classification of Animals.
Anatomy of the Egg. Anatomy of Fishes. Incubation. Ana-
tomy of Mammalia.’ In the Philosophical Transactions he pub-
lished a memoir on Luminous Animals, and contributed many minor
papers to the British Association, and to the Academie de Medicine
of Paris. His large work on Inflammation, containing his chief
discoveries in physiology and surgery, was published in Dublin
in 1838; and in the Transactions of this Academy there are by him
two valuable memoirs, the first in vol. xiii., on Curvature of the

VOL. I. 2H

364

Spine, and the second, on the Anatomy of the Brain of the Chim-
panzee, inserted in the second part of the nineteenth volume, which
has been this evening laid before the Academy, but of which, un-
fortunately, he did not live to witness the formal publication.

“« Dr. Macartney was a Fellow of the Royal Society, and of the
Linnean Society of London, and an Honorary Fellow of the King
and Queen’s College of Physicians in Ireland. He was also a Fo-
reign Associate of the Academy of Medicine of Paris, and member
of many of the most eminent scientific societies of the Continent of
Europe and of America.

“The Reverend James Horner, D. D., engaged in the constant
practice of the sacred duties of his profession, did not take any part
in the proceedings of the Academy, but will be long remembered by
many amongst us for the interest he always manifested m our suc-
cess, the amenity of his manner, and the benevolence of his heart.

‘“‘ The engrossing occupations of an active political life had also
so completely removed the Right Hon. Sir John Newport, Bart.
from the pursuits to which this Academy is devoted, that it is only
necessary formally to record his loss, and that he ,had not contri-
buted to our proceedings.”

The Treasurer presented the following Abstract of his
Account with the Academy for the year ending this 16th of
March, 1843:

“tadnspaly, “NOG “IKTd SAWVE

‘naubeg

#9 LL LO6F

=

* 2 + Squerre Ay Samsvory,

~
ea

* ‘sfosuog quod od g ‘og ss

fal
co
fel

ca ‘yo0}g ‘queo aed $e uo spueprarg ‘‘
‘+ + + Saga auo Loz o[qeIg Jo yuoy

8
I
Ge siD
0 0
7

‘yunoooy jo sourjeg “0D 3 au0og aed ‘yseQ “*
. . ac ter eae . . ‘s00,7 eoueryUn

~~
pa

‘suoI}Isodmog ajirT

oo 2

16° TT @ ‘spuvy Sdeinsvety, ul ‘oq =“
OL IL 88¢ 2 ‘puvjory Jo yueg ur couereq ‘*
Il €L 989 * + + pred sotapung <q
We

* + = syorydrzosqng jenuuy “‘

Lali

Bet or

* * + *p9ATed0 Solapuns Ioz yseg ‘*
‘yore WOT “ipne aod se ‘oouryeq oj,

“a

"sh8t ‘HOUVIN HIOT

‘KWAGCVOW HSIN] TVAOY 9y7 YpM JUNODIP Ur ‘waunsnas Ty, “NOP ‘Wig SUNVE

366

The auditors appointed by Council to examine the Trea-
surer’s accounts reported as follows :

“¢ We have examined the original Account,* with the vouchers
produced, and found it to be correct; and we find that there is a
balance in bank of £288 11s. 10d., and in the Treasurer’s hands,
£2 11s. 94d., making a total balance of £291 3s. 73d.

“ (Signed,)
“FRANC SADLEIR.
“ SamugeL Lirron.”
“¢ March 16, 1843.”

‘¢ The treasurer reports that there is £1085 17s. 1d. in 3 per
Cent. Consols, and £1665 4s. 2d. in 35 per Cent. Government
Stock, to the credit of the Academy in the Bank of Ireland; the
latter known as the Cunningham Fund. He also reports, that
eleven members owe their annual subscriptions, due 16th March
last, and that two members are owing their two years’ subscriptions
to the same date. There are no other arrears due. He has also to
report, that the Annual Parliamentary Grant for the current year,
amount £300, has not yet been placed to the credit of the Academy
_ inthe Bank of Ireland, but that there is no reason to doubt that it
will be done within a few days.

“< (Signed,)
“ James Pim, Jun.,
‘© Treasurer.”

The ballot for the Annual Election having closed, the
President requested the Rey. Charles Strong and Mr. Call-
well to assist the officers in examining the balloting lists.

The Scrutineers reported that the following gentlemen
were duly elected Officers and Council for the ensuing year:

President—Sir William Rowan Hamilton, LL.D.

Treasurer—James Pim, Jun., Esq.

Secretary to the Academy—J. Mac Cullagh, Esq. LL.D.

Secretary to the Counctl—Robert Kane, M. D.

* Entered in Treasurer’s book.

367

Secretary of Foreign Correspondence—Rev. Humphrey
Lloyd, D.D.

Librarian—Rev. William H. Drummond, D.D.

Clerk and Assistant Librarian—Edward Clibborn.

Committee of Science.

Rev. Frane Sadleir, D.D., Provost of Trinity College ;
Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D. ; James
Mac Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.;
Robert Ball, Esq.; Robert Kane, M.D.

Committee of Polite Literature.

His Grace the Archbishop of Dublin ; Rev. Joseph Hen-
derson Singer, D.D.; Samuel Litton, M.D.; Rev. William
Hamilton Drummond, D.D.; Rev. Charles Richard Elring-
ton, D.D.; Rev. Charles William Wall, D.D.; John Anster,
LL.D.

Committee of Antiquities.

George Petrie, Esq., R.H.A.; Rev. J.H. Todd, D.D.;
Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq. ;
Joseph Huband Smith, Esq.; James Pim, Jun. Esq.; Cap-
tain Larcom, R.E.

The President then appointed, under his hand and seal,
the following Vice-Presidents :

Rev. Humphrey Lloyd, D.D.; Rev. James Henthorn
Todd, D.D.; Rev. Joseph Henderson Singer, D.D.; James
Apjohn, M. D.

368

April 10.
RICHARD GRIFFITH, Ese., in the Chair.
George James Allman, Esq., Henry Lindsay, Esq., John
M‘Mullen, Esq., Hon. and Very Rev. Henry Packenham,

Dean of St. Patrick’s, Goddard Richards, Esq., and-John
Wynne, Esq., were elected Members of the Academy.

Dr. Todd, V.P., read a translation of an Ivish deed or
agreement made in the year 1526, between Conla Mac Geo-
ghegan, chief of the Kinel Fiacha, and Breasal Sionnach,
alias Fox, chief of the Clan Tadgan,—both of Westmeath.

The agreement was, that Mac Geoghegan should be
lord over Fox and his country under certain conditions,
which are specified, and of which the principal is, that Mac
Geoghegan is to do his best for the protection and defence
of Fox and his country. The deed adds, “‘ if Mac Geoghegan
should on any occasion fail to do his best for the protection
and sustainment of the Fox in his lordship, that he would
do for himself; that he no longer have rent, nor privilege,
nor lordship over him, but every one be for himself.”

One passage proves that the custom of holding the half
yearly assemblage (opeaczap) on the Ist of November and
the Ist of May was then kept up. ‘‘ Every general assembly
of Samhan [All Saints’ day] or of Bealtine [May day] that
shall be in Mac Geoghegan’s country, shall be held at
Baileath-an- Urchair, or at Corr-na-Sgean, and the Fox and
the nobles of his country shall attend.”

It is known from other sources that the Brehon laws, and
the authority of the hereditary Brehons, were kept up in
many parts of Ireland to a much later period: the following
passage therefore, which contains an allusion to the Brehon,
is not surprizing. ‘ And whenever either an Englishman
or an Irishman sues the Fox or any one of his country, they

369

shall submit to pay whatever is decided upon by Mortogh
Mac Egan, or whoever may be the Brehon at the time, &c.”

The original of this deed, which is in Irish, is in the pos-
session of Sir Richard Nagle, the lineal representative of
Mac Geoghegan, who has kindly permitted a copy of it to
be taken and deposited in the Library of the Academy.

The great body of the document is uninjured and legible;
the only imperfection which occurs is in the following pas-
sage at the end, which contains the signatures and date of
the agreement.

‘“* These are they of the Foxes’ country who are present
with us, viz. the Fox himself, and the two sons of Edmund,
viz. Murtogh and Phelim; and the two sons of Brian Fox,
viz. Breasal and Cucogry ; and Murtogh, son of Owen, son
Oteriash ss i.e. the Ollamh (poet or historian) of Fox... .
and myself James O’Cionga [or king] the son of Carbry
O’Cionga, who was present at the making of this agreement,
and who wrote it. And it was on the Fast [i. e. the Eve] of
St. Adamnan this agreement was made; and particularly on
Wednesday; and it was on a Friday it was written. And
this is the year of the Lord at this time, viz. six years, and
twenty, five hundred and one thousand years [1526], and
the 22nd day of the month of August.

* 54 Tam the Mac Geoghegan. »« Iam the Fox.” [Here
follows a line in the characters of the consonant Ogham, but
so much effaced that although the key is known, it has been
found impossible to decipher it. The last word only is le-
gible, which is Graine, or Grace, a woman’s name: then
follows] ‘are in Ireland. » We are the sons of Edmund
Fox. »& We are the sons of Brian Fox.”

Mr. Mallet gave a notice of recent improvements in the
formation of Mosaic pavements.

379

April 24.
SIR WILLIAM BETHAM, in the Chair.

The Chairman informed the Academy, that Sir Richard
O’ Donnell had consented to deposit the Cathach, containing
a MS. of the Psalms in Latin, by St. Colombkill, in the Mu-
seum of the Royal Irish Academy.

ReEsotvep,—That the marked thanks of the Academy be
returned to Sir Richard O'Donnell for his kindness.

Read, a letter from the Rev. T. R. Robinson, accom-
panying a box containing an original Pyrometer of Wedge-
wood, presented to the Academy by Miss Edgeworth,
(H. M.R.I. A.)

“* Dear Mac Cutaen,

“Our friend, Miss Edgeworth, has requested me
to present from her to the Academy a Wedgewood’s Pyro-
meter, which, as unfortunately I cannot attend this evening,
I commit to your care. This instrument is remarkable, as
being the first attempt to place within reach of the manu-
facturer and the chemist an easy method of measuring, at
least approximatively, the temperature of their furnaces. It
consists, as is well known, of a pair of converging bars, which
measure, by a graduation on them, the contraction of clay
cylinders that have been heated; this remains permanent,
and were it, as Mr. Wedgewood supposed, a function of
temperature alone, would suffice for all practical purposes.
Many circumstances, however, have interfered with its gene-
ral employment. The set of clay pieces which were used in
the first instance were made of natural clay found in Corn-
wall. By these the numbers given in treatises of chemistry
for the fusing points of the more refractory metals were de-
termined, and I think it probable that Mr. Kirwan used them
in his researches; Sir James Hall, I think, did not. Mr.

371

Wedgewood had stated in his memoir that the supply of the
clay was inexhaustible; but when the stock first made was
disposed of, he was unable to find the identical spot where
it had been obtained, and the contraction of the new speci-
men was different. Had he used it as he did the other, and
merely directed the employment of a number by which to
multiply the indications of the scale, no inconvenience would
have resulted ; but he thought he might bring it to an iden-
tity by adding ‘earth of alum,’ obtained by precipitating
alum by carbonate of potassa; a product which Apjohn or
Kane will tell you is very far indeed from being pure alumina.
This unhappily made the contraction irregular, and the clay
pieces much less capable of resisting a high heat. Its indi-
cations were found to differ from those of the first set, and
it fell into disuse, especially for two reasons. The first that
Wedgewood had assigned to his degrees, a value enormously
too large, so that he supposed the extreme heat of a furnace
to be about 30000 of Fahrenheit, when it is only 4000.
Many years since, in our Transactions, I had pointed out
this error, and corrected it, with tolerable success, as was
long afterwards confirmed by Daniell and Prinsep. The se-
cond, that a long exposure to a low heat produces the same
contraction as a short exposure to a high. This is said by
Sir James Hall to have been established by Dr. Kennedy,
whose experiments, however, are no where published; and
I confess that I doubt the fact. Guyton De Morveau has
even made an observation which may account for the mistake.
He found that similar pieces exposed for half an hour in a
powerful furnace, one surrounded by siliceous sand, the
other by powdered charcoal, marked 90 and 60, in conse-
quence of the different conducting powers of these media.
Now it is possible that the Scotch philosopher may have
overlooked this influence, and not allowed time enough for
the higher temperature to be fully transmitted. The py-
rometers of Daniell and others which have since been con-
VOL, II. I

372

trived, are so much more cumbrous and elaborate than this,
that I hope it may yet be revived; and if so, the chemists,
who may construct pieces for themselves, would find it useful
to compare them with Wedgewood’s old standard. A single
cylinder is sufficient for this, as after measuring a compara-
tively low temperature, it will still contract when submitted
toahigher. This I know to have been one of the original
and genuine set presented to the late Mr. Edgeworth by its
inventor, and therefore, independent of its probable utility,
precious asa relic of two such men, and still more so as the
gift of our illustrious countrywoman to a body, of whose
scientific triumphs she is proud, and in whose welfare I know
her to be deeply interested.
« T. R. Rosinson.
* April 24, 1843.”

ResotveD,—That the letter be referred to Council, for
special notice and attention.

H. Smith, Esq. exhibited an ancient dress, found in a
bog at a considerable depth, near the Abbey of Kilkenny.

A number of interesting antiquities, found at Ballyrowan,
in the Queen’s County, by Mr. Harrison, were presented by
the Rev. B. I. Clarke, to the Academy.

The thanks of the Academy were presented to Mr. Clarke
for his donation.

Sir Wm. Betham made a communication on the antiquity
of certain languages.

DONATIONS.

Astronomical Observations made with Ramsden's Zenith
Sector, and Catalogue of the Stars which have been observed
at the different stations of the Ordnance Survey in England

373

and Scotland. London, 1842. Presented by the Master
General of the Hon. Board of Ordnance.

Ordnance Survey of the County of Clare, in seventy-seven
sheets, including the Title and Index. Presented by His Ex-
cellency the Lord Lieutenant.

Battle of Magh Rath. Presented by the Irish Archeolo-
gical Society.

Memoires de la Société de Physique et d'Histoire Natu-
relle de Genéve. Ninth volume. 1841, 1842, Presented by
the Society.

On the Public Institutions for the Advancement of Agri-
cultural Science which exist in other Countries. By Charles
Daubeny, M.D. Presented by the Author.

Transactions of the Cambridge Philosophical Society.
Vol. VII. Part 3. Presented by the Society.

Proceedings of the Academie Royale de Bruxelles. Nos.
1 to 9 inclusive. Vol. IX.

Comptes Rendus des Seances de l’Acudemie des Sciences.
Nos. 1 to 7 inclusive, from 2 Janvier to 13 Fevrier, 1843.
Presented by the Academy.

Annales del Observatoire Royale de Bruxelles. 'Tome I.
Presented by M. Quetelet.

Archives du Museum d’ Histoire Naturelle de Paris. Livy-
raison 3. Presented by the Museum.

ane, Mules

yr A

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1843. No. 40.

May 8.
SIR Ws. R. HAMILTON, LL.D., President, in the Chair.

I. G. Abeltshauser, Esq. was elected a member of the
Academy.

The special thanks of the Academy were voted to Miss
Edgeworth for her donation of Wedgewood’s Pyrometer.

Professor Mac Cullagh read the following communication.

On the Laws of Metallic Reflexion, and on the Mode of making
Experiments upon Elliptic Polarization.

Several years ago, as the Academy are aware, I made an
attempt to investigate the laws according to which light is
reflected at the surfaces of metals, and I then proposed cer-
tain formulee which represented, with sufficient accuracy, all
the facts and experiments which I was able to collect upon
the subject (see the Proceedings of the Academy, vol. i. p. 2,
October, 1836; Transactions, vol. xviii. p. 71, note). But
in order to test these formule satisfactorily, it was neces-
sary to obtain measurements far more exact than any that
had previously been made; and for this end I devised an
instrument, which was constructed for me by Mr. Grubb,
and of which a brief description has been given in the Pro-
ceedings, vol. i. p. 159. I regret to say, however, that no-

VOL. II. 2K

376

thing of much consequence has yet been done with the
instrument. Some preliminary trials of its performance were
indeed made in the summer of 1837, and the results of one
of these shall presently be given; but an accidental strain
which it suffered, while I was preparing to undertake a series
of experiments, caused me to discontinue the observations
at the time; and being then obliged to superintend the
printing of my essay on the Laws of Crystalline Reflexion
and Refraction (Transactions R. I. A., vol. xviii. p. 31),
my attention was drawn afresh to this latter subject, respect-
ing which some new questions suggested themselves, which
I thought it right to discuss in notes appended to the essay.
I was not afterwards at leisure to take up the experimental
inquiry, until the beginning of the year 1839, when I began
to think of putting the instrument in order for that purpose.
The strain which it had suffered rendered some slight alte-
rations necessary ; and I now resolved to make additions to
it also, with the view of operating upon the fixed lines of the
spectrum, as a few trials had convinced me that measures
sufficiently precise could not be obtained without employing
light of definite refrangibility. I wished, moreover, to take
the opportunity which the nature of the proposed experi-
ments presented, of verifying the theory of Fresnel’s rhomb,
or rather of verifying, by means of the rhomb, the formule.
which Fresnel has given for computing the effects of total
reflexion, when it takes place at the common surface of
two ordinary media. I wrote therefore to Munich for se-
veral articles which I wanted; among others, for a set of
rhombs cut at different angles, out of different kinds of
glass. But while I was waiting for these some months
elapsed, and in the meantime I got sight of a new theory,
which, from its connexion with my former researches, pos-:
sessed more immediate interest, and the pursuit of which,
in conjunction with other studies and various engagements,
caused me again to suspend the inquiry respecting the laws
of metallic reflexion. . I allude to the Dynamical Theory

377

of Crystalline Reflexion and Refraction, communicated to
the Academy in December, 1839 (Proceedings, vol. i. p. 374).
This was followed soon after by a general Theory of Total
Reflexion (Proceedings, vol. ii. p. 96), founded on the same
principles. The latter theory, forming a new department
of physical optics, and involving the solution of questions
not previously attempted, was analytically complete when it
was communicated to the Academy in May, 1841; but its
geometrical development has since required my attention
from time to time, and has not yet been brought to that de-
gree of simplicity of which it appears to be susceptible
(see Proceedings, vol. ii. p. 174). Indeed I have found that,
in this instance, the geometrical laws of the phenomena are
by no means obvious interpretations of the equations re-
sulting from the analytical solution of the problem; and in
endeavouring to verify such supposed laws I have often been
led to algebraical calculations of so complicated a nature that
it has been impracticable to bring them to any conclusion,
and I have been obliged, from mere weariness, to abandon
them altogether. On returning, however, to the investigation,
after perhaps a long interval of time, I have usually per-
ceived some mode of eluding the calculations, or of directly
deducing the geometrical law; and when the theory comes
to be published in its final form, no trace of these difficulties
will probably appear.

From the causes above-mentioned, combined with fre-
quent absence from Dublin, the researches which I had
entered upon, respecting the action of metals upon light,
have been hitherto interrupted; and as it may still be some
time before they are resumed, I venture, in the meanwhile,
‘to submit to the Academy the results already spoken of,
which were obtained on the first trial of the instrument, and
which afford the best data th can yet be had for compari-
son with theory.

The results, it must be confessed, are those of very

2K2

378

rough experiments, made one evening (about the month
of July, 1837) in company with Mr. Grubb, before I had
received the instrument from his hands, and merely with
the view of showing him, when it was finished, the kind of
phenomena that I proposed to observe with it, and the mode
of observing them. But the instrument was so far superior
(in workmanship at least) to any apparatus previously em-
ployed for this sort of experiments, that it was impossible,
without great negligence in using it, not to obtain measures
of considerable accuracy. I did not, however, at the time,
set much value on these measures, because I expected shortly
to possess a series of observations made with every possible
precaution; but having chanced to preserve the paper on
which they were noted down, I was tempted, a few days ago,
to try how far they agreed with my formule; and the agree-
ment turns out to be so close, that [ think myself justified im
publishing them. Besides, it will be curious hereafter to
compare them with more careful measurements.

Before we proceed, however, to the details of the experi-
ments, it may be well to give the formule ina state fitted for
immediate application. The light incident on the metal
being polarized in a certain plane, let a denote the azimuth
of this plane, or the angle which it makes with the plane of
incidence; and as the reflected light will be elliptically pola-
rized, or,in other words, will perform its vibrations in ellipses
all similar and equal to each other, as wellas similarly placed,
put 8 for the angle which either axis of any one of these
ellipses makes with the plane of incidence, and let 6 be another
angle, such that its tangent may represent the ratio of one
axis of the ellipse to the other. Then when the optical con-
stants m and y (of which I suppose the first to be a number
greater than unity, and the second an angle less than 90°)
are known for the particular metal, the angles @ and 8 may
be computed for any value of a, at any given angle of inci-
dence, by the following formule :

379
(v’— v) sin 2a
2f+(v'+v) cos 2a’
2g sin 2a

v+v+ 2fcos Du?
in which f and g are constant quantities given by the expres-

sions 1 ( -) ‘
= |mM—— =(|m + —]}sin B
ne ( -) cosx, § + = )sinxs (8)
and pv, v’ are quantities depending on the angle of incidence
2, in the following way.. Let #’ be an angle such that

fan Lf pease
(a)

sin 26 =

sin 2 M

Sat) er ae ee (c)
sinz cosy
and put
cosz
= D
eos Ms ( )
then will 1 ; 2 Lg?
vy=-——4B, y af Be (z)
mn v

The angles 0 and 6 are given by immediate observation with
the instrument; and from their values at any incidence, and
for any azimuth a of the plane of primitive polarization, we
can find the constants m and x, which we may afterwards
use to calculate the values of @ and 3 for all other incidences
and azimuths, in order to compare them with the observed
values. It is indifferent, in the formule, whether 0 be re-
ferred to the major or the minor axis of the elliptic vibration,
as also whether tan G3 be the ratio of the minor to the major
axis, or the reciprocal of that ratio; but in what follows
we shall suppose 6 to be the inclination of the plane of inci-
dence to that axis, which, when a is 45° or less, is always
the major axis; and # shall be supposed less than 45°, in
order that its tangent may represent the ratio of the minor
axis to the major.

When the azimuth a is equal to 45°, the formula (a) become

v’—v : 2g
tan 20 = FF? sin23 = pe (F)
from which we may deduce the remarkable relation
tan23— g

cos 20 f” (¢)

380

showing that, in the case supposed, the ratio of tan26 to
cos 26 is independent of the angle of incidence. In the ex-
periments which I made with Mr. Grubb this azimuth was
always 45°; and the following Table contains the results
of observation compared with those obtained by calculation
from formule (F). The experiments were made upon a
small disk of speculum metal; and in the calculations I have
taken M = 2.94, y = 64° 25’.

Value of 0. Value of B.

Angle of
Incidence. Observed. Caiculated. Observed. Calculated.

65° 55’ QI s) Se 1G) 23°" 0"
70 41 15 44 33 7 33
75 45 | —9 16 34 10 34 6
80 15 | —29 25 At 0 26 53
84 22 —37 25 16 47 1a) 7)

The light used in these observations was that of a candle
placed at a short distance, and was admitted through small
apertures at the ends of the tubes. (See the description of
the instrument in the Proceedings, vol. i. p. 159). The Nicol’s
prism inthe first tube having been secured in a position in which
its principal plane was inclined 45° to the plane of incidence,
and the two arms having been set at the proper angle with
the surface of the metal, the Fresnel’s rhomb and the Nicol’s
prism in the second tube were moved simultaneously, until
the image of the candle became as faint as possible. Had
light perfectly homogeneous been employed, the image could
have been made to vanish altogether; but instead of vanish-
ing, it became highly coloured, and our rule in observing was
to make the blue at one side of it, and the red at the other,
equally vivid, so as to get results which should belong, as
nearly as possible, to the mean ray of the spectrum. When
this was done, the angles 9 and (3 (subject however to certain
corrections which will be hereafter explained) were respec-
tively read off from the divided circles belonging to the
rhomb and the prism. The observations were made at large

381

incidences, because it is within the last thirty degrees of
incidence that the phenomena go through their most rapid
changes.

If we now cast our eyes on the above table, making due
allowance for the uncertainty arising from the dispersion of
the metal, we shall be struck with the agreement between
the calculated and observed numbers. The differences are
greatest in the last two observations, which however were
really the first; for the observations were made in the in-
verse order of the incidences, and their accuracy may have
improved as they went on. However that may be, the dif-
ferences are quite within the limits of the errors of observa-
tion; and they are actually less than those which Fresnel
found to exist between calculation and experiment in the
much simpler case of reflexion at the surface of a transparent
ordinary medium, when he proceeded to verify the formula
which he had discovered for computing the effect of such
reflexion.—See the Table which he has given in the Annales
de Chimie, tom. xvii. p. 314. |

It may seem extraordinary that these experiments should
have been in my possession for nearly six years, before I be-
came aware of their close agreement with my formule; but
the fact is, that I did not regard them with much interest,
‘because, from the circumstances in which they were made, I
did not expect more than a general accordance with theory.
‘And even now, I am in no haste to infer the absolute exac-
titude of the formule, though they are found to represent
the phenomena so well. It was far more allowable to infer
that the formula of Fresnel was exact in the case just men-
tioned, though it appeared to represent the phenomena less
perfectly. For, to say nothing of the small number of our ex-
periments, the present is a much more complicated case, and
the phenomena depend on two constants instead of one, so that
the formule might be slightly altered, and yet perhaps con-
tinue to agree very well with rough experiments. Where
there is only one constant this is not so probable. Again,

382

there is one of the quantities in the preceding formule which
may be greatly altered without producing more than a slight
effect on the values of 0 and 3. This quantity is the ratio
of sinz to sin#’, which, according to the value in formula (c),
is a number so large as to make the angle ¢’ always small, so
that its cosine never differs much from unity; and therefore
if the above ratio were taken equal to any other large num-
ber, the value of » in formula (p) would remain nearly the
same, and consequently the values of 0 and 6 would be but
slightly changed. -

It is with regard to the value of m as a function of the
incidence that I entertain the greatest doubts, and if any
defect shall be found in the formule I think it will be here.
The relations (c) and (p), from which » may be deduced in
terms of ¢, were not indeed adopted without strong reasons ;
but I am not entirely satisfied with them, because, when we
reverse the problem, and seek to determine the constants M
and x from the observed values of 9 and ( at a given inci-
dence, the results are rather. complicated and involved,
though the approximate determination is easy enough. As
the formule are in a great measure built upon conjecture,
we must not be disposed: to receive them without the
strongest experimental proofs; and it will certainly require
experiments of no ordinary accuracy to decide some of thé
questions which may be raised respecting them.

When plane-polarized light is incident on a metal, if its
vibrations be resolved in directions parallel and perpendicu-
lar to the plane of incidence, the effect of the reflexion is to
change unequally the phases of the resolved vibrations; and
it may be useful to have the formule which express the diffe-
rence of phase after reflexion, and the ratio of the amplitudes
of vibration. Put ¢ for the difference of phase; and sup-
posing, for simplicity, the incident light to be polarized in
an azimuth of 45°, let o be angle less than 45°, such that
tano may represent the ratio of the reflected amplitudes

383

respectively perpendicular and parallel to the plane of inci-
dence; then we shall have

2 DF.
— (9) —_ © .
tang =———, — cos2a = cat (H)
from which we may infer that
sing tan2o= Bs (1)

i

or that the product on the left side of the last equation is
independent of the angle of incidence. It is to be observed
that the relations (c) and (1) are independent of the value of
gu, and may hold good though that value should require to be
changed.

All the preceding formule are merely mathematical con-
sequences of those which I published long ago in the Tran-
sactions of the Academy (vol. xviii. p. 71). The formule
which I had previously given in the Proceedings (vol. i. p. 2)
are slightly different, and, I think, less likely to be exact,

because they are less simple, and do not lead to any of the
remarkable relations which may be deduced from the others.

Having had occasion, in the course of the few experi-
ments which I made with the instrument before mentioned,
to study the nature of Fresnel’s rhomb, which constitutes an
important part of it, I shall here describe the method which
must be followed in order to obtain true results, when the
rhomb is employed in observations on light elliptically pola-
rized. A ray in which. the vibrations are supposed to be
elliptical is given, and what we want is to determine the
ratio of the axes of the elliptic vibration, and their directions
with respect to a fixed plane passing through the ray; in
other words, to determine the angles which we have denoted
by B and @ in the case of a ray reflected from a metal. For
this purpose the ray is admitted perpendicularly to the sur-
face at one end of the rhomb, and after having suffered two
total reflexions within, passes out perpendicularly to the sur-

384

face at the other end. Then causing the rhomb to revolve
about the ray, we shall find two positions of it in which the
emergent light will be plane-polarized, these positions being
readily indicated by a Nicol’s prism interposed between the
rhomb and the eye; for such a prism, by being turned round
the ray, can make the light totally disappear when it is
plane-polarized, but not otherwise. ‘These two positions of
the rhomb will be exactly 90° from each other; in one of
them the principal plane of the rhomb (the plane of reflexion
within it) will be parallel to the major axis of the elliptic vi-
bration, and the angle which it makes with the plane of in-
cidence on the metal will be equal to 6: while in the same
position the angle which the principal plane makes with the
plane of polarization of the emergent ray (as given by the
Nicol’s prism) will be equal to 3. In the other position, the
principal plane will be parallel to the minor axis of the
elliptic vibration, and the corresponding angles will be equal
to 90°—@ and 90°—{ respectively. This, however, proceeds
on the supposition that the rhomb is exact. When it is not
so, which is of course the proper supposition, and a very ne-
cessary one in the experiments with which we are concerned,
there will still be, generally speaking, two positions of it in
which the emergent ray will be plane-polarized, or in which
a disappearance of the light may be produced by the Nicol’s
prism; but these positions will no longer be 90° from each
other, nor will the principal plane, in either of them, coincide
with an axis of the elliptic vibration. If we now measure the
angles between the different planes as before, and denote
them by 6, 3’ in the first position, and by 90°—6”, 90°—3”
in the second, we shall find that 0’ and 0” are unequal, but
we shall have SB’ equal to 8”. The values of 0 and £ will
then be given by the formulz
/ Ws

fhe 2 Bi 5 cos 28 = cos (0’— 6"). (k)

The error of the rhomb may easily be found. Supposing

cos2(3’

385

the vibrations to be resolved in directions parallel and per-
pendicular to its principal plane, the rhomb is intended to
produce a difference of 90° between the phases of the re-
solved vibrations, or to alter by that amount the difference
of phase which may already exist; but the effect really pro-
duced is usually different from 90°, and this difference, which
I call ¢, is the error of the rhomb. The value of ¢ is given by
the formula
sin (0/ — 0”

tans = ie 3 (t)
and as the error of the rhomb is a constant quantity, we
have thus an equation of condition which must always sub-
sist between the angles 0’—6” and 3. For any given rhomb
the sine of the first of these angles is proportional to the
tangent of twice the second, and therefore 0’/—6" constantly
increases as (3 increases towards 45°, that is, as the axes of
the elliptic vibration approach to equality. When (3 is equal to
45°—4«, we have 0’— 6"=90°; and for values of (3 still nearer
to 45°, the value of sin (6/—6”) becomes greater than unity,
that is to say, it becomes impossible, by means of the rhomb,
to reduce the light to the state of plane-polarization.. This
is a case that may easily happen with an ordinary rhomb
in making experiments on the light reflected from metals;
because at a certain incidence, and for a certain azimuth of
the plane of primitive polarization, the reflected light will be
circularly polarized.

The rhomb which I used in the experiments tabulated
above, was made by Mr. Dollond, and was perhaps as accu-
rate as rhombs usually are; it was cut at an angle of 544°, as
prescribed by Fresnel. Its error was about 38°, and the value
of 0’—6”, at the incidence of 75°, was about 7°. But in
another rhomb, also procured from Mr. Dollond, and cut at
the same angle, the value of #’—6”, under the same circum-
stances, was about 20°, and the value of < was therefore

386

about 8°. ‘The angle given by Fresnel was calculated for
glass of which the refractive index is 1.51; and the errors
of the rhombs are to be attributed to differences in the re-
fractive powers of the glass. I was not at all prepared to
expect errors so large as these when I began to work with
the rhomb, and they perplexed me a good deal at first,
until I found the means of taking them into account, and of
making the rhomb itself serve to measure and to eliminate
them. The value of the rhomb as an instrument of research
is much increased by the circumstance that it can thus de-
termine its own effect, and that it is not at all necessary to
adapt its angle exactly to the refractive index of the glass.
It may also be remarked, that this circumstance affords a
method of directly and accurately testing the truth of the
formule which Fresnel has given for the case of total re-
flexion at the separating surface of two ordinary media; for we
have only to measure the angle of the rhomb and the refrac-
tive index of the glass, and to compute, by Fresnel’s for-
mula, the alteration which the rhomb ought to produce in
the difference between the phases of the resolved vibrations ;
which alteration of phase we may then compare with that
deduced, by means of the formule (x) and (x), from direct
experiment.

If, in each position of the rhomb, we measure the angle
which the plane of polarization of the emergent ray makes
‘with the plane of incidence on the metal, and call the two
angles respectively y’, y’, we shall have

7 — 7 — ey 7” = 9” ait (a (m)

and therefore
yty'= +0” = 20, 213! = y’—y' + 0'—0"; (x)
from which it appears that if the rhomb were perfectly exact,
that is, if & and 6” were equal to each other, the angle @
would be half the sum of y’, y”, and the angle £ half their
difference. It would then be sufficient to measure the angles
y' and y”, in order to get 0 and B accurately. And if the

387

rhomb were erroneous, the true value of 8 would still be
half the sum of y’, y”; but the true value of would not be
discoverable without measuring the angles 6’, 0", by the help
of which it can be deduced from the second of formule (n),
combined with the second of formule (x). Nor can we dis-
cover whether the rhomb is erroneous or not, without mea-
suring the angles 0’, 0”; and therefore as these angles must
be measured in any case, the former method of determining
0 and is to be preferred.

In making experiments on elliptically polarized light, a
plate of mica or any other doubly refracting crystal, placed
perpendicular to the ray, may be used instead of Fresnel’s
trhomb. If the thickness of the crystalline plate be such that
the interval between the two rays which emerge from it is
equal to the fourth part of the length of a wave, for light
of a given refrangibility, the plate will, for such light, per-
form all the functions of the rhomb; the principal plane of
the rhomb being represented by the plane of polarization of
one of the emergent rays. But unless the light be perfectly
homogeneous, this method is liable to great inaccuracy in
practice, since the effect of the plate in producing or altering
the difference of phase between the two rays which interfere
on their emergence from it, is inversely proportional to the
length of a wave, and will therefore be extremely different
for light of different colours, and will change very per-
ceptibly even within the limits of the same colour. Itis true,
the effect of the rhomb also varies with the colour of the
light: but this variation is trifling compared with that which
exists in the other case. It was for this reason that I em-
ployed the rhomb in my experiments, instead of a crystalline
plate. The apparatus, however, is much simplified by using
such a plate; and if any one chooses to do so, and to work
with homogeneous light, he must take care to follow, in every
respect, the directions which I have given for conducting
experiments with the rhomb. ‘The two cases are precisely

388

similar; and if if be necessary not to neglect the errors of
the rhomb, it is certainly not less necessary to take into ac-
count those which may arise from a want of accuracy in the
thickness of the plate, considering how difficult it is to make
the thickness correspond exactly to the particular ray which
we wish to observe.

I have been induced to enter into these particulars, re-
specting the mode of making experiments on elliptic polari-
zation, because the subject is one which has not hitherto
been studied; nor does it seem to have occurred to any one
that any precaution was requisite beyond that of getting the
rhomb cut as nearly as possible at the proper angle, or the
crystalline plate made as nearly as possible of the proper
thickness. This, indeed, was quite sufficient for ordinary
purposes. For example, light polarized in a plane inclined
45° to the principal plane of the rhomb or of the plate,
would, as far as the eye could judge, be circularly polarized
after passing through either of them. Notwithstanding a
certain error in the angle of the one, or in the thickness of
the other, such light would, when analysed by a rhomboid of
Iceland-spar, give two images always sensibly equal in inten-
sity. But an error which could not be at all detected in this
way, might produce a very great effect in such experiments
as those upon the metals, and, for the purpose of comparison
with theory, might render them entirely useless, if in the
first method of observing we relied upon one set of obser-
vations, taking (suppose) the values of 6’ and 3’ for the true
values of 0 and £3; or if, inthe second method, we contented
ourselves with merely measuring the angles y’ and y”. j

The necessity of attending to the foregoing rules and re=
marks will appear from an examination of the experiments
of M. de Senarmont, published in the Annales de Chimie,
tom. Ixxiii. pp. 351-358. In these very elaborate experi-
ments, which were made upon light reflected at various inci-
dences from steel and speculum metal, the author followed

389

a plan similar to that which I have adopted, and which, in a
general way, I had previously sketched in the Proceedings
of the Academy (vol. i. p. 159). There was this difference,
however, that he used a plate of mica instead of Fresnel’s
rhomb. Now as he worked with common white light, the
use of the mica plate must have rendered two kinds of errors
unavoidable. In the first place, it would be impossible
always to take the observations for the same ray of the
spectrum; and next, as a consequence of this, the thick-
ness of the plate would be generally inexact for the particu-
lar ray to which the observations happened to correspond.
If the thickness of the plate were exact for a certain ray, it
would be very sensibly inexact even for the neighbouring
parts of the spectrum; and as the part of the spectrum to
which the observations belonged was continually changing,
the results obtained for different incidences and azimuths
would not be comparable with each other, even though, in
each separate case, the error of the plate were allowed for
and eliminated. The values of 0, however, as determined
by M. de Senarmont, would be correct, so far as this error is
concerned ; those of (3 alone would be erroneous. For the
values of @ were determined in two ways: by measuring the
angles 6’, 0”, and taking their sum for 20; also by measur-
ing the angles y’, y", and taking their sum for the same quan-
tity. Now each of these methods gives a true value of 0,
because by the preceding formule we have 20 = # + 9” =
7’ + 7”; and this accounts for the agreement, shown by the
tables of M. de Senarmont, between the values* of 20 ob-
tained by these different methods. But the values of 3 were
deduced from the angles y’, y’, by simply making their dif-

* Or rather the values of 180° + 20; because the angle w, the double of which
appears in the tables of M. de Senarmont, is equal to 90°-++ 6. The angles which
he calls y, and y, are equal to 90°-++- y” and 90° + y’ respectively. It therefore
comes to the same thing, whether the one set of angles or the other is supposed
to be measured. The letter B has the same signification in both notations,

390

ference equal to 23; and we see by the second of formule (wn)
that, when the plate is not of the proper thickness, this value
of 2 is erroneous by the whole amount of the angle 6’ — 0”,
the difference between (3’ and (3 being supposed so small that
it may be neglected. As M.de Senarmont proceeded on the
common assumption that when the thickness of the plate-has
been adjusted to that part of the spectrum to which the ob-
servations are intended to refer, it may afterwards, through
the whole series of experiments, be regarded as exact, he
necessarily conceived 9’ and 6” to be the same angle; and it
was on the principle of taking an average between two mea-
sures of the same quantity, that he made the supposition
20 = 0’ + 6”, which happened to be correct. When there-
fore he found 6’ and 0” to be different, he of course looked
upon the difference as merely an error of observation, which
it would be superfluous to tabulate. Not having the values
of this difference, therefore, we have not the means of im-
mediately correcting the values of 23. But as observations
were made for several azimuths at each angle of incidence,
we may use the values of 0 to determine those of 3; for when
at any incidence (except that of maximum polarization, where
6=0 for all azimuths) the values of 6 are known for two given
values of a, we can deduce the corresponding values of B, with-
out any other theory than that of the composition of vibrations.
The values. of (3 so deduced must indeed be expected to be
very inaccurate, partly because of errors in the observed values
of 0, partly because the observations in different azimuths do
not answer to the same ray of the spectrum ; but they will
be accurate enough to show the great amount of the error
committed by neglecting the difference 6’ — 6”. For ex-
ample, putting 0) and (> for the values. of 0 and 6 when
a = 45°, M. de Senarmont gives, at the incidence of 60° upon.
steel, 20, = 64°15’ (taking the mean of his two determina-
tions), and for the azimuths 55°, 30°, 25°, he gives 20 equal to
88° 5’, 37° 2’, and “9° 36’ respectively. Combining these

391

values of 20 in succession with that of 20), we get for 2B,
the series of values 32° 38’, 33° 28’, 34° 30’; the differences
between which are to be attributed to the causes above
stated. The mean value of 23, thus found is 33° 32’; while
its value, as given by M. de Senarmont, is only 28° 41’,
The difference 4°51’ is the value of 6’ — 6”, which, divided
by the tangent of 23,, gives 7° 19’ for the mean value of ¢,
the error of the mica-plate corresponding to that part of the
spectrum which was observed at the incidence of 60°.

At incidences nearer the angle of maximum polarization,
the errors are probably much greater. Beyond that angle
they again diminish, and in some cases they almost vanish.
Thus, at the incidence of 85° upon steel, with the value
of 20) and the value of 20 corresponding to a = 20°, we get,
by computation, a value of 23) which differs only by a few
minutes from that given by M. de Senarmont. Nearly the
same thing happens at the same incidence when we take
a= 25°. In these cases therefore the results belong to that
particular ray for which the thickness of the plate was
exact.

The observations of M. de Senarmont on speculum metal
were not carried beyond the incidence of 60°. He states
that he was unable to observe at higher incidences, on ac-
count of the uncertainty arising from the dispersion of the
metal; but though this cause operated in some degree, his
embarrassment must have been really occasioned by the in-
creasing magnitude of the difference ’ — 0”, as he approached
the angle of maximum polarization; that difference being
perhaps twice as great as in the case of steel. My own ex-
periments on speculum metal were all made, as has been
seen, at incidences greater than 60°.

The experiments of M. de Senarmont do not at all agree
with the formule ; and therefore I have been obliged to ana-
lyse his method of observation, and to show that it could
not lead to correct results. It is to be regretted that his

VOL. Il. DY,

392

method was defective, as the zeal and assiduity which he
has displayed in the inquiry would otherwise have put us in
possession of a large collection of valuable data.

I shall conclude by saying a few words respecting the in-
tensity of the light reflected by metals. The formule for
computing this intensity have been given in the Transactions
of the Academy, in the place already referred to; but they
may be here stated in a form better suited for calculation.
If we suppose yb and yl’ to be two angles, such that

M
cotany = iP cotan i’ = mu, (0)
and then take two other angles w, w’, such that
cosw = sin 2) cosy, cosw’ = sin2y’ cosy, (P)

we shall have

7 = tani, 7’ = taniw’, (a)
where r is the amplitude of the reflected rectilinear vibration,
when the incident light is polarized in the plane of incidence,
and 7’ is the amplitude of the reflected vibration when the
incident light is polarized perpendicularly to that plane; the
amplitude of the incident vibration being in each case sup-
posed to be unity. Hence when common light is incident, if
its intensity be taken for unity, the intensity 1 of the reflected

light will be given by the formula
1= 3(tan*dw + tan*d w’). (R)
If with the values of m and y determined by my experi-
ments we compute, by the last formula, the intensity of re-
flexion for speculum metal at a perpendicular incidence, in
which case « = 1, we shall find 1 = .583. This is consider-
ably lower than the estimate of Sir William Herschel, who,
in the Philosophical Transactions for 1800 (p. 65), gives .673
as the measure of the reflective power of his specula. The
same number, very nearly, results from taking the mean of
Mr. Potter’s observations (Edinburgh Journal of Science,
New Series, vol. iii. p. 280). It might seem therefore that

393

the formula is in fault ; but I am inclined to think that the
metal which I employed had really a low reflective power.
Its angle of maximum polarization was certainly much less
than that of the speculum metal used by Sir David Brewster
(Phil. Trans. 1830, p. 524), who states the angle to be 76°,
whereas in my experiments it was only about 733°; and any
increase in this angle, by increasing the value of M, raises
the reflective power. On the other hand, the maximum va-
lue of 8 (when a =45°) was greater than that given by Sir
David Brewster, namely, 32°; and any increase in 3 tends
also to increase the reflective power. Now it is not unrea-
sonable to suppose that the highest values of both angles may
be most nearly those which belong to the best specula; and
accordingly if we take 76° for the incidence of maximum po-
larization, and retain the maximum value of 9, namely 34° 37’,
which results from my experiments, we shall get m= 3.68,
xX = 66° 16’, and the value of 1 at the perpendicular incidence
will come out equal to .662, which scarcely differs from the
number given by Herschel.

It is clear from what precedes that the optical constants
are different for different specimens of speculum metal, and
this is no more than we should expect, from the circum-
stance that the metal is a compound, and therefore liable
to vary in its optical properties from variations in the pro-
portion of its constituents; but I am disposed to believe that
the same thing is generally true, though of course in a less
degree, of the simple metals, so that in order to render the
comparison satisfactory, the measures of intensity should
always be made on the same specimen which has furnished
the values of mand y. There is one metal, however, with
respect to which there can beno doubt that the experiments
of different observers are strictly comparable, when it is pure,
and at ordinary temperatures; I mean mercury. For this
metal Sir David Brewster states the angle of maximum pola-

394

rization to be 78° 27’, and the maximum value of 6, when
a = 45°, to be 35°; from which I find m=4.616, y = 68° 13’,
and, at the perpendicular incidence, r= .734. Now Bouguer
observed the quantity of light reflected by mercury, but not at
a perpendicular incidence. His measures were taken at the
incidences of 69° and 783°, for the first of which he gives, by
two different observations, .637 and .666; for the second, by
two observations, .754 and .703, as the intensity of reflexion.
(See his Traité d’Optique sur la Gradation de la Lumiere,
Paris, 1760; pp. 124, 126). If we make the computation from
the formula, with the above values of m and y, we find the
quantities of light reflected at these two incidences to be, as
nearly as possible, equal to each other, and to seven-tenths
of the incident light, the intensity of reflexion being a mini-
mum at an intermediate incidence; and if we suppose these
quantities to be really equal at the incidences observed by
Bouguer, we must take the mean of all his numbers, whichis
.69, as the most probable result of observation. This result
differs but little from one of the two numbers given by him at
each incidence, and scarcely at all from the result of calculation.

The angle at which the intensity of reflexion is a mini-
mum, when common light is incident, may be found from the
formula

(n+ 7) @ TY 2 = (u— | Vv (f? + g’)—4cosx, (s)

which gives the value of u,and thence that of?. This incidence
for mercury is, by calculation, 75° 15’, and the minimum va-
lue of 1 is .693, which is less than its value at a perpendicular
incidence by about one-eighteenth of the latter. According
to the formule, the reflexion is always total at an incidence

of 90°.

Rev. Charles Graves communicated certain extracts from

395

a work of the late Dr. Cheyne, on a Deranged State of the
Faculty of communicating by Speech or Writing.*

Dr. Allman read a paper “‘ on a New Genus of Hydra-
form Zoophytes.”

The author discovered the animal on which he founded
the new genus in the Grand Canal near Dublin, in October,
1842. The genus of which this zoophyte constitutes as yet
the only known species, will finda place in the family of the
tubulariade, and occupies a position between coryne and
tubularia, differing from the former in the possession of a
polypedome, and from the latter in the scattered arrange-
ment of its tentacula. The tentacula, as in both the last
mentioned genera, are filiform; and in this character a point
of distinction is at once found between the new genus and
Hermia, Johust.

To the new zoophyte Dr. Allman assigned the name
Cordylophora lacustris.

May 22.
SIR Wm. R. HAMILTON,LL.D., President, in the Chair.

Right Hon. the Earl of Dunraven was elected a member
of the Academy.

Dr. Osborne read some observations on the deprivation
of the faculty of speech while the intellect remains entire,
and in which the defect does not arise from paralysis of the
vocal organs. The communication was intended as a sequel

* This work having been since published, the extracts are not here given.

396

to Dr. Cheyne’s observations read at the last meeting, and
was chiefly intended to refer to a case published by Dr. Os-
borne, which afforded some peculiar opportunities of inves-
tigating the nature of this affection.

The subject of this case was a gentleman of about 26
years of age, and of very considerable literary attainments.
He was a Scholar of Trinity College, and also a proficient
in the French, Italian, and German languages. When re-
siding in the country, one morning, after bathing in a neigh-
bouring lake, he was sitting at breakfast, when he suddenly
fellin an apoplectic fit. A physician was immediately sent
for, and after being subjected to the appropriate treatment,
he became sensible in about a fortnight. But although re-
stored to his intellects, he had the mortification of finding
himself deprived of speech. He spoke, but what he uttered
was quite unintelligible, although he laboured under no pa-
ralytic affection, and pronounced a variety of syllables with
the greatest apparent ease. When he came to Dublin his
extraordinary jargon caused him to be treated as a foreigner
in the hotel where he stopped ; and when he went to the
College in quest of a friend he was unable to express his wish
to the gate-porter, and succeeded only by pointing to the
apartments which his friend had occupied. The circum-
stance of his having received a liberal education, and his
tractable disposition, rendered this case peculiarly favour-
able for ascertaining the true nature of the affection, and
the result of Dr. Osborne’s observations during several
months were as follows:

1. He perfectly comprehended every word said to him,
and his conduct and habits were those of a man in a sound
state of mind, and were exactly those which his friends stated
to be peculiar to him before the seizure. He had no pa-
ralysis, and the motions of his mouth and tongue were exe-
cuted with the force and rapidity of ordinary health.

397

2. He perfectly comprehended written language. He con-
tinued to read his newspaper every day, and when passing
events were spoken of, proved that he hada clear recollection
of all that he read. Having procured a copy of Andral’s
Pathology in French, he read it with great diligence, having
lately intended to embrace the medical profession.

3. He expressed his ideas in writing with considerable
fluency, and when he failed it appeared to arise merely from
the want of the association with spoken language, which
caused confusion and uncertainty, the words being ortho-
graphically correct, but frequently not in their proper places.
He translated Latin sentences accurately, and also wrote
correct answers to historical questions.

4. His knowledge of arithmetic was unimpaired, he added
and subtracted numbers of different denominations with un-
common readiness ; also played well at the game of drafts.

5. His recollection of musical sounds appeared to be un-
impaired, for when the tune of Rule Britannia was played he
pointed to the shipping in the river.

6. His power of repeating words after another person
was almost confined to certain monosyllables ; and in repeat-
ing the letters of the alphabet he could never pronounce
k, gy U, v, w, x, and g, although he often uttered those sounds
in attempting to pronounce the other letters. The letter z
also he was very seldom able to pronounce.

7. In order to ascertain and place on record the peculiar
imperfection of language which he exhibited, the following
sentence from the By-laws of the College of Physicians was
selected, viz. “ It shall be in the power of the College to exa-
mine or not examine any Licentiate previously to his admission
to a Fellowship, as they shall think fit.” Having set him to
read this aloud, he read as follows: ‘* An the be what in the
temother of the trothotodoo to majorum or that emidrate ein
einkrastrai mestreit to ketra totombreidet to ra fromtreido as
that kekistret.” ‘The same passage was presented to him in

~ | ee ped SS ree

398

a few days afterwards, and he then read it as follows: “ Be
mather be in the kondreit of the compestret to samtreis amtreit
emtreido am temtreido mestreiterso to his eftreido tum bried
rederiso of deid dat drit destrest.”

We observe here those rb bastablck which are of most
frequent use in our language, as the, be, what, 2n, that, his,
and was, along with several syllables almost peculiar to the
German language, which he was engaged in studying at the
time of the apoplectic seizure ; but the main feature in the
case was, that although he knew when he spoke wrong, yet
that he was unable to speak right, notwithstanding he arti-
culated very difficult and unusual syllables.

As in this case the recollection of the meaning of words
was retained, and it was proved that there was no paralytic
affection interfering with pronunciation, but that even in the
act of endeavouring to imitate another person, he could not
pronounce the right word, Dr. Osborne concluded that the
affection was not (as has been usually described).a loss of the
faculty of language or of the memory of names, while the
memory of things remains, but that it consisted in a loss of
the recollection how to use the vocal apparatus.

In stammering it is obvious that the patient knows the
mode in which the word is to be pronounced ; he begins it
rightly, but is prevented from finishing it by debility or
spasm on the part of the muscles, causing them to resist his
efforts.. In this patient, on the contrary, the words which he
could write, and understood perfectly, he was unable to com-
mence the first syllable of, and instead of them uttered’
words compounded from other languages. His ear afforded
him very little assistance, as his attempts to repeat what had
been read were scarcely better than his reading. The or-
gans were not paralysed, neither were they affected by
spasm, nor was he ignorant of the sounds to be uttered: it
only remains then that he was ignorant of the art of pro-

399

ducing those. sounds, and as he was previously in possession
of this art, we are justified in asserting that he forgot it.

It may appear unaccountable why we should be liable to
forget the use of the vocal organs, but never forget the use
of the other voluntary muscles. ‘Thus while we have those
instances of persons pronouncing one word when they in-
tended another, we have no instance of an individual running
when he wished to stand, or leaping when he wished to sit
down. This, however, admits of being adequately explained,
by the nerves concerned in the muscular apparatus of speech
being derived from the brain and highest portions of the
spinal cord, and consequently liable to be disturbed by apo-
plectic affections; while the nerves of the limbs being derived
from the cervical plexus, or lower portions of the spine, are
unaffected, except by such causes as may produce paralysis.

Dr. Osborne referred to the Ephimerides Curiose for a
case in which the art of writing was retained, while that of
speaking was lost; and also alluded to that of Zacharias in
the Sacred Scriptures, who, although deprived of speech, is
related to have written ‘‘ The child’s name is John.”

Those instances which have been recorded of persons
after wounds or apoplectic seizures ceasing to speak their
usual language, and resuming the use of some other lan-
guage with which they had been familiar at a former period,
appear to be of the same nature as the present. The recol-
lection of one language, and its train of associate actions
being lost, it was most probable that the vocal organs should
move in that train to which they had formerly beenaccustomed,
and fall into the use of another language. It is highly pro-
bable that a similar occurrence would have taken place in
this patient if he had only cultivated one language besides
English, but having been conversant with five languages,
the muscular apparatus ranged among them, forming a kind
of polyglot jargon, which was formed without any rule, was
inconsistent with itself, and wholly unintelligible.

VOL. II. 2M

400

Although Dr. Osborne did not enter upon the medical
treatment of the case, yet he considered that the effect of
the plan adopted to recover his speech afforded an additional
proof that this patient had not lost the faculty of language,
but only the art or knack of speaking. He commenced
learning to speak de novo like a child, by repeating after
another person first the letters of the alphabet, and subse-
quently words. This was avery laborious task. Sometimes
he was able to pronounce words which at other times he
found impracticable, but his progress may be estimated by
his repeating after another the same By-law of the College
of Physicians in the following terms: “ lf may be in the
power of the College to enhavine or not ariutin any Licentiate
seviously to his amission to a spolowship as they shall think
jit.’ A month or two afterwards he repeated the same By-
law perfectly well, with the exception of the word power,
which on this occasion he called prier. ‘This gentleman
soon afterwards went to the country, where in a few months
he was carried off by a fever, and Dr. Osborne learned no
further particulars respecting him after he left Dublin.

Sir William Hamilton remarked that Dr. Robinson’s mean
refractions, published in the second Part of the Nineteenth
Volume of the Transactions of the Academy, might be re-
presented nearly by the formula,

Rr = 57,546 tan (0—4” xr); (1)
or by this other formula,
R cot +R? sin 3”,8 = 57,346 ; (2)

Rr being the number of seconds in the refraction correspond-
ing to the apparent zenith distance 0, when the thermometer
is 50°, and the barometer 29,60 inches.

The first formula seems to give a maximum positive de-
viation from Dr. Robinson’s Table, of about a quarter of a
second, at about 80° of zenith distance; it agrees with the

401

Table at about 83° 10’; is deficient by a second at about
84° 30’; and by $” at 85°.

The second formula, which may be reduced to logarithmic
calculation by the equations,

log tan 29 = log tan 0 + 2,81296, t (3)
log rk = logtanp + 3,24657,
does not agree quite so closely with Dr. Robinson’s Table,
in the earlier part of it; but the error, positive or negative,
seems never to exceed half a second, within the extent of
the Table, that is, as far as 85°.

It appeared to Sir W. H. worth noticing, that the results
of such (necessarily) long and complex calculations, as those
which Dr. R. had made, could be so nearly represented by
formule so simple: of which, indeed, the first is evidently
analogous to Bradley’s well known form, but differs in its
coefficients. “The second form is more unusual, and gives
(approximately) the mean refraction as a root of a quadratic
equation. It has been used (with other logarithms) by
Brinkley, for low altitudes.

DONATIONS.

Address to the Geological Society of London. By Rode-
rick J. Murcheson, F.R. S.A. Presented by the Author.

Report of the Meeting of the British Association held at
Manchester in 1842. Presented by the Association.

Statutes relating to the Admiralty, to the 8th of Geo. III.
Presented by Captain Portlock.

Proceedings of the Glasgow Philosophical Society. 1841-
1842. Presented by the Society.

Memoirs published by the Society of Sciences in Holland.
Vol. II. Second Series.

Proceedings of the American Philosophical Society. Vol.
II. Parts 24 and 25.

Transactions of the American Philosophical Society. Vol.
VIII. New series. Parts 2 and 3. Presented by the So-
ciety.

402

Fifth Annual Report of the Loan Fund Board in Ireland
for 1843. Presented by the Commissioners.

Communication to the Right Hon. Sir Robert Peel, Bart.
By Jeffries Kingsley, Esq. Presented by the Author.

Bulletin des Sciences de la Societé Vaudoise des Sciences
Naturelles. Nos. 1-4. Presented by the Society.

Sur les Figures Roriques et les Bandes Coloriées produites
par l’ Electricité. Par M. P. Riess. Presented by the Author.

E:xpériences sur la non caloricité propre de l’ Electricité.

Sur les relations qui lent la lumiere a l Electricité.

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vitesse de propagation de UElectricité. Par M. Le Prof.
Elie Wartmann. Presented by the Author.

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Manchester. New Series. Vol. VII. Part.1. Presented
by the Society.

List of Premiums of the Society for the Encouragement of
Arts, Manufaciures, and Commerce, for 1843-45. Presented
by the Society. 5

Transactions of the Geological Society of London. Se-
cond Series. Vol. VI. Part 2. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1843. No. 41.

June 12.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Sir William Betham read the following letter from Sir
Richard O’Donel, Bart. :
April 24th, 1848.
** My pear Sir WILLIAM,

** T have to apologise for all the trouble I have
given you about the Caah, but several circumstances have
come to my knowledge within the last few days, which induce
me to desire that it should be placed in the Royal Irish
Academy, next to the Cross of Cong; but I would not take
any step in the matter without first consulting you, and
having done so, I write you this note to request you will be
so good as to make known my wishes to the Dublin Society
upon the subject, and to have it removed to the Royal Irish
Academy, upon their taking charge of it as my property,
placing it during the day beside the Cross of Cong, and
having it each night placed in a fire proof box.

“I again beg leave of you to pardon me for all this trou-
ble, and to accept my thanks for your kindness at all times,
and believe me,

* Dear Sir William,
“‘ Very sincerely yours,

““Ricnarp O’DoneEt.
“ Sir William Betham,

Record Tower, Castle.”
VOL. Il. 2N

404

Resotvep,—That the thanks of the Academy be given
to Sir Richard O’Donel, Bart., for his valuable deposit, and
that the custody of it be accepted by the Academy on the
terms proposed by him.

Sir Wm. Betham gave an account of the Caah.

Professor Kane read a notice of some recent Determina-
tions of the Heat developed during the Formation of certain
Compounds of Chlorine, by Dr. Andrews.

The present results were obtained by a similar method
to that described in the last volume of the Transactions of
the Academy. The chlorine, however, was employed in the
dry state, and the compounds being formed without the pre-
sence of water, the heat of combination was deduced from a
single direct experiment. In the case of potassium, an im-
portant modification of the apparatus was required, which
will be described when the full details of the experiments
are communicated to the Academy. The numbers in the first
column are the immediate results of experiments, and ex-
press, in degrees of Fahrenheit’s scale, the heat produced
during each reaction, in reference to the chlorine as unit,
that is, the degrees through which a weight of water equal
to that of the combining chlorine would be raised by the heat
developed in the formation of each compound. ‘The num-
bers in the second column express the same heat, referred
to the combining metal as unit, and are deduced by calcula-
tion from the others.

K +(Cl..5379° .. 5954°,
Sn + Cl,.. 1621°.. 1346°.
Sb, + Cl;.. 1570°.. 1145°.
As, + Cl;.. 1268°.. 898°.

Dr. Allman read a notice of a new species of Linaria.
This plant was discovered growing on the banks of the
River Bandon, and Dr. Allman considered it sufficiently dis-

405

tinct to entitle it to rank as anew species. Specimens of the
plant collected by Dr. Allman were seen in London by Mr.
H. C. Watson, who recognized them as identical in species
with a Linaria, gathered by himself in two English localities,
and, moreover, that they corresponded with the Antirrhinum
Bauhin of Gaudin’s Flora Helvetica, ZL. Italica, Koch. In
accordance with these views, a paper by Mr. Watson ap-
peared in the second Number of Sir W. J. Hooker’s London
Journal of Botany, adding L. Bauhini to the Flora of Britain.

To the claim, however, of L. Bauhini to be admitted into
the British Flora, Dr. Allman could not assent; so far at
least as this claim depended on the identity of the Irish with
the Continental plant. He had carefully examined the Irish
Linaria, and convinced himself not only of its distinctness
from L. Bauhini, but of its claim to rank as a new species.
To Linaria repens it is closely allied, indeed there is some
difficulty in separating it from this plant as a distinct species.
Dr. Allman, however, conceived that specific characters
would be found in the flowers, which not only differ in colour
from those of L. repens, but also in their larger size, and in
the greater relative as well as absolute length of the spur.
To the new Linaria he gave the specific name sepium, and
described it as follows:

Linaria sepium. Lin. radice repente, foliis subglaucis
lineari-lanceolatis, calcare incurvo corollam zquante, semi-
nibus trigonis.

Radix repens. Caulis erectus simplex v. subramosus,
Paniculatus. Folia subglauca, lineari-lanceolata, sparsa,
inferiora sepe verticillata. Bractee lanceolate, pedicello
breviores, Calycis lacinie lanceolate. Flores in paniculam ex
racemis erectis constantem dispositi, et odorem suavem at
tenuem exhalentes. Calcar incurvum corollam equans, la-
bium superius, tubus et calcar grisei, striis palidé purpureis
eleganter signati: labium inferius diluté luteum, striis pa-
lidé purpureis et parum distinctis notatum: palatium villis

2N2

406

saturaté luteis vestitum, villis purpureis quemque marginem
investientibus, Capsula globosa, dehiscens superne pluribus
valvulis lanceolatis. Semina nigra, trigona, lateribus ineequa-
libus muricatis, marginibus in alas tres productis.

A L. repente differt hzec species calcare longiore, corolla
majori et labio inferiori luteo; a L. vulgari discrepat floribus
minoribus corolla striis signata et toto flore, preter labium
inferius et palatium, coloris lutei experti: ad hoc semina tri-
gona signum certum prestant quo hec species a L. vulgari
dignosci potest; ab Antirrhino Bauhini differt caule erectiori,
foliis angustioribus, colore florum pistillo glabro et seminibus
trigonis.

Habitat in sepibus juxta flumen Bandon. —Florebat
Junio, Julio et Augusto 4.

Rev. Dr. Kennedy Bailie commenced the reading of a
paper on ‘ Certain Greek Inscriptions copied on the Sites
of Ancient Teos and Aphrodisias in Asia Minor.”

DONATIONS.

Journal of the Franklin Institute. Vols. II. and IV
Third Series. Presented by the Institute.

Proceedings of the Zoological Society of London. Part
10. 1843. Presented by the Society.

Tribes and Customs of Hy-Many. By John O’Donovan,
Esq. Presented by the Irish Archeological Society.

Astronomische Nachrichten. Nos. 462-477.

Annales des Sciences Physiques et Naturelles d Agriculture
et d’ Industrie, publiées par la Société Royale d' Agriculture,
& ce. de Lyon. Tomes I. II. and III. Presented by the So-
ciety.

Second Mémoire sur les Kaolins. Par M. Brongniart.
Presented by the Author.

407

June 26.

SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Present, His Excellency Earl De Grey, Lord Lieutenant,
Visitor of the Academy.

Dr. Kennedy Bailie read in continuation the Account of
his Researches in Ancient Teos and Aphrodisias, in Asia
Minor.

Previously to entering on his selection of notices with
respect to the Teian, &c. inscriptions, he thought it proper
to offer a few remarks on that part of his former essay which
relates to the subject of the inscriptions from Sardes and
Pergamus.

The passages more particularly referred to are those in
pages 132-4, and 149-50, on which certain observations were
made either explanatory of, or modifying, the author’s con-
clusions, as expressed therein. The result in the case of the
Sardian titulus has been, that it must no longer be consi-
dered as referrible to the ages of Hadrian or of the Antonines,
as he was at first led to suppose; and in that of the Perga-
menian, that the document may be so interpreted as not to be
in anywise connected with the question of Hadrian’s adoption
by Trajan.

The new readings illustrative of these points were sub-
mitted to the notice of the Academy.

The author then proceeded to a detail of his researches on
the sites of the ancient Teos and the neighbouring port-town
of Cherrezidz, which is mentioned by Strabo. This last he
considers as occupied by the modern village of Sighadjék.

