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PROCEEDINGS

OF THE

ROYAL IRISH ACADEMY.

VOL. III.

>=."
a SS

> Z
SSS

DUBLIN :
PRINTED BY M.H. GILL,

PRINTER TO THE ACADEMY.

MDCCCXLVII.

Br rat Oe
sah ea

CONTENTS.

VOLUME II.

—— e—_
1845-1847,

PAGE.
Tueory of Quaternions. By Sir W. R. Hamilton. . . . 1, 109, 273
Returns laid on the Table by order of Council. . . 17

Letter read from Rev. T. R. Bobi, D. D., on ie Periodical
Meteors of 10th August. . . . - 18

An Account of two remarkable Halos hg eee staan’ in
May and June last. By Rev. H. Lloyd, D.D. . . . . 18

On an ancient wooden Table and Dish, sg ap in Peat or Turf Bog.
By Rev. Thomas Porter, D. D. 21

On the original Use of certain Golden Oitoaahenits ane wilted Arti-
cles in the Museum of the Boxall Irish aren By Robert

Ball, Esq. . . 25
On Diverging Infinite Sethe, and on certain aes iintencea iia e-

with. By Professor Young, of Belfast. . . . ey
On the Subject of Total Reflexion. By Professor Mac ene - 49

On Algebraic Triplets. By Rev. Charles Graves, A.M. 51, 57, 80, 105

On ‘ Dugald Stewart’s Explanation of certain Processes in the
Human Understanding.” By the Rev. James Wills. . . . . 65

On two undescribed Alge. By Dr. Allman. . . irene 67)
On LordRosse’s Telescope. By the Rev. T. R. Bone. . 68,114
A Letter read from Charles Bourns, Esq., giving an Account of the

Excavation made in the Round Tower of Lusk. . . . 68

On the Construction and Results obtained with the Six- foot ae
flecting Telescope of the Earl of Rosse. (Seep.114), . . . 74

On the present State of the Ancient Ecclesiastical Remains of Iona.
By J. Huband Smith, Esq. . . : - 76

On some Geometrical Theorems Laide to Blip PinGisey By
Wm. Roberts, Esq., F.T.C.D. . . - . Spe eT,

~ On the maximum Amount of Resistance navies. to sustain ra of
Earth. By John Neville,Esq. . . .- 84

On a new Photographic Enea which he calls the Catalysotype
By Dr. Thomas Woods. . 89

vi CONTENTS.

PAGE.
A Sealed Packet, deposited with the pay Le Robert Mallet,
Esq., opened at his request. . . Bi ve
A Note from Edward Clibborn, oi on Gola Guumene lately
found near Naas. . . 99
On ancient Wax Tablets, pr sntan to the Academy by fe Ree 5
Spencer Knox. By Rev. J.H. Todd, D.D. . 99
On _ the Quantity of Rain which fell at oohaees during fae
Years since 1827. By Rey. ThomasKnox. .. . 100

Descr iption of a remarkable Lunar Halo and Parasalene seen in in
Queen’s County. By E. W. Chetwoode, Esq., and others. . . 103

Notice of a New Electric Clock. By Richard Sharpe, Esq. . . . 105
On an ancient Inscription on a Tombstone. By George Petrie,

(Ot i Oe eo cso 6 8G idesogep oso 5 WDE!
Suggestions relating to the Improvement in eee Ace

Railways. By R. Mallet, Esq. . . . . oes) eS:
On two Methods of soln planadrage Bauations fe the Rey.

Charles Graves. . ras aA ety so SNE
On the Crotal. By Robert Bal, LDS 9G ie. ee - + 135
Notice of an Ogham Stone found in the County of Weston . . 136
On the Zodiacal Light. By E.J. Cooper, Esq. . . . - 138

On the Storm of the 6th of July, 1845. By William ney rat 140
Account of recent Excavations in the Round Towers of Clonmac-

noise. By Colonel Harry D. Jones,R.E. . . . - 144
Account of Rubbings exhibited from a Rock at Drumlish. By
Colonel Harry D. Jones, R.E. . . . , or ene 147

On Algebraic Curves and Surfaces. By Charlds Gave Brdops ie Ls
On the Authorship of the Poem entitled the “ Exile of Erin.” By

the Rev. W.H. Drummond, D.D. . . . . 157
Memoir of the Dublin hang oe Society of 1683. apy W. R.

Wilde, Esq. -. . oie folk eelOO
On Phonetic Bierce By the na Dr. Hincks. - « 177, 189

On an ancient Way-side Cross. By J. Huband Smith, Esq.. . . 180
On Discontinuous Functions. By George Boole, Esq., of Lincoln. 182

‘Dr. Allman announced the addition of Diotis Maritima to the Irish
RaaRas ey oy ale SR US IT Dk SEINE Sa eS

On the icttinia of Balihdeakee By Robert Mallet, Esq. . 186, 192

Observations on abnormal Movements of the Magnets in the Dublin
Observatory. By the Rev. H. Lloyd, D.D., President. . . . 192

Address to the Academy of Sir W. R. Hamilton, on eur from

the Presidency. . . 199
Inaugural Address of the Rev. H. Liged D. D., on es Election to
the Presidency ofthe Academy. . . . - 203

On a certain Definite Caney ca By George Boole, Bsa. =
of Lincoln. ..

CONTENTS. vil

PAGE.
On the Larva State of Plumatella, and on the Sanne of Polycera

Quadrilineata. By Dr. Allman. . . ow 2lSs220
On an Irish Manuscript preserved in the Roya Libsaty, Paris, Bo

the Rev. J. H. Todd, D. D. - 223
On a Rubbing from the Dorbetcne of William oO Byte. ‘By J.

Huband Smith, Esq. . . 229
On a Provision in the Fetus of the Spine Dog Fish. By Rabat

Ball, Esq. . . .- 230
On pees in the Life of F Shalapere By the me N. J. Hal.

pin. 5 : . . « 231, 233
Some Banal on vioannetir By E. I. Casitbe, Esq. . . 236, 258, 294
On the Variations of the Magnetic Declination of Dublin. By the

Rev. H. Lloyd, D.D., President. . . . . 236, 237
On the Apteryx Australis. By R. Ball, Esq. . . . 247
On the Remains of a Cedar Ship found near eae County of

Down. By G. A. Hamilton, Esq., M.P.. . 248
On “ A North House,” in the Demesne of EAmiidh: sie the Opin:

ing of a Tumulus near SH 7 G. A. Hamilton, Bas :

NG RS ee Mice 249
On the Equilibrium id Motion of Blastic, Solid, sid Fluid Bodies.

By the Rey. Samuel Haughton, F. T. C.D. » «202
The Book of Armagh, deposited in the Library of the Koala oo)
Remarks on presenting a Collection of Celtic a ee W.R.

Wilde, Esq. . . . . 260

On Persepolitan Writing. ‘By the Bee Riward iene D. D. "963, 265

The Objects, Construction, and Use of certain new Instruments for
Self-Registration of Earthquake Shocks. By R. Mallet, Esq. . 266

Some Observations on two Passages of Archimedes de pare et

Cylindro. By C. T. Barnwell, Esq. . . . 268
On the Anemometer of Osler. ke Rey. H. Lloyd D. D., Presi-

dente). v= - 20
Address to the Earl “of Besborough Lea eawecake ‘es with

his Answer. . . 297
On a new Instrument for ee: tid! Magnetic Dip. By ‘ih

Rev. H. Lloyd, D. D., President. . . 298

On the Discovery of Iron Cores in certain Bee Abdoutties in ef
Museum of the +e a Edward er as sas , Curator

ofthe Museum. . . 299
Observations made at Markr ee eee on Le Verrier s Pidied

Communicated by E. J. Cooper, Esq. . . . . . . . 3801, 363
Ona definite Integral. By Rev. William Roberts. . . . 305

On Theorems of central Forces. By Sir W. R. Hamilton, LL. D. 308

Some Observations on Sir William Hamilton’s Communication. By
Rev. Charles Graves. . . Stee Bee eG

An Account of the Formation of ‘the meade at i copeetazel: and

Vill CONTENTS.

general Remarks on the Classification of the Antiquities found in
the North and West of Beene a! J.J. A. nice Esq., of

PAGE,

Copenhagen. . . . .310, 327
On Persepolitan Writing. By ee ae Hineks. . . 315, 344, 359

On the Date of the MS. called the Book of ee By Rev.

Charles Graves. . . . 316, 356

On the Use of distributive Signs of Onebad bus both teal and imagi-
nary, in the Construction of ee of Algebra. By the Rev.

CharlesGraves. . . - tee Oe 325
A new Method of expressing, in Aantal Language, the Noatoutan
Law of Attraction, &c. By Sir W.R. Hamilton, LL.D. . 344
Professor Madler’s Work, Die Centralsonne. Exhibited by Sir
W.R. Hamilton, LL.D. . . Beene, te 353
A Chart of observed Places of Le Verman s Pion Exhibited by
Sir W. R. Hamilton, LL.D. . . . ib.
On the Attraction of Ellipsoids. By tis MacCullagh, LL. D. 367
On the Rotation of a Solid Body. By James MacCullagh, LL. D. 370
On the supposed Identity of the Agent in the Phenomena of ordi-
nary Electricity, voltaic Electricity, Electro-magnetism, Magne-
tico-electricity, and Thermo-electricity. By M. Donovan, Esq. 372,
402, 427, 467
An Account of a Fragment of an ancient purl MS. of the Gos-
pels. By Rev. J.H. Todd, D.D. . . 374
On the Lines of Curvature on the sien of fr Bllipsoid. By
M. Roberts, F. T. C. D. Sas weer 383
A Theoremrelating to the Sere gic Bs M. Hehe E.T. c. D. 385
On the Anatomy of the Elephant. By Robert Harrison, M.D. ib.
Letter from E. J. Cooper, Esq., on the Discovery of anew Comet. 399
On the diurnal Changes of Temperature recorded at the Magneti-
cal Observatory of Trinity Cees By Rev. H. Hors: D. D.,
President. . 401
On a Theorem of Hodographie Tacks eB Sir W. R. fee
milton, LL.D. 5 Linteheets coe ees,
On the Structure “of oh Fruit ea Meghocie of Denier in
some of the Hepatic, &c. On the external Clmae of Chelu-
rus, Phil., &. By G.J. Allman, M.D. . . 419
On the Composition of Essential Oil of Laurus Sadan, By Sir
Robert Kane. . . . ac 425
On the Equation of Siintiaces of the ccna Gus ‘Byte Fates Mac
Cullagh, LL.D. 429
Remarks on the Same. By Rey epaies Cenen 434
Researches in Thermo-chemistry. By James Apjohn, M. D. 435
An ancient Irish Brooch exhibited, belonging to the Rev. Richard
Butler. . . 441
On certain Properties Oar the saiaees of Aaa Degree By s. 5 K.
Ingram, Esq. . Se Gi SR eos Sepa 442

CONTENTS,

On some ancient Inscriptions in Scotland. By John Ramsay, Esq.,
of Heading-hill, Aberdeen... . . . . ~ » oie ee a ae

Some Remarks on the Beane Communication. (By eres Pe-
oie spl SQeiey <i) =) = .

On a Mode of ascertaining the Dene mil State of ne Weather. By
Lieutenant Steevenson, R.N. . fhe alge tas
On the Development of a Pencuek in Bactorials: of the eutte
upon which it depends. By Rev. Charles Graves.
On an antique Gold Ornament, the propery of the Earl of Tete
__ By Rey. Charles Graves. .
A Theorem of Anthodographic Bockman By ‘Sir W. R. Ha.
mil tonsela Ly. Dae Mil fos eats ave Zahm,

On some Improvements in the Concivtatieh ee ae of the Gal.
vanic Battery. By Rev. Dr. Callan, Professor of Natural Philo-
sophy in the College, Maynooth. . .

On the MSS. relating to Ireland in the Burgondian Library at
Brussels. By S. H. Bindon, Esq.

On certain Properties of Curves and Surfaces of the second Degree
By J. K. Ingram, Esq.

On the Application of the Calculus of Ginteniinnd’é to the Theory of
the Moon. By Sir William R. Hamilton, LL.D.

On the Composition and aes Beau ties of Ba a jie
Apjohn, M.D. . sais. We

On the Effect of Heat in lessening the Affinity of the wisn of
Water. By Rev. T.R. Robinson, D.D. . . .

On an Extension of a Theorem of Euler. By Bes ser Tee

Ona Theorem respecting Products of Sums of aos Mena el
John T. Graves, Esq. . . ah :

On the Association of Ideas. By ae fined Wills. Sy ead

On a Leaden Seal of Herbert de la Mara. By Sir William Poche

On the Solution of linear differential Equations, and’other Equations
of the same kind, by the pena of een ce Rev. Charles
Graves. . . p

On the Gavin of Sates of the scbud Degree. a oe
George Salmon. . . 56

On the Mission of the Father Hoge de Borge to o Begin in in 1644.
By S. H. Bindon, Esq.

1X
PAGE.

445

Oxsects Exarsirep,—pp. 247, 260, 263, 266, 270, 272, 441, 460, 465.

Reso.urions,—pp. 25, 65, 73, 109,110, 111, 138, 151, 191, 192, 201,
237, 260, 263, 272, 356, 416, 507 531.,.

Exection oF CounciL,—pp. 69, 186, 201, 221, 416, 531.

Exection or Mempers,—pp. 1, 17, 25, 64, 72, 74,77, 105, 109, 138,

186, 191, 203, 233, 259, 305, 325, 355, 383, 419, 455, 507.
b

217,

151,

x CONTENTS.

Donarions,—pp. 16, 21, 22, 54, 64, 65, 72, 73, 74, 76, 100, 110, 137, 149,
150, 176, 184, 191, 193, 202, 221, 231, "236, 258, 260, 263, 272, 295,
303, 324, 354, 361, 381, 408, 417, 435, 454, 465, 505, 529, 539.

Rerorts or Counciz,—pp. 70, 194, 411.
Treasurer's Account,—p. 795.
By-Laws RELATING TO Honorary Mempers,—p. 355.

APPENDICES.
PAGE.
Minutes of Council, No. I. BRK: 6 c i
Meteorological Journal, from Ist January to 3st December, 1844.
By George Yeates, Esq. No. II. niteno Sc | sayin
Illustrations from Geometry of the Thoaey of Algebra Quater
nions. By Sir W. R. Hamilton. No. III. GG soos

Synopsis of the Accounts of the Royal Irish Academy, ites 17th
March, 1816, to 31st March, 1846. No. IV. . . . facing page |

Additional pp pleaion of his Theory of Algebraic Quaternions

By Sir W.R. Hamilton. No. V._. oie li
Meteorological Journal, from Ist sihaaley to 31st December, 1845.

By George Yeates, Esq. No. VI. .. . : Ixi
On the Peculiarities of the mee of the he By ‘Prose

Harrison. No. VII... .. . — Ixvii
Accounts of the Royal Irish Academy, ae let April 184, to

31st March, 1846. No. VIII... . . . [xxxili
Meteorological Journal, from Ist oe to Blot December, 1846.

By George Yeates, Esq. IOs IDKo G5 +. Xevil

Abstract of the Account of the Academy. No. x. CRRA | cei clii

Account of the Royal Irish ee from Ist ae 1846, to 31st
March, 1847. No, XI. . , cv

INDEX
OF CONTRIBUTORS’ NAMES TO PROCEEDINGS.

VOLUME III.

Allman, 67, 184, 218, 220, 419.—Apjohn, 435, 521,

Ball, 25, 135, 230, 247.—Barnwell, 268.—Betham, 534.—Bindon, 477,
538.—Butler, 441.—Boole, 182, 217.—Bourns, 68.

Callan, 471.—Chetwode, 103.—Clibborn, 99, 299.—Cooper, 138, 236,
258, 294, 301, 363, 399.

Donovan, 372, 402, 427, 467..-_Drummond, 157.

Graves, Rev. C., 51, 57, 80, 105, 111, 151, 309, 316, 325, 356, 434, 455,
460, 536.—Graves, J. T., 527.

Halpin, 231, 233.—Hamilton, G. A., 248, 249.—Hamilton, Sir W. R., 1,
109, 199, 273, 308, 344, 353, 417, 465, 507.—Harrison, 385.— Haugh-
ton, 252.—Hincks, 177, 189, 263, 265, 315, 344, 359.—Hogan, 140,

Ingram, 442, 502.

Jones, 144, 147.

Kane, 425.—Knox, Rev. T., 100.

Lloyd, 18, 192, 203, 236, 237, 270, 298, 401.

Mallet, 108, 186, 192, 266.—Mac Cullagh, 49, 367, 370, 429.
Neville, 84.

Petrie, 108, 452.—Porter, 21.

Ramsay, 445.—Roberts, Rev. M., 383, 385.—Roberts, Wm., 77, 305,—
- Robinson, 18, 68, 114, 525.—Rosse, Lord (see Robinson).

Salmon, 536.—Sharpe, 105.—Smith, J. H., 76, 180, 229.—Stevenson,
454.

Todd, 99, 228, 374.
Worsaae, 310, 327.—Wilde, 160, 260.—Wills, 65, 531.— Woods, 89.
Young, 526.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1844-45. No. 48.

November 11, 1844.

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

His Grace the Duke of Leinster, Most Noble the Marquis
of Downshire, Baron Farnham, and Baron Wallscourt, were
elected Members of the Academy.

The Chair having been taken, pro tempore, by the Rev.
J. H. Topp, D.D., V.P., the President gave an account of
some additional researches in the theory of Quaternions, or of
a new system of Imaginaries in Algebra.

In the theory which Sir William Hamilton submitted to
the Academy in November, 1843, the name quaternion was
employed to denote a certain quadrinomial expression, of
which one term was called (by analogy to the language of or-
dinary algebra) the real part, while the three other terms
made up together a trinomial, which (by the same analogy)
was called the maginary part of the quaternion: the square
of the former part (or term) being always a positive, but the
square of the latter part (or trinomial) being always a nega-
tive quantity. More particularly, this imaginary trinomial
was of the form iz +jy + kz, in which 2, y, z were three real
‘and independent coefficients, or constituents, and were, in se-
veral applications of the theory, constructed or represented by

VOL. III. B

2

three rectangular coordinates; while 7; 7, & were certain ima-
ginary units, or symbols, subject to the following laws of
combination as regards their squares and products,

P= Pak = — 1, (A)
UJ hegk =o kt 7, (B)
ji=—h, kj=—1, hRo=-7, (C)

but were entirely free from any linear relation among them-
selves; in such a manner, that to establish an equation be-
tween two such imaginary trinomials was to equate each of the
three constituents, zyz, of the one to the corresponding con-
stituent of the other; and to equate two quaternions was (in
general) to establish rourR separate and distinct equations be-
tween real quantities. Operations on such quaternions were
performed, as far as possible, according to the analogies of
ordinary algebra; the distributive property of multiplication,
and another, which may be called the associative property of
that operation, being, for example, retained: with one impor-
tant departure, however, from the received rules of calculation,
arising from the abandonment of the commutative property of
multiplication, as not in general holding good for the mixture
of the new imaginaries; since the product jz (for example) _
has, by its definition, a different sign from 7. And several
constructions and conclusions, especially as respected the geo-
metry of the sphere, were drawn from these principles, of
which some have since been printed among the Proceedings
of the Academy for the date already referred to.

The author has not seen cause, in his subsequent re-
flections on the subject, to abandon any of the prineiples
which have been thus briefly recapitulated; but he conceives
that he has been enabled to present some of them in a clearer
view, as regards their bearings on geometrical questions; and
also to improve the algebraical method of applying them, or
what may be called the caLCULUS OF QUATERNIONS.

Thus he has found it useful, in many applications, to dis-
miss the separate consideration of the three real constituents,

3

2 Y, 2, of the imaginary trinomial 7x+jy+z, and to denote
that trinomial by some single letter (taken often from the
Greek alphabet). And on account of the facility with which
this so called imaginary expression, or square root of a nega-
tive quantity, is constructed by a right line having direction in
space, and having «, y, = for its three rectangular components,
or projections on three rectangular axes, he has been induced
to call the trinomial expression itself, as well as the line which
it represents, a vecror. A quaternion may thus be said to
consist generally of a real part and a vector. The fixing a
special attention on this last part, or element, of a quaternion,
by giving it a special name, and denoting it in many calcula-
tions by a single and special sign, appears to the author to
have been an improvement in his method of dealing with the
subject: although the general notion of treating the consti-
tuents of the imaginary part as coordinates had occurred to
him in his first researches.

Regarded from a geometrical point of view, this alge-
braically imaginary part of a quaternion has thus so natural
and simple a signification or representation in space, that the
difficulty is transferred to the algebraically real part; and we
are tempted to ask what this last can denote in geometry, or
what in space might have suggested it.

By the fundamental equations of definition for the squares
and products of the symbols ¢, 7, k, it is easy to see that any
(so-called) real and positive quantity is to any vector what-
ever, as that vector is to a certain real and negative quantity ;
this being indeed only another mode of saying that, in this
theory, every vector has a negative square. Again, the product
of any two rectangular vectors isa third vector at right angles
to both the factors (but having one or other of two opposite
directions, according to the order in which those factors are
taken); a relation which may be expressed by saying, that

‘the fourth proportional to the real unit and to any two rect-
angular vectors is a third vector rectangular to both; or, con-
B2

4

versely, that the fourth proportional to any three rectangular
vectors isa quantity distinct from every vector, and of the kind
ealled real in this theory, as contrasted with the kind called
imaginary.

Now, in fact, what originally led the author of the present
communication to conceive (in 1843) his theory of quaternions
(though he had, at a date earlier by several years, speculated
on triplets and sets* of numbers, as an extension of the theory
of couples, or of the ordinary imaginaries of algebra, and also
as an additional illustration of his views respecting the Sci-
ence of Pure Time), was a desire to form to himself a distinct
conception, and to find a manageable algebraical expression,
of a fourth proportional to three rectangular lines, when the
DIRECTIONS of those lines were taken into account; as Mr.
Warren{ and Mr. Peacock{t had shewn how to conceive and
express the fourth proportional to any three lines having di-
rection, but situated im one common plane. And it has since
appeared to Sir William Hamilton that the subject of quater-
nions may be illustrated by considering more closely, though
briefly, this question of the determination of a fourth propor-
tional to three rectangular directions in space, rather in a geo-
metrical than in an algebraical point of view.

Adopting the known results above referred to, for propor-
tions between lines having direction in a single plane (though
varying a little the known manner of speaking on the sub-
ject), it may be said that, in the horizontal plane, ‘* West is
to South as South is to East,” and generally as any direction
is to one less advanced than itself in azimuth by ninety de-
grees. Let it be now assumed, as an extension of this view,
that in some analogous sense there exists a fourth proportional

* See Transactions of the Royal Irish Academy, vol. xvii. p. 422. Dublin,
1835.

} Treatise on the Geometrical Representations of the Square Roots of Ne-
gative Quantities, by the Rey. John Warren. Cambridge, 1828.

ft Treatise on Algebra, by the Rev. George Peacock. Cambridge, 1830.

5

to the three rectangular directions, West, South, and Up;
and let this be called, provisionally, Horward, by contrast to
the opposite direction, Backward, which must be assumed to
be (in the same general sense) a fourth proportional to the
directions of West, South, and Down. We shall then have, in-
versely, Forward to Up as South to West; and therefore, as
West to North: if we admit, as it seems natural and almost ne-
cessary to do, that (for directions, as for lengths) the inverses of
equal ratios are equal; and that ratios equal to the same ratio
are equal to each other. But again, Up is to South as South
to Down, and also as North to Up: and we can scarcely avoid
admitting, or defining, that (in the present comparison of di-
rections) ratios similarly compounded of equal ratios are to be
considered as being themselves equal ratios. Compounding,
therefore, on the one hand, the ratios of Forward to Up, and
of Up to South; and on the other hand the respectively
equal (or similar) ratios of West to North, and of North to
Up, we are conducted to admit that Forward is to South as
West to Up. By a reasoning exactly similar, we find that
Forward is to West as Up to South; and generally that if
X, Y, Z denote any three rectangular directions such that
A:X::Y:Z, A here denoting what we have expressed by
the word Forward, then also A: Y:: Z: X (and of course, for
the same reason, A: Z:: X: Y); so that the three directions
XYZ may be all changed together by advancing them in a
ternary cycle, according to the formula just written, without
disturbing the proportionality assumed. But also, by the
principle respecting proportions of directions in one plane, we
may cause any two of the three rectangular directions XYZ
to revolve together round the third, as round an axis, without
altering their ratio to each other. And by combining these
two principles, it is not difficult to see that because Forward
_has been supposed to he to Up as South to West, therefore
the same (as yet unknown) direction ‘‘ Forward” must be
supposed to be to any direction X whatever, as any direction
_ Y, perpendicular to X, is to that third direction Z which is

6

perpendicular to both X and Y, and which is obtained from Y
by a right-handed (and not by a left-handed) rotation, through
a right angle, round X; in the same manner as (and because)
the direction West was so chosen as to be to the right of South,
with reference to Up as an axis of rotation. Conversely we
must suppose that if any three rectangular directions, XYZ,
be arranged, as to order of rotation, in the manner just now
stated, then Z: Y:: X: A; orin other words, we must admit,
if we reason in this way at all, that the direction called
already Forward, will be the fourth proportional to ZY X.
And if we vary the order, so as to have Z to the left, and not
to the right of Y, with reference to X, then will the fourth
proportional to ZY X become the direction which we have
lately called Backward, as being the opposite to that named
Forward.

Again, since Forward is to Up as South to West, that is
in a ratio compounded of the ratios of South to East and of —
East to West, or in one compounded of the ratios of West to
South, and of any direction to its own opposite ; or, finally, in _
a ratio compounded of the ratios of Up to Forward and of
Forward to Backward, that is, in the ratio of Up to Back-
ward, we see that the third proportional to the directions For-
ward and Up is the direction Backward: and by an exactly
similar reasoning, with the help of the conclusions recently
obtained, we see that if X be any direction in tridimensional
space, then A: X:: X:B; B here denoting, for shortness,
the direction which has been above called Backward.

The geometrical study of the relations between directions
in space, combined with a few very simple and guiding prin-
ciples respecting the composition of relations generally, might
therefore have led to the conception or assumption of a certain
pair of contrasted directions, namely, those which we have
called Forward and Backward, and denoted by the letters A
and B. And these are such that if we conceive a quantitative
element to be combined with each, and give the name of
POSITIVE UNITY to the unit of magnitude measured in the di-

7

rection of Forward, but that of Negative Unity to the same
magnitude measured backward; and if we extend to this po-
sitive unity and to lines having direction in space the received
definitions of multiplication, that ‘ Positive Unity is to Mul-
tiplier as Multiplicand is to Product,” and that ‘‘ the product
of two equal factors is the square of either ;”’ we may then
consistently and naturally be led to assert the same results as
those already enunciated from the theory of quaternions re-
specting the product of two vectors, in the two principal
cases, first, where those two vectors are rectangular, and se-
cond, where they are coincident with each other. And thus
may we justify, or at least interpret and explain, the funda-
mental definitions (A) (B) (C) of this theory, by regarding
the symbols 7k as denoting three vector-units having three
rectangular directions in space.