The most interesting of the inscriptions which he brought
from these sites is a fragment of one of an early date, at
least coeval with those which Chishull has published in his
celebrated work on the Antiquities of Asia, from copies

408

made by the late Sir William Sherard in 1709 and 1716. It
related, as far as can be collected from the extremely muti-
lated state of the monument, to a treaty of Asylumship (aovA‘a)
between the inhabitants of this district of Asia Minor and
certain other States of Greek origin, amongst which there
are fragments of the names of the Agrigentines, the Coans,
the Polyrrhenians (of Crete), also of the people of Delphi.

This notice was concluded with a translation of the
Titulus, which contained such supplementary matter as the
author deemed requisite to complete the sense.

He then proceeded to notice two other inscriptions, one
of which he regarded as marking the site of the Temple of
Bacchus, in Teos, of which Vitruvius has made mention;
and the other as a remnant of the inscribed monuments of
the ancient Chalcis, which lay contiguous to Teos.

The first of these is remarkable, from its containing a
notice of the election of a female of rank to serve the office
of High Priestess of Asia.

The second informs us of the existence of a Gerusia, or
House of Assembly for the Seniors, in the city to which it
belonged. Whether this was Chalcis (as conjectured ae i
or Teos, is uncertain.

In proceeding to Gheyerah (the representative of Aphro-
disias in Caria), the site of Tralles was noticed ; as also were
the Tituli, which Pococke and others have copied from the
ruin at present existing in the ancient acropolis.

The Temple of Aphrodite, extensive remains of which still
exist, in Aphrodisias, was then noticed; as also the probable
site of the Agora. Near this the first of the Aphrodisian in-
scriptions was copied, which is remarkable from its contain-
ing notices of a gradation in dignity amongst the Archons of
the city, as also amongst the Neopei, or Trustees of the
Temple of Aphrodite.

The inscription in honour of Constantius and one of his
colleagues, over the west portal, was next explained, and

409

reasons were assigned for supposing that the name of Julian,
the Apostate, had been erased by the Christian inhabitants
of the city, from this monument.

The next inscription which was noticed contains an allu-
sion to the office of Asiarch, which led the author of the
Memoir to offer some explanations in reference thereto, prin-
cipally on the mode of election to, and the duties, of, that
station.

The next brought under consideration was a fragment, ca-
pable of being restored so as to present the first two petitions
of the Lord’s Prayer; a supposition in perfect consistence
with the history of the town.

Several others were also noticed ; the most remarkable
and interesting of which was a tomb-inscription of consider-
able length, copied from the eastern side of the rampart.
The discussion of this led to many remarks on the mode
adopted amongst the Greek colonists of Asia Minor to ex-
press degrees of descent, on the terms of their sepulchral
architecture, and on the laws regulating tomb-property.

Connected with this subject was a series of observations
on the office of the Stephanephore. This appears to have
been partly of a civil nature, partly pontifical, in accordance
with which the right of wearing diadems was granted to
functionaries of this class, as to the Flamines amongst the
Romans.

The Memoir closed with some details respecting a series
of reliefs, which the author discovered on the exterior of the
southern wall. These, though placed in juxta-position, did
not all refer to the same subject. There are two interposed,
which appear to be altogether symbolical in their meaning,
or at least to possess a mythical character, and to have been
intended as illustrations of some mythical circumstance.

A suggestion was offered, that perhaps it would be
worthy the attention of archeologists, to adopt means to
have these sculptures removed from their present position,

410

and deposited in some museum. ‘They appeared to the au-
thor to be curious and valuable specimens of ancient art, and
are, in all probability, connected with the mythical legends
of the Cretan people, with whom the early inhabitants of
Aphrodisias were closely connected.

The Rev. Dr. Todd, V. P. gave an account of a Stone
with an Ogham Inscription, which was found with many
others in a cave at Fortwilliam, in the county of Kerry, and
sent up to the Provost and Senior Fellows of Trinity Col-
lege.

After having given a short account of the different kinds
of Ogham spoken of by Irish grammarians, and exhibited
the key usually given for reading the particular kind of
Ogham to which the inscription on the stone found at Fort-
william belongs, Dr. Todd proceeded to show the inapplica-
bility of this key to the interpretation of the inscription.
The whole subject of the Ogham inscriptions, he stated, was
one which was involved in great obscurity, and although
very abundant materials exist for investigating it, it has never
yet been fairly examined. Several treatises on the subject
are to be found in our ancient MSS., but no Irish scholar
seems as yet to have had the courage to enter upon the
study of them. Numerous inscriptions on stones, similar to
that now exhibited to the Academy, are also to be found,
particularly in the south and west of Ireland, but accurate
copies of these inscriptions are no where accessible. Dr.
Todd suggested this as a suitable subject for a prize, if ever
the Academy should return to the former practice of offering
a prize for an essay on a given subject. In this case, how-
ever, he recommended that the prize should be offered, not
for the best essay or theory for the explanation of the Ogham
character, but, in the first instance, for the most accurate
and best authenticated collection of copies, or fac similes, of
the inscriptions themselves.

The following engraving gives a correct view of the stone,

411

which is four feet five inches high, and in its broadest part
at the base four feet six and a half inches in circumference,

and an exact copy of the inscription:

0 00 |
‘ = 10
Ce LIL Pie erate | UNOo noo conte

Sn yaasttO te TL) // A) A

SN (eet
mM fil

Mr. Griffith read a notice by Mr. Hemans, of a Disloca-
tion in the Calp near Killester.

The President, on presenting to Dr. Kane the Cunning-
ham Medal, awarded to him for his Researches on the Nature
of Ammonia, gave an account of the progress of his dis-

coveries.

412

It is now my duty to inform you, that a Cunningham Medal has
been awarded by the Council to Dr. Robert Kane, for his Researches
on the Nature and Constitution of the Compounds of Ammonia, pub-
lished in the First Part of the Nineteenth Volume of the Transac-
tions of this Academy. It would, indeed, have been much more
satisfactory to myself, and doubtless to you also, if one of your
Vice-Presidents, who is himself eminent in Chemistry, had under-
taken the task which thus devolves upon me, of laying before you a
sketch of the grounds of this award; but at least, my experience of
your kindness encourages me to hope, that while thus called upon
officially to attempt the discharge of a duty, for which I cannot
pretend to possess any personal fitness, or any professional prepara-
tion, I shall meet with all that indulgence of which I feel myself to
stand so much in need.

Although, in consequence of the variety of departments of
thought and study which are cultivated in this Academy, and the
impossibility of any one mind’s fully grasping all, it is likely that
many of its members are unacquainted with the details of chemistry,
yet it has become matter of even popular knowledge, that in general
the chemist aims to determine the constitution or composition of
the bodies with which we are surrounded, by discovering the natures
and proportions of their elements. Few need, for instance, to be
told that water, which was once regarded as itself a simple element,
and which seems to be so unlike to air, or fire, or earth, has been
found to result from the intimate union of two different airs or
gases, known by the names of oxygen and hydrogen, of which the
one is also, under other circumstances, the chief supporter of com-
bustion, is an ingredient of the atmosphere we breathe, and is closely |
connected with the continuance and healthful action of our own
vital processes, by assisting to purify the blood, and to maintain
the animal heat; this same gas combining also, at other times, with
some metals to form rusts, with others acids, with others again
alkalies and earths, entering largely into the composition of marble
and of limestone, and, in short, insinuating itself, with a more than
Protean ease and variety, into almost every bodily thing around us
or within us; while the other gas which contributes to compose
water, though endowed with quite different properties, is also ex-

413

tensively met with in nature, especially in organized bodies, and in
particular occurs as an element in that important substance, on the
confines of the mineral and organic kingdoms, to which the Re-
searches of Doctor Kane relate; ammonia being, as all chemists
admit, a compound of hydrogen and nitrogen, which last-named
gas is well known as being the other chief ingredient (besides oxy-
gen) of atmospheric air.

Again, it is generally known, to those who take an interest in
physical science, as a truth which is almost the foundation of
modern chemistry, that the elements of bodies of well-marked and
definite constitutions, such as pure (distilled) water, or dry (anhy-
drous) ammonia, are combined, not in arbitrary, but in fixed and
determined proportions; for example, the oxygen contained in any
quantity of pure water weighs exactly, or almost exactly, eight
times as much as the hydrogen contained in the same quantity, but
occupies (when collected and measured) a space or volume only
half as great ; and the nitrogen contained in any given amount of
dry ammoniacal gas, is to the hydrogen with which it is combined,
by weight as 14 to 3, and by volume in the proportion, equally fixed,
of 1 to 3.

Yet such results as these, respecting the constitution of com-
pound bodies, however numerous and accurate they may be, are
still not sufficient to satisfy the curiosity, or to terminate the re-
searches of chemists. They aspire to understand, if possible, not
only the w/¢imate constitution of bodies, or the elements of which
they are composed, and the proportions of those elements, but also
the proximate constitution of the same bodies, or the manner in
which they arise from other intermediate and less complex com-
pounds. Water, for instance, is believed to enter, in many cases,
into composition with other bodies, as water, not as oxygen and
hydrogen. Has ammonia any such component, which itself is
composite? It is admitted to consist of one volume of nitrogen,
combined with three of hydrogen. Can any order be discovered in
this combination, any proximate constituent, any simpler and earlier
product, from which the ammonia is afterwards produced? Until
experiments decide, it appears not impossible, may seem even not
unlikely, that nitrogen may combine (more intimately than by mere

414

mixture) not only with thrice but with twice or once its own volume
of hydrogen, and that thus other substances may be formed, from
which, by the addition of new hydrogen, ammonia may result. It
is interesting, therefore, to inquire whether either of these conceived
possibilities is actually realized in nature; whether these two im-
portant gases do ever actually combine with each other in either of
these two proportions. In the symbolic language of chemists, as
usually written in these countries, the compound NH, is well known,
being no other than ammonia ; but does NH* or does NH, exist ?

An eminent French chemist, M. Dumas, in examining a sub-
stance, which he called oxamide, and which was one of the results
of the action of oxalic acid on ammonia, was led to the conclusion,
that the last mentioned compound of nitrogen and hydrogen, name-
ly NH., does really exist in nature, and he proposed for it the name
of amide. The same chemist considered it also to exist in the
substance formed by heating potassium in ammoniacal gas; and
the same combination, amide, had been (I believe) regarded as a
proximate constituent of certain other compound bodies, such as
urea, sulphamide, and carbamide, before Dr. Kane’s researches on
the White Precipitate of Mercury. Yet it has been judged by
Berzelius, that the investigations of Dr. Kane have assisted in an
important degree to establish the actual existence (der wirklichen
existenz) of amide, or of amédogene (as Kane prefers to call it,
from its analogy with oxygen and cyanogen), and have thrown
much light upon its chemical history and relations.

In fact, the body oxamide, which seems to have first led Dumas
to infer the existence of amide, was one of those organic com-
pounds, respecting which it has often been found difficult, by che-
mical inquirers, to pass with confidence from the empirical to the
rational formula; from the knowledge of the wltimate elements
(or of those which are at present to be viewed as such), and of the
proportions in which they combine, to a satisfactory view respecting
the proximate elements, or intermediate and less complex combi-

* The compound NH, or as it is otherwise better written, HN, has been sus-
pected to exist, as one of the proximate elements of melamine and of some con-
nected bodies. See Gregory’s edition of Turner’s Chemistry, 1840, page 757.

415

nations on which the final result depends. Oxamide may be, and
was considered to be, probably composed of amide and carbonic
oxide (in the foregoing notation, NH,+C,0,); but it was perceived
to admit also* of being possibly compounded of nitric oxide and a
certain combination of carbon and hydrogen (NO,+C,H,); or of
cyanogen and water(C,N-++-H,O,). And even the amidides of potas-
sium (KNH,) and of sodium (NaNH,), have, from the energetic
affinities of those metallic bases, been thought to prove less decisively
the existence of amidogene itself, than the amidide of mercury
(HgNH,) discovered by Dr. Kane, in hisanalysis of the white preci-
pitate of the last mentioned metal. (Trans. R.I.A., vol. xviii. part iii.)

Although this precipitate had been long known, and often ana-
lyzed, erroneous views (as they are now regarded) were entertained
respecting its composition, and it had, for instance, been supposed
to contain oxygen, till Kane pointed out the absence of this element,
and showed, with a high degree of probability, that the proximate
elements were the chloride and the amidide of mercury; white pre-
cipitate being thus a chlor-amidide of that metal (HgC1+HgNH,, if
the Berzelian equivalent of mercury be adopted, instead of its double).
Ullgren, a friend of Berzelius, obtained the chemical prize from the
Swedish Academy of Sciences, for the year 1836, for a paper in
which, having with great care repeated and varied the experiments,
he confirmed this and other connected results of our countryman;
and Berzelius himself, in his Report read to the above-mentioned
Academy in 1837, on the recent progress of the Physical Sciences
in Europe (to which Report allusion has been made above), ex-
pressed his opinion that these researches of Kane were among the
most important of the preceding year.

In the essay for which your Council have awarded the present

* L’Oxamide peut donc, a volonté, étre considérée comme un composé de cyano-
géne et d’eau, ou bien comme un composé de deutoxide d’azote et d’hydrogéne
bicarboné, ou bien enfin comme un composé d’oxide de carbone et d’un azoture
@hydrogéne différent de l’ammoniaque.—Dumas, sur l'Oxamide, &c. Annales de
Chimie et de Physique, tome xliv. page 142.

f Diese Untersuchungen von Kane gehoren meiner Ansicht nach zu den wich-
tigeren des verflossenen Jahres.—Wohler’s German Translation of Berzelius’s
Report, Jahres-Bericht iiber die Fortschritte der physischen Wissenschaften,
17th year, page 179. (Tiibingen, 1838).

416

prize, Dr. Kane has pursued his researches on ammonia, and has
shown, with apparently a high probability, that there exist ami-
dides (though not yet insulated) of other* metals besidesm ercury,
especially of silver and copper; that is, combinations of these me-
tals with the proximate element amide or amidogene. He has also
given, in great detail, a series of analyses performed by him on a
large number of compound bodies, of which some had been imper-
fectly examined before, while others were discovered by himself.
But as it would lead into far too great length, and too minute detail,
if any attempt were made at present to review these laborious pro-
cesses of analytical chemistry, and as indeed they derive their chief
philosophical interest from the views with which they have been
associated, it may be proper to attempt no more than a very brief
(I fear that it will also be a very inadequate) sketch of those views.

Dr. Kane considers that in ammonia, which, in the usual lan-
guage of chemists, is said to consist of one atom of nitrogen and
three atoms of hydrogen, one of these atoms of hydrogen is more
loosely combined than the two others with the nitrogen, so as to be
capable of a comparatively easy replacement, by many, perhaps by
all, of the metals, as well as by organic radicals; the other two
atoms of hydrogen being already, in the ammonia itself, and not
merely in the products of such replacement of hydrogen by metals,
combined in a particular way with the one atom of nitrogen, so as
to form that substance named amide or amidogene, which was de-
tected by Dumas (as has been mentioned) in performing the analysis
of oxamide. From Dr. Kane’s own study of the combinations of
this substance amidogene (H, N), with metals, he infers it to be a
compound radical of feebly electro-negative energy, analogous to
that important one cyanogen (C, N), of which the discovery by Gay-
Lussac has exercised so powerful an influence on modern chemistry.
He considers this radical, amidogene, as existing ready formed, in
combination with hydrogen, in ammonia; which latter substance is
thus, according to him, to be regarded as amidide of hydrogen ;
and as, in this respect, analogous to water, and to the hydro-
ceyanic, hydro-sulphuric, and muriatic acids, that is, to the oxide,

* Dr. Kane has since made it probable that there exist amidides of palladium
and platinum also. (Phil. Trans. 1842, part ii.)

417

cyanide, sulphuret, and chloride of hydrogen; from all of which
bodies it is possible, as from ammonia, to expel an atom of hydro-
gen, and to replace it by an atom of metal,—if indeed hydrogen be
not (as there seems to be a tendency to believe it to be) itself of
metallic nature, notwithstanding its highly rarefied form. By de-
veloping this view of the constitution and function of ammonia, Dr.
Kane has offered explanations of a large number of replacements of
that substance by others, some of which replacements (I believe)
were known before, while many have been discovered by himself.

One of the most remarkable points in Dr. Kane’s views is the
way in which he considers the ordinary salts of ammonia. Many
of these are known to contain an atom of water, the existence of
which led to the proposition of the very remarkable theory by Ber-
zelius, of the existence in them of a compound metal ammonium,
which has not indeed been insulated, but has been found to form,
in combination with mercury, a certain metallic amalgam. Dr,
Kane looks upon these salts as double salts of hydrogen. He con-
siders them to contain ammonia ready formed, united with a hydrated
acid or with a hydrogen acid. He seeks to establish the similarity
of the common ammoniacal salts to those complex metallic ami-
dides, whose nature he has developed by analysis.

Thus, for example, the well-known body, sal-ammoniac, is, in
the Berzelian view, regarded as chloride of ammonium; but, in
the view put forward by Dr. Kane, it is chlor-amidide of hydrogen.
The former view supposes that the ammonia robs the hydrochloric
acid of its hydrogen, to form, by a combination with it, a metallic
base, NH,, with which the chlorine unites ; as this last element com-
bines with the metal sodium, in the formation of common salt. The
latter view supposes that in the action between hydrochloric acid and
dry ammoniacal gas, thereis no separation of the chlorine from the
hydrogen,—no breaking up of a previously existing union,—no
overcoming of the affinity which these two elements (chlorine and
hydrogen) have for each other; but an exemplification of a general
tendency of chlorides, oxides, and amidides of the same or similar
radicals, to unite, and form chlor-oxides, chlor-amidides, or oxami-
dides. Sal-ammoniac is, according to Kane, a double haloid salt;
he looks upon it as being a compound exactly analogous to the
white mercurial precipitate, which was first accurately analyzed by

418

himself; the one being HCl + HAd (if Ad be the symbol of amido-
gene), while the other is HgCl ++ HgAd, so that the mercury in the
latter takes the place of the hydrogen in the former.

It was, however, in the oxysalts, such as the sulphate of am-
monia, that the presence of an atom, or equivalent, of water, or
at least of the elements required for the composition of such an
equivalent, appears to have suggested to Berzelius the theory, that
what seemed to be hydrate of ammonia (NH,+ HO) was really oxide
of ammonium (NH,-+ 0). There are, undoubtedly, many tempta-
tions to adopt this view, besides the high reputation of its pro-
pounder. One is, that it assimilates the constitution of sulphate of
ammonia to what seems to be regarded by the greater number of
modern chemists, as the probable constitution of other sulphates,
nitrates, &c., for example, the sulphate of iron. When green
vitriol is to be formed by the action of sulphuric acid upon iron,
it is requisite to dilute the acid with water, before the action will
take place. The hydrogen of the water then bubbles off, but what
becomes of the oxygen which had been combined with it? Does
it combine immediately, and as it were in the first instance, with
the iron, to form oxide of iron, on which the anhydrous sulphuric
acid may act, to produce sulphate of oxide of iron, according to
the view which seems, till lately, to have been adopted: or does
this oxygen, from the water, combine rather with the sulphuric
acid to produce a sort of oxide thereof, and does this sephat-ozygen
act on the pure metallic iron to form with it a swlphat-oxide, as
many eminent chemists now appear to think? Whatever may -
be the final judgment of those who are entitled to form opinions on
questions such as these, it cannot, I conceive, be justly said, that
the questions themselves are unimportant. They touch on. points
connected with the philosophy of chemistry, are essentially con-
nected with its theory, and cannot always be without an influence
upon its practice.

Now according to the Berzelian view of sulphate of ammonia,
that is the salt produced by the mutual action of sulphuric acid,
water, and ammonia, this salt is properly a sulphat-oxide of the
compound metal ammonium (NH,+S0,), inthe same way as green
vitriol, on the view last mentioned, is sulphat-oxide of iron

419

(Fe + SO,), or as sulphate of potash is sulphat-oxide of potassium
(K + SO,), and this analogy is doubtless pleasing to contemplate.

Dr. Kane does not entirely reject this Berzelian theory of ammo-
nium; he acknowledges that the substance NH,, which he regards as
subamidide of hydrogen, and compares to some suboxides, pos-
sesses metallic properties, and is a proximate constituent of certain
compounds, especially of the ammoniacal amalgam; but he con-
‘teives that the evidence for the existence of ammonia itself, in
many of the ammoniacal salts, is too strong to be resisted: and he
looks upon the hydrated ammonia, which is found to combine with
sulphuric and other oxacids, as being not, in general, oxide of am-
monium, but oxyamidide of hydrogen ; the sulphate of jammonia
being thus a bibasic compound, of which one base is ammonia,
while the other base is water.

Between the conflicting opinions of such men, supported each
by powerful arguments and analogies,—and it will easily be con-
ceived that in so short a sketch as this, and upon such a subject, it
has been found impossible by me to mention even the names of all
the eminent chemists whose experiments and writings should be
studied, by persons inquiring for themselves,—not only do I not ven-
ture to express any judgment of mine, but I conceive also that your
Council did not desire to express on their part any decision. To jus-
tify the present award, it was, I believe, deemed by them sufficient,
that great research and great talents had been brought, in the inves-
tigations of the author to whom that award has been made, to bear
on an important subject, which has derived, from those investiga-
gations, an additional degree of importance. Whatever may be the
final and unappealable judgment of those persons who shall, at
some future time, be competent and disposed to pronounce it, we
need not fear that the honour of this Academy shall have been com-
' promised by the recognition which the Council have thought it
right on the present occasion to make, of that combination of genius
and industry, which has already caused the researches of Kane to
influence in no slight degree the progress of chemical science, and
has won for him an European reputation.

The President then presented the Gold Medal to Dr.
Kane, and the Academy adjourned for the summer.
VOL. Il. 2.0

420

July 31. (Extraordinary Meeting.)
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

ResoLtvepD,—On the recommendation of Council,—That
the Treasurer be empowered to sell stock in the 3 per cent.
Consols, to the amount of £300, in order to pay Mr. Gill’s
bill for printing Transactions to March 16, 1843, amount
£264 10s. 4d., and the rent of the Academy House to 31st
July, 1843.

Resotvep,—On the recommendation of Council,—That
the Treasurer be empowered to sell such 33 per cent. stock,
being the Cunningham Fund, as shall amount to £50, to-
wards defraying the cost of medals.

Sir William Betham presented to the Academy certain
casts from the sculptures on the inside of the tower of
Ardmore.

Dr. Lloyd having taken the Chair, the President gave an
account of some researches in the Calculus of Probabilities.

Many questions in the mathematical theory of probabili-
ties conduct to approximate expressions of the form

p =<-\, dt e*;

that is,
p = 0(),
6 being the characteristic of a certain function which has been
tabulated by Encke in a memoir on the Method of Least
Squares, translated from the Berlin Ephemeris, in vol. ii.
part 7 of Taylor’s Scientific Memoirs; p being the proba-
bility sought, and ¢ an auxiliary variable.
Sir William Hamilton proposes to treat the equation

p = 9%)
as being in all cases rigorous, by suitably determining the
auxiliary variable ¢, which variable he proposes to call the

421

argument of probability, because it is the argument with
which Encke’s Table should be entered, in order to obtain
from that Table the value of the probability p. He shows
how to improve several of Laplace’s approximate expressions
for the argument #, and uses in many such questions a trans-
formation of a certain double definite integral, of the form,
453
T
=O(r(l+yst+ws?Pt+.. is

) dr y due-* u cos (2s*7uV)

in which

u=ltaqw+aui'+...

vro1l+pPiw+Pou'+...
while vj; vo,...depend on a,...(3;,... and on7; thus

yy = dq — Pir”.
The function @ has the same form as before, so that if, for
sufficiently large values of the quantity s (which represents,
in many questions, the number of observations or events to
be combined), a probability p can be expressed, exactly or
nearly, by the foregoing double definite integral, then the
argument t, of this probability p, will be expressed nearly by
the formula,
t=r(1+v, 57 4+ 57°).

Numerical examples were given, in which the approxi-
mations thus obtained appeared to be very close. For in-
stance, if a common die (supposed to be perfectly fair) be
thrown six times, the probability that the sum of the six
numbers which turn up in these six throws shall not be less
than 18, nor more than 24, is represented rigorously by
the integral

sin Vz eee 6x

6
j QTAASB.
ae ) , or by the fraction 22448 ;

QCz
oi =\" = 6sinx
while the approximate formula deduced by the foregoing
method gives 27449 for the numerator of this fraction, or for
the product 6° p ; the error of the resulting probability being

therefore in this case only 6-°. The advantage of the method

422

is that the quantity which has here been called the argument
of probability, depends in general more simply than does the
probability itself on the conditions of a question; while the
introduction of this new conception and nomenclature allows
some of the most important known results respecting the mean
results of many observations to be enunciated in a simple
and elegant manner.

DONATIONS.

Historias e Memorias da Academia Real des Sciencias de
Lisboa. Tome XII. Parte 2.

Discurso lido em 22 de Janeiro de 1843 na sessao pub-
lica da Academia Real des Sciencias de Lisboa. Por J.J. da
Costa de Macedo. Presented by the Academy.

Le Petit Agriculteur. Par N. C. Seringe. Presented by
the Author.

Astronomical Observations made at the Radcliffe Obser-
vatory, Oxford, in 1840. By M.J. Johnson, Esq. Presented
by the Governors.

Archives du Museum d’ Histoire Naturelle. Tome III.
Liv. 3, et Tome II. Liv. 4. Presented by the Museum.

Remarks on Safety Lamps. By Doctor Reid Clanny,
H.M.R.I.A. Presented by the Author.

Transactions of the Royal Society of Edinburgh. Vol.
XV. Part 3. Presented by the Society.

Proceedings of the National Institution for the Promotion
of Science at Washington. D. C. for 1840 and 1842. Parts 1
and 2. Presented by Thomas Sewall, M. D., Professor of
Medicine in Columbia College, U. S.

Memoirs of the Chemical Society of London for 1841-38.
Vol. I. Presented by the Society.

Numismatic Chronicle. No. XXII. Presented by the
Numismatic Society.

Statistical Returns of the Dublin Metropolitan Police for
1842. Presented by the Commissioners,

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1843. No. 42.

November 13.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Dr. Allman drew the attention of the Academy to cer-
tain undescribed peculiarities in the anatomy of Anthoce-
phalus, a genus of Entozoal worms. The points especially
dwelt upon by Dr. Allman were the remarkably definite ar-
rangement of the hooks with which the proboscides are fur-
nished, and the singular apparatus destined to effect the
retraction and exsertion of the latter organs. The probos- _
cides were described as communicating each with a distinct
tube, which extending through the entire length of the ani-
mal, terminates posteriorly in an oval dilatation, with thick-
ened walls. The retraction of the proboscides consists in
an inversion, by which they become invaginated in the tu-
bular appendage. This invagination is effected by means of
a muscular filament, which is attached by one extremity to
the internal surface of the cul de sac of the proboscis, and
may be thence traced through the tube as far as the oval
body in which the latter terminates.

The mode by which the exsertion of the proboscides is
effected would appear to be as follows:—These organs,
together with their tubular prolongation through the ver-
micular body of the Entozoon, are filled with a transparent
fluid, which during the inversion of the proboscides is ex-

VOL. Il. 2P

424

pelled into the more posterior parts of the tubular prolon-
gations, and into the oval bodies in which these terminate.
Mr. Bergin had pointed out to Dr. Allman the existence of
muscular fibres in the walls of the oval dilatations. The
contraction, therefore, of these muscles, will cause the con-
tained fluid to impinge upon the inverted extremity of the
proboscis, which will thus be forced outwards, and the pro-
boscis injected with the fluid. The source of this fluid would
appear to be in the oval bodies themselves, whose structure
is, in all probability, glandular, and which, besides possessing
a contractile power, by which the contents of their cavities
are expelled, would seem also to be the secerners of the fluid
which plays so important a part in the protrusion of the
proboscides.

The Chair having been taken pro tem. by the Rev. H.
Lloyd, D. D., Vice-President,

The President read a paper on a new gating of Imagi-
nary Quantities, connected with a theory of Quaternions.

It is known to all students of algebra that an imaginary
equation of the form 27= —1 has been employed so as to
conduct to very varied and important results. Sir Wm. Ha-
milton proposes to consider some of the consequences which
result from the following system of imaginary equations, or
equations between a system of three different imaginary quan-
tities :

= Paii=—aA; (a)
pk, opie 45s Wet S75 (B) ©
jiz—k, kj=-i, tha=-j; ©

no linear relation between 2,7, i being supposed to exist, so
that the equation
2= 4,
in which
Q=wtixetyythks,
Yaw + ia +ijy + ke’,

425

and w, x, y, 2, w’, x’, y’, 3’ are real, is equivalent to the four
separate equations,
CS CRC ee RS ate
Sir W. Hamilton calls an expression of the form @ a qua-
ternion; and the four real quantities w, x, y, z he calls the con-
stituents thereof. Quaternions are added or subtracted by
adding or subtracting their constituents, so that
etdv=uwtw tie@te)tiyty) +42 +2’).
Their multiplication is, in virtue of the definitions (a) (B) (c),
effected by the formulz
ad = Qe! = ww" + ia! + jy! + ke",
w'=ww' —xx'—yy’—s2', |
e's we' +aw'+y2 —3y’,
y! = wy byw +22 — we,
ewe’ +euw+ay—yn’, 3}
which give
w!? + al? + y/? + 2/? — (w? +2? + y? +2”) (w?+a?+y” a 2”),

(D)

and therefore
ml! = ue’, (z)
if we call the positive quantity
b= VEO EP ES

the modulus of the quaternion @. The modulus of the pro-
duct of any two quaternions is therefore equal to the product
of the moduli. Let

w= cos 0,

£2 =psin 0 cos ¢,

y = wsin @ sin ¢ cosy,

z = psinO sing sind;

|
(F)
J

then, because the equations (D) give
ww"! + aw’ a! 4 yy" + e/a! = w (w”? + a? + y+ a”);
ww! + val’ — yy +e" = w! (w? + a? ty? + 2);
2PR2

426
we have

cos 6’ —=cos @ cos 6’ — sin @ sin &’ (cos¢ cos’ + sing sin ¢’ cos ( —w’)),
cos? =cos6’ cos 0” + sin 0’ sin 8” (cos¢’ cosd” + sin @’ sing” cos wv} (G)
cos @’ = cos 0" cos 0 + sin 8" sin 9 (cos @” cos + sin p” sin cos ('""— p)).
Consider x, y, = as the rectangular coordinates of a point

of space, and let r be the point where the radius vector of
x,y, 2 (prolonged if necessary) intersects the spheric surface
described about the origin with a radius equal to unity; call
R the representative point of the quaternion @, and let the
polar coordinates @ and y, which determine rR upon the
sphere, be called the co-latitude and the longitude of the re-
presentative point R, or of the quaternion @ itself; let also “
the other angle 6 be called the amplitude of the quaternion ;
so that a quaternion is completely determined by its modulus,
amplitude, co-latitude, and longitude. Construct the repre-
sentative points r’ and r”, of the other factor @’, and of the
product @”; and complete the spherical triangle rr’ R”, by
drawing the arcs RR’, R’R”, RK’ R. Then, the equations (4)
become

cos@” = cosO cos’ — sin®@ sin@’ cosRR’,

cos@ = cos cos 0” + sin @ sin 0” cos R’R”,

cos 6’ =cos0”cos@ + sin@’sin9 cosr’R,

and consequently shew that the angles of the triangle rr’ x”
are

R= 0, URS 6) RS ar; (a)
these angles are therefore respectively equal to the ampli-
tudes of the factors, and the supplement (to two right
angles) of the amplitude of the product. The equations (D)
show, further, that the produci-point Rr” is to the right or
left of the multiplicand-point Rr’, with respect to the mul-
tiplier-point R, according as the semiaxis of + 2 (or its in-
tersection with the spheric surface) is to the right or left of
the semiaxis of + y, with respect to the semiaxis of + x:
that is, according as the positive direction of rotation in
longitude is towards the right or left. A change in the

427

order of the two quaternion-factors would throw the pro-
duct-point rk” from the right to the left, or from the left to
the right of rR’.

It results from these principles, that if rr’R” be any
spherical triangle; if, also, a 3 y be the rectangular coordi-
nates of rR, a’ 3’ y’ those of Rr’, and a” 3” y” of rR", the centre
of the sphere being origin, and the radius being unity ; and
if the rotation round +2 from + y to +3 be of the same
(right-handed or left-handed) character as that round R from
R’ to rR”; then the following formula of multiplication, ac-
cording to the rules of quaternions, will hold good:

{cosr+(éat+jB+hy)sinr} {cosr’+(ia’ +jP’+hy’) sink’ }
= — cosr”+(ta”+ 7B" +hy”) sink”. (1)
Developing and decomposing this imaginary or symbolic
formula (1), we find that it is equivalent to the system of the
four following real equations, or equations between real
quantities :
—cosR” = cosR cosk’ —(aa'-+ BB’ + yy’)sinRsinR’;
a” sink” = asinR cosr’ + a’ sink’ cosr + (By’ — yf’) sinksink’ ;
sin” = B sink cosr’ + sink’ cosk + (ya’— ay’) sinRsinr’; (k)
y" sink” = y sink cosr’ + y’sinr’ cosr + (a 8’ — Ba’) sink sink’.
Of these equations (x), the first is only an expression of the
well-known theorem, already employed in these remarks,
which serves to connect a side of any spherical triangle with
the three angles thereof. The three other equations (x) are
an expression of another theorem (which possibly is new),
namely, that a force = sinr”, directed from the centre of
the sphere to the point Rr”, is statically equivalent to the sys-
tem of three other forces, one directed to r, and equal to
sink cosR’, another directed to rR’, and equal to sin R’ cos R,
and the third equal to sink sinr’sinRkR’, and directed to-
wards that pole of the arcrr’, which lies at the same side of
this arc as R”. It is not difficult to prove this theorem other-
wise; but it may be regarded as interesting to see that the
four equations (Kk) are included so simply in the one formula

428

(1) of multiplication of quaternions, and are obtained so
easily by developing and decomposing that formula, accord-
ing to the fundamental definitions (a) (B) (c). A new sort of
algorithm, or calculus, for spherical trigonometry, appears to
be thus given, or indicated. And by supposing the three
corners of the spherical triangle rr’ Rr” to tend indefinitely
to close up in that one point which is the intersection of the
spheric surface with the positive semiaxis of 2, each coordi-
nate a will tend to become = 1, and each # and y to vanish,
while the sum of the three angles will tend to become = 7;
so that the following well known and important equation in
the usual calculus of imaginaries, as connected with plane
trigonometry, namely,

(cosR +-ésin R) (cosR’ + isinr’) = cos(R-++R’) + Zsin(R +R),

(in which 2? = — 1), is found to result, asa limiting case, from
the more general formula (1).

In the ordinary theory there are only two different square
roots of negative unity (+ ¢ and — 2), and they differ only
in their signs. In the present theory, in order that a qua-
ternion, w+72x2 + jy + kz, should have its square = — 1,
it is necessary and sufficient that we should have

w=0, @4+7/4+2=—41;
we are conducted, therefore, to the extended expression,

Y —1 =icos¢+/sin¢ cosy +h sing siny, (L)
which may be called an imaginary unit, because its modulus
is = 1, and its square is negative unity. To distinguish one
such imaginary unit from another, we may adopt the nota-
tion,

i, = ia + 78 + ky, which gives 2, = — 1, (L’)
R being still that point upon the spheric surface which has

a, 9, y (or cos ¢, sing cosy, sing siny) for its rectangular
coordinates; and then the formula of multiplication (1) be-

429

comes, for any spherical triangle, in which the rotation round
R, from R’ to R”, is positive,
(cos R+é, sin R) (cos R’ + Z, Sin R’) = — cosR” +2, sink”. (1’)
If Pp” be the positive pole of the arc rx’, or the pole to
which the least rotation from r’ round R is positive, then the
product of the two imaginary units in the first member of
this formula (which may be any two such units), is the fol-
lowing :
dp tp! = — COSRR’+ Zp Sin RR’; (m)
we have also, for the product of the same two factors, taken
in the opposite order, the expression
Zn 2, = — COSRR’ — Zp SINRR’, (x)
which differs only in the sign of the imaginary part; and
the product of these two products is unity, because, in gene-
ral,
(w + ix + jy +hz) (w—ia—jy—ks)=w'?+a°+y'?+2"; (0)
we have, therefore,
Pte Oye Ol (P)
and the products 7,2, and iy 7, may be said to be rectprocals

of each other.
In general, in virtue of the fundamental equations of de-

finition, (A), (8), (c), although the distributive character of
the multiplication of ordinary algebraic quantities (real or
imaginary) extends to the operation of the same name in the
theory of quaternions, so that
Q(e’ +e”) = ee’/+aQ”, &e.,
yet the commutative character is lost, and we cannot gene-
rally write for the new as for the old imaginaries,
aq = QQ,

since we have, for example, jz = — ij. However, in virtue of
the same definitions, it will be found that another important
property of the old multiplication is preserved, or extended

4:30

y

to the new, namely, that which may be called the associative
character of the operation, and which may have for its type
the formula
Qa. QQ”. ow. Ql’ _— QQ’. Q” Ql” Qi’:
thus we have, generally,
a. ea!’ = aa’. Q", (Q)

Q. Q’ QQ!” = eQ’. Q” Q!”’ =e Q’Q!. als (Q’)
and so on for any number of factors; the notation @Q’ 9”
being employed to express that one determined quaternion,
which, in virtue of the theorem (@), is obtained, whether we ~
first multiply @” as a multiplicand by @’ as a multiplier, and
then multiply the product @’@” as a multiplicand by @ as a
multiplier ; or multiply first @ by @, and then Q” by ea’.
With the help of this principle, we might easily prove the
equation (p), by observing that its first member = ?,%y t =
—G&=— 1.

In the same manner it is seen at once that

dp dp . dg! dau . agi din «eee Oss) de — (— is (P’)

whatever 2 points upon the spheric surface may be denoted
by R, RB’, R%5 R/”,... R™—): and by combining this principle
with that expressed by (™), it is not difficult to prove that
for any spherical polygon, rr’...R"—"), the following for-
mula holds good :
(cosR + @ sin R) (cosR’ + éy sink’) (cosR” + ?yy sin R”)
»e(cosrx@) + i sinrk@—) =(—1)”, (R)

which includes the theorem (1’) for the case of a spherical
triangle, and in which the arrangement of the points may
be supposed, for simplicity, to be such that the rotations
round R from Rk’ to R”, round R’ from Rr” to rR”, and so on,
are all positive, and each less than two right angles, though
it is easy to interpret the expression so as to include also the
cases where any or all of these conditions are violated.
When the polygon becomes infinitely small, and therefore

431

plane, the imaginary units become all equal to each other,
and may be denoted by the common symbol 7; and the for-
mula (R) agrees then with the known relation, that
w7—R+7—RB/+7—R" 4+... $7 —R"")) = 27.

Again, let r, rR’, R” be, respectively, the representative
points of any three quaternions Q, Q’, a”, and let R,, R,, R,
be the representative points of the three other quaternions,
QQ’, a’Q”, e/a”, derived by multiplication from the former ,
then the algebraical principle expressed by the formula (@)
may be geometrically enunciated by saying that the two
points r, and r, are the foci of a spherical conic which
touches the four sides of the spherical quadrilateral Rr’R’R,,,;
and analogous theorems respecting spherical pentagons and
other polygons may be deduced, by constructing similarly
the formule (@’), &c.

In general, a quaternion Q, like an ordinary imaginary
quantity, may be put under the form,

Q= p(cosé + (—1)3 sin#) = w + (—1)*r, (s)

provided that we assign to (—1)*, or VY —1, the extended

meaning (L), which involves two arbitrary angles; and the

same general quaternion @ may be considered as a root of a
/ quadratic equation, with real coefficients, namely,

Q’—2we+p =0, (s’)
which easily conducts to the following expression for a quo-
tient, or formula for the division of quaternions,

Q!§ 2w—ea
qo! Q”’ — = = ar (s”)
« Q he

I
F Q F pes
if we define Q~'Q" or 7 to mean that quaternion Q’ which
gives the product @”, when it is multiplied as a multiplicand
by @ asa multiplier. The same general formula (s”) of di-

vision may easily be deduced from the equation (0), by writing
that equation as follows,

432

_ w—tax—jy—kz Ps he 4)
“wEeppee ©)
or it may be obtained from the four general equations of
multiplication (p), by treating the four constituents of the
multiplicand, namely, w’, x’, y’, 3’, as the four sought quan-
tities, while w, x, y,2, and w”, x” y”, #”, are given; or froma
construction of spherical trigonometry, on principles already
laid down.

The general expression (s) for a quaternion may be raised
to any power with a real exponent q, in the same manner as

(w+ ia + jy + kz)

an ordinary imaginary expression, by treating the square
root of — 1 which it involves as an imaginary unit 7, having
(in general) a fixed direction; raising the modulus mp to the
proposed real power; and multiplying the amplitude 0, in-
creased or diminished by any whole number of circum-
ferences, by the exponent g: thus,

(u(cos 8+ i, sin 8))1 = p41 (cos q (0+ 2n7)+ insing (0+ 2nz)), (7)
if g be real, and if x be any whole number. For example, a

quaternion has in general two, and only two, different square
roots, and they differ only in their signs, being both included

in the formula, ; 4

(u(cos 0+ i,sin 8))? = 1(cos G +nm)+2,sin Gt nn)), (T’)
in which it is useless to assign to m any other values than 0
and 1; although, in the particular case where the original
quaternion reduces itself to a real and negative quantity, so
that 0 =z, this formula (7’) becomes

(—pi= pti, or simply (“Wis wi, (2)

the direction of 2, remaining here entirely undetermined; a
result agreeing with the expression (L) or (x’) for Y—I. In
like manner the quaternions, which are cube roots of mary
are included in the expression,

A 2n7 ae es
13 = cos a + 7, sin "gr Cae),

433

é, denoting here again an imaginary unit, with a direction
altogether arbitrary.
If we make, for abridgment,

2
FQ=14 T+ + pogt ke. (v)

the series here indicated will be sii convergent, whatever
quaternion @ may be; and we can always separate its real
and imaginary parts by the formula,

S (wtir) =f (w) (cosr +% sinz); (v’)
which gives, reciprocally, for the inverse function f—', the
expression

S—"(u(cos@ + é, sin6)) =logu+2,(0+2n7), (v”)
w being any whole number, and logy being the natural, or
Napierian, logarithm of yu, or, in other words, that real quan-
tity, positive or negative, of which the function f is equal to
the given real and positive modulus y. And although the
ordinary property of exponential functions, namely,

F(2) -S@) = fare),
does not in general hold good, in the present theory, unless

the two quaternions @ and Q’ be codirectional, yet we may
raise the function f to any real power by the formula

(Fo + iar)! =f(qw + int + 2nm)), (0)
which itis natural to extend, by definition, to the case where
the exponent g becomes itself a quaternion. The general
equation,

Qf = Q/; (v)
when put under the form
(Pw tian) = f (wl + t7), (v’)
will then give
gw! ity (9 = fu ia (r+ 2n7)} v")
w+ (r+ nz)? :

and thus the general expression for a quaternion g, which is

q=

434

one of the logarithms of a given quaternion Q’, to a given base
Q,, is found to involve two independent whole numbers and
n’, as in the theories of Graves and Ohm, respecting the ge-
neral logarithms of ordinary imaginary quantities to ordinary
imaginary bases.

For other developments and applications of the new
theory, it is necessary to refer to the original paper from
which this abstract is taken, and which will probably appear
in the twenty-first volume of the Transactions of the Aca-
demy.

November 30. (Stated Meeting.)

REV. H. LLOYD, D.D., Vice-President, in the Chair.

The Rev. Dr. Todd, V.P., presented to the Academy, in
his name and that of Mr. O’Donovan, a volume containing
tracings made from Irish MSS. preserved in the College of
St. Isidore at Rome, by the Rev. Dr. Lyons, who had sent
them from Rome, some to Mr. O’Donovan, and the re-
mainder to Dr. Todd.

The thanks of the Academy were voted to Mr. O’Donovan
and also to the Rev. Dr. Lyons, for the important service
he has rendered to Irish literature, by making known the
existence of these MSS.

The Rev. Dr. Todd made some remarks on the progress
of the Catalogue, made by Mr. Eugene Curry, of the Irish
MSS. in the Library of the Academy.

The miscellaneous character of the MSS., almost every
volume of them containing tracts or poems, wholly uncon-
nected with each other, rendered it impossible to attempt
any previous classification. Mr. Curry, therefore, took the
MSS. in the order in which they stood on the shelves of the
Library, hoping that all the important objects of a classifica-

435

tion might be attained by the means of proper Indexes after
the work is completed.

The method pursued was to give a description of the
contents of each volume, enumerating the several tracts of
which it consists, describing its state of preservation, no-
ticing, as far as possible, its defects or imperfections, and
identifying, whenever it could be done, the handwriting of
the scribe or scribes by whom it had been written. Particular
attention has been paid to the history of every important
MS. ; the quotations made from it by historians or lexi-
cographers have been verified, and, where practicable, the
various hands through which it has passed, and the means
by which it became the property of the Academy, have been
accurately detailed and recorded.

In this way many opportunities have occurred of correcting
mistakes which have been made by various writers on Irish
subjects—mistakes, which must always be numerous in the
history of a people, whose ancient literature is still in manu-
script, and in a language which is every day becoming more
obsolete and obscure. These mistakes Mr. Curry has always
corrected with temper, and with due allowance for the diffi-
culties under which the authors to be corrected must neces-
sarily have laboured; although it must be confessed that
sometimes blunders may be found of a nature well calculated
‘to try the patience or rouse the indignation of an Irish scholar.

Another object of great importance which Mr. Curry has
kept steadily in view during the progress of the Catalogue,
has been the noticing of other copies of the tracts or poems
described, whenever the existence of such copies was known
to him: and his accurate acquaintance with the contents of
the Irish MSS. of Trinity College, and those in the posses-
sion of Messrs. Hodges and Smith,* the only two great col-
lections accessible to him for this purpose, rendered Mr.
Curry peculiarly well qualified for such a task.

* Since purchased by the Academy.

436

In reference to the history of the MSS., of such of them,
at least, as are of any high antiquity, it was of great im-
portance to collect together the numerous memoranda,
short scraps of poetry, dates, signatures, and other entries,
which are frequently to be found on the margins of MSS.
These are often mere scribbling, and often written from pure
wantonness, or for the purpose of trying a pen; but they
very frequently contain information of singular interest,
shewing who were the ancient owners or possessors of the
MS., and sometimes giving facts and dates of which we have
no other record. A most remarkable example of the value
of these apparently trifling scribblings will be found in Mr.
Curry’s account of the Leabhar Breac, upon whose history
the most important light has been thus thrown.

The autograph volume of the Four Masters, which is
one of the glories of the Academy’s Library, may also be
mentioned as a MS., whose history Mr. Curry’s researches
have greatly illustrated. By a comparison of it with the MS.
(also an autograph) in the Library of Trinity College, Mr.
Curry has succeeded in identifying the handwritings of its
different compilers, and to assign to each the portion of these
Annals which he appears to have compiled, or at least to
have transcribed.

When any document occurred of peculiar interest, as an
historical tale, or ancient deed, or singular narrative, Mr.
Curry has very generally given an abstract of its contents.
This has been sparingly done, from a wish to avoid swelling
the Catalogue to too great a bulk; but it is of more im-
portance than it might seem to be at first view, especially if
the Catalogue should ever be published, as furnishing to those
who are at a distance, the means of identifying the works
described with MSS. in other collections.

Dr. Todd having read some extracts from Mr. Curry’s
Catalogue in illustration of the foregoing remarks, concluded
by stating, that about five volumes still remained to be cata-

437

logued, including the important volumes, the Books of Lecan
and Ballymote, whose examination would take some months,
and that the Council have therefore been under the necessity
of applying to the Academy for a further grant of money to
enable Mr. Curry to complete the work.

It was resolved by the Academy that the sum recom-
mended by the Council be granted for this purpose.

December 11.
SIR Wm. R. HAMILTON, LL.D., President, in the Chair.

Matthew Dease, Esq., William M‘Doughall, Esq., Sir
Montague Chapman, Bart., James H. Pickford, M. D., Ed-
ward Bewley, M.D., and James S. Eiffe, Esqrs., were elected
Members of the Academy.

Professor Kane read a paper on the Chemical Compo-
sition of the plants of Flax and Hemp.

In those plants which are cultivated for the purpose of being
ultimately employed as food, it is found that certain consti-
tuents are withdrawn from the soil, partly of an organic and
partly of an inorganic character, which give to the plant, or
to certain portions of it, the constitution that adapts it for
sustaining the animal organism. Thus nitrogen, alkalies,
and lastly, phosphates, &c., are found as components of
plants, and the value of the crop yielded by a certain surface
of ground is proportional, generally speaking, to the materials
which the crop has taken up. If, therefore, wheat, or oats,
or potatoes exhaust a soil, the agriculturist does not suffer
thereby, for he is paid for the materials of which they have
exhausted it, and when he replaces that loss of material by
fresh manure he but invests a certain capital, to be delivered
at a profit in the next season.

Many plants not employed as food, but ancillary to our
civilization as luxuries, or as utilized in the arts, are similarly

eRe

438

circumstanced. ‘Thus when indigo or tobacco is grown, the
object is to obtain the greatest possible development of the co-
louring or of the narcotic principle. For this purpose, elements
are necessary of which the soil is thereby deprived, but the
impoverishing of the soil is paid for, by its materials being
sold as the valuable portion of the plant. In such cases,
therefore, to sustain the fertility of the soil, a continued sup-
ply, from external sources, of the materials which the plants
take up is required. The farmer must supply in the manure
the elements which he sends to market in the grown plants.

Dr. Kane then proceeded to point out that this principle
was limited as to certain classes of plants, by the fact, now
clearly established by the concurrent investigations of vege-
table physiologists and of chemists, that certain vegetable
substances, and those of high importance to mankind, were
not formed of materials abstracted from the soil, but were
produced by the vital action of the plant upon the consti-
tuents of the atmosphere. This class of bodies he charac-
terized as being constituted, generally, of carbon, united with
hydrogen and oxygen in the proportions which form water.
The carbonic acid of the atmosphere, with the watery vapour
constantly existing in it, supplies the elements of sugar, gum,
starch, and ligneous fibre, and the oxygen of the carbonic
acid, evolved by the vital action of the plants, tends, as it is
well known, to ameliorate the air we breathe. When, there-
fore, we take the sugar, or the woody fibre of a plant, we
have a material, formed, as to its elements, independent of
the soil. For its formation is required a plant in healthy
vegetation, and for the plant to be in healthy vegetation, it:
may require to abstract from the soil various materials, so that
the crop may actually be of a highly exhausting nature. Still
those materials do not go to the sugar or to the fibre; they
exist in other portions of the plant; and if the sugar or fibre
be the valuable portion of the crop, as in reality usually oc-
curs, the elements which render its production costly are re-
jected, and let to waste; they do not subserve any future

439

useful purpose, although nothing should be easier than to
apply them thereto.

Such is actually, according to Dr. Kane’s idea, the con-
dition of the growth of one plant of the highest importance to
agricultural industry in Ireland—that of flax, and also of ano-
ther, which although not now grown here, has been grown with
success, and, as he conceives, might still be cultivated with con-
siderable advantage, the hemp. In flax and hemp the valuable
portion of the plant is ligneous fibre ; the purer this fibre is, the
more its value increases; yet the pure fibre contains no ele-
ment derived from the soil. It is well known to be produced
solely by the atmospherical constituents. Hence the intense
exhausting nature of the flax and hemp crops, which makes
them be dreaded by agriculturists, notwithstanding the high
money value of the crops, arises, according to Dr. Kane,
from causes of which the effects may be obviated by attention
to the true conditions of the growth and composition of the
plants, so that those fibre-crops, such as flax and hemp,
from being the most exhausting and expensive, may be ren-
dered the least injurious to the land, and perhaps amongst
the cheapest that can be grown.

As the chemical composition of these plants had never
been examined, Dr. Kane devoted himself to the determina-
tion, as well of their organic as of their inorganic constituents,
and from an extensive series of analyses, of which the de-
tails are given in the memoir, arrived at the following

results :

Composition of the stem of hemp, dried at 212°. F.
Garhanse iota ee se) Seis es BOLO
lip d romenii rests re hs inl) a Oe
Oxysems for ai fa Ok ae
Nittrogeny 6/0 i guia Sire. et ae
A SHESS Ae 5 Pe etree Ae tea as

100.00

VOL. Il. 2a

440

Composition of the leaves of hemp, dried at 212°.

Carbon) is\)- 06 6s ea 2 ae oO

Hydrogen* °°). 0. 2 2 og

Nitrogen: % 201.) Sa ae ee

Oxygen i) oP ee) ee ROD

Ashes )). hres SH. SO es cee OO
100.00

The ashes of the hemp plant were found to consist of
Potash 05) ey ee) ee oe ee

Soda sie sh ibsts we ien meted 72
HAMES Wu. wer eadeoutliouh ilar ge mp ace
Miaonesia, (<a) li.) oe ES

Naraniay fre.) its SP ee. ay
Silica ges th og. Oak: COMES ES Geis
Phosphoric acid . 3) 5.9. 3.22
Sulphuric acid iis Be ee ei Lalo
Chlorine! ere Ae a Oe AGS
Garboniciacid 2% A974 25 es SO SILO

100.00

Dressed hemp fibre was found to give but 1.4 per cent.
of ashes, when dried at 212°. Its organic composition need
not be given, as it is identical with that of ordinary woody
fibre, which is well known. It therefore contains no ni-
trogen.

The characteristic constituents of the hemp plant are
seen to be nitrogen and lime. In these it is peculiarly rich,
and with these it is the duty of the agriculturist abundantly
to supply it.

When hemp is steeped in order to separate the fibrous
bark from the internal stem, it is known that the water dis-
solves certain substances out of the plants, and thereby ac-
quires narcotic properties. Dr. Kane evaporated a quantity
of the hemp liquor to dryness, and analyzed the extract so

441

obtained, in order to trace what action the steeping had ex-
erted on the plant. He found the composition of the hemp
extract, dried at 212°, to be,

Gemeee te he ste tose eee eee
Tah Oi, a ata lae dae imei amen ts 151)
Witrocen ee 88
Speech ss es Loe
JN Coho onda ldap plague manent ieee gare: 2 BE 8)

100.00
If we exclude the ashes, the organic part consisted of

GABOR mics 5) a= firitt Be A wan ee ODOO
Pv aTOse I 4 ‘ay. Wivig, pleas ~ uni

NEO E Tes su, 2s opahinge Bible Ad afk Se
Oxcrres 5 ond ois} hgedae See aOe
100.00

This composition approaches to that of the azotized ani-
mal substances, and surpasses the animal manures usually
sold. The water in which hemp has been steeped contains
thus most of the nitrogen of the plant, and if poured over
the soil should serve efficiently to restore its fertile powers.

The ashes of the hemp extract require also to be noticed,
for the plant, in steeping, gives up to the water especially its
soluble constituents. The ashes of the leaves of hemp con-
tain in 22 parts only 1.77 soluble in water, or 8.05 per cent.,
whilst the ashes of the hemp extract contain in 49.2 parts,
29.70 parts soluble in water, or 60.4 per cent. Thus almost
all the alkaline constituents of the ashes are dissolved out
by the water, whilst the earthy materials remain associated
with the residual portions of the stem.

Dr. Kane next examined the stem, as it remains after
treatment for the fibre, by steeping and peeling. Dried at
212° this hemp residue consisted of

2Q2

442

Gasbanii® eo So eR G80

Hydrogen)... i Oe AES ee As
Nitrogen >. 3070); See aes 43
Oxy Pe ics en RRS seiner. see
Ashes. ict ys wees oat an ee

100.00

The ashes contained but a trace of alkali, and itis seen
that the nitrogen has almost disappeared.

From these researches it is plain that, by the quantity of
nitrogen, of phosphoric acid, of potash, of magnesia, and of
lime, which the hemp takes from the soil, it must be, as ex-
perience proves it, a highly exhausting crop; but as the ma-
terials so abstracted are not found in the valuable fibre, but
in the residual stem, the chaff, and the steeping liquor, all
these are available for the purpose of restoring to the soil
what had been taken up, and in fact, if it were possible to
carry on the processes of the preparation of the fibre without
loss, the same nitrogen and inorganic constituents might, as
it would appear from these chemical inquiries and from phy-
siological researches, serve for any number of successive
crops of hemp; the fibre alone, generated at the expense of
the atmosphere, being sent out and sold, and thus the crop
be absolutely deprived of all exhausting quality to the soil.

Dr. Kane’s inquiries regarding the flax plant were of a
precisely similar character to those described already in the
case of hemp, and have led him to similar conclusions affect-
ing the practical culture of this important plant. The gene-
ral results of his analyses are as follows:

Stem of flax dried at 212°; the plant had its usual
amount of leaves, but the seed vessels had not ripened.

Cambon. % 413 2a 5 a Sa
Hydrogen. -ganiaaip 6G ioe
Nitrogen.) q,veeuen. i 2 es oe
Oxygen) ki Sep ariis teh ME ABD
Ashes: .\0o> Tie teal aya. B00

100.00

nT a

443

There is a great difference here shewn between the com-
position of the plants of hemp and flax, though they resemble
each other so much in their uses. The hemp contains a
large amount of nitrogen, the flax very little. The hemp
contains more oxygen than would form water with the hy-
drogen. Flax, on the contrary, contains an excess of hydro-
gen. The difference is also remarkable in the composition
of the ashes.

The ashes of the flax plant consist of

Paibash er Her Po Sa Se ee gees
Sh te aA eM SY SAR tet oS Be
eg te EES ee A. Pr
Miaonesia 70% 2) Foe Pe Fe
manning! .) Soe ee moe EGS
Silty te PSS er, aha nn Se ace
Phosphoricacid . . . . . . 10.84
pulphuric acid 0)... ee B6p
Chiorme’ Se ee Ne a
Carhonie acid’ 8°) SO AS.

100.00

The great quantity of lime which characterized the hemp
here disappears, and the peculiar quality of the ash is the
presence of soda and potash in equal quantities, much mag-
nesia, and especially the large proportion of phosphoric acid.
Dr. Kane has not met with any analysis of the ash of a
plant yielding the same amount of phosphoric acid, and
hence the exceedingly exhausting power of the flax crop is
easily understood.

Dr. Kane notices in this ash of flax, that the potash,
soda, sulphuric acid, and chlorine are in a very simple rela-
tion to each other, the numbers given above coinciding
closely with those of two atoms each of sulphuric acid and
chlorine, six of potash, and nine of soda. So that if (in the
ash) all the soda be taken as carbonate, the potash will be

444

divided equally among sulphuric, muriatic, and carbonic
acids. Dr. Kane thinks that this simplicity is probably acci-
dental, but suggests it for attention in subsequent analyses
of flax ashes from other localities.

The steeping of flax to loosen the coat of fibrous bark is
accompanied by the solution of certain constituents of the
plant, as in the case of hemp. The extract of the steeping
water was analyzed ; it yielded, dried at 212°,

Carbon’ . 1. % 0. Way enh: BeOS
Hiydrogen .. . ©. 0.06. 0 ae
Nitrogen |... US Ga uch. . mene
Oxyeen se 5 6.0 UL Ra Oca
Bishies oes, er enel ee ek

100.00

The organic part of this extract consisted therefore of

Carbone. 46.15 ose BR cep ees ce Oe
PL ydmopeny 6 jai e/a sh he ete pee
Nitrogen isi. aie. Coli pen Se
Oxyaen's5 sek emt: ware OOO,

100.00

Here, as in the case of hemp, the nitrogen of the plant is
concentrated, but the total quantity of nitrogen is not half so
great. In the ash of the extract, as in the case of hemp, the
soluble alkaline matters also preponderate. ‘The ashes of
the plant yielded 33.90 per cent. of matters soluble in water ;
whilst the ashes of the flax-steep extract yield 60 per cent.
of matters soluble in water. ‘The flax-steep is therefore rich
in all the materials necessary to produce a new generation of
plants; and Dr. Kane stated, as a satisfactory confirmation
of the views put forward in his memoir, that in many in-
stances where agriculturists have sprinkled land with the
water in which flax has been steeped, they have found it a
most active manure.

After the flax fibre has been removed from the rotted

445

stem, the residue, or chaff, was found to be composed as

follows:
Carbonssa ee fois see ae beremedB0-34

Iivdraeenss ius ssc vide tae dsBS
NMR GSHI ge.) Gee Se 24
Pipe R se. ii i) «ie 00 ys VOLS
ys Se Se GS Sa Cie ae ise Ce ee ne 9

100.00

This is almost identical in composition with the residual hemp
stem, and may therefore be applied to the same uses. Restored
to the soil with the steep water, it should give back all that
the crop of flax had taken from the grounds, and thus the
valuable fibre being generated by the atmosphere, the great
source of expense in the cultivation of the plant might be
removed, .

Dr. Kane finally placed before the Academy certain
tables, in which, taking the average quantity of produce from
a statute acre of fibre-crops and of food crops, and comparing,
from the data supplied by the analyses of Sprengel, Bous-
singault, and his own, the weights of materials of which the
soil is exhausted by each crop, it appeared that the fibre
crops were actually more exhausting than the food crops;
whilst the agriculturist profits by the materials that the food
crops take out of the ground, and the substances taken up
by the fibre crops from the soil are at present actually re-
jected as waste and valueless. Hence it is, as Dr. Kane
considers, of much interest to the agricultural industry of
Ireland that the views of economizing the residues of the
preparation of flax and hemp, put forward in his memoir, be
tested by practical men, as, if they be found correct, and that
those residues may be applied with success to prepare and
fit the soil for another crop, those fibrous plants will be
practically deprived of their exhausting qualities, and the
greatest disadvantage, under which their extensive cultivation
in this country labours, may be removed.

446

Professor Mac Cullagh gave an account of his researches
in the Theory of Surfaces of the second Order, in connexion
with a former communication which he had made to the Aca-
demy on the same subject. ‘These researches are contained
in the following paper.

ON THE SURFACES OF THE Seconp ORDER.

There is hardly any geometrical theory which more re-
quires to be studied, or which promises to reward better
whatever thought may be bestowed upon it, than that of
the surfaces of the second order. My attention was drawn
to it, many years ago, by the consideration of mechanical
and physical questions. In the dynamical problem of the
Rotation of a Solid Body, and in the investigation of the
properties of the Wave-Surface of Fresnel, I found, so long
since as the year 1829, that the ellipsoid could be employed
with very great advantage; while the discussion of these
questions, but especially of the former,* suggested pro-
perties of the ellipsoid and its kindred surfaces which I
might not otherwise have perceived. In this manner I
was led to consider systems of confocal surfaces, and thence
to notice the focal curves, which I discovered to be analo-
gous, in the theory of the surfaces of the second order, to
the foci in that of the plane conic sections. That theory
now began to interest me on its own account, and, guided
by analogy, I struck out the leading properties possessed
by the surfaces in relation to their focal curves; but the
interference of other matters prevented me from continu-
ing the inquiry. I had done enough, however, in this and

other parts of the theory, to open new views respecting
aN a Nl Ea

* The Theory of Rotation, here spoken of, was completed in the year 1831 ;
but, from causes which need not be mentioned at present, it was not pub-
lished. The investigations relative to Fresnel’s Waye-Surface will be found in
the Transactions of the Royal Irish Academy, vol. xvi. p. 65; vol, xvii. p. 241.
See also vol. xxi. p. 32, of the same Transactions.

447

it; and the results at which I had arrived seemed so fitted
for instruction, that when I was appointed Professor of
Mathematics in the University, I made them the subject of
the first lectures which I gave in that capacity, in the be-
ginning of the year 1836. Next year the heads of these
lectures were communicated to this Academy, in a paper of
which a very short abstract appeared in the Proceedings.*
The subject soon became a favourite one among the more ad-
vanced students in the University, who are, for the most part,
excellent geometers, and in the present Article very little
will be found which is not well known amongst them; very
little, indeed, which was not communicated to the Aca-
demy on the occasion just mentioned, or which may not be
gathered, in the shape of detached questions, out of the
Examination-Papers published yearly in the University Ca-
lendar. But as nothing has yet been published on the sub-
ject in a connected form, except the brief notice in the Pro-
ceedings of the Academy, and as mathematicians in other
countries attach some importance to researches of this
kind, and appear to be in quest of certain principles which
are familiar to us here, it seems proper to collect together
the chief results that have already been obtained, in order
that persons wishing to pursue these speculations may be
better able to judge where their inquiries should begin, and
in what direction further progress is most likely to be made.

PART I.—GENERATION OF SURFACES OF THE SECOND ORDER.

§ 1. The different species of surfaces of the second order
are obtained, as is usually shown in elementary treatises,
by the discussion of the general equation of the second de-
gree among three coordinates; but it is necessary that we
should also be able to derive these surfaces from a common
geometrical origin, if we would bring them completely within

* Proceedings of the Royal Irish Academy, vol. i. p. 89.

448

the grasp of geometry. Now as the different conic sections
may (with the exception of the circle) be described in plano
by the motion of a point whose distance from a given point
bears a constant ratio to its distance from a given right line,*
it is natural to suppose that there must be some analogous
method by which the surfaces of the second order may be
generated in space. Accordingly I have sought for such a
method, and I have found that (with certain analogous ex-
ceptions) every surface of the second order may be regarded
as the locus of a point whose distance from a given point
bears a constant ratio to its distance from a given right line,
provided the latter distance be measured parallel to a given
plane; this plane being, in general, oblique to the right line.
The given point I call, from analogy, a focus, and the given
right line a directrix ; the given plane may be called a direc-
tive plane, and the constant ratio may be termed the modulus.