But farther, we derive from this view of the whole subject
an illustration (if not a confirmation) of the remarkable con-
clusion that the so-called real and positive unit + 1 is not (in
this theory) to be confounded with any vector unit whatever,
but is to be regarded as of a kind essentially distinct from
every vector. For this positive unit + 1 is in the direction
above called Forward, and denoted by A. Now if this could
coincide with a direction X in tridimensional space, then,
whatever this latter direction might be supposed to be, we
could always, by the general formula A: X:: Y: Z (where X
is arbitrary), deduce the inadmissible proportion X: X:: Y:: Z,
in which the two directions in one ratio are identical, but
those in the other are rectangular to each other. If then we
resolve to retain the assumption of the existence of a fourth
proportional A to three rectangular directions in space, as
subject to be reasoned on at all in the way already described,
and as determined in direction by its contrast to its own oppo-

site B (corresponding to an opposite order of rotation in the
system XYZ), we must think of these two opposite directions
A and B as merely laid down upon a scale, but must abstain

8

from attributing to this scaLE any one direction rather than
another in tridimensional space, as having such or such a
zenith distance, or such or such an azimuth, rather than such
or such another. And the progression on this scale from ne-
gative to positive infinity, obtained by combining a quanti-
tative element with the contrast between two opposite direc-
tions, corresponds less to the conception of space itself (though
we have seen that considerations of space might have sug-
gested it) than to the conception of time; the variety which
it admits is not ¢rz- but wni- dimensional; and it would,
in the language of some philosophical systems, be said to
appertain rather to the notion of intensive than of extensive
magnitude. Though answering precisely to the progression
of the quantities called real in algebra, it has, when viewed
from the geometrical side, somewhat the same sort of imagi-
nariness, and yet (it is believed) of wtility, as compared with
lines in space, which the square root of an ordinary negative
has, when compared with positive and negative quantities.
This analogy becomes still more complete when we observe
that (in this theory) the fourth proportional to any direction
X in space, and either of the two directions A or B upon the
scale, is the direction opposite to X; so that, 7fa vector-unit
in any determined direction X had been taken for positive
unity, then each of the two scalar units in the directions A
and B (in common, it is true, with every vector-unit perpen-
dicular to X) might have been called, by the general nomen-
clature of multiplication, a square root of negative one.

It is, however, a peculiarity of the calculus of quaternions,
at least as lately modified by the author, and one which seems
to him important, that it selects no one direction in space as
eminent above another, but treats them as all equally related
to that extra-spatial, or simply scaLar direction, which has
been tecently called ‘‘ Forward.” In this respect it differs in
its processes from the Cartesian method of coordinates, andseems
often to admit of being more simply and directly applied to

9

the treatment of geometrical problems, because it requires no
previous selection of axes, rectangular or other. The author
is, indeed, aware that the cooperation of other and better ana-
lysts will be necessary in order to bring the method of quater-
nions to anything approaching to perfection. But he hopes
that an instance or two of the facility with which some ques-
tions at least allow themselves to be treated by this method,
even in its present state, may not be without interest to the
Academy. And he conceives that two examples in particular,
one relating to the composition of translations, and the other
to the composition of rotations in space, may usefully be se-
lected for statement on the present occasion.

As preliminary illustrations of the operations employed, it
may be remarked that for any system of lines having direction
in space, it is required by many analogies (and is, for lines in
one plane included among the definitions or results of the
theories of Mr. Warren and Mr. Peacock), that the swm should
be regarded as being equal to that one line which constructs
or represents the total effect of all the different rectilinear
motions which are expressed by the different summands.
’ Vectors are therefore to be added to each other by a certain
geometrical composition, exactly analogous to the composition
of motions or of forces, and following the same known rules.
Scalars, on the other hand (that is to say, the so-called real
parts of any proposed quaternions), admitting only of a pro-
gression in quantity, and of a change of sign, without any
other changes of direction, are to be added among themselves
by the known rules of algebra, for the addition of positive and
negative numbers. ‘The addition of a scalar and a vector to
each other can be no otherwise performed, or rather indicated,
than by writing their symbols with the sign + interposed ;
each being, as we have seen, in some sense, imaginary with

respect to the other. ‘These operations of addition are all of
the commutative, and also of the associative kind; that is to
say, the order of all the summands may be changed, and any

10

group of them may be collected or associated into one partial
sum.

Scalars are multiplied, as well as added, by the known
rules of ordinary algebra, for the multiplication of real num-
bers, positive or negative; because the positive unity of the
system has been assumed to be itself a scalar, and not a vector
unit.

For the same reason, to multiply any vector by any scalar
a, isin general to change its length in a known ratio, and to
preserve or reverse its direction, according as a is > or < 0;
the product is therefore a new vector, which may be denoted
by aa. The same new vector is obtained, under the form aa,
when we multiply the scalar a by the vectora. Ifa a and
b+ 3 be two quaternion factors, of which a and 6 are the scalar
parts, and a, 3 the vectors, then with a view to preserving the
distributive character of multiplication, it is natural to define
that the product may be distributed into the four following
parts :

(a+a) (6+) = ab+aB+ab-+ af.

And if the multiplicand vector § be decomposed into two parts,
or summands, one = [3, and in the direction of the multiplier
a, or in a direction exactly opposite thereto, and the other
= 2., and in a direction perpendicular to the former (so that
3, and (3, are the projections of 8 on a itself, and on the plane
perpendicular to a), then it may be farther defined that the
multiplication of any one vector [3 by another vector a may be
accomplished by the formula

aB = a(R; + 2) = a; + a2;
in which, by what has been shewn, the partial product af3, is
to be considered as equal to a scalar, namely, the product of
the lengths ofa and (3, taken with the sign — or +, accord-
ing as the direction of (3; coincides with, or is opposite to that
of a; while the other partial product aj, is a vector, of which
the length is the product of the lengths of a and (3,, while its

11

direction is perpendicular to both of their’s, being obtained
from that of (3., by making it revolve right-handedly through
a right angle round a as an axis. These definitions, which
are compatible with the formule (A) (B) (C), and may serve
to replace them, will be found sufficient to prove generally,
and perhaps with somewhat greater geometrical clearness than
those formule, the distributive and associative properties of
quaternion multiplication, which have been already stated to
exist. They give easily the following corollaries, which are
of very frequent use in this calculus :

as + Ba = 2aR, = — 2 AB cos(A, B); (a)

a — Ba = 2aR, = 2yABsin (A, B); (b)
A and B denoting here the lengths of the lines a and (3, and
(A, B) the angle between them; while y is a vector-unit per-
pendicular to their plane, and such that a right-handed rota-
tion, equal to the angle (A, B), performed round y, would
bring the direction of a to coincide with that of 2. For
example, when 3 =a, then B= A, (A,B) =0, and

aB= Pa=a =~ A’,

so that the length A of any vector a, in this theory, may be
expressed under the form

A=V/= fae (c)
More generally we have the equation

ap — Ba = 0, (d)
when the lines a and f are coincident or opposite in direction ;

while, on the contrary, the condition for their being at right
angles to each other is expressed by the formula

ap + Ba = 0. (e)
These simple principles suffice to give, in a new way,
__ algebraical solutions of many geometrical problems, of various

degrees of difficulty and importance. Thus, if it be required,
as an easy instance, to determine the length of the resultant

12

of several successive rectilinear motions, or the magnitude of
the statical sum of several forces acting together at one point,
as a function of the amounts of those successive motions, or
of those component forces, and of their inclinations to each
other, we have only to denote the components by the vectors
Qj) dz) - . - dy, and their sum by a, the corresponding magni-
tudes being A;, A,,... An, and A; and the equation
a=ataa+..- + an
will give, by being squared,
Cig Thay pirate! Seay Chae
+ aj ag + aga, +... + aantang+...;
that is, by the foregoing principles (after changing all the
signs),
AZ = 7A,2 a: Agcer any
+ 2A, A, cos(A,, Ag) +... + 2A, An cos (A; An) +...5
a known result, it is true, but one which can scarcely be de-
rived in any other way by so very short a process of calcula-
tion. For it is not quite so easy, on the algebraical side of
the question, to see that

(22)? + (2y)? + (22)? = Se? + y? + 2?) + 23 (wa'+ yy’ + 22’),

however easy this may be, as it is to see that

(2a)? = X(a?) + S(aa’ + a’a): (f)
although the geometrical interpretation of the first of these
two formule is of course more obvious than that of the latter,
to those who are familiar with the method of coordinates, and
not with the method of quaternions.

Again, let us consider the more difficult problem of the
composition of any number of successive rotations of a body,
or, at first, of any one line thereof, round several successive
axes, through any angles, small or large. Let the axis of the
first of these rotations have the direction of the vector-unit a,
(a® = — 1), and let the amount of the positive rotation round
this axis be denoted by a, which letter here represents still a

13

scalar or real number. Let 8 be the revolving line, consi-
dered in its original position ; (3’ the same line, after it has
revolved through the angle a round the axis a. The part, or
component, of (3, which is in the direction of this axis, is that
which was denoted lately by (3,; and the formula (a), when
multiplied by — 3a, gives, as an expression for this part,

Bi = 3 (8B — aBa), (g)
because it has been supposed that a= —1. This part of 6
remains unaltered by the rotation. The other part, or com-
ponent of 3, is, in like manner, by (b),

Bz = 4(8 + aBa) ; (h)
and this part is to be multiplied by cosa, in order to find the
part of ’, which is perpendicular to a, but in the plane of a
and RB. Again, multiplying by a, we cause 3. to turn through
aright angle in the positive direction round a, and obtain, for
the result of ¢hzs rotation,

a2 = 3 (a8 — Ba);
an expression which is the half of that marked (b), and which
is to be multiplied by sin a, in order to arrive at the remaining
part of the sought line ’, namely, the part which is perpen-
dicular to the plane of a and B. Collecting, therefore, the
three parts, or terms, which have been thus separately ob-
tained, we find,

PB’ = Bi + (cosa + asina) Bz
=} (B— aa) +4 cosa (8 + apa)
: + isina (aB— a)
= ((cos$).B— (si 5) . aa + cos 5 sin 5: (aB— Ba) ;

that is,

= (cos $ +a sin 5) pB (cos 7 —asin 5 : q)*

* [Note added during printing. |—The printing of this abstract, having been
delayed, the Author desires to be permitted to append the following remarks:

14

the operations here indicated being thus sure to make no
change in the part 3,, which is in the direction of the axis of
rotation, but to cause the other part (2 to revolve round that
axis a through an angle =a. Again, let the same line //
revolve round a new axis of rotation denoted by a new vector
unit a’, through a new angle a’, into a new position 8”; we
shall have, in like manner,

If we should make, for abridgment
Z —
a tan ian ua Y
the formula (i) for any single rotation might be thus written,

B= (+7) BA +y)- @’)

And if we then made
Sia+jyshz, SP Six,+jy,+hz, yS=ir+jutho,

i. j, k, being the same three rectangular vectors, or imaginary units, as in
the formule (A) (8) (c), but z, y, z, 2’, y’, 2’, A, p, Vv, being nine real or
scalar quantities, we should obtain the same general formula for the trans-
formation of rectangular coordinates (with the same geometrical meanings
of the coefficients A, w, v,) as that which Mr. Cayley has deduced, with a
similar view, but by a different process, and has published, with other
«‘ Results respecting Quaternions,” in the Philosophical Magazine for Fe-
bruary, 1845.

The present writer desires to return his sincere acknowledgments to
Mr. Cayley for the attention which he has given to the Papers on Qua-
ternions, published in the above-mentioned Magazine: and gladly recog-
nizes his priority, as respects the printing of the formula just now re-
ferred to. But while he conceives it to be very likely that Mr. Cayley,
who had previously published in the Cambridge Mathematical Journal some
elegant researches on the rotation of bodies, may have perceived, not only
independently, but at an earlier date than he did himself, the manner of
applying quaternions to represent such a rotation; he yet hopes that he
may be allowed to mention, that a formula differing only slightly-in its nota-
tion from the formula (i) of the present abstract, with the corollaries there
drawn respecting the composition of successive finite rotations, had been
exhibited to his friend and brother Professor, the Rev. Charles Graves, of
Trinity College, Dublin, in an early part of the month (October, 1844),
which preceded that communication to the Academy, of which an account is
given above.

15

B° = (cos + + a’ sin= -) B’ (cos ¢ oar a’ sin ear (j)

and so on, for any number x of rotations. Let the last posi-
tion of (3 be denoted by [3, ; and since it can easily be proved,
by the theory of the multiplication of quaternions, that the
continued products which present themselves admit of being
thus transformed :

(x—1) (n—1) ’ ,
a a a a
cos a@—) sin abe (cos a’ ine )
( age a 2 g + D
( @4 @ sin— cos” + an sin =
cos a sin— )=cos— + an sin —;
2 2 2 a ie

a ‘ <)( a’ iad >)
eaiedly = os — —a' sin— )...
(cos a sin 5 cos 5 — a’ sin 5

ar G21) a@—)) an « Gn
— — a") gi =cos— — in — ;
( 00s 5 a sin 5 cos 5 & 8 23

|
|
& (k
ie
|
|

in which a, is a new vector unit, and @, a new real angle, we
find that the result of all the ~ rotations is of the form

a (cos + a, sin sy pB (cos — ay sin = (1)

It conducts, therefore, to the same final position which would
have been attained from the initial position B, by a single
rotation = dp, round the single axis a,; the amount and axis
of this resultant rotation being determined by either of the
two equations of transformation (k), and being independent of
the direction of the line (3 which was operated on, so that they
are the same for all lines of the body.

If the present results be combined with the theorem
marked (R), in the account, printed in the Proceedings of the
Academy, of the remarks made by the Author in Novem-
ber, 1843, it will at once be seen that if the several axes of
rotation be considered as terminating in the points of a sphe-
rical polygon, and if the angles of rotation be equal respec-
tively to the doubles of the angles of this polygon (and be
taken with proper signs or directions, determined by those

angles), then the total effects of all these rotations will vanish ;
*

16

or, in other words, the body will at last be brought back to
the position from which it set out.

Finally, it may be mentioned that the author is in posses-
sion of a general method for expressing by quaternions the
tangent planes and normals to curved surfaces; and that in
applying this method to find the cone of tangents enveloping
a given sphere, and drawn from a given point, the geometrical
impossibility of the problem, when the point is an internal
one, is expressed by the square of a vector becoming in this

case positive.

The special thanks of the Academy were voted to Doctor
Simpson of Christiania, for his donation of a fac simile of an
Irish MS, in the Library of Copenhagen.

DONATIONS.

Statutes of Trinity College (1844), Dublin.

Catalogue of the Egyptian Manuscripts in the Library of
Trinity College, Dublin. By Edward Hincks, D. D.

A Catalogue of Roman Silver Coins in the Library of
Trinity College. Presented by the Provost and Senior
Fellows.

Recueil des Actes de la Séance Publique de l Académie
Imperiale des Sciences de St. Petersbourg, tenue le 29 De-
cembre, 1840, et 12 Janvier, 1843.

Memoires de l Académie Imperiale des Sciences de St.
Petersbourg ; sixth series. Sciences Mathématiques, tom. 3,
livraisons 4, 5, 6; tom. 4, livraison 1. Sciences Politiques,
tom. 6, livraisons 4, 5, 6; tom. 7, livraisons 1, 2, 3. a

17

November 30. (Stated Meeting.)

JAMES APJOHN, M.D., Vice-President, in the Chair.

Mons. Arago, of Paris, was unanimously elected an Hono-

‘rary Member of the Academy.

Certain Returns ordered by the Council, on the Ist July,
to be furnished to the Academy, were laid upon the table,

1. A List of all Papers or Essays read before the Academy,

in the departments of Belles Lettres and Antiquities, which
were referred to Council for publication, from the 17th
March, 1828, to 17th March, 1844, containing the dates
of such reading, the names of the authors, whether or-
dered by the Council for publication, and, if published
in the Transactions, with the dates of the Council’s order
for publication.*

. A statement of all payments made by the Academy for
wood-cuts and engravings for Proceedings and Transac-
tions, from 1816 to 1845, inclusive.

. A statement of all payments made by the Noadenig for
letter-press printing, from 1816 to 1845, inclusive.

. Extract from Minutes of Council, June 29th, 1840, con-
taining Mr. Petrie’s contract to supply the Academy with
450 copies of his Essay on the Round Towers, at thirty
shillings per copy.

. A statement of premiums, in money and medals, given by
the Academy from 15th March, 1828, to June 24th, 1844.
. A statement of the available assets and liabilities of the
Academy.

. * With the view of making this Return as full as possible, it also included

the Papers on Science which were read, and it was continued to 24th June,
1844, when the session ended.

VOL. Ill. Cc

18

December 9, 1844.
REV. J. H. TODD, D.D., Vice-President, in the Chair.

Read, a letter from Rev. T. R. Robinson, D. D., on the
periodical Meteors of the 10th August.

Rev. H. Lloyd gave an account of two remarkable halos
and paraselene, observed in May and June last :

On the 27th of June, at 10" 30™ p. m., a very remarkable
phenomenon of paraselene was seen in Dublin. The moon
was encompassed, as usual, by a halo, whose radius was about
22 degrees, but so faint, that its presence was unnoticed by
some of the observers. A cross of light traversed the place
of the moon, the arms of which were horizontal and verti-
cal, the light fading off insensibly towards their extremities.
The remaining parts of the space within the halo were darker
than the surrounding sky. At the extremities of the horizon-
tal diameter of the circle were two brilliant paraselene, having
tails of light extending from the moon; of these the eastern
was the most distinct. ‘The whole phenomenon is represented
in the lithograph sketch in the Appendix.

This beautiful phenomenon was witnessed by many observ-
ers. The appearances are briefly described in the records of
the Magnetical Observatory, by the assistant whose duty it
was to observe at 10 p. m.; and I have likewise received notes
of them from Mr. O’Neill, formerly my assistant in the ob-
servatory (who has likewise furnished me with an interesting
sketch), and from our Assistant Secretary, Mr. Clibborn.

The state of the sky at 10 p.m., shortly before the appear-
ance of the phenomenon, is thus recorded in the day-book of
the Observatory: ‘* Sky all very lightly overcast ; small dark
masses of cumulo-stratus above the southern horizon, the moon
shining weakly through them.” ‘The barometer had been
rising uninterruptedly during the 27th, and the three days -

19

which preceded it, and continued to rise until the morning of
the 29th; at the time of the phenomenon it stood at 30.052.
The temperature of the air was 55.0, and that indicated by the
wet-bulb thermometer 53.4. During the phenomenon the
sky is described in Mr. Clibborn’s notes as “‘covered with a
white fog, apparently composed of a thin stratum of very
opaque and fine vapour, sufficient to obscure the stars, which
I do not recollect having noticed near the moon, nor within
the limits of the imperfect circle.” The halo was faint, ex-
cepting those parts of it which were at about the same altitude
as the moon, and where the prismatic colours were distinctly
visible. The intensity, however, was continually changing,
apparently with the changes of brilliancy of the moon’s disc.
‘The arch was all along quite imperfect at top, where we
could at no time discover any trace of a false moon, or even
any diffused light or appearance of arch.”

‘¢ The true moon,” writes Mr. Clibborn, ‘‘ appeared to be
elongated, and its outline was hazy and indistinct; that of
the false moons was still more so. At times,” he adds, ‘* we
were disposed to think there were three false moons on the
eastern side, placed a little behind and above each other,
with three distinct tails of light stretching towards the east.
On the west, the moon was too diffuse to say that any appear-
ance of the kind at any time presented itself.”

«« The whole phenomenon disappeared, by the clouds clos-
ing over the moon, at 7 minutes before 11 o’clock.”

From some rough measurements made by Mr. Clibborn, it
seemed that the two false moons were not exactly at the same
altitude as the true moon, appearing to fall below it by about
half its own diameter. ‘‘ The false moon towards the east was
the more perfect ; and the tail which extended from it appeared
to fade away into space, and must have been perceptible for
_30 or 40 degrees.”

The most remarkable, and at the same time the most un-
common feature of this phenomenon was the beautiful cross,

20

which was sharply defined and distinct throughout, except at
the ends of the arms, where its light gradually melted away.
On looking through the numerous notices of paraselenz, which
are to be found in the early volumes of the Philosophical
Transactions, I find but one, seen by Hevelius at Dantzie,
in the year 1660, which was similar to the present phenome-
non, or to that of the preceding month described by Dr. Ro-
binson. The non-appearance, in any instance, of a complete
vertical circle, seems to forbid the supposition that this cross
can have been produced, like the horizontal white circle, by
reflection from the facets of the prisms of ice. It is probably
a phenomenon of diffraction ; and indeed it is described by one
of the gentlemen who witnessed it, as resembling the cross of
light which one sees, in looking at the sun or any bright ob-
ject, through the silk of an umbrella. It would be impor-
tant, with reference to the physical explanation of the pheno-
mena, that the light, both of the horizontal circle and of the
cross, should be analyzed with a tourmaline or double-refract-
ing prism. ‘The received explanation of the former may thus
be easily tested ; for, it follows from the hypothesis upon which
that explanation rests, that the light of the circle must be
partially polarized in every part, the polarization increasing
with the distance from the moon or sun on either side, up to
a certain angle, at which it should be complete, and again
diminishing from that point to 180° of distance, where it should
disappear.

A lunar halo, with a pair of false moons, similar to that above
described, but without the cross, was seen at Bandon, in the
County of Cork, on the night of the Ist of May. The appear-
ances are thus described by ‘Mr. Richard Allman: ‘* A faint
halo surrounded the moon, at a distance which appeared equal
to that of the pole star from the nearest point in the Plough.
In this halo, at the extremities of the horizontal diameter, ap-
peared two nebula-like, luminous masses, between which an
intermittent stream of faint light seemed to play. I first per-

21

ceived it about 11 o’clock. It continued unchanged for about
an hour.” The phenomenon was seen, under a much more
complex form, by Mr. Lowe, at Lenton, Nottinghamshire (see
Phil. Mag., Nov. 1844), and the fact indicates the very wide
outspread of the high cirrus and cirro-stratus cloud, by the
frozen particles of which it is produced. The existence of this
cloud in the neighbourhood of the moon is also recorded in
the Day-book of the Dublin Magnetical Observatory, at 10
p. M. of the same night. It would be interesting, in this point
of view, to multiply the records of such phenomena, so as to
be able to trace the extent and limits of the cloud in question.
I find, in the Philosophical Transactions, that a remarkable
halo surrounding the sun, accompanied with parhelia, was seen
on the same day (Oct. 20, 1747), at Paris and Berlin; but
the evidence derivable from such a fact is incomplete, in the
absence of any account from intermediate stations.

Rev. Thomas Porter, D.D., presented an ancient wooden
table and dish, and communicated the following notice:

The wooden table and‘dish to which this notice relates,
were dug up in a peat moss, or turf-bog, near the road from
Donaghey, in the townland of Killygarvan, parish of Desert-
ereight, or Dysertcreaght, County of Tyrone.—( Ordnance
Survey, Sheet 38.) They were found four or five feet below
the surface. With the dish there was a quantity of hazel
nuts. Each article was cut out of a solid piece of wood, ap-
parently fir. The table is of an oblong shape, with the ends
curved inwards towards the centre.

The four short legs, about six inches high, are in the form
of truncated cones, and about four inches thick. They are con-
nected at their bases, except on one side, by a low rim, about
one inch high, in the longest side of which are two holes,
capable of admitting a cord or thong.

The dish was a long oval, four or five inches deep, clum-

22

sily hollowed out of a piece of a trunk of fir. Its length,
when found, was exactly the same as the extreme length of
the table, two feet. Its breadth was about ten inches, and
just sufficient to cover the extremities of the four legs, but
not to allow of its lying between them. It has since split
lengthwise, in such a manner as to alter its proportions mate-
rially. In the edge of one side, where it has been somewhat
injured, are the marks of two holes, exactly answering to the
two in the rim under the table. From those particulars it
may be inferred that the table was used by persons who sat
on the ground at their meals; and that the dish, when not in
use, was attached by a thong to the under surface of the table,
which might be hung against the wall of the dwelling, or
slung on the baggage when the owners migrated from place
to place in the woods. It is not improbable, too, that the
curved ends of the table may (as has been suggested by an
observant person) have been of use in transferring meal, when
ground in a quern or hand-mill, from the table to the dish.
Possibly, also, the rim on the under surface may have been
of use in kneading dough for cakes, the table being inverted
for that purpose.

The workmanship and appearance of both articles are
rude in the extreme, and indicate a very low state of civiliza-
tion in the people who used them.

Nothing very remarkable has been found in the same bog,
or in any of the many adjoining ones, except some stags’
horns, whieh were dug up in the next little valley, in the
townland of High Cross, and which are now in the posses-
sion of John Lindesay, Esq., of Loughry.

DONATIONS.

Annales des Sciences Physiques et Naturelles d Agricul-
ture et d Industrie. Publices par La Sociéte Royale d Agrt-
culture, §c. de Lyon. Tome V. Année 1842.

23

Flora Batava, door Jan. Koops. (132.) Presented by
the King of Bavaria.

Synopsis of the Carboniferous Wutheatone Fossils of Ire-
land. Presented by the Author, Richard Griffith, Esq.,
\Y Gb an

Greenwich Astronomical Observations, 1842. Appen-
diz to do., 1842. Presented by the Royal Astronomical
Society.

Proceedings of the Zoological Society of London. Part 2.
(243). Reports of the Council and Auditors of do. Presented
by the Society.

Proceedings of do., with Plates in Illustration of the
Papers abstracted, Session 1843, 1844. Vol. 1V., No. 98.
Presented by the Society.

Journal of the Statistical Society of London. Vol. VII.
Part 3. Presented by the Society.

Statistical Returns of the Dublin Metropolitan Police,
Jor the Year 1843. Presented by the Commissioners.

Journal of the Franklin Institute. Third Series. Vol. VI.
Presented by the Institute.

Sixth Annual Report of the Commissioners of the Loan
Fund Board of Ireland. Presented by the Commissioners.

Fourteenth Annual Report of the Belfast District Asylum
Sor the insane Poor. March, 1844. Presented by the Go-
vernors.

Tenth Annual Report of the Poor Law Commissioners,
1844 (London). Presented by the Commissioners.

The First Part of the Ninth Volume of the Transactions,
with the new Laws of the Batavian Society of Experimental
Philosophy. Presented by the Society.

The Blade of an ancient Bronze Sword, mounted with
a modern Iron Hilt, found in the County Kerry. Presented
by Maurice O’Connell, Esq., M. P.

Several Cannon Balls found on both Sides of the Boyne,

24

in the Neighbourhood of Oldbridge. Presented by Lieutenant
Newenhan, R. N.

An ancient Bronze Spear-head, from Roscommon. The
Boss of a Shield. A small Bronze Celt. A decade Ring and
Cross. A copper Fibula. Presented by Abraham White
Baker, Esq. a i

A perforated Stone, found in the Grave-yard at Kille
Derry, Derry Art. Presented by Lord George A. Hill.

PROCEEDINGS

OF —

THE ROYAL IRISH ACADEMY,

1844-45. No. 49.

January 13, 1845.

SIR Wn. R. HAMILTON, LL.D., President, in the
| Chair.

Robert Scott Bradshaw, Esq., Thomas Davis, Esq., Sir
Richard Franklin, M. D., Edmund Getty, Esq., George A.
Hamilton, Esq., M. P., Henry G. Hughes, Esq., Capt. Henry
James, R. E., Francis L’ Estrange, Esq., Edward Lucas, Esq.,
John Phillips, Esq., Thomas N. Redington, Esq., M. P., Mar-
mion W. Savage, Esq., and Richard Sharp, Esq., were elected
Members of the Academy.

It was moved by Sir Wm. Betham, and seconded by P. D.
Hardy, Esq., ‘‘ That a Committee, not members of the Coun-
cil, be appointed to examine the Returns laid on the able of
the Academy on the 30th of November last, to inquire into
the facts therein stated, and to report thereon; and that the
Committee consist of Sir William Betham, Lieut.-Col. Harry
D. Jones, R. E., Thomas Hutton, Esq., William Hogan,
Esq., and Aquilla Smith, Esq., M. D.”

Which motion, having been put, was negatived without
a division.

Mr. Robert Ball read a notice on the original use of cer-
VOL. Ill. D

26

tain Golden Ornaments, and other articles, in the Museum
of the Royal Irish Academy.