To find the equation of the surface so defined, let the
axis of z be parallel to the directrix; let the plane of xy
pass through the focus, and cut the directrix perpendicularly
in A, the coordinates being rectangular, and their origin ar-
bitrarily assumed in that plane; and let the axis of y be pa-
rallel to the intersection of the plane of xy with the directive
plane, the angle between the two planes being denoted by ¢.
Then if we put x, y; for the coordinates of the focus, and
22, Y2 for those of the point A, while the coordinates ofa point
S upon the surface are denoted by 2, y, 2, the distance of
this last point from the focus will be the square root of the
quantity

(e—a) + (y—m) + 2°;

and if a plane drawn through S, parallel to the directive
plane, be conceived to cut the directrix in D, the distance SD
will be the square root of the quantity

* This method of describing the conic sections is due to the Greek geometers.
It is given by Pappus at the end of the Seventh Book.of his Mathematical Col-
lections.

449

(w— a2)? seo’ + (y—ye)” 3

so that, m being the modulus, the locus of the point S will be
a surface of the second order, represented by the equation
(z—m) + Ym) + 2° = mf (w— a»)’sec’p + (y—Yyo)’$, (1)
which, by making

A= 1—m’sec’9, B= 1—m’,

G = mx, sec’*o—a), H= mM Yyo—Yi, (2)

K = m? (x? sec? + ys’) — x — yr’,
may be put under the form

ax? + By? +3?+2Ge 4+ 2ny = K, (3)
showing that the plane of zy is one of the principal planes of
the surface, and that the planes of xz and yz are parallel to
principal planes.

Before we proceed to discuss this equation, it may be
well to observe that as it remains the same when ¢ is changed
into — ¢, or into 180°— 4, the directive plane may have two
positions equally inclined to the plane of xy, and therefore
equally inclined to the directrix. Indeed it is obvious
that, if through the point S we draw two planes making
equal angles with the directrix, and cutting it in the points
D and D’ respectively, the distances SD and SD’ will be
equal. Every surface described in this way has consequently
two directive planes; and as each of these planes is parallel
to the axis of y, their intersection is always parallel to one of
the axes of the surface. This axis may therefore be called
the directive axis. The directive planes have a remarkable
relation to the surface, as may be shown in the following
manner :—

Suppose a section of the surface to be made by a plane
which is parallel to one of the directive planes, and which
cuts the directrix in D; then the distance of any point S of the
section from the focus F will have a constant ratio to its dis-
tance SD from the point D; and, as the locus of a point

450

whose distances from the two points F and D are in a con-
stant ratio to each other, is a plane or a sphere, according as
the ratio is one of equality or not, it follows that the section
aforesaid will be a right line in the one case, and a circle in the
other. Hence it appears that all directive sections, that is,
all sections made in the surface by planes parallel to either
of the directive planes, are right lines when the modulus is
unity, and cércles when the modulus is different from unity.

Since the equation (3) is not altered by changing the
sign of ¢, or by changing ¢ into its supplement, we may sup-
pose this angle (when it is not zero) to be always positive
and less than 90°; for the supposition @ = 90° is to be ex-
cluded, as it would make the secant of ¢ infinite, and the
directive planes parallel to the directrix. In the discussion
of the equation there are two leading cases to be considered,
answering to two classes of surfaces. The first case, when
neither A nor B vanishes, gives the ellipsoid, the two hyper-
boloids, and the cone; the second, when either or each of
these quantities is zero, includes the two paraboloids and
the different kinds of cylinders.

§ 2. First Class of Surfaces.—When neither a nor B va-
nishes, we may make both e and u vanish, by properly as-
suming the origin of coordinates. Supposing this done, we
have

2 = m>x28ec’>, Y= mys, (4)
the equation of the surface being then
Ax’? + By? +2? = kK, (5)

in which the axes of coordinates are of course the axes of the
surface. When kis not zero, the surface is an ellipsoid or hy-
perboloid, having its centre at the origin of coordinates; when
k = 0, the surface is a cone having its vertex at the origin.

Eliminating x, y. from the value of k, by means of the
relations (4), we get

A B
Kees ay + joe! 3 (6)

l—a

a

451

and eliminating 2, y; in like manner, we get

K = A(1l—a)a.” + B(1—B)y2”; (7)
from which expressions it appears that, every thing else re-
maining, the focus and directrix may be changed without
changing the surface described. For in order that the sur-
face may remain unchanged, it is only necessary that K should
remain constant, since A and B are supposed constant. This
condition being fulfilled, the focus may be any point F whose
coordinates 2, y, satisfy the equation (6), and A (the foot of
the directrix) may be any point whose coordinates 22, yo
satisfy the equation (7); it being understood, however, that
when one of these points is chosen, the other is determined.
The locus of F (supposing k not to vanish) is therefore an
ellipse or a hyperbola,* which may be called the focal curve,
or the focal line; and the locus of A is another ellipse or
hyperbola, which may be called the dirigent curve or line:
the centre of each curve is the centre of the surface, and
its axes coincide with the axes of the surface which lie
in the plane of zy. Moreover, as the quantities 1 — a and
1 — Bare essentially positive, the two curves are always of
the same kind, that is, both ellipses, or both hyperbolas;
and when they are hyperbolas, their real axes have the
same direction. The directrix, remaining always parallel
to the axis of s, describes a cylinder which may be called
the dirigent cylinder.

Since, by the relations (4), the corresponding coordinates
of F and A have always the same sign, these points either
lie within the same right angle made by the axes of « and y,
or lie on the same axis, at the same side of the centre. And
as these relations give

A B
ry— X= bowen? y-Nn= ae (8)

* In the Proceedings of the Academy, vol. i. p. 90, it was stated inadver-
tently that “‘if we confine ourselves to the central surfaces, the locus of the
foci will be an ellipse.”

452

it is easy to see that the right line AF is a normal to the
focal curve; for the quantities x, — a, and yz — y; are pro-
portional to the cosines of the angles which that right line
makes with the axes of x and y respectively, while the values
just given for these quantities are, in virtue of the equation
(6), proportional to the cosines of the angles which the nor-
mal to the focal curve at the point F makes with the same
axes.

It may also be shown that if the directrix prolonged
through A intersect a directive plane in a certain point, and
if a right line drawn through F, parallel to the directrix,
intersect the same plane in another point, the right line join-
ing those points will be a normal to the curve described in
that plane by the first point.

§ 3. To find in what way the focal and dirigent curves are
connected with the surface, let the equations (5), (6), (7)
(when x does not vanish) be put under the forms

Uy ye pant) Sag

ick oun Ge @)
ay? ye boy Yo
—4++-=1, — +=] {10
Py a0 Po Tie: : ( )

so that the quantities P, @, R may represent the squares of the
semiaxes of the surface, and Pj, Q), Po, Qo the squares of the
semiaxes of the curves, these quantities being positive or ne-
gative, according as the corresponding semiaxes are real or
imaginary. ‘Then we have

K K
P= -, e=-, R=K;
A B
Pp; = P(1 — a), Q, = e(1l — B), (11)
P. _ P — . Q .
arise, pee 2 eau

whence it follows that

Pi)Pp = P*, 1 Qa = 2, (12)

453

and also that

P} = P—R, Q; = Q—R. (13)
From equations (12) we see that Pp, and P, have always the
same sign, as also Q; and Q,; and that, neglecting signs, the
semiaxes of the surface are mean proportionals between the
corresponding semiaxes of the focal and dirigent curves.
These curves are therefore reciprocal polars with respect to
the section made in the surface by the plane of xy; and it
would be easy to show that the points F and A are recipro-
cal points, or that a tangent applied at one of them to the
curve which is its locus has the other for its pole.

The focal curve, when we know in which of the principal
planes it lies, is determined by the conditions (13), and as it
depends on the relative magnitudes of the quantities P, Q, R,
it will be convenient to distinguish the axes of the surface,
with relation to these magnitudes. Supposing, therefore,
the quantities Pp, @, R to be taken with their proper signs,
as they are in the equation (9), that axis to which the
greatest of them (which is always positive) refers, shall be
called the primary axis; and that to which the quantity
algebraically least has reference, shall be termed the se-
condary axis; while the quantity which has an intermediate
algebraic value shall mark the middle or mean axis. Then,
since both Pp, and Q, will be negative, if rk be the greatest of
the quantities aforesaid, the focal curve cannot lie in the
plane ofthe mean and secondary axes. Its plane must there-
fore pass through the primary axis; it will be the plane of
the primary and mean axes, if R be the least of the three
quantities ; but the plane of the primary and secondary axes,
if R be the intermediate quantity. In the former case the
curve will be an ellipse, in the latter a hyperbola ; and we
shall extend the name of focal curves to both the curves so
determined, though it may happen that only one of them
can be used in the generation of the surface by the modular
method, as the method of which we are treating may be

454

called, from its employment of the modulus. A focal curve
which can be so used shall be distinguished as a modular fo-
cal ; but each focal, whether modular or not, shall be sup-
posed to have a dirigent curve and a dirigent cylinder con-
nected with it by the relations already laid down.

Since P, — @, = P— Q, the foci of a focal curve are the
same as those of the principal section in the plane of which
it lies, and they are therefore on the primary axis of the sur-
face. It will sometimes contribute to brevity of expression,
if we also give the name of primary to the major axis of an
ellipse and to the real axis of a hyperbola. We may then say
that the primary axes of the surface and of its two focal
curves are coincident in direction; and that (as is evident)
the foci of either curve are the extremities of the primary
axis of the other.

If k be supposed to approach gradually to zero, while a
and B remain constant, the focal and dirigent ellipses will
gradually contract, and the focal and dirigent hyperbolas will
approach to their asymptotes, which remain fixed. When k
actually vanishes, the surface becomes a cone; the two
ellipses are each reduced to a point coinciding with the ver-
tex of the cone, and each hyperbola is reduced to the pair of
right lines which were previously the asymptotes. The diri-
gent cylinder, in the one case, is narrowed into a right line ;
in the other case it is converted into a pair of planes, which
we may call the dirigent planes of the cone.

§ 4. We have now to show how the different kinds of sur-
faces belonging to the first class are produced, according to
the different values of the modulus and other constants
concerned in their generation.

I. When m is less than cos ¢, the quantities A, B, K, P,Q, R
are all positive, and Q is intermediate in value between eb and
rR. ‘The surface is therefore an ellipsoid, and its mean axis
is the directive. As the quantities 1—a and 1 —B are
always positive, the focal and dirigent curves are ellipses.

455

Here we cannot suppose kK to vanish, as the surface would
then be reduced to a point.

When ¢ = 0, that is, when the directive planes coincide
with each other, and therefore with a plane perpendicular to
the directrix, so that SD is the shortest distance of the point
S from the directrix, the surface is a spheroid produced by
the revolution of an ellipse round its minor axis, and the
focal and dirigent curves are circles.

II. When m is greater than unity, a and B are negative ;
and if k be finite, it is also negative; whence P and Q are po-
sitive, and R is negative. Also, supposing ¢ not to vanish,
Qis greater than p.- The surface is therefore a hyperboloid
of one sheet, with its real axes in the plane of ry; and the
directive axis is the primary. The focal and dirigent curves
are ellipses. But when ¢ = 0, the surface is that produced
by the revolution of a hyperbola round its imaginary axis,
and the focal and dirigent* are circles.

If k= 0, which implies, since a and B have the same
sign, that x, Yi, 22, Yy2 are each zero, the surface is a cone
having the axis of z for its internal axis; and the focal and
dirigent are each reduced to a point. The focus and di-
rectrix are consequently unique; the focus can only be the
vertex of the cone, the directrix can only be the internal axis ;
and the directrix therefore passes through the focus. The
directive axis, which coincides with the axis of y, is one of the
external axes; that one, namely, which is parallel to the
greater axes of the elliptic sections made in the cone by
planes perpendicular to its internal axis. This is on the
supposition that ¢ is finite; for, when ¢ = 0, the cone be-
comes one of revolution round the axis of z.

III. When ™ is greater than cos ¢, but less than unity,
we have a positive and B negative, and the species of the

* When the term dirigent stands alone, it is understood to mean a dirjgent
line.

VOL. Il. 2)

456

- surface depends on kx. It is inconsistent with these condi-
tions to suppose p = 0, and therefore the surface cannot, in
this case, be one of revolution. The value of k may be
supposed to be given by the formula

| eer

—(n—), (14)

which contains ye the relative coordinates of the focus and
the foot of the directrix, and is a consequence of the equa-
tions (6) and (8).

1°. Ifk is a positive quantity, the surface is a hyperboloid
of one sheet, with its secondary axis in the direction of x;
the primary axis, as before, is the directive, but the focal and —
dirigent are now hyperbolas.

2°. If kK is a negative quantity, the surface is a heen:
loid of two sheets, having its primary axis coincident with
that of z The secondary axis is the directive; the focal
and dirigent are hyperbolas.

igiesa at

* (a9 a x)? hi

3°. Ifx = 0, the surface is a cone, having the axis of x
for its internal axis; the directive axis being, as before, that
external axis to which the greater axes of the elliptic sec-
tions, made by planes perpendicular to the internal axis, are
parallel. The axis of = is the other external axis, which
may be called the mean azis of the cone, because it coincides
with the mean axis of any hyperboloid to which the cone is
asymptotic. As a and B have different signs, it is evident,
from the equations (6) and (7), that the focal and dirigent
are each a pair of right lines passing through the vertex,
each pair making equal angles with the internal axis. Two
planes, each of which is drawn through the mean axis and a
dirigent line, are the dirigent planes of the cone.

The corresponding focal and dirigent lines are those
which lie within the same right angle made by the internal
and directive axes; and since by the equations (6) and (8)
the value of k may be written

457

K = & (%— 1) +H (Y2—m): (15)
we see that, as K now vanishes, the right line joining corres-
ponding points F and A upon these lines is perpendicular to
the focal line. Of the two sides of the cone which are in
the plane of xy, one lies between each focal and its dirigent ;
and it may be inferred from the equations, that the tangents
of the angles which the internal axis makes with a focal
line, with one of these sides of the cone, and with a dirigent
line, are in continued proportion, the proportion being that
of the cosine of @ to unity. And hence it follows, that these
two sides of the cone, with a focal line and its dirigent, cut
harmonically any right line which crosses them.

§ 5. From this discussion it appears, that the ellipsoid and
the hyperboloid of two sheets can be generated modularly,
each in one way only, the modular focal being the ellipse
for the former, and the hyperbola for the latter; but that
the hyperboloid of one sheet can be generated in two ways,
each of its focals being modular, and each focal having its
proper modulus. The cone also admits two modes of gene-
ration,* in one of which, however, the focus is limited to the
vertex of the cone, and the directrix to its internal axis.

* The double generation of the cone, when its vertex is the focus, may be
proved synthetically by the method indicated in the Examination Papers of the
year 1838, p. xlvi (published in the University Calendar for 1839). Supposing
the cone to stand on a circular base (one of its directive sections), and to be cir-
cumscribed by a sphere, the right lines joining its vertex with the two points
where a diameter perpendicular to the plane of the base intersects the sphere,
will be its internal and mean axes. Thenif P be either of these points, V the
vertex, C the point where the axis PV cuts the plane of the base, and B any
point in the circumference of the base, the triangles PVB and PBC will be si-
milar, since the angles at V and B are equal, and the angle at P is common to
both triangles; therefore BV will be to BC as PV to PB, that is, in a constant
ratio. It is not difficult to complete the demonstration, when the focus is sup-
posed to be any point on one of the focal lines.

2Rr2

458

But when the hyperboloid of one sheet, or the cone, is a
surface of revolution, it has only one mode of modular ge-
neration. In cases of double generation, the directive planes
of course remain the same, as they have a fixed relation to
the surface. A modular focal, it may be observed (and the
remark applies equally to surfaces of the second class), is
distinguished by the circumstance that it does not intersect
the surface. The only exception to this rule are the focal
lines of the cone, which pass through its vertex. A focal
which is not modular may be called wmbilicar, because it
intersects the surface in the umbilics; an umbilic being a
point on the surface where the tangent plane is parallel to
a directive plane. Thus the focal hyperbola of the ellipsoid,
and the focal ellipse of the hyperboloid of two sheets, are
umbilicar focals, and pass through the umbilics of these
surfaces ; but the hyperboloid of one sheet has no umbilics,
and accordingly both its focals are modular, and neither of
them intersects the surface. The umbilicar focals and di-
rigents have properties which shall be mentioned here-
after.

An umbilicar focal and the principal section whose plane
coincides with that of the focal are curves of different kinds,
the one being an ellipse when the other is a hyperbola; but
a modular focal is always of the same kind with the coinci-
dent section of the surface, being an ellipse, a hyperbola, or
a pair of right lines, according as the section is an ellipse,
a hyperbola, or a pair of right lines; and when the section
is reduced to a point, so likewise is the modular focal.

The plane of a modular focal always passes through the
directive axis. When the directive axis is the primary, as
in the hyperboloid of one sheet, both focals are modular.
But in the ellipsoid and the hyperboloid of two sheets,
where the primary axis is not directive, only one of the
focals can be modular. The plane of an umbilicar focal is

459

always perpendicular to the directive axis; and therefore,
when that axis is the primary, there is no umbilicar focal.*
When the surface is doubly modular, the two moduli
m,m’ are connected by the relation
cos” sin?
Sh SR a (16)

m2 m2

where @ is the angle made by a directive plane with the
plane of the focal to which the modulus m belongs. One
modulus is greater than unity; the other is less than unity,
but greater than the cosine of the angle which the plane of
the corresponding focal makes with a directive plane. In
the hyperboloid of one sheet, the less modulus is that which
belongs to the focal hyperbola. In the cone, the less
modulus belongs to the focal lines. Of the two moduli of a
cone, that which belongs to the focal lines may be termed
the linear modulus; and the other, to which only a single
focus corresponds, may be called the singular modulus.

§ 6. Second Class of Surfaces.—In this class of sur-
faces, one of the quantities a, B vanishes, or both of them
vanish.

I. When m = cos 9, and ¢ is not zero, A vanishes, but B

* If the first of the equations (10), when P, and q, are both negative, be
supposed to express an imaginary focal, there will, in a central surface, be three
focals, two modular and one umbilicar; the two modular focals being in the
principal planes which pass through the directive axis, and the umbilicar focal
in the remaining principal plane. Then, when we know which of the axes is
the directive axis, we know which of the three focals is imaginary, because the
plane of the imaginary focal is perpendicular to the primary axis. A modular
focal may be imaginary, and yet have a real modulus; this occurs in the
hyperboloid of two sheets. In the ellipsoid, the imaginary focal has an
imaginary modulus. In all cases the two moduli are connected by the relation
(16).

It will appear hereafter, that the vertex of the cone is an umbilicar focus.
The cone has therefore three focals, none of which is imaginary; but two of
them are single points coinciding with the vertex.

460

does not; and the surface is either a paraboloid or a cy-
linder.

1°. If the surface is a paraboloid, we may suppose the
origin of coordinates to be at its vertex, in which case —
H and k vanish, and we have the relations

G—o%— %, Yr = Y2 COs” ps
2 2 2 2 2 (17)
Lo + yo cos’ — a — vy =O;
the equation of the surface being
y’ sin? d + 2? + 26x = 0, (18)
which shews that the paraboloid is elliptic, having its axis
in the direction of #, and the plane of ay for that of its
greater principal section. From the relations (17) we obtain
the following,
yr tan’? + 26x, + & = 0, (19)
Yo’ sin? g cos’ @ + 2Ga,— G?=0;
from which we see that the focal and dirigent curves are
parabolas, having their axes the same as that of the surface ;
and their vertices equidistant from the vertex of the surface,
but at opposite sides of it. The concavity of each curve is
turned in the same direction as that of the section zy. The
focus of the focal parabola is the focus of the section xy, and
its vertex is the focus of the section xz of the surface; its
parameter being the difference of the parameters of these
two sections. The parameter of the section vy is a mean
proportional between the parameters of the focal and diri-
gent parabolas.
2°. If the surface is a cylinder, we may make @ and u
vanish, by taking the origin on its axis. We then have

Lo = 2 = y2 cos’ ¢,
K ss ye tan? p m4 Bai uf $3 29}
the equation of the cylinder, which is elliptic, being
y’ sin? @ +2” =K. (21)
Here the focal and dirigent are each a pair of right lines

461

parallel to the axis of the cylinder, and passing through the
foci and directrices of a section perpendicular to the axis.
The corresponding focal and dirigent lines lie at the same
side of the axis.

II. When m =1, and ¢ is not zero, B vanishes, but a
does not.

1°. If the surface is a paraboloid, and the origin of co-
ordinates at its vertex, the quantities c and k vanish; same
the equation of the surface becomes

x’ tan? @ — 2* = 2uy, (22)
and we have the relations

— — 2
K=>4Y%— Ms; XL) = XQ Sec’ gp,

Xo? sec’ + Yo = ay — We = 0. (23)

The paraboloid is therefore hyperbolic, its axis being that
of y, which is also the directive axis; and as the tangent of
¢@ may have any finite value, the plane of zy, which is that
of the focal curve, may be either of the principal planes
passing through the axis of the surface. The relations (23)
give

x, sin? ¢ — 2Hy, — H” = 0,

2” tan? @ sec” @ — 2HY. + H? = 0, (24)

for the equations of the focal and dirigent, which are there-
fore parabolas, having their axes the same as those of the
surface, and their concavities turned in the same direction
as that of the section xy; their vertices being equidistant
from the vertex of the surface, and at opposite sides of it.
The focus of the focal parabola is the focus of the section
xy, and its vertex is the focus of the section yz, its para-
meter being the sum of the parameters of these two sections.
The parameter of the section xy is a mean proportional
between the parameters of the focal and dirigent parabolas.

2°. If the surface is a cylinder, and the origin on its
axis, Gand H vanish, and we have

462

% = x2 8eC’ g, I = Yo, (25)
—K = 2,’ sin’ ¢ = 2,” tan’ ¢ sec” ;
the equation of the cylinder, which is hyperbolic, being
a tan? @ — 2? = — kK. (26)

The focal and dirigent are each a pair of right lines pa-
rallel to the axis of the cylinder; the corresponding lines
passing through a focus and the adjacent directrix of any
section perpendicular to the axis. The directive planes are
parallel to the asymptotic planes of the cylinder.

In this case, if k = 0, the surface is reduced to two di-
rective planes, and the focal and dirigent to the intersection
of these planes.

III. When m= 1, and ¢ = 0, both a and B vanish, and
the surface is the parabolic cylinder. If, as is allowable,
we suppose cg and xk to vanish, the equation of the cylinder
becomes

s* + 2uy= 0, (27)

and we have
H>=Y—-Y> 11 = L5
ty + yy — ty — yy = 0; a

whence
yi = — 3H, Yo = oH. (29)

The focal and dirigent are each a right line parallel to the
axis of x, the former passing through the focus, the latter
meeting the directrix of the parabolic section made by the
plane of yz. The plane of zy is the directive plane.

§ 7. We learn from this discussion, that, among the surfaces
of the second class, the hyperbolic paraboloid is the only
one which admits a twofold modular generation; the modu-
lus, however, being the same for both its focals. In the
elliptic paraboloid the modular focal is restricted to the plane
of that principal section which has the greater parameter;
we shall therefore suppose a parabola to be described in
the plane of the other principal section, according to the

463

law of the modular focals; the law being, that the focus of
the parabola shall be the focus of the principal section in the
plane of which the parabola lies, and its vertex the focus of the
principal section in the perpendicular plane. ‘The parabola
so described will have its concavity opposed to that of the
surface ; it will cut the surface in the umbilics, and will be
its umbilicar focal, the only such focal to be found among
the surfaces of the second class. We shall of course sup-
pose further, that this focal has a dirigent parabola connected
with it by the same law as in the other cases, the vertices of
the focal and dirigent being equidistant from that of the
surface and at opposite sides of it, while the parameter of
the dirigent is a third proportional to the parameters of the
focal and of the principal section in the plane of which
the curves lie. The two focals of a paraboloid are so re-
lated, that the focus of the one is the vertex of the other.
The cylinders have no other focals than those which occur
above.

§ 8. In this, as in the first class of surfaces, the right
line FA, joining a focus F with the foot of its corresponding
directrix, is perpendicular to the focal line ; and the focal
and dirigent are reciprocal polars with respect to the section
ay of the surface. ‘These properties are easily inferred from
the preceding results; but, as they are general, it may be
well to prove them generally for both classes of surfaces.
Supposing, therefore, the origin of coordinates to be any
where in the plane of «wy, and writing the equation of the
surface in the form

(c@—nyY + Y— n+? =1L(e— 2)? +u(y—y)’, (80)
which, when identified with (3), gives the relations

A=1-—t1, B=1—yM,
G = L% — %}, H= MY2— i> (31)
nike 2
K = Lag + Myo” — 2) — ys

464

we find, by differentiating the values of the constants @, H,

and kK,
Ldas = dx, Mdy2 = dy,

32
Li dz + MY2dy2 —X, da, — y, dy, = 0. (32)

Hence we obtain
(a2 — 2) day + (y2— 91) dy, = 0; (33)

an equation which expresses that the right line joining the
points F and A is perpendicular to the line which is the
locus of the point F.

Again, the equation of the section xy of the surface being

ax? + By? + 2exH + 2Hy=K; (34)

the equation of the right line which is, with respect to this
section, the polar of a point A whose coordinates are x2,

Y25 is
(ax, + G) a + (By, + H)y=K —Ga,— Hy; (35)

but the relations (31) give

Ato + G=%—%, BYz +H=Yo— Yi;
K— G@2 — HY. = %(%2—2%)) +i (Y2— Y1)3

and hence the equation (35) becomes

(a2 — 2) (« — a1) + (Yo — mi) (¥ — M1) =9, (37)

which, as is evident from (33), is the equation of a tangent
applied to the focal at the point F corresponding to A.
This shows that the focal and dirigent are reciprocal polars
with respect to the section xy, and that in this relation, as
well as in the other, the points F and A are corresponding
points.

Supposing F’ and A’ to be two other corresponding
points on the focal and dirigent, if tangents applied to the
focal at F and F’ intersect each other in T, the point T will
be the pole of the right line AA’ with respect to the section
xy, as well as the pole of the right line FF’ with respect to

465

the focal ; and hence if any right line be drawn through T,
and if P be the pole of this right line with respect to the
section, and N its pole with respect to the focal, the points
P and N will be on the right lines AA’ and FF’ respectively.
Now it is useful to observe that the distances AA’ and FF’
are always similarly divided (both of them internally or
both of them externally) by the points P and N, so that
we have AP to A’/P as FN to F’N. This property may be
proved directly by means of the foregoing equations; or it
may be regarded as a consequence of the following theo-
rem:—If through a fixed point in the plane of two given
conics having the same centre, or of two given parabolas
having their axes parallel, any pair of right lines be drawn,
and their poles be taken with respect to each curve, the dis-
tance between the poles relative to one curve will be in a
constant ratio to the distance between the poles relative to
the other curve.* In fact, the poles of the right lines
TF, TF’, with respect to the focal, are F, F’; and their poles
with respect to the section xy are A, A’; therefore, since
the focal and the section xy may be taken for the given
curves, and the point T for the fixed point, the ratio of
FF’ to AA’ is the same as the ratio of FN to AP or of F’N
to A’P, and consequently the distances FF’ and AA‘ are si-
milarly divided in the points N and P.

§9. In the equation (30), considered as equivalent to
the equation (1), the constants Lt and m are both positive ;
but the properties which have been deduced from the
former equation are independent of this circumstance, and

* There is an analogous theorem for two surfaces of the second order which
haye the same centre, or two paraboloids which have their axes parallel. If
through a fixed right line any two planes be drawn, and their poles be taken
with respect to each surface, the distance between the poles relative to the one
surface will be in a constant ratio to the distance between the poles relative to
the other.

466

equally subsist when one of these constants is supposed
to be negative (for they cannot both be negative). This
leads us to inquire what surfaces the equation (30) is
capable of representing when the constants L and m have
different signs; as also, for a given surface, what lines are
traced in the plane of zy by points F and A, of which 2,
y, and x5, Y are the respective coordinates. After the ex-
amples already given, this question is easily discussed, and
the result is, that the only surfaces which can be so repre-
sented are the ellipsoid, the hyperboloid of two sheets, the
cone, and the elliptic paraboloid—that is to say, the um-
bilicar surfaces together with the cone; and that, for an
umbilicar surface, the locus of F is the umbilicar focal, and
therefore the locus of A is the corresponding dirigent ; while
for the cone the points F and A are unique, coinciding with
each other and with the vertex of the cone. A geometrical
interpretation of this case is readily found; for as L and m
have different signs, the right-hand member of the equation
(30), if m be the negative quantity, is the product of two
factors of the form

Sf (@ —%)+aly—y), Sf (e — %2)— SY — x),
in which f and g are constant; and these factors are evi-
dently proportional to the distances of a point whose coordi-
nates are x, y, 3, from two planes whose equations are

f(e— 72) + 8y-—y)=9, fle—m)—sy—y) =

which planes always pass through a directrix, and are in-
clined at equal and constant angles to the axis of x or of y.
Therefore, if F be the focus which belongs to this directrix,
the square of the distance of F from any point of this surface
is in a constant ratio to the rectangle under the distances of
the latter point from the two planes. And these planes are di-
rective planes; because, if a section parallel to one of them
be made in the surface, the distance of any point of the sec-
tion from the other plane will be proportional to the square

467

of the distance of the same point from the focus ; and, as the
locus of a point, whose distance from a given plane is pro-
portional to the square of its distance from a given point, is
obviously a sphere, it follows that the section aforesaid is the
section of a sphere, and consequently a circle; which shows
that the plane to which the section is parallel is a directive
plane. Thus,* the square of the distance of any point of

* In attempting to find a geometrical generation for the surfaces of the se-
cond order, one of the first things which I thought of, before I fell upon the
modular method, was to try the locus of a point such that the square of its dis-
tance from a given point should be in a constant ratio to the rectangle under its
distances from two given planes; but when I saw that this locus would not
represent all the species of surfaces, I laid aside the discussion of it. Some
time since, however, Mr. Salmon, Fellow of Trinity College, was led inde-
pendently, in studying the modular method, to consider the same locus; and
he remarked to me, what I had not previously observed, that it offers a pro-
perty supplementary, in a certain sense, to the modular property; that when
the surface is an ellipsoid, for example, the given point or focus is on the focal
hyperbola, which the modular property leaves empty. This remark of Mr.
Salmon served to complete the theory of the focals, by indicating a simple
geometrical relation between a non-modular focal and any point on the surface
to which it belongs.

In a memoir ‘* On a new Method of Generation and Discussion of the Sur-
faces of the second Order,” presented by M. Amyot to the Academy of Sciences
of Paris, on the 26th December, 1842, the author investigates this same
locus, conceiving it to involve that property in surfaces which is analogous to
the property of the focus and directrix in the conic sections; and the im-
portance attached to the discovery of such analogous properties induced M.
Cauchy to write a very detailed report on M. Amyot’s memoir, accompanied
with notes and additions of his own (Comptes vendus des Séances de l Académie
des Sciences, tom. xvi. pp. 783-828, 885-890; April, 1843); and also occa-
sioned several discussions, principally between M. Poncelet and M. Chasles,
relative to that Memoir (Comptes rendus, tom. xvi. pp. 829, 938, 947, 1105,
1110). But the property involved in this locus cannot be said to afford a
method of generation of the surfaces of the second order, since it applies only
to some of the surfaces, and gives an ambiguous result even where it does
apply. It is therefore not at all analogous to the aforesaid general pro-

perty of the conic sections, and moreover it was not new when M. Amyot

468

the surface from an umbilicar focus bears a constant ratio to
the rectangle under the perpendicular distances of the same

brought it forward. Mr. Salmon had in fact proposed it for investigation
to the students of the University of Dublin, at the ordinary examinations
in October, 1842; and it was published, towards the end of that year, in
the University Calendar for 1843, some months before the date of M. Cauchy’s
report, by which the contents of M. Amyot’s memoir were first made known.
‘The parallelism of the two given planes to the circular sections of the surface
is also stated in the Calendar; but this remarkable relation is not noticed by
M. Amyot, nor by M. Cauchy. (See the Examination Papers of the year 1842,
p. xly, quest. 17, 18; in the Calendar for 1843.) It is scarcely necessary to
add, that the analogue which M. Amyot and other mathematicians have been
seeking for, and which was long felt to be wanting in the theory of surfaces of
the second order, is no other than the modular property of these surfaces, which
appears to be not yet known abroad. M. Poncelet insists much on the im-
portance of extending the signification of the terms focus and directrix, so as
to make them applicable to surfaces; and he supposes this to have been effected,
for the first time, by M. Amyot. These terms however, applied in their true
general sense to surfaces, had been in use, several years before, among the
mathematical students of Dublin, as may be seen by referring to the Calendar
(Examination Papers of the year 1838, p.c; 1839, p. xxxi).

The locus above-mentioned, being co-extensive with the umbilicar property,
does not represent any surface which can be generated by the right line,
except the cone. To remedy this want of generality, M. Cauchy proposes to
consider a surface of the second order as described by a point, the square of
whose distance from a given point bears a constant ratio either to the rectangle
under its distances from two given planes, or to the sum of the squares of these
distances. This enunciation, no doubt, takes in both kinds of focals, and all the
species of surfaces; but the additional conception is not of the kind required by
the analogy in question, nor has it any of the characters of an elementary prin-
ciple. For the given planes, according to M. Cauchy *s idea, do not stand in any
simple or natural relation to the surface; and besides there is no reason why,
instead of the sum of the squares of the distances from the given planes, we
should not take the sum after multiplying the one square by any given positive
number, and the other square by another given positive number ; nor is there
any reason why we should not take other homogeneous functions of these dis-
tances. This conception would therefore be found of little use in geome-
trical applications; while the modular principle, on the contrary, by employing

a simple ratio between two right lines, both of which have a natural connexion

469

point from two directive planes drawn through the direc-
trix corresponding to that focus; and it is easy to see that
this ratio, the square root of which we shall denote by , is
equal to L — , or, neglecting signs, to the sum of the nu-
merical values of L and m. Of course, if the distances from
the directive planes, instead of being perpendicular, be
measured parallel to any fixed right line, the ratio will still
be constant, though different. For example, if the fixed
right line for each plane be that which joins the corres-
ponding umbilic with either focus of the section xy, the ratio
of the square to the rectangle will be the square of the
number msec ¢, where m is the modulus, and ¢ the angle
which the primary axis makes with a directive plane.

When the umbilicar property is applied to the cone, the
vertex of which is, as we have seen, to be regarded as an
umbilicar focus, having the directive axis for its directrix, it
indicates that the product of the sines of the angles which
any side of the cone makes with its two directive planes is a
constant quantity.

It is remarkable that the vertex of the cone affords the
only instance of a focal point which is at once modular and
umbilicar, as well as the only instance of a focal point which
is doubly modular. ‘This union of properties it may be con-
ceived to owe to the circumstance that the cone is the
asymptotic limit of the two kinds of hyperboloids. For if a

with the surface, lends itself with the greatest ease to the reasonings of geometry.
Indeed the whole difficulty, in extending the property of the directrix to surfaces
of the second order, consisted in the discovery of such a ratio inherent in all
of them; a ratio having nothing arbitrary in its nature, and for which no other
of equal simplicity can be substituted.

It may be proper to mention that the term modulus, which I have used for
the first time in the present paper, with reference to surfaces of the second
order, has been borrowed from M. Cauchy, by whom it is employed, however,
in a signification entirely different. Several other new terms are also now in-
troduced, from the necessity of the case.

470

series of hyperboloids have the same asymptotic cone, and
their primary axes be indefinitely diminished, they will ap-
proach indefinitely to the cone; and, in the limit, the focal
ellipse and hyperbola of the hyperboloid of one sheet will
pass into the vertex and the focal lines of the cone, thus
making the vertex doubly modular, while the focal ellipse
of the hyperboloid of two sheets will also be contracted
into the vertex, and will make that point umbilicar.

When the two directive planes coincide, and become one
directive plane, the umbilicar property is reduced to this,
that the distances of any point in the surface from the point
F and from the directive plane are in a constant ratio to
each other; and therefore the surface becomes one of re-
volution round an axis passing through F at right angles to
that plane, the point F being a focus of the meridional section,
or the vertex if the surface be a cone. When the directive
planes are supposed to be parallel, but separated by a finite
interval, we get the same class of surfaces of revolution, with
the addition of the surface produced by the revolution of an
ellipse round its minor axis; the point F being still on the
axis of revolution, but not having any fixed relation to the
surface.

§ 10. If in the equation (30) we supposed the right-hand
member to have an additional term containing the product
of the quantities a — x, and y — yo, with a constant coeffi-
cient, all the foregoing conclusions regarding the geometrical
meaning of that equation would remain unchanged, because
the additional term could always be taken away by assigning -
proper directions to the axes of x and y. If, after the re-
moval of this term, the coefficients of the squares of the
aforesaid quantities were both positive, the locus of F would
be a modular focal of the surface expressed by the equation;
but if one coefficient were positive and the other negative,
the locus of F would be an umbilicar focal. The equation
in its more general form is evidently that which we should

471

obtain for the locus of a point S, such that the square of
its distance SF from a given point F should be a given ho-
mogeneous function of the second degree of its distances
from two given planes ; the plane of zy being drawn through
F perpendicular to the intersection of these planes, and
X,Y being the coordinates of any point on this inter-
section, while x,, y, are the coordinates of F. The point F
might be any point on one of the focals of the surface de-
scribed by S; the intersection of the two planes (supposing
them always parallel to fixed planes) being the correspond-
ing directrix.

These considerations may be further generalised, if we
remark that the equation of any given surface of the second
order may be put under the form

(o—a)-+(y—y)? + (ea) =u(w— 2) + ly — yo)? N (2a)!
AL (y— Y2)(2—22)-+M(%— @2)(2# — 22) +N/(L—22)(Y—Yo), (38)

where L, M, N, L’, M’, N’ are constants, and 2, 4, 2; are con-
ceived to be the coordinates of a certain point F, and
X25 Yo, %2 the coordinates of another point A. The con-
stants L’,M’,N’ may, if we please, be made to vanish by
changing the directions of the axes of coordinates ; and when
this is done, the new coordinate planes will be parallel to
the principal planes of the surface. Then, by proceeding as
before, it may be shown that, without changing the surface,
we are at liberty, under certain conditions, to make the
points F and A move in space. The conditions are ex-
pressed geometrically by saying that the two surfaces, upon
which these points must be always found, are reciprocal
polars with respect to the given surface, the points Fand A
being, in this polar relation, corresponding points; and that
the surface which is the locus of F is a surface of the second
order, confocal with the given one, it being understood that
confocal surfaces are those which have the same focal lines.
The surface on which A lies is therefore also of the second
VOL. Il, 2s

472

order, and the right line AF is a normal at F to the sur-
face which is the locus of this point. Moreover, if through
the point A three or more planes be drawn parallel to fixed
planes, and perpendiculars be dropped upon them from
any point S whose coordinates are 2, y, 3, the right-hand
member of the equation (38) may be conceived to represent
a given homogeneous function of the second degree of these
perpendiculars; and the given surface may therefore be
regarded as the locus of a point S, such that the square
of the distance SF is always equal to that function.

§ 11. In the enumeration of the surfaces capable of being
generated by the modular method, we miss the five follow-
ing varieties, which are contained in the general equa-
tion of the second degree, but are excluded from that me-
thod of generation by reason. of the simplicity of their
forms—namely, the sphere, the right cylinder on a circu-
lar base, and the three surfaces which may be produced
by the revolution of a conic section (not a circle) round
its primary axis.* These three surfaces are the prolate sphe-
roid, the hyperboloid of two sheets, and the paraboloid
of revolution; and the circumstance that the foci of the
generating curves are also foci of the surfaces, renders it
easy to investigate their focal properties.+ In point of sim-
plicity, the excepted surfaces are to the other surfaces of
the second order what the circle is to the other conic sections,
the circle being, in like manner, excepted from the curves
which can be generated by the analogous method én plano; and
the geometry of the five excepted surfaces may therefore be
regarded as comparatively elementary. ‘These five surfaces

* The case of two parallel planes is also excluded, but it is not here taken
into account. The case of two parallel right lines is in like manner excluded
from the corresponding generation of lines of the second order. —

+ A paper by M. Chasles, on these surfaces of revolution, will be found in
the Memoirs of the Academy of Brussels, tom. v. (An. 1829).

473

were, in fact, studied by the Greek geometers,* and, along
with the oblate spheroid and the cone, they make up all the
surfaces of the second order with which the ancients were ac-
quainted. Except the cone, the surfaces considered by
them are all of revolution; and there is only one surface
of revolution, the hyperboloid of one sheet, which was not
noticed until modern times. ‘This surface is mentioned (un-
der the name of the hyperbolic cylindroid) by Wren,} who re-
marks that it can be generated by the revolution of a right
line round another right line not inthe same plane. As tothe
general conception of surfaces of the second order, the sug-
gestion of it was reserved for the algebraic geometry of Des-
cartes. In that geometry the curves previously known as sec-
tions of the cone are all expressed by the general equation of
the second degree between two coordinates ; and hence it
occurred to EKuler{ about a century ago, to examine and
classify the different kinds of surfaces comprised in the
general equationof the second degree among three coordinates.
The new and more general forms thus brought to light have
since engaged a large share of the attention of geometers ;
but the want of some other than an algebraic principle of con-
nexion has prevented any great progress from being made
in the investigation of such of their properties as do not im-
mediately depend on transformations of coordinates. This
want the modular method of generation perfectly supplies,
by evolving the different forms from a simple geometrical
conception, at the same time that it brings them within the
range of ideas familiar to the ancient geometry, and places
their relation to the conic sections in a striking point of view.

* The hyperboloid of two sheets, and the paraboloid of revolution, were
known by the name of conoids. Archimedes has left a treatise on Conoids and
Spheroids, as well as a treatise on the Sphere and Cylinder.

} In the Philosophical Transactions for the year 1669, p. 961.

{£ See his Introduclio in Analysin Infinitorum, p. 373 ; Lausanne, 1748,

see

474

It may be well to remark that the excepted surfaces are
limits of surfaces which can be generated modularly, as the
circle is the limit of the ellipse in the analogous generation
of the conic sections. Thus the sphere is the limit of an
oblate spheroid, one of whose axes remains constant, while
its focal circle is indefinitely diminished ; and the right cir-
cular cylinder is the limit of an elliptic cylinder, whose focal
lines are conceived to approach indefinitely to coincidence
with each other and with the axis of the cylinder, while one
of the axes of the principal elliptic section remains constant.
In these cases the dirigent lines, along with the directrices,
move off to infinity. The other three excepted surfaces
correspond to the supposition ¢ = 90°, which was excluded
in the discussion of the general equation (1). For if we
make m sec ¢ = n, the quantity which constitutes the right-
hand member of that equation may be written

n? (a — 0)? 40? (y — yo) cos? 9

and if we suppose m to remain finite and constant, while
approaches to 90°, and m indefinitely diminishes, this quan-
tity will approach indefinitely to n?(« — a,)?, which will be
its limiting value when ¢ = 90°. But x — zy is the distance
of the point S from a fixed plane intersecting the axis of
perpendicularly at the distance x, from the origin of coordi-
nates ; and therefore, in the limit, the equation expresses
that the distances of any point S of the surface from the
focus F and from this fixed plane, are to each other as n to
unity, that is, in a constant ratio; which is a common pro-
perty of the three surfaces in question. This property also
belongs to the right cone, but the right cone does not rank
among the excepted surfaces. ch

§ 12. We have seen that, when the modulus is unity,
any plane parallel to either of the directive planes intersects
the surface in a right line; whence it follows, that through
any point on the surface of a hyperbolic paraboloid two right

a

475

lines may be drawn which shall lie entirely in the surface.
The plane of these right lines is of course the tangent plane
at that point, and therefore every tangent plane intersects
the surface in two right lines. This is otherwise evident
from considering that the sections parallel to a given tan-
gent plane are similar hyperbolas, whose centres are ranged
ona diameter passing through the point of contact, and
whose asymptotes, having always the same directions, are
parallel to two fixed right lines which we may suppose to be
drawn through that point. For as the distance between the
plane of section and the tangent plane diminishes, the axes
of the hyperbola diminish ; and they vanish when that dis-
stance vanishes, the hyperbola being then reduced to its
asymptotes. The tangent plane therefore intersects the
surface in the two fixed right lines aforesaid. The same
reasoning, it is manifest, will apply to any other surface of
the second order, which has hyperbolic sections parallel to its
tangent planes; and therefore the hyperboloid of one sheet,
which is the only other such surface,* is also intersected in
two right lines by any of its tangent planes. These right
lines are usually called the generatrices of the surface.
From what has been said, it appears that the generatrices
of the hyperbolic paraboloid, and the asymptotes of its sec-
tions (all its sections, except those made by planes parallel
to the axis, being hyperbolas), are parallel to the directive
planes. The generatrices of the hyperboloid of one sheet,
and the asymptotes of its hyperbolic sections, are parallel to
the sides of the asymptotic cone ; because any section of the

* The double generation of these two surfaces by the motion of a right line
has been long known. It appears to have been discovered and fully discussed
by some of the first pupils of the Polytechnic School of Paris. This mode of
generation had, however, been remarked by Wren, with regard to the hypre-
boloid of revolution. It does not seem to have been observed, that the existence
of rectilinear generatrices is included in the idea of hyperbolic sections parallel

to a tangent plane.

476

hyperboloid is similar to a parallel section of the asymptotic
cone, and when the latter section is a hyperbola its asymp-
totes are parallel to two sides of the cone.

PART II.—PROPERTIES OF SURFACES OF THE SECOND ORDER.

§ 1. In the preceding part of this paper it has been ne-
cessary to enter into details for the purpose of communicat-
ing fundamental notions clearly. In the following part,
which will contain certain properties of surfaces of the se-
cond order, we shall be as brief as possible; giving demon-
strations of the more elementary theorems, but confining
ourselves to a short statement of the rest..

Many consequences follow from the principles already
laid down.

Through any directrix of a surface of the second order
let a fixed plane be drawn cutting the surface, and let S be
any point of the section. If the directrix and its focus F be
modular, and ifa plane always parallel to the same directive
plane be conceived to pass through S and to cut the direc-
trix in D, the directive distance SD will be always parallel to
a given right line, and will therefore be in a constant ratio to
the perpendicular distance of S from the directrix. This
perpendicular distance will consequently bear a given ratio
to SF, the distance of the point S from the focus. And the
same thing will be true when the directrix and focus are
umbilicar, because the perpendicular distance of the point
S from the directrix will be in a constant ratio to its distance
from each directive plane drawn through the directrix.

The fixed plane of section will in general contain another
directrix parallel to the former, and belonging to the same
focal ; and it is evident that the perpendicular distance of S
from this other directrix will be in a given ratio to its dis-
tance SE’ from the corresponding focus F’, the ratio being
the same as in the former case. Hence, according as the
point § lies between the two directrices, or at the same side

477

of both, the sum or difference of the distances SF and SF’
will be constant.

If the plane of section pass through either of the foci, as
F, this focus and its directrix will manifestly be the focus
and directrix of the section. In this case the plane of section
will be perpendicular to the focal at F. And if the surface
bea cone, the point F being anywhere on one of its focal lines,
the distance of the point S from the directrix will be ina
constant ratio to its perpendicular distance from the dirigent
plane which contains the directrix, and therefore this per-
pendicular distance will be in a given ratio to the distance
SF. Now calling V the vertex of the cone, and taking SV
for radius, the perpendicular distance aforesaid is the sine
of the angle which the side SV of the cone makes with the
dirigent plane ; and SF, which is perpendicular to VF, is
the sine of the angle SVF. Consequently the sines of the
angles which any side of a cone makes with a dirigent
plane and the corresponding focal line are in a given ratio to
each other.

§ 2. Conceive a surface of the second order to be inter-
sected in two points S, S’ by a right line which cuts two
parallel directrices in the points E, E’, and let F, F’ be the
foci corresponding respectively to these directrices. The
perpendicular distances of the points S, S’ from the first di-
rectrix and from the second are to each other as the lengths
SE, S’E, SE’, S’E’ respectively, and therefore the ratios of
FS to SE, of FS’ to YE, of FS to SE’, and of F’S’ to S‘E’
are all equal.

Hence, the right line FE bisects one of the angles made
by the right lines FS and FS’; and the right line F’E’ bi-
sects one of the angles made by F’S and F’S’.

When the points S,S’ are at the same side of E, the
angle supplemental to SFS’ is that which is bisected by the
right line FE. Now if the point S be fixed, and S’ap-
proach to it indefinitely, the angle SFE will approach inde-

478

finitely to a right angle. Therefore ifa right line touching the
surface meeta directrix in a certain point, the distance between
this point and the point of contact will subtend a right angle
at the focus which corresponds to the directrix. And if.acone
circumscribing the surface have its vertex in a directrix, the
curve of contact will be in a plane drawn through the cor-
responding focus at right angles to the right line which joins
that focus with the vertex.

When the surface intersected by the right line SS’ is a
cone, suppose this line to lie in the plane of the focus F and
its directrix, that is, in the plane which is perpendicular at
F to the focal line VF (the vertex of the cone being de-
noted, as before, by V); the angles made by the right lines
Fit, FS, FS’, are then the same as the angles made by planes
drawn through VF and each of the right lines VE, VS,
VS’; and the last three right lines are the intersections of
a plane VSS’ with the dirigent plane on which the point E
lies, and with the surface of the cone. ‘Therefore if a plane
passing through the vertex of a cone intersect its surface in
two right lines, and one of its dirigent planes in another right
line, and if a plane be drawn through each of these right
lines respectively and the focal line which belongs to the di-
rigent plane, the last of the three planes so drawn will bisect
one of the angles made by the other two. And hence, if a
plane touching a cone along one of its sides intersect a diri-
gent plane in a certain right line, .and if through this right
line and the side of contact two planes be drawn intersecting
each other in the focal line which corresponds to the dirigent
plane, the two planes so drawn will be at right angles to each
other.

Let a right line touching a surface of the second order
in S meet two parallel directrices in the points E, E’, and let
F, F’ be the corresponding foci. Then the triangles FSE
and F’SE’ are similar, because the angles at F and F’ are right
angles, and the ratio of FS to SI’ is the same as the ratio of F’S

479

to SE’. Therefore the tangent EE’ makes equal angles with
the right lines drawn from the point of contact S to the foci
F, FE’. When the surface is a cone, let the tangent be per-
pendicular to the side VS which passes through the point
of contact ; the angles FSE and F’SE’are then the angles
which the tangent plane VEE’ makes with the planes VSF
and VSF’, because the right line FE is perpendicular to the
plane VSF, and the right line F’E’ is perpendicular to the
plane VSE’. Therefore the tangent plane of a cone makes
equal angles with the planes drawn through the side of con-
tact and each of the focal lines.

Supposing a section to be made in a surface of the second
order by a plane which cuts any directrix in the point E,
if the focus F belonging to this directrix be the vertex of a
cone having the section for its base, the right line FE will be
an axis ofthe cone. For if through FE any plane be drawn
cutting the base of the cone in the points S, S’, one of the
angles made by the sides FS, FS’ which pass through these
points will always be bisected by the right line FE; and this
is the characteristic property of an axis.

§ 3. Two surfaces of the second order being supposed
to have the same focus, directrix, and directive planes, so
that they differ only in the value of the modulus m, or of the
umbilicar ratio « (see Part I. § 9), let a right line passing
through any point E of the directrix cut one surface in the
points S, 8S’, and the other in the points So, S,, and conceive
right lines to be drawn from all these points to the common
focus F. Since, if ratios be expressed by numbers, the ratio
of FS to SE (or of FS’ to S’E) is to the ratio of FS, to SE
(or of FS, to 8,E) as the value of m for the one surface is to
its value for the other, when the focus is modular, or as the
value of u for the one surface is to its value for the other
when the focus is umbilicar, the sines of the angles EFS,
and EFS (or of the angles EFS, and EFS’) are in a con-
stant proportion to each other, because these sines are pro-

480

portional to those ratios. And since the right line FE bi-
sects the angles SFS’ and S,FS), both internally or both
externally, in which case the angles SFS, and S’FS, areequal,
or else one internally and the other externally in which case
the angles SFS, and S’FS, are supplemental, it is easy to
infer, from the constant ratio of the aforesaid sines, that in
the first case the product, in the second case the ratio of the
tangents of the halves of the angles SFS,) and S/FS, (or of
the halves of the angles SFS, and S’FS,) is a constant quan-
tity.

If the point S’ approximate indefinitely to S, the right
line passing through these points will approach indefinitely
to atangent. ‘Therefore when two surfaces are related as
above, if a right line passing through any point E of their
common directrix intersect one surface in the points So, Si,
and touch the other in the point S, the chord S)S, will sub-
tend a constant angle at the common focus F, and this angle
will be bisected, either internally or externally, by the right
line FS drawn from the focus to the point of contact. And
the angle EFS being then a right angle, the cosine of the
angle SFS, or SFS, will be equal to the ratio of the less value
of m or uw tothe greater.*

§ 4. Among the surfaces of the second order the only one
which has a point upon itself for a modular focus is the cone,
the vertex of which is such a focus, related either to the in-
ternal or to the mean axis as directrix. In the latter rela-
tion the vertex belongs to the series of foci which are
ranged on the focal lines. To see the consequence of this,
let V be the vertex of the cone, and VW its mean axis
perpendicular to the plane of the focal lines. On one of
the focal lines and its dirigent assume any corresponding

* See Exam. Papers, An. 1639, p. xxxi. questions 9, 10. These and some
of the preceding theorems were originally stated with reference to modular foci
only. They are now extended to umbilicar foci.

481

points F and A, and let AD be the directrix passing through
A. ‘Then if a directive plane, drawn through any point S
of the surface, cut this directrix in D and the mean axis in
W, the ratio of SF to SD will be expressed by the linear
modulus, as will also the ratio of VF to WD, since V isa
point of the surface, and WD is equal to the directive dis-
tance of Vfrom AD. But since V is a focus to which the
mean axis is directrix, the ratio of SV to SW is expressed by
the same modulus. Thusthe triangles SVF andSW Dare simi-
lar, the sides of theone being proportional to those of the other.
Therefore the angle SVF is equal to the angle SWD;; that
is to say, the angle which the side VS of the cone makes
‘ with the focal line VF is equal to the angle contained by two
right lines WD and WS, of which one is the intersection of
the directive plane with the dirigent plane VWD corres-
ponding to VF, and the other is the intersection of the di-
rective plane with the plane VWS passing through the mean
axis and the side VS of the cone.

Hence it appears that the sum of the angles (properly
reckoned) which any side of the cone makes with its two
focal lines is constant. For if F’ be a point on the other
focal line, and D’ the point where the directrix correspond-
ing to F’ is intersected by the same directive plane SWD,
it may be shown as above that the angle SVF’ is equal to the
angle SWD?’, that is, to the angle made by the right line
WS with the right line WD’ in which the directive plane in-
tersects the dirigent plane corresponding to VE’. Conceiv-
ing therefore the points F, F’, S, and with them the points
D, D’, to lie all on the same side of the principal plane
which is perpendicular to the internal axis, the right
line WS will lie between the right lines WD and WD’, and
the sum of the angles SVF and SVF’ will be equal to the
angle DWD’, which is a constant angle, being contained by
the right lines in which a directive plane intersects the two
dirigent planes of the cone. ‘This constant angle will be

482

found to be equal, as it ought to be, to one of the. angles
made by the two sides of the cone which are in the plane of
the focal lines, namely to the angle within which the inter-
nal axis lies.

If we conceive the cone to have its vertex at the centre of
a sphere, and the points F, F’,S to be on the surface of this
sphere, the arcs of great circles connecting the point S with
each of the fixed points F, F’ will have a constant sum. The
curve formed by the intersection of the sphere and the cone
may therefore, from analogy, be called a spherical ellipse,
or, more generally, a spherical conic, because, by removing
one of its foci F, F’ to the opposite extremity of the diame-
ter of the sphere, the difference of the arcs SF and SF’ will
be constant, which shows that the spherical curve is analo-
gous to the hyperbola as well as to the ellipse. Hither of
these plane curves may, in fact, be obtained as a limit of the
spherical curve when the sphere is indefinitely enlarged, ac-
cording as the diameter along which the enlargement takes
place, and of which one extremity may be conceived to be
fixed while the other recedes indefinitely, coincides with the
internal or with the directive axis of the cone. The fixed
extremity becomes the centre of the limiting curve, which is
an ellipse in the first case, and a hyperbola in the second.

The great circle touching a spherical conic at any point
makes equal angles with the two arcs of great circles which
join that point with the foci, because the sum of these arcs
is constant. This is identical with a property already de-
monstrated relative to the tangent planes of the cone. In-
deed it is obvious that the properties of the cone may also
be stated as properties of the spherical conic, and this is
frequently the more convenient way of stating them.

§ 5. If the sides of one cone be perpendicular to
the tangent planes of another, the tangent planes of the
former will be perpendicular to the sides of the latter. For
the plane of two sides of the first cone is perpendicu-

es

483

lar to the intersection of the two corresponding tangent
planes of the second cone; and as these two sides ap-
proach indefinitely to each other, their plane approaches to
a tangent plane, while the intersection of the two correspond-
ing tangent planes of the second cone approaches indefi-
nitely to aside of the cone. ‘Thus any given side of the one
cone corresponds to a certain side of the other; and any
side of either cone is perpendicular to the plane which
touches the other along the corresponding side. This rea-
soning applies to cones of any kind.

Two cones so related may be called reciprocal cones.
When one is of the second order, it will be found that the
other is also of the second order, and that, in their equations
relative to their axes, which are obviously parallel or coinci-
dent, the coefficients of the squares of the corresponding va-
riables are reciprocally proportional, so that the equations

2 2

2
Px” + ay’ + R2? = 0, ~+2+—=0, (1)

express two such cones which have a common vertex. These
cones have the same internal axis, but the directive axis of
the one coincides with the mean axis of the other, and it may
be shown from the equations that the directive planes of the
one are perpendicular to the focal lines of the other. The
two curves in which these cones are intersected by a sphere,
having its centre at their common vertex, are reciprocal
spherical conics. In general, two curves traced on the sur-
face of a sphere may be said to be reciprocal to each other,
when the cones passing through them, and having a common
vertex at the centre of the sphere, are reciprocal cones. Any
given point of the one curve corresponds to a certain point
of the other, and the great circle which touches either curve
at any point is distant by a quadrant from the corresponding
point of the other curve.

By means of these relations any property of a cone of the
second order, or of a spherical conic, may be made to produce

484

a reciprocal property. Thus, we have seen that the tangent
plane of a cone makes equal angles with two planes passing
through the side of contact and through each of the focal
lines; therefore, drawing right lines perpendicular to the
planes, and planes perpendicular to the right lines here men-
tioned, we have, in the reciprocal cone, a side making equal
angles with the right lines in which the directive planes of
this cone are intersected by a plane touching it along that
side. Itis therefore a property of the cone, that the inter-
sections of a tangent plane with the two directive planes
make equal angles with the side of contact; a property which
it is easy to prove without the aid of the reciprocal cone.

The two directive sections drawn through any point S of
a given surface of the second order may, when they are cir-
cles, be made the directive sections of a cone, and this may
obviously be done in two ways. Each of the two cones so
determined will be touched by the plane which touches the
given surface at the point S, because the right lines which
are tangents to the two circular sections at that point, are
tangents to each cone as well as to the given surface; there-
fore the side of contact of each cone bisects one of the an-
gles made by these two tangents; and hence the two sides of
contact are the principal directions in the tangent plane at
the point S, that is, they are the directions of the greatest
and least curvature of the given surface at that point; for
these directions are parallel to the axes of a section made in
the surface by a plane parallel to the tangent plane, and the
axes of any section bisect the angles contained by the right
lines in which the plane of section cuts the two directive
planes. Niet

§ 6. It has been shown that the sum of the angles which
any side of a cone makes with its focal lines is constant.
Hence we obtain the reciprocal property, that* the sum of

* This property, and that to which it ‘is reciprocal, as well as some other
properties of the cone, were, together with the idea of reciprocal cones and of

485

the angles (properly reckoned) which any tangent plane of a
cone makes with its two directive planes is constant. This
property may be otherwise proved as follows.

Through a point assumed anywhere in the side of con-
tact, let two directive planes be drawn. As the circles in
which the cone is cut by these planes have a common chord,
they are circles of the same sphere; and a tangent plane ap-
plied to this sphere, at the aforesaid point, coincides with
the tangent plane of the cone, because each tangent plane
contains the tangents drawn to the two circles at that point.
The common chord of the circles is bisected at right angles
by the principal plane which is perpendicular to the direct-
ive axis, and therefore that principal plane contains the
centres of the two circles and the centre of the sphere. Now
the acute angle made by a tangent plane of a sphere with
the plane of any small circle passing through the point of
contact, is evidently half the angle subtended at the centre
of the sphere by a diameter of that circle; therefore the
acute angles, which the common tangent plane of the cone
and of the sphere above-mentioned makes with the planes of
the directive sections, are the halves of the angles subtended
at the centre of the sphere by the diameters of the sections,
But the diameters which lie in the principal plane already
spoken of, and are terminated by two sides of the cone, are
chords of the great circle in which that plane intersects the

spherical conics, suggested by my earliest researches connected with the mechani-
cal theory of rotation and the laws of double refraction. I was not then aware that
the focal lines of the cone had been previously discovered, nor that the spherical
conic had been introduced into geometry. Indeed all the properties of the cone
which are given inthis paper were first presented to me in my own investiga-
tions. Its double modular property, related to the vertex as focus, was one of
the propositions in the theory of the rotation of a solid body, and was used in
finding the position of the axis of rotation within the body at a given time. But
the modular property common to all the surfaces of the second order was not
discovered until some years later.

486

sphere; and the halves of the angles which they subtend
at its centre are equal to the angles in the greater segments
of which they are the chords, and consequently equal to the
two adjacent acute angles of the quadrilateral which has
these chords for its diagonals. Hence, as two opposite
angles of the quadrilateral are together equal to two right
angles, it follows that the four angles of the quadrilateral repre-
sent the four angles, the obtuse as well as the acute angles,
which the tangent plane of the cone makes with the planes
of the directive sections; the two angles of the quadrilateral
which lie opposite to the same diagonal being equal to the
acute and obtuse angles made by the tangent plane with the
plane of the section of which that diagonal is the diameter.

Thus any two adjacent angles of the quadrilateral may
be taken for the angles which the tangent plane of the cone
makes with the directive planes. If we take the two adja-
cent angles which lie in the same triangle with the angle x
contained by the two sides of the cone that help to form the
quadrilateral, the sum of these two angles will be equal to
two right angles diminished by «x; and if we take the two
remaining angles of the quadrilateral, their sum will be equal
to two right angles increased by «; both which sums are
constant. But if we take either of the other pairs of adja-
cent angles, the difference of the pair will be constant, and
equal to x.

The same conclusion may be deduced as a property of
the spherical conic. Let a great circle touching this curve
be intersected in two points, one oneach side of the point of
contact, by the two directive circles, that is, by two great
circles whose planes are directive planes of the cone which
passes through the conic and has its vertex at the centre of
the sphere. Since the right lines in which the tangent plane
of a cone intersects the directive planes are equally inclined
to the side of contact, the arc intercepted between the points
where the tangent circle of the conic intersects the directive

487

circles is bisected in the point of contact ; therefore, either
of the spherical triangles whose base is the tangent arc so in-
tercepted, and whose other two sides are the directive circles,
has a constant area; because, if we suppose the tangent arc
to change its position through an indefinitely small angle,
and to be always terminated by the directive circles, the two
little triangles bounded by its two positions and by the two
indefinitely small directive arcs which lie between these posi-
tions, will have their nascent ratio one of equality, so that
the area of either of the spherical triangles mentioned above,
will not be changed by the change in the position of its base.
But in each of these triangles the angle opposite the base
is constant; therefore the sum of the angles at the base is
constant.

From this reasoning itappears that if a spherical triangle
have a given area, and two of its sides be fixed, the third
side will always touch a spherical conic having the fixed sides
for its directive arcs, and will be always bisected in the point
of contact.

§ 7. The intersection of any given central surface of the
second order with a concentric sphere is a spherical conic,
since the cone which passes through the curve of intersection
and has its vertex at the common centre, is of the second
order. The cylinder also, which passes through the same
curve and has its side parallel to any of the arcs of the given
surface, is of the second order; and the cone, the cylinder,
and the given surface are condirective, that is, the directive
planes of one of them are also the directive planes of each
of the other two. This may be seen from the equations of
the different surfaces; for, in general, two surfaces, whose
principal planes are parallel, will be condirective, if, when
their equations are expressed by coordinates perpendicular
to these planes, the differences of the coefficients of the
squares of the variables in the equation of the one be pro-

VOL. Il, 2T

488

portional to the corresponding differences in the equation of
the other.

If any given surface of the second order be intersected
by a sphere whose centre is any point in one of the principal
planes, the cylinder passing through the curve of intersection,
and having its side perpendicular to that principal plane, will
be of the second order, and will be condirective with the
given surface. This cylinder, when its side is parallel to the
directive axis, is hyperbolic; otherwise it is elliptic. If
a paraboloid be cut by any plane, the cylinder which passes
through the curve of section and has its side parallel to the
axis of the paraboloid, will be condirective with that surface ;
and it will be elliptic or hyperbolic, according as the para-
boloid is elliptic or hyperbolic.*

If two concentric surfaces of the second order be recipro-
cal polars with respect to a concentric sphere, the directive
axis of the one surface will coincide with the mean axis of
the other, and the directive planes of the one will be perpen-
dicular to the asymptotes of the focal hyperbola of the other.
When one of the surfaces is a hyperboloid, the other is a
hyperboloid of the same kind ; the asymptotes of the focal hy-
perbola of each surface are the focal lines of its asymptotic
cone; and the two asymptotic cones are reciprocal.