Mr. Ball having urged on those who study antiquities
the importance of applying observation and analogy to the
solving of antiquarian difficulties, shewed how these instru-
ments of inquiry should be applied, by the study of races of
mankind at present existing, whose state may be supposed
somewhat similar to that in which the people were into whose
history inquiry is proposed to be made; it being fair to look
for like effects from similar causes. He referred to a former
paper, read January, 1844, in which he shewed how metal
celts, identical in form with those found in Ireland, were
used at the present day on the east coast of Africa; and how
stone celts, also similar to those of Ireland, were used in
Mexico. Applying the same reasoning to explain the object
and use of the golden ornaments called by some diadems, by
others gorgets or collars, he mentioned that in the Sandwich
Islands the natives used stone celts precisely similar to those
found in Ireland; they also had those curious lentilform discs
of stone, precisely identical with those found in Ireland, and
to which sundry fanciful uses have been ascribed, but which
Cook and others found to be used as bowls in a favourite
game of the natives, who had bone bodkins, &c., similar to
those of olden time in Ireland; it was, therefore, little more
than was to be expected, to find analogies to the golden or-
naments found associated with the celts and bowls to which
‘Mr. Ball referred. This, he maintained, he had done, in one
case at least, that of the golden ornament referred to, which
has its representative in the Sandwich Isles, where gold is
not known. . Sharks’ teeth, mother of pearl, feathers, and bas-
ket work, are so put together, as was shewn by the figures
exhibited, as in all but material to resemble the ornaments of
gold in the most striking manner.

From the way in which the ornaments of the Sandwich

4

27

Islanders are stated to be worn, Mr. Ball declared he could
not doubt the golden ornaments were worn in a similar
manner. The Sandwich Island articles to which he alluded
formed a part of the fine collection made in Cook’s voyages,
and deposited in the Museum of the University. He trusted
he would:be able to make many of the weapons and orna-
ments therein contained useful in throwing light on Irish an-
tiquities. He referred to several curious instances, where the
use of hypothesis had misled antiquaries, and where observa-
tions of existing people had set their opinions aside. He men-
tioned that he had recently proved, that an article long exist-
ing in the University Museum, and known as the best example
of an old form of a trumpet, had, by the discovery of its re-
maining parts, proved to be a chemical instrument for burning
gas, or inflammable vapour; and he concluded by stating,
that the article figured in the seventeenth volume of the Trans-
actions of the Royal Irish Academy, as an astronomical
instrument of the ancient Irish, proved to be a piece of chain
armour. ‘These two last mistakes he gave as examples of a
want of exactness of observation, and of the mischief of hy-
pothesis.

The Secretary read a paper by Professor Young of Bel-
fast, on Diverging Infinite Series, and on certain Errors in
Analysis connected therewith.

The subject of diverging series is one of considerable per-
plexity in analysis, and has given occasion to theories of ex-
planation involving views and statements entirely opposed to
the general principles of algebraical science. It has, for in-
stance, been affirmed of such series—when they present them-
selves as developments of finite expressions—that, though
algebraically true, they may, nevertheless, be arithmetically
false. By some they are considered to justify conclusions
palpably erroneous and absurd, as, for example, that

D2

28

1) Se Ns es eee

while by others they are regarded as meaningless results, and
have thus been altogether rejected from analysis.

It is impossible to avoid the occurrence of these series:
they present themselves at a very early stage of algebra, in
the form of geometrical progressions and binomial develop-
ments; and thenceforward are continually met with by the
analyst up to the remotest applications of the integral calculus.
The existing vagueness and indecision, as to the proper mode
of interpreting such series, is thus a matter of some concern,
as calculated to retard the progress of science, to diminish our
confidence in some of the truths of analysis, and to give cur-
rency to results involving error and contradiction.

In the present communication it will be my endeavour to
ascertain the causes of the perplexities and discrepancies above
adverted to, and to discover the legitimate interpretation of
diverging infinite series; from which it will, I think, follow
that certain expressions received into analysis as the sums of
several of these, are erroneous. The fact that Poisson, Cauchy,
Abel, and indeed most of the modern continental writers, re-
ject diverging infinite series, and pronounce them to have no
sums, does not render such an endeavour the less necessary ;
inasmuch as the analytical operations, in virtue of which finite
values have been attributed to extensive classes of these series
by Euler and subsequent investigators, remain, I believe, un-
impugned. Widely different methods appear to concur in
furnishing the same numerical results for such series; as, for
instance, the method of definite integrals, and that deduced
from the differential theorem, both so frequently applied by
Euler to effect the summations of series of this kind; and the
numerical results obtained by him have often, apparently, been
verified by later computers; some of whom have employed
methods quite distinct from those of Euler; as, for instance,

29

Horner, who arrived at Euler’s results by aid of considerations
drawn from the theory of continued fractions.*

So long, therefore, as the admitted operations of analysis
thus conduct to conclusions—and conclusions, too, mutually
confirmatory of one another, though arrived at by very diffe-
rent paths—we are surely not authorized in summarily reject-
ing them as meaningless or absurd, merely on account of any
inherent difficulties involved in them. ‘The only ground for
such rejection, that can generally be considered as sufficiently
cogent by analysts, must be errors in the reasoning by which
those conclusions are reached. In attempting, therefore, now
to point out the existence of these errors, it will be perceived
that I proceed on the assumption that nothing has as yet been
advanced, by the rejectors of diverging infinite series, against
the reasonings of Euler, Lacroix, and others, in reference to
this matter; more especially that the method of definite inte-
grals, and that depending on the differential theorem, have
not as yet been shewn to be erroneous. I may be wrong in
this supposition ; if so, 1 should feel most. anxious to withdraw
this Paper, rather than obtrude upon the attention of the
Academy the discussion of a topic already disposed of—and,
doubtless, in a more complete and satisfactory manner—else-
where.

I.—As noticed above, the first step in the general theory
of series occurs under the head of geometrical progression ; the
form of the series proposed for summation being

a+ax + ax? + av®+ &e. (1)
where it is to be observed that the ‘‘ &c.” implies the endless
progression of the terms beyond az*, according to the law ex-
hibited in the terms which precede ; excluding, however, every
thing in the form of supplement or correction. The general
expression for the sum of n terms of this series is known to be

* Annals of Philosophy: July, 1826, p. 50.

n

s=7- =. (2)

Now it is customary to write the development of = as fol-
lows, viz.

—_ = atax+ ax? + ax + &e. (3)

Ye al,
and then to commit the mistake of confounding this with the
series (1) above; overlooking the fact that the “‘ &c.” in the one,
except under particular restrictions as to the value of z, is
very different, as to the meaning involved in it, from that in

the other.
If we dispense with the ‘‘ &c.” in the series (1), we may
write that series thus :

atar+azr? +an+...+ ax’, (4)
the sum of which will be truly expressed by the formula (2),
by making 2 infinite; as that formula is perfectly general.

; ; a
But this same formula gives for res the development
ax” *

l—2 (5)

ag taxtae tan... + a0? 4

l—a2
shewing that the ‘&e.” in (3) differs from that in (1) by a
quantity which is infinitely great, whenever a is not a proper

function: except in the single case of x= —1. When «
is a proper fraction, the two series become identical by the
ax”
evanescence of ‘
l—z

It thus appears that — is not the fraction which gene-

rates the series (1), « being unrestricted: what this fraction
really generates is exhibited in (5) above, an equation which
is always true, whatever arithmetical value we assign to a;
and to obtain the general expression for the sum of (1), we

* As the exponent in this last expression is infinite, it seems unnecessary
to write it om + 1.

31

b.)

a F i
must connect to aa the correction — : a correction

1—a2
which is ambiguous as to sign, when z is negative.

When z is > 1, the series, omitting this correction, is © ;
the correction itself is also oo, and opposite in sign: it is the
difference of these two infinites which is the finite undeveloped
expression.

There is thus no discrepancy between a geometrical series
and the expression which generates it: nor is it the case that
by connecting the two by the sign of equality, we shall have
an equation algebraically true, but in certain cases arithme-
tically false, as has been frequently affirmed of late. The re-
verse of this affirmation is the more correct statement ; inas-

much as by interposing the sign of equality between =
and the series (1), instead of the series (5), we have an equa-
tion algebraically false, though, within certain limits, arith-
metically true: this last circumstance arising from the fact
that the omitted correction, which renders the equation alge-
braically defective, would have vanished of itself, between the
arithmetical limits adverted to, had it been introduced. Thus,
the series noticed at the commencement of this paper, viz.

14244484416 + &.,
and which is intended to represent the development of os

arises from expressing the general development of — in the
—2
defective form
ltatertetatt...+2°,
instead of, in the accurate form,
Ltatetortait...-a° 4+

which defective form introduces arithmetical error only when
aw exceeds unit. When x = 2, the error arising from this de-
fect is infinitely great; the true form giving, in that case,

ic}

x
l—2’

32
—~1l=1+4+2+4+4484164...—27=Hn—~o,
which involves no error or contradiction.

It hence appears that when the geometrical development
is a converging series, for an arithmetical value of the common
ratio, no error can arise from the omission of the supplemen-
tary correction, which is always necessary for the completion
of the algebraic form of that development; but that when the
arithmetical value of the ratio is such as to render the series
divergent, the algebraic error necessarily introduces an arith-
metical error infinitely great: the correction of the algebraic
form furnishes, in such a case, the expression o — o, that is
the difference of two infinites, for the finite undeveloped nume-
rical value: and in this there is nothing inexplicable or pecu-
liar.

We see, therefore, that in passing from the convergent to
the divergent state of a geometrical series, we have no oc-
casion for any new principle, such, for instance, as the sign of
transition, introduced by Dr. Peacock, in the discussion of
this subject, in his very valuable and instructive Report on
Analysis, presented at the third meeting of the British Asso-
ciation. If there only be strict algebraic accuracy between
the finite expression and its developed form, there will neces-
sarily be equally strict numerical accuracy, whatever arithme-
tical values be given to the arbitrary symbols: a truth which
must indeed universally hold in all the results of analysis.

Ii.—The developments of the binomial theorem, as well
as those considered above, have also been the source of much
perplexity and misinterpretation, when they have assumed a
divergent form. In contemplating these developments, the
fact has been overlooked, that although, when interminable,
they each involve an infinite series, whose terms succeed one
another, according to a certain uniform law, yet that series
alone is not the complete algebraical equivalent of the unde-
veloped expression: a supplementary function of the symbols

33

employed is always necessary to such completeness. This

has already been seen in the development of or(1—2)"’,

l—a2
which is a particular case of the binomial development: be-

@o

sides the series, the supplementary expression = is neces-

jas
sary to the complete algebraical equivalence of the two mem-
bers of the equation. And it is plain, from the nature of
common division, that a like supplementary addition must be

made to the infinite series furnished by the development of
1

(1—2)"
(1—2)!, (l—2), &e., it is equally plain that, however far
the extraction be extended, we approach no nearer to the ac-
tual exhaustion or annihilation of the algebraic remainder ;

or (1—a)-". In the extraction of roots, too, as in

and therefore we are not authorized to dismiss this remainder
and to account it zero, when general algebraic accuracy is to
be exhibited ; although, as in geometrical series, we may do
this in those particular numerical cases in which the remainder,
if retained, would vanish. It thus appears that, calling the
remainder after n terms, whether x be finite or infinite, f(2),
the ordinary binomial series, to terms, will be the complete

development, not of (— a)"; but of (1 —a — f(2))" ; and

therefore that, if this series be equated to (la) merely, it
will require a supplemental correction to produce strict alge-
braical equivalence; which correction must be such as to
vanish for those numerical values of x, which cause f(x) to
vanish.

These values are all those which render the series diver-
gent: for, as well known, we can, in every such case, approach
by the series alone as near to the numerical value of the un-
developed expression as we please. It is thus only when the
" series ceases to be convergent, that the correction adverted to
has any arithmetical existence, adjusting the equality of the

34

two sides of the equation, and precluding the inconsistency so
frequently affirmed to have place between them.

From these simple considerations, it is easy to explain and
reconcile such results as

2a 24a*® 2.4.6a° 2.4.6.8a7

for all arithmetical values of x; the ‘‘ &c.” being regarded as
comprehending all that is necessary to render the second mem-
ber of the equation a complete algebraical equivalent of the
first. When x exceeds a’, the series becomes divergent ; and
the first member of the equation becomes imaginary: and
since it is impossible that any imaginary quantity can enter
the series, it follows that it isin the supplementary correction
under the “ &c.” that such quantity must occur, when in that
correction a value greater than a? is given to 2,

From what has now be shewn, it may, I think, be legiti-
mately inferred—as far, at least, as geometrical and binomial
series are concerned—

1. That whenever any such series becomes divergent for
particular arithmetical values, what has been called above the
supplementary correction becomes arithmetically effective,
and cannot be disregarded without arithmetical error.

2. And that so far from such series being, as usually
affirmed, always algebraically true, though sometimes arith-
metically false, on the contrary, they are always algebrai-
cally false, though sometimes arithmetically true :—true in
those cases, namely, and in those only, in which the proper
algebraic correction becomes evanescent.

11 1.—Let us now pass to the consideration of other classes
of diverging series.

There are two ways of investigating the differential of
sin 2, or of sin mx: one by proceeding, as Lagrange has done,
by actual algebraic development; and the other by employing
the method of limits, independently of development. Accord-
ing to Lagrange, we must proceed upon the assumption that

35

sin ma = Ax + Ba? + cx® + &e.
justifying this assumption on the ground that x and sin ma
vanish together; which can be considered valid only so long
as m = o is excluded. In fact, whether we seek the deve-
lopment of sin mz after the manner of Lagrange, or by the
theorem of Maclaurin, it is essential to the very nature of the
investigation that the unknown coeflicients a, B, c, &c. be all
assumed to be finite. We cannot conclude, therefore, from
dsinmz
dx
infinite: and similar considerations forbid the conclusion that

Lagrange’s reasoning, that = m cosmz, when m is

dcosmx . Leen ,
ae = — msin mz, in like cireumstances. The method of
Cm

limits equally militates against such a conclusion; thus, if the
function were sin 2, we should have

sin (w +h) — sina = 2sin$hcos(a + $h),

or
sin(a +h) —sinz — sinth
Sti Aad ne Dena za T; cos (a + 3h);
2
‘ : sinth ; Ae
and since i; = 1, in the limit, or when A = 0, we should
2
safely infer that ao = cosa. But, by proceeding in like

manner with sinmz, we should have

sin (ma + mh) — sinmax sing mh
— -- in ——__

h mh
from which, if m be infinite, it could not be inferred that
dsin mz

dx

sintmh

5 mh
that value when h = 0; nor that, in like circumstances,
cos(mx + 4mh) =cosmx. We have nothing to justify the
d sinkh sink mh
= and —4——

2 h 2 mh

cos (mz + }mh),

= mcos mx; since we have no right to affirm that

tends to 1, as diminishes, and finally terminates in

assertion that are the same at the limits

36

when m is infinite: and it should create no surprise if conclu-
sions, deduced from this assumption, prove to be absurd.
Bearing this in remembrance, let us take the series
5 = sing — 4sin2a + 4sin3a2 — &e.
first given by Euler, and which is known to be rigorously
true for all values of « below z.*
From this series the following results have been deduced
by differentiation, and they have been pretty generally re-
ceived into analysis :

+= cos2 — cos 22 + cos3a — cos4xz + &e.
0 = — sing + 2sin 2a — 3sin3a2 + 4sin42 — &e.
0 = — cosa + 2?cos2x — 3?cos3a + 4°cos4a — &c.

and, generally,
0 = cosa — 2" cos2a-+ 3% cos3a —4™" cos 4a + &e.
0 = sing — 2+! sin2a 4+ 3%+!sin3da—4"T!sin4da + &c.

so that putting 2 = 0 in the first of these, and « = 2 in the

second, we have
O=1— 243% — 44 &e,
O= 1 — Bm tly 5xtl _ Tt 4 &e,
results which are all inadmissible; because, from the outset,
it is assumed that
dsin mx

dx

though m be infinite.
In reference to the preceding results, Abel justly asks :
‘¢ Peut-on imaginer rien de plus horrible que de débiter

0O=1—2% + 3% 4" 4 &e,

ou n est un nombre entier positif?’’}

. dcos mz pat:
=m cosma, and 7 = — msinmz;
‘x

* It will be shewn, towards the close of this Paper, that it is true for all
values up to z inclusive.
+ Guvres Completes, tome ii. p. 266.

oT

It is plain that, however far such a series as this be ex-
extended, a supplementary correction is always necessary to
complete the equation; which correction must be infinite in
value if the series be infinitely extended : and the analytical
considerations offered above fully accord with this statement,
the contrary of which could never have been entertained had
not analysis seemed to justify the strange conclusion. All
that analysis really authorizes us in saying, in reference to the
extreme cases here considered, is—as the French analysts ex-
press it—that ‘la méthode ordinaire est en défaute.”

Having mentioned the name of Abel in connexion with
this subject, it may not be out of place to notice here, that
that distinguished genius seemed inclined to trace the erro-
neous results above to another cause: ‘‘ On applique aux
series infinies toutes les opérations, comme si elles étaient
finies ; mais cela est-il bien permis? Je crois que non. Ou
est il demontré qu’on obtient la differentielle d’un série infinie
en en prenant la differentielle de chaque terme?” And he
then adduces the result,

4 = cosa — cos2z2 + cos3a — &e.

which he pronounces to be ‘ résultat tout faux.”*

But I submit that no such results of differentiation can
ever be absurd, unless the absurdity attaches to one or more
of the individual terms.

In the former part of this paper the examination was re-
stricted to those classes of diverging series which arise from
the development of fractions into geometrical series, and from
the expansion of a binomial: but it is plain that the reasonings,
in reference to the former developments, equally apply to

those which arise from any fraction f2 ne; ; and the reasoning,

in reference to the latter, equally aa to any root or power
of (x). And, in what is shewn above, we see how divergent

* Cuvres, tome ii. p. 268.

38

trigonometrical series, arising from differentiating convergent
forms, are to be understood.

1V.—It remains now to be noticed that in some of the
more advanced parts of analysis—especially in the doctrine of
definite integrals—conclusions have been reached which seem
to contradict the proposition endeavoured to be established in
this Paper, viz. that convergent infinite series have no finite
sum. But all such conclusions will be found upon examina-
tion to originate in mistake. I proceed to examine the more
important of these.

The following has been recently offered, by a very cautious
writer, in support of the statement that “1+ 2+4+4-+ &c. ad
infinitum, is an algebraic representative of — 1, though it only
gives the notion of infinity to any attempt to conceive its
arithmetical value” :

b
\o-%de rae \ a—?dx = a~ —b, which is finite ;
a

0 m +m “9
y x dz = + om, \"o8da =+o, (de ——— za

If, then, we construct the curve whose equation is y = a~,
and if OA =—m, OB =-+™m, we find the areas PAOY...
and QOBY...both positive and infi-
nite, which agrees with all our notions
derived from the theory of curves. Again,
if we attempt to find the area PY QB,
by summing PAOY and YOQB, we
find an infinite and positive result, which P Q
still is strictly intelligible. But if we : | |

Y

want to find the area by integrating at

2 :
once from P to Q, we find, as above, — —, a negative result,
m

for the sum of two positive infinite quantities. The integral
then, y being infinite between the limits, takes an algebraic
character, standing in much the same relation to the required
arithmetical result, which must have been observed in diver-

39

gent series. ‘ Thus, &c.,” as quoted above.* The analogy
thus apparently established is traceable to an oversight, of
very easy detection, in the preceding integrations ; which, in
the correct form, will stand as follow :

0
(oda Se
) ada = +o - od
m
-, adding,
im 2
y a dz = 20 — —.
—m m
Or thus,

=2a0-—-.
m

But errors of a much more important kind occur in all the
applications of definite integrals to the summation of diverging
series: a mode of summation first, I believe, adopted by
Euler, and very generally employed by subsequent analysts.
A single example of this method will be sufficient to shew the
character of the errors adverted to; which, though so glaring
as almost to obtrude themselves upon the attention, have not
hitherto, so far as I know, been noticed by any writer. Any
one of the examples given by Euler (Institutiones Calc. Diff),
and afterwards by Lacroix (Traite du Calcul. &c., tome iii.),
will answer the present purpose: I shall take that at page
573 of the English edition of the smaller work of Lacroix,
viz.

s = 14#—1.2241.2.368—&c. (6)

which, Sir John Herschel remarks, is such that ‘‘ however

* De Morgan’s Differential and Integral Calculus, p. 571.

40

small a value we attribute to ¢, the series must always diverge
after a certain number of terms.’’*

The reasoning by which a finite sum is determined for s,
when ¢ = 1, is as follows:

= = l.dt—1.2¢dt+1.2.3@dt— &e. (7)
aa (= =t—1.¢+41.20 — &e. (8)
=t— st (9)

a = (1 — s)dt — tds,

or,
‘ ds 14+¢ 1
de eee, eee 2

and from this is found, for s, the definite integral

Lic

s=-eé y edt;
t 0

from which it is inferred that “if ¢ = 1, or the above integral

be taken from ¢ = 0 to ¢ = 1, we have the expression for the

value of the series

Sp os Mee

Now several objections lie against the preceding reasoning :
in the first place it is assumed, in the final step, that s vanishes,
for ¢= 0, notwithstanding that ‘* however small a value we
attribute to ¢ the series must always diverge,” and thus at
length furnish terms infinitely great: and in the next place it
is assumed—and the assumption is somewhat similar to that

* If, however, ¢ be indefinitely near to zero,.the ‘certain number of
terms” adverted to in the text, will be indefinitely great; that is, the diver-
gency will be indefinitely postponed: the series therefore cannot be consi-
dered as divergent up to the limit t=0; yet, as the statement in the text
seems to imply this, I have considered it to be comprehended in the hypo-
thesis; although, as I have shewn, the point is of no moment in the matter
under discussion.

41

already animadverted upon at page 35—that the series (7) is
strictly the differential of the series (8) which involves the
term 1.2.3...(u—1)é”, n being infinitely great, and for the
differential of which the calculus seems to make no provision.
But, waiving these objections, the deduction (9) is palpably
erroneous, and altogether fatal to the final conclusion. For
the series s is evidently coextensive with the series (8), and
so, of course, is s¢; that is, if (8) contain m terms, so also must
st: if therefore a new term ¢ be prefixed to — sé, in order that
t— st may commence with the same terms as the series (8),
the series ¢ — s¢ will contain » + 1 terms; that is, however
great m may be, ¢ — s¢ will contain, besides the whole of the
series (8), an additional term still more remote: so that if
be infinite, and we assume, as above, that the two series are
equal, we commit an error infinitely great. And this is the
error, thus introduced, which will be found to vitiate all
Euler’s processes for summing divergent series by definite in-
tegrals: an error which obviously has no existence for the
convergent cases of those series; since the additional term,
noticed above, is, in such cases, not infinite, but zero. We
may safely infer, therefore, that the results so often quoted in
analysis, viz.

1—1 + 1.2—1.2.3 + .... = -596347362324

I1—1.2 + 1.2.8 —....... = °621449624236

1—1.2.3 + 1.2.3.4.5..... = °343279002556
&e. &e.

all involve errors infinitely great; and this, as it ought to be,
is quite consistent with the common-sense view of diverging
infinite series,

V.—There is another method of investigation by which
these erroneous results appear to be established: the method
suggested by the well-known differential theorem. But, as
in the processes already considered, so here, that theorem will
be found upon examination to be applicable only to convergent

series. This will be manifest from what follows,
VOL. III. E

42

The differential theorem may be satisfactorily established
by conducting the investigation thus :

Let
a— ba +ca?— dv’? +&. = s
— ba + ca” — dx? + &e. = s—a (10)
o. —b+ cat dx? + ex — &e, = (11)

Consequently, by adding these two equations together, and
representing the numerical differences b—c, c—d, d—e, &c.
by A, A’, A”, &c., there will result the equation

— b6—A.c-+ A2?— A" 2? + &e, = “= E (s—a) (12)
“. —ba— A.2? + Al.a?— A”.a* + &e. = (a4 + 1) (s—a) = 8
s/
: Gaia
that is,
s=a— be + 2aF [O—A.a 4+ A’.a?—A”.2° + &e.] (13)
i z+1° «+1

And by treating the series within the brackets as the original
was treated, and so on, we shall finally obtain the transfor-
mation

a@+l (#+1)? («+1)°
or putting a = 0, and dividing by — x, we have
b — cx + dx® — ex? + &.=
b A. LNG Ce ie
e+l i (a+1)? a5 (~+1)? 13 (a+1)* igh
which is the usual form of the theorem.

Now the preceding reasoning is inadmissible except the
proposed series be convergent; that is, except 7x” approaches
to zero as n approaches to infinity, 7a” standing generally for
the n term of (10). Forin (12), which results from the sum of
(10) and (11), this n”, or final term, is regarded as zero, and
is neglected ; inasmuch as it is by this term that the series (10)

43

extends beyond the series (11) to the right ; a fact which is
of no moment when this term merges in zero, but of infinite
consequence when it merges in infinity. In such a case there-
fore, a numerical error, of infinite amount, is committed at
this step of the reasoning. Again, if the series within the
brackets at (13), have its terms, like those of the original,
tending to infinity, another numerical error of infinite amount
comes to be introduced; and so on. In fact, just as in the
method of definite integrals, before discussed, it is assumed, at
each step of the reasoning, that terms infinitely great are ex-
eluded; and not only so, but that the terms ultimately dimi-
nish to zero. In the contrary case, therefore, the differential
theorem is altogether inapplicable, leading to results which
are equally inadmissible, whether the terms of the series in-
crease without limit, or remain stationary in value: forming
what has been called a neutral series. In this latter case the
error committed will be finite; in the former it will be infinite.
That an error is really committed in the application of this
theorem to neutral series, will be more explicitly shewn pre-
sently.

Notwithstanding the imperfections noticed above, it should
create no surprise that, in the applications of the differential
theorem to particular diverging series, we so often obtain the
algebraic function whose development really gives rise to the
series, although no numerical approximation to the diverging
series itself. ‘The function, whose development gives rise to
the series, being represented by f(x), the series itself may be
represented by f(x) — 9(#), agreeably to what has already
been shewn in the former part of this Paper: it is the neglect
of the function $(«), in the particular application considered,
that introduces the infinite numerical error into (13) ; leading
us to conclude that, for the proposed value of #, f(z) =s, in-
stead of f(~)—9$(2)=s. Now if there exist a convergent case
of s, that is a case in which ¢(x) = 0, the differential theorem
will compute it, furnishing the proper function of x, f(z),

E2

44

which accurately expresses the series in all its convergent
cases, and of which the development gives rise to the series in
its general form. When no such function f(z) really exists,
then it is only to the numerical value of an approximate func-
tion that our computation tends in particular numerical cases ;
as, for instance, in such a case as that considered at p. 39.

It may be worth while to notice here, as an immediate in-
ference from the differential theorem, that when a series, pro-
ceeding according to the powers of w, and extending to infi-
nity, has its coefficients such that their differences at length
become zero, that series is always the development of a rational
fraction whose denominator is some integral power of (1+ 2).

There is, I think, a mistake committed in always attri-
buting this theorem to Euler. It was published by Stirling,
in his Methodus Differentialis, so early as 1730; and I believe
no mention of it occurs in the writings of Euler till long after
this date.

VI.—As far as I know, there is but one other general
analytical principle that has been affirmed to give countenance
to doctrines opposed to those attempted to be established in
the present Paper: the principle, namely, that when an alge-
braic expression, for continuous numerical values of the va-
riable, approaches continuously to a certain finite numerical
value, this value properly expresses the ultimate, or limiting
state of that expression. In virtue of this principle, it has
been stated* that, ‘* Poisson would admit 1?— 2?4 3?— 4? +
... = 0, since there is no question that, g being less than
unity, the mere arithmetical computer might establish, to any
number of decimal places, the identity of 1?—27g 4 3°g?_...
and (l—y) (l+g)~.”t But I submit that the series here

* Transactions of the Cambridge Philosophical Society, Part II. 1844.
+ In order that the series 12— 2?g + 3%9?_.... may become convergent
after n terms, there must evidently exist the condition

n+1\2 n 2
— 1, whence ——);
( = yo< w ence 9 < (<*>)

45

proposed exceeds the powers of computation more and more
as g approaches to 1; involving at length terms infinitely
great, and thus tending to no finite limit. In other words,
however many terms of this series be summed, the results
would diverge more and more from zero as g approaches to 1 ;
and would actually become infinite when g reaches this limit.
The conclusion, therefore, that 1?—2? + 3’—...= 0 is, as
in the other instances discussed in this Essay, erroneous to an
infinite extent: and it thus affords one more example of the
truth of the doctrine here advanced.