When any number of central surfaces of the second order
are confocal, or, more generally, when their focal hyperbolas
have the same asymptotes, it is obvious that their reciprocal
surfaces, taken with respect to any sphere concentric with
them, are all condirective.

§ 8. If a diameter of constant length, revolving within a

*T have introduced the terms directive and condirective, as more general
than the terms eyclic and biconcyclic employed by M. Chasles. The latter terms
suggest the idea of circular sections, and therefore could not properly be used
with reference to the hyperbolic paraboloid, or to the hyperbolic or parabolic

cylinder, in each of which surfaces a directive section is a right line.

489

given central surface, describe a cone having its vertex at
the centre, the extremities of the diameter will lie in a sphe-
rical conic. And if the cone be touched by any plane, the
side of contact will evidently be normal to the section which
that plane makes in the given surface, and will therefore be
an axis of the section. As the axes of a section always bi-
sect the angles made by the two right lines in which its
plane intersects the directive planes of the surface, and as the
cone aforesaid has the same directive planes with the given
surface, it follows that theright lines in which a tangent plane
of a cone cuts its directive planes are equally inclined to the
side of contact ; a theorem which has been already obtained
in another way.

If a section be made in a given central surface by any
plane passing through the centre, the cone described by a
constant semidiameter equal to either semiaxis of the sec-
tion will touch the plane of section; for if it could cut that
plane, a semiaxis would be equal to another radius of the
section. Denoting by 7,7’ the semiaxes of the section, con-
ceive two cones to be described by the revolution of two
constant semidiameters equal to 7 and r’ respectively. These
cones are condirective with the given surface, and have the
plane of section for their common tangent plane. Supposing
that surface to be expressed by the equation

a y? 2
EN ila RIT Ne (2)

and the directive axis to be that of y, the axis of «x will be
the internal axis of one cone, say of that described by 7, and
the axis of 2 will be the internal axis of the other cone.
Let « be the angle made by the two sides of the first cone
which lie in the plane xz, and «’ the angle made by the two
sides of the second cone which lie in the same plane; the
former angle being taken so as to contain the axis of x within
it, and the latter so as to contain within it the axis of z.

272

490

Then, considering 7,7’ as radii of the section zz of the sur-
face, we have obviously

1 cos?4x , sin? 4x Lak ‘Wiese!

217 ne 24!
1 008 ak sin’ 2k = 1245 — + (4+ )cose’
72 R P P R P ae

observing that when these formule give a negative value for
r or 7, in which case the surface expressed by the equation
(2) must be a hyperboloid, the direction of r or r’ meets, not
that surface, but the surface of the conjugate hyperboloid
expressed by the equation

x y? id Om
at igitnaen es Tae (4)

Now calling 0 and 6’ the angles made by the tangent plane
of the cones with the directive planes of the given surface,
which are also the directive planes of each cone, the angles
x, k’ depend on the sum or difference of 0 and 0’. If the
latter angles be taken so that their sum may be equal to the
supplement of «, their difference will be equal to x’, and the
formule (3) will become

a= 3(t 4) — a(t) cos (0+ 0%

aOR. CHE (5)
wa= (S++) —3(Z—*)cos@ - 6,

by which the semiaxes of any central section are expressed
in terms of the non-directive semiaxes of the surface, and of
the angles which the plane of section makes with the direc-
tive planes.*

* See the Transactions of the Royal Irish Academy, vol. xxi., as before
cited. The formule (5) were first given, for the case of the ellipsoid, by
Fresnel, in his Theory of Double Refraction, Mémoires de 1’Institut, tom. vii.,
p. 155.

491

§ 9. From the centre O of the surface expressed by equa-
tion (2) let a right line OS be drawn cutting perpendicu-
larly in & the plane which touches the surfaceat S. Let o
denote the length of the perpendicular O3, and a, (3, y the
angles which it makes with x, y, z. Then

o = Pcos’a + Qcos*3 + Ros *y. (6)

From this formula it is manifest, that ifthree planes touching
the surface be at right angles to each other, the sum of the
squares of their perpendicular distances from the centre will
be equal to the constant quantity Pp + @+ R, and therefore
the point of intersection of the planes will lie in the surface

of a given sphere. If another surface represented by the
equation

Po Qo Ro

be touched by a plane cutting OS perpendicularly in 2), and
if oo be the length of OS,, then

oo” = Py Cos a + Qy)cos 73 + Ry Cos *y;

and therefore when the two surfaces are confocal, that is,
when

P—Py=Q—Q=R—R=—f,

we have o? — o,? = k, which is a constant quantity. Hence
if three confocal surfaces be touched by three rectangular
planes, the sum of the squares of the perpendiculars dropped
on these planes from the centre will be constant, and the
locus of the intersection of the planes will be a sphere.

The focal curves of a given surface are the limits of sur-
faces confocal with it,* when these surfaces are conceived,

* It was by this consideration, arising out of the theorems given im this and
the next section about confocal surfaces, that I was led to perceive the na-

ture of the focal curves, and the analogy between their points and the foci of

492

by the progressive diminution of their mean or secondary
axes, to become flattened, and to approach more and more
nearly to.a plane passing through the primary axis. And it
will appear hereafter, that if a bifocal right line, that is, a
right line passing through both focal curves, be the inter-
section of two planes touching these curves, those two planes
will be at right angles to each other. Therefore the locus
of the point where a tangent plane of a given central surface
is intersected perpendicularly by a bifocal right line is a
sphere. The primary axis of the surface is evidently the
diameter of this sphere.

Hence we conclude that the locus of the point where
a tangent plane of a paraboloid is intersected perpendicu-
larly by a bifocal right line is a plane touching the parabo-
loid at its vertex. For a paraboloid is the limit of a central
surface whose primary axis is prolonged indefinitely in one
direction, and a plane is the corresponding limit of the
sphere described on that axis as diameter. As this consi-
deration is frequently of use in deducing properties of para-
boloids from those of central surfaces, it may be well to state
it more particularly. It is to be observed, then, that the
indefinite extension of the primary axis at one extremity
may take place according to any law which leaves the other
extremity always at a finite distance from a given point, and
gives a finite limiting parameter to each of the principal sec-
tions of the surface which pass through that axis. The
simplest supposition is, that one extremity of the axis and the
adjacent foci of those two principal sections remain fixed,
while the other extremity and the other foci move off, with
the centre, to distances which are conceived to increase with-
out limit. Then, at any finite distances from the fixed

conics. And I regarded that analogy as fully established when I found (in March
or April, 1832) that the normal at any point of a surface of the second order is
an axis of the cone which has that point for its vertex and a focal for its base.

493

points, the focal curves approach indefinitely to parabolas,
as do also all sections of the surface which pass through the
primary axis, while the surface itself approaches indefinitely -
to a paraboloid ; so that the limit of the central surface is a
paraboloid having parabolas for its focal curves. The limit
of an ellipsoid, or of a hyperboloid of two sheets, is an ellip-
tic paraboloid, having one of its focals modular and the
other umbilicar, like each of the central surfaces from which
it may be derived; and the limit of a hyperboloid of one
sheet is a hyperbolic paraboloid, having, like that hyberbo-
loid, both its focals modular.

§ 10. Let the plane touching at S the surface expressed
by equation (2), intersect the axis ofa in the point X, and let
the normal applied at S intersect the planes yz, zz, xy, in
the points L, M, N respectively. Since the section made in
the surface by a plane passing through OX and the point S
has one of its axes in the direction of OX, it appears, by an
elementary property of conics, that the rectangle under OX
and the coordinate x of the point S is equal to the quantity
p; but that coordinate is to LS as OS oro isto OX, and
therefore the rectangle under o and LS is equal to Pp. Simi-
larly the rectangle under o and MS is equal to q, and the
rectangle under o and NS is equal to r. Thus the
parts of the normal intercepted between the point S and
each of the principal planes, are to each other as the
squares of the semiaxes respectively perpendicular to these
planes; the square of an imaginary semiaxis being regarded
as negative, and the corresponding intercept being measured
from S in a direction opposite to that which corresponds toa
real semiaxis.

The rectangle under o and the part of the normal inter-
cepted between two principal planes, is equal to the difference
of the squares of the semiaxes which are perpendicular to
these planes. This rectangle is therefore constant, not only

494,

for a given surface, but for all surfaces which are confocal
with it.

Hence the part of the normal intercepted between two
principal planes bears a given ratio to the part of it inter-
cepted between one of these and the third principal plane,
whether the normal be applied at any point of a given sur-
face, or at any point of a surface confocal with it. .

If therefore normals to a series of confocal surfaces be all
parallel to a given right line, they must all lie in the same
plane passing through the common centre of the surfaces,
because otherwise the parts of any such normal, which are
intercepted between each pair of principal planes, would not
be in a constant ratio to each other.

The point S being the point at which any of these paral-
lel normals is applied, the plane touching the surface at S is
parallel to a given plane, the perpendicular OS dropped
upon it from the centre has a given direction, the plane
OS® is fixed, and the directions of the lines OL,OM, ON
in which this plane intersects the principal planes are also
fixed. And as the angle OSS is always a right angle, and
the normal at S is always parallel to O3, the distance SS
bears a given ratio to each of the distances OL, OM, ON,
and therefore also to each of the intercepts MN, LN, LM.
Hence, since the rectangle under O% and any one of these
intercepts is constant, the rectangle under OS and S3 is
constant.

Therefore if a series of confocal central surfaces be
touched by parallel planes, the points of contact will all lie
in one plane, and their locus, in that plane, will be an equila-
teral hyperbola, having its centre at the centre of the sur-
faces, and having one of its asymptotes perpendicular to the
tangent planes. This hyperbola evidently passes through two
points on each of the focal curves, namely the points where
the tangent to each curve is parallel to the tangent planes.

If a series of confocal paraboloids be touched by parallel

495

planes, it will be found that the points of contact all lie in a
bifocal right line, and that the normals at these points lie in
a plane parallel to the axis of the surfaces; so that the part
of any normal which is intercepted by thetwo principal planes
is constant. This theorem may be proved from the two follow-
ing properties of the paraboloid:—1. A normal being ap-
plied to the surface at the point S, the segments of the
normal, measured from S to the points where it intersects
the planes of the two principal sections, are to each other in-
versely as the parameters of these sections. 2. Supposing
the axis of x to be that of the surface, the difference between
the coordinates x of the point S and of the point where the
normal meets the plane of one of the principal sections, is
equal to the semiparameter of the other principal section.

§ 11. Let a tangent plane, applied at any point S ofa
surface of the second order, intersect the plane of one of its
focals in the right line ©, and let P be the foot of the per-
pendicular dropped from S upon the latter plane. The pole
of the right line ©, with respect to the principal section
lying in this plane, is the point P. Let N be its pole with
respect to the focal. Then if T be any point of the right
line ©, the polar of this point with respect to the section
will pass through P, and its polar with respect to the focal
will pass through N; and if the former polar intersect the
dirigent curve in A, A’, and the latter intersect the focal in
F, F’, the points F, F’ will correspond respectively to the
points A, A’,and the distances AA’ and FF’ will be similarly
~ divided by the points P and N (See Part I. § 8). But since
the point S is in the plane of the two directrices which pass
through A and A’, the lengths AP and A’P, which are the
perpendicular distances of S from the directrices, are pro-
portional to the lengths FS and F’S. Therefore FN is to
F’N as FS is to F’S, and the right line NS bisects one of the
angles made by the right lines FS and F’S. And as thisholds
wherever the point T is taken on the right line ©, that is,

496

in whatever direction the right line FF’ passes through the
point N, it follows that the right line NS is an axis of the
cone which has the point § for its vertex and the focal for
its base. Further, if FF’ intersect © in the point Q, we
have FN to F’N as FQ is to F’Q, because N is the pole of
© with respect to the focal; therefore FQ is to F’Q as
FS is to F’S, and hence the right line QS also bisects one of
the angles made by FS and F’S. The right lines NS and
QS are therefore at right angles to each other, and as the
latter always lies in the tangent plane, the former must be
perpendicular to that plane.

Consequently the normal at any point abe a surface of the
second order is an axis of the cone which has that point for
its vertex and either of the focals for its base.

It is known that when two confocal surfaces intersect
each other, they intersect everywhere at right angles; and
that through any given point three surfaces may in general
be described, which shall have the same focal curves. If three
confocal surfaces pass through the point S, the normal to
each of them at S is an axis of each of the cones which stand
on the focals and have S for their common vertex. The
normals to the three surfaces are therefore the three axes of
each cone.

If the points at which a series of confocal surfaces are
touched by parallel planes be the vertices of cones having
one of the focals for their common base, each of these cones
will have one of its axes perpendicular to the tangent planes.
Therefore when an axis of a cone which stands on a given
base is always parallel to a given right line, the locus of the
vertex is an equilateral hyperbola or a right line, according
as the base is a central conic or a parabola.

§ 12. A system of three confocal surfaces intersecting
each other consists of an ellipsoid, a hyperboloid of one
sheet, and a hyperboloid of two sheets, if the focals be
central conics; but it consists of two elliptic paraboloids

497

and a hyperbolic paraboloid, if the focals be parabolas. In
the central system, the ellipsoid has the greatest primary
axis, and the hyperboloid of two sheets the least; and the
focal which is modular in one of these surfaces is umbilicar
in the other. The asymptotic cones of the hyperboloids
are confocal, the focal lines of each cone being the asymptotes
of the focal hyperbola. In the system of paraboloids, the
two elliptic paraboloids are distinguished by the circum-
. stance that the modular focal of the one is the umbilicar
focal of the other.

The curve in which two confocal surfaces intersect each
other is a line of curvature of each, as is well known ;* and
a series of lines of curvature on a given surface are found by
making aseries of confocal surfaces intersect it.

Now ifa series of the lines of curvature of a given surface
be projected on one ofits directive planes by right lines paral-
lel to either of its non-directive axes, the projections will be
a series of confocal conics ; and when the surface is umbili-
car, the foci of all these conics will be the corresponding
projections of the umbilics.{ When the surface is not um-
bilicar, its directive axis will be parallel to the primary axis
of the projections.

The same line of curvature has two projections, accord-
ing as it is projected by right lines parallel to the one or to
the other non-directive axis. In the ellipsoid these projec-
tions are always curves of different kinds, the one being an
ellipse when the other is a hyperbola; but in a hyperboloid
the projections are either both ellipses or both hyper-
bolas. In the hyperbolic paraboloid the projections are
parabolas. In the elliptic paraboloid, one of the projections
is always a parabola, and the other is either an ellipse or a
hyperbola.

* See Dupin’s Développements de Géométrie.
+ Exam. Papers, An. 1838, p. xlvi., quest. 4; p. xcix., quest. 70.

498

The corresponding projections of two lines of curvature
which pass through a given point of the surface, are confo-
cal conics intersecting each other in the projection of that
point, and of course intersecting at right angles.

§ 13. A bifocal chord is a bifocal right line terminated
both ways by the surface.* _ In a central surface, the length
of a bifocal chord is proportional to the square of the dia-
meter which is parallel to it; the square of the diameter
being equal to the rectangle under the chord and the pri-
mary axis.

More generally, if a chord of a given central surface touch
two other given surfaces confocal with it, the length of the
chord will be proportional to-the square of the parallel dia-
meter of the first surface, the square of the diameter being
equal to the rectangle under the chord and a certain right
line 2/, determined by the formula

PQR
=") @ = 89)’ ‘
wherein it is supposed that the equation (2) represents the
first surface, and that P’, e’” are the quantities corresponding
to P in the equations of the other two surfaces.

In any surface of the second order, the lengths of two
bifocal chords are proportional to the rectangles under the
segments of any two intersecting chords to which they are
parallel.

In the paraboloid gah by the ane

2

£42

P=

if x be the length of a nat chord making the angles 8
and y with the axes of y and z respectively, we have
1 _ cos *83 4 08 ci

joy Lp q ®)

* The theorems in § 13 are now stated for the first time.

499

§ 14, At the point S on a given central surface expressed
by the equation (2), let a tangent plane be applied, and
let k, k’ be the squares of the semiaxes of a central section
made in the surface by a plane parallel to the tangent plane ;
each of the quantities 4, k’ being positive or negative accord-
ing as the corresponding semiaxis of the section is real or
imaginary, that is, according as it meets the given surface or
not. Then the equations* of two other surfaces confocal
with the given one, and passing through the point S, are

2 2 2 a y”

# y ae EMP: es
=a ya a mY aa TE a LRN Gay (9)

Q

The given surface is intersected by these two surfaces re-
spectively in the two lines of curvature which pass through
the point S; the tangent drawn to the first line of curvature
at S is parallel to the second semiaxis of the section, and the
tangent drawn to the second line of curvature at S is parallel
to the first semiaxis of the section.

When two confocal surfaces intersect, the normal applied
to one of them at any point S of the line of curvature formed
by their intersection lies in the tangent plane of the other,
and is parallel to an axis of any section made in the
latter by a plane parallel to the tangent plane. Sup-
posing the surfaces to be central, if two normals be applied
at the point S, and a diameter of each surface be drawn pa-
rallel to the normal of the other, the two diameters so
drawn will be equal and of a constant length, wherever the
point S is taken on the line of curvature; the square of that
length being equal to the difference of the squares of the
primary axes of the surfaces, and the diameter of the sur-
face which has the greater primary axis being real, while
that of the other surface is imaginary. As the point
S moves along the line of curvature, each constant diameter

* Exam. Papers, An. 1837, p.c., quests. 4, 5, 6; An. 1838, p.c., quests. 71, 72.

500

describes a cone condirective with the surface to which it
belongs; the two cones so described are reciprocal, and the
focal lines of the cone which belongs to one surface are
perpendicular to the directive planes of the other surface.

When two confocal paraboloids intersect, if normals be
applied to them at any point S of their intersection, and a
bifocal chord of each surface be drawn parallel to the nor-
mal of the other, the two chords so drawn will be equal and
of a constant length, wherever the point S is taken in the
line of intersection of the surfaces ; that constant length
being equal to the difference between the parameters of
either pair of coincident principal sections.

§ 15. The point S being the common intersection of a
given system of confocal surfaces, of which the equations
are

x Ph ayes x g
—4+24 551, [4+54+—5=1,
P Q R Q
(10)
Ad y? 2? a
pit gi ty

suppose that another surface A confocal with these, and ex-
pressed by the equation

ae y? 2
—+=++—=!1 11
Pramas Ge : ( )

is circumscribed by a cone having its vertex at S. Ifthe
normals applied at S to the given surfaces, taken in the order
of the equations (10), be the axes of new rectangular coor-
dinates &, n, Z, the equation of the cone, referred to these
coordinates, will be*

* The equation (12) was obtained in the year 1832, and was given at my
lectures in Hilary Term, 1836. The most remarkable properties of cones
circumscribing confocal surfaces, are immediate consequences of this equation.
That such cones, when they have a common vertex, are confocal, their focal lines
being the generatrices of the hyperboloid of one sheet passing through the ver-

— =

E n° a ,
Soas aces oop = 0. (12)

The surfaces of the given system, in the order of their
equations, may be supposed to be an ellipsoid, a hyperbo-
loid of one sheet, and a hyperboloid of two sheets; the axes
of x, y, z being respectively the primary, the mean, and the
secondary axes of each surface. Then P is greater than Pp’,
and Pp’ greater than Pp”.

The normals to the given surfaces are the axes of the cone
expressed by the equation (12); and if the surface A be
changed, but still remain confocal with the given system, it
is obvious from that equation that the focal lines of the cir-
cumscribing cone will remain unchanged, since the differences
of the quantities by which the squares of €, n, ¢ are divided
are independent of the surface A. As P’ is intermediate
in value between P and p”, the normal to the hyperbo-
loid of one sheet is always the mean axis of the cone; the
focal lines lie in the plane &Z, and their equation is

ey eee PS (13)

which shows that they are parallel to the asymptotes of a
central section made in the hyperboloid of one sheet by a
plane parallel to the plane &Z, since the quantities rp’ — p and
p’ — p” are (including the proper signs) the squares of the
semiaxes of the section which are parallel to & and Z re-

tex, was first stated by Professor C. G. J. Jacobi, of Konigsberg, in 1834.
See Crelle’s Journal, vol. xii., p. 137. See also the excellent work of M.
Chasles, published in 1837, and entitled ‘‘ Apercu historique sur l’Origine
et le Developpement des Méthodes en Géométrie ;” p. 387. The analogy which
exists between the focals of surfaces and the foci of curves of the second order
was supposed by M. Chasles to have been pointed out in that work for the first
time (Comptes rendus, tom. xvi., pp. 833, 1106); but that analogy had been
previously taught and developed in the lectures just alluded to.

502

spectively. The focal lines are therefore the generatrices
of that hyperboloid at the point S.
When r, = 0, the ea (12) becomes
2

Syst (14)
which is that of the cone standing on the focal ellipse and
having its vertex at S. When qa = 0, the same equation
becomes

Sc oe | (15)

which is that of the cone standing on the focal hyperbola,
and having its vertex at S. The normal to the hyperboloid
of one sheet at the point S is the mean axis of both cones;
the normal to the ellipsoid is the internal axis of the first
cone and the directive axis of the second, while the nor-
mal to the hyperboloid of two sheets is the directive axis of
the first and the internal axis of the second.
The three surfaces expressed by the equations

(16)

are a confocal system, having their centre at S, and being
respectively an ellipsoid, a hyperboloid of one sheet, and a
hyperboloid of two sheets. ‘They intersect each other in the
centre of the system expressed by the equations (10), and
their normals at that point are the axes of a, y, z respectively.
The relations between the two systems of surfaces are there-
fore perfectly reciprocal. From the equations (14) and (15)
it is manifest that the asymptotic cones of the hyperboloids
of one system pass through the focals of the other.

§ 16. The point S being the intersection of a given sys- |

tem of confocal paraboloids whose equations are

ee ee

508

ye i
a7, + T= x + h 5
Pp q
where p—p’=q— q'=4(4—/h’), and p—p"=q—q"
= 4(h —h”); suppose that another paraboloid A confocal
with these, and expressed by the equation

2 2
Fie F=2+h, (18)

Poi Fe
is circumscribed by a cone having its vertex at S. Then if
the normals applied at Sto the given system of surfaces,
taken in the order of their equations, be the axes of the coor-
dinates &, n, Z respectively, the equation of the circumscribing
cone will be

2 2 2

LAS" sips 27 ee sleas =0; (19)

Bea RD iy Eng Letina has ed
showing that those normals are the axes of the cone, and
that the focal lines of the cone are independent of the sur-
face A, provided it be confocal with the given surfaces. If
the hyperbolic paraboloid be the second surface of the given
system, the parameter p’ will be intermediate in value be-
tween p and p”, and the equation of the focal lines of the
cone will be

2 2
na “E a
Bae ke! Ba aD
which is the equation of a pair of right lines parallel to the
asymptotes of a section made in the hyperbolic paraboloid by
a plane parallel to the plane €Z, since the quantities p’— p
and p’ — p” are proportional to the squares of the semiaxes
of the section which are parallel to € and Z respectively. The
focal lines are therefore the generatrices of the pcurlic
paraboloid at the point S.
VOL, I. 2u

210) (20)

504

Putting po and q alternately equal to zero in the equa-

tion (19), we get

ei; PEER 2 ae

[Des Mae giae! 2 q a,
the equations of two cones which have a common vertex at
S, the first of them standing on the focal which lies in the
plane xz, the second on the focal which lies in the plane xy.
The mean axis of each of these cones is the normal at S to
the hyperbolic paraboloid; the internal axis of either cone
is the normal to the elliptic paraboloid which has the base
of that cone for its modular focal.

As the cones which have a common vertex, and stand on

the focals of any surface of the second order, are confocal,
they intersect at right angles. Therefore when two planes

passing through a bifocal right line touch the focals, these

planes are at right angles to each other. And as cones
which have a common vertex, and circumscribe confocal
surfaces, are confocal, two such cones, when they intersect
each other, intersect at right angles. Therefore when a
right line touches two confocal surfaces, the tangent planes
passing through this right line are at right angles to each
other.

§ 17. When two surfaces are reciprocal polars* with re-
spect to any sphere, and one of them is of the second order,
the other is also of the second order. Let the surface B be
reciprocal to the surface A before mentioned, with respect to
a sphere of which the centre is S; and suppose R’ and R,to
be any corresponding points on these surfaces. ‘Then the
plane which touches the surface A at the point R, intersects
the right line SR’ perpendicularly in a point K, such that the
rectangle under SR’ and SK is constant, being equal to the

* Transactions of the Royal Irish Academy, vol. xvii., p. 241 ; Exam. Papers,
An, 1841, p. exxvi., quest, 4.

ba

505

square of the radius of the sphere. Now if the point K
approach indefinitely to S, the distance SR’ will increase
without limit, the surface B being of course a hyperboloid ;
and if through S any plane be drawn touching the surface
A, aright line perpendicular to this plane will evidently be
parallel to a side of the asymptotic cone of the hyperboloid.
The asymptotic cone of B is therefore reciprocal to the
cone which, having its vertex at S, circumscribes the surface
A. Hence, as the directive planes of a hyperboloid are the
same as those of its asymptotic cone, it follows that the direc-
tive planes of the surface B are perpendicular to the gene-
ratrices of the hyperboloid of one sheet, or the hyperbolic
paraboloid, which passes through S, and is confocal with
the surface A. And this relation between two reciprocal
surfaces ought to be general, whatever be the position of the
point S with respect to them ;* for though it has been de-
duced by the aid of the circumscribing cone aforesaid, it
does not, in its enunciation, imply the existence of such a
cone. This conclusion may be verified by investigating the
equation of the surface B in terms of the coordinates &, n, Z.
Suppose o to be the radius of the sphere with respect to which
the surfaces A and B are reciprocal. Then if A bea cen-
tral surface expressed by the equation (11), and having
Eo, no; So for the coordinates of its centre, the surface B will
be represented by the equation

(Boe: (EE) ay (2) — Fg) S
Siig (Eo E + non + ZS) ea p 3
but if A be a paraboloid expressed by the equation (18), the
equation of B will be
(p — po) & + (p! — py) + (p” — po)
= 4p’ (Ecosa + n cos + Z cos y),

where a, [3, y are the angles which the axis of x makes with

(22)

(23)

* This relation was first noticed by Mr. Salmon.

506

the axes of &, 1, Z respectively. In the first case, the equation
(22) shows that the directive planes of B are perpendicular
to the right lines expressed by the equation (13); in the
second case, the equation (23) shows that the directive
planes of B are perpendicular to the right lines expressed
by the equation (20).

When the surface A is a paraboloid, and the distance of
the point R from its vertex is indefinitely increased, the
plane touching the surface at R approaches indefinitely to
parallelism with its axis, and the right line SK, perpendicu-
lar to that plane, increases without limit. Therefore the
surface B passes through the point S, and is touched in that
point by aplane perpendicular to the axis of A.

When the point S lies upon the surface A, the coefficient
of the square of one of the variables, in the equation (22) or
(23), is reduced to zero, and the surface Bisa paraboloid hay-
ing its axis parallel to the normal applied at S to the surface
A. This also appears from considering that when S is a
point of the surface A, the normal at that point is the only
right line passing through §, which meets the see B at
an infinite distance.

Ifa series of surfaces be confocal, their reciprocal sur-
faces, taken with respect to any given sphere, will be condi-
rective.

When the equations of any two condirective surfaces are
expressed by coordinates perpendicular to their principal
planes, the constants in the equations may be always so taken
that the differences of the coefficients of the squares of the
variables in one equation shall be equal to the corresponding
differences in the other. Then by subtracting the one equa-
tion from the other, we get the equation of a sphere. There-
fore when two condirective surfaces intersect each other,
their intersection is, in general, a spherical curve. But when
the surfaces are two paraboloids of the same species, their
intersection is a plane curve.

507

§ 18. Through any point S of a given surface four bifo-
cal right lines may in general be drawn. Supposing the
surface to be central, let a plane drawn through the centre,
parallel to the plane which touches the surface at S, intersect
any one of theseright lines. ‘Then the distance of the point
of intersection from the point S will always be equal to the
primary semiaxis of the surface.*

If through any point S of a given central surface a right
line be drawn touching two other given surfaces confocal
with it, and if this right line be intersected by a plane drawn
through the centre parallel to the plane which touches the
first surface at S, the distance of the point of intersection
from the point S will be constant, wherever the point S is
taken on the first surface. If this constant distance be called
2, and the other denominations be the same as in the formula
(7), the value of 7 will be given by that formula.+

Professor Mac Cullagh communicated the following note
relative to the comparison of arcs of curves, particularly of
plane and spherical conics.

The first Lemma given in my paper on the rectification
of the conic sections (Transactions of the Royal Irish Aca-
demy, vol. xvi., p. 79) is obviously true for curves described
on any given surface, provided the tangents drawn to these -
curves be shortest lines on the surface. The demonstration
remains exactly the same; and the Lemma, in this general
form, may be stated as follows.

Understanding a tangent to be a shortest line, and sup-
posing two given curves E and F to be described on a given

* Exam. Papers, An. 1838, p. xlvii., quest. 9.

Tt In the notes to the last mentioned work of M, Chasles, on the History of
Methods in Geometry, will be found many theorems relative to surfaces of the
second order. Among them are some of the theorems which are giyen in the
present paper; but it is needless to specify these, as M. Chasles’s work is so
well known.

508

surface, let tangents drawn to the first curve at two points
T, ¢, indefinitely near each other, meet the second curve in
the points P, p. Then taking a fixed point A on the curve
E, if we put s to denote (according to the position of this
point with respect to T) the sum (or difference) of the are
AT and the tangent TP, and s + ds to denote the sum
(or difference) of the arc A¢ and the tangent ¢p, we shall
have ds equal to the projection of the infinitesimal are Pp
upon the tangent; that is, if a be the angle which the tan-
gent TP makes with the curve F at the point P, we shall
have ds equal to Pp multiplied by the cosine of a.

Now through the points P, p conceive other tangents
T’P, ¢’p to be drawn, touching the curve E in the points
T’, 2’; and let s’ and ds’ have for these tangents the same
signification which s and ds have for the former tangents.
Supposing the nature of the curve F to be such that it al-
ways bisects, either internally or externally, the angle made
at the point P by the tangents TP and T’P, it is evident that
ds = + ds’, and therefore either s + s’ or s — s’ is a con-
stant quantity.

A simple example of this theorem is afforded by the
plane and spherical conics. If the curves E and F be two
confocal conics, either plane or spherical, and tangents
TP, T’P be drawn to F from any point P of E (the tangents
being of course right lines when the curves are plane, and
arcs of great circles when they are spherical; in both cases
shortest lines) it is well known that the angle TPT’ made
by the tangents is always bisected by the conic E. The
angle is bisected internally or externally according as the
conics intersect or not. Hence we have the two following
properties* of confocal conics :—

* The first of these properties was originally given for spherical conics by
the Rey. Charles Graves, Fellow of Trinity College, in the ‘notes and addi-
tions” to histranslation of M. Chasles’s Memoirs on Cones and Spherical Conics,

509

1. When two confocal conics do not intersect, if one of
them be touched in the points T, T’ by tangents drawn from
any point P of the other, the sum of the tangents TP, T/P
will exceed the convex arc I'l’ lying between the points of
contact, by a constant quantity.

2. When two confocal conics intersect in the point A, if
one of them be touched in the points T, T’ by tangents
drawn from any point P of the other, the difference between
the tangents TP, T’P will be equal to the difference be-
the arcs AT, AT’.

These properties give the readiest and most elegant so-
lution of problems concerning the comparison of different
arcs of a plane or spherical conic. Any arc being given on
a conic, we may find another arc beginning from a given point,
which shall differ from the given are by a right line if the
conic be plane, or by a circular arc if the conic be sphe-
rical.

DONATIONS.

Memoires de la Société Géologique de France. Tom. 5.
Parts 1, 2. Presented by the Society.

The Tenth Annual Report of the Royal Cornwall Poly-
technic Society. (1842.) Parts 1 and 2. Presented by the
Society.

Bulletin de Academie Royale de Brucelles, from 5th of
November, 1842, to 8th of July, 1843.

p- 77 (Dublin, 1841). Mr. Graves obtained it as the reciprocal of the pro-
position, that when two spherical conics have the same directive circles, any
tangent are of the inner conic divides the outer one into two segments, each of
which has a constant area. Both properties, with the general theorem relative
to curves described on any surface and touched by shortest lines, were after-
wards givenin the University Calendar. See Exam. Papers, An. 1841, p. xli.,
quests. 3-6; An. 1842, p. Ixxxiii., quests. 30-34. These two properties of
conics were communicated, in October 1848, to the Academy of Sciences of
Paris, by M. Chasles, who supposed them to be new. See the Comptes rendus,
tom. xvii. p. 838.

510

Ordnance Survey of Tipperary, in 93 Sheets, including
Title and Index. Presented by His Excellency the Lord
Lieutenant.

Oberon’s Vision in the Midsummer Night’s Dream. Wlus-
trated by the Rev. N. J. Halpin. Presented by the Author.

Oversight over det Kongelige Danske Videnskabernes
Selskabs Forhandlinger og dets Medlemmers Arbeider, 1
Aaret, 1841. By Professor Oersted. Presented by the
Author.

The Numismatic Chronicle and Journal of the Numisma-
tic Society of London for July, 1843, (No. 21). Presented
by the Society. —

PROCEEDINGS

THE ROYAL IRISH ACADEMY.
1844. No. 43.
January 8.

SIR Wm. R. HAMILTON, LL.D., President, in the Chair,

William Henry and John Neville, Esquires, were elected
Members of the Academy.

The President read a letter from the Rev. James Ken-
nedy Bailie, D.D., presenting his “ Fasciculus Inscriptionum
Grecarum.”

The special thanks of the Academy were given to Dr.
Bailie for his donation.

Robert Ball, Esq., read a notice of the Means used by
the Ancients for attaching Handles to the Stone and Meta
Implements called Celts.

Mr. Ball stated that many years since, the lamented Dean
Dawson proposed to him to put handles to the four most re-
markable forms of celts, witha view of discovering the probable
manner in which these instruments were used. He accord-
ingly did affix the handles (exhibited to the Academy), and
they appeared satisfactorily to answer the question: but re-
cent observation has convinced him that in two at least of
these hypothetical mountings he was incorrect, as proved,
he thought, by a stone celt mounted, which was a short time
since brought from a mine in Mexico, and an iron one—a
war weapon—brought a few weeks since from Little Fish
Bay in Africa. As he deemed the subject one of interest to

VOL. Il. Dix.

512

antiquarians, he described as follows the mounting of the
recent implements alluded to, which, he conceived, may fairly

be assumed as the manner used in olden time for celts of
similar form.

3 INCHES.

—y
ee
LY,

The Mexican stone celt (No. 1) (whichis the property of
Mrs. Lyle) was mounted by placing a slender rod ateach side

513

of it, in the direction of its length, so that the larger ends of
the rods would have overlapped each other about two inches,
had they not been separated by the body of the instrument ;
a small cord was then loosely wound round the ends of the
rod and the included celt: when thus arranged, the smaller
ends of the rods were brought together and tied, forming
what sailors call a Spanish Windlass. The elasticity of the
rods keeping a constant strain, makes a more effective handle
than it would appear possible to form by ordinary tying, and
with much less expense of time and trouble. The iron celt
(No. 2) kindly given to Mr. Ball by Captain Adams, R.N., is
fixed in the bend of a club formed like a Scotch golf stick ;
by this arrangement, while the iron is so fixed that a stroke
serves to make it only the faster, the effectiveness of the
weapon is much increased by the weight of the knob at its
end. The accompanying figures illustrate the foregoing.

Mr. Ball observed that these were, he thought, proofs of
the value of seeking explanation of antiquarian difficulties,
by observing the analogies afforded by the less civilized por-
tions of the human race, rather than by indulging in hypo-
thetical fancies.

Mr. Oldham read a brief notice of a stone with Ogham
characters in the County of Waterford.

The stone referred to (fig 1) is well known throughout that
portion of the country, by the name of Ballyquin stone. It
stands on the road to Curraghmore from Carrick-on-Suir,
about three miles and a half from that town. This road is
comparatively a new one, and the stone has been left standing
about three feet from the ditch on the south side. It isa
single block of the hard and coarse red conglomerate, . so
abundant in the neighbourhood, and in the adjoining range
of the Commeragh mountains. In height it is eight feet, and
tapers gradually but irregularly from about four feet at the
base, to about one foot three inches at the top, and is about

2x2

514

one foot or a little more in average thickness. The sides of
the stone are rough, and do not exhibit any trace of chisel-
ling or tooling, further than possibly a rude dressing with

Fig. 1.

yur

\
iy

the hammer; but along the south east corner of the stone
(as it now stands), and extending from the summit to near
the base, are a series of Ogham characters of peculiar
interest. These have been carefully worked, the bottom of

515

the cuts or grooves which form them being quite smooth and
even, notwithstanding the very unfavourable texture of the
stone, composed as it is of pebbles varying in size, compo-
sition, and hardness. Some of these markings or letters are
imperfect, from injuries which the stone has received, or
from wear by exposure, but the drawing (fig. 1) gives a
tolerably accurate idea of its present state.

This Ogham differs in some respects from any with which
Mr. Oldham was acquainted. There is no combination of
more than four letters or grooves in it, and if the corner of
the stone be considered the centre line, to which these let-
ters should be referred, several of them do not come up to
that line, and in one case two appear interrupted or discon-
tinued in the centre; that is, there are portions of the cut
or groove corresponding to each other at both ends, but they
do not pass over the corner or central line. Mr. Oldham’s
object was, however, more particularly to add another to the
collection of Ogham inscriptions, and thus increase the data
from which some clue to these now unknown quantities might
perhaps be obtained. He was the more anxious to do this,
as this stone had been altogether omitted on the Ordnance
Maps of the County of Waterford recently published.

This stone is mentioned by Ryland in his History of Wa-
terford, who merely notices the existence of some defaced
markings. He alludes to the occurrence of caves in the
fields adjoining. Ballyquin is also the name of the town-
land in which the stone stands.

Mr. Oldham also presented drawings of some Oghams now
in the Cork Institution, and remarked how very desirable it
was that they should be published at once, the originals
being so liable to injury, either from accident or design.
Fig. 2, is a block of sandstone, very rough and unhewn, the
surface on which the letters or marks are cut being the only
flat one on the stone. It is about four feet six inches in

516

length, of which the letters extend two feet; one foot ten
inches broad at the top, and tapers rudely to the base.

Ms

i Aah thin, |

i
B

all

ool

Fig. 3 was “ dug out of an ancient fort or rath at Burnt-
fort, near Mallow, in the County of Cork, on the property of
H. Purcell, Esq.” It is of talcose mica slate, coarse-grained ;
the broad face is exceedingly rough and uneven; the nar-
row one more smooth and regular, being the natural cleavage
of the rock. It is nearly seven inches wide on the narrow
side, and fifteen on the broad, and about five feet high along,
being nearly a parallelogram. The cuttings are nearly
similar throughout in depth and care of execution.

Fig. 4 was found at Glounaglough, parish of Aghabolloge.
The entire stone is five feet seven inches long ; eleven inches
and a-half broad at top, and nearly nine at the bottom.
It is of a clayey-slate rock. The letters do not extend further
down the stone than one foot ten inches; it is nearly of the
same thickness all through, forming a thin slab. On the face
of the stone there are scrapings, and the lower letters are

517

not formed by a regular groove, as the upper are, but have
all the characters of such scratches as would be formed on a

stone by sharpening knives or other edged tools.

Fig. 4.

Sasi es =i vies
wh

i
f
Pa
i
if

Fig. 5 is of sandstone, rudely chiselled on the faces and
sides, and roughly rounded on the corners of the back, the
back itself being flat. It is two feet eight inches high; eleven
inches and a-half at the broadest part, and about seven inches
thick. In shape it has a rude resemblance to the ordinary
form of a coffin. The letters are distinct grooves, but they
do not appear to be all of the same age, as some are very
evidently new or recent, and, as in Fig. 3, very similar to the
scratches formed by sharpening tools.

The Cork Institution is indebted to the zeal of Messrs.
Windele and Abel for these valuable Ogham stones.

Dr. Apjohn read a notice, by the Rev. Thomas Knox, on
Cyanogen, as a Food for Plants.

518

Liebig having proved in his work on Agricultural Che-
mistry that the nitrogenous compounds of vegetables are de-
rived principally from the decomposition of ammonia, and
that the carbon is derived from the carbonic acid of the at-
mosphere, it occurred to me to try (while experimenting on
some manures) whether a source of each might not be found
in some salt of cyanogen (c,”). ‘This, I think, the following
facts will make probable. The salt I used for this purpose
was the ferro-cyanuret of potassium,

(K, Cfy — (OR N; + Fe + Ky.

EXPERIMENTS.

A piece of grass was selected in the garden, as being as
even and equal as possible, and five plots were marked out
on it, side by side, each containing exactly ten square yards ;
they were marked out by pegs in the corners, and a line put
round each while the salts were putting on, and during the
cutting of the grass. They were then manured as follows,
on the 17th of June last:

No. 1. Muriate of Ammonia, 3 oz.
2. Aqua Ammonia of the shops, 3 a pint; with Linseed
Oil, 4 pints.
3. Nothing.
4. Yellow Prussiate of Potash, 3 oz. In the usual state,
as sold by druggists, in crystals.
Phosphate of Soda, 13 oz.
Pearl Ash, 3 oz.
Sulphate of Magnesia, 13 oz.
Carbonate of Ammonia, 3 oz.

The salts on these two last plots were not laid on till the
26th of June, which gave them a slight disadvantage. They
were all mown on the 25th of September, and weighed fresh
the moment they were cut, when the weights were as fol-

lows:

519

No. 1. 232 lbs. when dry 73 lbs.
ead 6 uy 53
3. 213 be 61
4, 323 rf 93
5. 283 » 83

I cannot depend on the dry weight, nor draw any conclu-
sions from it, though it follows nearly the same proportion as
the fresh grass; the weather had been very wet, and it had
been left too long exposed to it.

The great advantage of the plot manured with the prus-
siate of potash over the others is very remarkable; for about
a month it seemed rather inferior to that manured with the
muriate of ammonia; but after that time the difference be-
came very perceptible to the eye or foot.

The final advantage of No. 4 above No. 1 is at the rate of
38 cwt. of fresh grass, or 83 cwt. of dry grass to the acre.
The reason of this superiority cannot arise from the nitrogen
alone, as the quantity of é¢ in the three ounces of muriate of
ammonia (applied to No. 1) actually exceeds that in the three
ounces of ferro-cyanuret of potassium, in the proportion of
13 to 11. It must, therefore, be sought for in the other ele-
ments of the salt.

Supposing this salt to be absorbed by the plant, and
decomposed in the same manner as the ammoniacal salts,
the plant will then obtain carbon and potash, as well as the
nitrogen, in the nascent state, which seems to be the only
way in which carbon can be assimilated. In fact almost every
element required by the plant is contained in this one com-
pound, and obtained by one and the same decomposition.

I beg leave to lay these facts before the Academy, as they
may prove interesting to those engaged in the subject of
manures, and may tend to throw a little further light on the
subject of the food of plants, should they be confirmed onrepe-
tition ; but I fear they can be of no service to the practical agri-

.

520

culturist, from the high price of all the compounds of
cyanogen.

Mr. George Yeates read a paper containing the results of
a Meteorological Journal for the year 1843.—See Appen-
dix V.

The Rev. H. Lloyd communicated a letter written many
years ago to his father, the late Dr. Lloyd, Provost of
Trinity College, by Mr. Mac Cullagh, who was then a
Fellowship-Candidate in the College. It relates principally
to a mechanical theory (that of the rotation of a solid body)
which Mr. Mac Cullagh was occupied with at that period,
and which he had occasion to allude to at the last meeting
of the Academy. The following is an extract from the letter.
The beginning and the date are wanting.

«“ THEorEM I.—If a rigid body, not acted on by any extraneous
forces, revolve round a fixed point O, and if an ellipsoid be described
having its semiaxes in the direction of the principal axes passing
through O, and equal to the radii of gyration round them ; thena
perpendicular to the invariable plane being raised from O to meet the
surface of the ellipsoid in I, the line OI (which is fixed in space, as
the ellipsoid revolves with the body) will be of a constant length
during the motion ; and a perpendicular from O upon the plane which
touches the surface at I, will always be the axis of rotation, and will
vary inversely as the angular velocity.

“ Corollaries.

“©1. Since every radius which is nearly equal to the greatest or
least semiaxis of an ellipsoid must lie near that semiaxis, it appears
that if, in the beginning of the motion, the point I be near the vertex
of either of these semiaxes, it will always be near it, since OI remains
constant ; and therefore, by the preceding construction, the axis of
rotation will always remain near the same semiaxis. Hence the ro-
tation about the axes of greatest and least moment in any body is
stable. The rotation about the axis of mean moment is unstable,
because the radii of an ellipsoid, which are nearly equal to the mean
semiaxis, do not: alllie near that semiaxis. ° “

521

‘¢ These things are evident from considering the trace of the con-
stant line OI on the surface of the ellipsoid, and observing that, in
general, its projection on the plane of the greatest and least axes is a
hyperbola, and its projections on the other two planes ellipses.

“2. Butif OI be equal to the mean semiaxisb(aand c being the
greatest and least) it will always intersect the body in the same plane,
and the ellipsoid in a circle. For there are two circular sections
through the mean axis; and therefore if the point I be at any instant
in either of them, it will remain in it during the motion. It would
be easy to show also, that the axis of rotation, connected with OI by.
the construction in the proposition, will in this case always remain in
a given plane within the body.

‘3, If two axes (or moments) of the ellipsoid are equal, OI will
describe in the body a conical surface round the third, and the
axis of rotation will always be in the same plane with OI and that
third axis, and these three lines will make constant angles with each
other ; also the perpendicular on the tangent plane, and therefore the
angular velocity, will be constant. These things are evident merely
from considering that the ellipsoid becomes one of revolution.

«4, Whatever be the forces applied to the body, the varying plane
of the maximum of areas and the axis of rotation are always con-
nected by the construction in the proposition. But the angular
velocity is no longer inversely as the perpendicular,

« To find the axis about which a body restrained by a fixed point
O, and acted on by given forces, will begin to revolve, is usually
considered a problem of great complexity. But it may be elegantly
solved by means of the ellipsoid described above. Reduce the given
forces to a single one through the fixed point O, and a pair; raise a
perpendicular to the plane of the pair from O to meet the ellipsoid
in I; a perpendicular from O to the tangent plane at I will be the
initial axis of rotation.

“‘ The construction is true whether the forces that set the body
in motion be impulses or pressures. If they be impulses, and no
external forces subsequently act on the body, the axis of rotation
will vary its position both in the body and in space ; its course in the
body is determined by the preceding theorem, as well as the variation
of the angular velocity. The motion of the body in space depends
mainly on the two following theorems and the rectification of the ellipse.

522

Let the principal axes of the ellipsoid (or ca

a, b, c) be OA, OB, OC.

«¢ THEOREM IJ.—If a perpendicular IP A -
be let fall from I on any of the principal Ke
planes (as AOC), the areolar velocity of P Gi
round O will be proportional to the perpendicular IP.

«¢ By areolar velocity I mean the increment of the area (as POp)
divided by the increment of the time when taken indefinitely
small.

«Since IP = +/(OI? — OP?), the position of OI, and therefore of
the axis of rotation at any given time, may be determined from this=
theorem by the method of quadratures; and it may be reduced
to the rectification of the ellipse.

« THEoreEM .II1].—Let a plane passing through the fixed line OI
and any of the principal axes (as OB), intersect the plane AOC in
OQ, and the invariable plane (to which OI is perpendicular) in a
straight line which may be called OR; the angular velocity of OR
is inversely as the square of OQ; and hence if OR be always taken
equal to OQ, the point R will describe in the invariable plane areas
proportional to the times.

“Since OQ is known at any time by the preceding proposition,
the position of OR at any time will be known from this by the me-
thod of quadratures. Also the inclination of the plane AOC to the
invariable plane is known, since it is equal to the angle OIP.
Hence the position of the body at any instant is completely deter-
mined.

‘For an application of the theoremslet us take the following prob-
lem :—-The body revolving round a line indefinitely near the greatest
or least of the principal axes, to find the time of an oscillation. By
the time of an oscillation I mean that in which OI, and consequently
the axis of rotation, returns to the same position within the body.

‘« Let the axis of rotation be indefinitely
near OA. Then w, y, 2 being the coordi-
nates ae we pig Yt-y +2 OP= Fk,

nae — sens = v4 —= |]. Therefore

Taiyo cfiitesaped oo oRovigy ke
ler al’ ten a) mae

Hence the locus of P is an ellipse whose semiaxes a’ and b’ are

by¥(@—h) acv@—k).
Wea By Vee *

and therefore its area

abe (a? — k*)

Vie Oe)

ral! =

« But I ought to have mentioned, as part of Theorem II., the me-
thod of determining in general the areolar velocity of P. Let the
angular velocity multiplied by the cosines of the angles which the
axis of rotation makes with OA, OB, OC be denoted (as is usual) by
Pq. These have constant ratios to the perpendiculars, as 1P,
drawn in that proposition ; and in that case the areolar velocity of P is
equal to 4 (b? — k*)q: and similarly when AOC is any of the other
principal planes. Hence, in the present instance, the areolar velocity
= 4 (a? — k*)p; and therefore the time of an oscillation

it Q-7be
Pp V (a — 6?) (a? — a®)

from the above value of the area of the ellipse, and observing that,
since OI is indefinitely near OA, IP and therefore p may be re-
garded as constant.

“If T denote the time of one revolution of the body round its

: F 2 ; 5
axis, then ultimately T= a and therefore the time of an oscilla-

tion is to the time of a revolution as the rectangle under the semiaxes
of the section BOC is to the rectangle under the eccentricities of
the other two sections. A similar theorem holds when the body re-
volves round a line indefinitely near the least principal axis. The
times of small oscillations of different magnitudes are equal, as in the
pendulum.

«« Many particular consequences might be deduced from what has
been said; but it will be better to mention some new theorems
about moments of inertia and centrifugal forces.

524

“The forces resulting from the centrifugal forces of abody of any
figure, revolving round an axis passing through a fixed point O, may
be found elegantly by the ellipsoid of which we have already made
so much use. Leta plane at right angles to the given axis OK,
and cutting it in K, touch the ellipsoid ;
in I; the centrifugal forces will be re-
duced to a pair whose moment is OK X
KI x «* (w being the angular velocity),
whose plane is OKI, and direction as

marked in the figure ; and a single force
equal to Mpa?, p being the distance of
the centre of gravity from OK.

‘If OK pass through thecentre of gravity, there remains only the
pair. The perpendicular OK is the radius of gyration for the axis
OK. Particular consequences of these things are numerous.

«¢ Any line, taken at random in a body, may not be a principal axis.
All the principal axes parallel to a given line lie in the same plane;
and the points of their lengths which must be fixed, in order that they
may be principal axes, will lie in a hyperbola. Suppose in this case
the point O (preceding fig.) to be the centre of gravity, and OK to
be parallel to the given line, and describe through I an equilateral
hyperbola whose asymptotes are OK and OL; then all the
principal axes, as O’K’, O”K", parallel to OK, lie in the plane
OKI, and the points O’, O” of their lengths, which must be fixed,
are at their intersections with the hyperbola.

“By means of theorems of this nature, all of which are proved
geometrically, without any calculation, I have been able to give a
complete geometrical solution of the problem of the motion of a solid
body not acted on by any forces. If it be acted on by given forces,
the differential equations in A, B, C and @, g, r, which are given by
all the writers on mechanics, are direct consequences of the first
principles, without the intervention of any calculation.

* * * * * * * *

«« Another thing with which I had occupied myself is the attrac-

* Multiplied by the mass of the body, or by M.

525

tion of ellipsoids. Having written out a simple demonstration ofa
very elegant known theorem relating thereto, I shall subjoin it sepa-
rately.

* * * * * = * *

« The proposition above alluded to depends on the following theo-
rem, which may be very simply proved :—If from the extremities
A, B, C of the semiaxes of an ellipsoid whose centre is O, there be
drawn three parallel chords Az, Bg, Cy, meeting the surface of the
ellipsoid in «, 6, y; and if a perpendicular from «on OA meet it in 7,
a perpendicular from 6 on OB meet OB in s, and a third from y on
OC meet OC in ¢; then will

Ar Bs Ct

aa’ + BB tT Co =

AA’, BB’, CC’ are the whole axes.

«: The proposition itself is this :—If the particles of a homogeneous
ellipsoid attract inversely as the square of the distance, and if a, 6, c
be the semiaxes, and A,,B,,C, its attractions on points placed at
their vertices, then will

Ao By Co
a epee oe = oF

« The attractions are here, as is usual, represented by lines; the
attraction of an indefinitely small part of the solid being represented
by its volume divided by the square of its distance from the attracted
point.

«¢ The attraction being thus measured, it is evident that if from the
vertex of a pyramid, whose transverse sections are indefinitely small,
as a centre, with any radius, a sphere be described whose surface is
penetrated by that of the pyramid, the attraction of the pyramid on
a point at its vertex will be to its length, as the intercepted surface
of the sphere is to the square of its radius.

«Let A, B,C be the three vertices of the axes, and from them let
parallel chords Az, B8, Cy be drawn; from whose extremities «, 8, y
let perpendiculars be let fall on the respective axes, meeting them
in r, s,t; then by the preceding theorem

526

Ar Bs Ci
AW * BB tT COT"

Let now two other chords be drawn from A making with Az very
small angles, so as to form with it the edges of a very small pyramid,
and let other chords parallel to them be drawn from B and C, forming
also with BZ and Cy the edges of two other small pyramids. Ima-
gine a sphere fixed in space, from whose centre are drawn three lines
parallel to the three chords drawn from A, or from B, or from C, and
conceive the surface of the pyramid, of which they are the edges, to
penetrate that of the sphere ; then will the attractions of the three py-
ramids, reduced each to the direction of the axis passing through its
vertex, be to Av, Bs, Cé as the intercepted surface of the sphere to
the square of its radius ; and therefore the sum of each of those at-
tractions, divided respectively by AA’, BB’, CC’, will be to unity in
the same ratio. Conceive pyramids thus related to be multiplied in-
definitely, and the spheroid willbe exhausted at once from each of the
three points A, B, C, while half the surface of the sphere is exhausted
by the parallels drawn from its centre. Hence it appears that the
sum of the whole attractions at A, B, C, divided respectively by
AA’, BB’, CC’, is to unity as the surface of a hemisphere to the
square of its radius, or as 24 to 1; and therefore

Ay By Cy
mis wie aca ae

January 22.
REV. James H. TODD, D. D., Vice-President, in the Chair.

Mr. W. H. Hudson exhibited specimens of Irish books,

now in the course of publication in Cork, which are litho-
graphed. He described the advantages which that process
presents over types, for composition in the Irish character.

Dr. Kane read a paper on the Chemical Composition of
the different kinds of fuel found in Ireland.

—.,

eer BY

527

Although this country is recognized as destitute of the
great development of the coal strata, which has proved so
important an element in the industrial progress of Great
Britain, yet there are known to exist several coal districts,
some bituminous and some anthracitous, as well as deposits
of wood coal, which, with the great extent of turf-bog occu-
pying the surface in many places, may be considered as stores
of fuel, available and sufficient for the supply of the interior
of the country for a very long time. In order, however, to
be able to calculate the economic value, or calorific power*of
any of these Irish fuels, and so to compare them with the
corresponding fuels in other countries, it was necessary to
know their elementary composition; and hence, in order to
lay the basis of a true estimate of the worth of our native
fuels, Dr. Kane commenced the series of analyses which
formed the present communication.

In order to exhibit all the relations of the composition of
these fuels, that might be useful in drawing practical con-
clusions, Dr. Kane adopted two distinct modes of analysis:
one, exhibiting the real elementary composition; the other,
which he terms the practical analysis, representing the rela-
tion of the ashes, and of the fixed and volatile constituents
of the fuel. He also in each case ascertained the quantity
of oxygen which the fuel was capable of taking up, in order
to be perfectly consumed. As the analysis of fuels is known
to present some difficulty, it is necessary to mention briefly
the precautions taken in order to secure accurate results.

The point first determined was in each case the quantity
of ashes present. To effect this a certain weight of the fuel
was burned in a current of hot air, until all traces of organic
material disappeared. The residual ash was then weighed.

To conduct the determination of the carbon and the
hydrogen of the fuels, the methods were varied according to
the nature of the substance, with turf, lignite, and the bitu-
minous coals. The proper weight of the material having

VOL. II. Qy

528

been dried at 212° F., was in some cases mixed with
chromate of lead, and the analysis conducted in the ordinary
manner ; in other cases, the substance was mixed with black
oxide of copper, and some chlorate of potash having been
placed in the end of the analysis tube, the operation was
conducted in the usual way to near the termination, when
the chlorate of potash being heated, a stream of oxygen gas
passed through the apparatus, and burned out the last traces
of the organic substances.

“These two modes gave almost identical results with the
same fuel, and there is no necessity for distinguishing
amongst the analyses, of which the results follow, those that
were done in the one way or in the other.

It was found, however, that the anthracite could not be
perfectly analysed by either of these modes: the difficulty
of burning away the last portions of the carbon was so great.
Hence a totally different plan was adopted for that variety
of fuel. An analysis tube of Bohemian glass having been
taken about a foot long, the substance to be analysed was
placed in a little boat of platina foil, and introduced into the
tube nearone end. ‘To this end was fitted a tube containing
dry chloride of calcium to collect the water; then the potash
absorbing apparatus, then another potash absorbing appa-
ratus, and finally a tube containing dry potash. These three
were for the purpose of separating the carbonic acid perfectly
from the excess of oxygen, and also to prevent the oxygen
from carrying away any moisture from the potash liquor.
The other end of the tube was connected with a gazometer
full of pure oxygen gas, which, streaming over a large sur-
face of fused chloride of calcium, was rendered perfectly
dry. The apparatus being so adjusted, the analysis tube
was heated to redness by charcoal, so that the oxygen gas
passed through five or six inches of red hot tube before
coming to the ignited anthracite. The analysis was thus
conducted, as it were, with the hot blast, and the combustion
was in all cases quite perfect. This kind of process would

529

only answer with such fuels as anthracite, which contains
very little hydrogen; but with those it succeeded perfectly.

Such were the means taken for the organic elementary
analysis. ‘The nitrogen was not separately determined, as
the results were only required for economic calculations,
and the minute trace of nitrogen does not there become impor-
tant. Its weight (in all cases very small) is included in the
number assigned tooxygen in the results of the analyses.

The practical analysis was conducted by very strongly
igniting a weighed portion of the fuel in a platinum crucible
the cover of which fitted so closely as to prevent any sensi-
ble combustion of the residual coke. The weight of ashes
being known, the pure coke was then found.

The determination of the reducing power of the fuel by
means of litharge, requires very considerable care in prac-
tice in order to get satisfactory results. The principal point
to be attended to, is to use a roomy crucible, and to apply a
quick and strong heat, so that the litharge shall at once run
thin. When this is done, the results with the same fuel are
very uniform, and with different fuels are fully comparable ;
although in no case is so much lead got as should be in
theory obtained from the conversion of the carbon and
hydrogen of the fuel, minus its oxygen, into carbonic acid
and water. The deficiency is usually proportional to the
quantity of volatile matter in the fuel, and is not in any case
large, provided proper care be taken. Hence Dr. Kane
considers, and the opinion is also held by Berthier, that the
result is so near the truth as to be quite available as a prac-
tical and ready measure of the heating power of the fuel.

The general nature of the inquiry, and the methods em-
ployed, having been thus described, it is only necessary to
add the numerical results of the analysis.

In order that the results might represent as far as prac-
ticable the average composition of the fuel, in each case
rather a large mass was broken up, and its coarse powder

2x2

530

well mixed. Some ounces of this were then reduced to
impalpable powder, and from this all the portions to be
operated upon were taken.

I. ANTHRACITES OF THE SOUTH OF IRELAND.

Three specimens of this kind of coal were analysed :
1, from the Rushes Colliery, Queen’s County ;
2, 5, the Pollough Vein, Castlecomer, Co. Kilkenny;
3, ,, the Sweet Vein, Kanturk, County Cork.

The anthracites have no tendency to froth or cake in
cokeing. They give off little or no inflammable gas on being
ignited, but usually the masses break up quite small, espe-
cially if the heat be suddenly applied. The ashes are almost
always red, owing to peroxide of iron remaining after the
combustion of the iron pyrites, which the anthracite gene-
rally contains.

Rushes anthracite—0.375 grammes gave:
Waters yh es a a ONS,
Carbonic acid. . . . 1.238
Light red ashes . . . 0.014
The Pollough anthracite. 0.364 grammes gave:
Water th cin cian as, yohe «ty pO
Carbonic acid . . . . 1.086
Brown ashes . . . . 0.036
The Sweet Vein anthracite—0.293 grammes gave :
Waiter: 5 1 ihsien) ei, c0098
Carbonic acid. . . . 0.928 -
- 0.305 gave . . . 0.026 ashes, white.
These coals consisted, therefore, of :
Rushes. Pollough. Sweet Vein.
Carbon. . . . 90.04 81.36 86.37
Hydrogen. . . 38.50 2.41 3.71
Oxyaene ics bot een 6.34 1.40
FASEB eke 5.) he ae 9.89 8.52

100.00 100.00 100.00

~~. ne

531

Of these coals the Sweet Vein was perfectly free from
sulphur; the Rushes coal contained but a minute trace ;
but the Pollough coal contained a good deal, and as the
sulphurous acid produced during its combustion should be
absorbed by the potash, and counted as carbonic acid in the
analysis, it was necessary to correct the above result by a
direct determination of the sulphur. For this purpose 3.526
grammes of the coal were boiled with aqua regia, and the
liquor precipitated by chloride of barium. The sulphate of
barytes obtained weighed 1.589 grammes, corresponding to
45.07 per cent., containing 6.18 of sulphur.

Now, 6.18 sulphur give 12.36 sulphurous acid, and sub-
tracting that from the carbonic acid obtained in the elemen-
tary analysis, then converting the sulphur into bisulphu-
ret of iron, and subtracting the pyrites from the ash,
there comes out, as the true composition of the Pollough
coal :

Ash, free fromiron . . . 2.19
Bi-sulphuret ofiron . . . 11.58
Carhon 2 eins aay hate EGA?
Hydrogen ss) :2 vely sei tin ese 224i.
Oxyaen Pos srt ceili er PBAO

’ giving of pure an-
thracite 86.23.

100.00

It is interesting to contrast the composition of the really
organic part of these three varieties of coal.
Rushes. Pollough. Sweet Vein.
Carbon. . . . 93.53 87.46 94,39
Hydrogen. . . 3.63 2.79 4.05
‘Oxygen... 2.84 9.75 1.56

100.00 100.00 100.00

By the praetical mode of analysis these coals were found
to give, per cent. :

532

Rushes. Pollough. Sweet Vein.

Volatile matter . . 9.85 10.40 10.35
Pure coke . . . 86.42 19.71 81.13
PNISHES: Yay vo TERE Ce ai 9.89 §.52

100.00 100.00 100.C0

The result of ignition with litharge was, that
One part of Rushes coal gave . 31.8 of lead.
Pollough py... 5. waite <p sp Dou Ae
Sweet Vein orate,” page cBOD cine
Hence they correspond respectively.
100 parts of Rushes to. . 93.5 of pure carbon.
100 _s—=,, Pollough . . 73.5 Ge
100 ,, Sweet Vein . 85.3 "
And in average 100 parts of Irish anthracite may be consi-
dered to possess a calorific power equal to 84 parts of pure
carbon.
II. COAL OF THE CONNAUGHT BASIN.

The coals examined were all from the collieries of Brah-
lieve mountain, forming the western division of the Lough
Allen coal field. The specimens were furnished through
the kindness of Colonel Jones, member of the Shannon Com-
mission. The results were as follow:

AUGHABEHY COAL,

A rich, black coal, easily broken. Sp. gr. 1.274. When
heated, it gives off a good deal of inflammable gas, and leaves
a light grey, porous, coherent coke.

Its elementary analysis was effected :

0.472 grammes gave:
Carbonicacid . . . . . 1.379 grammes.
Water) 0 .o. 2 aye inns es 65 ve
0.921 grammes gave of white ashes, 0.099, or 10.75
per cent. ;

333

Hence it contained:

“CHL DG COR IRON tee eet ee bia ere! 01!)
RCE 8 y's ne a. ng al pas
ONvoeMAN eR). be. 8 We ea) lnee
SNCS ce re ats ee LUO

100.00

ROVER COAL.

This coal is rather brown in aspect, and splits easily into
cubical fragments. On ignition it gives out gas, but does
not froth. Its coke is porous, slightly coherent.