The general analytical principle announced above has
been misapplied, or improperly neglected, in many important
inquiries connected with series. It may not be uninstructive
to advert more particularly to some instances of this.

At page 267 of the second volume of his works, Abel has
the following remark: ‘¢ On peut démontrer rigoureusement
qu’on aura, pour toutes les valeurs de w inférieures a 7,

3 = sine — 4sin2v7+4sin3a — &ce.

Il semble qu’on pourrait conclure que la méme formule aurait
lieu pour z= 7; mais cela donnerait

2
and as G+) is itself less than 1 for every finite value of n, however
n

great, it follows that g may approach so near to | as to postpone the point
of convergency beyond any finite limit; which is tantamount to saying that
this point can never actually be reached. The series, therefore, cannot tend
to merge into zero as g approaches to 1; so that zero is not the limit to
which the series continuously approaches as g approaches continuously to 1;
and therefore the general principle stated in the text does not countenance
the conclusion that 1? — 2? + 3?—....= 0.

I cannot help regarding the criterion of convergency proposed by Cauchy
(Cours d’ Analyse, p. 152) as open to objection; since, according to it, we
should pronounce a series to be convergent under circumstances in which
the point of convergency would be postponed beyond any finite limits: more-
over, what security have we that neutrality may not have place before diver-
gency commences ?

46

7 : i f
5 = sine — 4sin 27 + 4sin37 — &e. = 0,

resultat absurde.”

Now the formula, agreeably to the general principle here -
affirmed to be in fault, does really comprehend the limiting
case «7, as well as all the cases up to this; for when x
reaches this limit all the signs of the series become plus ; and
as it is known that

l+34+34+274+&. =o,

the series presents a particular case of 0X; which it is wrong
to declare to be 0, in contradiction of its legitimate interpre-

tation, “ on the left. This error has led Abel into other mis-

takes of consequence: thus, at page 90 of his first volume, he
says that the function
“sing — $sin2¢+ 3sin3¢— &e.

a la propriété remarquable pour les valeurs ¢ = 7 et $= —7
d’étre discontinue.” And at page 71 the same erroneous view
has induced him to animadvert upon a certain principle of
Cauchy, which the true interpretation of the matter would
have tended to confirm.

Fourier, Poisson, and many other modern analysts, have
also made similar mistakes in their general investigations re-
specting series. Thus, to quote Professor Peacock as to the
views of the former,

6

Ae 20 Ae :
“cosa = “5 sin 2a + 35 sin4d a + BY sin6a + &e. |

a very singular result, which is, of course, true only between
the limits 0 and 7, excluding those limits.”*

~The series is, however, true including the limits: for when
« = 0, the signs are all plus ; and, as it is easily shewn that

2

4 6
Tyhigg tha yith Bei

* Proceedings of the Third Meeting of the British Association, p. 257.

47

we here again have a case of 0 x o, correctly interpretable
by the left hand member of the equation; that is, the right
hand member, when z = 0, is accurately 1. When «= 7, the
- signs of the series all become minus: therefore the true value
in that case is — l.

Before concluding this subject it may be proper to observe,

that the investigation, whence the series for 5 is usually de-

duced, is deficient in generality. Whenever logarithms are
employed in connexion with imaginary quantities, the imagi-
nary forms of the logarithms, as well as the real, ought always
to be introduced into the investigation : hence the logarithmic
expression, from which the series alluded to is derived, should
be written thus:

peace | OR eS

5 eros 4 +&c.4 2k /—]

log u=u—u-'—

By substituting in this ewV—! for w, and then dividing the re-
sult by 2% —1, we shall have the correct and general form,

: ee sin22 ee sin32 sin4z
2 2 3 4

where & is any whole number, positive or negative, deter-
minable in any particular case, so as to conform to the first
member of the equation: regarding that first member, # not
x

Dy

I have here used the limited logarithmic forms of Euler,

+ &e. + kr,

exceeding 7, as indifferently either - or kh +

and not the more general ones furnished by Mr. Graves’s
theory of imaginary logarithms,* since these limited forms
are sufficient for all the veal values in the general result.

It now merely remains to be shewn that, as briefly stated
at page 43, the differential theorem is inapplicable, not only
when the proposed series is divergent, but also when it ceases
to be convergent, and becomes what Hutton has called a neu-

* Philosophical Transactions, Part I. 1829.

48

tral series. Thus—although the contrary has often been
affirmed—we cannot legitimately infer from this theorem,
without the aid of an additional principle, that

1—1+1—14+1—1+4+&e=14.

For, as already shewn, the series within the brackets at (13)
is deficient by a quantity, which in this case is = 1. Intro-
ducing this, (13) gives for s the ambiguous result $+ 4;
that is, 1 or 0. The additional principle adverted to, and _
which is absolutely essential to the received conclusion, is that
already stated at page 44; or, as Dr. Whewell briefly ex-
presses it, ‘‘ that what is true wp to the limit, is true at the
limit.”

The differential theorem, therefore, can never be employed
with success to sum either a divergent or a neutral series; or
to convert either into a convergent series.

There has been supposed to exist a perfect analogy between
1—1+41—1+4 &c., as the limiting case of 1—g+g’?—g°+ &c.,
and 1°—2? + 3’—4° + &c., as the limiting case of 1—2?g +
3°7’—4°9° + &e., and that, in consequence of this analogy,
we have as much right to affirm that 1?—2?+4 3?—4? + &e.
is accurately expressed by 0, the limiting case of (l1—g)
(1+ )-*, the fraction which generates 1? — 2?g + 3°g?—4’g?+
&c., as that 1 — 1+ 1—1+ &c. is accurately expressed by

2. l : 3
3, the limiting case of i , the fraction which generates
g

l~g+ 7 —g'? + &e. But there is a total absence of analogy
between these two instances: the series 1—g + g?— g?+ &c.
presents a series of convergent cases from g = 0, uptog=1;
and whatever rule or formula enables us to find the summation
in_all cases must necessarily enable us to find it in the extreme
positive limits 0 and 1; for no values, short of those limits,
can be the first and last of the admissible cases. But this rule
or formula of summation, whatever it be, is constructed con-
formably to certain hypotheses; viz. that the convergent

49

series expressed by it, commences, in all cases, with a finite
quantity, such that the terms of the series, by continual dimi-
nution, tend to zero.

The circumstances are very different with respect to
1? — 2° + 3°9?— 479°+ &e. As observed in the foot-note at
p. 44, the commencement of convergency, in the limiting case,
is at a term infinitely distant from the origin of the proposed
series, and infinitely great. What analogy can there be be-
tween the general converging series—if it may be so called—
of which this is a limiting case, and ordinary convergent se-
ries? And can it be affirmed, of any one of its cases, that the
terms necessarily tend to zero? The answers to these ques-
tions will, I think, destroy all idea of analogy in such examples
as those adduced above.

I have been compelled, in several parts of the present
Paper, to dissent from certain doctrines and opinions promul-
gated by some very distinguished writers on analysis. In de-
veloping the principles and views here submitted to the Royal
Irish Academy, I could not easily avoid a reference to these.
I trust, however, that I have done so in no captious or un-
candid spirit: I have only been anxious to arrive at truth in
an inquiry of acknowledged perplexity, and ofinterest, perhaps,
in the estimation of some, sufficient to justify the attempt.
There are one or two points of analytical delicacy involved in
this inquiry, which may perhaps be open to further discussion :
if I have myself fallen into error in my treatment of these, I
hope I shall be indulged with the same candour and conside-
ration which I have endeavoured to exercise towards others.

Professor Mac Cullagh made a communication on the
subject of Total Reflexion.

In the case of total reflexion the vibrations which take place
in the rarer medium are in general elliptical, and when this
medium is a crystal, the equations by which the ellipse of vi-
bration is determined are very complicated. The projection

50

of this ellipse upon the plane of incidence may, however, be
easily found by the remark in p. 102 of the present volume ;
the projecting cylinder is therefore known, and as the ellipse of
vibration is a section of this cylinder, the question of deter-
mining the ellipse is reduced to that of determining its plane.
For this purpose Mr. Mac Cullagh gave the following rule.
Having constructed the ellipsoid of indices (that whose axes
are parallel to the axes of elasticity, and inversely proportional
to the three principal velocities of propagation in the crystal)
let its two planes of circular section intersect the aforesaid
cylinder. The curves of intersection will be ellipses, which
shall be supposed to have a common centre O in the axis of
the cylinder. Let OP, OP’ be the greater semiaxes of these
ellipses, and OQ, OQ’ the less semiaxes; the lengths of the
two former being denoted by p, p’, and the lengths of the two
latter by g, 9’. Join the extremities P, P’ of the greater
semiaxes, and the extremities Q, Q’ of the less semiaxes; and
divide each of the right lines PP’, QQ’, in the ratio of

Vp? — q? to Vp?—q”. Then a plane drawn through the
centre O and the two points of division will be the plane of
vibration. In the application of this rule some precautions
are to be observed, but they need not here be insisted on.
The foregoing rule was deduced (in the year 1843) from
the general equations by a peculiar use of imaginary quanti-
ties, after the author had several times tried in vain to obtain a
geometrical interpretation of those equations by considerations
of a more obvious and ordinary kind. This use of imaginaries
is founded on a remarkable theorem relative to the ellipse, by
which it appears, that the plane of an ellipse and its spectes
(that is, the directions and the ratio of its axes) may be ex-
pressed by two imaginary constants, just as the direction of a
right line in space is expressed by two real constants. By
means of this theorem—which it is unnecessary to repeat, as
it has been published in the University Calendar (Examina-
tion Papers of the year 1842, p. lxxxiv.)—we may find such

51

properties of elliptical vibrations as are analogous to those of
rectilinear vibrations; and it was in this way that the above
rule was discovered. It is analogous (though it scarcely ap-
pears so at first sight) to the rule by which, in the theory of
Fresnel, the direction of rectilinear vibrations is determined,
when the plane of the wave is given.

The Rev. Charles Graves read the first part of a paper on
Algebraic Triplets.

The object which he proposes to himself is to frame, for
the geometry of three dimensions, a theory strictly analogous
to that by which Mr. Warren has succeeded in representing
the combined lengths and directions of right lines in a plane.
In carrying out this design Mr. Graves has necessarily been
led to the consideration of new imaginaries.

For the sake of clearness it will be desirable to take, in
the first instance, a brief survey of the fundamental properties
of algebraic couplets, depending, as they do, upon the nature
of the symbol /— 1. The correspondence between received
notions and the views now put forward will thus be made
more apparent.

If we take the binomial or couplet x + Y—1.y, in
which « and y are real quantities, and multiply it by a similar

couplet 2 + FY AE is y1, the product will likewise be a bino-
mial of the same kind, 2 + V — 1. Yo; and between the
constituents of the three couplets there exists the relation
(a + y’) (a? + yy) = ise + ine (a)
But couplets may be more readily compared after undergoing
a simple transformation. Such an expression as x+ /—1.y
may be reduced to the form reV—"? by making r= Va + 9,
and 9@= tan-1(2. Hence it appears that if we agree to call

7 the modulus and @ the amplitude of a couplet, the following
theorems will be true:

52

1. Iftwo couplets be multiplied together, the modulus of
the product will be equal to the product of the moduli of the
Jactors.

2. The amplitude of the product will be equal to the sum
of the amplitudes of the factors.

One of the most important analytical properties of the

couplet «+ VY —1.y consists in this, that the equation
a+V/—l.y=0

is equivalent to two, viz. = 0 andy = 0.

As regards the geometric interpretation of the foregoing
results, it is sufficient to observe that the symbol Vv —1 has
been explained as denoting rotation through a right angle;

whilst the couplet # + V—1. has been taken to represent
both the length and the direction of the right line drawn from
the origin to the point whose rectangular coordinates are # and
y: the length of this right line is obviously 7; and it is in-
clined to the axis of w at an angle equal to 0.

The problem now proposed by Mr. Graves is to assign two
distributive symbols, . and x, of such a nature that (1) the sum
or product of two triplets, «+ w-—+x«z and 2+ w; + «2, shall
be itself a triplet of the same form: that (2) there shall be
theorems concerning the moduli and amplitudes of triplets,
similar to those already enunciated for couplets: that (3) the
equation «+ 4-+«z=0 shall be equivalent to the three,
«=0, y= 0, 2=0: and that (4) the symbols x and « shall
admit of a geometric interpretation analogous to that which has
been provided for the symbol V —1.

The preceding conditions will be complied with, if we as-
sume. and « to be distributive symbols of operation, which,
when combined, are subject to the following laws:

k(@) =a: (a) =a: «*(a) = (a): (a) =«c(@).
We must, at the same time, agree to regard .(1) and «(1) as
units absolutely differing in kind from each other and from

53

the real unit. This, in fact, satisfies the third condition. As
?(a) = x(a) we may, for the future, dispense with the symbol
x, and write the triplet in the form «+.cy+’z, or more shortly
thus (2, y, Z).

In the first place, it is evident that the sum or product
of two triplets is itself a triplet.

Next, supposing (a, y, 2). (@, Ys 21) = (Ha, Yo, 22) we
shall have the modulus of the product equal to the product of
the moduli of the factors, if we call the expression a + y? +
2? + («4+0) (ay + yz + 2x) the modulus of the triplet (a, y, z).
And this modular theorem involves in it two others of the
same kind, concerning the purely real moduli, « + y + z, and
x+y? + 2° — ay —yz— zx. According as we bring the
triplet into different forms by changing the variables in it,
there will be either two theorems relating to moduli, and one
relating to amplitudes, or one modular theorem, and two con-
cerning amplitudes.

For the purpose of geometric interpretation let us suppose
the three positive portions of the axes of rectangular coordi-
nates to meet the surface of a sphere, whose centre is at the
origin, in the points x, y, z, through which a small circle of
the sphere is described, and let us give the name of symmetric
axis to that diameter of the sphere, which passes through the
poles of this circle. Now if we conceive the real unit placed
on the axis of a, (1) on the axis of y, and .°(1) on the axis of
z, we may interpret the symbol ¢ by saying that it denotes a
conical rotation round the symmetric axis through an angle
of 120 degrees. Three such operations, executed successively
on the real unit,, will bring it back to its original position
on the axis of x. This is in accordance with the equations

(a) = (a) = F(a) = a:
in virtue of which we may regard :(1) as a purely imaginary
cube root of positive unity.

Mr. Graves mentioned that, since he had obtained per-

54

mission to read the present paper, Sir William R. Hamilton
had kindly communicated to him the abstract and the proof
sheets of a memoir by Professor De Morgan, on Triple Al-
gebra. That paper contains the discussion of a system of
triplets, which is most closely connected with the one now
proposed: the only difference being that Professor De Mor-
gan uses what are in fact new imaginary cube roots of negative
unity.

Mr. Graves thinks that in the interpretation and generali-
zation of his results he has met with greater success; but he
fully concedes to Professor De Morgan the prior possession
of what must be looked upon as fundamental in this theory,
the conception of symbols which act upon each other in the
same manner as the imaginary cube roots of unity. Mr.
Graves also stated that his brother, John T. Graves, Esq.,
had anticipated him in the idea of using cube roots of positive
unity in the constitution of algebraic triplets. -

The remaining portion of the paper, having reference
chiefly to the interpretation of the formule obtained in the
multiplication of triplets, was postponed until the next meet-
ing of the Academy.

Mr. George Yeates presented a tabular Return of the Ob-
servations made by him with Barometer, Thermometer, and
Rain Gauge, at his residence, near Portobello, County of
Dublin, during the year ending 31st December, 1844.—(See
Appendix, No. 11.)

DONATIONS.

An Essay on Aerial Navigation. By Joseph M‘Sweeny,
M.D. Presented by the Author.

Archeologia, Vol. XXX., and Index to Vols. X VI. to
XXX., inclusive. Presented by the Society of Antiquaries
of London.

J. H. R. Mott's Advice and Instructions for playing the

5D

Piano with Expression and brilliant Execution. 2 vols. Pre-
sented by the Author.

Philosophical Transactions for 1844. Part 2. Pre-
sented by the Royal Society.

Memoires del Institut de France. (Morales et Politiques.)
Tome IV. Presented by the Institute.

Journal of the Royal Asiatic Society of Great Britain
and Ireland. No. XV. Part 2. Presented by the Society.

Memoires Couronnés del Academie Royale de Bruxelles.
Tome XVI. (1843).

Recherches Statistiques, par A. Quetelet, H. M. R. I.
Academy.

Observations des Phénoménes périodiques.

Resumé des Observations magnétiques. (1843).

Instructions pour 0 Observation des Phénoménes perio-
diques.

Annales de ? Observatoire Royal de Brucxelles. (1844).

Annuaire de l Observatoire Royal de Bruxelles. (1843-
44).
' Bulletin de 0 Academie Royal de Bruxelles. (From 5th
August, 1843, to 3rd August, 1844).

Presented by the Academy.

Laws of the Philosophical Society of Leeds. 1841.

Report of the Philosophical Society of Leeds. 1825-6, and
1831-1844.

An Account of an Egyptian Mummy, presented to the
Museum of the Philosophical Society of Leeds.

Transactions of the Philosophical Society of Leeds. Vol. I.
Part 1. Presented by the Society.

1. Proceedings of the American Philosophical Society,
Srom April to December, 1844. Nos. 30 and 31.

2. A Discourse in Commemoration of Peter S. Du Ponceau,
LL.D.., late President of the American Philosophical So-

ciety, delivered before the Society, on the 25th October, 1844.

By Robley Dunglison, M.D. Presented by the Society.

56

1. Report of Her Majesty's Commissioners of Inquiry into
the State of the Law and Practice in respect to the Occupation
of Land in Ireland.

2. Evidence taken before the Land Commission in Ireland.
Parts 1 and 2. Presented by the Lord Lieutenant.

Contributions towards a Fauna and Flora of the County
of Cork. By Dr. Harvey, J. D. Humphreys, and Dr. Power.
Published by, and presented by the Cuvierian Society of
Cork.

Obits and Martyrology of Christ Church. Presented by
the Irish Archeological Society.

Facts connected with the social and sanitary Condition of
the working Classes in the City of Dublin. 1841. By Tho-
mas Willis, F.S.S. Presented by the Author.

Observations made at the Magnetic and Meteorological
Observatory, at Toronto, in Canada. Vol. I. for 1840, 1841,
1842. Presented by Her Majesty’s Government.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1844-45. No. 50.

January 27, 1845.

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

The Correspondence (see Appendix, No. 1.) was read
from the Minutes of Council.

The Rev. Charles Graves read the continuation of his
paper on Algebraic Ahlen

The triplet x + w +z, or (a, y, > being employed to
represent the right line drawn from the origin to the point
whose rectangular coordinates in space are x, y, and z, it be-
comes a matter of interest to determine the position of the
right line which represents the product of two such triplets.
For this purpose it will be convenient to lay down some defi-
nitions.

1. The symmetric axis is the right line drawn from the
origin, so as to make equal angles with the three positive por-
tions of the axes of coordinates.

2. The symmetric plane is a plane passing through the
origin, and perpendicular to the symmetric axis.

3. The modular plane is the plane containing the axis of
x and the symmetric axis.

4. The radius, r, of the triplet (#, y, z) is the right line
drawn from the origin to the point a, y, z.

VOL. Ill. r

58

5. Its vector angle, p, is the angle between the radius
and the symmetric axis.

6. The amplitude, w, of the triplet (a, y, 2) is the angle
between the modular plane and the plane containing the radius
and the symmetric axis.

We are able to determine the radius, vector angle, and
amplitude, of the triplet (72, p2) w2), which is formed by mul-
tiplying together two triplets (7, p, w) and (7, p,, w:), by means
of the following equations, in which s stands for the angle be-
tween the symmetric axis and the positive portion of any one
of the axes of coordinates.

71, COS COSP; = 72 COS S COSpy (1)

77, SiN p Sin py = 72 SINS sin py (2)

wo + Ww = Wo. (3)

It appears from the first two of these equations that whe-

ther we call geste or P the modulus of the triplet, it
coss sins

will be true to say that the modulus of the product is equal to
the product of the moduli of the factors.

The third equation asserts, that the amplitude of the pro-
duct is equal to the sum of the amplitudes of the factors.

As the real unit is supposed to be placed on the axis of a,
we shall obtain the following theorem by dividing the second
of the preceding equations by the first :

The tangents of the vector angles of the real unit, of the
two factors, and of the product, form a proportion.

Mr. Graves stated that Sir Wm. Hamilton had been the
first to announce that if the real unit line, the factors, and the
product line, be projected upon the symmetric axis, the pro-
jections will form a proportion in the simple sense of that
term: whilst the projections of the same lines on the symme-
tric plane form a proportion, according to the higher sense in
which Mr. Warren uses the same word.

The former of these theorems is merely the geometric in-

09

terpretation of equation (1): the latter of equations (2) and
(3).

The following cases deserve special attention :

If either of the factor lines coincides with the symmetric
axis, the product line must also coincide with it.

If either of the factor lines is contained in the symmetric
plane, the product line must also be contained in it.

But if one coincides with the symmetric axis, and the
other with the symmetric plane, the product line will vanish.

Startling as these consequences may appear, they are to
be explained by reference to the geometric meaning of the
symbols x and’; both of which, according to the interpreta-
tion assigned to them, are inoperative to move a right line out
of either the symmetric plane or the symmetric axis.

The analytical difficulty raised by the last case seems to
force us to admit that the vanishing of a product does not ne-
cessarily imply the vanishing of a factor. In the present in-
stance it is caused by the vanishing of one of the moduli of
multiplication belonging to each of the factors.

The length of the product line is equal to the product of
the lengths of the factor lines only in the case where the vector
angle of one of the factors is equal to the vector angle of the
real linear unit (where p or p, = 8).

Having thus interpreted the results of multiplication by
means of the existing trigonometry, Mr. Graves proceeded to
show how the use of a new kind of trigonometry gives in-
ereased symmetry and flexibility to the present theory of
algebraic triplets.

The foundations of this new calculus are thus laid. Using
the exponential development we shall find

ew=Atmwt ey

where

Sant ig ~°
OG: + ta3.456 + &.

Ree

60
iB eGR eG ae
Li? esa t qo Sainiem

-£ 5 8

s+ esas + Tasers Pee

Again,
e*% = X, + Oy + lv,

where X,, 1, v, are the same functions of y that X, mu, v are of
@. Hence we have

eo tex— A+ im + PN,
A standing for AA, + pu, + vv, M for Av, + pA, + vp, and ‘N
for Ap, + pv, + vA,

The three functions, A, m, an w depending, each of them,
on two variables, ¢ and x, hold the same place in the present
calculus that cosine and sine hold in the received trigonometry.
And as the sum of the squares of cosine and sine is always
equal to unity, so the equation

A? + yw? + nN? — 3 AMN = 1
holds good, no matter what be the amplitudes @ and x.

The importance of these formulz in our theory of triplets
is most obvious. Fora triplet x + vw + ?z may in general be
thrown into the form m(A + um + .’N), which, as we have
seen, is equivalent to me?+“x. So that if m be called the
modulus, and ¢ and x the amplitudes, of the triplet, we shall
find, on multiplying two triplets together, the following theo-
rems to be true:

The modulus of the product is equal to the product of the
moduli of the factors.

Either of the two amplitudes of the product is equal to the
sum of the two corresponding amplitudes of the factors.

The modulus m is connected with the constituents of the
triplet (x, y, 2) by the following equation,

mat y+ 2? — 3xyz,°
with respect to which it is to be observed that the right hand
member is the product of

61

e+ytzand aty?+2°—ay—y2—24,
the two real moduli which have previously been shewn to be-
long to the triplet (x, y, z.)—See page 53.

Mr. Graves stated that he had obtained a multitude of
formule concerning the functions A, M, and N, analogous to
the fundamental formule of trigonometry. Amongst the more
remarkable of these he pointed attention to one corresponding
to the well-known theorem of Moivre.

By pursuing a similar course we may frame a theory of.
multiplets, admitting a like interpretation. In order to ac-
complish this we must assume a symbol «, such that x"(1)=1,
whilst 1,«(1), «°(1), «°(1) ... &c. are looked upon as units abso-
lutely differing in kind as much as unity differs from — 1.
The development of e*? into the form a + KB + Ky + &e. will
give usaset of functions, a, B, y--.- each depending upon
one variable ¢: and again, the expansion of e@ Fextev+...-
furnishes us with a series of » functions, a, B, r, &c, each
depending upon (n—1) variables ¢, x, ~, &c. The multiplet
a+tx«b+x’c + &c. being now written in the form m(a+ «B+
er + &c.), which is equivalent to meetx| vt Se...) it
is evident that, if we call m the modulus, and 4, x, ~, &c. the
amplitudes of the multiplet, we shall have the same theorems
concerning moduli and amplitudes that have been already
established in the case of the multiplication of couplets and
triplets.

If, for instance, we form a quadruplet (w, x, y, z) by the
aid of the symbol «, which is a pure imaginary fourth root of
positive unity, we shall find that the quantities [w+a+y+2],
[(wt+y)—(#+2z2)], and [((w—y)* + (e—2)’] are all moduli
of multiplication. The product of the three is equal to m*.

Mr. Graves mentioned that his elder brother, Mr. John T.
Graves, had been the first to conceive the notion of employ-
ing the functions A, », and pv in the interpretation of this
theory of triplets; but as they involve only one variable it is
not possible to bring a triplet in general into the form

m(A + y+ rv).

62

The President stated that the remarkable researches re-
specting algebraic triplets, made lately by Professor De
Morgan and John T. Graves, Esq. in England, and here by
the Rey. Charles Graves, had led him to perceive the follow-
ing theorem :

If the three symbols &, n, 2, or rather their squares and
products, be supposed to satisfy the three following ‘* equa-
. tions of signification :”

E (bn + c0) = a(x’ + 2),

n (eG + a&) = 5 (2? + &?),

€ (@& + bn) = ce (& + 0’);
and if, by the help of these three equations, we eliminate any
three of the six quadratic combinations &, »?, 2°, En, nZ, Zé,
from the development of the ‘ formula of multiplication,”

(u& + vm + we) (2"E + yn + 20)
= (af + yn + 26) (WE + y'n + 22),

and then treat the three remaining combinations of the same
set (€, &c.) as three entirely arbitrary and independent mul-
tipliers: the three separate equations thus obtained between
the fifteen real quantities abeuvwaycx'y' 2’ xy” z" will be
such, that whether we project the four lines (wu, v, w), (#7, y, 2),
(a’, y’, 2'), (2, y”, 2”), on the axis (a, b, ¢,) itself, or on the plane
perpendicular to that axis, the four projections thus obtained
will in each case form a proportion ; the proportionality of
the projections on the axis being of the kind considered in
ordinary algebra, and the proportionality of the projections
on the plane perpendicular to the axis being of the kind con-
sidered by Mr. Warren; that is to say, the lengths of these
last projections are proportionals in the usual sense, and the
rotation from the first to the second is equal to the rotation
from the third to the fourth.

Sir W. Hamilton has been able to prove this theorem by
treating the three real equations between the fifteen rectan-
gular co-ordinates a, b, c, &c. according to the known methods

63

of algebraical geometry. He has also arrived at simplifi-
cations of this proof by introducing the ordinary imaginary
Ws, hy treated by the ordinary rules; but his first investiga-
tion, and the one which he prefers, has been founded on the
rules of the calculus of quaternions, and consists in resolving
by those rules the system of the two equations :
ap’ + p’a _ap+pa_ap”—p"a ap — pa.
ap’ + pa av-+va’ ap) — pla av—va’
in which
aia +jb+hke,
v=iutyv + kw,
p= ta +yy + kz,
po = ta! + jy! + he’,
= ta!’ + jy" + kz",
2, J, k, being (as in former communications respecting quater-
nions) three imaginary units connected by the nine non-linear
relations
eh = — 5 yh, jh, hi); fo — hk, j= — 1, k= —7.
The phrase ‘‘ equations of signification” is borrowed from
Mr. De Morgan. If the theorem be particularized, so as to
correspond to that gentleman's system of triplets, by making
Pay =o aS b= a
then the equations of signification reduce themselves to

=n, n= —f&, = — én,

and the formula of multiplication resolves itself into the three
relations

a! = aa! + y2! + zy’,

y! = ay’ + ya! — 22,

2" = az! + za! — yy’.
On the other hand, some of the results of the systems of the
two Messrs. Graves may be reproduced by taking the same
unit-line, u=1, v= w= 0, but employing that other axis
for which a =b-=c. The equations of signification give
then, more simply,

64

Pre gap pate, Sas
and the terms in 2”, y”, 2”, are all to be taken with positive
signs. Sir William Hamilton pretends to no farther merit
in the matter than to that of having sought to illustrate, by
-generalizing in one direction, the foregoing points of the
theories of his friends.

February 10, 1845.

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

Robert Forster, Esq., William Le Fanu, Esq., Reverend
George Longfield, John M. Neligan, M. D., William Justin
O’ Driscoll, Esq., Nicholas P. O’Gorman, Esq., Algernon T.
Preston, Esq., and James Emerson Tennant, Esq., M.P.,
were elected Members of the Academy,

The President read a paper on Quaternions.—See Appen-
dix, No. III.

A stone celt was presented by the Rev. Dr. Walsh, H. M.,
from Captain Walsh.

February 24, 1845.

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

Matthew Baker, Esq., Patrick Joseph Blake, Esq., John
D'Arcy, Esq., Rev. Nicholas John Halpin, Samuel Haughton,
Esq., F. T. C. D., William Hogan, Esq., C. E., James Mac-
donnell, Esq., C. E., Right Hon. David R. Pigot, Matthew
R. Sausse, Esq., Walter Sweetman, Esq., R. William Town-

65

send, Esq., Alexander Taylor, M.D., and George Yeates,
Esq., were elected Members.

Lieutenant-Colonel Jones (R. E.), on the part of the
Shannon Commissioners, presented to the Museum a collection
of ancient bronze weapons, ornaments, and other articles,
found recently in the excavations made in the bed of the
Shannon. And he offered, on the part of the Commission, to
assist the Committee of Antiquities in conducting any anti-
quarian researches they might propose in the neighbourhood
of that river. Whereupon it was

Resotvep,— That the Committee of Antiquities be re-
quested to put themselves in communication with the Shannon
Commissioners, with reference to their obliging proposal.

John Anster, LL.D., read the conclusion of the paper by
the Rev. James Wills, “‘ On Dugald Stewart’s Explanation of
certain Processes in the Human Understanding.”

Mr. Wills commenced by referring to his former paper,
in which he had endeavoured to rectify the elementary prin-
ciple, from which he considered the true theory of the in-
tellectual powers as being deducible. As in that. paper he had
explained the origin and formation of those fixed associations
which were the results of habit; so in the present paper it
was his purpose to deduce from the same primary law the
class of unfixed and accidental associations.

Before entering upon this statement, the Author dwelt at
some length on the nature of the method by which he had
arrived at his results. This he described as being, in the
strictest sense, a method of observation. He had, he said,
excluded all consideration of the metaphysical writers; and
though he might coincide with many of their opinions, he
would disclaim any authority, or ground of inference, but the
~ simplest and most scrupulous investigation of the facts, which
he would endeavour so to exemplify as to convey his results

66

\

to the Academy. He also made some remarks on the diffi-
culty of this method, by reason of the complexity of the men-
tal operations, and the impossibility of otherwise attesting the
results than by the exposition of the inquirer’s own thoughts,
and the appeal to the consciousness of others.

The Author then went on to explain the elementary law of
simple apprehension, and shewed that however numerous or
varied might be the objects presented in any single instant to
the apprehension, the result must be one single idea—being a
whole in itself, and of which all the components must be
apprehended strictly as parts. From this fact he observed
that the entire process of memory could be deduced. For
this purpose he stated a case framed with a view to explain the
ordinary process by which incidents and circumstances are re-
called, by means of their association as parts or as wholes; so
that either the part might recal the whole, or the whole the
part.

The Author then explained how this operation might be
accidental, or the effect of design. The first would be the case
of mere passive remembrance ; the other the active recollection
of the will. The first would mostly be the result of the actual
presence of some portion of the combined ideas; the other
must be arrived at by an effort in which the mind succeeds in
placing itself in some position of relation to the required idea,
so as to fulfil the condition of the theory. To meet the only
difficulty which might be suggested by this exposition, the
Author pointed out, that the occasion which might require
such an effort must necessarily present a first link in a chain
of associations, from which every subsequent step would be a
result similarly occurring in its order, so far as the operation
might happen to be rightly directed, and the materials within
the compass of the mind engaged in it.

The Author observed that the various causes of memory
described by philosophers, are merely the circumstances at-
tending the process here described. He observed that every

67

means of association by which ideas can be combined, might
serve the same purpose in the same manner, and that the same
reasoning would apply; though he only considered it neces-
sary to follow the inquiry with regard to the large class of
accidental associations which are the main ground of the or-
dinary work of memory.

He next entered into an inquiry as to the comparative
durability of the different classes of associations. This, he
observed, must depend on their distinctness, and their cohe-
rency: and hence he inferred that, generally, visible objects
are the most easily recalled; and that certain combinations
of sound might be next in order: after these might be
reckoned the class of professional associations. He remarked
upon the expedients used in the systems of artificial memory,
as founded on this principle; and strongly condemned the
methods, as being a substitution of false combinations, instead
of those founded on the real relations of things,

The Author then went on to apply his theory to some
known phenomena in derangement, dreaming, &c.: and con-
cluded with some general statements upon the sum of his
results, and the progress he had made in his inquiry.

A paper was read by Dr. Allman, containing a notice of
two undescribed algz, which clothe the face of the rock over
which the water trickles in the “ Dripping Well” of Knares-
borough. They are referrible to the genus Microcystis,
Menegh.

Dr. Allman also noticed the occurrence in Ireland of the
genus Phylacttidum of Kutzing, which thus becomes an ad-
dition to the British Flora. The beautiful little alga now
noticed, which appears specifically distinct from P. elegans,
Kutz., was discovered by Dr. Allman, during the autumn of

_1843, in a small, rapidly running rivulet near Banden, in the
County Cork.

68

The following alge were also now, for the first time, re-
corded as additions to the Irish cryptogamic Flora:

Calothrix mirabilis, forming little tufts attached to stones
and mosses, in a small stream trickling over a rock near
Clonmel.

Nostoe muscorum, on a little-used foot-path, Castleknock,
County Dublin.

Nostoc sphericum, on the surface of a moist rock, Clonmel.

Euaster rota, in a small pond near Bandon, entangled
with other alge.

Euaster oblonga, along with Desmidium mucosum and D.
Borreri, in a peat pit, Sheaghy, County Cork.

Desmidium Suwa@rtzii, in an old peat pit, Howth.

Desmidium cylindricum, in an old peat pit, Howth.

Desmidium mucosum, in a peat pit, Sheaghy.

Desmidium Borreri, in a peat pit, Sheaghy.

Leptomitus pisidicola, growing on a dead Caddis-worm in
Lough Bray, County Dublin.

The President read a note from the Rey. Dr. Robinson,
respecting Lord Rosse’s telescope.

The Secretary read a letter from Mr. Charles Bourns,
giving an account of the excavation made in the interior of
the Round Tower of Lusk.

Mr. W. R. Wilde made some observations on the human
skulls which were presented by Mr. Bourns, and which had
been found within the tower.

69

March 15, 1845. (Stated Meeting.)

REV. JAMES H. TODD, D.D., Vice-President, in
the Chair.

This being the day appointed by Charter for the Stated
Meeting and annual election, the following Officers and Mem-
bers of Council were chosen for the ensuing year:

President—Professor Sir Wm. Rowan Hamilton, LL.D.

Secretary—James Mac Cullagh, LL.D.

Secretary to the Council—Robert Kane, M. D.

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

Librarian—Rev. Wm. H. Drummond, D. D.

Clerk and Assistant Librarian—Edward Clibborn.

¢ .
Committee of Science.

Rev. Frane Sadleir, D. D., Provost; Rev. Humphrey
Lloyd, D. D.; James Apjohn, M.D.; James Mae 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 H. Drummond, D.D.; Rev. Charles
Graves, A.M.; Rev. Charles W. Wall, D. D.; John Anster,
LL.D.; Rev. Samuel Butcher, A. M.

Commitiee of Antiquities.

George Petrie, Esq., R. H. A.; Rev. James H. Todd, D.D. ;
-Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq. ;
J. Huband Smith, A. M.; Captain Larcom, R. E.; William
R. Wilde, Esq.

70

A volume of Mr. Petrie’s work on the Round Towers of
Ireland, was laid upon the table.

The Secretary read the following Report from the Coun-
cil, which was adopted, and ordered to be entered on the
Minutes :

‘¢ Among the occurrences of the past year, the Council have
to notice the acquisition by the Academy of a considerable collec-
tion of Irish manuscripts. This collection was purchased from
Messrs. Hodges and Smith for 1250 guineas ; of which sum so large
a share as £600 was very liberally granted for the purpose by Her
Majesty’s Government. The remainder, with the exception of
£100 contributed from the funds of the Academy, was raised by
subscription from the Members of the Academy and the Public ge-
nerally ; and the Council are gratified in referring to this new
instance of the right feeling and proper spirit which have, of late
years, been manifested in the case of national remains; but, at the
same time, they have to express their regret that the known exis-
tence of this feeling has had the effect of greatly increasing the price
of such relics in the market.

‘‘For the purpose of arranging and displaying the large col-
lection of Antiquities now in the possession of the Academy, the
room in which the meetings of the Academy used to be held has
been converted into a Museum ; and, at the trifling expense of £150,
a new Board Room has been fitted up, in which the meetings of the
present Session have been held. For the economy with which these
arrangements have been made, the Academy are mainly indebted to
the suggestions of their excellent Assistant Librarian, Mr. Clibborn,
who cheerfully sacrificed part of his own accommodation, in order
that the proposed changes might be carried into effect. The regu-
lation of the Museum, and the adoption of such measures as may be
necessary for the security of the valuable collections therein depo-
sited, are objects which the Council recommend to the immediate
attention of their successors.

‘** The Council are informed that a volume by Mr. Petrie, on the
Round Towers of Ireland, will be ready in a few days, and will be

71

laid on the table of the Academy at the Stated Meeting. This work
will of course be submitted to the new Council before it is received
as apart of the Transactions; and it will be the duty of the Coun-
cil to report upon it to the Academy, with reference to the engage-
ment entered into with Mr. Petrie.

‘The number of Members elected during the past year has been
unusually great. The following are their names:

‘* LIST OF MEMBERS OF THE ROYAL IRISH ACADEMY, ELECTED SINCE
THE 16TH MARCH, 1844.

_ 1. W.S. O’Brien, Esq.,M.P. 25. Marmion W. Savage, Esq.

2. The Marquis of Kildare. 26. Richard Sharp, Esq.

3. W. H. Harvey, M. D. 27. Robert Forster, Esq.

4, Charles Hanlon, Esq. 28. William Le Fanu, Esq.

5. Maxwell M‘Master, Esq. 29. Rev. George Longfield.

6. Thomas Oldham, Esq. 30. John M. Neligan, M. D.

7. Philip Reade, Esq. 31. W. Justin O’Driscoll, Esq.

8. Henry Roe, Esq. 32. N. P. O’Gorman, Esq.

9. Robert Wilson, Esq. 33. Algernon T. Preston, Esq.
10. Duke of Leinster. 34. J. E. Tennant, Esq., M. P.
11. Marquis of Downshire. "35. Matthew Baker, Esq.

12. Lord Farnham. 36. P. Joseph Blake, Esq.

13. Lord Wallscourt.” 37. John D’Arcy, Esq.

14. Robert S. Bradshaw, Esq. 38. Rev. N. John Halpin.

15. Thomas Davis, Esq. 39, Samuel Haughton, Esq.

16, Sir Richard Franklin. 40. William Hogan, Esq., C. E.
17. Edmund Getty, Esq. 41. James Macdonnell, Esq., C. E.
18. G.A. Hamilton, Esq.,M.P. 42. Right Hon. David R. Pigot.

—
©

. Henry G. Hughes, Esq. 43. M. R. Sausse, Esq.
- H. James, Esq. (Capt.R. E.) 44. Walter Sweetman, Esq.

ho
i=)

21. Francis L’Estrange, Esq. 45. RK. W. Townsend, Esq., C. E.
22. Edward Lucas, Esq. 46. Alexander Taylor, M. D.

23, John Phillips, Esq. 47. George Yeates, Esq.

24, T. N, Redington, Esq., M.P.

“Total elected, from 16th of March, 1844, to 16th March, 1845,
"—forty-seven.

72

« The following are the Members deceased within the year :

Life Members. Annual Members.
* Rey. Charles Boyton, D.D., | William Henry, Esq., 1844.
1822. Matthew O’Conor, 1837.
* Hugh Ferguson, M. D., 1824. Honorary Member.
* Rev. Thomas Goff, 1802. Francis Baily, Esq., LL.D.,
* William Webb, Esq., 1808. F.R.S., &c., 1826.

** The distinguished name of M. Arago, Perpetual Secretary of
the Academy of Sciences of Paris, has been added to the list of Ho-
norary Members.

‘* The list of Honorary Members has lost a name well known
to science, that of Francis Baily, Esq., late President of the As-
tronomical Society of London, of which he was one of the principal
founders. On the worth of his character, and on the value of his
services to scietice, it is needless to dwell, as Sir John Herschell
has already done justice to them, in a Memoir read to the Society
over which he presided, and which, up to the period of his death,
was the object of his unceasing care and attention.”

Mr. Robert Ball, on the part of the Dean of Lismore,
presented the seal of the late Archbishop of Cashel.

The thanks of the Academy were voted to the Dean of
Lismore.

April 14, 1845.

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

Joseph Allen Galbraith, Esq., James Jameson, Esq., and
John Francis Waller, Esq., were elected Members of the
Academy.

Reap,—The Resolution of Council passed at the meeting
of 7th April, viz.

73

«¢ That the Volume which has been printed by Mr. Petrie,
as the twentieth volume of the Transactions, be received as
such; and though it cannot be regarded as a complete Work,
that, nevertheless, the Council do recommend it to be taken,
as acquitting Mr. Petrie of his engagements to the Academy.

RESOLVED UNANIMOUSLY,— That the recommendation of
Council be received and adopted.

Reapv,—The following letter from Messrs. Hodges and

Smith :
‘© 104, GRAFTON-STREET,
“ April 14th, 1845.

‘¢Srr,—Having been informed that a person of the name of
O’Brien, in the County of Clare, had some curious ancient docu-
ments which he would dispose of, we went down to that county for ’
the purpose of examining them. We found his collection to con-
sist chiefly of family documents and papers of little moment, with
the exception of four pages of the celebrated work known by the
name of Leabhar Breac. Those pages contain a beautiful Latin
Hymn to St. Patrick, by Secundinus, and other interesting matter.
They have been missing for upwards of fifty years, and we have
now much pleasure in restoring them to the Academy, whose pro-
perty the Leabhar Breac has been for many years; and we also
beg to present two copies of Mac Firbis’s work on the Genealogy of
ancient Irish Families, written in 1650, and another volume con-
taining an abstract of the same great work, written by James
M‘Guire, in 1721; and, fifthly, a very good copy of Keating’s
History of Ireland, written in 1712.

** We have the Honour to be, Sir,
‘“¢ Your very obedient Servants,

‘* HopGEs anp SMITH.
‘“* To the Secretary of the

Royal Irish Academy.”
- Resotvep,—That the thanks of the Academy be given
to Messrs. Hodges and Smith for their donation.
VOL. III. G

74

Rey. Dr. Todd presented, in the name of the Rev. James
Spencer Knox, a curious book, found near Maghera, com-
posed of tablets made of wood, and covered with wax.

The President, under his hand and seal, appointed the
following Vice-Presidents :

Rev. Charles Wm. Wall, D. D.; George Petrie, Esq. ;
James Mace Cullagh, LL.D.; Thomas A. Lareom (Captain,
R. E.)

His Excellency the Lord Lieutenant having attended as
a visitor, :

The Rev. Dr. Robinson proceeded to give an account of
the construction and results obtained with the six foot reflect-
ing telescope of the Earl of Rosse.

April 28, 1845.

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

The Treasurer presented the following abstract of the
Annual Account, as audited, for the year ending 31st March,
1845 :

“LOINSDIAL J

8 G 961F

It 241 S11
6 PF G89Z

are DOD Has
—
Lomi
inn)
Ya}
~~

6 9 G6PFI

‘TIVE “U ‘paubig

adreyosiqy [240 ,],

a eae ull oY} JO MOAT Ul soUL[eg
ob Soe ‘ + + = ganqipuedxy [eq0 7,

+ ere . . . . . . . Piet . Ssuynysrvy pue jong
. . . e . . . . . . . . . SOX? J, pure que yy
ee ee 8 oe ee a se Reno

Fon ee ee ee ee ee gombyuy
. . . . . . . . . ‘ . . . iJ ° SolLle[eg
‘+ + 5 + + + + + 98eqsog pue souesduizu0d

Lut ° ' * ' 7 * + + + saredea 107309
9 1 181 °° ° * * ‘* Wood-paeog uo sareday
9 8 6 . . . . . . . . . . SNOP00 AA
g Me, PEI . . . . . . . . . . . syoog
0 Il SSEI . . . . . . . . . . . “SST

? sydiaosnurypy pue syoog
Ys honac f

UNUVAOSIG GAL

8 & 96L6F| * * * adavyD [eq07,

weoomauooooceo

3

ree
ao 3
a ae
es

wo
OL 1tG are Cape . . ae - 8 8 suorisodu0g aT a
0 O1Z@ ees Sy “ae at SEG ae ee oat ee | SaoleooUBAqa | ©
91 I&€ Sh ees ss ss suorndiaosqng jenuuy
0 1% S\de. ee ae es SS vane sonia
8 92 stot oss 4 4 + 2 + 8 + yo09g uo spueprarq
G 8g9 “sss ss © “SSI USIay oseyoand 037 suo1eu0q
LI OFT “ay ae Se et SR oo ener Me Aonseed
0 009 or ae Oe “SSIN 10F FuRTH pe1oodg yuemussA0y
0 008 “eee se quer TenuUUYy JUEUIUTeA0) |
G OG “ss ss + +s qunosoy s,1vak yee] Uo coueleg
‘SF

‘aA9UVHO FHL

‘SPSL ‘HOUVNW IS1€ CAGNA UVAA UOT LNOAOOOV SATUASVAUL AO LOVULSAV
‘ANUGVOV HSIUI TVAOU

76°

Rev. Dr. Todd presented, from Lord Granville Somerset,
a copy of the Charters of the Duchy of Lancaster.

Colonel Jones, R. E., presented a printed description and
drawing of an antique tombstone, of the natural size, found at
Athlone.

Mr. J. Huband Smith read an account of the present state
of the ancient ecclesiastical remains of Iona.

After alluding to the difficulty of procuring accommodation
in this remote island, and the impossibility of obtaining more
than a mere glance at the details of the group of ecclesiastical
buildings, in the way in which they are now usually seen by
tourists, Mr. Smith went into a very minute account of the
Nunnery, with its grave-yard, containing some interesting
monuments. He then described two ancient causeways, and the
church of St. Oran, which he supposes to be the most ancient
edifice on the island, though he declined to express any definite
opinion as to its age. Of the doorway of this church Mr.
Smith exhibited a very careful drawing, on a large scale, as
well as others of some of the most remarkable tombstones in
the Releg Oran. He then proceeded to give some account of
the grave of St. Columba, adjoining to the great western door
of the cathedral, the nave, chancel, and aisles of which, toge-
ther with its noble square tower, he described in detail, with
measurements which he had carefully taken.

The numerous drawings made by Mr. Smith, from his
own sketches on the spot, contributed not a little to convey
a more satisfactory idea of various particulars than any verbal
description could have done; and, with many rubbings taken
from tombstones and crosses, enabled him to correct some
errors into which Pennant and other writers had fallen, in the
deciphering and translation of certain Irish inscriptions yet
remaining at Iona. Mr. Smith lastly noticed the Cross of
Inverary, which is said to have been brought from Iona at
the time of the Reformation, and produced a very careful

17

rubbing of the entire Cross, giving the elaborate patterns on
both sides, and the curious inscription along its edge, which
he translated; and he then concluded by expressing his con-
viction, that notwithstanding that during the five days he
remained at Iona he was unceasingly occupied, he had, never-
theless, left much unnoticed, with regard to the numerous
group of buildings in the vicinity of the cathedral, as well as
of many interesting localities in the interior of the island,
connected with the history of the celebrated St. Columbkille
and the Culdees.

May 12, 1845.
CAPTAIN LARCOM, R. E., Vice-President, in the
Chair.

Charles Bournes, Esq., W. C. Dobbs, Esq., Wm. Henn,
Esq., D. B. Starkey, Esq., and Benjamin Wilme, Esq., were
elected Members of the Academy.

Mr. William Roberts, F. T.C.D., read a paper on some
Geometrical Theorems relative to Elliptic Functions.

It is well known that the are of a spherical ellipse is ex-
pressed by an elliptic function of the third order, with a circu-
lar parameter: and it has been also proved (see M. Liouville’s
Journal of Pure and Applied Mathematics, vol. ix.) that the
are of the intersection of a sphere with a cone of the second
degree, one of whose external principal axes is a diameter, and
whose vertex is situated on the surface, may be made to sup-
ply a general representation of the three elliptic transcendants ;
at least with the aid of the modular transformations, which
have been given by Lagrange and M. Jacobi. ‘The object of
the present communication is to shew that these results are
but particular cases of the general theorem, that the are

78

of any symmetrical intersection of a sphere with a cone of the
second order (i. e. when the centre of the sphere lies upon one
of the principal axes of the cone) may be expressed by elliptic
functions. This is easily deduced from the following formule
for the rectification of the class of spheric curves represented
by the polar equation,

sin’ pF(w) + sin 2A cosp = 1 (a)
where X is aconstant. Let s,, s,, denote the two ares which

correspond to the same value of the polar angle w, and we will
have

2 72 29 d
ee ae Aut ome =

F—cos?A F
4p? 4 F?—4F 4 sin?2X
pee sin f/ $ ee go. F

F’ denoting the derived function of F(w).

Now in the case of the intersection of a cone and sphere,
such as we have described, F(w) is a linear function of cos 2w,
and each of the foregoing integrals is reducible to an elliptic
function of the third kind. ;

In the case of the spherical ellipse, the two ares s, sg are
equal; and when the vertex of the cone is upon the surface, the
second are s, vanishes altogether.

The same relation between the principal angles of the
cone, and the distance of its vertex from the centre of the
sphere, will cause the parameters in both the functions II to
vanish. And it is remarkable that, in this case, when the sum
and difference of the arcs s,, s,, are each expressible by a trans-
cendant of the first order, the curve will coincide with the
locus of the vertex of a spherical triangle, the base of which is
given, and of which the product of the sines of the semi-sides
is constant, and less than the square of the sine of the fourth
part of the base.

This result is strikingly analogous to M. Serret’s theorem
on the rectification of the Cassinian curve, published in M.
Liouville’s Journal, vol. viii. p. 145.

ee ee

79

If the moduli of the two functions which express the va-
lues of s, + s, be complementary, the curve will coincide with
the locus of the vertex of a spherical triangle whose base is
given, and of which the product of the tangents of the semi-
sides is constant, and less than the square of the tangent of
the fourth part of the base.

Equation (a) may be transformed into

—sin 2X
tan’ p — 2tan? sad ine oe
—2F(w)
where F(w) simply is written for ae The class of plane

curves whose polar equation

ri — 27r°F(w) + c# = 0
is analogous to the above, may be rectified by similar formulas.
These are

Poel pees SV (A) ae
a= ah (SoS © dw

Each of these integrals will be reducible to an elliptic function
of the third order, provided that F(w) be a linear function of
cos 2w. The following curves, among others, possess this
property: first, the locus of a point, such that, tangents being
drawn from it to two equal non-intersecting circles, their
rectangle is constant, and less than the square of the tangent
drawn to either from the point midway between their centres:
secondly, the locus of the intersection of tangents to an
ellipse which include a given angle. ‘This curve is composed
of two closed branches concentric with the ellipse, and satisfy-
ing the given condition by angles which are supplemental.
The well-known property of the lemniscate may be ex-
tended to the locus of the orthogonal projections of the centre

‘of an ellipse or hyperbola in general upon its tangents. First,
in the case of the ellipse, the curve may be derived by taking

80

the locus of a point, such that tangents being drawn from it
to two equal intersecting circles, their rectangle may be con-
stant, and equal to the square of half the common chord.

If the circles do not intersect, and if the rectangle under
the tangents be equal to the square of the tangent to either
- from the middle point between the centres, the locus will give
the curve derived from an hyperbola, whose real axis is greater
than the imaginary.

To get the curve when the imaginary axis is greater than
the real, we must take the locus of a point, such that lines
being drawn from it to meet the circumferences of two equal,
non-intersecting circles, and subtending right angles at their
centres, their rectangle may be constant, and equal to the
sum of the squares of the radius, and of half the distance be-
tween the centres.

There exist in spherical geometry numerous properties of
an analogous character.

The Rev. Charles Graves made a communication relative
to the new functions employed by him in the interpretation of
his theory of Algebraic Triplets.

The three functions a, m, N, defined in p. 60, possess so
many interesting properties that they seem to deserve distinc-
tive appellations. The first is symmetrical with respect to its
two amplitudes, g and y; and its properties are in the main
analogous to those of the trigonometrical function cosine. On
the other hand, m and n are not symmetrical functions of p
and y; but either of them may be obtained from the other by
interchanging the two amplitudes; and they correspondinmany
respects to the trigonometrical sine. Mr. Graves proposes
then to call a the cotresine, and and n the éresines of mi
and x: and he designates them respectively by the symbols

cotr[¢, x], tres[¢, x], tres[y, ¢]-
As in trigonometry cos @ = cos (2i7 + $), and sing=

81

sin (2ir + @), é being any integer number; so also in this cal-
culus,

cotr[@, x] = cotr[¢+2ir, x— 277]

tres [p, x] = tres [p+2i7, y—2ir]

where 7 = Wi The quantity 7 holding in the present theory

the same place that 7 does in the calculus of sines. From the
theorem of Moivre we learn that

(cosp+ 47 sing)” =cosm(p+2tr)+ Y —l.sinm (p+ 2t7).
The corresponding theorem already announced by Mr.
Graves may be written as follows:

(cotr[, x] + etres[¢, x] + Ptres[yx, ¢])”
=cotr[m(¢ + 2tr), m(x—2ir) | +ctres [m( + 2ir), m(x—2zr)]
+ tres[m(y — 2ir), m(p + 2ir)].

Among the most important consequences flowing from the
preceding theorem is a mode of resolving an equation of the
form

2" — pz” +. g2"—r = 0

into its cubic factors. For this purpose we must first reduce
the equation to the form

y"—3cotr(a, B)y*" + 3cotr(—a, —B)y"—1=0. (6)

Now it will be found that if we multiply together the three
expressions

a — cotr[¢,x]— tres[¢,x]— tres[x, ¢]

x — cotr[, x] — atres [¢, x] —a°tres[y, 9]

a —cotr[¢, x] — a°tres[p, x] — atres[y, 6]
EE 38

2

in which a stands for , the cube root of +1, the
product will be } 2- x
«2®—3cotr[¢,x]a* + 3cotr|—¢, —x]z—1.
Hence it may be proved that each of-the cubic factors of (6)
will be of the form :

82
1 UF it :
y°—3cotr [- (a+ 2:7), (B— Qi) |y®

1
+3cotr| — = (a+2ir), — “(8 —2ir) |y—1.