Its elementary analysis was :

3.196 grammesgave . . . 0.237 of ashes,
equivalent to 7.41 per cent.
0.489 gramme gave:

WRENS cot such artes Lie ntl e cs eo Oe LD,

Carbonieacid: <0. 3.) «> se «aS

Hence it contained :
CORIO Te ho ae ee ase Re eng SR
VarOSenG Wy woes rw ce 2s Cane
Oy CON s 4 phair eth Mee sre tes OLE
Ashes Cay te Pelion RPP NS oe evs, 70 6c ea
100.00

The practical analysis of these two coals gave the follow-
ing results :
Aughabehy Coal.—13.418 grammes gave on ignition
10.340 of coke.
Rover Coal.—14.300 gave on ignition 11.770 of coke.
Hence they consisted of :
Aughabehy. Rover.
Volatile matter) 2"*> 925.10) 2°" 1.70
Pure'coke*.."t 2. OOO. 2. wae
NGHES sce slice th OME ne (ier al

100.00 100.00

534

Specimens of coal from the Celtnaveena and the Meena-
shama collieries were also examined in this manner, with
the following results :

Celinaveena Coal.—4.772 grammes gave by ignition
11.960 of coke.

1,091 gramme gave 0.164 of white ashes.

Meenashama Coal.—6.280 grammes gave 5.095 coke.

8.778 gave 0.742 of ashes.

Hence they consist of—
Celtnaveena. Meenashama.
Volatile matter . . . 19.10 . . 18.90
Pure.coke ».,. . . >. 65.87... ... 6146
Ashes 25. san) eee) oS aa ae GMa:

100.00 100.00

Each of these varieties of coal was examined as to the
quantity of oxygen it absorbed by reducing litharge.

1 part of Aughabehy coal produced 26 parts of lead.

1 part of Rover coal produced 283 parts of lead.

1 part of Celtnaveena coal gave 26 of lead.

] part Meenashama coal gave 25 of lead.

100 parts are therefore equivalent
Of aa to . 77 parts of pure carbon.

Rover. . . 84 .
Celtnaveenan . . 77 He
Meenashama . . 73

These coals are similar in appearance to the Aughabehy,
but are more slaty. When ignited they give off inflammable
gas, but donot froth. Their coke is dense.

It is thus seen that the Aughabehy is the most bitumi-
nous of these coals, whilst the Rover is the least so, and
that in fact the latter approaches closely in its composition
to the anthracite of the Munster coal field.

539

Ill. COAL ON THE TYRONE BASIN.

Of this locality two kinds of coal were examined, from
opposite sides of the field, the new Drumglass Colliery, and
the colliery at Coal Island.

COAL ISLAND COAL.

It is slaty in structure, dull coloured; sp. gr. 1.267.
On ignition it gives off much gas, froths, and leaves a very
porous coke.

2.814 gave 0.328 of ashes almost white.
8.830 grammes gave after ignition 5.390 of coke.

It hence consisted of

Wolagie matter .°. . «... «4: +. 238.96
IPUIPEHCOKE i.e) “capde dcesne you erase) p4AOFOD
Wishes me mean hue cet Ge Ro EGS
100.00

In its elementary analysis, 0.563 gramme gave:
Water ee Ne a He Cae oy Gat ge MOP g cn GEG,
@arbomie acid. te cee ee Le Qa

Whence results the composition
Garba 2 Bathe Wesel eas at i ODS
Plyuirosen, 60" oy ee te sys a OBO
Oxyseny) 2 Neer ee ee ae kOe
AGN ss neste ett sere ap eek sct) oguet 4 GeksOO

100.00

On ignition with litharge, one part of this coal gave 263
of lead, hence 100 parts correspond to 78 of pure carbon.

NEW DRUMGLASS COLLIERY.

This coal is brilliant, black, friable, frequently mixed
with pyrites, which oxidize on exposure to the air._ Its
ashes are consequently reddish. On ignition it gives off
much gas, froths, and produces a light porous coke. Its
practical analysis was as follows :

536

1.977 grammes gave of brown ash 0.342.
11.540 gave on ignition 5.920 of coke. It consisted

hence of —
Volatile matter . . . ... =. =. 48.70

Pure coke Sor ie th Oey Taare ee amt 01)
Ashes 8 Ls ee aS OMe ies xe omit, MMe
100.00.

When ignited with litharge, one part produced 22 parts
of lead. 100 parts of it are therefore equivalent to 65 parts
of pure carbon.

IV. COAL OF THE ANTRIM DISTRICT.

The coal of Ballycastle is dull, black; sp. gr. 1.279.
On ignition it gave out much gas, frothed, and left a porous
coke. On its practical analysis it gave in 100 parts

Wolatile- matter ie. S28) yee) Coy ea ooo
Puareicoke: 7) 1k pike. ih eon reed. Amel
PsN eS ey Pane AiG | wes aneurin keen ae mea igh 1)

One part of it produced 25 of lead, and 100 are therefore
equivalent to 713 parts of pure carbon.

V. LIGNITES OF LOUGH NEAGH.

Having thus determined the composition, and more im-
portant practical relations of the coals from the several coal
districts of Ireland, Dr. Kane proceeded to examine the
nature of the deposit of lignite which is found among the
tertiary beds along the southern extremity of Lough Neagh.
As these investigations had solely a technical object, the
silicified wood of that district did not require any notice,
but only such wood-coals as were capable of use as fuel,
Two specimens were examined. They retained all the
structure of wood, and were of a deep brown colour. When
ignited they gave off gas, which burned brilliantly, and left a
dense black charcoal.

On elementary analysis, they gave the following results:

a

537

No. 1.—1.887 gave 0.163 of a reddish ash containing
much iron.

0.489 grammes gave:
Watcer inate. atu bt 2 et eO 262
Ghrbeiciacid » 6 06.0) oe ey Co 050

No. 2.—3.393 grammes gave of slightly reddish ashes
0.550.
0.648 gramme gave
Waters... Niet MOGIe Re... OA29
Carbonic acidis Si 2)... ata Pe 1220

These lignites consequently consisted of
No. l. No. 2.

Carbogy: ots t8 Ef 8 $986 51.36
Fy drogen je mnodign ost xrmltct A129 7.35
Oxyaee niki. sca, 26.65 25.08
ASHI OL AG. PRD 6.64 16.21

100.00 100.00
The results of the practical analyses were as follows:

No. 1. No. 2.
Volatile matter aqs + «gu; 57.00 53.70
Pure charcoal . . . . . 33.66 80.09
Ashes. . gait « "tow uses DERE 16.21

By ignition with toe No. 1 gave 193 parts of lead,
and No. 2 gave 16.7 parts. They hence were equivalent in

100 parts.
No. 1.—To 58 parts of pure carbon.
No. 2,— 99 50 99

VI. TURF.

The specimens of turf were selected from Cappoge, in
Kildare, and Kilbeggan, in Westmeath, on different sides
of the great Bog of Allen, and from Kilbaha, in Clare.
When ignited, turf gives off inflammable gas, and leaves a
light, easily combustible charcoal.

The elementary analyses were as follows :

KILBEGGAN TURF.
Q 7 7 .
.J80 grammes gave:

538

Wiaterisn ini) S) Seas Tee 2380
Carbonic acid . . . . . . . 0.857
Ashes’ (ci 220). See bee i OOF
KILBAHA TURF.
3.435 grammes gave 0.277 of. a light reddish ash.
0.663 gramme gave:
Wratten)! .e5 oo ee ge} |e Onans
Carbonic acid... cuerg spree As
CAPPOGE TURE.
10.566 grammes gave 0.270 of ashes.
0.500 gramme gave :
Wratten A! Mae Wen eee beat
Carbonic acid. . . . . « © 0.935

From these results follow the composition :
Kilbeggan. Kilbaha. Cappoge.

Carbon . . 61.04 51.13 51.05

Hydrogen . 6.67 6.33 6.85
Oxygen . . 8046 34.48 39.55
Ashess . .) “1.83 8.06 2.55

100.00 100.90 100.0

In the practical analysis of turf it is necessary to attend
to the physical constitution of the fuel, as, even with the same
chemical elements, the heating power, and the proportion of
fixed and volatile parts, will vary with the denseness of tex-
ture of the fuel. Important differences exist also in the
characters of the turf taken at different depths below the
surface of a bog. These circumstances require to be care-
fully attended to in practice.

When ignited, there were obtained from specimens of

light surface turf :
Cappoge. Kilbeggan.

Volatile matter. . . 73.63 15,50
Pure charcoal . . . 23.82 92.67
ASHES -o32) pa), ee un OS 1.83

100.00 100.00

539

and from deep-seated turf,
Kilbaha. Cappoge.
Volatile matter . 72.80 70.10
Pure charcoal . 19.14 23.66
Aishesio iis o.t... 806 6.24

100.60 100.00
Of these varieties of turf it was found that on ignition
with litharge,
1 part light Cappoge turf gave 13.0 of lead,
1 y Kilbeggan turf ,, 14.2 ,,
1 is Kilbaha turf AFT MIG) wiktas
and hence that 100 parts corresponded, of
Cappoge turf to 37 of pure carbon.
Kilbegean,, 41 45) 2 45
Kilbaha Pec: |) a eae
By means of these investigations Dr. Kane trusted that
the chemical nature, and economic value of the fuels of Ire-
land might be considered as established, and thus one step
made towards a correct knowledge of the circumstances un-
der which this country is placed as to those important mate-
rials of industry. The question as to the extent of those
deposits, the real quantity of each fuel available in practice,
as well as the mode in which those deposits have had their
origin, pass from the domain of chemical inquiry, and hence
have been left by Dr. Kane to those geological philosophers
whom the Academy proudly enumerates amongst its mem-
bers.
Dr. Apjohn and Mr. R. Mallet made some observa-
tions.

- Si Fs wand ina

PROCEEDINGS

or

THE ROYAL IRISH ACADEMY.

1844, No. 44.

February 12.
REV.James H. TODD, D. D., Vice-President, in the Chair.

Henry Clare, Esq., was elected a member of the Aca-
demy, and the Rev. Charles Graves was elected a member of

the Committee of Polite Literature.
¥

Mr. Ball made a communication on a collection of the
Irish names of animals, which he had been for many years
collecting from ancient manuscripts, dictionaries, persons
speaking the Irish language at present, &c. He stated that
for one important addition he was indebted to Mr. Curry,
who pointed out in a manuscript poem, said to be of the fifth
century, ascribed to Caoilte, one of Finn Mac Coole’s heroes,
and which is certainly older than the year 1000, a portion,
in which the names of one hundred animals are recorded in
a list of the ransom paid for the celebrated Finn Mac Coole,
when a prisoner. Some of the names mentioned have not yet
been translated. Mr. Ball observed on the value of such a
collection as a means of throwing light on the names of places
in Ireland, and urged the interest that naturalists of other
countries felt, in preserving the names by which animals
were known in their native places, as a sufficient reason for
desiring to preserve those of Ireland. He stated his inten-
tion of having the collection he had made properly digested

542

and arranged by a competent person, and that he would
then offer it tothe Academy for publication.

Professor Mac Cullagh made some remarks, of which the
following is the substance, concerning the letter communi-
cated by Mr. Lloyd at a former meeting (see Proceedings,
p- 520).

The letter read by Mr. Lloyd at alate meeting of the
Academy, was written by me immediately after the examina-
tion for Fellowships, which was held in Trinity College, in
the year 1831. I had been a candidate on that occasion;
and Dr. Bartholomew Lloyd, to whom the letter was ad-
dressed, had been one of the examiners. ‘The letter con-
tains, among other things, several theorems taken froma geo-
metrical theory of Rotation, with which I had been previously
occupied. Soon after it was written, I returned to that
theory, for the purpose of improving it in one part where I
felt it to be defective, and where, indeed, I experienced the
chief difficulty ; I mean the part which relates to finding the
position of the body at any given time. The method given in
my letter for doing this by quadratures, had occurred to me
in 1829 ; but I was, of course, not satisfied with it, and I
had in the interval made some attempts to find a method
more elegant, and, as far as possible, really geometrical. In
the autumn of 1831 I succeeded completely in this, and no
further additions of any consequence were made to the
theory. The position of the line OI within the body, at any
given time, was found by an elliptic function of the first kind,
the modulus and amplitude of which are given immediately
by geometrical considerations; the modulus of the function
being in fact the ratio of the two moduli of the cone which
that line, stationary in space, describes within the body.
This result was deduced from Theorems I. and II. of the let-
ter. Thecone reciprocal to that just mentioned was used to
find the position of the body in space. This reciprocal cone,

543

carried about with the body, always touches the invariable
plane ; the side of contact, at any instant, being that which
corresponds to OI, and which therefore lies in the plane
passing through OI and the axis of rotation. The angle de-
scribed in the invariable plane by the side of contact is the
sum or difference of two angles, one of which is proportional
to the time, and the other is the angle described by that side
in the surface of the cone. As the latter angle is measured
by the are of a spherical conic, it followed, on comparing
this result with the integral given by Legendre in his dis-
cussion of the question of rotation, that the arc of a spheri-
cal conic represents an elliptic function of the third kind
with a circular parameter.

The curve described by the point I on the surface of the
ellipsoid, is a spherical conic; and it now appears in what
way the consideration of this mechanical question led to the
study of the properties of cones and spherical conics. From
theorems relating to centrifugal forces and principal axes of
rotation, I was further led to consider systems of ellipsoids
and hyperboloids having the foci of their principal sections
the same; and then the focal curves presented themselves
as the limits of these surfaces. The properties of the focal
curves and of confocal surfaces occupied me, at intervals, in
the year 1832 ; but in the latter part of that year my atten-
tion was diverted from these subjects, and it was not until
1834 that I began to think of writing down and _ publishing
the results of my inquiries respecting them. In doing so, I
wished to be able to assign a geometrical origin to the sur-
faces of the second order, the theory of these surfaces being
intended to precede that of rotation; and in seeking for
such an origin, I found the modular property. But not long
after (in the summer of 1834) happening to look into a French
scientific journal, I learned that M. Poinsot had just read
to the Academy of Sciences of Paris a memoir in which he
treated the question of rotation geometrically, by a method

VOL. II. 22

644

substantially the same as mine. This caused me to give up
the design of writing on that subject; and, my thoughts
then turning to the theory of light, the subject of surfaces of
the second order was also dropped.

Another form of Theorem I. is given by the property of
reciprocal ellipsoids. Ifa second ellipsoid be constructed,
having its centre at O, and its semiaxes coincident with, and.
inversely proportional to those of the first, and if this ellipsoid
be touched by a plane parallel to the invariable plane, it is
obvious, from the relations of reciprocal ellipsoids, that the
tangent plane will be fixed in space, and that the right line
which joins the point of contact with the point O, will always
be the axis of rotation, and will be proportional to the angu-
lar velocity. This form of the theorem, though not men-
tioned in the letter, was nevertheless employed in my theory
of rotation. Itis the form given by M. Poinsot, who uses
only the second ellipsoid ; and it has the advantage of de-
termining geometrically (as M. Poinsot has remarked) the
successive positions of the body in space, independently of
the consideration of time; for the ellipsoid evidently rolls
upon the fixed plane which it always touches. This advan-
tage, however, though evident when stated, I do not recol-
lect that I had distinctly perceived.

The theorem mentioned in my letter, for finding the mo-
ment of the centrifugal forces, is the same (making allowance
for the difference of the ellipsoids) with one given by
M. Poinsot, which he speaks of as “‘ a simple and remarkable
theorem, containing in itself the whole theory of the rotation
of bodies ;” and of which he further observes, as I have done,
that “ translated into analysis, it gives immediately the three
elegant equations which are due to Euler, and which are
usually demonstrated by long circuits of analysis.” It was,
in fact, from this theorem, by means of the principle of
the composition and resolution of rotatory motions, that my
theory, as well as that of M. Poinsot, was deduced. I may

545

add, that I also employed M. Poinsot’s beautiful theory of
couples, which has introduced so much clearness into the
fundamental doctrines of mechanics.

Mr. G. Wilkinson read a paper on the existence of the
pointed arch in the early buildings of Ireland, prior to the
introduction of Gothic architecture.

Mr. Petrie offered some remarks on Mr. Wilkinson’s com-
munication.

Dr. Allman noticed the occurrence in Ireland of Frederi-
cella Sultana, and entered into certain details of its zoological
and anatomical characters. This zoophyte has been very
imperfectly described, and is moreover burthened with a dis-
cordant synonomy which has involved its history in no small
obscurity. The difficulty which is thus necessarily con-
nected with the attempt to determine the true Fredericella
Sultana, Dr. Allman endeavoured to remove, by reducing to
some sort of order the mass of synonymes in which it is in-
volved. It would appear to be the Tubularia Sultana of
Blumenbach, its original discoverer; the Plumatella Gelat-
énosa of Dr. Fleming; the Plumatella Sultana of Sir J. G.
Dalyell; and the Pvedericella Sultana of Gervais. It would
appear also that the zoophyte described by Mr. Varley, in a
late number of the London Physiological Journal, is the
same as the present.

By some singular oversight, Dr. Fleming, in the descrip-
tion of his Plumatella Gelatinosa, refers to the Tubularia
Gelatinosa of Pallas, described in the “‘ Elenchus Zoophy-
tarum.” The Tubularia Gelatinosa of the Elenchus, how-
ever, is quite a different animal; it belongs to the group with
crescentic disks, and is identical with the free variation of
Plumatella repens.

The author, in entering into the details of its anatomical
structure, drew attention to the high ascidiform type which

222

546

it presented. He also noticed a hyaloid membrane of great
tenuity which surrounds the base of the tentacular plume,
and extends upwards for about the fourth of the length of
the plume, being adherent to the tentacula, and constituting
a kind of calyciform appendage to the base of the crown.

He mentioned the existence of this calyciform membrane
in Plumatella and Cristatella, but would not speak positively
as to its presence in lcyonella ; from Paludicella it is cer-
tainly absent, a fact which, along with several others, tends to
approach this elegant zoophyte to the marine Ciliobrachi-
ates.

Dr. Allman also alluded to a singular valve-like organ
with which the mouth is furnished, exactly similar to that
found in Plumatella, and described by the Author at the late
meeting of the British Association. This organ he has also
detected in Cristatella.

Through the external tunic of the polypidom will be
found scattered, numerous silicious particles of no definite
figure, and the Author considered himself justified, from the
observations which he had made upon the fresh-water
zoophytes, to come to the general conclusion that in the
corneous polypidom of these animals, silica replaces the cal-
careous deposits of the marine species.

February 26.
ROBERT BALL, Esa., Treasurer, in the Chair.

The Secretary read a paper by the Rev. Dr. Hincks,
“ On the Defacement of Divine and Royal Names on Egyp-
tian Monuments.”

An attempt is made in this paper to specify the several
occasions, on which the principal defacements of Egyptian

547

monuments took place; mentioning the principal ones which
suffered on each occasion. The occasions specified are
four.

I. The dethronement or death of Q. Amuneth (circa
1325, B.C.), when her monuments were defaced by her
brother Thothmos III. The propylon at Elassassif is the
principal one defaced on this occasion.

II. The change in the religious views of Amenothph IV.
(the sun-worshipper of El Tell) (ci7ca 1250, B. C.), which led
him to deface all the figures and titles of the God Amoun, and
all names of which his name formed a part. ‘The monuments
defaced on this occasion are referred to three classes.

1. Those which were never restored, as the lesser obelisks
at Karnac.

2. Those in which the sun-worshipper substituted another
“name for what he defaced ; as ina cartouche of his own cited
by M. Prisse, and in those of his supposed grandfather
Amenothph III., where he substituted a repetition of the
prenomen for the defaced phonetic name.

3. Those in which the names and figures that were de-
faced have been restored by subsequent kings. Instances of
this are the Lateran Obelisk at Rome, the great obelisks at
Karnac, and those cartouches in which the name of Ame-
nothph III. appears cut over the repetition of his przeno-
men; the latter having been previously substituted for the
original name.

III. The overthrow of the sun-worshippers and restora-
tion of the worship of Amoun, on which occasion all the
monuments of the intrusive worship were destroyed, as at
Karnac, Gebel Tounh, and Ell Tell (a few years after the
preceding occasion). The tomb of the king called Skhai,
the father of the sun-worshipper, was violated at this time ;
and this was probably the occasion on which the royal name
on the lion, presented by Lord Prudhoe to the British
Museum, was obliterated. It was that of Amenothph IV.

548

IV. The hostility to the god Seth, Nahas, or Noubti,
which arose in the minds of the Egyptian priests, and which
led to the defacement of all monuments in which he appears
as a beneficent god, and of his name when forming a part of
names of kings. The time when this hostility arose, and the
cause of it, are yet unexplained ; but it could not have led to
this defacement sooner than 1100, B. C. ‘This defacement is
conspicuous on the statues of Menephthah III. at Turin and
London, and the Flaminian Obelisk of Menephthah I. at
Rome, and frequently at Karnac.

It is incidentally mentioned that Pone, or Penne, is Lower
Egypt; its extremities being mentioned in a papyrus in the
British Museum in connexion with Ebo, or Elephantine, as
the limits of Egypt. And the titles ‘‘ King of Penne,”
‘‘ King of the Pure Country,” which occur in the second car-
touches of many Egyptian kings, are shewn to imply that the
kings bearing those titles were only kings of parts of Egypt;
a King of Penne, or Lower Egypt, like Horus, always imply-
ing a King of Keme, or the pure country, ae. of Upper
Egypt, as Skhai and Amenothph IV. were.

Mr. E. Clibborn made a communication respecting the
Hycsos, or Shepherd Kings, tending to shew that they were
descendants of Isaac.

March 16. (Stated Meeting.)

SIR Ws. R. HAMILTON, LL. D., President, in the
Chair.

ResotveD,—That the Rev. J. D’A. Sirr’s collection of
Irish Antiquities be purchased on the terms recommended
by Council. The terms being a payment of £350, the

—- ©

549

cancelling of his arrears, and his being made a Life Member
of the Academy.

The Secretary of Council read the following Report :

In presenting to the Academy the Report of Proceedings during
the past year, the Council does not find it necessary to enter into
much detail, as the events of that period have not been of any con-
siderable importanceor unusual character.

The Second Part of the 19th Volume of our Transactions has
been published and distributed to the members of the Academy.
The 20th volume, which will be altogether occupied by Mr. Petrie’s
Essay on the Round Towers, is still at press. The delay in its pub-
lication arises mainly from the number and importance of the artistic
illustrations ; and it is expected that the retarded progress of this
work will be fully compensated for, in the opinion of the Academy,
by its excellence, when brought out.

Several Memoirs are already prepared and printed for the 2Ist
Volume of the Transactions, and the Proceedings of last Session,
which compose Part VII., have been lately distributed to the mem-
bers.

Since the date of the last Report the attention of the Council
has been given to the means of providing for the exhibition and
guarding of the collection of Irish Antiquities. The plans proposed
for this object have been already submitted to the Academy, but are
not as yet in any way carried into effect; the Council being, on the
one hand, restricted by want of funds, and, on the other, as it was
found that the duration of tenure of the Academy House becomes
uncertain after a few years, it was thought advisable not to expend
much money on alterations in the building, until some definite ar-
rangement had been made concerning its future tenure. For this
purpose the Council have been in communication with the law
agents of the Academy, but no decisive result has been as yet arrived
at. It is a question of great importance to the Academy, for, at
present, from the want of place for exhibition, the antiquarian treasures
which we possess, and to which, we trust, each year will make large
additions, are practically inaccessible to the public. Some of the

550

best evidences of the activity and utility of this Institution are hidden
from the public eye, and thus the influence of the Academy, and its
claims for public sympathy, are narrowed, and deprived of force.

The Donations to the Antiquarian Museum during the past
year have been few in number, most probably owing to the circum-
stances just now described. .

The work of cataloguing the Irish Manuscripts in the library
of the Academy is still in progress, but is expected to be terminated
in a few weeks. The time occupied in this work, and the extent,
three vols. folio, to which the Catalogue has gone, will be understood
when it is considered that, not merely the name, but also an abstract
of the contents of each MS. are inserted in the Catalogue, which will
thus in itself become a very valuable addition to our library.

About a year ago the Council received a communication from
the Booksellers to the Academy, Messrs. Hodges and Smith, regard-
ing the purchase of a collection of Irish Manuscripts in their pos-
session. A Committee of Council, appointed for the purpose, re-
ported that the Manuscripts were of much interest, and worth the
price which Messrs. Hodges and Smith had set onthem. The funds of
the Academy did not, however, admit of the Council taking any direct
steps for their purchase, but an application has been made, through
his Excellency the Lord Lieutenant, for some assistance towards
their purchase from the Government. His Excellency has expressed
on this, as on all occasions, the greatest anxiety to advance the ob-
jects of the Academy, but as yet no final answer has been received
from the heads of the Government in England.

The Library of the Academy has been increased during the
past year, by numerous donations of scientific and literary works, for
which, at the several meetings, thanks have been voted to the donors.
An interchange of Transactions has been kept up with most of the
eminent scientific institutions of Europe and America, there having
been added during the past year :

The Academy of Sciences of Metz, the Royal Academy of
Amsterdam, with whom we did not previously correspond, and the
Museum du Jardin des Plantes, at Paris, the correspondence with
which had been accidentally interrupted.

551

During the past year seventeen new members have been elected
into the Academy. Their names are as follows, viz. :

George J. Allman, M.D. Rt. Hon. The Earl of Dunraven.
Rev. Francis Crawford. Matthew Dease, Esq.

Henry Lindsay, Esq. William M‘Dougall, Esq.

John M‘Mullen, Esq. Sir Montague L. Chapman, Bart.

Hon. and Very Rev. Henry Pak- James H. Pickford, M.D.
enham, Dean of St. Patrick’s. Edward Bewley, M.D.

Goddard Richards, Esq. James S. Eiffe, Esq.

John Wynne, Esq. William Henry, Esq.

I. George Abeltshauser, A.B. John Neville, Esq.

Out of our list of members we have to deplore the loss of
several since the date of our last Report; most of them, certainly,
persons whose energies, being devoted to other spheres, rendered
their connexion with this Academy only nominal: but some, and
especially one, whose connexion with us was of the closest and most
endearing kind, whose scientific labours in various climates were of
an extent and diversity which, while they created for him a dis-
tinguished reputation, unfortunately sapped the foundations of his
health.

List of Members of the Royal Ivish Academy deceased since the
16th of March, 1843.

Robert Bateson, Esq. Major-General Sir Joseph O’Hal-

Thomas Coulter, M.D. loran, K.C.B.

Right Hon. William Vesey Lord Rev. Thomas Prior, D.D.
Fitzgerald and Vesci. Rt. Hon. John Radcliffe, LL.D.

Arthur Hume, Esq.

Honorary Members deceased:
His Royal Highness the Duke of Professor Wallace.
Sussex.

Amongst the honorary members had been reckoned his Royal
Highness the Duke of Sussex. His exalted rank removed him from
in any way personally contributing to the advancement of knowledge,
but he favoured its cultivation by his august patronage, and filled for
many years the office of President of the Society of Arts, having a
decided taste for practical mechanics, and leaving behind him, at his

052

death, a very valuable and numerous collection of clocks and watches.
In the year 1830 he was elected to the Presidency of the Royal
Society of London, and was present at the meetings of that illustrious
assemblage, whenever his health, which, unfortunately, was delicate, or
the other demands upon his time, unavoidable from his exalted rank,
admitted of his so doing. He was nominated an honorary member
of this Academy, of course not for any special scientific merits, but
that we might show some consonance of feeling with the scientific men
of London who elected his Royal Highness to the most exalted sci-
entific position of the British Empire, the chair of Newton.

Professor Wallace, of Edinburgh, was known to the mathema-
tical world for various memoirs, into the details of which it is not
necessary to enter. His works were not of a character to influence
the progress of general science in any material degree, although they
manifested powers of inquiry and analysis of a very creditable
amount.

Of the ordinary members of the Academy whom we have lost
during the past year, the Lord Fitzgerald and Vesci, the Right Hon.
Judge Radcliffe, Arthur Hume, Esq., the Rev. Thomas Prior, D.D.,
and Major-General Sir Joseph O’Halloran, do not require special
notice. They were all men publicly known, and recognized as of
eminent ability in the various professional pursuits to which they had
devoted themselves. Success of no ordinary kind was the result of
their exertions, and has connected the names of some permanently
with history. It can hence be understood that, except by a general
desire to promote the objects of this Academy, by which, we trust,
every member is actuated, they were not able to take any part in
our proceedings.

We cannot, however, pass so briefly from the name of Robert
Bateson, late M.P. for Derry. Separating himself from the whirl of
merely trivial and political pursuits, to which young men of his age
and station are unfortunately in this country almost exclusively de-
voted, he engaged in the cultivation of literature and antiquities with
a zeal and ability which promised to bear the best fruit. The
ancient monuments and history of his native country specially oc-
cupied his attention, but not exclusively; and whilst travelling in
Palestine, for purposes of literary inquiry, amongst those scenes in

553

which the most important acts of human history have been per-
formed, he was seized with fever, and expired in Jerusalem.

The position which Dr. Coulter occupied in this Academy, in
our University, and in science generally, rendered it the duty of the
Council to prepare, with more than ordinary care, a sketch of his life
and labours, such as might not be derogatory to his fame ; and, hap-
pily, the task was undertaken by one who, from long acquaintance
and intimate friendship with the deceased, was enabled to speak mi-
nutely of his personal career; and whose own extensive and profound
acquaintance with almost every department of knowledge, which this
Academy has had so often occasion to admire, enabled him to judge
correctly of the aspects in which the labours of Doctor Coulter
should be placed. The following biography of Doctor Coulter has
been drawn up for this Report by the Rev. Dr. Robinson.

“ It is an old saying, that science has its martyrs as well as reli-
gion; we may add that it has its Forlorn-hope as well as war, urged
to the adventure by loftier and nobler impulses, encountering in its
pursuit even a greater amount of suffering and danger; but too often
unnoticed and unrewarded. Its heroism is of too high an order to
be appreciated by vulgar minds ; the wise and good, who alone value
it, are comparatively few and powerless, and the triumphs which it
achieves are not in unison with the evil tendencies and passions
which unhappily predominate among mankind. Therefore it finds,
in the Present, neglect, perhaps scorn or contemptuous pity of the
folly which wasted on such unprofitable pursuits the powers that, if
otherwise directed, might have commanded wealth, rank, and power.
But the Present ere long becomes the Past ; all of its glittering ar-
ray which is not based on the eternal and immutable principles of
virtue and truth moulders to dust; the stream of time in its flow
washes all that is earthy from the ruin, and leaves in imperishable
brightness the grains of gold and gem which it contained, the trea-
sure of the Future. In this sacrifice of self to science, few have sur-
passed the associate, whose loss, during the last year, it is my painful
duty to announce to you; and a brief notice of his history may
therefore be permitted:

«¢ Thomas Coulter was born in 1793, near Dundalk. His parents
died during his childhood, but the loss was in part supplied by the

554

guardianship of a good and intelligent uncle. From an early age he
was devoted to field sports, which he followed with a minute at-
tention to the habits of his game, that belonged more to the natu-
ralist than to the sportsman. Bees were another favourite object ;
and he possessed that remarkable power of handling these irritable
insects with impunity, which attracted so much notice in Wildman
and others. He had in after-life the same privilege as to serpents ;
of which some members may recollect an amusing exhibition in this
room ; his secret being the union of gentleness and courage.

‘«¢ He was prepared for college by Dr. Neilson, the author of a
well-known Irish Grammar, from whom, perhaps, he derived that
intense interest in the antiquities of our native land, which charac-
terized him to the last. One proof of it deserves to be recorded for
example’s sake. There stood on his property an ancient building,
described in Wright’s Louthiana, as a Ship Temple, which the te-
nant was converting into lime. The young landlord had him prose-
cuted and punished for the trespass, to the surprise of many who
were in the practice of similar misdeeds.’ In the University he had
the good fortune to be placed under the care of the late Dr. Lloyd,
whose esteem and regard he possessed in a high degree; though the
prevailing bias of his mind prevented him from equalling in mathe-
matical attainments some of his fellow-pupils. He pursued that
science only so far as it ministered to other objects. But in practi-
cal mechanics, in Chemistry, Physiology, and above all, in Entomo-
logy and Botany, he far outstripped his college contemporaries, and
while yet an undergraduate, his collections of Irish insects and
mosses were such as might have been owned with credit by a veteran.
But his success made him only the more conscious of his deficiencies,
and determined him to seek abroad the means of supplying them.
Having spent one or two summers in Paris, where he made very ex-
tensive dried collections of the plants of the Jardin des Plantes,
he established himself in 18—, at Geneva, where, under the auspices
of De Candolle, he found all that he could desire. How well the
three or four years which he spent there were employed, appears
from the memoir on the Dipsacez, which he then published, and still
more from his Herbarium, of which the European part was then formed,
and compared with De Candolle’s own collection; a work, which when

555

considered as the result of almost unaided individual exertion, may well
be called gigantic.* The consciousness of power excited him to en-
terprize, and on his return from the Continent, in 1824, he arranged
an expedition to explore a considerable portion of America. His
intention was to commence at Buenos Ayres, cross the great plains
to Mendoza and Chili, to explore the western side of the Cordilleras,
and the Lake of Titicaca; thence to California, and to return by
Mexico, or by the Columbia river and Canada. For this he had
actually made arrangements, and it is to be regretted that he did not
execute it. He had every requisite for success among half civilized
or savage races: a noble and commanding person; great ‘stature,’
strength, and dexterity in the use of arms; good temper, courage, and
presence of mind: a combination of qualities, which Bruce only, of
modern travellers, possessed in the same degree, while he was far
behind him in practical science.

‘¢ He was, however, induced to change part of his plan, and com-
mence with Mexico, engaging as medical attendant to the establish-
ment of the Real del Monté Mining Company for three years, during
which time he hoped to complete the Mexican Flora, and afterwards
to resume his original design.t

« But in that unhappy country, there was found neither probity
nor peace. The English companies were regarded as legitimate ob-
jects of plunder, and several of those whom they employed retired in
sickness or despair from their posts.

«« Under such circumstances he felt himself called to go beyond
his peculiar duty, and undertook the charge of one of the company’s
principal mines, the Veta Grande, though such work was entirely new

*His Herbarium (including the Mexican and Californian plants), contains
about 150,000 specimens.

t+ ‘‘ While in Mexico he collected, at a very great expense, plants of seventy
species and varieties of Cacti, and sent them to the late Provost, the Rev. Dr.
Lloyd, then Bursar, to be presented to the College for their botanic garden.
He sent, at the same time, a similar collection to his friend, the late Professor
De Candolle, for the Geneva Botanic Garden. Many of them were then very
valuable, and unknown in European collections. One of them, a fine tall-grow-
ing species, has been named Cereus Coulteri, and may now be seen, as well as
other interesting species, in the College Botanic Garden.

556

to him; he, however, soon acquired the necessary knowledge, and
under his management the concern became productive. This mea-
sure was fortunate for his employers, but not for himself. It dis-
tracted his attention from his primary object, detained him for more
than a year in a district barren and uninteresting to the botanist,
and, above all, mixed him up with the cabals and personal feelings
which seem inseparable from such corporate bodies, and in which the
high-minded and open-hearted always have the worst. At the close
of his engagement he passed to California, where, and in Sonora, he
spent four years, always actively employed on his primary objects,*
and involved in spirit-stirring adventure; at times exposed to the
Indian arrows, or compelled to defend his countrymen from the at-
tacks of revolutionary patriots; exploring a burning waste of sand,
when the thermometer reached 140, or nearly perishing by the bites
of poisonous but almost invisible insects. At one time his metal-
lurgic skill had acquired for him considerable wealth, which, during a
botanical excursion, was plundered in some political convulsion.

“¢ The industry and energy with which he carried on his botanical
inquiries, is abundantly shewn by the fact,that the herbarium which he
collected under such circumstances contains upwards of 50,000 speci-
mens of 10,000 to 11,000 species, the far greater proportion of which
was collected and preserved by himself; and that in connexion with
the herbarium he had gathered specimens about the size of a 16mo.
book of nearly 1,000 descriptions of woods, most, if not all of which
are accompanied by dried specimens of the foliage and inflorescence

* «¢ One of his most interesting discoveries in California is a tall-growing
pine, having cones a foot or more in length, and six inches in diameter. This
has been named by the late Professor Don, at the desire of Mr. Lambert, Pinus
Coultert. It is quite hardy, and plants of it may now be seen in various collec-
tions in England and Ireland. It was found in the mountains of Santa Lucia,
near the mission of San Antonio, in lat. 36°, within sight of the sea, and at an
elevation of 3,000 or 4,000 feet above its level, growing intermixed with
another fine species, Pinus Lambertiana, also introduced, and rising to the
height of from 80 to 100 feet, with large permanent spreading branches, and —
a trunk three or four feet in diameter. There are two small plants of it
in the College Botanic Garden, and the cones may be seen in the College Her-
barium.”

557

of the trees from which they were taken ; the whole gathered by him-
self, and being, perhaps, the largest collection of this particular kind
ever made by any unaided individual.

« At the end of this period he returned to Europe with an im-
mense increase to his collection, but with a constitution irreparably
injured by the hardships which he had encountered ; and even at
home he was destined to meet a severe loss. In the transport from
London to Dublin, a case containing his botanical manuscripts, and
the materials of a personal narrative, disappeared, and could never be
traced; so that of the latter, nothing remains except a brief account
of Upper California, published in the 5th volume of the Journal of
the Geographical Society, and the former are totally lost, except some
communications to De Candolle and Lambert. After this his chief
anxiety was to secure the herbarium, which had cost him so much,
from dispersion or neglect; and in this at least he was not disap-
pointed. It has become the property of our University, and the
task of arranging it was the employment of his few remaining years,
which were devoted to that work with a concentrated energy that
shewedhis consciousness of his days being numbered. It wascompleted
for the European part, and about 8,000 ofthe American specimens 3
but the remaining packages are well furnished with memoranda, so
that for them also the arrangement is practicable. That the posses-
sion of this invaluable treasure must give a powerful impulse to the
study of Botany among us is sufficiently obvious; but it is doubly
interesting to a scientific body like this, as an evidence of the increas-
ing importance attached to the study of Natural History in the
highest and most influential quarter. That important branch of
knowledge has hitherto been too much neglected in university edu-
cation; but better prospects are opening; and to this the influence
of one so good and highly gifted as Dr. Coulter seems mainly to have
contributed. Should our hopes be realised, there is no doubt that
he would have regarded it as an ample compensation for all his suf-
ferings.”

The ballot for the annual election having closed, the
Scrutineers reported that the following gentlemen were
elected Officers and Council for the ensuing year :

558

President—Sir William Rowan Hamilton, LL. D.

Treasurer—James Pim, Jun., Esq.

Secretary to the Academy—James Mac Cullagh, LL. D.

Secretary to the Council—Robert Kane, M. D.

Secretary of Foreign Correspondence—Rev. Humphrey
Lloyd, D. D.

Librarian—Rev. W. H. Drummond, D. D.

Clerk and Assistant Librarian—Edward Clibborn.

Committee of Science.

Rev. Franc Sadleir, D. D., Provost of Trinity College ;
Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D. ;
James Mac Cullagh, LL. D.; Robert Ball, Esq.; Robert
Kane, M. D.; G. J. Allman, M. B.

Committee of Polite Literature.

His Grace the Archbishop of Dublin; Samuel Litton,
M. D.; Rev. William Hamilton Drummond, D.D.; Rev.
Charles Graves, A. M.; Rev. Charles W. Wall, D. D;
John Anster, LL. D.; Rev. S. Butcher, A. M.

Commitiee of Antiquities.

George Petrie, Esq.; Rev. James H. Todd, D.D.;
Henry J. Monck Mason, LL.D; Samuel Ferguson, Esq. ;
J. Huband Smith, A. M.; James Pim, Jun., Esq. ; Captain
Larcom, R. E.

The President then appointed, under his hand and seal,
the following Vice-Presidents :

The Rev. James Henthorn Todd, D. D.; James Ap-
john, M. D.; the Rev. Charles W. Wall, D. D.; and George
Petrie, Esq.

The Auditors appointed by Council to examine the
Treasurer’s accounts reported as follows:

559

‘¢We have examined the above Account,* with the vouchers
produced, and have found it to be correct ; and we find that there
is a balance in bank, amounting to £203 18s. 3d., sterling, and in
the Treasurer’s hands, 6s. 14d.” ;

“ (Signed, )
« JosEpH CARSon.
« THomas A. Larcom.”
“ March \5th, 1844.”

“ The Treasurer reports, that there is £1117 10s. 10d. in 3 per
Cent. Consols, and £1643 19s. 6d. in 34 per Cent. Stock, the
latter known as the Cunningham Fund. He also reports that there
are due this 16th March, 1844: :

Zentrance fees, at.£0 Bs. pero. 2. 4 =. «- £0 tO O

6 Arrears of two years, at £4 4s.per. . . . 25 4 0

ae Wo.” ione'year,. "£2 “Os per A. #29 52 10 O

170 Subscriptions for the past year, now due, at

MD Diner URE YE NE aE SS SP eB BS zis! Dlg
Balance unappropriated in the Bank of Ireland,
£203 18 3

Balance in Treasurer’s hands, . . O 6 14 £204 4 44

£649 8 4k

“ Signed for James Pim, Jun., Treasurer.
«“ EpwarD Curpporn, Clerk, §c.”

April 8.
JAMES APJOHN, M.D., Vice-President, in the Chair.

The Marquis of Kildare and William Smith O’Brien,
Esq., M. P., were elected Members of the Academy; and

* Entered in Treasurer’s book-

VOL. II. OA

560

Robert Ball, Esq., was elected Treasurer of the Academy,
in the room of James Pim, Jun., Esq., who resigned.

Dr. Apjohn read a paper by Mr. Thomas Knox, ‘On
the Purification and Ventilation of Vessels from bad Air.”

In reperusing lately Professor Daniell’s interesting re-
searches* ‘‘on the spontaneous evolution of sulphuretted
hydrogen in the waters of the western coast of Africa and
of other localities,” a method occurred to me of purifying the
cabins of vessels, and the sleeping apartments in houses,
which would be as efficacious as Professor Daniell’s, with-
out being liable to the objection of having free chlorine
always present producing its enervating effects.

The method I propose is this: to have air pumped
through tubes extending from the steam engine to the cabins.
The extremities of the tubes should dip into vessels contain-
ing solutions of chlorine or metallic solutions; the last solu-
tion, being of lead, would indicate when the solutions were to
be renewed, by the black precipitate of sulphuret of lead.
At the further end or top of the cabins there should be cor-
responding tubes to allow the foul air to be removed ; these
latter would be unnecessary when there was a fire, the draft
being sufficient to remove the foul air.

As we can absorb or destroy all vapours, miasma, &c.,
this method would apply to all unhealthy regions of the
world, and would render habitable parts of the world which
at present lie deserted and waste. Sierra Leone would cease
to be the grave of Europeans, and the Pontine Marshes
would no longer exhibit a ghostlike peasantry.

EXPERIMENTS.

Chambers made of wood, with air-tight windows, having
apertures in the sides, into which the tubes would fit, could

* Phil. Mag., July, 1841.

561

be made at little expense, and sent to Sierra Leone and the
Pontine Marshes; in the latter place the pumps might be
worked by water conveyed from the mountains or other
cheap motive power.

Dr. Apjohn read a paper “On the hygrometric Cor-
rection in barometric Formule for the Measurements of
Heights.

If the atmosphere were of one uniform temperature
throughout, destitute of moisture, or in a constant hygrome-
tric condition, and if the intensity of gravity were also con-
stant, it is well known that the difference of the altitude of
any two points in the atmosphere would be represented cor-

rectly by the formula p = m x log. i m being a constant

quantity, and p and p’ being the respective pressures at the
lower and upper stations, as measured by the barometer, or
in any other way. A correction for temperature has been
long applied by augmenting or diminishing the approximate

height, or m xX log. 7 by the amount that a column of air

of this length would expand or contract if its temperature

were changed from 32° to : 5 Ge t being the temperature of

the lower, and @ that of the upper extremity of the serial
column, by which the expression becomes
pamxlog.2 x (1+-=_—).
hee 493
Such is, I believe, a correct account of the present form
of the barometric formula, at least when we neglect the cor-
rection for variations of gravity, which is, however, in gene-
ral so small as to be safely negligible. The presence of
moisture in the air, or rather its varying amount, must ob-

viously exercise some disturbing effect on this formula; but
3A2

562

though this has been generally admitted by those who have
turned their attention to the subject, I am not aware that
any attempt at estimating its exact amount has been as yet
made; and as the correction for moisture is frequently of
considerable magnitude, and may, in my opinion, be applied
with as much accuracy as that for temperature, I have taken
the liberty of occupying, for a few moments, the time of the
Academy with an explanation of the method which it has oc-
curred to me to devise, and with which, from some trials I
have made of it, I have every reason to be satisfied.

Let p be the pressure, and ¢ the temperature of the air at
the lower station, ¢” the dew point of the air, and f” the force
of the included vapour ; and let p’, 0, 0’ and F” represent the
corresponding quantities at the upper station. This being
understood, a little consideration will suffice to shew that
the presence of the aqueous vapour produces on the for-
mula a twofold deranging effect. It augments the values of
p and p’ beyond what they would be in dry air, and it pro-
duces an alteration in the length of the column of air between
the two stations additional to that which results from the dif-
ference between its mean temperature and 32°, or the freez-
ing point. The first of these is obviated, or, in other words,
the correction for it is made, by substituting for p and p’ in
the approximate formula, p — f” and p’ — F”’, by which it
becomes

D= m X log. ae
pi—F

Having thus eliminated the effects of the tension: of
aqueous vapour upon the pressures, we have next to esti-
mate the conjoint influence of it and temperature, in elon-
gating the pillar of air between the two stations. ‘The theory
of mixed gases and vapours enables us to do this, provided
we can assign proper mean values to the temperature, the
pressure, and the force of vapour of the aerial column in ques-

563

t+
2.
this must be very nearly its true value. For the same reason,
fl+ pF”
2
let us assume the mean value belonging to the pressure as
V (p —f") —f") x xX (pr — "— KF’).

Nowa volume v of dry air at 32° undera pressure 7, if raised
to a temperature ¢”’, becomes

461 + ¢”
493!
and if saturated with vapour at this temperature, the tension
of such vapour being s”, it will become
461 + 4!’ T
493. — 3"
This is the volume of the air when raised to ¢” and satu-
rated with vapour at this temperature ; and if this volume
of air have its temperature further changed, we shall say to ¢,
then its bulk will be represented by the expression
461 + ¢” T 461+ ¢ 461 +t T
498% wae? 1G 8 498) oe
substituting, then, in this expression instead of v the value
of the length of the column of air between the two sta-
tions supposed dry, and at 32°, v

tion. The mean temperature its usually taken as , and

the mean force of vapours may be set down as ; and

ox

UX

tae

—_ FF?

m x lo
BF

and for 7, ¢, and s” their proper mean values as already ex-
plained, the barometric formula finally becomes

(t+-0)
ey Deak ot
D =m X log. ae x 7493
V p=) & pF)
V (p ate ai x (p'— Gia) — 1 bf’ +r”)

I may add here, that the correction for moisture is far

from being insignificant in its amount, as may be seen by

564

the following example. Let us suppose, that when the ap-
proximate height, corrected for temperature, amounts to
2700 feet (a height reached by several of our Irish moun-
tains), the mean value of 7, or the pressure to be used in the
final factor of the formula, is 27.3, and of the force of va-
pour, 0.3 of aninch, its value when the dew point is 43.6,
then the elongation of the aerial column resulting from mois-
ture is 975 = goth of 2700 = 30 feet. It will, of course,
have been observed that the correction for aqueous vapour
differs from that for temperature in the circumstance of being
always positive ; and this coincides perfectly with the obser-.
vation I have had frequent occasion of making, namely, that
in damp states of the atmosphere heights calculated by the
formule in general use are all appreciably less than the truth.

And here I may be permitted to observe, that the great
Laplace, in discussing the barometric formula, in his “ Sys-
téme du Monde,” has fallen into a slight oversight; for as a
rude method of compensating for the effect of the aqueous
vapour present in the atmosphere, he proposes, that in ap-
plying the correction for temperature the coefficient of the
expansion of gases should be augmented from .00375, its
value for one degree Centigrade, to .004. Now this would
certainly produce the desired effect at.all temperatures above
32°; but as below 32° this equation is subtractive, the aug-
mentation of the coefficient, instead of diminishing, would
increase the error. The following is the passage referred to:

‘“‘ Les vapeurs aqueuses répandues dans Il’atmosphére,
etant moins denses que lair, a la méme pression et ala
méme temperature, elles diminuent la densité de l’atmos-
phére; et comme, tout étant égal d’ailleurs, elles sont plus
abondantes dans les grandes chaleurs; on y aura égard en
partie, en augmentant un peu le nombre .00375 qui exprime
la dilatation de lair pour chaque degré du thermométre.
Je trouve que l'on satisfait assez bien a l'ensemble des ob-
servations, en le portant a 0,004; on pourra done fair usage

565

de ce dernier nombre, du moins jusq’a ce que I’on soit par-
venu par une longue suite d’observations sur l’hygrométre, a
introduire cet instrument dans la mesure des hauteurs par le
barométre.””*

I may in conclusion observe, that in assuming, with the
view of calculating the expansion produced by moisture, that
the pressure to be employed is the geometric mean of the
corrected pressures given by the barometer at the two sta-
tions, I am quite aware that I am assigning to it but an ap-
proximate value. An exact expression for the pressure to
be employed admits of being investigated ;} but its intro-
duction into the formula, while it would give the latter com-
complexity of form, and thus render it less suited for prac-
tical use, would conduct to results not appreciably different
from those given by the more simple methods just ex-
plained.

Mr. Clibborn presented to the Acadcmy an ancient stone
image, called in some places a Shela-na-gig; and read the
following extract from a letter from Dr. Charles Halpin:

*¢ About two years ago, as I drove past the old grave-
yard of Lavey Church, I discovered this curious figure, laid
loosely, in a half reclining position, on the top of a gate pier
that had been built recently, to hang a gate upon, at the an-
cient entrance of the old church-yard. I believe the stones
used in building those piers were taken from the ruins of

* Systeme du Monde, p. 89.

log. 2
+ Let -—- , m being the modulus of the common system of logarithms,

1
up
‘=p. Then ifv be the column of dry air, and that, when saturated with mois-

ture whose force is f, it becomes v', we will have

v=vX

P

P—f ;

For the very elegant expression for Pp I am indebted to my friend, Professor
Renny.

566

the old church of Lavey (there is scarcely a trace of the
old church on the site it occupied); and I think probable,
that this figure was found amongst them, and laid in the
position in which I found it, by the masons employed at the
work. I was not aware of its real value, until apprised of it
by my brother, the Rev. N. J. Halpin. He immediately re-
cognized it as a ‘ Sheela-na-gig,’ and the most perfect of
any he had seen. I thought it my duty to protect this pre-
cious relic from the hammer.

** Lavey church lies about fifty miles north-west of Dub-
lin, on the mail-coach road. There is a neat new church
near the site of the old one.”

Mr. Petrie having expressed a desire that some further
information should be given about this figure, and others,
of the same kind, of which, he understood, there were two in
the museum of the Academy, which had belonged to the late
Dean Dawson:

Mr. Clibborn explained that he had received notices or
outlines of ten other figures, of the same kind, which had
been found in old churches and castles, and from their posi-
tion in the walls, sometimes hid in the eourse, and from the
difference of the stone, it was probable they had been used
in older buildings, so that their actual antiquity could not be
determined by the age of the buildings in which they had
been found. From the form of the stones on which several
of these figures were carved, it was surmised that some
of them had been originally used as grave-stones, and proba-
bly intended to act as charms to avert the evil eye, or its
influence, from the place. ‘These figures have a great simi-
litude to others used elsewhere for this purpose formerly, as
well as at present, by the natives of the east coast of Africa.

He also explained that, about five years ago, when, in
company with several advocates of the O’Brien theory of the
Round Towers of Ireland, he was led to express an opinion
that, possibly, these buildings, though erected subsequently

567

to the introduction of nominal Christianity into Ireland,
might still have, to a certain extent, some analogies to views
entertained by the African and Asiatic ascetics, and which
might have been imported into Ireland by the first Chris-
tians, in the third century ; who, if from Africa or Spain, may
have brought with them more or less of Gnosticism (or
views analogous to it), and with it notions and practices not
very unlike, apparently the same originally with those, by
which the author above-mentioned endeavoured to explain
the nature and origin of the Round Towers. The first no-
minal Christians, if he had been correctly informed, who
came to Ireland, were lay ascetics ;* and, like the ascetics of
Egypt and the East, they selected secluded valleys in the
mountains, or islands in lakes, where they gave themselves
up to those penitential observances calculated, according to
their views, to destroy the ‘“ Hylic, or material,” to. humble
and conquer the “ psychic, or animal,” and to elevate and culti-
vate the ‘“‘ pneumatic, orspiritual,” principle of their natures.

It was argued that, if the tower was the residence of
the Irish ascetics during their lives, it may have been con-
sidered the type of the plus, male, “‘ pneumatic,” or spiritual
principle ; and so the earth, grave, crypt, or church near it,
in which were deposited the bodies, or material principles of
the deceased, originally derived from mother earth, may
have been considered the type of the negative female, hylic,
or material principle, and have been considered analogous
to Ge, or De-meter, to whom the body of the dead returned,
by interment; and, hence, it was argued that, if O’Brien’s
theory were true in this qualified sense, it should apply to
the churches or graves near the towers or residences of the
ascetics, where we should find types or indications of the
negative principle. Mr. R. P. Collis, who was present, im-

* See Moore’s Hist. p. 221. The extract from St. Patrick’s letter: ‘‘ubi nun-

quam pervenerat qui baptizaret, aut clericos ordinaret, aut populos consummaret.”

568

mediately mentioned the female figure at Rochestown, and
stated that he had heard of several others in the same neigh-
bourhood, and he recommended an inquiry into the subject,
which led to the discovery of several more figures of the
same kind in different places.

The ‘‘hylic principle,” including the materials composing
the body, was little more than the locus, where the batile of
the two other principles was fought during the life of the as-
cetic;* and if he persevered to death in the practices pre-
scribed for the evolution of the pneumatic principle, and lost
his life in these observances, or in the fulfilment of the duties
which belonged to this system, his victory over the hylic or
psychic principles was complete, and he was said to have
arrived at ‘* perfect virtue,” and consequently became, ac-
cording to Asiatic views, an inferior, or little Bauddha, which
may, possibly, give us an original of the name of Monaster-
boyse; in Irish, the monastery of Boaithin, or the little
Bauddha. The legend of St. Colum Cille, who struck his
crosier against the glass ladder, by which he went to heaven,
which belongs to this place, and which strongly corroborates
a Ceylonese legend, increases the suspicion, that the system
which was called here Christian, originally may have been
analogous to that ascetic system which existed under the
same name in Egypt and the East, and was closely allied to
Bauddhism, which was, and is, a system of Asceticism,} and

* This doctrine is the same, or nearly the same, as that which is called
Dualism, which attributes creation and life to the action and reaction of two
principles, plus and minus, or positive and negative, which were personified. by
the ancients under every species of antagonism. The fighting dogs and serpents
of the Irish are, apparently, manifestations of it, applied specially to the daily
strife, or ‘‘ cross,” of these two principles in the body of the ascetic.

{ When O’Brien’s book was written our knowledge of the Bauddist system
was very limited. Now its antiquity, history, principles, and corruptions, are
better understood, through the labours of Mr. Princep, Fa-hian’s Travels,
The Mahavansa, &c.

569

mixed up with more or less pure Gnosticism; for, “ the
greatest part of the Gnostics adopted very austere rules of
life, recommended rigorous abstinence, and prescribed severe
bodily mortifications, with the view of purifying and exalt-
ing the mind,” like the Irish ascetics. ‘‘ These tenets were
revived in Spain, in the fourth century, by a sect called
Priscillianists,” where they may have been, to a certain de-
gree, suppressed by the instrumentality of missionaries and
seculars from Rome. The same system which existed in
Spain previously, and which planted those views there after-
wards, may have also planted them here; and the same
means which suppressed them there for a time, may have
here suppressed them; or there may have been, to a certain
degree, for several centuries, a compromise between the ad-
vocates of both systems, and that which was finally adopted
here, and dalled Christianity, may have, in a covert way,
contained much Gnosticism, particularly that branch of it
which was adopted by the ascetics, or Culdees, and small
religious communities, and by whom the first towers may
have been originally built.* It is a curious circumstance,
not hitherto noticed by any writer on the Round Towers,
that the technical term for a Bauddist monastery in the East,
is a tower; no matter whether it be a cave in the earth, or
a cabin or palace on its surface.

We may add to these notices another notion of the

* The following extract, from the very old Irish MS. called the Speckled
Book, in the Academy, will explain and confirm what I have stated concerning
Irish asceticism: ‘‘ When, then, said St. Bartholomew, the Son of God was
born, he was tempted by the Devil, but Christ overcame, by fastings in the wil-
derness, him who overcame Adam, in Paradise, through gluttony; for it was
meet that Christ, the son of the Virgin, should overpower him who overpowered
Adam, the son of the virgin, i.e. the son of holy earth; for the (mother) earth
of which Adam was formed was virgin, because it had not then been polluted
by iron, nor by the blood of man, nor had it been opened for the interment of

man in it at that time.”

570

Gnostics, which was, ‘‘ that malevolent genii presided in
nature, and occasioned diseases and calamities, wars, and
desolations; induced them to apply themselves to the study
of magic, in order to weaken the powers, or suspend the in-
fluence, of these malignant agents.” This doctrine of their’s
was, no doubt, extended and carried out fully in every mode
and form, and led them to consider themselves, and all things
living on the earth, to be under the influence and subject to
the evils caused by the instrumentality of these evil genii, who,
in some cases, attached themselves to individuals, who were
then said to have the evil eye, or who became afflicted with
what is termed ‘“‘ covetousness,” which blasted everything
which they desired, and made it unlucky; and its possessor
was shunned and avoided, as he was subject to that malign
influence which is technically termed the “evil eye.” This
influence was greatly dreaded by the living, for themselves,
their children, cattle, and goods, and their houses; and in
many places, even now, people put up over their doors, over
their hearths, and in many other places, talismans, to give
them good luck, or to take away or neutralize the evil look,
which brings them bad luck, by averting the evil eye, also con-
sidered to bea distinct individuality, or genius. The term
** good look,” or “luck,” is incorporated into the English lan-
guage, though the belief of the evil eye is nearly lost in Eng-
land, where it was universal. It still exists in Scotland, and
we find it also in Ireland, where various methods are still
practised to avert its influence from children, cattle, churns
of milk, houses, &c.

One of the most efficacious is the horse shoe, which is
called “the lucky horse-shoe” for this reason, and it is
“nailed to doors and gateways for luck, by people who have no
notion that they are, probably, putting up equivalents for
those hideous figures which the people call shela-na-gigs,
one of which was lately discovered at Kiltynan Castle, by

dtl

Mr. Thomas Oldham, which held the lucky horse-shoe in
one hand, and a cross, or dagger, in the other.

_ The horse-shoe, and the triangle, A. or N, &c., and the
trefoil, are all, apparently, emblems for the same antidote,
which the evil eye abhors, and by which the mechanic’s wife
was not only able to identify the evil genius himself, but to
eject him from her house, and save her husband’s body and
soul, the stake which he proposed to play for. In this coun-
try the peasantry are said to entertain similar notions of
the great efficacy of the same means, which is said to be
*‘ capable of driving the Devil away,” the use for which, it is
surmised, these figures were intended.

Mr. William Hackett, the moment he saw a drawing of
one of the figures, declared it was a “fetish;” the African
name of a figure which closely resembles the shela-na-gigs,
and is commonly used for the purpose of averting the evil
eye, and giving good luck. On the north coast of Africa
certain emblems, carved in stone, are placed over the doors
for this purpose; and formerly it would appear that certain
parts of animals were used instead. In Italy the peasantry,
in the neighbourhood of Naples, have a complete system
‘of magic” for averting the evil-eye, which consists, to
a great extent, of exposures and practices, which are com-
pared to the ancient orgies, and calculated to eject or avert
the evil eye, or genius, from a place, and drive him and his
colleagues, and their influence, beyond certain limits.

These figures were, probably, intended as fetishes, or
charms, to keep off the evil eye, or its influence; and, con-
sequently, they are found placed over doors of churches and
castles, &c. In many instances they are evidently much
older, and of a totally different material and style of art, to
the building in which they are found. The workmanship is
quite unequal, and the style of the figures differ very much.
They are not copies of a common original, but, generally,

572

the most hideous and frightful-looking female figure which
the stonecutter could devise. There is, however, in the -
best sculptured figures a certain expression of countenance
which resembles that of death. In these the hair is very
long, and there is no appearance of the tonsure, which occurs
in others. The former have a strong resemblance toa Mith-
raic figure, published in the Archzologia, XIX. p. 74, and
also to another figure, in Ingrami “ Monumenti Etruschi,”
T. 3, Tav. XXIIi. Both of these, it is thought, were also
used as fetishes, or figures intended to drive away the evil
influence, and obtain good luck instead.

The hair of some of the figures appears to be intended to
represent a peculiar tonsure, and the persons of women repre-
sented are apparently attenuated by fasting and thatcourse of
life which the Gnostics and ascetics so strongly insisted on, as
the means of gaining the victory over the hylic or psychic
(together, the evil principle) in themselves, and what St.
Bridget so ably contended for in herself, and those who
placed themselves under her rules. In these almost skeleton
figures we have an: analogy between the rule of abstinence
of the Gnostics, and also their notion about amulets, abraxes,
fetishes, and the evil genius; and hence the probability,
that the use to which they have been assigned is the
correct one, independent of any other considerations which
arise from the practices now said to be efficacious in Ireland,
&c., in ejecting the evil genius, or averting the evil eye; and
which formerly, as well as at present, were common in Africa,
Italy, Spain, Ireland, &c.

With the ancient Egyptians the crux ansata appears to
have been the great emblem of good luck, prosperity, and
soforth. It appears to have been the antidote to the evil
eye which we find mentioned in Prov. xxiii. 6, and xxviii. 22,
and the Gnostics and early Egyptian Christians appear to
have adopted it, without any alteration or change in its form
from that used by the old Egyptians. The crux ansata ap-

573

pears to have been a substitute for the gesture called the
fico of the ancient Romans and modern Neapolitans, which
combined the Dualism, or positive and negative principle.
It is still used, according to the Canon De Jorio, when a lay
Neapolitan wishes another good luck, when he is going on
an expedition, &c. And we find the fico, combined with
other emblems into the form of the cru# ansata, in the mu-
seum at Naples, where there are many examples analogous
to many Gnostic emblems, which are well known; some of
which have been published by the Rev. Dr. Walsh. One
found in the baggage of Prince Charles Edward, after the
battle of Culloden, has on it a woman, in a better style of
art than that of the shela-na-gigs; but, probably, intended
for the same purpose, ‘‘as a charm” to avert the evil eye,
and gain the good luck instead.

The crosses which are placed round certain enclosures
in Ireland, and act as termini, or boundary marks, had _ pro-
bably the same use formerly, to keep off the evil-eye and its
influence from the enclosure, so that the sleep of the dead
might not be disturbed ; hence the request to pray for the re-
pose of the soul of Bran, on the tombstone in the museum,
and the usual “may he rest in peace”; terms calculated to
neutralise the disturbing influence of the evil- eye principle.
In Asia and Africa things owned by individuals are frequently
tabooed, or marked with the cross, or circle, crescent, or
both combined, which, it is believed, protects them from the
evil-eye, and consequently from being coveted by people,
or rendered unlucky. This practice, or the notions which
caused it, appears to be almost as old as man himself,
and is found incorporated into the language, and occupying a
greater or less proportion of the popular belief in every
country. The pattern which composes the tracery on our
cross of Cong, and other old Irish shrines, reliquaries, and
the tomb at Cashel, which represents an animal like a dog
or serpent always worrying itself, or another creature of the

574

same kind, may probably be a type of the doctrine of absti-
nence or mortification of the flesh,* which to the ascetic was
his daily cross, and antidote to the hylic or evil principle,
which he considered himself bound to bear, and which his
master before him had borne victorious to death, and by
which he became exalted to the highest rank in heaven, con-
sistent with our extract from the Irish MS., in which we find
at least one of the doctrines mentioned, which the ascetics
magnified into a constant rule of life, and made it the means
of conquering the evil principle in themselves, to which these
figures, it is thought, may have been charms or external an-
tidotes, like the cross and bells, &c., which they ornament,
which are covered with dog and knotted serpent patterns,
crossing each other continually, and supposed to be.emble-
matic of the ascetic principle, or daily cross, and antidotes
of the evil eye or principle. By this rule the stone in the
museum presented by Mr. Webber, which apparently re-
presents two dogs fighting, may have been an ingenious
device to hide from common eyes, but to exhibit this princi-
ple where it would be understood, instead of a shela-na-gig
of the common form, and so it may have been intended
originally as a fetish or charm to the house or castle from
whence it was removed. Besides the three figures now in
the Museum, I have been informed of the existence of many

* The emblem, or device, for Christianity on the Roman medals, given by
the Rey. Dr. Walsh, is analogous to the monstrous figures of the double dog
and serpent patterns referred to, which, it is surmised, may be emblems of the
ascetic principle. He observes: ‘‘It may be that Dioclesian wished to repre-
sent only the depraved and corrupt sectarians, of which this figure (zn his plate)
is the emblem; and that his more atrocious colleague, careless of distinction,
exhibited the genius of Christianity, under any form, as equally the object of his
persecution.” There is a figure called the Idol, at Cashel, with fish-tail ex-
tremities, with a face like the shela-na-gig presented by Mr. Halpin. It ap-
pears to connect, or identify, the designs on the Roman medals with those Irish
figures,

575

Shela-na-gigs in different parts of Ireland ; but have received
drawings and exact descriptions of five others only.

1. The first discovered and described by Mr. R. P.
Collis. It is in the gable of an old church at Rochestown,
County Tipperary. This figure is called a Shela-na-gig, by
the country people, and as it was the first found it has sup-
plied the name to all the others.