From the result just obtained Mr. Graves deduces a sin-
gular geometrical theorem analogous to the celebrated one of
Cotes.

But it must be observed here that the geometrical propo-
sitions to which we are led in interpreting formule involving
tresines, do not, in general, relate to the lengths of lines.
If x, y, z and 2’, y’, 2’ be respectively the rectangular co-
ordinates of two points in space, the distance between them is
expressed by the quantity / (a —2)? + (y’—y)? + @ —2z)
But this is not the function of x, y, z, a’, y’, 2’ that the for-
mule in question commonly bring before us: they most fre-
quently introduce, instead of it, the function

V (a2) + (yy) + (2 — 2) — 3 (a/—2) (y’—y) (2/=2)
which Mr. Graves proposes to call the cubic modulus of the
line joining the points x, y, z and 2’, y/, 2’. This cubie mo-
dulus may be written in aform which suggests important con-

sequences.
If we put
x =meotr[¢,x| a’ = m’cotr[ ¢’, x’]
y = mtres[¢, x] y' = m’' tres [¢’, x]
z= mtres[y,¢] 2’ = m' tres [ x’, ¢’]

it becomes

J m3 — 3m™meotr| p— p's X— x'}+3m'm?cotr[ o’—¢, x/—x]—m*

Thus we have the modulus of the line joining two points in
space expressed by means of the differences of their corres-
ponding amplitudes and the moduli of the right lines drawn to
them from the origin :—a result analogous to the fundamental
proposition in plane trigonometry, by which the length of one
side of a triangle is found from the two remaining sides and the

83

included angle. Having now got the notion of the modulus
of aright line in space, we may easily advance to the con-
ception of the modulus of a curved line: for we may regard it
as the sum of the moduli of the elements of the curve : so that
to find m, the modulus of the curve itself, we employ the formula

m= § vV/ dx? + dy? + dx? — 3dx dy dz.
The right line drawn from the point 2, y, 2 to another point,

2’, y’, 2’, may be looked upon as having amplitudes as well as
amodulus. In order to determine them we put

a —a« = mcotr[¢, x] :y’—y=mtres[¢, x] :2/—2z = mtres[y; p]:
m being the modulus of the right line.

For the purpose of illustrating his views, Mr. Graves has
discussed the surface whose equation in rectangular coordinates
is

e+ y+ 2— sayz = 1.
As might be expected, this surface possesses numerous pro-
perties which admit of being stated in such a manner as to
exhibit a striking similarity to those of the circle. The three
coordinates 2, y, z belonging to any point on it, may be put
equal to cotr[¢, x], tres[¢, x], and tres[y, ¢]; and we may
call ¢ and x the amplitudes of the point. It will also be con-
venient to designate the point, whose amplitudes are —@ and
—x;, as reciprocal to the point whose amplitudes are and x.

Amongst other theorems relating to this surface, which
Mr. Graves proposes to name the surface of tresines, the fol-
lowing may be considered as deserving attention :

1. The angle between the tangent planes at any two points
on the surface is equal to that between the radii drawn to the
two reciprocal points.

2. The measure of curvature at any point is equal to
—r,—“: r, denoting the radius of the reciprocal point.

3. The surface is one of revolution : and it is its own polar
reciprocal with reference to a sphere whose centre is at the
origin of coordinates and whose radius is unity.

84

The curve of double curvature, or curve of tresines, defined

by the equations

x = cotr[¢, o]

y = tres [¢, 0]

z = tres [o, ¢]
appears likewise to be most fertile in properties analogous to
those of the circle. The following were stated by Mr. Graves:

1. The angle between the tangents at any two points on
the curve is equal to that between the two corresponding radit.

2. The angle between the osculating planes at any two
points on the curve is equal to the angle between the radit
drawn to the two reciprocal points.

3. The angle of contact at a point on the curve is there-
Sore equal to the torsion at the reciprocal point.

4. The element of the curve described by the reciprocal
point is double the elementary area described by the radius
vector.

5. The polar reciprocal of the developable surface formed
by the osculating planes is itself the curve of tresines.

6. The product of the radii of curvature at any point and
at its reciprocal is equal to unity.

7. The radius vector traces a logarithmic Piya upon a
plane parallel to the symmetric plane.

Mr. John Neville read a paper on the maximum Amount
of Resistance required to sustain Banks of Earth and other
Materials.

Let CDE be any bank of
earth, sand, or other material,
and CE the position of the
line of repose with respect to
the horizon and bank ; then if
we put CA, the perpendicular
from C on DE produced =f,
the 2 DEA = 36; the angle
ECA =; andthe Z ACF, which the fracture CF makes

85

with CA, = ¢; then when the horizontal resistance R, neces-
sary to support the wedge FCD, is a maximum,*

sec.c / tanb tanc+1—1

tang =
tance

(1)

ee ee aes + Ui
Mey My WA eiutanel? xv ?

(2)

where W = the weight of a cubical unit of the stuff in FDC.
Equation (2) may be changed into the following,

Se ca +cote— Ytanb+cotc)? (3)

a simple form to calculate the values of R from.
Also if CO is drawn parallel to DE, and we put

= GK = ZUCO; 6= 2 OCH =F ca).
and H = CD the slant height of the face: then

tan (c—) = tan Z FCE = yptan?9 + tand tand — tan$ (4)
and

H?w tan 0
hae 2 * tan § — and (c— 9); (6)

where d=c —b = Z ECD.
When 6=0, CD coincides with CA, and we get from
equation (1)
secc —1
tance

tan ¢ = = tani 3 C5

which shews that the equation of Prony holds good, whatever
the inclinations of CD and DE to the horizon may be, if these
lines continue at right angles to each other. We also get
from equation (2) or (5) in this case,

* Generally we have R= W X DCF tan. FCE, for any fraction CF; a
very simple expression for finding the value of the resistance when the posi-
tion of the fracture is given.

86

Be = tan? ic, (6)
which shews the value of R retains the same form whatever
the inclination of CD may be, if DE continues at right angles
to it, as may also be seen, in the more general case, from equa-
tion (2) or (5).

When 0 = c — 6, DE stands at the angle of repose, and
when infinite, from equation (4), the fracture CF becomes
parallel to it; and from equation (2) or (5) may be had, by
reduction,

— — x sin? (c—d). (7)

As in loose stuff DE can never stand ata steeper inclination
than the angle of repose, equation (7) gives the greatest value
Ran ever attain; the height of the face H being constant.
When 6 = 0, H vertical, and ec = 34°, which corresponds to
a slope of repose of 14 to 1 nearly, we get, by comparing
equations (6) and (7),

Rin (6): R in (7) : : 283: 687 :: 3: 7, nearly.

In fluids the ratio will be as 1 to 1, and when the angle of
repose is 90°, the ratio will be as 1 to 4; for tan?3c:sin’c::
3c?:c?::1:4: hence no instance can occur wherein, the face
H being vertical, the value of R can exceed four times the
value when the top DE is horizontal.

Equation (4) gives the following simple geometrical con-
struction for finding the line CF. Draw any line MO, cut-
ting the line of repose CE at right angles in K, and termi-
nating in the face CD at M, and in the line CO parallel to
DE, the top, in O. On MO describe a semicircle, cutting
CE, the line of repose, in H; from O as centre, with OH as
radius, describe an arc to cut OM in I; join C to I, and pro-
duce CI to F; then the wedge FDC will require the maxi-
mum resistance. When DE is at right angles to DC, the
angle ECD is bisected by EF.

87

The equations apply also to finding the value of R and
position of CF for ‘* dwarf walls” CD, at the toes of cuttings
or embank-
ments ;___ but
when the frac-
ture CF lies
inside the top
of the slope
DG, the value
of R and po-
sition of CF
are found as follows:

Produce EG to A, and draw CA so that ACOD=
AGOA, and as, therefore, AFAC = FGDC, we have only
to determine R, and draw CF as if the bank to be supported
was CAE.

In the Encyclopedia Britannica, seventh edition, article
‘“‘Masonry,” by Tredgold, there are given the following equa-
tions:

—1-+ (tance tan*7 + tan’? + tanc tan? +)!»
tan z

feo); tana

Sea[ tani + tance + —— 2( tance tani soot * + 8
where a = 4 ECa, which the
plane of fracture CE makes
with the vertical line Ca;
e = Z ACa; 7 = the com-
plement of the angle of repose ;
h= AC the vertical height,
and S = the weight of a cubi-
cal foot of the material in SS

ACE, AE being horizontal: and the following table of calcu-
lated values of R from equations (26) and (25) :

“(25)R=

88

Water, .

Fine dry sand,

Do. moist .
Quartz sand, dry,

& 0b

Angle
of
Repose.

Qo
33°

35°

Weight of S.

62:5ibs.
92 —
119 —
102 —

Value of R. | Value of R
when c= 0° | when c=10°

R=311hk2? |R=312h2
R=13-8h? | R= 4-8 h2
R=17-°8h?} R= 6:2 h?
R=13-77h?} R= 4:6h2

Now, using the same data, and calculating from equations
(6) and (2) here given, the values will be as follow:

Value of R. | Value of R

Angle when 6 = 0, | whend = 10°

of | Weight of W.| and C D ver-| and D E ho-

Repose tical: equa-| rizontal:

tion (6). | equation(2).
1 | Water, . 0° 62 5ibs R=3lih? |R=slih2
2 ne sand, dry, 33° 92 — R=13-5h2 |R= 97h?
3 moist, 119 — R=17-5h? | R=12-6h2
4 ais sand, dry, 35° 102 — R=138h?2 | R= 9:7 h2

The values in the last column have been calculated from
equations (2) and (5) respectively, which gave the same
results when the latter is multiplied by sec?b, as h?
sec?b =n”: they are fully double those given by Tredgold,
and made use of by him in calculating the dimensions of re-
taining walls given in another Table. The differences in the

Tables, when b=0, are immaterial. Equation (25) is, how-
ever, incorrect, as will be seen by squaring the second part of
equation (3) here given, actually, when we get

)

, in Tredgold’s

tanctan?+1_
tan?2

this being the case, his equation is then reducible to equation

(3). Equation (23) can also be reduced to the form of equation

(1), which is general, whether DE is horizontal or inclined.

h2-w
= Stan

Ss( tane + tad -+ ———2 Wy) caeenn = +

Whence it appears that the term Seo

equation (25) under the square root, should be

89

Mr. Thomas Bergin read the following communication
from Dr. Thomas Woods of Parsonstown, on a new photo-
graphic process, which he calls the Catalysotype. Mr. Ber-
gin also read two letters from H. Fox Talbot, Esq. (M. P.)
to Dr. Woods, and his answer.

While investigating the property that sugar possesses, in
some instances, of preventing precipitation, I noticed that
when syrup of ioduret of iron was mixed in certain proportions
with solution of nitrate of silver, the precipitate was very
quickly blackened when exposed to the light, and I thought
that, if properly used, it might be employed with advantage
as a photographic agent. If not entirely without profit, it
would hardly repay the trouble of reading the history of all
the experiments I tried in order to prove whether or not this
idea were correct, for there were many difficulties to be over-
come, and unexpected hindrances to be surmounted, before I
could be certain of success. However, the results at which I
have arrived make me hope that my trouble has not been
thrown away, and that a photographic process has been dis-
covered, which is more manageable, and more satisfactory,
than any which has before been used; and I think that the
pictures produced by it are more minutely and delicately
brought out, and the time for their production at least not
longer than is required by any other method.

To enter very minutely into the particulars, or to explain
the rationale of the process would be too tedious; however,
it is so simple, that those who will feel any pleasure in trying
it will, Iam sure, easily succeed, and to attempt any expla-
nation of its theory would, in the present state of our know-
ledge of light, be advancing a mere hypothesis; I will, therefore,
only state generally the method in which the. paper is pre-
pared, and then briefly giving my reasons for such parts of
the process as are not at first sight obvious, will thereby
enable the experimenter to be guarded against the failures that
these precautions are intended to overcome.

VOL. Ill. H

90

Let well-glazed paper (I prefer that called wove post)
be steeped in water to which hydrochloric acid has been added
in the proportion of two drops to three ounces. When well wet,
let it be washed over with a mixture of syrup of ioduret of iron
half a drachm, water two drachms and a half, tincture of
iodine one drop. When this has remained on the paper for a
few minutes, so as to be imbibed, dry it lightly with bibulous
paper, and being removed to a dark room, let it be washed
over evenly, by means of a camel-hair pencil, with a solution
of nitrate of silver, ten grains to the ounce of distilled water.
The paper is now ready for the camera. The sooner it is
used the better ; as when the ingredients are not rightly mixed,
it is liable to spoil by keeping. The time I generally allow
the paper to be exposed in the camera varies from two to
thirty seconds ; in clear weather, without sunshine, the me-
dium is about fifteen seconds. With a bright light, the pic-
ture obtained is of a rich brown colour ; with a faint light, or a
bright light for a very short time continued, it is black. For
portraits out of doors, in the shade on a clear day, the time
for sitting is from ten to fifteen seconds. If the light is strong,
and the view to be taken extensive, the operator should be
cautious not to leave the paper exposed for a longer period
than five or six seconds, as the picture will appear confused
from all the parts being equally acted on. In all cases, the
shorter the time in which the picture is taken the better.

When the paper is removed from the camera no picture
is visible. However, when left in the dark, without any other
preparation being used, for a period which varies with the
length of time it was exposed and the strength of the light, a
negative picture becomes gradually developed, until it arrives
at a state of perfection which is not attained, I think, by
photography produced by any other process.* It would seem

* The picture, when developed, is not readily injured by exposure to mode-
rate light; it ought, however, to be fixed, which may be done by washing it
with a solution of bromide of potassium, fifteen or twenty grains to the ounce,
or iodide of potassium, five grains to the ounce. It may either be applied with

91

v

as if the salt of silver, being slightly affected by the light,
though not in a degree to produce any visible effect on it if
alone, sets up a catalytic action, which is extended to the
salts of iron, and which continues after the stimulus of the
light is withdrawn. The catalysis which then takes place
has induced me to name this process, for want of a better
word, the Catalysotype. Sir J. Herschelland Mr. Fox Talbot
have remarked the same fact with regard to other salts of
iron, but I do not know of any process being employed for
photographic purposes which depends on this action for its
development, except my own. e
My reason for using the muriatic acid solution, previous
to washing with the ioduret of iron, is this: I was for a long
time tormented by seeing the pictures spoiled by yellow
patches, and could not remedy it, until I observed that they
presented an appearance as if that portion of the nitrate of sil-
ver which was not decomposed by the ioduret of iron had
flowed away from the part. I then recollected that Sir J.
Herschell and Mr. Hunt had proved that iodide of silver is
not very sensitive to light, unless some free nitrate be pre-
sent. I accordingly tried to keep both together on the paper,
and after many plans had failed, 1 succeeded by steeping it in
the acid solution, which makes it freely and evenly imbibe
whatever fluid is presented to it. 1am sure that its utility is
not confined to this effect, but it was for that purpose that I
first employed it. My reason for adding the tincture of iodine
to the syrup is, that having in my first experiments made use
of, with success, a syrup that had been for some time pre-
pared, and afterwards remarking that fresh syrup did not an-~
swer so well, | examined both, and found in the former a
little free iodine; I therefore added a little tincture of iodine

a camel-hair pencil, or by immersion. The picture must then be well washed
in water, to remove the fixing material, which would cause it to fade by expo-

sure to light.
H 2

92

with much benefit, and now always use it, in quantities pro-
portioned to the age of the syrup.

The following hints will, I think, enable any experimen-
tor to be successful in producing good pictures by this pro-
cess, In the first place, the paper used should be that called
‘wove post,” or well-glazed letter-paper. When the solu-
tions are applied to it, it should not immediately imbibe them
thoroughly, as would happen with the thinner sorts of paper.
If the acid solution is too strong, it produces the very effect
it was originally intended to overcome; that is, it produces
yellow patches, and the picture itself is a light brick-colour,
on a yellow ground. When the tincture of iodine is in excess,
partly the same results occur; so that if this effect is visible,
it shews that the oxide of silver which is thrown down is
partly re-dissolved by the excess of acid and iodine, and their
quantities should be diminished. On the contrary, if the sil-
ver solution is too strong, the oxide is deposited in the dark,
or by an exceedingly weak light, and in this case blackens
the yellow parts of the picture, which destroys it. When this
effect of blacking all over takes place, the silver solution should
be weakened. If it be too weak, the paper remains yellow
after exposure to light. Ifthe ioduret of iron be used in too
great quantity, the picture is dotted over with black spots,
which afterwards change to white. If an excess of nitrate of
silver be used, and a photograph immediately taken before
the deposition of the oxyde takes place, there will be often,
after some time, a positive picture formed on the back of the
negative one. The excess of the nitrate of silver makes the
paper blacker where the light did not act on it, and this pene-
trates the paper, whereas the darkening produced by the light
is confined to the surface. The maximum intensity of the
spectrum on the paper, when a prism of crown glass is used,
lies between the indigo and blue ray. The difference of
effect of a strong and weak light is beautifully shewn in the
action of the spectrum: that part of the paper which is ex-
posed to the indigo ray is coloured a reddish brown, and this

93

is gradually darkened towards either extremity until it be-
comes a deep black.

I have not had many opportunities of experimenting with
the Catalysotype, but it certainly promises to repay the trou-
ble of further investigation. ‘The simplicity of the process,
and the sensibility of the paper, will, no doubt, make it be
extensively used. It has all the beauty and quickness of the
Calotype without a tenth of its trouble, and very little of its
uncertainty; and, if the more frequent use of it by me, as
compared with other processes, does not make me exaggerate
its facility of operation, I think it is likely to be practised
successfully by the most ordinary experimenters.

SUPPLEMENT TO THE PRECEDING PAPER.

P. S.—Since the preceding Paper was written I have
been experimenting with the Catalysotype, and one day hay-
ing had many failures, which was before quite unusual with
me, Iam induced to mention the cause of them, for the benefit
of subsequent experimenters. ‘The paper I used was very
stiff, and highly glazed, so that the solution first applied was
not easily imbibed. ‘The blotting-paper was very dry and
bibulous. When using the latter, I removed nearly all the
solution of iron from the first, and, of course, did not obtain
the desired result.

While varying the process in endeavouring to find out the
cause just mentioned, I discovered that the following propor-
tions gave very fine negative pictures, from which good posi-
tive ones were obtained :—take of syrup of ioduret ofiron, dis-
tilled water, each two drachms; tincture of iodine, ten to twelve
drops: mix. First brush this over the paper, and after a
few minutes, having dried it with blotting-paper, wash it
over in the dark (before exposure in the camera) with the fol-
lowing solution, by means of a camel-hair pencil:—take of
nitrate of silver one drachm; pure water one ounce: mix.
This gives a darker picture than the original preparation, and,
consequently, one better adapted for obtaining positive ones;

94

it also requires no previous steeping in an acid solution. To
fix the picture, let it be washed, first in water, then allowed
to remain for a few minutes in a solution of hydriodate of pot-
assa (five grains to the ounce of water), and washed in water
again. The paper I use is the common unglazed copy paper,
but such as has a good body. I have tried the same paper
with the original preparation, and find it to answer exceed-
ingly well; it does not require in this case, either, an acid so-
lution. The same precautions and hints apply to the amended
as to the original process: such as when it blackens in the
dark, there is too much caustic used; when it remains yellow,
or that it is studded with yellow spots, too much iodine; when
marked with biack spots, too much iron. It.is necessary to
mention these, on account of the varying strength of the ma-
terials employed.

The following is the correspondence laid before the Aca-
demy on the part of Dr. Woods:

“ Lacock Anppey, CHIPPENHAM,
“11th March, 1845.

‘“Srr,—Excuse my addressing you on the subject of a Paper
which you sent to the British Association at York, last September,
containing the description of a photographic process.

‘Some years ago I described a process for obtaining camera
pictures without using any second wash. It was described nearly
as follows in the specification of my English patent: Take codtsed
paper, wash it with gallic acid, dry it, and keep it in store for sub-
sequent use. This is called to-gallie paper from its constituents.
When wanted, take a sheet of io-gallic paper, wash it with nitrate

"of silver, and put it in the camera. The image obtained is generally,
at first, invisible, but it rapidly developes itself when removed from
the camera, requiring no further care, except ultimately to fix it.
Instead of gallic acid, sulphate of iron answers the same purpose
perfectly. The same effect is very often, but not always, produced
in the ordinary Calotype process, which I described in 1841; indeed
I discovered it in that way.

“The process which you have called Electrolysotype appears to

95

me to be strictly analogous to the above. If I comprehend your
description, you use an iodised paper in which iodide ofiron is em-
ployed instead of iodide of potassium.

‘¢ You may be quite right in attributing the effects to Electro-
lysis, but then it follows that my Calotype process, with all its
variations, must result from the same cause.

“* Tam, Sir,
‘* Your obedient Servant,
“« H. Fox Ta.sor.
‘““Dr. Woods.”
** Lacock ABBEY,
“18th March, 1845.

‘“«Sir,—I have to acknowledge the receipt of your courteous
letter of the 15th instant, upon which I beg leave to make a few ob-
servations. In my Calotype process, iodide of silver is decomposed
by the joint influence of light and a deoxydising agent (gallic acid).
Mr.Hunt has shewn that sulphate of iron may be substituted for gallic
acid, and he calls the process so altered Energiatype. But since tan-
nin and other substances may also be substituted for gallic acid, each
of these variations in the process would require, on the same princi-
ple, to have a separate name, which would, surely, be inconvenient.
In your method, iodide of silver is decomposed by the joint action
of light and iron; the three reacting substances being the same as
in Mr. Hunt’s Energiatype; and therefore, imperfect as the theories
of photography confessedly are, I cannot persuade myself that a
catalytic action can take place in your process, wz/ess it also takes
place in the Energiatype and in my original Calotype process: I
therefore cannot help considering these three processes as variations
of the same, and not essentially different. I hope, however, you
will not consider me as detracting in the least from your valuable
labours: my remarks only refer to the nomenclature of the science.

If I am not mistaken, the three methods I have named produce
pretty nearly identical results, though I speak from experience of
only two of them, Mr. Hunt’s and my own. Both of these are
nearly certain in operation, very rapid, giving a camera picture of
a bright object in a second of time, and requiring no second wash
if enough of the deoxydising agent is employed in the first wash.
It is. customary to make the positive copies on a different paper,

96

which I have called photogenic drawing-paper, consequently, the
Jinal results of the two processes cannot anyhow be distinguished.
I thank you for your courtesy in mentioning that you are about
to send a Paper on the subject to the Royal Irish Academy by the
hands of Dr. Robinson. May TI request that this letter and my
former one, with the permission of the Academy, may be read to
them on the same occasion, if Dr. Robinson will kindly take charge
ofthem. It may be left to their scientific judgment to say whether
a new principle is involved or not in your experiments. If any
new principle be involved, then a distinctive name, such as you
have given, is, of course, desirable,—otherwise it would not be so.
I would refer also to the instance of the Daguerreotype, now so dif-
ferently managed from what it used to be at the time of its first
promulgation. It is now at least a hundred times more rapid in
its effects, but it still continues to be called the Daguerreotype.
On the other hand, I believe it is not affirmed that any process on
paper has been discovered more rapid or more certain than the
Calotype; I am not aware of any such having been as yet described.
We should certainly be very grateful to any one who discovered a
more rapid process, depending on new combinations; but if I do
not err in defining the Calotype process as depending on a combi-
nation of iodine, silver, and a deoxydising agent, your process
would be included in that definition, unless good reasons to the
contrary could be shewn, all which I willingly leave to the judg-
ment of the scientific world: and, thanking you for your polite

attention in so soon answering my last letter,

“¢ T remain, Sir,
‘* Your’s very truly,

“* H. Fox Tarot.

“« P,S.—If your process does anything which the Calotype can-
not do, or does it better, I willingly admit its importance; but I
apprehend that you are not aware of the facility and rapidity with
which our Calotype operations are now conducted. Indeed, that
was my chief reason for troubling you with a letter, as your Paper
read at the York meeting mentioned the spontaneous development
of photogenic images as something new, whereas it is a phenomenon

97

of very frequent occurrence in the Calotype, and always occurs
when we use the io-gallic paper.”

‘* PARSONSTOWN,

“* March 25, 1845,

‘« Srr,—I am sorry I did not receive your letter before Dr. Robin-
son left this town, which I should have done, it being dated March 18:
I did not get it until March 24. I will, however, forward it to him,
and I am sure he will, with his usual kindness, make whatever use
of it he thinks right. I will ask him to have it laid before the Aca-
demy with my Paper. I agree with the observations you make on
my Paper on general principles. There is no doubt at all that
your Calotype, Mr. Hunt’s Energiatype, and my Catalysotype, if I
may be allowed, for the present, to call it so, are all pretty similar
_ in their modes of action, and perhaps they all come to the same point
in the end,—the decomposition of the salt of silver; but, as I said
in my former letter, if new modes of producing this effect were not
to be named, why call your process Calotype—why call Mr. Hunt’s
Energiatype, &c., as they all agree in their general results with
the first experiments made with light on the nitrate of silver? Why
not regard them all merely as ézstances of the same general princi-
ple, and not isolate them, as it were, by designating each by a par-
ticular name? You will say now that I agree with your ideas: I
always did. I think that cumbering science with a multiplicity of
hard names for every particular fact is very bad ; but the christen-
ing of my process has been forced on me by a similar line of con-
duct in others ; and when a nomenclature sufficiently good appears
(a task which I wish you would undertake), I will be the first to
blot out the word Catalysotype.

‘‘T do not pretend to any discovery; nor do I think, my pro-
cess, in its chemical character, distinct from the general mass of
facts in active chemistry. I merely regard it as a new combination,
acting with great facility, very little complication, and, though not
involving a new principle, being developed without requiring any
second wash, which I looked on as characteristic until you men-
- tioned the io-gallic paper, a process of which I was certainly igno-
-rant before. You mention also Mr. Hunt’s Energiatype as being

similar to mine; but, as first published, it undoubtedly could have

98

no claim to the advantages mine possesses, either in facility of exe-
cution or rapidity of result. I think ‘he says it requires six or eight
minutes to accomplish what mine does in two or three seconds.
After my process was published by being read at the meeting of the
Association at York, the sulphate of iron was applied to iodised
paper, but not before. That proceeding has increased its sensibility,
and made it approach in sensibility to mine; but it obviously does
not interfere with my right to consider the Catalysotype my own
child, and to call it what I please. However, I think all experi-
mentors with light owe you a great debt, and should pay particular
attention and respect to your opinion on a subject for which you
have done so much ; I will, therefore, not insist on adhering to the
word Catalysotype, but leave the process to be dealt with as a fact
in the general history of active chemistry. For the present the
name must be borne with, as my Paper is written and given to Dr.
Robinson; but if it ever should be again spoken of, which is per-
haps not probable, we will not elevate it to the honour of a distinct

prefix.
“Tam, &e.

‘“*THomAs Woops.”

May 26, 1845.

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

A sealed packet was opened, with the consent of Mr. R.
Mallet, by order of the Academy, which he had deposited
with the Academy at the meeting of the 13th of November,
1843. Mr. Mallet then stated the subject matter of the en-
closed document to be certain propositions regarding improved
methods of working atmospheric railways, and that his object
in calling for the production of the packet upon this evening
was to claim his priority of invention, as similar plans have
been since proposed by French and English engineers.

A letter from Mr. Clibborn was read by the Secretary,
relating to the discovery of certain gold antiquities near Naas.

99

“26th May, 1845.

“« Srr,—lIt may be well to have a notice inserted in the minutes
of the meeting of this evening, of the discovery of three gold anti-
quities of considerable value, which were found recently in the
neighbourhood of Naas.

‘«‘ The most interesting of these articles is a gold torquis, which
I have purchased for the Marquis of Kildare’s collection. It dif-
fers in form from the two in the Academy collection, which were
found at Tara; and itis smaller than the largest of these, and
larger than the smaller ; its ends are also larger than those of the
larger torquis. In form, the ends resemble those of the small tor-
quis which the Academy purchased from the late Major Sirr. This
torquis weighs 18 oz. 4 dwts. and 6 grs. The principle of its con-
struction is quite manifest, for the four gold bands of which it is
made are not perfectly connected together in several places: thus
it exhibits a difference in its construction from the gold articles
from Africa, which resemble those twisted gold ornaments found
in Ireland.

“ The other two articles were gold rings, or bent round bars of

gold, one large enough to go round the eck of a man, and the
other to go round his wrist. The larger weighs 31 oz. 14 dwts. and
16 grs.; and the smaller one weighs 7 oz. 5 dwts. and 19 grs., being
a quarter of the weight of the larger. As the weights were ascer-
tained with great care, they may be depended on.

“The weight of the torquis has not been yet verified. It is,
for the present, deposited for inspection in the case with the gold
ornaments belonging to the Academy.

‘« Your obedient Servant,
“‘ EDWARD CLIBBORN,
“ Assist. Librarian, R. I. A.”

The Rev. Dr. Todd read a paper on the ancient Wax
Tablets which he had presented to the Academy on the 14th
of April last, on behalf of the Rev. J. Spencer Knox.

From the words still legible on the tablets it is evident
- that they had belonged to some schoolmaster, who had em-
ployed them in the instruction of his pupils, or to some

100

scholar, who had inscribed upon them his exercises in gram-
mar and dialectics: and from the words “hoc quuium,” which
occur on one of the pages, it would seem that the owner was
engaged in learning or teaching the trivium, i.e. the first
three of the seven liberal arts, in which the first Degree is still
taken in our Universities.

The characters inscribed on these tables, as far as Dr.
Todd was able to determine, were of the fifteenth century,
if not earlier. He shewed that the use of waxed tablets con-
tinued to the seventeenth century, and that there was no
foundation for the opinion maintained by a learned French
Dominican, Pére Alexandre, that the use of tablets of this
kind ceased in the fifth century.

Dr. Todd concluded by proposing that the special thanks
of the Academy be presented to Mr. Knox for this valuable
donation to the Museum ; and recommended that it be referred
to the Council to have drawings of the tablets immediately
made, lest they should receive injury from the ordinary heat of
the room, or otherwise.

Professor Allman made some observations on the wood
composing the tablets, which he submitted to microscopical

examination.

The Rev. Humphrey Lloyd read the following paper by
the Rev. Thomas Knox, on the quantity of Rain which fell
with different winds, at Toomavara, during five years since
1827.

I beg leave to lay before the Royal Irish Academy the
following results of the rain-gauge kept at River Glebe, Too-
mavara, for five consecutive years.

The amount of rain is given separately for the eight prin-
cipal points of the wind; and the curves in the accompanying
plates are formed (as mentioned in a former communication)
by taking on each of the eight points, distances from the

101

centre respectively proportional to the amount of rain which
had fallen when the wind was in that direction ; by then con-
necting these spaces a curve is formed, which shews at a
glance the character of the rain for that particular period.
The plates are only drawn for the mean results, which are the
only ones of any importance. ‘The period of five years is
rather shorter for very accurate mean results than could
have been wished, but absence from home after that period
had elapsed put a stop to the observations.

There are one or two points to which I wish to draw atten-
tion. First of all, taking the average monthly rain at three
inches, the first six months of the year are below the ave-
rage, the other six months above it. November and July are
by far the two wettest months in the year; and in each the
greatest amount is from S. W. April is much the driest
month, and there is nearly as much rain in it from the northern
portion of the compass as from the southern.

With regard to the gross amount which fell from each
point in the entire year, that which fell from S. S. W. and
W. is much above the average. From the other points it is
below it.

There is a curious circumstance with regard to the curve
of the entire year (Plate 6): that if it be divided by a line
running N. E. and S. W., then the rain on either side of this
line is equal all but a fraction of an inch. This is the more
remarkable, as these two points had been fixed on by Profes-—
sor Dove, in his Paper on the Winds, as being the points of
greatest and least barometric pressure. ‘That is to say, the
wind supposed at S. W., any shift of it, either towards S. or
W. produces a rise of mercury; and also any shift on either
side of N. E., a corresponding fall.

Now in the rain the greatest amount is from S. W. (cor-
_tesponding with the lowest state of mercury). The least is
from N. E. (where the mercury is highest), and on either side
‘of this line it varies regularly, as an inspection of the Plate

102

(No. 6) will shew. For instance the amounts from W. and S.
are nearly equal, and both less than S. W.; N. E. and S.
still less; N. and E. still decreasing ; and N. E. the least of
all. Whether this analogy between the barometric pressure
and amount of rain is accidental or not remains to be proved.

The following table shews the numerical average of the
rain. The detailed tables and curves will be published in the
Transactions of the Academy.

8. 8S. W. | W. |N.W.| N. |N.E. E. | 8.E || Total.

YEARLY AVERAGE
EACH Point. 6.548 | 10.639 | 6.034 | 2.789 | 2.352 | 2.172 | 2°251 | 3.173 || 35.958

January . 573 +721 -609 171 -162 .096 | .180} .306 2.918

mn
2a |February| 1655 | ‘668 | -397| 1935] ‘136 | :167| .175| .332 || 2.766
64 |March .| .635| .914| -679| .977.| .130| .064| .122 | .237 || 2.957
aA | April «| 175 | .375 | °404| 1192] .200| .153 | .088] .118 |} 1.704
2 |May. .| :359| [595 | .280| 1110] 1184 | .289| .251| -290 |} 2.359
$26 |June. .| .613| 1.936] .285| 1074 | .058] .181 | .062 | .189 || 2.699
sug [July. -| 517 | 1.148 | .568 | .443 | .398 | .281 | .242 | 110 | 3.712
SS bo August .| .588 | 1.440 | .408| .262 | .242 | .187 |) .147| .152 || 3.427
2S @ | Septem. | .711 | 1.020] .597 | .299] .237| .157 | .058| .304 |] 3.313
3 5g | October.| .387| .797 | -651| 1269] .412| .206] .117]| .195 || 3.033
25 |November| .629 1856 | .556| (983 | .165 | .234] .580} .550 || 3.844

Go) | December] .706 .969 | ~500 .139 .038 -157 -229 | .390 3.228

Winter .| .645| 786] .535 | 915] .112 | .140| .195 | .343 || 2.911
Spring .| .390] 595 | .454] 1193] .171 | .169| .154 | .215 |) 2.341
Summer | -973 | 1:275 | .420| .961 | .233 | .216 | .150 | .150 |) 3.278 |
Autumn | .576| 891] .601 | 960} .268] .199 | .352| .350 || 3.397

Monthly Mean
during each
Season for 5 ys.

Winter . 8.912
Spring . -020
Average for five years, total of suaniver ee
Autumn || 10.190

Average Year |} 35.958

There is one particular in which this separating the gross
amount of rain into the eight portions, as brought by dif-
ferent winds, may be useful, viz., to ascertain the respective
specific gravities, and the amount of saline matter brought
from each direction; this may be useful in regard to agricul-
tural matters. For instance, we could easily suppose a case
of two portions of land, not many miles asunder, but on dif-
ferent sides of a high range of hills, getting very different
amounts of salt from one being exposed to, and the other
sheltered from that wind in which the greatest amount was

——— a

103

found ; but by this mode of collecting the rain, an accurate
mode of estimating this is within our reach.

To this branch, namely, an examination of solid and
gaseous matter brought in the rain from each direction, I hope,
on a future occasion, to find time to turn my attention to.

Rev. H. Lloyd read an extract from a letter from Edward
W. Chetwode, Esq., describing a remarkable lunar halo and
paraselene, seen in the Queen’s County, on the night of the
21st of May.

‘© T send a rough sketch of what struck me last night as a
most beautiful and uncommon appearance, seen from our
hall-door at twelve o’clock: the moon, with cruciform rays,
surrounded by a halo; two bright spots 7m directum with the
horizontal arm of the cross, on the periphery of the halo; a
crescent light, not quite so intense as the horizontal spots,
also on the periphery, in directum with the perpendicular axis
of the cross; and at a considerable distance above it (perhaps
the distance of halo-radius) another much larger crescent,
looking as if it were the base of another halo circle. The sky
had a good many of those electric sweepings of light through
it at the time. No doubt there was a fourth bright spot on
the halo, but it was hid by a dense mass of trees. The two
horizontal spots, which were very bright, had decided rainbow
colours, strongly marked.”

The second figure in the lithographic plate at the end of the
part represents the phenomenon described by Mr. Chetwode.

The phenomenon was likewise seen in the neighbourhood
of Dublin, although not in so developed a form. The follow-
ing are the notes of its appearance, as observed at Sandy-
Cove, by Digby Starkey, Esq.

‘© Ten minutes after eleven, p.m. Wind N.W. Mist
across the sky to the North, East, and South, in striz, as
represented above. The line passing through the moon, and
the eastern and western mock moons, dipped a little to the

104

South West. The illuminated line from the western mock
moon was not traceable to any distance, nor did a mock moon
appear in the North, opposite to the moon. The red rays were
next the moon. The phenomenon was faint and ill-defined ;
the eastern and upper moons scarcely discernible. It dis-
appeared in about half an hour after it was first observed.

‘‘ No observation being taken at these hours at the Mag-
netic Observatory, there is no record of the phenomenon as
observed there. But the observer at ten, p.m. has noted as
follows :—Sky all covered with very fine long cirrostrati, ex-
tending across the entire sky from North to South. Haze
visible about the moon. ‘The barometer, at this hour, stood
at 29.978; the thermometer at 48.4; wet thermometer, 47.1.

Professor Allman made the following observations on the
same phenomenon.

Observed between the hours of 10 and 11 o'clock, p. m.,
on the 21st May, 1845, a thin haze spreading over the sky.
The arm of the cross which approached more nearly to the
horizontal was slightly inclined to the horizon, at an angle
which, as far as the unassisted eye could determine, might
have been about 15°. The other arm was perpendicular to
this. The diameter of the circle included within the halo was
equal to about forty diameters of the moon. At the points
where the cross, if produced, would have intersected the halo,
were paraselene. ‘The two lateral paraselene were more con-
stant in their appearance than the superior, which was visible
only two or three times during the observation. ‘The lower
part of the halo was not visible. ‘The moon itself was imme-
diately surrounded by an ordinary blur-like halo, which was
more intensely luminous than the cross, and within the mar-
gins of which it was wholly confined. ‘The extremities of the
paraselene, which were placed upon the halo, were obscurely
prismatic ; but I could determine nothing satisfactory as to
the order of the colours. The arms of the cross were inter-

105

mittent in visibility, that which was opposite to the left hand
of the spectator being the most so.

After 11 o’clock the appearance became more and more
obscure, until the cross was replaced by an obscure blur. The
paraselene also disappeared, while the halo, though diminished
in brightness, continued some time longer.

June 9, 1845.
CAPTAIN LARCOM, R. E., Vice-President, in the
Chair.

James Claridge, Esq., Adolphus Cooke, Esq., Windham
Goold, Esq., Charles Croker King, M. D., and Charles Wye
Williams, Esq., were elected Members of the Academy.

Mr. Richard Sharpe read a notice of a new electric clock,
on the principle of Mr. Wheatstone’s telegraphic instruments.

The Rev. Charles Graves made a further communication
relative to Algebraic Triplets, and their Geometric Inter-
pretation.

Besides the system of algebraic triplets developed in former
communications to the Academy, Mr. Graves has conceived
another, which appears to admit of an interpretation in some
respects more closely analogous to Mr. Warren’s geometrical
representation of imaginary quantities.

As the symbol /—1 may be taken to indicate a rotation
in the plane of x from the axis of x to the axis of y, it seems
natural to conceive another symbol representing a rotation in
the plane of wz, from the axis of 2 to the axis of z. The re-
petition of either of these operations would reverse the direc-
tion of a right line originally placed on the axis of a: and

VOL. III. I

106

therefore they are both equally fitted to serve as geometric
representations of the square root of negative unity. But
what is more, there is an infinite number of geometric ope-
rations of which this is equally true. For instance, rotation
through two right angles in any plane passing through the
axis of « would reverse the direction of a line placed upon that
axis.

Let us take then two symbols, ¢ and 7, denoting distinct
distributive operations, such that

(1) =7(1) = —1: 90) = 71),
and form with them and the three real magnitudes 2, y, 2 the
expression

atiytjet+ 9%.

As it depends upon three quantities, it may be looked upon as
a triplet ; whilst it is, in some sense, a quadruplet, being
made up of units of four different kinds: for there is reason to
regard #(1) as an imaginary unit, differing both from #(1)
and j(1).

Before we proceed to consider the results arrived at in the
multiplication of such triplets, it will be convenient to change
their form. For this purpose let us put

z= mMcos¢cos'y, y= msingcosy, z= mcosPsiny;
= will thus be transformed into
m(cos¢ cosy +7sin¢ cosy +jcos¢ siny +Ysingsinx), which
is evidently equivalent to me#tx,

If then we call m the modulus, and ¢ and x the amplitudes
of the triplet, it will appear that the modulus of the product of
two triplets will be equal to the product of the moduli of the
factors: and each amplitude of the product will be equal to
the sum of the corresponding amplitudes in the factors.

The modulus and amplitudes of the triplet (2, y, z) are
derived from its constituents by the equations

the expression x+7y+jz+7

107

yz?
2

ma=ety+ot+ 5

eS ON i Lape (aN,
@ = tan (@) > ¥ = tan (=)

Hence if x, y, z be the rectangular coordinates of a point in
space, the modulus of the right line drawn to it from the ori-

gin is a fourth proportional to the projections of this line upon
the axis of x and the planes of zy and wz. And the amplitudes
are the angles between the axis of a and these two last pro-
jections.

The construction thus obtained for the product of two
right lines obviously coincides with Mr. Warren’s in the case
where z = 0.

The nullity of the triplet a+iy+jz+7 = involves the

three equations, x= 0, y=0, z= 0.

But, however well these triplets fulfil the requisitions of
multiplication, we find they will not stand the test of addition.
The sum of two such triplets is not necessarily a triplet; nor
can we add two of them together, unless they happen to have
a common amplitude.

What has been here said may readily be extended, for we
might develope the expression etx +*v + &¢., in which ¢, 7, h,
&c. represent (z — 1) distinct square roots of negative unity,
into a series of terms, such as

A+ iB+jc +hkp+...
acorn CB Pe Ee
Sas rept gh area as ta is

= gh +...
and, conversely, we may reduce a multiplet
a+ib+je+hd+...
ae Gan. OG
La ora apa a re a
... bed
-+- pha + eee

108

depending upon » constituents a, b, c,d, &e., to the form
met +ix +h +...

The modulus m, and the amplitudes ¢, y, p, ... of the multi-

plet, will be found by the equations

Ce a Bn b?e2 b2c?d?

mae EP Eed D+ — sh ioe hema) Hipage

tans lei Xi tan “(9 y = tan S Ser MG Sadigs

The nullity of the multiplet involves the m equations

a0’ b= 0 Pe =P d SON ge

What has been already proved in the case of distinct square
roots of negative unity, may be applied, mutatis mutandis, to
multiplets of the form met %x+*/+---, in which 7, j, k, &c.
are used to denote wholly distinct geometric, or purely ima-
ginary 7“ roots of positive or negative unity.

Mr. Graves noticed that triple integrals such as (\§ V dxdydz
may sometimes be advantageously transformed, by putting
& = MCOSH Cosy, y = msing cosy, and z= mcospsiny : the
element dzdydz will then be replaced by m?cos pcos x dmdp aX

On the other hand, if we put

a= meotr[¢,x], y = mtres[¢,y], and z = mtres[y, 4],
we should transform the same integral into \\§ Vn*dmdgdy.

Mr. Petrie gave an account of an inscription on an ancient
Irish tombstone at Athlone.

Mr. Mallet read extracts from letters by the Rev. Dr.
Robinson and others, relating to suggestions for the improve-
ments in working atmospheric railways.

A letter was read from Messrs. Hodges and Smith, stating
that, contrary to their directions, 500 copies of Mr. Petrie’s
volume on the Round Towers had been printed, instead of

Pa a ee

109

450, as volumes of the Transactions of the Academy, and
offering the fifty copies which still remained on hands at the
same price as the former ones, namely, thirty shillings a copy.

ReEsoLveD, on the recommendation of Council, that this
offer be accepted.

June 23, 1845.
GEORGE PETRIE, ESQ., Vice-President, in the Chair.

James Strathearn, Esq., Daniel Conolly, LL.D., David
Moore, Esq., Rev. Classon Porter, and James Talbot, Esq.,
were elected Members of the Academy.

The following notice, by the President, Sir William R.
Hamilton, of a theorem derived from his Researches on Qua-
ternions, was read.

Let AC’A’B’ be called a spherical
parallelogram, if A’, B’, C’ bisect
the sides BC, CA, AB of a spherical
triangle ABC; and let it be said that
the corner A of the triangle is the
point which completes the parallelo-
gram when A’B/ and A’C’ are given
as two adjacent sides thereof.

‘Take any spherical quadrilateral, KLMN, and any point
on the same spheric surface, P; draw the four ares PK, PL,
PM, PN, and complete, in four points, K’, L’, M’, N’, the four
spherical parallelograms, of which the given pairs of adjacent
sides are PK, PL; PL, PM; PM, PN; PN, PK. Then
the four new points, K’, L’, M’, N’, form a new spheric qua-
drilateral, such that its four sides, K/L’, L’M’, M’N’, N’L’,
touch a certain spherical conic, having the poles of the dia-
gonals KM, LN of the old quadrilateral for its foci.

This theorem was stated to follow as an easy corollary from
what Sir William Hamilton had already communicated to the
Academy respecting quaternions.

110

Certain encaustic tiles and other antique remains were
presented to the Academy by Richard Cane, Esq., of St.
Wolstan’s, they having been found on ‘the site of that ancient
abbey.

Reso_vep,—That the thanks of the Academy be given
to Mr. Cane for his donation.

The Secretary read the recommendation of Council at
their meeting of the 16th June:

‘¢ That Mr. Clibborn be appointed Curator of the Museum,
with an increased salary ; that an Assistant be supplied to Mr.
Clibborn, and also a Porter.”

ResoLvep,—That the recommendation of Council be
adopted, and that it be referred back to Council, in order that
the same may be carried into effect.

Caprain Larcom, V. P., having taken the Chair, Mr.
Petrie presented, upon the part of Dr. Stokes, to be deposited
in the Museum for the present, an ancient reliquary, called
the Fiacail Phadruig, or St. Patrick’s Tooth.

Resotvep,— That the thanks of the Academy be given to
Dr. Stokes for this deposit.

July 14, 1845. (Extra Meeting.)

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

Resotvep,— That an adjourned meeting be held on Mon-
day next, 21st instant, at eight o’clock, in order to afford an
opportunity to the Council to correct an informality in the
last Minutes of Council connected with the summonses for this
meeting, and that the Academy be duly summoned. .

Caprain Larcom, V. P., having taken the Chair, the
President read a communication on the Applications of the
new Imaginaries to some Dynamical Questions.—See Appen-
diz, No. III.

July 21, 1845. (Adjourned Extra Meeting.)

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

Reapv,—The following Resolution of Council, passed on
16th July, 1845:

«¢ ResoLveD,—That at the Adjourned Meeting of the
Academy, summoned for Monday, 21st July, it be recom-
mended to the Academy to authorize the Treasurer to sell
Stock to the amount of £400 sterling, for the purpose of dis-
charging existing liabilities.”

Resotvep,— That the Academy do approve of and adopt
the recommendation of Council, as now read; and that the
Treasurer be authorized to sell Stock to the amount of £400,
for the purposes described.

Mr. Perris, V.P., having taken the Chair, the President
continued-a paper on the Applications of Quaternions to some
Dynamical Questions.—See Appendix, No. ILI.

The President having resumed the Chair, the Rev. Charles
Graves read the following paper on two methods of solving
Biquadratic Equations.

I.—An equation being supposed to have a pair of imagi-
nary roots, a + VY —1.b and a— / —1.8, if we diminish all
its roots by the quantity a, the transformed equation would
plainly have two roots differing only in their signs. This
consideration suggested the following mode of solving the bi-
quadratic equation,

a+ anu + asa +a,= 0. (1)
Let its roots be diminished by a, a quantity to be determined

by the condition that the transformed equation, found by sub-
stituting y + a for x, shall have two roots which differ only in

112

their signs. In order that this condition should be fulfilled,
we must have, in the transformed equation, the sums of the
terms containing the even and odd powers of y separately
equal to 0; a must therefore be a root of the equation formed
by eliminating y between the two equations thus obtained.
In this manner, by avery simple process, we get the following
equation in a,

64a°+32a,0'+4(a,.”—4a,) a’—a,? = 0, (2)
which is of a cubic form.

Equation (2) will be at once recognized as equivalent to
the auxiliary cubic arrived at in Lagrange’s, and indeed in
every other known method of solving the biquadratic equation.
Nor is it difficult to shew why the roots of Lagrange’s auxiliary
cubic are thus related to the different values of the quantity a,
by which the roots of the equation (1) are diminished in the
method here presented.

iy Loy Xz, 4, being the roots of equation (1), Lagrange
seeks the equation whose roots are the expressions

& + Ly — U3 — Uy U3 + Ly — & — M2.
®, + &3 — Ly — Uy By + &y — Ly — Ws
® + Uy — #2 — 3 By + #3 — @ — ay

and finds it to be
u® + 8aous + 16(a.”—4a,)u? — 6442 = 0.

Comparing this with equation (2), we see that4da=u. If
then we put

t +%—%—%4= 4a, U3+%,—%—Ma=4Q,
U +, — % — X= 4a, ly, + %4— #%, — 4, = 4a;
H, + 4 — % — 43, = 4a; Uy + U3 — 24, — 4, = 4a,

and attend to the relation a, + 2 + #3; + 2,0, which sub-
sists, inasmuch as the equation (1) wants its second term, we

shall find
Ly — a = ¥(aXy — 2)
Hy — a) = % (a, — 2)
3 — dy = ¥(3a34+4%4)
y — A, = ¥(3a,+23)

113

and there are five other similar systems of equations, in each
of which, among the right-hand members, appear two expres-
sions, differing only in their signs: accordingly, if we diminish
the roots of the original equation (1) by any one of the six
quantities, a, A, @3 A, As, as, the transformed equation will
have two roots differing only in their signs.

II.—The second method of solution referred to by Mr.
Graves, was suggested by observation of the fact that the pro-
duct of the four quadrinomials,

w+ ie + Py + Pz
w+ ia + ity + iz
w+ Pat Py + iz
w+tatyt2z

in which ¢ stands for va is real, and equal to

wi—2(y? + 2xz)w? + 4y.2? 4+ 2*)w + (y?—2xz)?— (a? + 27).
Now if we identify this expression with the left hand member
of the biquadratic equations

w* + Aw? + asw + ay = 0,

we shall have three equations, from which to determine 2, y,
and z. By the elimination of x and z, we readily deduce from
these the reduct cubic ordinarily arrived at.

—

The President made some remarks on the solution of
equations of the third, fourth, and fifth degrees.

[The following Report of the communications made to the
Academy by Dr. Robinson, on the 25th of April, 1842, and
the 14th of April, 1845, has been received since the Proceed-
ings of these dates were printed.]

VOL, III. K *

114

ON LORD ROSSE’S TELESCOPE.

Dr. Robinson, when giving, in November, 1840, to the
Academy, an account of the three-feet telescope constructed
by the Earl of Rosse, had announced to them the intention of
that nobleman to attempt an instrument of double aperture
and focal length. The attempt had succeeded even beyond
expectation, and he hoped that a brief notice of its progress
and results would not be uninteresting ; more especially as he
felt that the approbation with which they had received his
former communication, and the importance which they at-
tached to Lord Rosse’s discoveries, had not been the least
powerful cause of the triumph which their countryman has
now achieved.

The speculum was cast on the 13th of April, 1842, ac-
cording to the principles which had been so successfully ap-
plied to the smaller mirrors; but with several changes of the
details, made necessary by the gigantic scale of the work.

It is well known to all who have experimented on specula,
that the alloy must be formed in the first instance, and re-
melted for casting at a much lower heat: otherwise the mirror
is full of pores. ‘The fusion must, in both cases, be effected
in covered crucibles, to preserve the definite proportions of
the alloy, which would be lowered by oxidation of its tin if
exposed to the draught of the furnace. It is also necessary
that the speculum be of uniform composition and superficial
density; and as it is impossible to fuse the requisite quantity
of metal for one of six feet in a single vessel, the different por-
tions must flow into the mould under circumstances as nearly
as possible identical. Much thought and many experiments
must have been expended before these conditions were so
completely fulfilled. The crucibles are, of course, cast iron ;
no earthen one being able to bear the pressure of such a mass
of fluid metal at so high a temperature. They are thirty
inches internal depth, and twenty-four diameter, weighing

115

about half a ton each, and manufactured with the precautions
pointed out by Lord Rosse (Phil. Trans. 1840). Notwith-
standing their great strength, they yield so much that it is
obviously hazardous either to use them frequently or to in-
crease their dimensions. ‘Three were employed at once, each
containing about one and a half tons of the alloy: they were
placed in furnaces whose mouths were level with the ground,
eight feet deep and four in diameter, disposed round a large
stack or chimney, into which their flues vent. The fuel is
turf, peculiarly fitted for this work, as giving a much more
manageable heat than coke ; about 2200 cubic feet of it are
consumed in a casting. The furnaces were filled with fuel,
and ignited at the top, on the preceding evening, that the
crucibles might be gradually heated; and in about ten hours
they were ready to receive the metal. This was unintention-
ally made of a lower standard than that of the three feet, in
consequence of the atomic number for tin being taken as
given in Turner’s Chemistry, 57.9 instead of 58.9, causing a
deficiency of about half per cent, too trifling to impair mate-
rially its reflective power, though it will certainly make it
more liable to tarnish. ‘That its uniformity might be insured,
each ingot of it was broken into three pieces, as nearly equal
as possible, and stored in three casks, each of which contri-
buted equally to form the successive charges of the crucibles
in an order regularly varying. They were charged at inter-
vals of two hours, and the whole was fused in twelve: they
were then withdrawn from the furnaces by a powerful crane,
and transported to the iron cradles of pouring frames, arranged
90° asunder round the mould.

The essential part of the mould is its base, composed of
hoop iron six inches broad, packed on edge in a strong frame
seven feet diameter, and supported by strong transverse bars
below. ‘The upper surface was turned to a convex segment
of a sphere, 108 feet radius, on the polishing machine, over
which a self-acting slide rest was fixed, whose frame was of

K 2

116

the same curvature. ‘This process required several weeks,
and it was then ground smooth by a frame filled with con-
eave blocks of sandstone. ‘The bed of hoops so prepared
being set exactly level, and heated sufficiently to blue its sur-
face (for the purpose of burning out the tallow with which its
interstices are filled, when not in use, to protect it from oxida-
tion), the wooden pattern of the speculum was placed on it,
and founders’ sand rammed round it to its top. The mould
thus formed was about a foot deep, the thickness of the spe-
culum, 54 inches in this instance, being determined by the
quantity of metal melted. By this arrangement, as Dr. Ro-
binson formerly explained to the Academy, the fluid metal
which comes in contact with the hoops is chilled at once into
a dense sheet about half an inch thick; the air which might
be entangled with it in pouring, escaping through their inter-
stices. The circumference sets much more slowly in conse-
quence of the inferior conducting power of the sand; and the
upper surface, which is only in contact with air, remains so
long fluid, that the greatest part of the shrinkage occurs
there ; its tendency to crack the cast is prevented, and the
coarse structure which it produces is confined to a place
where it is unimportant.