2. In the church at Dowth there is a Shela-na-gig,
carved in stone quite different to that which composes the
walls of the church. This figure appears to have been
originally a head or foot-stone of a grave. It was said to be
a figure of St. Shanahan, by the person who shewed me the
place. At Lusk there was a figure called the Idol, which
was buried by the late Rev. Mr. Tyrrell. It appears to have
been a Shela-na-gig also.

3. Found over the door of the keep of Ballinahinch
Castle, near Cashel. In this figure there is an appearance
of the tonsure. It was the opinion of the person who ex-
amined it, that it had been inserted in the wall, and might
have been taken from the ruins of the church, which are
quite near the Castle.

4. Found in the south front of Moykarkey Castle, County
Tipperary. This figure has a more finished and modern
air than any other of which I have drawings. The country
people have a legend, and call it Cathleen Owen.* It also
appears inserted into the wall, and there is a ruin of a church
quite near, from whence it might have been procured, to
bring ‘ luck about the house.”

5. Found in the wall of the old church on the White
Island, Lough Erne, in the demesne of Colonel Archdall.
This figure occurs lying on its side, and is in the course low
down near the door, and appears to have been a part of the

* This legend may be equally authentic as that about the dog and wolf stone,
presented by Mr. Webber.
VOL. II. 3B

576

materials ofan older building, which were used in the build-
ing of the church now inruins. In the same way one of the
figures in the Museum, from the Dawson collection, appears
to have been built into the wall of the church where it was
found. Under such circumstances, the actual antiquity of
these curious figures is quite problematical. ‘The subject
is a new one, and well deserving of the attention of antiqua-
ries, to whom this notice is submitted more as a suggestion
for consideration than as an opinion. The number of facts
known are few, and probably it may be premature to attempt
a generalization.

April 22.
SIR Wn. R. HAMILTON, LL. D., President, in the Chair.

Reap,—a letter from the Secretary of the Lord Lieu-
tenant, presenting to the Academy the stones containing
the inscription from the old bridge of Athlone.

Reso_vep,—That the thanks of the Academy be given
to His Excellency the Lord Lieutenant for his donation.

The Rey. Professor Graves read a paper on the Alge-
braic Geometry of Curves traced upon given Surfaces.

Let vu = ¢ (4, y, 2) =O be the equation of a surface re-
ferred to ordinary rectangular coordinates. Its complete
differential will be

pdx + ady + rdz = 0.
Making
x= sa:
R
Mr. Graves denominates x and y the normal coordinates of
a point on the surface. When they are known, the a, y, &
of the point are determined by the three equations

Q
and y =-,
R

P Q
u=0,-=x, and—=y.
R R

As P, @, R, are proportional to the cosines of the angles
which the normal at the point (x, y) makes with the axes ; it
is easy to shew that if we describe a sphere with its centre
at the origin and radius = 1, x and y will be at the same time
the rectangular spherical coordinates of that point on the
sphere at which the tangent plane is parallel to the plane
touching the surface u=o at the point (x,y). Thus, to
every point on the latter corresponds a point on the former :
and a succession of points, or a line of any kind, on the sur-
face U=o0 is in general represented by a succession of points,
or a line upon the auxiliary sphere.

As plane curves have been classed according to the de-
grees of the equations by which they are represented, so
curves traced on any given surface may be advantageously
distinguished by the degrees of the equations in x and y
which define them. For the properties of a curve, traced
on the surface u=o, and characterized by an equation of
the nth degree between x and y, are, so far as we regard
only the relations of normals or tangent planes along it,
identically the same as those of the spherical curve which
has the same equation. But the analogy between spherical
and plane curves of the mth degree has been already estab-
lished. Instead, then, of looking upon the shortestlines ona
surface as analogous to the right line, Mr. Graves directs
his attention to the line defined by the equation

ax + by +1=0, (A)
the geometrical character of which is, that the normal at any
point on it is always parallel to a fixed plane. Systems of
such lines upon any surface possess, in general, those pro-
perties of right lines which have been termed projective.

Thus, for instance: ‘If four lines of the first degree, di-
verging from the same point on a given surface, be cut ir

578

four points, a, , c, d, by another line of the same kind, we
shall have
sin [a, d]. sin [8, c]
sin [a, 6]. sin [e, d]
[a,b] being used to denote the angle between the normals to |
the surface at the points @ and b.

The normals along the line (A) are all parallel to the
tangent plane at the point whose normal coordinates are a
and b. Mr. Graves designates this point the pole of the line.
And if a and 6 be connected by an equation, so that the pole
describes some curve of the mth degree, the line (A) will
always touch another curve to which 7 tangent lines of the
first degree may in general be drawn from the same point.

=a constant,”

This relation between the curves being obviously reciprocal,
Mr. Graves calls them reciprocal curves. Here is laid the
foundation of a theory of polar reciprocals for curves traced
upon any given surface.

Amongst other exemplifications of this method, Mr.
Graves employs it to discuss the lines of greatest and least
curvature on the surface of an ellipsoid. Their equation in
normal coordinates is .

2 2 2
ee ee + aap =o
where a”, b?, c? are the squares of the semi-axes of the
ellipsoid, and #? is indeterminate.

Now, from the mere fact of this equation being of the
second degree, it follows that the sum or difference of the
angles between the tangent plane at any point ona line of
curvature and two fixed. planes is constant.

But further, all the spherical curves of the second de-
gree represented by the preceding equation are biconfocal :
and it is easy to shew that their common foci are the points
on the sphere which correspond to the umbilici of the ellip-
soid. Hence, the sum or difference of the angles between

579

the tangent plane at any point on a line of curvature, and
the tangent planes at two umbilici, is constant ; or, as the
tangent planes at the umbilici are parallel to the planes of
circular section, we have the following elegant theorem:

“The sum or difference of the angles between the tan-
gent plane at any point along a line of curvature on an ellip-
soid, and the two planes of circular section, is constant.”

The proposition just mentioned was, it is believed, first
published by Sir William Hamilton, in the Dublin University
Review, part (3) ; the short article which contains it being
dated June, 1833. It has also been published by Dr.
Joachimsthal, in a paper printed in the 26th vol. of Crelle’s
Journal, and dated January, 1842, where that geometer
claims it as “ novum neque inelegans.”

The reciprocal of the line of curvature has for its equa~
tion

a? — h? b— hb c? — h?
a zh b a Ce un?

in which if we make

a = and y = #,
we shall get the equation of the cone, whose generatrices
are parallel to the normals along the reciprocal of the line of
curvature, and whose vertex is at the centre of the ellipsoid.
After this substitution the last equation becomes

2 2 we
vty + 2 (+444) =0,

from the form of which it is evident that the cone passes
through the intersection of the given ellipsoid, and a con-
centric sphere having & for its radius. The properties of
this cone, and its relation to the lines of curvature, were first
noticed by Professor Mac Cullagh.*

* Proceedings of the Academy, yol. ii. p. 499.

580

For the quadrature of areas on the surface of the ellip-
soid Mr, Graves gives the following formula:
14+x?+ y’)idxdy
area = a°b*c* (2a Babibesele
(c? + a? x? + b? y’)
The President made some observations on the communi-
cation of Professor Graves.

Mr. Clibborn read a notice of certain points in Egyptian
History.

Reapv,— The following Report from the Council :

‘‘ That the Council do recommend to the Academy, at its next
meeting, to carry into effect the following recommendations of the
Committee of Antiquities, and to request a vote of the Academy
of £100 for the fitting-up of the Museum.

«¢]. That the resolution of the Academy, of the 30th of Novem-
ber, 1842, for making a new Board Room in the lower part of the
house, be carried into effect.

«<2, That the present Board Room be converted intoa Museum.

«« 3, That, for this purpose, two tables be provided, to stand across
the new Museum, opposite the piers. The present glass cases, ex-
cept that containing the Cross of Cong, to be placed on those tables,
and flat glazed cases to be added; the Cross of Cong to stand ona
separate pedestal between the tables, z. e. in the centre of the room.

‘* The Council having taken into consideration the best means
of exhibiting the antiquarian treasures contained in the Museum of
the Academy, and thus giving proper importance and utility to that
department, appointed a Committee, which recommended the adop-
tion of the resolutions of the Committee of Antiquities. These
have been adopted by the Council, and are now proposed for the
adoption of the Academy.”

Resotvep,—That this Report and Recommendation of
the Council be adopted, and that £100 be placed at the dis-
posal of the Council for the purpose specified.

581

DONATIONS,

Annuaire de? Académie Royale de Bruxelles. Néuvieme
Année 1843,— Annuaire de l Observatoire Royalde Bruxelles,
1843. Dixiéme Année.—Rapport sur l’ Etat et les Travaux
de Observatoire Royal, pendant |’ Année 1841 et 1842.—
Résumé des Observations magnetiques et meteorologiques
faites a des Epoques determinees. (Extrait du tome XVI.
des Memoires.—Observations des Phenomenes periodiques
(Extrait des tomes XV., X VI. des Memoires).—Jnsiructions
pour Observation des Phenomenes periodiques.—Memoires
Couronnés et Memoires des Savans Etrangers. Publiés par
YAcademie Royale. Tome XV. partie 2.—Nouveaux Me-
motres de l Academie Royale de Bruxelles. Tome XVI. Pre-
sented by the Academy of Brussels.

Memoires de la Société Geologique de France. Tom. V.
Parts 1, 2. Presented by the Society.

Memoires de l Academie Imperiale des Sciences de St.
Petersbourg. Sixth Series.—Sciences Mathematiques et Phy-
siques. Tom. XIII. Livraisons 1, 2, 3.—Sciences Politiques.
Tom. VI. Livraisons 1, 3.—Sciences Naturelles. Tom. V.
Livraisons 1, 2.— Recueil des Actes des Seances Publiques,
tenues le 31 Decembre, 1841, et le 30 Decembre, 1842.—
Memoires presentes al’ Académie. Par divers Savans. Tom.
XVI. Livraison 5. Presented by the Academy of St. Peters-
burgh.

Sur ? Emploi de la Boussole dans les Mines. Par A Que-
telet. Presented by the Author.

Erster Zusatz, zu der Schrift Ueber den Galvanismus. Von
Gustav. Crusell. Presented by the Author.

Ninth Annual Report of the Poor Law Commissioners,
for 1843. Presented by the Commissioners.

Catalogue of the Museum of the School of Medicine,
Park-street, Dublin. By John Houston, M.D. Presented
by the Author.

5&2

Faune Ornithologique de la Sicile. Par Alfred Malherbe.
Présented by the Anthor. ;

Annales des Sciences Physiques et Naturelles, §c. Par
la Société Royale d’Agriculture, &c., de Lyon. Tom. IV.
1841. Presented by the Society.

Proceedings of the American Philosophical Society, May
25-30, 1843. Presented by the Society.

Transactions of the American Philosophical Society. Vol.
VIII., new Series, Parts 2,3. Presented by the Society.

PROCEEDINGS

THE ROYAL IRISH ACADEMY.
1844. No. 45.
May 13.

SIR Wu. R.HAMILTON, LL. D., President, in the Chair.

Wm. H. Harvey, M.D., was elected a Member of the
Academy.

Reap,—A recommendation of Council to the Academy,
to open a subscription list for the fund required to complete
the sum necessary for the purchase of Hodges and Smith’s
Irish MSS., and that the Academy be recommended to head
the list by a subscription of £100.

Reap,—A letter from Lord Adare to Mr. Petrie, regard-
ing a Grant from Government to the Academy, for the said
purchase ; and also a letter from Sir Robert Peel to Lord
Adare, in which he stated that he was ‘willing to recom-
mend to the Treasury to grant £600 for the purchase of the
MSS.,” ‘‘ on the condition that the whole collection shall be
purchased, and that the sum required to complete the pur-
chase of the whole shall be raised from other sources.”

ReEsoLveD, on the recommendation of Council,—That
the Academy do open a Subscription list for the fund above
mentioned, and that it do head the list by a donation of
£100.

Wm. R. Wilde, Esq., read a paper on the Pharos of
Corunna.
VOL. I. 3C

584

Mr. Wilde prefaced his observations by stating that he
had already published an account of this celebrated building,
which is situated at the extremity of the peninsula, on which
the town of Corunna stands, wherein he had cursorily men-
tioned, that independent of the architectural beauty of its
structure, its inestimable value as a beacon to mariners
crossing this portion of the Bay of Biscay, and its marking
the common entrance to the harbours of Corunna and Fer-
rol, what added “ still greater interest to it in the eye of the
traveller, was the fact of its enclosing within its massive
walls one of the most interesting monuments of antiquity—
the Pharos of Hercules—the oldest existing specimen of this
kind in Europe, and amongst the very few now anywhere
to be found.”*

These observations were those of an ordinary traveller,
who had no particular theory to support, and no peculiar
object in view, save that of eliciting truth, and recording,
with fidelity, what passed under his notice. Since then Sir
William Betham having, in his ‘‘ Etruria Celtica,” questioned
some of the statements put forth in this quotation, and find-
ing, as he states, some incongruity between the accounts
given by Mr. Wilde and Laborde, appears to have come to
the conclusion that the ancient Pharos is not included, as is
stated, within the walls of the modern Tower.

Mr. Wilde went on to say, that “being about to repub-
lish the original notice of this building, and feeling somewhat
piqued at the assertion of Sir William Betham, who, never
having seen the locality, laboured, I conceive, under such dis-
advantages as hardly entitled him to criticise, although, it
must be said, in the most kindly spirit, the description
which I had given from a personal examination on the spot,

* Narrative of a Voyage to Madeira and the Mediterranean, 2 vols. 8yo.
Ist edition, 1840, pp. 12-14.

585

I have, however, to thank him for having noticed the subject,
even in the manner which he did, for it has led to the disco-
very of a most interesting manuscript and two drawings, the
only ones, I believed, in existence, of the ancient and modern
Towers, which I beg leave to lay before the Academy, and
which I procured in the following manner:

‘‘When Sir William’s book appeared I wrote to the
British Consul at Corunna, requesting him to procure me
some information upon the subject of the ‘ Hercules Light,’ as
well as plans or drawings of the ancient and modern tower ;
and also to have made for me a copy of, or extracts from,
any work or archive, either in manuscript or print, which
might be still extant at Corunna, Betanzos, or Brigantia, or
any of the towns bordering the splendid harbour of Ferrol,
and where such a record would be most likely to have been
preserved; at the same time, from the present unsettled state
of Spain, and the various revolutions with which that un-
happy country has been visited, I hoped for, more than anti-
cipated, a favourable answer to my communication. After
the lapse of a considerable length of time I have received the
most confirmatory proof of my original position in these two
drawings, together with the Spanish manuscript, which I now
exhibit to the Academy, and which were discovered in the
bureau of an old architect in Corunna. This document, en-
titled, ‘ Copia de la representacion y mas documentos que
con fha de 16 de Marzo de 1786, dirigio, esta Junta de Go-
bierno condor Planos al Ecmo Sr. Marques de la Sonora,’
appears to be a Report presented to the Marquis De La So-
nora by a Government Commission, empowered to inquire
into and report upon certain improvements destined to be
put in force in the harbours of Corunnaand Ferrol, in 1786.
In this ‘ Memoria Sobre la antiquedad de la Torre de Her-
cules,’ it is recommended to repair the ancient Tower or
Pharos standing at the extremity of the peninsula, ‘ the

3c 2

586

only notice of which,’ says the writer of this Report, ‘is,
that it was in existence at the beginning of the fifth century,’
and was originally intended for the same purpose, namely, a
signal for the ships going to England. It may be remarked,
that so advantageous was the post considered, that in 1684
the Consuls of England, Holland, and Flanders, entreated of
the Spanish authorities to have the building repaired, and
stated that their Governments would, at their own expense,
defray the cost of keeping up a light on it.

‘* The preceding representations faithfully exhibit the
condition of the original Tower, as it stood in 1786, and
also that of the present modern casing of granite with which
it is surrounded.

“« The wood-engraving to the left represents the original
ancient Pharos, a square, hollow tower, surmounted by a
rotundo, which was crowned by a large flag, bearing evident

587

marks of the long-continued action of fire upon its surface.
At each of the corners there was a small square turret; one
of these is represented as still existing when this drawing
was made, but evidently of a much more modern construc-
tion than the rest of the building. At foot of the drawing
we find the following inscription: ‘ Fectt Trueva Alumnus
Academie ex Civitate portus Brigantini, anno 1797.

** An external winding staircase led to the top, and per-
mitted ingress to its internal apartments, through the small
apertures still existing in the tower. A small square but-
tress at each corner, portions of which were in existence
when this drawing was made, seems to have supported the
stair or external winding passage at the angles; and the
groove in the masonry still shews the position which such
originally occupied. We read of a similar mode of access
being employed on the exterior of the celebrated Pharos at
Alexandria, probably for the purpose of carrying up the
fuel, which was used to light the beacon that was placed at
top.

‘“* The mode of construction of this Tower is decidedly an-
tique, although the general architecture and stone-work does
not point out a period older than that of the Romans; and
the masonry, composed of stones of comparatively small size,
is cemented together by a lime-concrete, similar to that known
to have been employed, if not introduced, by this people.
The height of the Tower, from the base to the rotunda at
the top, was 82 royal Spanish feet, and the rotundo itself
was 11 more, making in all about 132 feet English. It was
31 feet broad on each side, and in the interior were two
walls crossing in the centre, each 43 feet in thickness. The
Tower was divided into chambers or compartments by three
stone floors, originally without any apertures in them, so that
these apartments could only have been entered from without.
The outer winding stair having been removed at some pe-
riod long prior to the date to which we now refer, apertures

588

were made in these stone floors, and ladders leading from
one flight to another, enabled persons to ascend to the top
from within. It is stated in this Spanish document that the
outer staircase was pulled down to build a convent in the
neighbourhood, but at what precise period history does not
record. The small Towers at the top are believed to have
been erected subsequent to the removal of the outer stair,
perhaps in 1684, when the British, Dutch, and Flemish
Consuls relighted this wide-spreading beacon.

“With regard to the precise date ofits destruction, all that
we can learn from Spanish authorities is, that when Molina
De Malaga wrote his description of Galicia, in 1549, this
staircase did not exist; for in this old poetic work we find
some rhymes referring to it, thus:

‘ Pues la Cortina tampoco la deso,
Gran Puerto do numa fortuna le corre.
Y hablo de aquerte por sola una Torre
Antiguo Castillo que Uaman el Vieso ;
Aquerte es do dicen que estaba el eyrep,
Mas es Sabuloso sabido lo que era
Estaba cereada de grand escalera
Que quien la deshiro no tubo consep.’

Of which the following exceedingly rough, but literal trans-
lation, may afford the English reader some idea:
But Corunna I do not like,
A Great Port where no fortune runs.
I speak of this only on account of a Tower,
An ancient Castle, which was called le Vieso (the old);
This is where they say lived the witch,
But it is a fabulous saying—whatever it was
Was surrounded by a large staircase,
Which whatever mounted could not find its way down.
““The origin of the original Tower, and its name, are
involved in much obscurity. Galician tradition assigns it to
the workmanship of Hercules himself. Some characters,
scarcely legible, on one of the stones, says the writer of this

589

Spanish manuscript, states that it was erected in honour of
some of the Czsars. Near its base was discovered a stone
bearing the following inscription: the translation of which is
attended with some
difficulty from de-

MARTI f facement, as well

as the number of

AVG. SACR ? contractions of the
Eo LV te lca an eth
LVPVS. pe oe
ARCHITECTVS.] :

scription at p. 593.
Baron Humboldt
statesthat Laborde,
who furnished him
with a copy of these

—————— Jines, likewise in-
formed him, I suppose from the inscription, that ‘ this
Pharos was constructed by Caius Sevius Lupus, architect of
the city of Aqua Flavia (Cheves), and that it was dedicated
to Mars.’

“‘ Strabo, indeed, affirms that Galicia had been peopled _
by Greek colonies, and according to an extract from the
Geographies of Spain, by Asclepiades, the Myrlean, an
ancient tradition, stated that the companions of Hercules
settled in these countries. Very few Spanish authorities
mention this ancient ‘ Jorre del Pharo, or, as it is some-
times called, The Iron Tower; and the appearance which it
must have presented when originally built, accords precisely
with the descriptions which we read of the ancient Pharos at
Messina, and also that at Alexandria, around which we know
there wound an external spiral staircase, so broad and so
gentle in ascent that it is recorded a car and-oxen could
with facility pass to the top. The Spanish manuscript, which

590

I now lay before theAcademy, refers its construction (in all
likelihood) to the time of Trajan, because none of the geo-
graphers who lived before this emperor mention it, not even
the accurate Mela, who alludes to other particularities on
this coast. This, however, is but a negative proof; and
even among later geographers the same silence is preserved.
There is, however, one record extant in a stanza to be
found in the old Spanish geographer Ororio, or Orosirus,
who lived in the beginning of the fifth century, to this
effect :

‘Ubi Brigantia Calletce Civitas Sita

Altissimum pharum & inter pauca

Memorandi operis ad speculam Britanice

Hrigit....’

“‘ Here we have the first notice of one of the purposes for
which this Tower was supposed to be erected, and also of
the ancient tradition, existing both in this country and in
Spain, of the British Isles being seen from the Pharos of
Hercules. Without, however, attaching any weight to the
story of our island being seen from this Tower, it may be
remarked, that if the ancients sailed directly northward from
it they would, owing to the concavity in the Bay of Biscay
in which the harbour of Corunna is placed, arrive at Cape
Clear, instead of Cornwall.

“The early writers upon Irish history and Irish tradi-
tions have made frequent allusions to this ancient struc-
ture, as the ‘Tuir Breoghan.’ It is mentioned under
this head in the Leabhar Gabhaltas, or Book of the Con-
quests, a translation of which was made by Henry O’Hart
about the year 1686, and the original, which is now in the pos-
session of Sir William Betham, contains this notice of it:
‘Then Lughaigh, the son of Ith, went to Tuir Breoghan,
or Corunna, and shewed his father’s dead body unto the
posterity of Breoghian,’ &c.; and from this Breoghain is, in

591

all probability derived the name of Brigantia, one of the
oldest cities in this part of Europe.

« Sir William Betham has, with great labour and ingenu-
ity, searched out and recorded, in his ‘ Etruria Celtica,’ the
various Irish authorities that refer to this building, and says,
that he has discovered references made toit in the Kugubian
Tables, which, he believes, speak of the early navigators
steering by the fire set up on the land when the ship left the
coast of Spain for the Turn or Carne; and in the same pas-
sage the triple-pointed hill of Cape Ortugal, the next most
prominent headland, appears to him to be referred to.

‘In another place Sir William Betham says: ‘ The name
of Corunna and the Groyne are both derived from the
river upon which the town stands,—Garonne, the rough
or boisterous river, as the Garonne of France.’ On this
passage, however, I may remark, that I cannot agree with
my brother Academician, for Corunna does not stand on any
river, and the only one in its neighbourhood, and that too
at a considerable distance across the harbour, is not the
Groyne or Garonne, but the Rio Burgo. The term Groyne,
however, is constantly applied by the early Spanish writers
to the Bay itself.

. “«‘ The term Corunna, or Colonna, may have been applied

in after-times by the Romans, from the circumstance of find-
ing the Tower or Column upon this headland, in the same
way that the appellation of Cape Colunna has been applied
to the island in the Grecian Archipelago on which was
erected the celebrated Suniam temple, the remarkable co-
lumns or pillars of which are still standing.

“ Again: ‘ There is, says Sir William, ‘ some incongru-
ity between the accounts of Mr. Wilde and Laborde. The
latter says, the lighthouse is situated ‘“ upon a very high
mountain, a league from the harbour;” and Mr. Wilde has
stated its position to be ‘about a mile to the S. W. of the
town, on a rock by the water's edge.” Any one, however,

592

at all acquainted with the locality, knows that there is no
such mountain in this vicinity as that described by Laborde,
and the-position of the Hercules Tower can easily be ascer-
tained by those who have not seen it by referring to any of
the Admiralty’s charts of the coast; and, moreover, a light
on “‘a very high mountain a league from the harbour” would
be of little service for nautical purposes.’

‘I find, however, on again referring to the work of La-
borde, that it consists of two parts—an itinerary, or journal,
which appears to have been written from personal observa-
tion, and a running comment, in the form of notes, and
printed in a smaller type, on the population, commerce, ad-
ministration, natural history, &c. &c. of the countries visited,
and which is evidently derived from other sources, and com-
piled from different authorities. It happens that this latter is
the part quoted by Sir William, and not the text of the Jour-
nal, where, at p. 435, speaking of the harbour, he says : ‘ The
harbour is in the form of a crescent; at the two points are
the castles of Sainte-Clare and Saint Martin, which defend
it, and a little island which shelters it from the north wind.
All travellers have mentioned the ancient tower which ex-
cites admiration from its height, and its strong and solid
walls. The Galicians declare that it was built by Hercules,
whose name it still bears; this is to attribute it to the Phe-
nician merchants who frequented this coast; but a Roman
inscription has been found near this tower, which ascribes it
to the god Mars. Ifitis really the work of the Phcenicians,
as its antiquity and the tradition lead us to believe, this ac-
count may be reconciled by supposing that the Romans,
wishing to preserve this monument, and in gratitude for their
victory over the Carthaginians, who sprung from the Phee-
nicians, consecrated it to their tutelary deity.’

“* As this was a matter of some popular interest in connex-
ion with the antiquities and early history of this country,
Mr. Wilde quoted several extracts from what Sir William

593

Betham has put together upon this subject, trom Giolla
Keavin, an Irish poet, who lived about a. p. 1072, in a poem
called Reim re Riogh, or the Race of Kings—from the An-
nals of the Four Masters—and from the Book of Ballymote ;
from all which it would appear that the Irish poets and
annalists were well acquainted, not only with the existence
of this Tower, but with many of the ancient bardic traditions
assigned to it: such as its being built as a watch-tower by
Breogin, the son of Braha, who is also said to be the founder
of the city of Brigantia, &c. &c.

“In the Spanish manuscript it is recorded that a stone
bearing the following inscription was found built into the
wall of an old house in the town of Corunna.

[LVPVS CONSTRVXIT EMV
LANS MIRACVLA MEMPHIS
GRADIBVS STRAVIT YLAM.

[VSTRANS CACVMINE NAVES

“ The writer of the manuscript thinks that the dilapidation
of the Hercules commenced in the middle ages, when it was
converted into a castle or fortress belonging to the Arch-
bishop of Santiago; that the stones and material of the
outer staircase were at this time removed, and that some
trace of them may still be found in the fortifications of the
old town.

‘The result of the commission to which allusion was made
at the commencement of this notice, was, that the Spanish

_ Government determined to leave. the ancient Pharos in ex-

594

istence, but to envelope it within the present modern granite
building, which was commenced in 1797, and is represented
in the right-hand figure of the engraving at page 586. Itis a
handsome square tower, built of close-grained white granite,
and not only contains between its massive walls the original
Pharos, but is made to resemble it as much as possible; and
on its exterior a projecting band of masonry exhibits the
line of the original external staircase.

““ No doubt can now any longer exist with regard to the
position and preservation of this most interesting remain,
the Pharos of Hercules. At foot of the drawing which Mr.
Wilde exhibited, the following inscription is decisive: ‘ Per-
spectiva que de muestra el estado de la terre antiqua Uamada
de Hercules quando de emprendio sure edificacion y revesti-
mento de canteria por orden del Real consulado du la Coruna.”

** To establish this fact, and to record some additional no-
tice regarding the traditions and early history of one of the
most interesting structures at present remaining in Europe,
must apologize for this lengthened notice.”

Col. Jones made a communication concerning the disco-
very in the River Shannon, of a large collection of ancient
bronze and iron weapons and utensils, &c., which he pre-
sented to the Museum of the Academy, on the part of the
Shannon Commission.

List of Antiquities found in the River Shannon at the under-

named places.
KEELOGUE.
150 Elfstones. 8 Small Brass Spear-heads.
I piece of soft Stone (petre- 8 Do. Iron do.
faction). 2 Iron Sword Blades.

10 Sword and Brass Spear- 10 pieces of Teeth.
heads. ' 1 piece of Deer’s Horn.

595

1 piece of Wood, partly pe- heads, Spurs, Ornaments
trefied. of Scabbards, Druid’s
3 Iron Battle-axes, or Toma- Rings, &c., &c.
hawks. 3 parts of a Matchlock, Bar-
10 Brass do. do. rel, and Tube.
41 sundry broken Spear-
BANAGHER.
4 Lead Moulds, one with 2 Iron Spear-heads.
stamp of Coins. 3 Brass Tubes or Pipes
1 Brass Dial. (ornaments).
3 Brass Spear-heads. 1 piece of Deer’s Horn.
SHANNON BRIDGE. DERRYHOLMEs.
1 Brass Pin. | 1 Iron Sword-blade.
BISHOP’S ISLAND. PORTUMNA.
1 Brass Vessel. 3 Pieces of Deer’s Horn.

3 Do. of Teeth.

ATHLONE.
6 Elf-stones. 1 Tin Box containing Coins.
1 Two-edged Sword and 1 Grape Shot.
Handle. 1 Corroded Padlock.
2 Spear-heads. Sundry small articles, Pipes,
5 Brass Pins. &c. (in a small Box).

ResotvEp,—That the special thanks of the Academy be
returned to Col. Jones and the Officers of the Shannon
Commission, for the collection of Antiquities now pre-
sented.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1844. No. 46.

May 27.

SIR Wm. R. HAMILTON, LL. D., President, in the Chair.

Captain O’Connor exhibited two twisted gold rings,
brought from Africa and there used as current money.

The President communicated a method of mentally ap-
proximating to the calculation of ancient eclipses, and applied
it to the eclipse of the moon recorded by Tacitus as having
happened soon after the death of Augustus.

Mr. J. Huband Smith drew the attention of the Aca-
demy toa report, that there was in contemplation the remo-
val of a portion, if not the whole of the celebrated mound of
New Grange, near Drogheda, to be broken up for the re-
pair of the roads.

REsoLvED,—That it be referred to the Council to take
steps to ascertain the truth of the report, and in the event
of its proving true to take proper means to ensure the
preservation of this great and important national monu-
ment.

598

June 10.

SIR Wo. R. HAMILTON, LL. D., President, in the Chair.

Charles Hanlon, Esq., Maxwell M‘Master, Esq., Thomas
Oldham, Esq., Philip Read, Esq., Henry Roe, Esq., and
Robert Wilson, Esq., were elected Members of the Aca-
demy.

Dr. Apjohn read an account of the constitution of
Jade, and also of two ores of Manganese from the South of
Cork.

Dr. Apjohn observed that these minerals had been re-
cently analysed in his laboratory, and as the results were
somewhat novel, he thought he might mention them to the
Academy; his principal object being that they might appear
in the Proceedings, for the information of mineralogists and
chemists.

The Jade submitted to analysis was wrought into orna-
ments of various kinds, which were brought to Europe by
Captain Baddeley, who was engaged in several of the opera-
tions of the recent Chinese war. Its colour is white, with a
tinge of yellowish green. It has a splintery fracture, and is
highly translucent. S.G.=2, 965. Hardness over 7, or be-
tween rock crystal and topaz. Alone before the blowpipe
it glazes, but with great difficulty, on the surface.

By exposure to a strong red heat, it gives off a little
water, and becomes opake. Fluxed in the usual manner
with carbonate of barytes, it was found to include no al-
kali. Another portion of it fused with a mixture of the car-
bonates of potash and soda, yielded the following quantitative
results:

999

62) (3)
BaP Me Bic ee ied anniee op cn OO2L... 1. 2a 21.10
Alumina and trace of Oxide
of Chrome ... . . 2.980 0,058 1.00
MSE ak: Pebhe eae Sa bs<"ye0 14.150 ager:
= 1,572" 97710
Marnesiats gy \~ jo. + |.-, 22.275, 11.076
Water ..) ...<: «4.2. .-.%-1.625_ .0.180 3.10
Meese ke ee iii « BO4g
100.000

From the numbers in columns (2) and (3), which, calcu-
lated in the ordinary manner, represent the relative numbers
of atoms of the various constituents, it is obvious that the
empirical formula of this mineral is
MgO
CaO
Now, these atoms may be grouped so as to form a tersilicate
of alumina, and a subsesquisilicate of lime and magnesia; so
that the following may be considered as the rational formula
of Chinese jade:

MgO

Ac; 0,3 SiO +9 (3 Wes

In looking into works on mineralogy, I find that nephrite
or jade has already been at least twice analysed, first, by
Saussure, and secondly by Kastner; and, from the account
given by Beudant, of the specimen examined by the latter,
it would appear to be the Chinese. variety. The result,
however, obtained by these chemists are quite irreconcileable
with each other, and with mine. Thus, Saussure found his
specimen to contain 3 per cent. less silex than I have de-
tected in mine, to include no magnesia, but instead thereof,
the oxides of iron and manganese, and about 20 per cent. of
mixed soda and potash. Kastner obtained 6 per cent. less
silex, about 7 per cent. more alumina, and 8 per cent. more

VOL. II. 3D

21 SiO; + Ac. O; + 27 +3 HO.

2 Si0s) + 3HO.

600

magnesia, but no lime. The three specimens, therefore,
differ as to the nature and relative proportion of their con-
stituents. I may add, that it is not possible to represent
the composition of any two of them by the same formula; so
that, admitting the correctness of the published analyses,
we are entitled to conclude that minerals really different are,
in works upon mineralogy, confounded together under the
name of Jade or Neptrite.

Of the ores of mangeneus, the first I shall notice is a spe-
cimen of psilomelanane, the black hematite of the older mi-
neralogists, which I received some months since from R. W.
Townsend, Esq., and which occurs a little to the north of
the village of Glandore, in a mixed schistoze and arenaceous
rock, which is coloured by Mr. Griffith, as old red sand-
stone. S. G.=4.071. Hardness between fluor spar and apa-
lite, occurs massive, but more generally in botryoidal and
concretionary forms. 'The following are its constituents,
determined by an analysis very carefully conducted :

GQ) ()
STE hades ty cit, Lib Ge mR eee a em
BBarytes) toe. 4 WOW ae es fe) eR yh 4) Oe ia
Oxide Copper . . . ~ . + 1.254 0.031
Red Oxide Mang. (Mn,0,) 14, or by pamenee 31.241 0.393
Oxygen, iis te ee TOD Perox. 50.545 1.152

Wester (008: Dilley Shee mic. leis jail a 7 nl A is ace EE

Confining our attention to the oxides of manganese and
the water, it is obvious, from the quotients in column (2) that
the composition of the ore is very accurately represented by
the formula Mn, O3, HO +3 Mn O,, or that it isa compound of
one atom of manganite and three of pyrolusite. In the psi-
lomelanite analysed by Turner, there were 4 atoms of ses-
quioxide to 15 of peroxide; in that analysed by Berthier, 3
of sesquioxide to 17 of peroxide. It is obvious, therefore,

601

that the specimen I have examined is a new variety. But it
is also peculiar in other respects. 1. It contains oxide of
copper in appreciable quantity, a substance not occurring in
the other psilomelanes, though it was found by Professor
Davy, of the Dublin Society, to the amount of 4.5 per cent.
in a Swedish ore of manganese, which he considered to be a
braunite (see Journal of Geol. Society of Dublin, vol. i.
part 3.) 2. The amount of barytes included by it is but
about one-third of that found in the ores examined by Ber-
thier and Turner.

As respects the manner of the existence of the barytes
always found in psilomelane, and in small quantity in some
of the other ores of manganese also; I may observe that it
is the opinion of some high authorities in science, of M.
Beudant, for instance, that zt and the dentoxide are chemi-
cally united, the latter performing the function of an acid.
If this idea be correct, it will follow that they are capable of
combining in at least two widely different proportions, for
the psilomelanes of Berthier and Turner -will, upon this
view, be represented by the formula 2 BoO, 3 Mn, QO, and
that which I have analysed by the formula Bo O, 6 Mn, O;, so
that the latter contains, combined with the same quantity of
barytes, four times as much sesquioxide of manganese as the
former.

This Cork psilomelane is obviously a rich ore of manga-
nese, though of course inferior to the purer forms of pyro-
lusite. It exists in quantity in the district which I have
mentioned, and some cargoes of it have been brought into
the Dublin market, but have, I am told, been objected to
by the manufacturers of the bleaching salt of lime, in conse-
quence of its excessive hardness, and the consequent diffi-
culty of reducing it to a fine powder.

About three years ago, I received from Captain Kitto, a
Cornish miner, long resident in the south of Cork, an ore of
manganese, which appeared so different from those with

602

which I was previously acquainted, that I was induced to

submit it to analysis. It occurs in the locality already men-

tioned, at Rowry, a little to the east of Glandore, in lumps:
of variable size, which, when broken, exhibit, though but il
developed, the faces of crystals belonging apparently to the

right prismatic system, mixed, however, here and there with

what would appear to be a brown hematite. Some of the

crystalline portion of the ore, very carefully selected, gave;

upon analysis, the following constituents:

eS aides
Sileagiey on, : Up cope is Soe per eaee Ra 9 BZ IO8
Perox. Iron. . . . . . . 34.88 0.436 20

Red Ox. Mangan. 50.67) _Sesquioxide 5.25 0.066 3
Oxygen... 6,52 Peroxide 51.94 1.188 54
Weaiter! mgs fee yeh aah Lay ea» OD BBO ae

100.00

These results do not conduct to any very probable formula.
But if we suppose that what is set down as sesquioxide is
really present as peroxide, a supposition which accords
sufficiently well with the analysis, then the composition of
this ore becomes yery simple, being represented by the
formula Fr, O;, HO+3 Mn Oy, that is by one identical with
that which we have found for the psilomelane, when we
substitute sesquioxide of iron for the sesquioxide of man-
ganese. I have no doubt that this represents its real
constitution, so that it may be safely set down as a new
and very distinct species. I may observe that this mineral .
answers well for yielding oxygen, but is uneconomical as a
source of chlorine, in consequence of the wasteful consump-
tion of acid, in order to the saturation of the peroxide of
iron; one-half in fact of the acid is uselessly expended.

Mr. William Andrews, Secretary to the Dublin Natural
History Society, read a paper upon the genera of Ferns

603

Trichomanes and Hymenophyllum. His remarks were
chiefly directed to the species of Trichomanes discovered by
him in September, 1842, in the western part of the County
of Kerry, and which presented a variety of growth and state
of fructification so much more developed and characteristic
of the genus of that beautiful fern than had hitherto been
met with in Ireland, that determined him to examine its
affinities with some of the exotic ferns, particularly with
those of the West India Islands.

The ‘Trichomanes was first discovered in Britain, by Dr.
Richardson, at Belbank, near Bingley, Yorkshire, a wretched
specimen of which is in the Banksian Herbarium, now in the
British Museum : a figure of a barren frond is given in Dill.
in Raii Syn. S. p. 127, t. 3. This specimen, however, not
having been found in fructification, was supposed to be
identical with the Filix (Trichomanes) pyxidifera of Plu-
mier, and was described as such by Hudson, in his Flora
Anglica, p. 461: and this name it retained until its disco-
very, in the month of October, 1804, at Turk Waterfall, near
Killarney, by Mr. Mackay, Curator of the Botanic Garden
of Trinity College. Mr. Mackay obtaining this beautiful
fern in fructification, forwarded specimens to Sir James
Edward Smith, who at once decided its distinctness from
Plumier’s plant, and considered it to be a new species, which
he named and figured in English botany as Hymenophyllum
alatum, from its winged stipe. The distinguished Robert
Brown, the first physiological botanist of the day, corrected
this specific appellation to that of brevisetum (Br. in Hort.
Kew. ed. 2, 5, p. 529), from the short and barely exserted
state of the receptacles that the Killarney plants generally
presented. Mr. E. Newman, who has devoted so much at-
tention to the specific characteristics of the British ferns,
formed the first view, that the Killarney species perfectly
agreed with Willdenow’s description (Sp. Plant. 5, p. 514)
of the Speciosum of Teneriffe, and published it as such, in

604

his first edition of the History of British Ferns. The speci-
fic name brevisetum, however, was still retained through
the several editions of the British Flora, until the discovery
by Mr. Andrews, in September, 1842, in a wild and wooded
glen in the western part of the County of Kerry. The
striking characters and fine state of fructification exhibited
by these splendid plants, the most rare and most beautiful
of British ferns, and now altogether confined to the south-
western parts of Ireland, led Mr. Andrews to examine mi-
nutely, and to trace their affinities with the numerous exotic
species of that beautiful genus; and from communications
with Sir William J. Hooker, and to the great kindness of
that most excellent botanist and encourager of science, and
the reference to his very extensive fern herbarium, it was
traced and detected to be the true Trichomanes radicans of
Swartz, setting aside the species brevisetum of the English
flora, and the Speciosum of Willdenow. Thus the mild
temperature of the south-western parts of this country pro-
duced, in the utmost luxuriance of tropical growth, a plant pe-
culiar to the West India Islands, and to the western coast of
South America. Tor. Scouler’s kindness Mr. Andrews was
also much indebted for specimens of Trichomanes radicans,
and T. Scandens, collected by Dr. 8. in Brazil, and which
enabled many doubts to be cleared.

Mr. Andrews noticed a very remarkable character of
fructification in the new variety from Kerry, ‘that the eap-
sules formed around the base of the receptacles within the
cylindrical involucres, and as the receptacles elongated and
became exserted considerably beyond the involucres, the
capsules continued forming in an even dense mass to the ex-
tremity of the receptacles.” This is described as of rare
occurrence in Trichomanes. ‘The Trichomanes reniforme
of New Zealand, and the Hymenophyllum fuciforme of
Chiloe, are noticed as having the capsules external to the
involucres, but their being exposed to view was supposed

605

merely to result from the spreading and shrinking of the
valves. Loxsoma appears to be the only recorded genus as
possessing that peculiarity of fructification.

The specific descriptions of Trichomanes radicans and
its synonyma, are fully given in part 2, p. 125, of that invalu-
able work, Species Filicum, by Sir J. W. Hooker, recently
published.

Professor Allman made some observations on Mr. An-
drews’s paper, in corroboration of its principles.

DONATIONS.

Proceedings of the Geological Society of London. Vol.
IV., Part 1. (1843). Presented by the Society.

Bulletin der Konigl. Akademie der Wissenschaften zu
Munchen. Nos. | to 55. .

Abhandlungen der Philosophisch. Philologischen Classe
der Koéniglich Bayerischen Akademie der Wissenschaften
zu Munchen. Dritten Bandes dritte Abtheilung, in der Reihe
der Denkschriften der XVIII. Band.

Abhandlungen der Mathematisch. Physikalischen Classe
der Kéniglich Bayerischen Akademie der Wissenschaften
zu Munchen. Dritter Band. Die Abhandlungen von den
Yahren, 1837, bis 43, enthaltend. Presented by the Aca-
demy of Munich.

Versuch einer objectiven Begrtindung der Lehre von der
Zusammenseizung der Krafte. Won Dr. Bernard Bolzano.
Presented by the Author.

Prodromus zu einer neuen, verbesserten Darstellungsweise
der héhern analytischen Dynamik. Vom Grafen G. Von
Buquoy, Ph. D., &c. Presented by the Author.

4h

iene

aes Py

eds ie Vg aT ee pete t
ae es pe

a ee ee

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1844. No. 47.

June 24.
SIR Ws. R. HAMILTON, LL. D., President, in the Chair.

ResotveD, on the recommendation of Council—That the
Academy do pay Mr. E. Curry £41 13s., for completing the
Catalogue of the Irish MSS. of the Academy, this sum in-
cluding the money due to him at present.

Sir William Betham gave notice that, at the next meeting
of the Academy, he would move for—

Ist. A list of all papers or essays read before the Aca-
demy, in the departments of Belles Lettres and Antiquities,
which were referred to Council for publication, from the 17th
of March, 1828, to the 17th of March, 1844, containing the
dates of such reading, the names of the authors, whether
ordered by the Council for publication, and, if published in
the Transactions, with the dates of the Council’s order
for publication.

2nd. An account of all sums of money expended for en-
graving copper-plates or wood-cuts, or making lithographs,
to illustrate such essays or papers, which, ordered by Coun-
cil to be published, have or have not yet appeared in the
Transactions of the Academy.

8rd. An account of all sums of money expended on ac-
count of paper and printing of any such essay or essays, or

VOL. Il. 3 E

608

papers, which have been commenced, and are now in pro-
gress of printing; with the amount of liability of the Aca-
demy for what has not yet been paid.

4th. A statement of the terms of any agreement or con-
tract entered into by the Council, with the author or authors
of any such paper or essay, and the sum or sums of money
advanced on that account.

5th. An account of all medals and rewards adjudged by
the Council, and paid to any author for papers and essays,
during the said period, from the 17th of March, 1828, to
the 17th of March, 1844, with the dates of such payments
and delivery.

6th. An account of the debts and liabilities of the Aca-
demy at this time, and also of their available assets.

It was moved by Dr. Apjohn,—That the Secretary of
Council be requested to provide the Academy, at the next
meeting, with the information required in Sir William
Betham’s notice.

The motion, after discussion, was withdrawn.

The Rev. H. Lloyd laid upon the table of the Academy a
magnetical instrument, which had been recently constructed
under his direction by Mr. Jones of London, and which he
proposed to denominate the ‘‘ Theodolite Magnetometer.”

Much attention had of late been given to the construc-
tion of small magnetical instruments, for the use of travel-
ling observers, and many improvements in their form had
been effected by Prof. Weber, Mr. Fox, and Lieut. Riddell.
Prof. Lamont had also recently adopted magnets of a very
small size in all the instruments employed by him in his
magnetical observatory, and had stated his conviction of
their superiority over the larger magnets hitherto in use.
Without entering at present into the grounds of this convic-
tion, in the unlimited form in which it had been asserted

609

by Prof. Lamont, Mr. Lloyd said that, as respects certain
instruments intended for observations of a particular kind,
there seemed now to be a pretty general agreement on the
subject. He had himself proposed an instrument for the de-
termination of the changes of the Magnetic Inclination, in
which the magnet was necessarily a small one; and the ad-
vantages of small magnets, in the delicate observation of
the absolute Horizontal Intensity, seemed now to be fully
recognized.

While engaged in considering the best form of an instru-
ment intended for observations of the latter class, Mr. Lloyd
was led to perceive, that the same apparatus might be made
to serve also in the determination of the Absolute Declina-
tion ;* and, by a few slight additions in the details of its
construction, in that of the varzations of the three magnetic
elements. It may likewise be employed for all the usual pur-
poses of a Theodolite ; and thus, with the addition of an or-
dinary Inclinometer, a Chronometer, and a Sextant, consti-
tute a complete magnetical equipment for the use of the tra-
velling observer.

The following is a brief description of the instrument.

A divided circle, similar to that of a Theodolite, is sup-
ported on a tripod base, with levelling screws. This circle is
nine inchest in diameter; it is divided to 10’, and subdivided
by two verniers to 10”. The upper plate of the circle has twot
projecting arms, each carrying a pair of adjustable Y sup-
ports for the reading telescope, at a distance of six inches from
the centre. ‘The telescope rests in these supports on a tran-

* It may be proper to observe that this arrangement had occurred to the writer
before he had seen. Prof. Lamont’s account of his magnetical Theodolite, an instru-
ment in which the same end is obtained, although by different means.

+ A circle six inches in diameter, and read to 20”, is sufficient for all the pur-
poses of a travelling observer.

+ One is sufficient, and the instrument will be so modified in all future construce-

tions on the same plan.

610

sit axis, which is rendered horizontal by the help of a riding
level. The aperture of the object glass is eight-tenths of an
inch; a glass scale, divided to the z35th of an inch, is fixed
in its focus; and the eye tube is made to move across the
scale in a dovetail slide.

The magnets are hollow cylinders, each furnished as a
collimator with an achromatic lens, and a fine line cut on
glass in its focus. There are four such magnets: two of
them being 32 inches long, and half an inch in exterior dia-
meter, and two 3 inches long, and three-eighths of an inch
in exterior diameter. The larger magnets are furnished
with a Y stirrup, in which they may be inverted; the smaller
magnets have the ordinary tubular stirrup, with a suspension
pin and screw socket. A hollow brass cylinder, of the same
dimensions as the larger magnets, and carrying a small hol-
low cylindrical magnet within, serves to determine the
amount of torsion of the suspension thread; it is likewise
fitted up as a collimator. .

There are two boxes, within which the magnets are to be
suspended... That belonging to the smaller magnets is a
rectangular box of copper, closed by mahogany sliding sides,
and having a circular aperture at each end filled with paral-
lel glass. It is 3} inches long, 14 inches wide, and 1 inch
deep, internally; and the thickness of the metal is a quarter
of an inch, so that it may act powerfully as a damper. A
suspension tube of glass, eight inches long, is screwed into
an aperture in the top of the box; and is furnished with a
graduated torsion cap at top, and a sliding suspension pin.
This box is made to fit on the centre of the upper plate
of the circle, and is capable of removal at pleasure. The
box employed with the larger magnets is of wood, and of
the same form as the copper box, but somewhat larger. It
is detached from the instrument, but may rest on the same
stand, A small wooden piece with a mirror serves to illumi-
nate the magnet collimator, either from above or from the

611

side, according as the light of day, or that of a lamp or
candle, is employed.

The measuring rod employed in deflection experiments
is a compound bar of gun metal, formed of two bars, the
lower of which has its surface horizontal, and the upper ver-
tical. Itis three feet in length,* and is graduated on its ver-
tical surface. It is placed upon the upper plate of the circle,
beneath the box, and at right angles to its longer sides; and
it is so fixed that it may be removed with ease, and replaced
exactly in the same position. The support of the deflecting
magnet slides upon the upper bar, and is furnished with a
vernier, by means of which the distance of the two magnets
may be determined with accuracy and ease.

The apparatus is furnished with two soft-iron hollow
cylinders, nine inches long, and three-fourths of an inch in
diameter, which fit in vertical sockets attached to the upper
plate of the circle. By this addition the instrument is con-
verted into an Induction Inclinometer, for the measurement
of the changes of the Inclination. By a slight addition to the
suspension apparatus, the instrument may likewise be used
as a Bifilar Magnetometer, for the measurement of the changes
of the Horizontal Force. These adaptations are, however, of
minor importance to the travelling observer, whose main con-
cern is with the absolute determinations ; and in a fixed ob-
servatory it is essential that there should be separate instru-
ments for the separate purposes.

The most convenient order of the observations to be made
with this apparatus, when oes by the travelling ob-
server, is the following.

1. Measurement of Absolute Declination.

The copper box and measuring rod being removed, one

* For the purposes of the travelling observer, it will be more convenient that
this rod should be in two pieces. Two single bars, placed edgewise, will suffice. ~

612

of the larger magnets is to be suspended within the wooden
box, which should be placed on the same stand with the di-
vided circle, at a distance not less than one foot from its
centre. The optical axis of the telescope, and that of the
magnet-collimator, are then to be brought nearly into the
same right line, by an azimuth movement of the top of the
stand, and by a small parallel movement of the box. The
torsion of the suspension thread is then to be determined by
the help of the brass cylinder, and to be removed by means
of the torsion cap. The magnet being then replaced, the
coinciding division of the scale is noted, with the magnet di-
rect and inverted, and the mean of the two readings is the
division corresponding to the magnetic axis. The verniers
of the circle being then read, the telescope is to be turned
until the division so found coincides with a fixed mark, whose
azimuth is to be determined at leisure. The latter deter-
mination is made by the help of the same Theodolite, used
in combination with the Chronometer or Sextant,

2. Observation of Vibration.

The upper plate of the circle is to be moved to its original
position, and clamped there.

The coefficient of torsion of the suspension thread being
determined, by the help of the torsion cap and glass scale,
the magnet is to be set in vibration, and the time of 200 vi-
brations determined in the ordinary manner. The arc of
vibration should be noted, by the help of the glass scale, at
the commencement and end of the observation, and the tem-
perature recorded at the same times.

3. Observation of Deflection.

The wooden box being removed, the metal box and the
measuring rod are to be attached to the upper plate of the
instrument. One of the smaller magnets is then to be sus-
pended; and the larger magnet being transferred to its sup-
port upon the measuring rod, at a fixed distance, the upper
plate and telescope are to be turned until the collimator line

613

of the suspended magnet is seen to coincide with the central
division of the scale of the telescope. The verniers of the
circle being then read, the deflecting magnet is reversed, and
the telescope is moved until there is a new coincidence. The
verniers being again read, the difference of the two readings
. is double the angle of deflection sought. It is necessary to
eliminate the changes of the Magnetic Declination, which may
occur between these two readings; and for this purpose the
wooden box and one of the spare magnets may be employed
by asecond observer. But the same elimination may be
made as effectually by asingle observer, by taking a series of
readings with the deflecting magnet alternately in the two
positions. Finally, the observation is to be repeated with
the deflecting magnet at the same distance on the other side
of the suspended magnet, and the mean of the two results
taken as the deflection corresponding to that distance.

The quantity sought may be inferred from the angle of
deflection at a single distance, with as much accuracy as is
generally attainable in observations made in the open air, or
in a tent; and, in such cases, it will generally be found more
advantageous to multiply the observations at the same dis-
tance, in the manner already mentioned, than to repeat them
‘at two or more distances. The distance should be about
five times the length of the magnets.

The preceding arrangement is suggested chiefly in regard
to the economy of time. But, when the observer has suffi-
cient leisure, it is desirable that the time of observation of
the two elements should be as near as possible to the epochs
of their principal maxima or minima, the periodical variation
being then least. For this purpose the observations should
be so arranged, that the middle of the observation of Inten-
sity may fall between 10 and 103 a.m.; and that of the ob-
servation of Declination between 1 and 13 p.m. In this case,
then, the preceding arrangement should be nearly reversed.
The observer should commence with the observation of de-

614

flection ; proceed at once to the observation of vibration,
determining the coefficient of torsion at the end ; and, lastly,
make the preliminary arrangements (of detorsion, &c.), for
the determination of the Declination, deferring the observa-
tion itself untill p.m. If there be a second observer, he
should undertake the observation of Inclination, and such
sextant observations as may be required for the determination
of the Latitude, the Time, or the true Meridian. ‘The obser-
vation of Inclination should be simultaneous with that of the
Horizontal Intensity ; the astronomical observations may be
made whenever most convenient.

The Theodolite Magnetometer may likewise be employed
with advantage in a fixed observatory, especially in observa-
tions of the absolute Intensity; and it is worthy of remark,
that if the differential instruments used in connexion with
it be small ones, the circle of this instrument may be em-
ployed in their adjustments, and their construction thus re-
duced to the simplest possible form.

Mr. Wm. R. Wilde read a notice of the opening of some
Tumuli, by Mr. Nugent, and the Rev. Dr. Todd (V. P.)
on the part of Mr. Nugent, presented a stone of a peculiar
form, found in one of the Tumuli described. :

The thanks of the Academy were given to Mr. Nugent,
for his communication and donation.

Mr. R. Mallet presented the results of his analysis of a
porcelain clay, discovered some years ago by him, at Howth,
and since extensively brought into use for the manufacture
of crucibles.

The clay is found upon the southern side of the penin-
sula of Howth, which consists principally of quartz rock ;
it exists in large concretionary masses, or highly irregular
beds, and appears to have reached its present position by

615

the transport of water. It is found of every degree of fine-
ness, from a coarse gritty mass of decomposing pebbles, with
occasional large nodules of friable felspar, to that of an im-
palpable colourless clay, like that of Dorsetshire, known as
pipe-clay. This is soft, sectile, adheres to the tongue, and
forms a strongly adhesive and plastic mass with water, capa-
ble of being moulded upon the potter’s wheel into the finest
forms.

It bakes perfectly white, or occasionally of the slightest
possible rosy tint of white.

Some of the masses of this mineral are strongly disco-
loured by iron and manganese, and imbedded in the finest
parts are occasionally found a few fragments of marine
shells, and bits of wood.

By washing with abundance of water, a fine quartzose
sand is separable from even the finest portions of this clay.
This sand is white, but water separates from it a little sand
of a darker colour, like common sea sand of the Dublin
coast, and a few microscopic flakes of mica.

A singular minute black worm is found in this clay,
which may be worth the attention of naturalists.

The clay, as dug out, does not efferversce with acid, and
is insoluble in them; it yields no soluble matter to water,
and appears to contain no alkali in any specimens yet ex-
amined.

Mr. Mallet, however, has reason to think that the less
fully decomposed portions of the clay may contain alkali in
a soluble condition, and hence render the material valuable
as a manure.

Some of the finest portion of the clay, washed from the
sand, and dried at a temperature of 212° Fah., was found by
Mr. Mallet to have the following composition. The analysis
having been conducted in the usual way, and with the usual
precautions, it does not seem necessary to detail its steps :

VOL. II. 3F

616

DUNCAN e is ee ok ee ne eT oO

Alumina, . Pe Va Ne yea)
HIME, rey eee es ye ee Oe
Macuesia,: ." aac. ar ee O05
Oxide of Iron," “sae eee flo
Wratten oc ot Seman be: MTD ()

99.01

As no washing completely removes the presence of sand from
this clay, which always feels gritty to a glass rod, and as it
contains comminuted mica, it could not be expected that its
analysis should present a precisely mineralogical result.

From the close analogy, however, which the above figures
present to the composition of various felspathic rocks, as
analysed by Beudant, Berthier, &c., there can be little doubt
but that the geothetic origin of this clay is the decomposition
of felspar, or other allied granitic minerals. In fact the re-
sults approximate to the formula (taking the iron and mag-
nesia together).

(Al, + Sis + Ca + Mg + FeO) + HO,

or,
3 (Al + Sis) + (Ca + Sis) + (Mg + FeO)+Si,;) + HO.
This clay is of very great economic value, and capable of
being used for the manufacture of the finer descriptions of
pottery or even of porcelain ; it has, however, hitherto only
been brought into use fer the manufacture of crucibles, by

Mr. Mallet.

The President read a paper on an improvement in the
double achromatic object glass.

DONATIONS.

Life of W.V. Morrison, Esq., M.R.I.A. By John
Morrison, Esq. Presented by the Author.

617

Bericht tiber die zur Bekanntmachung geeigneten Ver-
handlungen der Konigl. Preuss. Akadémie der Wissenschaf-
ten zu Berlin, 1842-1843.

Abhandlungen der Kéniglchen Akademie der Wissen-
schaften zu Berlin (1841). Presented by the Academy.

Abhandlungen der Koniglichen Gesellschaft der Wissen-
schafien zu Gottingen. Erster Band. Von den Jahren 1838-
1841. Presented by the Society.

Almanach der Kéniglichen Bayerischen Akademie der
Wissenschaften zu Miinchen (1843). Presented by the Aca-
demy.

Leitfaden zur Nordischen Alterthumskunde herausgege-
ben von der Kéniglichen Gesellschaft fiir Nordische Alter-
thumskunde (1837).

Die Kénigliche Gesellschaft fiir Nordische Alterthums-
kunde zu Kopenhagen (Jan. 27, 1842).

Memoires de la Société Royale des Antiquaires du Nord
1840-1843. - Presented by the Society.

Fasciculus Inscriptionum Grecarum. Edidit Jacobus
Kennedy Bailie, S.T.P. Presented by the Author.

' Proceedings of the Chemical Society of London. Part 6.
Presented by the Society.

Journal of the Statistical Society of London. Presented
by the Society.

Literarische Sympathien oder industrielle Buchmacherei.
By Dr. J. G. Fligel. Presented by the Author.

Bjorgynjar Hatfskinn. Presented by Dr. Robt. Graves,
M.R.I.A.

The Numismatic Chronicle for April, 1844. Presented
by the Numismatic Society.

Journal of the Franklin Institute. 5th Volume, 3rd Series.
Presented by the Institute.

An Olla Podrida, or Scraps Numismatic, Antiquarian,

618

and Literary. By Richard Sainthill. Presented by the
Author.

Journal of the Geological Society of Dublin. Vol. III. Part
1, No. 2. Presented by the Society.

Sixteen Specimens of Chinese Cash. Presented by Robert
Mallet, Esq.

Archives du Museum d’Histoire Naturelle. 'Tome III.
Livraison 4. Presented by the Directors.

Memorie deli I. R. Istituto Lombardo di Scienze lettere
ed Arti. Vol. I. Presented by the Institute.

Edinburgh Astronomical Observations. Vol. V., 1839.
Presented by the Royal Astronomical Society.

Greenwich Magnetical and Meteorological Observations,
1840-1841. Presented by the Royal Astronomical Society.

EL’ Art de connaitre les Pendules et les Montres. Par J.
B. A. Henri Robert. Presented by T. Hutton, Esq.

Puits Artesien de 0 Abattoir Grenelle. Presented by T.
Hutton, Esq.

On the Industrial Resources of Ireland. By Robert
Kane, M.D. Presented by the Author.

APPENDIX.
No. I.

LIST OF SUBSCRIBERS

VERY REV.

To

THE FUND

FOR THE PURCHASE OF THE

COLLECTION OF IRISH ANTIQUITIES, COINS, AND
MEDALS

OF THE LATE

HENRY R. DAWSON,

DEAN OF ST. PATRICK'S, DUBLIN.

a

The Names marked thus [*] are Members of the Royal Irish Academy.

* Adare, Edwin Visct., M. P.,

£ s.

d.

Waterloo Crescent, Deas 10 0 0

Armagh, Archbp. of, Rt. Hon.
and Most Rev. Lord J. G.
De la Poer Beresford,
Alley, George, Esq.,_ -
Adair, Thos. Benjamin, Esq, 2
* Anster, John, Esq., LL. D.,
* Apjohn, James, Esq., M.D.,

* Brady, Rt. Hon. Maziere,
(Chief Baron of the Ex-
chequer), .

* Brisbane, Sir Thomas M. Ay

* Beaufort, Captain R. N.,

* Barrington, Matthew, Esq:,

* Bolton, Chichester, Esq., .

* Borrowes, Robert, Esq.,

* Botfield, Beriah, Esq., M.P.,

* Bailie, Rev. Jas. Kennedy,
D. D.,

* Blood, Bindon, Bq. Balin
burgh, .

Brooke, William, Esq. eae
Bernard, Lord,
Barton, John, Esq.; : 2

* Bergin, Thomas F'., Esq., -

5 0
1 1
ia)
1 0
Len O
5.0
5 (0
5 0
5 0
ye W)
5 0
5 (0
3
3.0
3.40
2 0
2 0
1 10
68 14

oooco

Brought forward
Bennett, Robert, Esq. roa?
(Recorder), :
Butt, Isaac, Esq., LL. D.,

* Ball, Robert, Esq., .

* Banks; John T., M. D.,
Barrington, Edward, Esq.,
Barrington, Richard, Esq.,
Barlow, Wm. Thos., Esq., .

| * Bateson, Robert, Esq., .
| * Beatty, Thomas E., hie

M.D., .
. Beauchamp, H. C., ” Bsq., as
M.D.,
Bellingham, O’ econ Esq., a
* Benson, Chas., Esq., M.D.,
Bewley, Henry, Esq., -
Blacker, William, Esq.,_ .
Blair, James K., Esq., Tem-
ple, London,
Bland, F., Esq., - -
Boileau; G. W.., Esq.,
Boileau, S., Esq.,
* Bolton, W. E., Esq.,_ -
Bottomley, William, Esq.,
* Bowles, John A., Esq.,
Boyle, James, Esq.,

££ S., a:
68 14 0
DesleonO,
1 oalinei | PH)
Omer OC
Lt 0:0
10 0
1 0 0
1 0 0
10 90
1 70F 0
t 0 0
1 0 0
100
1 0 0
1 0y 0
10 0
1 0 0
1 0 O
1 0 0
10 0
10 0
10 0
100
90 16 0

Brought forward,
Brocas, Henry, Esq.,
Brocas, William, Esq., .
* Burrowes, John, Esq., .
* Burton, F. W., Esq., . .
* Butcher, Rev. S., F.T.C.D.,
* Butler, Rey. Richard, Trim,
Butler, Colonel, .
Butler, Rev. Wm. Ascher,
* Bruce, Haliday, Esq.,
Blacker, Stewart, Esq.,

* Cooper, E. J., Esq., M. P.,

* Callwell, Robert, Esq., .

* Courtenay, H., Esq.,

* Caulfield, Hon. Henry,
Cane, Richard, Esq.,

* Cane, Edward, Esq.,

* Carr, George, Esq.,- .
Clibborn, Edward, Ea bs
Close, Colonel, 3

* Conway, F. W., Bene :

* Cooper, J. Sisson, Esq.,

* Cusack, James, Esq., M.D.,
Clogher, Bishop of, Thé

Hon. and Rt. Rev. Lord
Robert Ponsonby Tot-
tenham,D.D., .. .
Curran, W. H., Esq.,
Caledon, Countess of,
Chapman, Benjamin James,
Esq., M.P.,_ .
* Chetwode, Edward Wilmot,
Esq.,. -
* Clendinning, Alex., Beg’ bai
* Croker, Charles P., ee 2
M. D.,
Galena dae Esq., FA
* Cane, Arthur, Esq... -
* Carmichael, Richard, Esq.,
M.D., ...

* Carmichael, Andrew, Esq.

* Carter, S., Esq., .

* Cash, Georse, Esq., .
Cather, Thomas, Esq., .

* Churchill, Dr., Gt

* Clarke, Thomas, Esq., .
Close, J. S., Esq., -

* Cole, tei Blayney, Esq., bs

* Colomb, Lieut.-Colonel,

* Combe, George, Esq., . .
Conyngham, Wm. ee

Esq, . aie te
Cooke, J. R., Eq, spi)

* Corballis, Jobe R., Esq.,
Corballis, James, Esq, ee

* Coulter, Thos., Esq., M. D.,

cooocoocoococoeoo

ocooco

!

£ os. d.
90 16 0
1050
1 0 0
10 0
1 0 0
1 0 0
10 0
10 0
1 0 0
10 0
10 0
20 0
10 0
10 0
5 60
pe (Y)
5 0
5 (0
5 (0
5 (0
5 60
5 0
5 0
3.0 0
3 0 0
2 0 0
20 0
20 0
20 0
2 0 0
1 0 0
1 0 0
1 0 0
Teor. 0
100
10 0
PESO (0
1 0 0
10 0
1 0 0
100
1 0 0
Po Or 0
1 0
1 0
1 0
1 0
1 0
219 16 0

Brought forward, 2
Cramer, Maurice, Esq.,_ .
Corrigan, D. J., Esq., M. D.,
Crosthwaite, Leland, Esq.,
Curry, William, Esq., .
Clinche, H. O. B., Esq.,
Curry, Eugene, Esq.,

De Grey, Thomas Philip
Earl (Lord Lieutenant),
and Donation of a large
Gold Collar, . . °

Dunraven, Wyndham Henry
Wyndham, Earl of, 4

Downshire, Arthur Blundell
Sandy Trumbull, we
Of nae:

Dick, Guintor Esq. 55 M. P.,
London,. .

* Darley, Frederick, Esq., x

| * Doyne, Charles, Esq., .

Digby, Thomas G., Esq., .

Daly, James, Esq., Bua

* Davidson, John, Jun., Esa: 5
Armagh, .

* Davy, Edmund, Esq. Ls
Deane, Sir Thomas,

* Dixon, Rev. R. V., .
Dobbs, Joseph, Esq.,
Doherty, John, Esq.,
Donegan, John, Esq.,

* Downes, George, Esq.,_ .

* Drummond, Rev. Dr., .
Duke, Jemmet, Esq.,

* Dunlop, Durham, Esq.,

* Elrington, Rev. Dr., . .
Enniskillen, William Wil-
loughby, Earl of,
Eliot, Lord, . . -
* Edington, William, Esq. Peale
Eustace, John, Esq., M. D.,
Edgeworth, M. P., Esq.,

Fitzwilliam, Chas. William
Earl,. .
Fortescue, Hugh, Earl of, .
* Foster, Hon. Justice,
Ferrier, James, Esq., . -
* Fitzgibbon, Gerald, Esq., .
Fortescue, Esq.,
* Ferrier, Alex. Jun., Esq., .
* Ferguson, Hugh, Esq.,M.D.,
* Ferguson, Samuel, Esq.,
Ferrier, Alexander, Esq., -
* Finlay, John, Esq., LL. D.,
Finn, Rev. Charles, P. P. .

—

Pl i)

come neh

to tv
oo. &

_
o

ee ee ee

_
o

Sorann

Sr ibe

16 0
0 0

0 0

0 0

0 0

10 0
10 O
0 0

0 0

0

0 0

0 0

0 0

10 0
0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

10 0
0 0

0 0

0 0

0 0

0 0

0 0

10 0
0 0

0 0

0 0

0 0

0 0

6 0

Brought forward, 389

Fitzgerald, John, Esq.,
Fitzpatrick, P. V., Esq.,
* Foot, Simon, Esq., . -
Foot, Lundy E., Esq., -
Forster, Robert, Esq., -
Fox, Rev. J. W. .

* Goff, Rev. Thomas, -
Goold, Thomas, Esq., .«

* Graves, Rev. C., F. T.C. D.,
Guinness, Arthur, Esq.,
Gordon, Robert, Esq., . .
Gordon, R., Esq., Chelten-

ham, .
Gosford, relma Earl of,

* Graves, Robert J., Eat

MoD eGo +

* Gueron; G. A., Esq., Ee

* Grubb, Thomas, Esq.) -
Guinness, Ben. Lee, Esq.,
Guinness, A. Lee, Esq.,

* Graham, Professor, (Edin-

burgh, :

* Grimshaw, Wrigley, Bsa,

Maps o
Gill, M. ee Esq; -
Goold, Fiantis, Esq.,
Gardant R. H., Esq.,

* Griffith, Richard, Esq.,
Guinness, W.N., Esq., «
Gilmore, J. B. Esq., Q.C.,
Garrett, Henry, Esq.,

Herbert, Hon. Sydney, .
* Hume, A. Esq.,
* Hutton, Thomas, Esq. .
* Hill, Lord George, A., 5
* Hudson, Henry, Esq., M. D.

* Hudson, William Elliott,

Esq., -
* Hanlon, Sir Ww. R., LL.D
P.R.1A., é
Hutchins, Samuel, Esq.; é
Hall, Lieut.Colonel H., Lon-
don, - S
Homan, Sir Ww. afte Bart.
* Hart, A. Searl, LL. D.,
F. T.C.D.,
Haughton, James, Esq., Avie
Haughton, William, Esq., .
Hone, Joseph, Esq., A
* Hope, Thomas C. Esq.,
M. D., Edinburgh,
* Horner, Rev. James,
Herrick, J. E., Esq.,
Hutton, Mrs. Thomas, .

ie st
6

Te 0
t.0
Lege)
Thy
0
Le 0
>..6(0
OL.
Hon)
3. (0
jE:
7 ee
20
2 70
Zz 0
2 0
a 0
2-0
ihe |
j ee
tO
1 0
1 0
1 0
1 0
i eat)
0 10
20 O
10 0
10 0
sym)
5 0
a, 0
38. (0
2 0
Die)
20
2-0
2 0
2 0
Fee (i)
Piet
DO
i bean) &
ikea
Sua!

ill

d. £

0 Brought forward, 517

0| Hackett, Michael, Esq.,

0 Haffield, Arthur, Esq., -

0; Hall, S. C., Esq., .

0) Hall, Mrs. ‘s. C., Be

0| * Hamilton ee Reg. etme

0 * Hamilton, Chas. W., Esq.,
| Hamilton, Dacre, Eeq:s 6

0 | * Hanna, Samuel, Esq., M.D.,

0| Hanna, William, Esq., .

0 | * Hardiman, James, Esq.,_ .

0 | * Harrison, R., Esq., M. D.,.

0 Hewson, John, Esq.,

* Hill, William, Esq...

0|* Hinks, Rev. Thomas, LL. D.

0 | * Houston, John, Esq., M. D.,
Hunt, Percival, Esq., M. D.,

Cl ce el el el el ae oe el

mooococooccocoocsocoocoooeoococoecorRS
coooocoseooooeoocoececeocooon

0 | * Hutton, E., Esq., M. D.,
0 Hutton, Henry, Esq., .-
0| Hutton, Rev. Joseph,
0| Hyndman, George C., Esq.,
0 | * Hemans, G. W., Esq., . 1
Healy, F. W., Esq., .
0 |
Irwin, Rev. Alexander, 3.0 0
0
0 | * Jones, Robert, Esq., ore ame
0 | * Jones, Colonel Harry D., PA Do
0 | * Johnson, Hon. Justice, 1 0 0
0 | * James, Sir J. K., Bart, . 1 0 0
0 | * Jellett, John H.,F.T.C.D., 1 0 0
0 Johns, Alexander, Esq., 0200
0 Johnson, Edmund, Esq., 10 0
Johnston, Rev. Richard, eon O
0| Jacob, John, Esq., M.D., 0 5 0
0
0 Kildare, Marquis of, . .10 0 0
0 | * King, Hon. James, . eros On: O
0 Kemmis, Henry, Esq., . One O
* Knox, G. James, Esq., . 5 0 0
0 | * Kent, William T., Esq., 3.0 «+0
| Kinsella, Rt. Rev. Dr., Dra vawi()
0 | * Kennedy, George A., Esq.,
0 RD) Sieirs Mate sce ie, Sonat NO
* Kerry, Knight of, (Right
0 Honourable Maurice Fitz-
0 gerald), . . 2 0
* Kane, R. J., Beg, M. D., 20-20
0 | * Kyle, William C., Est,
0 LEDs 20E 30
0 Kane, William, ESy ; err 050
0 | * Kelly, T. F., Esq., | et)
* Kelly, D. H. Esq., nos 20
0 Kerr, Doctor, . 0/0
0
0 Leinster, Augustus Frede-
0 nick, Dukelof . . . . 20: “0. 0
0 614 11 0

£

S.

Brought forward, 614 11

* Leitrim, Rt. Hon. Natha-
niel Earl of, .
Lorton, Robert Rdnerd
Viscount, 4 C
* Larcom, Captain R. E., °
* Lloyd, Rev. Hamphrey,D.D D.,
EST-C3D., ye Ae
Lucas, Edward. Esq., 5
Lismore, Very Rev. Henry
Cotton, LL. D., Dean of
* Lyle, Acheson, Esq.,
Latham, Oliver, Esq.,
Lindsay, John, Esq., . .
* Lambert, Rev. Charles J.,
* La Touche, G. D., Esq.,
* Lee, Rev. Wm., F. T.C.D.,
Lees, Doctor,. .
* Lenegan, J., Esq., . .
* Litton, Samael Esq., M. D., Le
* Lloyd, William T., Esq., .
* Longfield, William, Esq., .

* Mac Cullagh, James, Esq.,
LL. D., F. T.C.D.,
Midleton, anes A., Vis-
count, .
* Marsh, Sir H., eal /M. D.,
bd Macartney, J. Esq., M. D.,
* Monsell, William, Esq.,
Moore, Edward, Esq.,. .
* Murchison, Rod‘. Impey,
Esq., F.R.S., V. P.G.S.
* Mollan, John, Esq., M. D.
Macdonnell, Alex., Esq.
* Magrath, Sir George, M.D.,
* Maguire, William, Esq.,
Molyneux, Sir G. Bart.,
M‘Carthy, Alexander, Esq.,
Maturin, Edmund, Esq.,
Macan, John, Esq... . .
Mac Clean, Samuel, Esq., .
M ‘Carthy, Justin, Esq.,
Mac Donnell, James, Esq.,
M. D., Belfast, :
* Mac Donnell, J., Esq., M. D.
* Mac Donnell, Rev. Dr.,
FDC Dig yu
M‘Glashan, ie Esq, mc
* M‘Neece, Rev. T., F.T.C.D.,
* Mallet, Robert, Esq: ce
Martin, John, Esq., -
* Mason, H. J. M., Esq.
LL. D. (and onal of
a gold Fibula),
Massy, Hugh, Esq.,_ .
* Mayne, Rev. Charles, .

764

‘

. 20

5
5

oo

Wah ee peek fet ek eet et et BD OD DO DO

bo
_

er et eet et DD DD DD bO Co aoa a ©

— et

a

1
1
1

0

0
0

oooocoooococono op

i—)

ocooono

eooorrocoocooococo

oo

ooocoo

0
0
0

0

1V

d.
0

0

0
0

oooocoococcoocoeo co

So

ooococo

oooocoocococo

ooooco

ooo

0

£
Brought forward, 764

Meiklam, John, Esq.,
* Montgomery, Wm. F., Pe MA
M.D.,
Mullen, Gearee Bee Cone
* Mulvany, W. T., Esq.,
* Murray, William, Esq.,
* Mackay J. T., Esq., . .

* Newport, Sir John, Bart.,

® Nelson, Joseph, Esq.,
Newman, Miss, .
Norreys, Sir Chas. Denham

Orlando Jephson, Bart.,

* Newenham, Thomas, Esq.,

* Napier, Jeseph, Esq., .
Nicholson, Mrs.,. . .
Nicholson, G. A., Esq.,

* Nicholson, J. A., Esq., .
Nolan, James Joseph, Esq.,
Nugent, Daniel, Esq., . .
Nugent, William, Esq.,

* O’Halloran, Major Gen. Sir
Joseph, K.C.B., . .
O’Connell, Daniel, Esq.,
WGI ee cage
O'Hara, C. K., Esq.) Re
* O’Grady, M. M., Esq., M.D.,
* O’Brien, Sir ace Bart.,
* O’Ferrall, J. M., Esq., M.D.
O’Brien, A. S., nae M.P.
O’Brien, W. S., Esq., M.P.
O’Callaghan, iene Esq-, -
* O’Conor, Matthew, Esq., .
O’Dwyer, Andrew C., Esq.,
* Orpen, T. H., Esq., M. D.,
* Orpen, C. H., Esq., M. D.,
® Owen, John U., Esq., M.D.
* Owen, Jacob, Esq., . .«
O’Donovan, John, Esq.,

* Pim, James, Jun., Esq.,
Perry, John, Esq.,

* Pim, George, Esq., - -

* Portlock, Captain R. E.,
Pakenham, Hon. and Rev.

Archdeacon,

* Petrie, Geo., Esq., R. H. x

* Phibbs, William, Esq., -
Purser, John, Esq., .

* Parker, A., Esq.
Patterson, Chas. , Esq., M. D,
Patterson, R. , Esq. 6
Pepper, Colonel,

Perry, James, Esq.,
Pim, W. H., Esq.,

849 17 0

On Ll elle cell lll oe ol SS) bo GO Or

Se et et et et tt DD CO CO

wwaoc

et et et et et KD ODD DD OD

anooce ese?

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i—)

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——— a — i — i — i — ee —

ooocooocoo

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coco

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|

£

s.

Brought forward, 849 17

Pollock, G. A., Esq, . . 1
Porter, Charles, LL. D., . 1
* Porter, Rev. Thomas, D.D., 1

* Rosse, William Earl of . 10
* Robinson, Rev. T. at

1 DE DI Tt 5
Rossmore, We Wm. iar «192
Reid, Alexander, Esq, . 2

3 Reid, Rev. James, . . . 1
* Radcliffe, Rt. Hon. John,

DMT Diss .nts, ydiere erat oth
Ray, T. M., Esq, .- . - 1
Richardson, Miss, . . 1
Roberts, Marmaduke C., Esq. api
Roberts, Wm. B.C., Esq., 1

* Roberts, W., Esq., E.T.C.D., 1
Roe, George, Esq., - ree |
Roe, Henry, Esq, .- . . 1
Rothwell, R., Esq.,- - 1

* Roberts, Rev. J.C. ,E-T.C.D., 1
Radley, John, Esq., Soa

* Stokes, Wm., Esq., M.D., . 25
St. George, Richard James
Mansergh, Esq.,( with do-
nation of Bronzes § Coins.)
* Singer, Rev. Dr., F.T.C.D.,
Smith, George, Esq.,_ .
* Strong, Rev. Charles, .
Sweetman, Walter, Esq., .
* Smith, Joseph H., Esq., .
* Sadleir, Rev. Dr., F.T.C.D.
(Provost), . . -
* Sedgwick, Professor, (Cam-
bridge), -. .
* Smith, Aquilla, Esq, oe M. D.
St. George, Charles Man-
sergh, Esq., <« +. «
Sherrard, D. H., Esq.,
* Smyth, Capt., R. N. (Car-
AUD eae Mee oes arate
Somers, John, Esq.,. .
* Sadleir, Rev. William D,
EAC DS eyes
Sainthill, Rd., Esq., Cork,
Scully, Joseph, Esq, - «
Sharpe, Charles, Esq.,. .
Shirley, E. P. Esq., M. P.,
Shortall, Lieut. Gen., .
Smith, oe ey cele,
* Smith, Rev.G.S., . .
+ Smith, R. W., Esq...
* Sterling, Cap. = C. * (75th),

Oo Or Oy Or Or on

bo bo o> oo i)

m bh

ee

963

0
0
0

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oo o woOoooccocneo > oooocoocococoococoeo

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cooooocoocoeoso

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0
0
0
0

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* -

£
Brought forward, 963

Stewart, Henry, Esq., . .
Stewart, Colonel, . c
Stokes, J., Esq., .

Stokes, Miss,. . . . .
Stubber, R. H. Esq, . .
Stopford, Captain, :

Templetown, John Henry
Lord, + 5. +1 PS% yedt, «7,
© Todd, Rev. Dr., F.T.C.D.,
Tomb, George, Esq.,
* Thompson, J., Esq., . .
© Thompson, David P., Esq.,
Thompson, J., Esq., LL.D.,
Glasgow,
* Thompson, Thomas, M. D.,
Glasgow, . . RYN
Thompson, Wm., Esq. <
Tickell, Edward, Esq.,
* Tighe, Robert, Esq., hie
® Toleken, J., Esq., F.T.C.D.
Turner, Dawson, Esq.,
Todd, W.G., Esq.,. .

* Vignoles, Rev. Doctor, . .-

* Wall, Rev. Dr.,
* Williams, Richard P., Esq.,
* Wilson, Thomas, Esq., .
* Whiteside, J., Esq., A.M.,
* Wilkinson, George, Esq., .
Wilson, L. P., Esq., Lond.,

© Westenra, Hon. H.R., M.P.,

* Walker, R. Chambers, Esy.,

* Webber, Chas. T., Esq.,
Wypbrants, Robert, Esq., .
Wood, Thomas, Esq., M.D.,
West, Henry, Esq.,. . .

* Wall, Rev. Rd. H., D.D.,

* Wallace, W. B., Jun., Esq.,

* Wallace, R. A., "Esq., eine

* Warburton, Elliot, Esq.,

* Webb, William, Esq.,
Whitla, Francis, Esq., .

* Wilde, William R., Esq., .

* Wilson, Rev. James, Be
Woodward, Rey. F. B.,
Wright, Edward, Esq.,
Wynne, John, Esq., .
Webb, P.R., Esq., . -
Wood, William C., Esq., .

ee

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1

S.F.T.C.D. 10

SOR RF RP RE REP RP RP eee eee Nhyhaun

* Young, John T.,Esq., . 1
Allen, Edward, Esq, . . 1
1051

a
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_

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o

_
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0
0

eooceco

ocooceceoceccececeocoooceooeooecoao —)

ADDITIONAL SUBSCRIPTIONS.

PreSescids EE isnt) de

Brought forward, 1051 8 0 Brought forward, 1060 13 0

Baker, A. W., Esq.. . . 3 5 0} Knox, E.C., Esq, . . . 010 O
Benn, Edward, Esq... - 1 0 0} M‘Master, Maxwell, Esq., 100
Graham, F. R., Esq., . 010 0O| Otway,C.G.,Esq, .. 1 0 0
Griffith, Henry, Esq... . 2 0 0O| Pope,J.W., Esq, - - . 0 5 O
Henn, Thomas R., Esq... 1 0 0} Ray, T.M.Esgq.,collectedby 2 0 0
Hughes, W. J., Esq., . 1 0 O| Reade, W.M., Esq, . . 2 0 O
Knox, R. J., Esq.,. 010 0O| Sharp, Richard Esq., . 0 5 0
£1060 13 0! Total collected, £1067 13 0

——____
——

No. II.

ACCOUNT

OF THE

ROYAL IRISH ACADEMY,

FROM Ist APRIL, 1841, TO 3lst MARCH, 1842.

THE CHARGE.
£9 Sh) Oa ee santas

Balance in favour of the Public. as per last
Audit, . .. it eines Bie aia ese ad dvs hile ceo lata ieee Lees
Parliamentary Grant for 1841, Baht og eOOOre OlanO.
Quarterly Warrants from Treasury, So rounrsealy 1A Gal fees
Total from Treasury, . ——__| 446 17 8
THREE PER CENT. CONSOLS SOLD.
1841. SE Sosa
June 8, 9, £55 18s. 8d. at 888i, 49 7 3
Interest, 154 days, 014 3
50 1 6
Brokerage;’..\ 2,,6),.05.,1 6
1841. see 50 0 O
July, 20, 21, £238 11s.6d.at893, 213 16 6
Interest, 16 days, 0 6 3
214 2 9
Brokerage... 0 6.0
1842. ee 213 be 9
Feb. 9, 10, £300 at 883, . 266 5
Interest, 36 days, 017 9
26 a2 9
Brokerage; 5/0. 3.0 7.26
ee OOo eS
Total proceeds Consols sold, . . . |__| 630 12 90
1036 11 0

Vill

She Oe
Brought forward, 1036 11 0
INTEREST ON STOCK:
Be Wise land
Half year’s,on 1553 10 11, 32 per cents.,
Ditto ,, 1581 4 1, 32 - F
Ditto ,, 1525 2 9, 3 a
Ditto _,, 1286 11 3, 3
Total Interest on Stock, 97 0 8
PUBLICATIONS AND BOOKS SOLD:
Boone, Messrs., balance of their account to
4th January, 1842, . .
Clibborn, E., for Scientific Memoirs, to
16th Sie SA ey eae
Ditto, fice 6th N OV. “1841,
Ditto, Transactions and Proceedings, 16th
June, 1841,. . .. :
Ditto, ditto, 28th Now 1841,
Ditto, Wolf’s Letter, ditto, .
Total Publications sold, 37 19 O
One year’s rent of stable, to Nov. 1, 1841, 21 0 O

Lire COMPOSITIONS:

Lhomas Walson;Wsq:, yeh ame iets ie oe ORR
TS TG/e S00] 0) SEIN SIS0 Eee Mame ream y ce PM eon (ay allege OY)
d find Waco) Ral Roloc lan Me a Me tS ATES bh org 21 0 O
5. Bottield isge a) chs 2.) Veve epee s)he 21 0 O
James Thompson; Esq.,. js. - jc oe he ee Ore
mA. Clendinning, Hsq.)-) ee. -. Reh Ree Oa
eyes. ao Kes i ia eee re TE ts 18 18 O
G. 8. Gough, Esq., . . 18 18 0O
J. T. Mackay, Esq. (having subscribed

twenty years),. . 6 6 0

Total Life Composition, - . i —_——— 170 2 0

ENTRANCE FEEs:

William Monsell, Esq., . 5 5 0
Fe Dishe isd: ice les 5 5 0
W. E. Hudson, Esq., 5 5 0
G. F. Fitzgibbon, Esq., 5 5) 0
William ee we oe 5 5 0
Rev. J. Reid, : 5.5 O
W. Lee, Esq, . : Oy 0 wl
R. Jones, Esq., : Onto
Thomas Wilson, Esq., . 56 5 0
W. T. Mulvany, Esq., . 5 3-0
52 10 0/1362 12 8

i

1X

—

HO TO TOU OOO NM MMA HUA A TS

Brought forward, .
O. Sproule, Esq., . sh WtoNtea ne ee
James Patten, M.D.,

J. G. Jellett, Esq.,

J. Banks, M.D.,

W. Andrews, Esq.

John Burrowes, Esq.,

F. Churchill, M. D., é
Alexander Ferrier, J un., Esq. aes
William Hogan, Esq.,

W. J. Hughes, Esgq.,

Rev. Samuel Butcher,

W. Grimshaw, M.D.,

Durham Dunlop, Esq. i.
Alexander Clendinning, Esq, cs
William Roberts, Esq., .

Robert Bateson, Esq.,

Rev. Reginald Courtenay, -

Captain Stirling, .

Rev. R. Chatto,

Joseph Nelson, Esq.,

Rey. Thomas Stack, . i
Total Entrance Fees,

ANARAARAAAANAAAAMAAMRAAAD
ooooocooocoecocoocooocoocooocosR

162 15 0

ANNUAL SUBSCRIPTIONS AND ARREARS:
M. Longfield, Esq., . as
Wm. Stokes, M.D., .
W. R. Wilde, Esq., .
Earl of Ross, .

J. Kingsley, Esq.,

John Davidson, Esq.,
Rev. M. M‘Key, .
William Hill, Esq., .
A. Smith, M.D., .
Sampson Carter, Esq., -
Rev. C. Otway, .

W. Edington, Esq., .
E. Hutton, M.D.,
Bishop of Meath, .

M. M. O’Grady, M.D.,
Sir R. Morrison, .

J. Mollen, M.D.,
Charles W. Hawulton: Esq. Salis
Hon. James King, 5
John Ball, Esq.,

G. 8. Gough, Esq., .
W. Hemans, Esq.,

WNWNONNONNHNNNNNNNYNNNAAA EH
cococococoosesoosococoocoocoocS

eu ieare 8

<< |

14 0 {1525 7 8

er) NNN NNNNMNNNNNNNNNN KL KLEE

Or

F. W. Conway, Esq. .
W. T. Mac Cullagh, Esq,, .
G. D. La Touche, Esq.,
Lord Chief Baron, ;
Right Hon. the Lord Mayor, A
C. EH. Orpen, M.D., >
W.B.Wallace, Jun., Esq., ‘
George Carr, Esq., . :
Rey. F. C. Logan,

General O’Halloran,

R. Dickenson, Esq., .
Charles Vignoles, oe ©. E.,
iDwAther, WEsq:.t cts :
Archbishop of Dublin, . 9
Rey. J. D. Sirr, ,

G. A. Kennedy, M.D.,

R. A. Wallace, Esq.,
Thomas F. Kelly, Esq.,

W. Longfield, Esq., .

G. Wilkinson, Esq... . .
Sir Philip Crampton, Batrt.,
Thomas Newenham, Esq, .
Thomas KE. Beatty, M.D., .
Jacob Owen, Esq., ‘
R. C. Walker, Esq., . :
Sir Lucius O’Brien, Bart.,
W. T. Lloyd, Esq., .

M. O’Conor, Esq.,

J. Hart, M.D.,

R. Mallet, Esq. Se ae!
George M Dowell, Esq, 3;
Professor Davy, . ‘
Rev. James Wills,

J. T. Young, Esq.,

J. Anster, LL. D.,

J. H. Smith, Esq., .

F. Barker, M. D.,

R. Reid, M. D.,

G. Levinge, Esq., . .
Thomas Grubb, Esq., .

J. 8. Cooper, Esq., .

Rey. E. Marks, D.D.,
James Pim, Jun., Esq.,

R. W. Smith, Esq., .

J. Osborn, M.D.,

R. Adams, Esq.,

Brought ee ward, ..

or
NNN NYNYNYNNYNYNN NN YN NYNNYNNNNNNYNNNNNNNNNNNNNNNNYNNNNNNWNAO

—
NNMNNNMNNYNYNYNYNYNNNNYNNNNYNNYNNYNNNYNNYNNNNNNNNNYNNYNNNNYNYY SES

=p)

£ Soy i
1525 7 8

x1

Brought forward, .

Hon. Judge be ae

James Apjohn, M.D.,

W. Murray, Esq., . -

Rev. Charles Vignoles, D. Ds
W.F. Montgomery, M.D., . .
R. J. Kane, Esq., Hire
A. Lyle, Esq.,

J. Finlay, LL.D. . -

Sir Edward Borough, Bart.,
A. Jacob, M.D.,. .

Charles Doyne, Esq:, 1840,
Ditto, 1841,

E. J. Cooper, Esq,., .

E. Cane, Esq.,

G. Cash, Esq., -

W. Barker, M.D... . .
Eliott Warburton, Esq., .
Rev. R. Knox, . .

Robert J. Graves, M. D.,
Edward S. Clarke, Esq., .

J. D’ Alton, Esq.,

P. D. Hardy, Esq., .

Rev. James Gregory,
William Gregory, M.D.,
Abraham Palmer, Esq., 1840,

Ditto, 1841,
Archdeacon Disney, 1840,
Ditto, 1841,

W. Farran, Esq, . .
James O’Grady, LL. D.,

A. E. Gayner, Esq.,

S. Ferguson, Esq., . .

Rey. R. V. Dixon, Esq.,

F. W. Burton, Esq., .

H. Watson, Esq., 1841, :
James Whiteside, Esq., 1841,
H. H. Joy, Esq., 1841,

W. Armstrong, Esq., 1841,
G. G. Otway, Esq., 1841,

P. M. Murphy, Esq., 1841,
W. T. Kent, Esq., 1841,

E. Hutton, M.D., 1842,

C. T. Webber, Esq., 1842,
A. Abell, Esq., 1841,

Rev. James Carson, 1840, .

Total Annual Subscription and Arrear 5,

THe Tora CHARGE,

WONMNNNNNNNNNNNNNNNNNNNNNNNYNNNNNNNNNNNYNNNYNNNYNNNW

WNONNNNYNNNNNHNNNNNNNNNNNNNNNYNYNNNNYNNNYNNNNNNYNNNND?

£2 8.
1525 7 8

247 16 0

Lae oS

Xli

THE DISCHARGE.

ANTIQUITIES PURCHASED AND REPAIRED.

EpeaSs Oe
Geraghty, for silver ornaments,

3rd May, 1841, . . 0 7 6
Bambery, for cold torque, 7 th

June, 1841, . , - 50 0 O
Peters, for repairs of do., "10th do. 5 LOB
Smith, for fragment of gold, 12th

do. . 1 0 0
Donegan, ae fragments of do., 20th

J uly, 1841,. . . 610 0
Topham, for gold fibula, “4th Nov.

1841,. . ee CO). OD
Do., ae 18th Jan. 1842, 12 12 0
ee for mare ie 3rd Feb.

LOE sii ree tara

Hogarth, unrolling papyrus, -
Total Antiquities purchased and repaired,

Books, PrintTine, STATIONERY, &c.

Allen, J.W., lithography, to 19th July, 1841,
Branston, F. W., wood engravings for Pro-
ceedings, 23rd March, 1841, Z
Ditto, ditto, Ist @erahee 1841,
Du Noyer, G., for drawing on aroadenlock,
5th March, "1841, os
Duncan, J., engraving bells, 12th Feb. 1841,
Graisberry ‘and Co., printing, balance of ac-
count, 3lst Dec. 1839, . sige
Ditto, ; ditto, 29th March, 1841,
Hope, stationery, 16th Dec. 1841, . 4
Healy, ditto, 26th Jan. 1842, ‘ 4
Hodges and Smith, books, &., 31st Dec. 1840,
Ditto, ditto, 2nd Dec. 1841,
Kirkwood, engraving, on account, 26th April,
SAT) oh) yates te Mea Oe an oman 2a YS
Ditto, ditto, in full, 13th July, 1841,
Ditto, ditto, 15th Jan. 1842, .
Morrison, ditto, 13th May, 1841, .
Mullen, bookbinding, 3rd Jan. 1842, .

3%

S.

Nn oO [oo

2

d. ge a:
6
0
113° 11-6
0
0
0
0 |
0
0
1
4
0
4
ll
6
0
0
0
4
6.493 11 oe

Xili

Brought forward,
Oriental Translation Fund Subscription, les
Jan. 1841, . .

Pettigrew oad Galion, Directory, 28th J an.
1841, : ;
Ponsonby, stationery, 28th Dee ‘1841, :
Taylor, Messrs., Scientific Memoirs, 16th

March, 1841, abet
Ditto, dae 20th Sept. 1841,
Yeates, letter balance, 27th Jan. 1840,
Total Books, Printing, Stationery, &c.,

Coats, CANDLES, OIL, &c.

Allen, William, oil, to 26th June, 1841,

Ditto, ditto, 6th Jan. 1842, .

Daly, John, bog wood, 24th Feb. 1842,

Kenny, M., for coal, 14th Dec. 1841,

ee fiborne, for candles, 8th Feb. 1841,
Total Coals, Candles, Oil, &e., :

ConTINGENCIES, &c.
Clibborn, E., incidentals, to 26th June, 1841,

Ditto, ditto, 25th Sept. 1841,
Ditto, ditto, 31st Dec. 184], .
Ditto, ditto, 9th March, 1842,

Hodges and Smith, engrossing pans 18th
Jan. 1841,
Johnston and Co., advertising, Ist Jan. 1841,
Ditto, ditto, 8th Dec. 1841,
Mallet, Robert, postage, 10th Jan. 1842,
Nash, P., carriage to Park, 13th Nov. 1841,
eae J. D., carriage of parcels, 15th
May, 1841, ;
Smith, J. ae expenses to Drogheda 18th
Jan. 1842,
Williams, Thos. . and Co., ‘carriage ‘of books,
&c., 4th June, 1841, _ . :
Treasurers for stamps, &c., 7 th Feb. 1842,
Ditto, ditto, :
Total Contingencies, :

Repairs oF House, FurNITURE, &c.

Acheson, J bigs drugget, &c., to 3rd Nov.
1840, . .
Ditto, repairs, 29nd Oct. 1841,

— ee DD

oo ~T C oe oS Oo

or

Sarees
18 6
10 O
12 6
2 6
0 0
0 0
9 O
14 11
15 0O
15 O
0 O
12 6
7c
14 10
9 2
Siue
15 0O
9 0
13 6
6 0
10 6
15 0
12 7
me
17 9
0 9
17 4
6 0
3

Gs
113 ll

739 12

olay 2

Os

jor)

X1V

Brought forward,

Blackwall and Co., lamps and repairs, 30th
Nov. 1840,

Brown, John, cleaning windows, Qnd June,
184],

Ditto, repairs, “Dad Dee 1841,

Casey, P., repairs, locks, &c., 14th Sept. 1841,

Ditto, ditto, 31st Dec. 1841,

Clibborn, E., for sundries used in cleaning
house, &c., for year ending 16th July, 1841,

Edmonston and Co., sundries, lst June, 1840,

Flinn, R., cleaning ash-pit, &c., 7th August,
1841, . . 4

Hughes, H., a hemp mat, ‘and Sept. 1841,

Kane, M., washing down ae 3rd Ne Ov.
1841, . Q

Kane, C. , washing rollers me et Jo ane 1841,

Ditto, ditto covers, 29th Nov. 1841,

Keough, F., beating carpets, &c., 4th Sept.
1841,

Mullen, Wm., cleaning chimneys, 9th eel
1841, i

Ditto, repairs ee ditto, 17 th J uly, 1841,

Nannetti, G., plaster casts, &c., 11th ae
TSA ues ee

Perry and Co., furniture, &e., L1th Nov. 1841,

Surman, G., repairs, &c., 14th Nov. 1841,

Travell, G., fae and repairs, 3rd Nov.
SY a ee

Walker, Wnm., repairs, ere Se, 26th Oct.
1841, . .

Total Repairs oR Bence Tense aie oe be

Rent, TaxeEs, AND INSURANCE.
H. Truel, one year’s rent, to lst Feb. 1842, .

Grand Jury cess, one year, Michaelmas, 1841, _

Wide street tax, ditto, ditto, 1841,

Police tax, ditto, ditto, 1841,
Pipe-water, ditto,. 1st June, 1841,
Ministers’ money, ditto, Michaelmas, 1841,
Parish cess, ditto, ditto, 1841,

Paving and lighting, ditto, 5th Jan. 1842,
Watering street, ditto, ditto, 1841,
Insurance at Globe, £5 6s. 3d.)
Ditto, National, 5 6 3

Total Rent, Taxes, and Insurance,

Go

= OoOnNnre

—

a) S ooo oo oo

—
ONNWNNr hes

10

—_
He pe oo Neer’ ke)

— — a
~ © Or bo SO or Db wo

_
cx

mR

fis

oo oo loreer kia)

| TS Ono an oo ooo

Am OWODNADMWMOS

Sa ots
913 2 1
F236
147 11 10

1133) “aeus

XV

Brought forward, .

SALARIES, SERVANTS’ WAGEs, &c.

Clibborn, Edward, salary for three quarters of
a year, as assistant librarian and clerk, to
16th Dec. 1841, 2

Hamilton, Wallin, ‘salary and al-
lowances as porter, from 27th
Mar. 1841, to 12th Mar. 1842,
viz., 26th June, 1841,

Ditto, 2

25th Sept. 1841,

Ditto, 5 :

31st Dec. 1841, :

12th March, 1842,

Christmas allowances,
27th Dec. 1841,. . .

Livery cloth from An-
drews, 15th Dec. 1841,

Ditto, making, Dunn, 17th
Jan. 1842, R

Ditto, buttons, Wood-
house, 18th Dec. 1841,

Barragon coat, Simpson,
17th Feb. 1842,

Hat, Wright and Oxley,
17th June, 1840, :

Ditto, ditto, 21st
Dec. 1841, . . . 0 16

Aprons, St. Peter’s Repo-
sitory, 31st Dec. 1841,

£ A a:

joo
i=) j=) CNODMDAD

—
o nr i) he ON Oh

53

° bo Le po TW0OOCMO®

Co =
— md
(opyo ep)

6
0
0
0

0 310

Kane, B., as extra porter at Meetings, 28th

June, 1841, eae Bee RED en tel 9
Ditto, ditto, 28th Feb. 1842,
Orpen, Dr. Thomas H., salary as Treasurer,

for eight months and two ona to 30th

Noy. 1841,

Ditto, commission as Tecnsnuen, on £320 Be,
at 5 per cent.,

Smith, Dr. A., salary as 5 Treasurer, from 30th
Novy. 1841, fa 16th March, 1842, . .
Wisehart, James, salary as clerk at Meetings,

from 12th April, 1841, to 28th February,

S42 hv iacew!

Total Salas Servants’ Wages, oe

Oi de | es eS
L333 coer
90 0 0O
|
|
|
4418 14
Ty 1 0
146
1416 1
16 0 3
6 31l
3 5 0
177 8 103
1310 14 33

XVi

Brought forward,. . .|-. . . . }1310 14 34

THREE AND A HALF PER CENT. GOVERNMENT
Stock PURCHASED.

ts: = a.

PEAS 2 cost is" ae. bv ee ee = oo

BO Be RUDY eg eee eee ae he LS 5 |
—— Total cost of Three and
£55 13 10 a half per Cent. pur} | 5417 2
— chasedyie =. giro. ~

|

THREE PER CENT. CONSOLS PURCHASED. | |

Eero age © 402

6115 8 cost. Se 2 oo Sas aa

4612 7 ,, BE etn Orel

AQ AVS See » > las -s Let SORLS 2

A 102-02 os ae ae 2S PO ea a

Des tt: NOEs ole. aah teed FOO

DA Ae RANT eee a tt aD «ah = SO, ae | ES x

Te A Se. eRe See ea
—__. Total cost of Three per) |. |
£232 11 11 Cent. Consols Pap | 208 19 O
ee chased, . aa

157410 54
198 13 28

THE TOTAL DISCHARGE, .
Balance in favour of the Public, °.

The Charge as above, |
STATE OF THE BaLAnce.
1842. os ie

3lst March. In Bank of Ireland, . . - . . . .19017 1
In Treasurer's hands, as per this Account, 7 16 14

Balance as above,. . . £198 13 22

The Treasurer reports, that there is to the credit of the Academy in
the Bank of Ireland, £1052 6s. 8d. in Three per Cent. Consols, and
£1609 4s. 9d. in Three and a half per Cent. Government Stock, the
latter known as the Cunningham Fund.

(Signed), JAMEs Pim, Jun.,

31st March, 1843. Treasurer.

No. HI.

ACCOUNT

OF THE

ROYAL IRISH ACADEMY,

FROM Isr APRIL, 1842, TO 31st MARCH, 1843.

THE CHARGE.

Balance in favour of the Public, as corrected
by the Commissioners (£198 13s. 23d., less
3s. 10d.), .

Parliamentary Grant for 1842 (paid 1 16th
March, 1843), s :

Quarterly Warrants from Treasury,

Total from Treasury,

INTEREST ON STOCK:
Le 8 eds
Half year’s on 1609 4 5, 3% per Cents.,
Mitte, oo jy V F636i18") 5,35 3 :
Ditto, ,, 1052 6 8,3 ‘3
Ditto, ,, 1069 0 6,3
Total Interest on Stock (exclu-
sive of brokerage 5s.3d.), . }

PUBLICATIONS AND BOOKS SOLD:
Boone, Messrs., balance of their account to
2nd J Ea UCL henge
One year’s rent of Stable, to Nov. 1 1842,

Lire ComPosiTIONs :
Henry Hutton, Esq., ;
Robert Bateson, Esq., . . . .
W.V. Drury, Esq,, - 3
Stewart Blacker, Esq., .

H. L. Renny, Esq., . .
Total Life Gompositions;

d

£

300
146

28
28
15
15

21
21
15
21
21

Ss.

0
17

2
11
14
19

DAAano

ooo°oo

oSus sity. OS
198 9 43
44617 8
88 7 4
817 4
21 0 0
99 15 0
863 6 8h

XVII

Le) 28. Cel we ese ae
Brought forward,. . .| . . . . | 863 6 8b
ENTRANCE FEEs.
John Toleken, M.D, . . . . -1842, 5.5 (0
Robert Law, MD.) 20°. "yet x 5.65 (OO
Rey. R. Butler, Bis 5 es 5.5 (0
W. Blacker, Esq., fl, th piace 5 5 0
Bod. Chapman: Hisqs a” .*:..) ane 56 5 0
Sir Thomas Staples, Bart, . . . ,, 5.5 (0
mrtaur Kine, Rsq.. ee Lee 5 5 O
F. M. Jennings, Esq., - 56.65 «(OO
Rev. James Booth, cE, RR 56.5 «(0
Thomas Hodder, Esq., R. N. “jiten oh) Beleaay 5 5 0
Henry ution, Msg... s . 2) 5 5 5 0
Hon. Frederick PORSOUBY, tyre nS heeae ss 5. 5 0
peitemas: Cather, Msg...) 2). oto, 35 20
WEV Drury, M.D. Woe saa 5 5 0
Heat Oslo, Bisqis) <2 we pie vale ae es 5 6 O
Gaalmion Visa ee ih'4 |.) apt ee ean cy ag 5 5 0
Won. Gore, Moo teats ee ae k 5.65 COO
Stewart Blacker, Esq... . . ,, 5.5 0
Hien CulllyscHlS., o.. s Wiey matey hae 5 5 O
ET, emmy VEG, jaye <i se )ce, g 5 5 0
James Magee, Esq, . . iat 5 5 0
Total Entrance Bees, er ey | ee ee Sp

ANNUAL SUBSCRIPTIONS AND ARREARS.

Hugh Ferguson, M. D., due March 16, 1842, 7s We)
J. Davidson, Jun., Esq... . ,, B 2 2 0
Downes, Misys cnp.id .). 8 A 2 2 0
M. Barrington, Fisdiy s i- 1-0, ) 1G41: 2 2 0
Se adlardy.(Egg..¢ f/f fs) ee, BY 2 2 0
eH Mayne HSGs) 5 =. | +key Rs 2:2 0
John Mollan, M.D... . . ,, 1842, 22 0
W. Drennan, Esq. . . . ,, a 2 2 0
Archdeacon Disney, Si Pap meee iy 22 0
W. F. Conway, Esq, . . 4, 5 2 2 0
Ge Dla Touche, Esq. |}: 5, = 3p 22 0
Hy) Dany, Hisq., . ~ . | ..cnas 4 2 2 0
4G. Ay raver. Esq... 4-") aig 35 22 O
Sir L. O’Brien, Bart, . . ,, a 2°2 0
Bie Gare, TUS far oh. 3 the Ue Migs Pi 2. 2 0
James Apjohn, Esq... . . ,, ye Zia? 0
ee biehe, Bigg. i pe) w 3 ciecWegs Pa 2 2 0
W. Edington, Esq, . . . ,, aS Bit 2,10
William Bill, Bsq..) 2 32. y, a 2 2 0
AS Sms ase 8. te 5 2 2.0
42 0 0.) 973 tle se

xix

ee Ei Ne. Uae
Brought forward, : 42 973 11 84
W. Monsell, Esq., . due March 16, 1842.
W.B. Wallace, Esq, . . ,, 5
R. Jones, Esq.,_ - Dre Nees %
John Hamilton, Bags «Sin ie eee a
William Gregory, Esq... -. 5, a
G. Wilkinson, Esq., . . - 5; nt
G. W. Hemans, Esq., . - 5, ‘.
M. M. O’Grady, Esq., . - 5, x
William Murray, Esq., - - 3, A
Hon. James King, ... 4, nu
Gerald Fitzgibbon, Esq., . ,, 55
Rev. James Reid, . . - - 35 a
George Carr, Esq, . - + 4, if
Rev. H. F.C. Logan, . . - 5, as
Charles Vignoles, Esq., . - ,, a
John Hart, Esq., - - - + » 5
Sir William Betham,. . . ,, ate
Chichester Bolton, Esq., . ,, Pe
Godfrey Levinge, Esq, - . 5, x
Cre. Ho Orpen, M. Te fs -.3 aes

Be) Cooper, Esq: . 6 - + ni sy ss
me @arter, Hsq.,. %. SF. 6) + yi95 i
M. Longfield, Esq, . - + 5 a
Sir J. K. James, Bart, . . ,, ass
Hon. P. C. Crampton, . - » os
Rev. James Wills,. . . © 3 oS
Charles W. Hamilton, Esq-, _ ,, -
His Grace the Abp. of Dublin, ,, Ps
Thomas F. Kelly, Esq., - - 5, Ae

James Patten,M.D... . - 5; is
W. T. Mulvany, Esq., . - » a
geOhsproul, Msg. so. Mh, =
Rev. John West, D.D., . - 5, a
Thomas Newenham, Esq., - ;, a
ee DWickmson\JEsg- 6 f2 <A) ¢99 oe
R. Kane, M.D., 5
Hon. M. Brady (Lord Chief ef Baron), a
Rev. W. Lee, . . a5 BS
Awards UV WEy A sas cuaiee id ay lesllinios 35
Rk. A. Wallace, Esq. . . + 4 a
Sir E. Borough, Bart, . . ,, Pe
Wer. LloyaWEisa es lg) 55 3)
Thomas Fortescue, Esq, - ;, be
R. Adams, Esq, . . -. + 4 a

eel. Smith sg. es Sees op
Jacob Owen, Esq... . « - 5, A

DNMNYNNMNPNYNYNYNYNNYNNNYNYNYNNNNNNNNNNNYNNNYNNYNYNNYNYNNHNYNNYNNNNO®
ceeerecececococococoocooooocoecoeocooooocooooocooooooocooooocoocoooosg

@ WDWNNYNNNNNNNNNNNNNYNNNNNNYNNNNNNNNNNNNNYNNNNNNNNND

bo
= |

973 11 8b

—
vs

Brought forward,

M. Barrington, Esq., due March 16, 1842,

J. Finlay, LL.D.,

A. Palmer, Esq.,

James Pim, Jun., Esq.,
Mathew O’Conor, Esq., .
Arthur Jacob, M. D.,
W. Barker, M. D.,

F. Barker, M.D., . .
Thomas E. Beatty, M. D.,
Rey. Dr. Vignoles,
Simeon Hardy, Esq., .
J. Osborne, M. D.,

J. H. Jellett, Esq., .

R. W. Smith, Esq.,

T. Grubb, Esq.,

H. H. Joy, Esq.,

J. Anster, LL.D.,

F. W. Burton, Esq.,

J. W. Young, Esq., .
George M‘Dowell, Esq., .
William Stokes. M. D.,
R. Mallet, Esq.,

John Ball, Esq., :
W. FE. Montgomery, M. Dy,
G. A. Kennedy, M. D.,
W. T. Kent, Esq.,
Acheson Lyle, Esq., .
J. 8. Cooper, Esq., .-
General O’Halloran, .
A. E. Gayer, LL.D.,

R. E. Walker, Esq.,

W. R. Wilde, Esq.,

Rey. Dr. Marks, :
Elliott Warburton, Esq., 4

H. Coulson Beauchamp, M. D.

William Farran, Esq.. .
James Whiteside, Esq., .
P. M. Murphy, Esq., .

S. Ferguson, Esq., .

B. J. Chapman, Esq., .
Charles Doyne, Esq, .
Sir R. Morrisson,

W. E. Hudson, Esq., .
Ditto. ditto. :
Robert Graves, M. D.,

Very Rev. Dean Gregory,

29

WNW NWN NNNNNNNYNYNNYNYNNYNNNNYNNNNYNNYNYNNNYNYNNYNNNNNYNNNNMDB?

973 11

8

Brought forward, F
. due March te 1842,

P. D. Hardy, Esq.,
C. G. Otway, Esq.,
J. O’Grady. LL.D.,
John Dalton, Esq.,
G. Cash, Esq.,
John Burrowes, Esq,, .
John Hamilton, Esq.,

Frederick Darley, Esq., 1

Witrtor

H. Ferguson, M. D,
George “Downes, Esq. A
Sir P. Crampton, Bart.,
William Murray, Esq.,
A. B. Cane, Esq... .
John Davidson, Esq.,
Rev. S. Butcher,
Durham Dunlop,

E. S. Clarke, Esq.,

W. T. Mac Cullagh, Bq i

Ditto,

W. Edington, Esq.

R. Kane, “M. Dey Ne
C. Bolton, Esq.,

Dr. O’Grady,

Captain Sterling,

Sir E. Borough, Bart.,

Thomas Fortescue, Est i

E. Hutton, M. D.,
G. Carr, Esq.,

XXI

- 1842,

1843,

Total Annual Subscriptions an and Arrears,

THE ToTAL CHARGE,

Brg Cet at ean, Semen
235 4 0|973 11 8
Py aan O)
22 2= 0
2 2 0
2°20
2 R20
2 2 0
2) 2-0
2210
2230)
Py WPMD)
Ps A)
Despite (0)
22)
2 230
PA antakO)
2° 2° 0
2 F220
Phe Poi)
22-0
OND) ek)
2°02. 0
Drie ag)
Drees (0)
2 210
Pyne (0)
2 2 0
25a 10
2 2 0
22 0

a 06 0

. £11269 13 8}

XXil

THE DISCHARGE.

ANTIQUITIES PURCHASED AND REPAIRED,

Broderick, for two a fragments, i Nov.

1842, . .,
Donegan, for gold cup, “18th Feb. 1843,
Edwards, for warrant, 30th May, 1842,
Maguire, for silver pin, 8th April, 1842,
J. H. Smith, for seal, 31st March, 1842, .
Underwood, for silver seal, 2nd April, 1842,

Ditto, tracery, 28th May, 1842,
Ditto, crozier, 15th Nov. 1842, .
Ditto, silver relic, 14th Sept. 1842,

Total Antiquities purchased and repaired,

Books, Printine, Stationary, &c.

Allen, engraving, to 27th July, 1842, .

Ditto, lithography, 2nd Feb., 1243, . .

Betham, Sir W., for Dunop’s "Book, ‘4th J uly,
1842, :

Camden Society, subscription i 27th J uly
S42" Diced.

Curry, Catalogue of Manuscripts, 16th Jan.
1843, A

Ditto, ditto, "6th March, 1843,

Du Noyer, lithographs, to 5th Oct. 1842,

Hanlon, wood-cuts, lst Aug., 1842,

Hely, envelopes, 22nd October, 1842,

Johnston and Co., advertisements, 26th July,
1842, ..

Taylor, R. and J. E, twenty Scientific Me-
moirs, Part 10, Ond May, 1842, :

Total Books, Printing, Stationary, &c.,

Coats, CANDLES, OIL, &c.

Allen, William, oil, to 9th Dec, 1842, . .
Kenny, M., cokeand coal, to 9th April, 1842,
Ditto, coal, to 26th Jan.,1843, . . .
Rathborne, candles, to 16th March, 1842,
Wilson, T. P., coals, to 5th August, 1842,
Total Coals, Candles, Oil, &c.,

£

KSNON TOK pe

D bo
—

—_

—
ee Db Oo

a> w

—

—
o

a
wNmwowooe

iv}
.

Neje)

fo)

So Ww

SCONncdannwnro
SOOCOoOnaoo

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th
=
xX

i)
i=)
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@

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onooco

54 3 6

38 18 2

113 10 4

XXlii

Brought forward,

CoNnTINGENCIES, &c.
Clibborn, E., incidentals to May, 1842,

Ditto, ditto, 29th July, 1842,
Ditto, ditto, 21st Nov. 1842,
Ditto, ditto, 5th Jan. 1843,

Ditto, ditto, 6th March, 1843,

Post Office orders, Ist August, 1842, .
Robertson, carriage of parcels, oe wee
1842, : :
Rorke, for stamps, Ist Oct. 1842, :
Stamp on treasury warrant, 16th March,
SAS oe «eee ont
Total Contingencies, &6., z

Repairs oF House, &c.

Brown, J., cleaning windows to 2nd June,
1842, it sale erp et 7) ae
Ditto, ditto, to 2nd Dec., 1842,
Casey, S., iron works, &c., 16th July, 1842,
Clibborn, E., sundries used in cleaning house,
&e., 16th July, 1842, 2 ae
Ditto, ditto, to 16th Jan., 1843,
Flinn, B., cleaning ash pit, 10th May, 1842,
Mullen, W., sweeping a 3rd May,
1842,
Ditto, ditto, 14th J wy, 1842,
Ditto, ditto, 2nd Noy., 1842,
Total Repairs of House, &e., .

Repairs oF Furniture, &c.

Barrington, F., iron door, to 1st Aug., 1842,
Ditto, repairs on safe, 14th Dec., 1842,
Blackwell and O’Brien, repairs of lamps
globes, &c., 12th Nov., 1842,
Duffy, J., boards. to 25th Dec., 1842, ...
Ditto, frame and glass, 14th Feb., 1843,
Kane, C., washing rollers, 2nd J uly, 1842,
Kane, B., beating carpets, 21st July, 1842,
Bttledale. J., iron chest, 4th July, 1842, .
Yeates, G., scales and letter sare 25th Nov. s
1842, ..
Total Repairs © Paraitae kes re

i=) oo i) OoOrNNrw

— a

ooo Oo on

Aocodrnh ow

—

© Mer) oOMTO WO ®

oS
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iw)
i=) omMoooo lorwor)

If 3.38

16326

Li MinG

166 15 0

XXIV

Brought Sorward,

Rent, Taxes, InsurRANcE, &c.

Truell, R, H., half-year’s rent, to £ s. d.
Ist Aug., 1842, : oot 52p lA a6
Ditto, ditto, lst Feb., 1843, 562 4 6
Grand Jury cess, half-year, Easter,
71 SUE ae to ane, le
Ditto, ditto, Michaelmas, 1842,

104

4 1 3
3.15 0

o-l

Wide street tax, Easter, 1842,
Police tax, 25th March, 1842,
Ditto, 29th Sept., 1842, .

Oot.
cow.

4
Pipe water, 24th June, 1842, . . 1
Ministers’ money, 29th Sept., 1842, 2
Parish cess, 29th Sept. 1842, . . .. - 2
Paving and lighting, 5th Jan., 1843, . . . 12
Watering street, . . . . 1842,. 0
Poor rate, 24th March, 1842, . 21
Ditto, 10th Nov. 1842,. 2y1
Insurance at Globe,. . . . . 51
Ditto, National . . . . 21
Ditto, ditto, Ret oad
Ditto, ditto; ss; heme 4

DDH OD oo.

0
0
3
5
3
2

Total Rent, Taxes, Insurance,

SALARIES, SERVANTS’ WAGEs, &c.

Clibborn, Edward, salary for one year and a
quarter as assistant librarian and clerk,
to 16th March, 1843, . . . be reSell oH i0)
Hamilton, William, salary and ae
lowances as porter, from March
12th to March 26th, 1842, .
to June 25th, 1842,
to Sept. 24th, 1842,
to Dec. 31st, 1842, .
to March 11th, 1843, .
Christmas allowances, Dec. 25th,
1842, . ates gh a

oriole ool Mary

—_ —

me Oe eS Oe
So oasnNOoOnRS

bo

©

OWON®M OD

10

8

8

159 17 11

326 12 11

XXV

Lesh ds | eee or mae
Brought forward, . . -| 186 6 8 } 326 12 11
Smith, John, assistant porter, from £ s. d.
18th June to 18th July, 1842, 1 2 6
to 30th July, 1842, 010 0
L126
Kane, Bernard, extra evening porter, from
16th March, 1842, to 27th June, 1842, 1 4 6
Corcoran, messenger, to 15th March, 1842, <5, 30
Sinton, T., Assistant clerk, to 24th Dec. 1842, 4 0 0
Wisehart, A ames, salary asclerk <£ s. d.
at meetings, to 23rd May, 1842, 1 5 0
to 10th Jan., 1843, 110 0
to 27th Feb., 1843, 015 0O
—— | I)
Kane Robert, M.D., Secretary of Council, to
16th March, 1843, Ase 2 ORO
Pim, James, Jun., Treasurer, to 16th March,
MS435 we. BS RO MAA OF EO
Mac Cullagh, J sae Esq., Sie
tary of Council, to 16th March, o Siu.
1842, . . : 0 0
Ditto, oF Academy, 1 16th March,
1843, 221-00
oe 420 0
Drummond, Rev. W.H., Libra- £ s. d.
rian, to 16th March, 1842,. . 21 0 0
Ditto, ditto, 1843, . .21 0 O
SEE AOI OT 10
Singer, Rev. J. H., Secretary to Academy, to
16th March, 1842, Bie 21 0
Total Salaries, Servants “Wages, oe Pe ys) AUS ts
THREE AND A HALF PER CENT. GOVERNMENT
STocK PURCHASED.
Eee Shan a:
PIQUA COSTER t eas +, eo = [ee ae
TiS SEG he.) 1 GA AO SGA lean eo!)
—— Total cost of Three and
£55 19 5 a half per Cent. perf 56 13 5
——_——_———. chased, ——__—_——
(2h a0

XXV1

i es. d.'| een me
Brought forward, » wi). OE BO
THREE PER CENT. CONSOLS PURCHASED.
Est ide
ers LO cost, '2 9! She) «iy tah WoMeN ace uD AS: 5
MORNG Tj ts ko ks. lg when ee lees “1Oue6
BOG O ing | eee bss elke | Coma Mowe ie WeOO, Os. 0
—— Total cost of Three per
£342 11 O Cent. Consols pf — 331 14 11
——_—_-_— _. chased, Br ious dea eben
THE TOTAL DiscHARGE, s .|- . . . £1058 19 11

Balance in favour of the Public .|... . 210 13 94

The Charge as above, (p. xxi.). .|- . . . £/1269 13 83

STATE OF THE BALANCE.

1843. LNG eae
31st March, In the Bank of Ireland, . . .. . . 208 610
In Treasurer’s hands, as per this Account, 2 6 114

Balance as above, . . - £210 13 gi

The Treasurer reports, that there is to the credit of the Academy in
the Bank of Ireland, £1394 17s. 8d. in Three per Cent. Consols, and
£1665 4s. 2d. in Three and a half per Cent. Government Stock, the
latter known as the Cunningham Fund.

(Signed,) JAMES Pim, Jun.,
31st March, 1843. Treasurer.

No. IV.

ACCOUNT

OF THE

ROYAL IRISH ACADEMY,

FROM Isr APRIL, 1843, TO 3lst MARCH, 1844,

THE CHARGE.

Balance in favour of the Public, as Boe Jast: | £08 eri dulgetG) ) Bersy ol.
Audit, , 210 13 gk
Parliamentary Grant for 1843 (paid Jan, ws
1844), . : 300 0 O
Quarterly ene om Treasury, . Re eee A Oh ae S
Total from Treasury,. . . |——— 446 17 8
THREE PER CENT. CONSOLS SOLD:
1843, August 12, 14, £300, at 945 er, | 282 11 3
Interest ‘40 ayia cele sue 019 8
283 10 11
Brokerage, . : 07 6
Total Proceeds Consols sold, eS Ee ee
Otp 33 PER Cent. STOCK SOLD:
1843, August 12, 14, £50, at 101g per,. | 50 16 3
Interest 40 days, . . . - Vega AO
51 0 1
Brokerage, . ON ; OF Fes
Total Proceeds ald 35 per
cent. Stock sold, 3 ant if arernl, OU ee. LO
INTEREST ON STOCK:
Sua:
Halfyear’son 1665 4 2, 34 per Cents. | 29 1 4
Ditto; 0 2643 19) Gp3k .. -| 284s ae
Dio ead soe Wee 2. | 20ab eas
WGioaess, OS MINE 1b 10, 30... o.| (keene
Total Interest on Stock (ex-
clusive of brokerage, 5s. sr Fe. oe 95 6 4
1087 0 Oo

XXVill

eDoetpmeh | as Gk
Brought forward,. . .| . . . . {L087 O O%
PUBLICATIONS AND Books soLD:
Boone, Messrs., balance of their account.to
Bist December, US43h05 mega, Games ees ese ee 14 6 3
One YEAR’s RENT OFSTABLEto Nov. 1,1843, | . . . . 21 0 O
Lire Compositions:
d= Picktord Mee We Fetes it ae ees Seal een eeu ine 15 15 O
ENTRANCE FEEs:
Hon. and Very Rev. the Dean of St. Pa-
trick’s, . . +) ee oe B43 5 6 0
Goddard iRichards. Esq., j Re ares Hy a
Rey. F. Crawford, é a 5 5 O
J. Wynne, Esq, .. 5 5 5 5 (0
J. George ipelestenaees) Esq ; si 5.65 (0
G. J. Allman, MD. .2 5 5 5. 0
H. L. Lindsay, Esq., #5 56 5 0
Rey. John Homan, . + 5.5 0
John M‘Mullen, Esq., . » 5 5 0
Matthew Dease, Esq., . » 5 5 0
J. Pickford, M. D., i 5 5 0
Sir M. Chapman, Bart, - 5.5 (0
E. Bewley, M.D., i 5 5 0
J. Neville, Esq., . 5 56 5 0
Henry Clare, Esq.,. . - 5 5 0
William Henry, Esq.,. . ss 56 5 0
William M‘Dougall, Esq., : se 56 5 0
Total Entrance Fees, ‘ ee | 89n oO

ANNUAL SUBSCRIPTIONS AND ARREARS:
W. Andrews, Esq., due March 16, 1843,
C. T. Webber, Esq...
The Archbishop of Dublin,
William Hill, Esq., . :
Sir Thomas Staples, Bart.,
F. M. Jennings, Esq.,
James Pim, Jun., Esq.,
Rev. William Lee, i
William Gregory, M.D.,
W. Longfield, Esq., .

Rev. R. V. Dixon, 5
Ditto, see Sie 1843,

Rey. Richard Butler, Ne

J. Nelson, Esq., . .

G. D. La Touche, Esq., Bs

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3110 0 |1227 6 32

XXix

2 th

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is
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Brought forward, . .
J. T. Banks, M. D., due March 16, 1843,
A. Smith, M.D.,
Thomas N ewenham, Esq, - Behe
F. W. Conway, Esq.,
W. Blacker, Esq, . .
Sir J. K. James, Bart., .
Jacob Owen, Esq., .
Sir W. Betham, Knt.,
William Hogan, Esq.,
W. Drennan, Esq., . .
Hon. Justice ae ae LE D.,
G. Fitzgibbon, Esq., .
Rey. James Wills,
W. B. Wallace, Esq.,
W. T. Mulvany, Esq., .
F. Churchill, M.D.,.
A. Ferrier, Esq., .
J. S. Cooper, Esq., .
John Mollon, M.D., .
F, W. Burton, Esq.,
W. T. Lloyd, Esq., .
G. Wilkinson, Esq,., .
J. Wynne, Esq., . .
Thomas F. Kelly, LL. Dy
Sir L. O’Brien, Bart.,
Charles Vignoles, Esq.,
Edward Cane, Esq.,
G. W. Hemans, Esq.,
John Finlay, LL.D.,
Charles Doyne, Esq.,
Rev. Thomas Stack, .
R. A. Wallace, Esq.,
Thomas Grubb, Esq.,
Rev. R. Chatto,
Rev. James Reid,
John Toleken, M.D.,
James Patten,M.D., . .
Right Hon. Chief Baron, .
Edmund Davy, Esq.,
C. W. Hamilton, Esq., .
J. H. Jellett, Esq., .
James Apjohn, M.D.,
E. J. Cooper, Esq., .
R. Adams, Esq., . .
C. E. H. Orpen, M.D.,

—

o WW NW NWNNNNDNWNNNNN NNN NNNNN NH NNNNN NNN NNN NNNNNNNNNNS #

9 99

—
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0 [1227 6 a

XXX

8.) Gs) ee ES Oe
Brought forward, . . 126 0 O {1227 6 3%
Hon. James King, due March 16, 1843, a 2"0
M. Longfield, LL.D. . . ,, As 2 2 0
Rev. H. F. C. Logan, D. Pe a 3 2 2 0
J. Osborne, M.D., . . 4 A 2 2 10
J. Huband teh Hsgi} ee a 2 2 0
G. A. Frazer, Esq., AGP tioned (3 i 2°20
Abraham Abell, Esq... . ,, 1842, 2 2 x()
Ditto, . MS, 1843, P Ada i 0)
William Barker M. Da, tt, Hs 2° 2 0
Robert Tighe, Esq... . . ,, os 2 2 0
R. Law, M.D., . Ris a 2 2-0
Rey. John West, D. 1D: a fe 2 2 0
R. Graves, M.D, . . . 4, pe 2 2 0
John Ball, HISGeers 2 area Rt, x Pasties 0)
T. E. Beatty, M.D.,. . . ,, Py 2 2 0
H. C. Beauchamp, M.D., . ,, Bs 2 2 0
R. C. Walker, Esq... . . ,, Pr 2°2 0
W. Monsell, Esq, . . - 4, 3 2 2 0
William Stokes, M.D.,. ._,, _ 2 2 0
gs ee Young, Histisc os). 8s, 6 2-20
ReReid Meeps ae eS Be, . 2 2 -0
Rev. Matthew Horgan,. . ,, 1841, 2 2 0
Oliver Sproul, Esq, . . ,, 1843, 2 2 0
Arthur Jacob, M.D. . . ,, m 2 2 0
Je Hi Oyneh, Esq. 2b hes 1842, 2 2 0
R. W. Smith, Esq, . 5.4 1843, 22 0
Wrigley Grimshaw, M.D., __ ,, ma Qe 2) 0
John Hart, M.D. . .. ,, a 2 2 0
M. Barrington, Esq., . . ,, Me 2 2 0
He. doyi sq, >.) oe: : 2 2 0
J. Anster, LL.D, . . . ,, va 2 2 0
W.. Re Walde, Esq... 2) seat bi 2 2 0
W.. T. Kent, Esq. hy. 55 Pe 2 2 0
R. Dickinson, Bsq.,. > :" ,, . 2 2 0
RK. Mallet; squ tS 2 . ie; a 22 0
S. Carters Bisg., i. 0 tr ae sf 2 2 0
M. O’Conor, Esq., . A: en ee 2 2 0
W. F. Montgomery, M. D., oe ie 2 240)
G. M‘Dowell, Esq, . . . ,, be 2 2 0
Ditto, . . a 1844, 22 0
Rev. Edward Marks, D. De 5 1843, 2 2 0
G. A. Kennedy, M.D.,. . ,, 55 2 2 0
A. Lyle, Esq.,. . Rea ie a3 2 2 0
F. Churchill, M. JD elles Seu al 1844, 2 2 0
B. J. Chapman, Esq., ee tang 3 2 2°70

———

220 10 0 |1227 6 32

XXX1

LO Swe Lee = Sie de
Brought forward, . . .| 22010 0 |1227 6 3§
William Farran, Esq., due March 16, 1843, Zien 20
E. S. Clarke, Esq., ee 5 Pepa AO)
‘John Dalton, Esq., . . 2 2 0
Total Annual Subscriptions and Arrears, —- 226 16 0

Toe Tova. CHARGE,. §..|). . ss £/1454 2 33

XXXii

THE DISCHARGE.

ANTIQUITIES PURCHASED AND REPAIRED.

Armstrong, Robert, drawing of the Magrath
tomb, 18th October, 1844, . .

Davis, E., great seal of George L., Nov. 13th,
1843,

Donegan, John, fae antique ‘gold Hic:
Feb. 19th, 1844,

Gerin, Michael, a bronze antiquity, to a une
3rd, 1843, ..

Glennon, Richard, spear, Oct. 12th, 1843,

Reilly, Peter, shoes &c. to May 20th, 1843,

Ditto, a brass vessel, June 13th, 1843,

Ditto, sundries, Oct. 11th, 1843,

Sharkey, William, gold cinerary boxes and
fibule, -

Underwood, J., he bell, to August 11th,
1843, . . :

Ditto, celt, Oct. “10th, "1843,

Ditto, dirk, Nov. 3rd, 1843,
Total Antiquities purchased and repaired,

Books, PRinTING, STATIONERY, &c.

Allen, J. W., Lithography, &c., to July 4th,
LESS hot as

Curry, Eugene, “Catalopue of Manuscripts,
to April 7th, 1843,

Ditto, ditto, June, 5th, 1843,
Ditto, ditto, July 17th, 1843,
Ditto, ditto, Nov. 6th, 1843,

Ditto, ditto, Nov. 13th, 1843,
Ditto, ditto, from 11th Dec.,

1843, to Feb, 19th, 1844,

Dalton, John, for book on Drogheda, to ee
21st, 1843, ee

Gill, M. H., printing Proceedings ‘and Cir-
culars, mee 31st, 1842,

Ditto, ee Transactions, March
16th, 1843, Pas eemetae i Ta ae oe hs

oS

—

a
x

—_
bo
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14 11

—
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th

37

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&

XXXiil

Brought forward, .

Hanlon, George, for woodcut of — stone
to Nov. 18th, 1843, . .

Hodges and Smith, books, &e. 4 ‘to J une,
1843,

J poeeen and Co., advertising Transactions
to June 30th, 1843, :

Kirkwood, John, printing and engraving,
March, ‘24th, USA te

Mullen, G., book binding, to March 20th,
1843, . . A

Ditto, ditto, Gane 30th, 1848,

Ditto, ditto, Jan. 31st, 1844,

Oriental Translation Fund, subscription for
1842 and 1843, é

Perry and Co., paper, to June 28th, 1843,

Plunket, James, 24 sheets of drawings for
Catalogue of Antiquities, to Dec. 24th,
1843,

Reilly, John, four volume: Gf ne Seer
tions, Feb. 5th, 1844, Jee

Taylor, R. and J. E., twenty Scientific Me-
moirs, Part II., a Jan. 31st, 1843,

Total Books, Printing, Stationery, &e.,

Coats, CANDLEs, O11, &c.

Kenny, M., for stove coals, to July 20th, 1843,
Rathborne, J. & H., for candles, to May A,
US435. |. 4
Todhunter, J., le to March 30th, 1843,
Total Coals, Candles, Oil, &ec.,

CoNnTINGENCIES, &c.

Carriage of parcels, to Nov. 28th, 1843,

Clibborn, E., incidentals, to iss 3rd,
1843,

Ditto, per Soe

Clifford, for gum, to Oct. 23rd, 1843,

elecation 4 in Court of Exchequer, and car
hire, to Dec. 6th, 1843,

Elliot, carriage of parcels, to May 29th, 1843,

Fannin, ditto, May 22nd, 1843,
Ditto, ditto, Jan. 22nd, 1844,
Ditto, ditto, ditto,

Maguire, twine, June 16th, 1843,

Les ds
427 14 11

3.0 0

cs |—
—
~I
—
—

—
—
nr

— —_ oad
i=)

oooceoo ooo
cooooam j=)

(e0)

(eX)
—
TIT) KF Orwnnhd Oo

Lo ishe iat
BYV(ev tle @

718 15 10

XXXIV

Brought forward, . :

Pamplin, William, carriage of parcels, June
26th, 1843, : Baeitiekeee ly ence staan

Patten, J., ditto, Dec. 27th, 1843,

Postages, to June 23rd, 1843, . :

Ditto, Dec. 31st, 1843,

Ditto, ditto,

Postage stamps, to March 25th, "1843,

Power of attorney to Boyle and Co., to sell
Stock,

Stamp on Government ‘Grant, paid Jan. 4th,
1844,

Subscription ‘to Mr. Ryland, to reimburse
his expenses in carrying the Act of 6 & 7
Victoria, j

Total Contingencies, &e. .

Repairs oF Howuss, &c.

Brown, J., cleaning windows, to June 2nd,
NSA SMO Bon copie Wives Snecma ev ete

Ditto, glazing ditto, Feb. 3rd, 1843,

Clibborn, Edward, sundries used in cleaning
house, to July 16th, 1843,

Mullen, Wm., sweeping chimneys, to May
17th, 1843, :

Total Repairs ‘of House, &e.

Repairs OF FURNITURE, &c.

Allen, E., towels, to April 28th, 1843, :

Casey, Paul, repairing locks, to March 20th,
1843, .

Duffy, John, altering fable, to March 10th,
1843, .

Edmundson and Co., for lamps, &e., “to March
11th, 1843,

Kane, B. , removing and cleaning carpet J uly
Ist, 1843, 2 :

Perry and ee laces to J uly 6th, 1842,

Ditto, ditto, June 28th, 1843,

Sharp and Co., ee of clocks, S&C. March
7th, 1843, ;

Surnam, George, repairs, 8 April Ist, 1843,

Total Repairs of Furniture, &c.,

t
=
a2

ee
=o oo iS)

—

i) oo

bo >)

—

nr fa) conto K}§
—

&

SS:
718 15 10

d.

XXXKV

Brought forward, .

Rent, Taxes, Insurance, &c.

Borough rate, made 30th Sept. 1842,
Boyle and Co., allowance for poor rate paid
by them on ‘stable, to Nov. Ist, 1843,

Grand Jury cess, half year, Baster, 1843,
ant” Gs

Insurance at Globe, Dec. 25th, 1844, 5 13 6

Ditto, National, Dec. 26th, 1844,5 13 6

Ditto, ditto, Dec. 25th, 1844,4 2 6

Ministers’ money, to Sept. 29th, 1843,
Parish cess, to Sept. 29th, 1843,

Pipe water, to June 24th, 1843, . . pth
Police tax, to March, 25th, 1843, 2 3 9
Ditto, to Sept. 29th, 1e4sP VP G

Truell, R. H., half year’s rent, to
Aug. Ist, 1843, ea tines amen oe
Ditto, ditto, Feb. Ist, 1844, 52 4

lorzer)

Wide street tax, Easter, 1843, .
Total Rent, Taxes, Insurance,

SALARIES, SERVANTS’ WAGES, &c.

Clibborn, Edward, for one year’s salary as
Assistant Ajeet and Clerk, to March
16th, 1844, :

Conroy, P., delivering notices, to June 8th,
1843,

Dresemion Rey. W. i, Tops year’s s
salary, to 16th March, 1844,

Hamilton, Wm., wages and al-
lowance as porter, to April
29th, 1843, . . Make Aaa ace 2

Ditto, to July 15th, 1843, Sa Osle TS

Ditto, to Nov. 18th, 1843, . . 1117 0

Ditto, Christmas allowances, to
ec 25th. 1B43 05 1 cme ene) 70

Ditto, wages and mea Jan.
15th, 1844, 5 SAE oo 4

Ditto, ditto, Feb. 19th, "1844, 3 o7L0

——$—$<—_ ___—__|

ge

{

fg. od:

=
~I
DWAAD

33 14 0

174 15 6

911 10 2

XXXVI

TRS:
Brought forward,. . .| 174 15
£s. d.
Kane, Bernard, extra evening por-
ter, April 3rd, 1843, . . 8 0
Ditto, ditto, June 26th, 1843, i age ACG)
Ditto, ditto, Feb. 29th,
1844, Od A ane 0
3 10
Kane, Robert, M. D., Secretary of Council,
year’s salary, to March 16th, 1844, . .| 21 0
Lockett, J., for porter’s clothes,
to March 29th, 1843, ... 319 8
Ditto, jacket, Aug. 10th, 018 0
————————| AL ig
Mac Cullagh, J., Secretary of Academy,
year’s salary, to March 16th, 1844, . . 210
Pim, J.jun., Esq., Treasurer, year’s ‘salary,
to March, 16th, 1844, : 21 0
Singleton, J., for porter’s hat, to April 26th,
1843, . a 0 16
Sinton, Thomas, eee Clerk,
24 weeks, to March 25th, 1843, 210 0
Ditto, 4 weeks, June 13th, 1843, 4 0 O
Ditto, 3 weeks, Dec., 14th, 1843, 3 0 O
9 10
Smith, John, assistant porter
from March 17th to ae
20th, 1843, . . Oe OS 6
Ditto, to J une, 3rd, 1843, oe eee SM 6
Ditto, from July 29th to Jan.
Oth, 1844, . . 1 0 0
Ditto, from Jan. ‘29th es Feb.
13th, 1844, .... 010 0
3 18
Wiseheart, J., clerk at sae
to April 25th, 1843, 015 O
Ditto, June 13th, 1843, . 015 O
Ditto, from 14th Nov., 1843,
to Jan. 8th, 1844, : 010 0
Ditto, from 22nd Jan. to Feb.
12th, 1844, 0 5 0
2 6

Total Salaries, Servants’ Wages, &c.,

£ s. ad.
911 10 2

262 12 2

1174 2 4

XXXVIi

d. | £ &. d.
Brought forward, . | sac ta bg ee melee
|
THREE AND A HALF PER CENT. GOVERNMENT
STOCK PURCHASED.
25, THA
28 15 4 cost 29 4
THREE PER CENT. CONSOLS PURCHASED.
eg As
22 4 2 cost 20 17 3
CuNNINGHAM FouND.
West and Son, gold medal, to June 24th,
SL Ue feet AN tere rc hders sito sme, 19 15 10
THE TOTAL DISCHARGE,. . 1243 16 9
Balance in favour of the Public, . . | 210 5 64
The Charge as above, 1454 2 35
STATE OF THE BALANCE.
1843. £. §: a:
31st March. In Bank of Ireland, 3 aS 209) <6
In Treasurer’s hands, as per this Account, 019 33
Balance as above, . £210 5 64

The Treasurer reports, that there is to the credit of the Academy in
the Bank of Ireland, £1117 ls. 10d. in Three per Cent. Consols, and
£1643 19s. 6d. in Three and a half per Cent. Government Stock, the

latter known as the Cunningham Fund.
(Signed), RosBerT BALL,

31st March, 1844. Treasurer.

.

oy nd Coes

moray

Seda etn

Se

—
—_

ivi; yk Ae
i Su) Tae Os ee
Sovrtoo te saglik

rest et:

No. V.

METEOROLOGICAL JOURNAL

COMMENCING
lst JANUARY, 1843, anp ENDING 3lst DECEMBER, 1843,
BY

GEORGE YEATES.

——_

THE accompanying paper is a Meteorological Journal,
shewing the maximum and minimum points the Thermome-
ter indicated, the Height of the Barometer, and the Amount
of Rain.

The first column gives the thermometric results; the
second gives the barometric pressure, in inches and thou-
sands of-an inch; the third gives the amount of rain that
has fallen, in thousands of an inch. These observations
have been made as nearly as possible to 10 o'clock, a.m., each
day throughout the past year. They are tabulated each
month, so as to shew the quantity of rain that has fallen
during that period. Twelve months are then made up,
which shews the year’s rain to be 23.440 inches.

It may not be out of place to mention the description of
instruments which were made use of on the occasion.

The temperature was observed with a pair of Dr. Ruther-
ford’s self-registering thermometers. The barometer is simi-
lar to one first made by me for Dr. Apjohn, and under his
directions ; it is a very simple instrument, and extremely con-
venient for daily or rapid observations ; there is no floating
gauge used, nor is it necessary to make any observation at the
cistern; the fluctuations in the height here are nearly all
avoided, by very much increasing the area of the cistern over

h

xl

that of the tube; in this instance it is as 1 to 500, the diameter
of the tube being ;3,; it is graduated to the five-hundredth of
an inch, and reads as 1000. From this arrangement it is evi-
dent that any deviation produced in the surface of the cis-
tern, from the rise or falling of the mercury in the tube,
will be inappreciable, and does not amount to the errors of
observation. The rain-gauge is also similar to one which I
made for Dr. Apjohn at the same period. In superficial area
it measures 1000 inches; the rain is collected in a vessel
which is graduated into cubic inches, consequently, when
one inch by measure is indicated by the graduations, it de-
notes that 75/35 of an inch of rain has fallen on the surface
above, and as the receiver is graduated into cubic inches all
the way, it gives at once the decimal, until you come to 1000
cubic inches, which is equivalent to 1 inch of rain: this gauge
admits of the most simple verification.

xli

JANUARY.

Thermometer. Barometer. Rain. Wind.
Max. Min.
1 520° 33° 30.350 Aa Nae S. W.
2 | 40 | 34 30.150 | ... | S.W.byS.
S383 | 332 30. .. . | N.W.by W.
4 46 29 29.950 151 N. W.
5 40 35 30.104 080 N. W. by W.
6 47 3d 30.150 030 W.
7 A8 39 29.820 -009 W.

8 44 32 29.260 -150 W.
9 Al 30 29.470 050 S. W.
10 | 44 | 82 29.100 200 W.S. W.

11 36 29 29.010 .075 W.
12 |“3s6 | 29 29.016 1.050 W.
rs ese | 18h 28.100 .385 S. Ww.
14a) 32. | 180 28.726 .080 N. W.
15 35 26 28.950 a Reber: N.E.
16 37 26 29.850 .100 N. E.
17 44 30 30.100 -030 N.W.
18 48 42 30.314 CoO ores W.
19 | 49 | 42 30.400 sae Se W.
20 48 Al 30.120 aera te N. W.
21 | 46 | 38 29.500 sale me N.W..
22 48 42 29.755 Blew f S. W.
23 49 40 29.580 .004 Ss. W.
24 49 44 29.610 100 S.
25 49 Al 29.960 ARS a8 S. W.
26 49 46 30.050 .035 S. W.
27 52 46 29.864 at WE W. by S.
28 53 49 29.770 .025 W.
29 52 44 29.850 035 W. by S.
30 53 46 29.750 BS str S. W.
dl 48 48 29.550 sie W.

h 2

OSCONA a FO bY

=
bo — ©

ee
o Bm

DOoNNN NY Ke eS eS

Thermometer.

Max.
490°
47
Al
40
39
40
43
43
43
A2
40

Min.

39

xlii

FEBRUARY.

Barometer.

29.650
29.600
29.300
80.000
29.970
80.150
80.200
30.154
30.162
80.146
30.140
30.170
30.120
29.860
29.530

29.284 -

29.596
29.636
29.446
29.224
29.252
29.348
29.440
29.610
29.716
29.700
28.371
29.420

Rain. Wind.
.060 W. by S.
.095 W.
.130 N. W.
003 N. by W.
.008 N. W.

é N. by W
.040 N. E.

N. E.

: N. E.
-008 E, N. E.
.006 E.
.020 E.

E.
5 E.N.E
N.E
N. E.
N.N.E

take E. by N
020 E.
.675 S. E.

145 S. E.
090 E.
210 E.
115 E. S. E.
E. S. E.
E.
.010 E.

oCmANoa kk WO ND =

ct @ bD bb bO bO b WO WD WD WD DD BH ew BM MR RM ae ee
FHKE SCODNATRWNKFOSOHANOARWHN HEH SD

Thermometer.

Max. Min.
43° | 340°
45 28
44 32
42 27
39 33
4] 32
42 33
43 30
43 39
42 35
42 35
55 44
54 38
47 39
46 38
48 39
57 40°
56 41
54 42
53 4]
55 46
59 46
59 45
55 46
52 45
53 39
33 38
53 37
53 37
52 39
57 45

xliii

MARCH.

Barometer. Rain.
29.350 -100
30.070
30.216
30.468 meena
29.970 008
30.150
30.200
30.150
30.160 So giise
30.140 .060
30.140 -040
29.793" 025
29.650 = otic
29.518 .430
29.900 .070
29.826
29.620
29.892 Saaae
29.846 055
29.480 ERS ta
29.250 .085
29.200 .160
29.410 380
29.562 .100
29.850 -130
29.900
29.750
29.328
29.976
29.478
29.320

Wind.

E. by N.

xliv

APRIL.
Thermometer. Barometer. Rain. | Wind.
Max. Min. pire pares

1 59° 47° 29.250 015 S. E.

2 58 46 29.350 145 W.

3 62 44 29.700 030

4 58 40 29.200 130 W.

5 | 58 | 47 29,300 002 W. by S.

6 64 47 29.600 006 W.

7 56 46 29.320 465 S. W.

8 61 42 29.500 100 W.

9 59 42 29.774 090 W.
10 46 32 30.040 002 N. W.
11 49 33 30.150 090 N. W.
12 50 33 30.050 N. W.
13 54 32 30.076 : N.

14 53 40 29.950 010 N. W.
15 61 42 29.500 100 N. E.
16 54 44 29.950 N. W.
17 67 40 30.050 N. E.
18 62 44 30.050 E.

19 64 48 29.900 z E. by N.
20 67 48 29.650 .020 E.

21 65 46 29.750 055 N. W.
22 54 44 29.760 025 Ww.
23 55 40 30.010 .020 W.
24 62 42 29.970 350 N. E.
25 | 53 | 46 29.620 270 W. by N
26 53 85 29.600 155 N. by W.
27 58 36 29.850 195 W. by S
28 58 4l 29.650 340 W. by S
29 55 42 29.720 030 E. by N
30 | 63 | 43 30.020 E. by N

ONION RWDH KH

Thermometer.
Max. Min.

66° 43°
67 47
69 44
63 42
64 37
60 38
58 Al
59 42
62 42
67 46
62 45
64 50
62 50
67 43
64 49
67 49
54 47
60 44
66 46
64 45
51 46
55 47
59 47
62 43
60 44
63 50
60 48
60 48
62 45
63 46
62 50

xlv

MAY.

Barometer.

30.250
30.250
29.960
29.700

20.578
29.600
29.600
29.716
29.950
30.150
30.150
39.250
29.826
29.750
29.500
29.600
29.800
30.050
19.968
29.620
09.560
29.700
29.722
29.570
29.964
29.550
29.530
29.750
30.050
30.016
29.800

Rain.

020°

060

.016

002

.140

.205

xlvi

JUNE.
Thermometer. Barometer. Rain. Wind.
Max. Min. i

1 65° 540° 29,468 .300 E,

2 63 52 29.270 .268 S. W.

3 62 50 29.370 .024 N. W.

4 53 45 29.700 -240 W.

5 54 44 29.814 .590 W.

6 54 42 30.038 .035 N. W.

7 59 A6 29.600 01 5 W.

8 59 49 28.900 125 W..

9 61 49 29.400 .080 N. W.
10 62 48 29,944
11 63 49 30.210 N. W.
12 63 45 30.200 N. E.
13 71 50 30.128 Aiko. ae
14 70 49 30.050 .360 E. by N.
15/65. |. 53 30.050 .240 E.
16 65 53 30.114 E.
17 72 51 30.150 E.
18 70 53 30.128 E.
19 80 Bf 30.050 N. E.
920 72 51 30.250 N. E.
21 74 55 30.150 Ww.
92 65 55 30.150 N.
23 69 49 30.150 E.
24 74 52 30.130 W.
25 80 56 30.074 S. E.
26 74 52 30.300 S. E.
27 75 50 29.900 N. E.
28 78 55 29.850 ati W.
29 77 50 29.950 © Set W.
30 65 52 29.950 S. W.

JULY.
Thermometer. Barometer. Rain. | Wind.
Max. Min.

1 68° 55° 30.000 BR ut S. W.

2 72 56 29.864 .080 W.byS

3 73 57 29.850 E,

4 74 54 30.000 thet es E.

5 74 53 29.700 .120 W.

6 63 52 29.720 110 S. E.

7 70 53 29.760 .020 5. BE.

8 70 54 29.050 .020 W.

9 \"68 | 51 30.150 N.
10 71 54 30.250 N. E.
11 69 49 30.564 4 po ge N. W.
12 71 53 30.250 .120 W.
13 67 56 30.200 .380 W.
14 68 53 30.200 105 W.
15 65 58 30.140 W.
16 70 53 30,250 acy Be W.
17 71 58 30.250 .012 W.
18 76 58 29.950 .106 Ss. W.
19 74 54 29.850 N. W.
20 79 50 29.800 W.
21 65 | 58 29.800 W.
22 65 55 29.760 Sars ton Ss. W.
23 66 50 29.750 .020 N. W.
24 69 48 30.160 N. W.
25 69 54 30.250 AES Sot S. W.
26 -742 61 30.250 .060 W. by S.
27 72 54 30.150 .030 N. W.
28 67 53 30.006 115 W. by S
29 66 55 29.634 2315 W.by S.
30 68 52 29.700 -050 N. W.
31 68 52 30.000 110 N. W.

xl vii

CONOaM FR SO DY =

GC 0 bt Ww WH WD DD DD & BS Be ew eee ee
mMODCDOAN OU KE WONRK OH MANDEL WDD KO

Thermometer.

Max.
66°
70
70
68
64
75
74
70
73
74
77
73
73
73
67
65
74
78
78
78
71
74
73
71
70
71
71
72
71
70
73

Min.
57°
56
54
53
51

xl viii

AUGUST.

Barometer.

29.900
29.500
29.420
29.560
30.000
30.100
30.150
30.200
30.250
30.324
30.350
30.270
30.250 -
30.050 .
30.000
30.108 :
30.200 .
30.200
29.950
29.908
29.600
29.370
29.750
29.700
29.850
29.750
30.660
29.700
30.078
30.200
30.200

Rain. Wind.

- S. W.
220 W.

170 S. W.
280 W.
080 W
018 W.
: Ss. W.
110 S. by W.
W.
S. W.
S. by E.
E.
S. E.
.040 E.
N. E
E.
S. E.

: E. by S
.060 N. E.

By es N. E.
195 Ss. W.

ie S.
175 S. W.
.090 S. W.

Ss.

. S.
.030 S. E.
.073 N. W.

N. E.
S. W.

xlix

SEPTEMBER.
Thermometer. Barometer. Rain. Wind.
Max. | Min.

1 72° A480 30.250 E.

2 72 68 30.410 E.

3 74. 61 30.300 S. E.

4 74 51 30.500 N. E.

5 73 48 30.500 S.

6 74 49 30.370 W.

7 76 50 30.300 Ww.

8 80 56 30.272 E.

9 76 58 30.200 RNS 3 E.
10 75 59 30.000 .010 E.
11 67 53 29.950 .270 S. E.
12 70 46 30.400 S. W.
13 72 51 30.220 E.
14 66 50 29.958 a ae N. E.
15 66 o7 29.850 .065 W.
16 65 57 30.000 Ww.
17 64 57 30.150 E.
18 68 55 80.100 ai Su ger N. E.
19 70 55 30.300 035 E.
20 69 53 30.150 Ss.
21 69 58 30.300 N. E.
22 67 56 30.922 W.byS
23 64 45 30.624 N.
24 61 53 30.600 W.
25 62 48 30.450 N. W.
26 60 46 30.300 N. W.
27 57 Al 29.900 ees N. W.
28 54 35 30.000 .007 W.
29 54 45 30.100 Suerte W.
30 62 48 29.950 .250 W.

OCTOBER.

COND Oo FR O&O LO —

10

Thermometer. Barometer. Rain. Wind.

Max. Min.

63° 56° 30.050 etre W.
64 51 30.150 240 W.
61 49 30.100 | 004 W.
62 53 30.200 010 W.
69 52 29.950 te W. by S
68 57 29,500 - 060 W. by S.
70 57 29.500 .025 N. W.
64 61 29.850 510 N.

66 44 29.520 145 W.
58 40 29.870 025 Ss. W.
56 46 29.760 330 W.
54 |) 98 29.410 250 N. W.
00 37 29.690 040 S. W.
50 32 29.810 008 N. W.
49 30 29.870 W. by N.
49 33 29.750 ess N. W.
46 30 29.664 005 N. W.
46 35 29.618 140 W.
45 30 30.122 W. by N.
66 30 30.412 ovis W.
52 40 30.050 130 W.
55 44 29.810 .025 S. W.
58 46 30.050 . W.
55 48 29.600 -060 S. W.
54 37 29.430 -.600 W.
47 34 29.610 W. by N.
47 3l 29.400 Pp ti E. 3
46 3l 29.460 .420 W.
46 3] 29.500 : W. by S
44 32 29.400 .075 W.
44 30 - 29.550 -200 W.

|

omarnarhwnd re

Thermometer.

Max, Min.

45° 33°
48 31
52 42
55 43
54 35
57 43
55 45
50 37
43 32
49 41
52 44
49 44
48 at
45 35
44 31
44 35
50 40
48 37
44 34
48 34
50 42
54 40
40 38
46 34
- 44 32
53 42
54 48
ol 44
54 39
52 39

NOVEMBER.

Barometer.

29.650
29.800
29.400
29.500
30.030
29.820
29.700
29.716
29.916
29.400
30.050
30.120
30.250
30.320
30.150
30.150
29.600
29.330
29.460
29.580
29.350
29.350
29.490
29.470
29.450
29.300
29.450
30.100
30.450
30.100

Rain.

ii

DECEMBER.

Thermometer. Barometer. Rain. Wind.
Max. Min.

1 oO 59° 30.120 . W.

2 50 39 30.170 -004 W.

3 51 44 30.350 -004 S. W.

4 52 43 30.270 -003 8. W.

5 \We2 | 45 29.900 A W. by S

6 51 4] 30.350 -040 W.byS

7 | 53 | 43 30.100 012 W. by S

8 53 44 30.300 012 W.

9 640 1° 45 30.296 : W.
10 52 46 30.150 . W.
1] 49 36 30.100 -002 S. E.
12 50 45 30.350 -050 E. by §
13 50 43 30.320 -003 W. by S.
14 51 45 30.430 Ss. W.
15. NSg | Ae 30.350 S. by W.
16 | 50 | 48 30.450 a ie W. by S.
17 54 45 30.460 -004 S. W.
is | 50 | 43 30.450 W. by S.
19 49 44 30.300 5. W.
20 52 46 30.150 S. W.
21 53 4] 30.300 E. by N.
22 | 55 | 42 30.300 E. by N
23 54 45 30.250 ei S. by W.
24 57 53 30.400 -004 S. W.
25 | 56 | 48 30.310 E.
26 51 4] 30.350 N.W.
27 50 42 30.424 Was. We
28 51 47 30.460 8. E.
29 50 46 30.350 W. S. W
30 46 44 30.150 Wiss. Wi
31 50 43 30.100 WS.

hii

GENERAL RESULTS.

Amount oF Rain. Mean Temp.
Inches.

SECRET URE ct. <bte 4 pid one ow OOD op, AO
BP CBEMAGY iS vol e4 sche ok eee we L68S | 6 4. Be
Vern CHineseeniera nena ture oa Ue ere Mia GABA: alo ade? S
REPEC MC SE shy at ts lays oly sp gee ign een osOSeds: See. elite. | 2 AIRE.
Pye on Si) vic, s os shacai Re Liv eeaeleanl AAA G yk San GRE
CSS eBay 02-5 Uae), SM Nias SDM OT De og et ome
2) CLS Oi a oe APR DU eae oc a oP dee 7 MPa re
PMOLCMStay se Tone) “pln enthe! ss name ee Mag ead, Bab? 5 Sera gD
DEDEGIRDCE, fas 8h iam a0 es ae ie Pee oe MO HT lect ta eee
Wesabers (xtiey ss ah ier een eee enc OL eco uae (eee OO
INOVeMDER, © osu spac yes Sones earn we e998) ree 2 AG
Wecemberve us Se lee Ce aeeO a als oll

23.440

BAROMETER.

Greatest pressure, August27, . . .. . . . =. . 30.660
Lowest point, January 13, . ... . . . + . . « . 28.100

THERMOMETER.

Maximum, September 8,. . . . . . + + 80°
Minimum, February 16, . . -.... .- 2i

2, Grafton-street.

THE

ROYAL IRISH ACADEMY,

Marcu 16, 1843.

Watroness:
HER MOST SACRED MAJESTY
THE QUEEN.
Visttor :

HIS EXCELLENCY THE LORD LIEUTENANT OF
IRELAND.

President :
SIR WILLIAM ROWAN HAMILTON, LL. D.

DV ice-WPresidents.

Rev. Humesrey Luoyp, D. D.

Rev. JAMEs HentuHorn Topp, D. D.
Rev. JosepH Henperson Sincer, D. D.
James Apsoun, M. D.

COUNCIL.
Committee of Science.

Rey. Franc Sapzeie, D. D., | James Mac Cuzaes, LL. D.
Provost. Rev. Wo. D. Sapte, A. M.

Rey. Humearey Luoyp, D.D. | Rosert Batt, Ese.

James Apsonn, M. D. Rosert Kang, M. D.

A
Committee of Polite Literature.

His GRAcE THE ArcusisHop or | Rev. Wa. H. Drummonn, D. D.

DUBLIN. Rev. Cuas. R. Eirineton, D.D.
Rev Joserx H. Sincer, D. D. Rev. Coartes W. WaLzL, D. D.
SamugEt Lirron, M, D. JoHN AnsTER, LL. D.

Committee of Antiquities.

GrorGE Petrin, Ese., R.H.A. | Josepn H. Smiru, Esa.
Rey. James H. Topp, D. D. James Pim, Jun., Esa.
Henry J. Moncx Mason, LL.D. | Captain Larcom, R. E.
SAMUEL FEeRGusoN, Esq.

OD hicers.

Treasurer.—J AMES Pim, Jun., Esq.

Secretary of the Academy.—J ames Mac Cuuuaes, LL. D.

Secretary of Council_Rosert Kanes, M.D.

Secretary of Foreign Correspondence.—Rev. Humparey Luoyp, D.D.
- Librarian.—Rev. Witt1am H. Drummonp, D. D.

Clerk and Assistant Librarian —EDWARD CLIBBORN.

Notr.—The Members of the Academy are particularly requested
to communicate to the Assistant Librarian, any corrections in this
list which they may consider necessary.

MEMBERS.

The Names of Life Members are marked with an Asterisk.

* Adare, Edwin Viscount, M. P. F.R.S. F.R.A.S. Dun-
raven Castle, Glamorganshire, and 76, Eaion-square,
London.

* Andrews, Thomas, M.D. 65, Chester-square, Belfast.

* Armstrong, Andrew, Esq., A.M. 17, College.

* Arthur, Thomas, Esq.

* Ashburner, John, M.D. 55, Wimpole-street, London.

Abell, Abraham Esq. Cork.

Adams, Robert, Esq. V.P. Royal College of Surgeons.
11, Great Denmark-street.

Allman, George James, Esq. Grattan-street.

Andrews, William, Esq., Sec. Natural History Society.
18, Letnster-street.

Anster, John, LL.D. 5, Lower Gloucester-street.

Apjohn, James, M. D. Professor of Chemistry, Royal Col-
lege of Surgeons. V. P. Geological Society of Dublin.
—Vicxz-Presipenr. 28, Lower Baggot-street.

Armstrong, William, Esq. 5, Lower Dominick-street.

* Bailie, Rev. James Kennedy, D.D. <Ardtrea, Stewarts-
town.

* Bald, William, Esq., F. R. S. E.

* Ball, Robert, Esq. See. Royal Zoological Society of
Ireland. Local See. Botanical Society of Edinburgh.
3, Granby-row.

* Bateson, Sir Robert, Bart., M. P. Belvoir Park, Belfast.

* Bateson, Robert, Esq., D.L. Belvoir Park, Belfast.

b

iv
* Beaufort, Francis, Esq., F. R.S. F.G.S. F.R.A.S., &e.
Captain R. N. Admiralty, London.
* Benson, Charles, Esq., M.D. Professor of Physic, Royal
College of Surgeons. 34, York-street.
* Bergin, Thomas F., Esq., 5, Westland Row.
* Blacker, Stewart, Esq. 20, Gardiner’s-place.
* Blood, Bindon, Esq. Edinburgh.
* Bolton, William Edward, Esq. 5, Nelson-street.
* Botfield, Beriah, Esq., M.P. London.
* Boyton, Rev. Charles, D.D. Tullyagnish, Letterkenny.
* Boyle, Alexander, Esq. Killiney, and 35 College-green.
* Bruce, Haliday, Esq. 37, Dame-street.
Ball, John, Esq. 85, Stephen’s-green, South.
Banks, John T., M.D. 8, Lower Merrion-street.
Barker, Francis, M.D. Professor of Chemistry, Univer-
sity of Dublin. 22, Lower Baggot-street.
Barker, William, M. B. 8, Hatch-street.
Barrington, Matthew, Esq. 50, Stephen’s-green, East.
Beatty, Thomas E., M.D. 17, Merrion-square, North.
Beauchamp, Henry C., M.D. 114, Lower Baggot-st.
Betham, Sir William, Knt. Ulster King of Arms. F.S. A.,
F.R.A.S., V. P. Royal Dublin Society. Stradbrook
House, Black Rock.
Blacker, William, Esq. Armagh.
Bolton, Chichester, Esq. 1, Upper Merrion-street.
Booth, Rev. James, A.M. Bristol.
Borough, Sir Edward, Bart. 18, Leinster-street.
Brady, Right Hon. Maziere, A.M. Lord Chief Baron.
61, Harcourt-street.
Burrowes, John, Esq. 1, Herbert-street.
Burton, Frederick W., Esq., R.H.A. 65, Harcourt-street.
Butcher, Rev. Samuel, Fellow of Trinity College. College.
Butler, Rev. Richard. Trim.

* Callwell, Robert, Esq. 22, Herbert-place.

Vv

* Campbell, William W., M.D. Port Stewart, Coleraine.

* Carmichael, Andrew, Esq. 24, Rutland-square, North.

* Carmichael, Richard, Esq. 24, Rutland-square, North.

* Carne, Joseph, Esq., F. R. S. F.G.S. Penzance.

* Carson, Rev. Joseph, A. M., Fellow of Trinity College.
College.

* Caulfield, Hon. Henry. Hockley, Armagh.

* Chamley, George, Esq. 6, Belvidere Place.

* Charlemont, Francis William Earl of. Charlemont House.

* Chetwode, Edward Wilmot, Esq. Woodbrook, Portarlington.

* Clare, John Earl of. Mount Shannon, Killaloe.

* Clarkes Thomas, Esq. 123, Lower Baggot-street.

* Clendinning, Alexander, Esq. Westport.

* Colby, Lieut.-Colonel Thomas, Royal Engineers, LL. D.
F.R.S.L. and E. F.G.S. F. R.A.S. &e. Ordnance
Survey Office, Phenix Park, and Tower, London.

* Cole, Owen Blayney, Esq. Merrion-square, North.

* Colvill, William C., Esq. 6, Bachelor's Waik.

* Conroy, Edward, Esq. Kensington, London.

* Corballis, John R., Esq. 15, Baggot-street.

* Cork, Cloyne, and Ross, Right Rev. Samuel Kyle, D. D.,
Lord Bishop of. Cork.

* Coulter, Thomas, M.D. College.

* Courtney, Henry, Esq. 24, Fitzwilliam-place.

* Croker, Thomas Crofton, Esq., F.S.A. London.

* Croker, Charles P.. M.D. 7, Merrion-square, West.

* Cubitt, William, Esq., F.R.S. F.R.A.S. 8, Great
George-street, Westminster, London.

* Cusack, James W., Esq., M. D., Sec. Royal College of
Surgeons. 3, Kildare-street.

Cane, Arthur B. Esq. 60, Dawson-street.
Cane, Edward, Esq. 60, Dawson-street.
Carr, George, Esq. 18, Mountjoy-square, South.
Carter, Samson, Esq. Kilkenny.
Cash, George, Esq. Broomfield, Malahide.
b2

*

*

Vi

Cather, Thomas, Esq. 20, Blessington-street.

Chatto, Rev. Robert, A.M. Whickham Cottage, Gates-
head.

Chapman, B.I., Esq. Killua Castle, Athboy.

Churchill, Fleetwood, M.D. 136, Stephen’s-green, West.

Clarke, Edward 8., Esq. 18, York-street.

Conway, Frederick W., Esq. Rathmines, and 11, Trinity-
street.

Cooper, Edward J., Esq. M. P. Markree Castle, Colooney.

Cooper, Jonathan Sisson, Esq. 15, Upper Merrion-street.

Courtenay, Rev. Reginald.

Crampton, Hon. Justice, LL. D. 50, Baggot-street.

Crampton, Sir Philip, Bart. President, Royal Zoological
Society of Ireland. 3, Merrion-square, North.

Crawford, Francis, Esq. 51, aro ae

Culley, Robert, Esq. Kingstown.

Davis, Charles, M.D. 33, York-street.

D’Olier, Isaac M., Esq. Booterstown.

Drummond, Rev. William Hamilton, D. D.—Liprarian.
28, Lower Gardiner-street.

D’ Alton, John, Esq. 48, Summer-hill.

Darley, Frederick, Esq. 25, Lower Mitzwilliam-street.

Davidson, John, Jun., Esq. Armagh.

Davy, Edmund, Esq., F.R.S. Professor of Chemistry,
Royal Dublin Society.

Dickinson, Robert, Esq. 79, Lower Gardiner-street.

Disney, Ven. Brabazon William, Archdeacon of Raphoe.
16, Fitzwilliam-square, South.

Dixon, Rev. Robert Vickers, A.M. Fellow of Trinity
College. 10, College.

Downes, George, Esq., A.M. Black Rock.

Doyne, Charles, Esq. Newtown Park, Black Rock.

Drennan, William, Esq. 4, Eccles-street.

Drury, William V. M.D. Edinburgh.

Vii
Dublin, Most Rev. Richard Whately, D. D. Archbishop
of. V.P. Royal Zoological Society of Ireland. Pa-
lace, Stephen’s-green, North.
Dunlop, Durham, Esq. 6, Lower Abbey-sireet.

* Elrington, Rev. Charles Richard, D. D., Regius Professor

of Divinity, University of Dublin. Trinity College.

Edington, William, Esq. Treasurer of the Geological So-
ciety of Dublin. 18, Leinster-street.

* Fitzgerald and Vesci, Right Hon. William Vesey Lord,
D.C.L. F.R.S. Merrion-square, North.
* Fitzgerald, Rev. Michael.
* Fitzgerald, Right Hon. Maurice, Knight of Kerry.
* Fitz Wygram, Sir Robert, Bart. Connaught-place, London.
* Fortescue, Thomas, Esq., M. P. Ravensdale-park, Flurry
Bridge.
* Foot, Simon, Esq. Hollypark, county of Dublin.
* Frazer, R. Murray, Esq.
Fitzgibbon, Gerald, Esq. 29, Gloucester-street, Upper.
Farran, William, Esq. 16, Abbey-street.
Ferguson, Hugh, M.D. 62, Sackviille-street.
Ferguson, Samuel, Esq. 56, Lower Dominick-street.
Ferrier, Alexander, Jun., Esq., A.M. Rathmines.
Finlay, John, LL.D. 31, North Cumberland-street.
Frazer, George Alexander, Esq. Lieutenant R.N.

* Goff, Rev. Thomas. Black Rock.

* Gough, George Stephens, Esq., A. B.

* Graves, Rev. Charles, A.M. Fellow of Trinity College.
2, College.

* Grierson, George A., Esq. Queen’s Printing Office, 19,
Essex-street, West.

* Griffith, Richard, Esq., F.R.S.E. F.G.S. V.P. Geolo-
gical Society of Dublin. 2, Fitzwilliam-place.

vill
Gayer, Arthur E., LL.D. 47, Upper Mount-street.
Gore, William R., M.D. Limerick.
Graves, Robert J.. M.D. King’s Professor of the Insti-
tutes of Medicine. 4, Merrion-square, South.
Gregory, William, M.D. F.R.S.E. Aberdeen.
Gregory, Very Rev. James, A. M. Dean of Kildare. 17,
Fitzwilliam-street, Upper.
Grimshaw, Wrigley, M.D. 11, Molesworth-street.
Grubb, Thomas, Esq. 1, Upper Charlemont-street.

* Hamilton, Sir William Rowan, Knt., LL.D. F.R.A.S.
Astronomer Royal of Ireland, and Andrews’ Professor
of Astronomy in the University of Dublin.— PresipEnr.
Observatory, Dunsink.

* Hanna, Samuel, M.D., A.M. 18, Granby-row.

* Hardiman, James, Esq. Galway.

* Harrison, Robert, M.D. Professor of Anatomy and
Surgery, University of Dublin. 1, Hume-street.

* Hart, Andrew Searle, Esq., LL.D. Fellow of Trinity Col-
lege, College.

* Haygarth, William, Esq.

* Hill, Edward, Colonel.

* Hill, Lord George A. Updown House, Sandwich.

* Hincks, Rev. Thomas, LL.D. Belfast.

* Houston, John, Esq., M. B. 31, York-street.

* Hudson, Henry, Esq., M.B. 24, Stephen’s-green, North.

* Hume, Arthur, Esq. 63, Dawson-street.

* Hutton, Robert, Esq., F.G.S. Putney Park, Surrey, and
15, Manchester Buildings, London.

* Hutton, Thomas, Esq., F.G.S. V. P. Geological Society
of Dublin, Treasurer of the Royal Zoological Society
of Ireland. Elm-Park, and 116, Summer-hill.

* Hutton, Henry, Esq. 18, Gardiner’s-place.

Hamilton, Charles William, Esq., F.G.S. Sec. Geological
Society of Dublin. 13, Mountjoy-square, East.

*

a

*

*

ix
Hamilton, John, Esq. 13, Nassau-street.
Hardy, Simeon, Esq. 15, Fitzwilliam-square, North.
Hardy, Philip Dixon, Esq. Greenfield Lodge, Stillorgan,
and 3, Cecilia-street.
Hart, John, Esq., M. D. V. P. Royal Zoological Society
of Ireland. 3, Ely-place.
Hemans, G. W., Esq., C. E. 22, Marlborough-st.
Hill, William, Esq. Donnybrook, Doneraile, Cork.
Hodder, Thomas, Esq., R. M. Kildare-street.
Hogan, William, Esq. A.M. Fitzwilliam-place.
Homan, Rev. John, A. M. Seapoint House, Black
Rock. :
Horgan, Rev. Matthew. Blarney, Cork.
Hudson, William E. Esq. 39, Upper Fitzwilliam-street.
Hughes, William John, Esq. 49, Westland-row.
Hutton, Edward, Esq., M.D. 29, Gardiner’s-place.

Jessop, Frederick Thomas, Esq. Doory Hall, Longford.

Johnson, Hon. Justice, LL.D. 45, Harcourt-street.

Jones, Lieut.-Col. Harry D., M.I.C.E. ora Villa,
Donnybrook, and Custom-house.

Jacob, Arthur, M. D. V. P. Geological Society of Dublin.
Professor of Anatomy, Royal College of Surgeons.
23, Ely-place.

James, Sir John Kingston, Bart. 9, Cavendish-row.

Jellett, J. H., Esq., Fellow of Trinity College. College.

Jennings, Francis M., Esq. Cork.

Jones, Robert, Esq. Fortland, Dromore, West.

Joy, Henry Holmes, Esq., A. M. ‘Treasurer of the Geo-
logical Society of Dublin. 17, Mountjoy-square,
East.

Kelly, Dennis Henry, Esq. Castle Kelly, Mount Talbot,
Roscommon.

* Kiernan, George, Esq. London.

x

* Knox, Rev. Thomas. River Glebe, Toomavara, Nenagh.
* Knox, George J., Esq. 1,-Maddox-street, London.

* Knox, Rev. H. Barry. Deanery House, Hadleigh, Suffolk.
* Kyle, William Cotter,.LL.D. 8, Clare-street.

Kane, Robert, M.D. Professor of Natural Philosophy,
Royal Dublin Society—Srcretary oF CounciL.
Black Rock.

Kelly, Thomas F., LL. D. 88, Lower Mount-street.

Kennedy, George A., M.D. President of the King and
Queen’s College of Physicians.. 25, Talbot-street.

Kent, William T., Esq. 37, College-green.

King, Hon. James. Mitchelstown Castle, Mitchelstown.

Kingsley, Jeffries, Esq. 11, Westmoreland-street.

Knox, Rev. Robert. See House, Limerick.

* Larcom, Thomas A., Captain, R.E. Ordnance Survey
Office, Phenix Park.

* Lardner, Rev. Dionysius, LL. D. F. R. S. L. and E.,
F.R.A.S.

* La Touche, David Charles, Esq., Bank, Castle-street.

* La Touche, William Digges, Esq. 3, Fitzwilliam-square,
East.

* Leader, Nicholas P., Esq. Dromagh Castle, Castle Mills,
Cork.

* Leitrim, Rt. Hon. Nathaniel Earl of. Killadoon, Celbridge.

* Lenigan, James, Esq. Castle Fogarty, Thurles.

* Litton, Samuel, M. D. Professor of Botany, Royal Dublin
Society. 10, Lower Gloucester-street.

* Lloyd, Rev. Humphrey, D. D., F.R.S., Fellow of Trinity
College, Prof. Nat. Phil. Vicz-PresipENT AND SzE-
CRETARY OF FoREIGN CoRRESPONDENCE. 35, College.

* Luby, Rev. Thomas, D. D., Fellow of Trinity College.
15, College.

La Touche, George Digges, Esq. 91, Baggot-street.
Law, Robert, M.D. _ 34, Granby-row.

Xl

Lee, Rey. William, A.M., Fellow of Trinity College.
College.

Levinge, Godfrey, Esq. -Cullion, Mullingar.

Lindsay, Henry, Esq. Armagh.

Lloyd, William T., Esq. 10, Crescent, Upper Mount-st.

Logan, Rev. H. F. C., D.D. Oscott, Birmingham.

Longfield, Mountifort, LL.D. Professor of Feudal and
English Law, University of Dublin. 6, Pézwilliam-
square, West.

Longfield, William, Esq. 19, Harcourt-street.

Lyle, Acheson, Esq., A.M. ‘Treasurer of the Geological
Society of Dublin. 17, Gardiner’s-place.

Lynch, J. F., Esq. 19, Belvidere-place.

* Mac Carthy, Viscount de. Toulouse.

* Mace Cullagh, James, LL. D., F. R.S., Fellow of Trinity
College, Prof. Math.—SrecreTary OF THE ACADEMY.
College.

* Mac Donnell, John, M.D. 4, Gardiner’s-row.

* Mac Donnell, Rev. Richard, D.D. Senior Fellow of
Trinity College. College.

* Mackay, James Townsend, Esq. 5, Haddington Ter-
race.

* M‘Kay, Rev. Maurice, LL.D. Drogheda.

* M‘Neece, Rev. Thomas, A. M., Fellow of Trinity College.
College.

* Macniell, John, Esq., F.R.S. F.R. A.S., Professor of the
Practice of Engineering, University of Dublin. 9,
Whitehall-place, London.

* Magrath, Sir George, K.H. M.D. F.R.S. F.L.S. F.G.S.
Plymouth.

* Mahony, Pierce, Esq. 23, William-street.

* Marsh, Sir Henry, Bart. M.D. V.P. Royal Zoological
Society of Ireland. 24, Molesworth-street.

* Martin, Rev. John C., D.D. Killesandra.

xii
* Mason, Henry Joseph Monck, LL.D. Queen’s Inns,
Henrietta-street.
* Mayne, Rev. Charles, Killaloe.
* Miller, Rev. George, D.D. Armagh.
Mae Cullagh, W. Torrens, Esq. 8, Upper Gloueester-st.
Mac Dowell, George, Esq. Fellow of Trinity College.
26, College.
Magee, James, Esq. 39, Leeson-street.
Mallet, Robert, Esq. 8, Ryder’s Row, Capel-street.
M‘Mullen, John, Esq. William-street.
Marks, Rev. Edward, D.D. Molyneux Asylum, Peter-
street.
Mollan, John, M.D. 32, Gloucester-street.
Monsell, William, Esq. Tervoe, Limerick.
Montgomery, William F., M.D. 18, Molesworth-street.
Morrison, Sir Richard. 49, Upper Mount-street.
Mulvany, W. T., Esq. Dovehouse, Black Rock.
Murphy, Patrick M., Esq. 33, Lower Baggot-street.
Murray, William, Esq., 72, Lower Gardiner-street.

* Napier, Joseph, Esq. 17, Mountjoy-square, South.
* Nicholson, John A., Esq., M. B. Clontarf.
Nelson, Joseph, Esq. 7, Gardiner’s-place.
Newenham, Thomas, Esq. Sandford Cottage, Cullens-
wood,

* Odell, Edward, Esq. Carriglea, Dungarvan.
* O’Ferrall, Joseph M., Esq. 38, Rutland-square, West.
* O’Reilly, Miles John, Esq.
* Orpen, Thomas Herbert, M.D. 13, South Frederich-street.
* Orpen, John Herbert, LL. D. 13, South Frederich-street.
* Owen, John Underhill, M. D.

O’Brien, Sir Lucius, Bart. Dromoland, Newmarhet-on-

Fergus, Clare.
O’Conor, Matthew, Esq. 5, Mountjoy-square, South.

Xiil
O’Grady, Michael Martin, M.D. La Mancha, Swords.
O’Grady, James, Esq., LL.D. 25, Denszille-street.
Ogilby, Robert L., Esq. Dungiven.
O’ Halloran, Major-General Sir Joseph, K.C. B. 51, Up-

per Seymour-street, Portman-square, London.

Orpen, Charles Edward Herbert, M.D. Woodside, Liver-
pool.

Osborne, Jonathan, M.D. 26, Harcourt-street.
Otway, Cesar G., Esq., A. B.
Owen, Jacob, Esq. 2, Mountjoy-square, West.

* Parker, Alexander, Esq. Rathmines.

* Petrie, George, Esq., R.H. A. 21, Great Charles-street.

* Phibbs, William, Esq. Seajield, Sligo.

* Pim, George, Esq. Brennanstown, and 15, Usher's
Tsland.

* Porter, Rev. Thomas H., D.D. Ballymully Glebe, Dun-
gannon.

* Portlock, Joseph Ellison, Esq., R.E. F.R.S. F.G.S.
V. P. Geological Society of Dublin. V.P. Royal Zoo-
logical Society ofIreland. 50, Upper Sackville-street.

* Prior, Rev. Thomas, D.D. Senior Fellow of Trinity
College. College.

* Prior, James, Esq. 14, Oxford Terrace, Hyde Park,
London.

Packenham, Hon.and Very Rev. Henry, Dean of St. Pa-
trick’s. 19, Merrion-square, N., and Deanery-house.

Palmer, Abraham, Esq., M.B. 38, York-street.

Patten, James, A. M., M.D. Belfast.

Pim, James, Jun., Esq.— Treasurer. Monkstown Castle,
and 35, College-green.

Ponsonby, The Hon. Frederick. 36, Kildare-street.

* Radcliffe, Right Hon. John, LL.D. Judge of the Court
of Prerogative. 14, Hume-street.

XiV
* Renny, H. L., Esq. Assistant Professor of the Practice
of Engineering, University of Dublin. Sec. Geologi-
cal Society of Dublin. Royal Hospital.

* Rhodes, Thomas, Esq. Shannon Commission.

* Roberts, Rev. John Cramer.

* Robinson, Rev. Thomas Romney, D. D. Observatory,

Armagh.

* Rosse, Right Hon. The Earl of. Birr Castle, Parsons-

town.

* Rowan, Rev. Arthur B., A.M. Bellmount, Tralee.
Richards, Goddard, Esq. Ardamine, Co. Weaford.
Reid, Rev. James. Clontarf.

Reid, Robert, M.D. 16, Belvidere-place.
Roberts, William, Esq., Fellow of Trinity College. College.

* Sadleir, Rev. Franc, D.D. Provost of Trinity College.—
Provost's House, College.
* Sadleir, Rev. William Digby, A.M. Fellow of Trinity
College. 4, College.
* Singer, Rev. Joseph Henderson, D. D., Senior Fellow of
Trinity College.—Vicz-Presipent. 4, College.
* Smith, Rev. George Sidney, D. D. Professor of Biblical
Greek, University of Dublin. 9, College.
* Stewart, Hon. Alexander. 5, Foley-place, London.
* Stokes, Whitley, M. D., Lecturer in Natural History, Uni-
versity of Dublin. 16, Harcourt-street.
* Strong, Rev. Charles, A.M. Cavendish-row.
Salmon, George, Esq., Fellow of Trinity College. 24,
College.
Sur, Rev. Joseph D’Arey. Claremorris, Mayo.
Smith, J. Huband, Esq. A.M. 1, Holles-street.
Smith, Robert William, Esq. 62, Eccles-street.
Smith, Aquilla, M.D. 120, Lower Baggot-street.
Sproule, Oliver, Esq. 39, Blessington-street.
Stack, Rev. Thomas, Fellow of Trinity College. College.

XV

Staples, Sir Thomas, Bart. Sissane, Co. Tyrone, and 11,
Merrion-square, E.

Sterling, A.C. (Captain, 73rd Regt). Royal Barracks.

Stokes, William, M.D. Regius Professor of Medicine.
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* Trimlestown, John Thomas Lord. Trimlestown Castle.
* Turner, William, Esq.
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Toleken, John, Esq., M.D., Fellow of Trinity College.
College.

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* Westenra, Hon. H.R.

* Williams, Thomas, Esq. Drumcondra Casile, and 38,
Dame-street. :

XVI

* Williams, Richard Palmer, Esq. Drumcondra Castle, and
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XVil

HONORARY MEMBERS.

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XVH1

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X1x

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XxX

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F. R. A. S., Master of Trinity College, Cambridge.
Cambridge.

of Copper and Tin.

Relation to Cast

Characteristic Properties, in Working, &c. season et

Sea Water.

No of
Experiment.

Well known.

>

Several of these
Similar &c., are malleable at
J

>

high temperatures.

Bath Metal.
Dutch Brass.
Rolled Sheet Brass.
British Brass.
German Brass.
np Brass, Watchmakers.
Very Brittle,
Very Brittle, | Too hard to file or
Very Brittle, | turn, lustre nearly
Brittle, equal to Speculum
Brittle, Metal.
Very Brittle,
Barely malleable.
Brittle.
White Button Metal.
Brittle.
Brittle, well known.

presence.

cont anrohbe

All these alloys increase
the corrosion of cast iron in
sea water, when in their

Lu

cS)
=
N
s
s
ss
3
a
a4
°
1
—
)
A
1)
”
i]
<q
B

in sea water, when in
presence.

SPW EAI AAAAAADA SO

All these alloys decrease
the corrosion of cast iron

—_—_
Le

Well known.
Gun Metal, &c.
Gun Metal, &c.
Gun Metal and Bronze.
Hard Mill Brasses, &c.
Brittle, All these alloys
Brittle, found occasionally
Crumbles, 4 in bells, with mix-
Crumbles, tures, of Zn. and
Brittle, Pb.
Small bells, Brittle.
An Brittle.

Speculum Metal of authors.

oO Files, tough.

+p Files, soft and tough.
Well known.

ee

TABLE IJ.—Copper and Tin.
Every alloy of Cu. ++ Sn, increases
the corrosive action of sea water on
cast iron, in their presence; the maxi-

—————

The ult, . Buda -

before ase ven are those which each prism just sustained for a few seconds
The a F c

by ante xsnwall. They were alloyed in a peculiar apparatus, to avoid loss

No si 2
Zn, aioe d fusible metal, generally Cu. 4- Zn. + Pb.; or Cu. -4- Sn. +

[Procrgepines R. I, A., vol. ii, p. 95.

TABLES Nos. I. anv IL.,
‘operties of the Atomic Alloys of Copper and Zine, and of Copper and 7’

Showing the Chemical and Physical Pr ti
in.

= | 8 het 5 6 7 8 9 10 | a | 2 r
———| ———_ . ee Hae | }
z es ap
3 Chemical Constitution. | ComPosition by Welght pgm a2 fiat Hs |
s ied ‘eight. | S53 .. | Order £ | Order | Order
£ Hofeeat ae eee Seay el] as cp [Relation to Cast
5 — oh ae ame oes rere, Colour, ee oe Duc- 3 3 ree Fos. |Characteristic Properties, in Working, &c,|Ir0n, in Presence;
Ee tility. | ©S ‘&e.' | lity, te fo Wate
| ry 5 | ‘
= aa | 5» Be
[ Alea ce Oo} {8t6 | 8667 | Tile Red, 246) 8 | 1 | 99 | 15 | Welk
‘| Cu+ Zn. | 9072 + 9-98) gana 8605 | Reddish Yellow, 1 121 6 | 13 | a y £ cane °
# 9Cu.4+ Zn. | 8980 + 10:20] 3167 | 8607 | Reddish Yellow, 2 115 oa || ta é
4) 8Cu+ Zn. | 8860 i oa 7 2 5 | 4 11 20 | 13 Several of these|| ©
| 60 + 1140} 2851 8633 | Reddish Yellow, 3 128 i || 2
4 3} 7Cu4 Zn, | 8730 12-70) 9554 | gage | Hewat coe es 2 | 10 | 19 | 12 | Similar &c,, > sre malleable at|| 2 3
5 6 6Cu+ Zn. 8540 + 1460) 291-9 Bisby | Yellow ede ee 9 P 18 11 high temperatures. || ©
NS} 7 5Cu.+ Zn. | 88:02 -4 16:08! 190: | S415 | Yellowish Red; 2 call sll el) a6 || eB 223
EB) 8 4Cu+ Zn. | 7965+ 20:35) 1587 | 8-448 | Yellowish Red, 1 en ao) Boe | Sa ease gece
§ 9} 3 Cu. Zn. 7 Sere g He ‘ 5 4 3 | 15 § | Dutch Brass. gee
3] 10) 2Cu. ae liscaary Suaniaal|t cons alliaeoenn linea 1 Tere | SO |) AIT ze |) Rolletisheerssrase) SEE
=| Ul Cut Zn. | 497 + 50:53] 65:9 | 8-230 | Full Yellow, 2 Gail agit cecil ccale caltoceeeee eis
Si 12) Cut 22n. | 3285 + 67:15] 962 | b-283 | Deep Yellow, 193] 4 Oe eames ties
nlinsieatcacnae se anes. : "2 28 ep Yellow, BH) ws 7 | 10 | 6 |, _ Brass, Watchmakers. =
I Zu. + 17 Zn. 1524+ 6848 | 8019 7721 | Silver White, 1 21 0 22 5 5 | Very Brittle,
=] 1) 8 Cu +18 Zn. | 30:30 + 69:70! 8342 | 7-836 | Silver White, 2 29] 9 | 3 Very Brittle, 26
BS} 15] 8Cu+19 Zn. | 2917 4+ 70:83] 8665 | 8-019 | Silver Grey, 3 ait | cei Siu Rvecametical scomiaicrereoserallneese
%} 16] 8 Cu. +490 Zn. | 9812 4 71-88) soa | 7-03 |AshGrey 9 ale ll HON Stal Were soteleys art llustre nearly [3 aye
3) 17 8 Cu.421 Zn, | 9710 + 72:90] 9311 | 8058 | SilverGry, 2 Gay) ool ea ll ll a ete eauar yo seecultma (lV se er
E} 18) 8§Cu+22 Zn. | 26244 73:76} 963-4 | 7-882 | SilverGrey, 1 03] o | 20 8 5 | VeryiBritue, “ Boe
19) § Cu, 4+ 23 Zn. | 2539 + 74°61) 995-7 | 7-443 | Ash Grey, 4 aol) ol) ce |) ow |) lhsetigenttia cereal
20 Cu.+ 3 Zn. 24°50 + 75°50 128'5 T4409 Ash Grey, 1 31 0 16 2 4 Brie . Sra
21) Cu.+ 4 Zn. | 19°65 + 80:35) 1603 | 7-371 | AshGrey 2 19] 0 | 14 4 3 | White] SEs
a 3 A 3 | White Button Metal. 253
22) Cu+ 5 Zn, | 16:36 + sa64| 1931 | 6-605 | Very Dark Grey vs} oo} a7 | a 2 || Brite, Sie
23) + Zn. 0 + 100-00 $2°3 6895 | Bluish Grey, 152 | 13 12 23 1 | Brittle, well known. H] <=7
1) Cut Sn. | 10000 + 0} 3816 | 8667 | Tile Red, 46 | 1 2 Well k ‘
: 210 Cu+ Sn. 8429 4 15-71 | 3749 8501 | Reddish Yellow, 1 161 2 6 i ig Gan Metal, &e. g62
2) 3} 9Cu+ Sn. | 82:81 + 17:19] 3433 | 8-462 | Reddish Yellow, 2 aseaiil) vay |) iz) ‘| ds: |\Ntadell Ganinretsinees ei El
=] 4 8Cu+ Sn. | 8110-4 18-90] 311-7 | 8-459 | Yellowish Red, 2 veel 2h i om |) Ze Il sey I etmnncnitcen tances bis
Zi 5] 7Cu+ Sn. | 7897 + 21:03] 2801 | 8-728 | Yellowish Red, 1 136) 5 | 1 | 3 |-32 | Hard Mill Brasses, &c. Bens
S] 6 6Cu+ Sn, | 7620-4 28-71 | 248°5 | 8750 | Bluish Red, 1 97) 0 | 12 | 2 | a1 | Brite, ‘All these alloys|| £23 3
& 7] 5 Cu.+ Sn. 72:80 + = 27°20 | 2169 8°575 | Bluish Red, 2 49) 0 | 13 1 | 10 | Brittle, found occasionally || 4S =
= 8} 4Cu+ Sn. 6821 4 3179 | 1853 $400 | Ash Grey, 0-7 0 14 6 9 | Crumbles, in bells, with mix- || | ¢ o2
° 9} 3Cu.+ Sn. 6169 + 3831) 1537 8539 | Dark Grey, T.c. | 0-5 0 16 7 s | Crumbles, tures, of Zn, and|f G-s =¥
Lj 10) 2Cu+ Sn. | 51-75 4 48:25 | 1221 | 8-416 | Greyish White, 1] v.c.| 1-7] 0 | 15 | 9 | 7 | Brittle, Pb. stes
= in Cu. + Sn. 3492 4 65:08 90°5 8056 Whiter still, 2) Tc. 14 0 9 i 6 S il QS) 3
=| 12) Cut 2Sn | 21:15 + 7885 | 1494 Whiter stil, g/cc | 39) o | 8 | ia | g | Supe Bae 2a 3
=] 13} Cu.+ Sn. | 1517 + 84°83 | 208-3 Whiter still, 4) C.0.| 31] 0 5 | 1s) 94 \specut tal of auth irs
&}] WM) Cut 450, | 1182 + 8918} 267-2 Whiter still, 5) GC. | ga} 8 | 4 | 4 | 3 SRA oe Bes
15) Cu. + 5 Sn. 968 + 90°32 | 3261 Whiter still, 6| BE, | 25) 6 3 | 15 | 2 Biles, soft and tough. ase
16 + Sn 0+ 10000} 589 White, 7) RB | 27] 7 Li [stot estan lingeatienerss 33

= “Ae twed in Column 7th to denote character of fracture >—P,G. Fine Crystalline, .C. Coarse Crystalline, T.C. Tabular Crystalline, F.P. Fine Fibrous, C, Conchoidal, V.C. Vitreo-Conchoidal, V. Vitreous,

The "oaxima of ductility, malleabitity, hardness, and fusibility, are = 1.
The numbers in Column 6th denote Intenaty of shade of the same colour.
The atomle weights are those of the rope scale.
‘The specific gravities were determin 10 method indicated in Report “On Action of Air and Water on Iron."" ‘Trans. Brit. Ass. vol. vii. 208,
a ‘The ultimate cobeslon was determing) on prisms of (25 of an inch sjuaro, without having been hammerod or compressed after being cast. ‘The weights given are those which each prism just sustained for a few seconds 4
sipping
"The copper tisod in these alloys was granulated, and of the finest " tough piteh ;" the zinc was Mossleman's, from Belgium ; and the tin “ grain tin," from Cornwall. ‘They were alloyed in a peculiar apparatus, to avoid loss
by oxidation, and the resulting alloy vi by lysis.
No simple binary alloy of Cu. + Zn. or of Cu. + Sn, works as pleasantly in turning, planing, or filing, as if combined with a yery small proportion of a third fusible metal, generally Cu, +> Zn. + PU.; or Cu. 4-Sn. +
Zn. as is known to workers in metals, 2
[Puocespixos R.1, A,, vol. ii, p. 95.

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