On this occasion, besides the engrossing importance of the
operation, its singular and sublime beauty can never be for-
gotten by those who were so fortunate as to be present.
Above, the sky, crowded with stars and illuminated by a most
brilliant moon, seemed to look down auspiciously on their
work. Below, the furnaces poured out huge columns of
nearly monochromatic yellow flame, and the ignited crucibles,
during their passage through the air were fountains of red
light, producing on the towers of the castle and the foliage of
the trees, such accidents of colour and shade as might almost
transport fancy to the planets of a contrasted double star.
Nor was the perfect order and arrangement of every thing
less striking : each possible contingency had been foreseen,

117

each detail carefully rehearsed ; and the workmen executed
their orders with a silent and unerring obedience worthy of
the calm and provident self-possession in which they were
given.

It has been found that a good criterion of the time for
pouring the alloy into the mould is afforded by stirring it with
a pole of dry wood. This, as long as the temperature is above
a certain point, reduces the film of oxide which covers its
surface; and it becomes clean and bright, though a new film
forms immediately. At length as it cools this reduction no
longer occurs; and at a signal the three crucibles are emptied
into the mould by means of levers connected with the pivots
of their cradles. Though familiar with heavy castings, Dr.
Robinson had never seen any thing so magnificent as the
burning lake that was then produced ; and for many minutes
it rolled in heavy waves like those of quicksilver, which broke
in a surf of fire on the sides of the mould, effecting the most
perfect mixture of the metal. At last it became solid, and
was examined as it cooled, till it barely yielded to pressure
with an iron rod at its centre, which is the indication that it
may be removed to the annealing furnace.

This furnace extends along the fourth side of the mould :
it is a low square chamber lined with firebrick, with sides
about thirty inches thick, strongly hooped, and covered by
an arch, from the centre of which rises a flue. Its floor is
convex, of the same curvature as the speculum, and is heated
from beneath by nine arches, which communicate with lateral
flues. It opens towards the mould by a low arch a little wider
than the speculum ; but behind has merely an aperture to ad-
mit an iron bar. For some weeks the chamber and arches had
been kept full of burning turf, so that the whole interior was
of a full red heat. The speculum, also red hot (at which
temperature, it is to be remarked, the alloy has nothing of that
brittleness which characterizes it when cold, but is as tough
as malleable iron), was cleared from the sand, and encircled by

118

a strong ring attached to the bar above mentioned. By con-
necting this bar with a powerful capstan, it was drawn from
the bed of hoops, along strong beams covered with iron, to its
place in the centre of the annealing furnace. The ring was
then removed, and the rest of the chamber filled up with char-
coal ; the arches with fuel; all the flues and apertures were
closed carefully with masonry, and it was left to cool gradually
for sixteen weeks, during the first three of whieh the exterior
of the building was sensibly warm.

In the course of this year considerable progress was made
with various parts of the mounting ; and when Dr. Robinson
visited it in February, 1843, he found that the speculum had
been ground (on a machine similar to the old one, but of
strength proportioned toits work); that the foundations of the
piers were laid, the tube was in preparation, and the massive
frame-work and levers by which the speculum is supported in
the tube, were cast. This elegant contrivance requires some
explanation. Suppose the back of the mirror divided by two
concentric circles into three portions, of which the central
circle is cut by radial lines into six sectors, the middle zone
into nine segments, and the exterior into twelve, and that all
of these are equal. If each of these be supported by an equal
force applied at its centre of gravity, the speculum is obviously
in the most favourable condition as to flexure. The frame
mentioned above is rectangular with a cross-piece cast in one,
and weighs one ton and a half: it bears three strong triangles,
also of cast iron, supported at their centres of gravity on
hemispherical bearings. Each angle of each of these bears a
similar triangle, the angles of which give the twenty-seven
points of equilibrated bearing for the speculum. They do
not, however, press directly, but carry platforms of cast iron of
the shape of the areas which they are to bear, and made exceed-
ingly stiff by flanches at their edges, and by edge-bars crossing
them diagonally. A layer of felt is over these ; strong up-
rights from the frame ofa similar character prevent any lateral

119

shifting ; and the operation of the arrangement’ is found to be
perfect at all altitudes.

The construction of the tubes, the piers, the mechanism
of the counterpoises, occupied the remainder of this year and
the beginning of 1844. In August, a partial polish was given
to the mirror in order to verify its focal length (which was
found exactly fifty-four feet) ; and the observing galleries and
the apparatus for controlling the instrument in right ascension
were proceeded with. All these gigantic constructions (of |
whose prodigious mass some idea may be formed from the fact
that they contain, along with their other materials, more than
one hundred and fifty tons of iron castings), have been exe-
cuted in Lord Rosse’s workshops, by persons taken from the
surrounding peasantry, who, under his teaching and training,
have become accomplished workmen, combining with high
skill and intelligence the yet more important requisites of
steady habits and good conduct. It may also be mentioned
that (such was the clear and definite arrangement of the whole
in its inventor’s mind) nothing failed from first to last ; and it
was not necessary for him in any instance to retrace his steps.

At the beginning of February, 1845, the work being suffi-
ciently advanced to permit the use of the instrument without
personal danger, Dr. R. and his friend Sir James South were
invited to enjoy the trial of it. Its appearance is certainly
peculiar, and presents a striking contrast to the more compli-
eated framing of the three-feet telescope which is placed beside
it. At first sight, one wonders how it is to be moved, for
nothing attracts notice except the massive piers and the tube;
but a nearer approach shews that it is the perfection of mecha-
nical engineering. To have mounted it on the plan of the
three-feet would have been impracticable as well as useless.

The speculum with its supports is seven times the weight of
that in Herschel’s four-feet, and both on this account, and the
well-known principle that similar machines are weaker in pro-
portion to their bulk, such a stand must have been so heavy

120

as to present great obstacles to its motion. The vast surface
exposed to the action of wind must have made it unsteady ;
and its durability could not be great. Lord Rosse, therefore,
determined to confine the range of observation to the vicinity
of the meridian. There the stars are at their greatest altitudes,
and atmospheric influences affect them least ; their places can
be determined with most accuracy, and an equatorial move-
ment, so essential to micrometer measures, can be easily
obtained. With such optical power there will never be a
scarcity of objects for examination; and the restriction will
only be felt in the case of planetary bodies. The base of the
actual mounting is a very massive joint of cast iron; its lower
axis permitting motion in the meridian plane, its upper ina di-
rection perpendicular to that circle. On this is firmly bolted a
cubical wooden chamber, about eight feet wide, in which the
speculum is placed, one of its sides opening for the purpose. This
again carries the tube, which when vertical and viewed from the
interior of the chamber, is more like one of the old round towers
than any more ordinary object of comparison. It is fifty feet
long, eight feet in diameter in the middle, but tapering to seven
at the extremities: it is made of deal staves an inch thick,
hooped with strong iron clamp-rings, and secured from collapse
by iron diaphragms ; and carrying at its upper extremity the
apparatus of the Newtonian small mirror, which, from its great
weight and bulk requires to be counterpoised, The telescope
is moved in declination by a strong chain cable attached to its
top and passing over a pulley fixed at a proper height to the
north, down toa windlass on the ground which is wrought by
two workmen. East and west, near the top of the piers, large
iron pulleys are fixed, having free movement in azimuth, so
that their planes may always be in those of the traction: chains
suspending the counterpoise weights pass over these to the
sides of the tube. The weights, however, are constrained to
descend in quadrants of circles*by chain guys attached to the
frame which bears the declination pulley. It is easily seen

121

that their action is a maximum when the tube is level, and
nothing when it is vertical; but between these positions it
decreases more slowly than the downward tendency of the
tube. To correct this, the tube is connected with loaded
levers (placed to its south), by chains of such lengths that
one of them is not raised till it is at 40° altitude, and the other
at 80°; the latter being necessary for the return of it after it
has passed the zenith. The slow motion in declination was
not yet applied, but the ordinary one was quite convenient,
except for the difficulty of giving orders to the men, who were
sometimes seventy or eighty yards from the observer. A two-
feet circle, with a fine level and a pair of verniers, will also be
attached to the tube to give the declination ; its place was then
supplied by asmall protractor, five inches diameter, over which
was a strong screen to protect the assistant who attended it
from any such casualty as the fall of an eye-piece.

The eastern pier bears what may be called the meridian of
the instrument: it is a strong semicircle of cast iron, about
eighty-five feet diameter, and composed of several pieces accu-
rately planed. Each of these is bolted to the pier and sepa-
rately adjustable to a meridian line formed by straining a fine
wire over notches in two cast iron chairs firmly secured at the
north and south of the masonry. Sir James South took charge
of this delicate operation, and performed it with such precision
that when a transit instrument was adjusted by this line, it
gave the passage of Polaris to a small fraction of a second.
The telescope is compelled to move in the meridian, being
connected with this circle by a strong bar provided with fric-
tion rollers, that it may traverse it easily; and thus it can be
used as a transit instrument with considerable precision. But
this bar is racked, and attached to the tube by wheelwork, so
that a handle near the eye-piece enables the observer to move
it on either side of the meridian, and thus examine it before its
passage, or follow its motion. The movementis surprisingly
easy ; and a rough graduation on the bar supplies at present

122

the place of an hour circle for finding objects, for which it is
quite sufficient, except that the strong light required to set it
disturbs the repose of the eye. The elder Herschel has not
in the least exaggerated the importance of this when faint ob-
jects, especially nebule, are to be examined; and a better
contrivance is to be applied. The rack being perpendicular
to the meridian, gives a motion not strictly equatorial, but
easily made so: had the declination pulley been in a parallel
to the earth’s axis, passing through the great joint, and had
this latter been itself equatorial, this would have been the case ;
but the deviation is easily corrected by the addition of asecond
pulley altering the direction of the chain. Its range is half
an hour on each side of the meridian fora star at the equator ;
and Lord Rosse intends to effect it by clock-work, as is now
generally the case in large equatorials; though the problem is
much more difficult than in those instruments.

The western pier supports the stairs and galleries destined
to the observers. Up to 42° of altitude is commanded by the
first of them: a strong and light prismatic framing slides be-
tween two ladders attached to the southern faces of the piers:
it is counterpoised and is raised to any required position by a
windlass; its upper plane affords support for a railway on
which the observing gallery moves about twenty-four feet east
and west, two of its wheels being turned by a winch near the
observer. Three other galleries in succession reach to 5° below
the pole; these are each carried by two beams which run be-
tween pairs of grooved wheels, and are drawn forward, when they
are turned, by a mechanism of singular elegance. These are able
to hold twelve people, but one man can easily work them; and
though itis rather startling to a person who finds himself sus-
pended over a chasm sixty feet deep, without more than a specu-
lative acquaintance with the properties of trussed beams, all is
perfectly safe. Every bearing part has been proved to ten times
its utmost probable load, and the doors of the galleries open
inward, and are kept close by springs. From this point too is

123

obtained the most distinct perception of the telescope’s prodi-
gious bulk, which at a greater distance is not so striking, for
want of a standard of comparison; yet, notwithstanding the
hugeness of the masses to be moved, so effective are all the
arrangements that Sir James South found it was possible to
uncover the mirrors and find a given star in less than eight
minutes.

Unfortunately the whole month of February was of the
worst astronomical character ; and though the great speculum
had only the imperfect polish already noted, it was kept in the
tube as long as there were any hopes of seeing the great
nebula of Orion. That, however, was always clouded while
within its range. A few clear minutes on the 13th allowed
them to see some stars and clusters; but the only circum-
stances worth mentioning were, that it shewed the stars of
Castor far apart without an eye-glass,* and that the stars of
the cluster 67 Messier, which Sir J. Herschel describes as
being from the eleventh to the twelfth magnitude, were many
of them as bright as those of the first appear in a three and
a-half feet achromatic.

At length, when all hopes of Orion were lost in the twi-
light, the mirror was removed from the telescope, and polished
on March 3rd. Its frame is supported in the cubic chamber
of the tube by three strong screws which give the adjustment
of its optic axis. By unscrewing these, when the tube is ver-
tical, four wheels with which the frame is furnished come to
bear on a railroad fixed at the bottom of the chamber and
communicating over a bridge (laid from its door when neces-
sary) with another railway laid on an inclined plane of about
sixty feet. Itis drawn up this by the declination windlass,
and at its top runs on a strong truck by means of which it is
drawn a quarter of amile, on a common road, to the laboratory. ,

The polishing machine differs in nothing but size from that

* Only twenty-two inches of the mirror could act in this case.

124

described by Lord Rosse in the Philosophical Transactions.
It makes the speculum revolve once for twenty-four and a-half
strokes, and theeccentric once for eighteen. Fromseven toeight
strokes of twenty-four inches are made in the minute, and the
lateral movement of the speculum by the eccentric is fourteen
inches.* A screw whose nut runs on a railroad above the
machine lifts the speculum, with its frame and levers, from the
truck, and deposits it on the revolving platform, where it is
levelled, centred, and secured. The same apparatus serves
to move the polisher during its preparation and to apply it to
the speculum, so that it is even more manageable than that of
the three-feet was. It was cast with the transverse grooves;
the circular were cut in the lathe. The time required for
polishing is about six hours; and Lord Rosse has found that
this period cannot be exceeded without injury to the figure, in
consequence of the soft pitch being squeezed out, and the
harder and unyielding material coming into contact with the
iron of the polisher: unfortunately, this occurred to some extent
in the present instance. The ammoniacal solution of soap used
towards the close of the process, happened to be made with
ammonia prepared from gas liquor and containing some sub-

* These are the proportions which Lord Rosse prefers; but it must be
kept in mind that they change with circumstances. Probably they will not
answer for those specula which have an aperture larger than one-ninth of
their focal length, and certainly not for those which are perforated in the
middle. Dr. Robinson has made many experiments on one of the latter, fifteen
inches aperture and nine feet focus, with a machine nearly the same as Lord
Rosse’s; and he finds that the nature of the polishing depends on the figure
given in grinding. If the eccentric be regulated so as to make this hyper-
bolic, its action must be lessened in polishing so as to shorten the focus. In
this way it is possible to obtain very good results. He, however, prefers the
opposite course pointed out by Lord Rosse; grinding to an elliptic figure,
he polishes with a very long primary stroke, and small action of the eccen-
tric. A speculum thus polished shews « Arietis well separated and defined
with 940, and with 465 the fifth star in the trapezium of Orion’s nebula is
visible even when the acting surface is reduced to seventy-two circular
inches.

125

stance which acted on the mirror and produced a dulness that
was not removed till after three hours’ additional work. Lord
Rosse warned them that the figure must be imperfect, and
wished to repolish; but they overruled this proposal, and it
was replaced in the tube next day.

On examining it by diaphragm and discs, it was found
that, as he anticipated, the edge was not quite perfect. All
its zones showed & Urse Majoris very well with 560; but the
exterior six inches manifested, when the star was thrown out
of focus, that though of the same focal length, this portion was
irregular. Few other double stars were observed, as most of
the lucid interval from the 4th to the 13th of March was de-
voted to nebula, and after that it again became cloudy; but
enough were seen to satisfy them that the instrument possessed
a very high defining power. This, indeed, was evident from
the admirable exhibition of Regulus,seen on March 5th, neat
and round, without appendages or flare. Gamma Leonis, &
Virginis, 2 Come, and Gamma Virginis, were also well
shewn with powers of 400 to 800 on an unfavourable night ;
and the companions of vy Urse, and 245 of Struvé’s second
Catalogue, which appear in the Slough and Pulkova teles-
copes as of the eleventh and tenth magnitudes, seem in this
large stars.

Of planetary bodies, none were visible except D’Arrest’s
Comet and the Moon. The former, when viewed March
10th, presented nothing remarkable: the brighter portion, to-
wards the centre, shewed no abrupt change of light which
might indicate a solid nucleus; there was no resolvable ap-
pearance in the Coma, and the very minute stars with which
that part of the sky was dotted, were visible almost to its very
centre. Only one view of the moon was obtained, March 20th,
and it was shared with them by several visitors, who, when

once in possession of the telescope, were by no means disposed
to make way for the astronomers. The fascination of the
sight is, indeed, such, that one can scarcely withdraw the eye:

126

Dr. Robinson, therefore, and his friend, had but little time
for observation. He was, however, much interested by the
Vicinity of the craters named Hansteen and Mairan, in the
map of Beer and Meedler, where, besides the crowd of hills
described by them, these are an infinity of others not visible
even in the three-feet, but looking in this with 560 like grains
of sand. Are these fragments ejected from the crater? If
so, and if they occur round others, it would explain what had
always presented to him a great difficulty. The lunar craters
differ widely from those of earth; and most in this, that their
depression below the general surface is enormously greater
than the elevation of their walls above it, while the area of
the hollow is far greater than that of the latter. What, then,
became of the materials which had once filled it? He had
formerly supposed that they were in a fluid or gaseous state
when ejected; but the fact just mentioned seems to give the
true solution, and appears to account for them when combined
with the consideration of the feeble gravity on the moon, which
would permit the exploded fragments to be scattered over a
far larger space than with us. Another beautiful object was
the river-like valley that runs northward from the crater He-
rodotus: its raised banks, and their irregularities, were easily
seen; the internal and external shadows could have been satis-
factorily measured had a micrometer been applied. As it was,
the much greater breadth of the former showed at a glance
that this strange channel was sunk deep below the lunar sur-
face. ‘Taking-as a standard the measures given there by Beer
and Meedler, he had no doubt that they then saw without
difficulty spaces of eighty or ninety yards. It is difficult to
say @ priori what should be the minimum visible at the moon
in such a telescope. If we assume, as one extreme, the state-
ment of Amici, that the non-coincidence of two black lines on
paper can be seen at twenty-eight feet, when it amounts to
one-twelfth of an inch, or subtends 51”, then 311 feet should
be visible at the moon with 1000. On the other hand, Jurin

127

states (Smith’s Optics) that a piece of silver wire can be
seen on white paper, when it subtends 3”, a result depending
on the intensity of this metallic reflection. This would give
eighteen feet! Dr. Robinson finds that he can see the
spider lines of his circle without much contrast of light, when
they subtend to him 16”. This gives ninety-seven feet ;
but it must be remembered that aperture influences visibility
as well as magnifying power, though we cannot as yet estimate
its effect numerically.

The most important part of their observations were made
on nebule ; and, besides establishing completely the prodi-
gious superiority of this instrument over all yet constructed,
they have added some facts to our knowledge of these myste-
rious objects. A list of them was formed from the invaluable
catalogue of Sir John Herschel (Phil. Trans. 1833), compris-
ing such as, from brightness or any other peculiarity, seemed
deserving of notice ; of which forty were examined by Dr. Ro-
binson and also by Sir James South, except some which the
latter lost while making the transit observations required for
the meridian line.* They may be separated into three classes ;
those which are round and of nearly uniform brightness ;+
those which are round, but appear to have one or more nu-
clei ;{ and those which are extended in one direction, some-
times so much as to become long stripes or rays.§ Of the
first class, all that were examined are easily resolved, even
with a triple eye-piece of wide field and power 360, used for
finding the objects. In 854 the stars were seen through haze ;
in 1929 during twilight; and 1833 was noted as “ consisting

* Sir James South published an interesting and instructive notice of this
telescope in the Times, April 16, 1845.

+ Nos. 538, 739, 777, 844, 845, 854, 1797, 1833, 1907, 1929.

£ Nos.564, 706, 711, 743, 748, 749, 805, 843, 846, 1146, 1385, 1456, 1622,
1881.

§ Nos. 536, 604, 668, 791, 792, 810, 859, 1066, 1132, 1148, 1352, 1357,
1368, 1466, 1926. The numbers and the figures cited in the text are those
of Sir John Herschel’s catalogue.

128

of rather coarse stars, and resembling Messier 13.” Any in-
crease of brightness towards the centre seemed to proceed
from the greater depth of stars there rather than from any
notable difference of their magnitude. But the second class
presents much more interesting phenomena: the appearances
which previous observers had described as sudden condensa-
tion, nuclei, or even single or multiple central stars, proving
to be clusters of comparatively bright stars, surrounded by
much larger collections of minute ones. A very beautiful
example of this is 1456, fig. 41, M. 94, described in the cata-
logue as ‘‘very suddenly much brighter, almost up to a

2

nipple-shaped nucleus:” it proved, however, to be ‘‘a vast
circular cluster of stars, with ragged filaments, in which, and
apparently central, is a globular group of much larger stars,
power 400.” The same system of arrangement (which seems
very common) occurs also in 706, 748, 805, and many others:
it is also found in the magnificent clusters 1663, M. 3; 1558,
M. 53; and 1916, M.5. In these, the splendour of which
is not to be described, besides the stars visible in other instru-
ments (which here seem of the first or second magnitude), the
whole field is crowded with others much smaller, to such a de-
gree that, had the first been absent, these would still have been
noted as remarkable objects. The interior group is not, how-
ever, always central or symmetrical, but has knots of greater
condensation, which sometimes (as in 1385) are"alone visible
in smaller telescopes, and then look like ‘twin nebule ;”
at others (as in 739), like stars. In 1622, fig. 25, M.51,
which is so well known from a sort of resemblance to Saturn,
and from the more exact analogy which, as Sir John Herschel
has well remarked, it bears to the Milky Way, we have ano-
ther different development of this arrangement. Here also
the central nebula isa globe of large stars; as indeed had
been previously discovered with the three feet telescope: but
it is also seen with 560 that the exterior stars, instead of being
uniformly distributed as in the preceding instances, are con-

129

densed into a ring,
terior. Were the centre absent, we should have a ring ne-
bula ;* and were the line of vision near the plane of this ring
it would become one of those rays with a bright nucleus and

parallel band or satellite nebulz which occur so frequently in

although many are also spread over its in-

the catalogue. In comparing it with our own sidereal system,
Dr. R. thinks we should consider the stars visible to the naked
eye, and the larger telescopic classes as constituting the cen-
tral cluster, while the Milky Way represents the exterior and
minuter stars either disposed in an irregular ring or in a stra-
tum, two of whose dimensions are much greater than the
third. We have no reason for believing that the comparative
brightness of stars depends only on their distances ; 61 Cygni
is not more remote than a Lyre; much less can we assume
that our stars are uniformly distributed: Orion, the Pleiades,
Proesepe, the clusters in Perseus, M. 36 and 37, with many
others, are evidently mere knots of condensation in our imme-
diate neighbourhood, our peculiar cluster; and it seems a
mere arbitrary assumption to fancy that, were we transported
to a remote part of the Milky Way, we should see any thing
similar to our present sky.

The nebulz of the third class which were examined seemed
to differ from this type only by being seen obliquely, and
therefore projected into ellipses sometimes almost linear. In
this last case they proved much more difficult of resolution,
probably from greater optical condensation, and yielded most
easily towards their minor axes. In these the nucleus of
brighter stars is sometimes extended like the exterior portion,
as in 602, which is of considerable length and easily resolved :
the central part has three knots, of which two are represented
in fig. 70, all the rest having been invisible. 668 is similar,

* It is possible that the exterior part of M94, may be merely a circular
disc of stars: the absence of the central giobe would make this a planetary
nebula: but it is possible that these differ from the annular only in degree;
all the latter which he has seen haying faint nebulosity within them,

VOL, Ill. L

130

but the central part is of more uniform character. In general,
however, the nucleus is globular, and remarkable from the
comparative smallness of its diameter, and its very condensed
appearance. Lither the stars which compose it are few in
number, or more closely compacted than is usual. 1132,
M. 98, is a good example: “ the long ray is resolved, except
at the very extremities, with 560 ; the globular nucleus-is seen
with 1280 to consist of very close stars.” 1148, described as
*¢a nucleus with two branches, a star north following,” ap-
peared to Dr. R. as “an irregular ring of stars round a
brighter group, but having an appendage like that of M. 51,
in which is the bright star seen by H.” 1357, fig. 37, isa
similar object, both ‘‘ the ray and appendage being full of
stars, but the nucleus requires a higher power to resolve it
than the night will bear.” In 1466, fig. 84, the nucleus pro-
jects on each side of the ray, so that its diameter must be
greater than the thickness of the exterior stratum.

He could not leave this part of his subject without calling
attention to the fact that no REAL nebula seemed to exist
among so many of these objects chosen without any bias: all
appeared to be clusters of stars, and every additional one which
shall be resolved will be an additional argument against the
existence of any such. ‘There must always be a very great
number of clusters, which from mere distance will be irresol-
vable in any instrument; and if it prove to be the case that all
the brighter nebulz yield to this telescope, it appears unphi-
losophical not to make universal Sir J. Herschel’s proposi-
tion, that ‘“‘a nebula, at least in the generality of cases, is
nothing more than a cluster of discrete stars.”

These observations will suffice to show how much may be
hoped from this telescope; but they are far from being a fair
measure of its powers, being made at very low temperatures.
Almost always the thermometer was at 22° or 20° when they
ceased working; and on one occasion it was as low as 17°
the lowest he remembered in Ireland. In such circumstances

131

it is notorious that even small reflectors act very imperfectly :
and he was therefore unprepared for any tolerable action of
this gigantic speculum. In the day time it was of course
colder than the air, and, if uncovered before that had sunk to
its temperature, was covered with dew: when this went off it
always defined sharply. The huge mass of metal cooled much
more slowly than the atmosphere; and as the difference in-
creased, the performance of the telescope was deteriorated.
This arose from no change of figure, as he satisfied himself
by throwing the stars out of focus ; it was probably the result
of currents in the tube occasioned by this difference of tempe-
rature. How far it will be possible to obviate this by mecha-
nical means, remains to be tried ; but it is certain that the in-
convenience does not increase in a higher ratio than the power
of the telescope, as he had formerly apprehended. On the
same nights, it defined quite as well as the three-feet with a
far lower power ; and therefore, it is reasonable to expect that
it can be used with advantage much more frequently than he
once supposed.

Enormous as is its illuminating power, it might be in-
ereased one-third, by using it with the front view, supposing
it can be properly figured for this oblique action. Without
that, he fears that in an instrument where the aperture is so
large compared with the focal length, the definition would be
imperfect. He verified this by an experiment with the
three feet, and found that though the light was increased
quite as much as he expected, yet the perfection of the image
was utterly destroyed for large stars. There was no exact
focus, but merely two places where the sections of the cone
of rays were smallest. One, the least exceptionable, shewed
a flare in the direction of the slope like a comet’s tail: at the
other this disappeared, but the star became a sort of curved
rectangle with rays from its corners. In the Newtonian
form this speculum a few nights before had defined Z Orionis
very well with 500; but now y Leonis could not be seen

132

double with any power; the companion of Rigel (some way
from the meridian however) was lost in the flare, and even
that of Polaris, though perfectly visible, was sadly disfigured
by it. It was of course useless to try more difficult tests, as
even this degree of imperfection would make it utterly incapa-
ble of resolving such objects as the nuclei of the long nebule,
be its illuminating power what it may. One thing, however,
deserves notice, that in consequence of removing the second
reflection, the colours of the stars come out with extraordinary
splendour.* (3 Cygni, for instance, had a pureness and bril-
liancy of yellow, in the large star, which was new to him,
though he had seen it in many first-rate telescopes. Lord
Rosse does not apprehend any insurmountable difficulty in
applying his method to give the form necessary for aplanatic
oblique reflection: more than one plan for this has occurred
to him; and Dr. R. believes it is his purpose, as soon as the
six-feet has its machinery completed, to try them on one of
the three-feet specula, and, if successful, to alter the great
one.

As it is, Dr. R. congratulates the “Academy and their
country on the success of this matchless instrument; to which,
as nothing at all approaching to its power has yet existed, so
it is not probable that there will soon beany superior. It has
been reported that the French Government, at the suggestion
of M. Arago, are about to construct an achromatic of a metre
aperture. Supposing homogeneous discs of glass can be obtained
and wrought of that magnitude, there remain other difficulties.
The optician who proposed to supply them stated that they
would weigh at least four hundred pounds; now these, when
mounted, must be supported by at most two lateral bearings ;
and it is known that a very moderate pressure produces in

* The lenses of achromatics have often a tinge of green or straw colour
which modify the colour of objects seen through them. Something of this
may perhaps cause the predominance of green and ‘‘cinereus” which exists
in the Dorpat catalogue.

133

glass a double refraction, most injurious to its performance in
an object glass. But supposing this and the equally probable
change of curvature from the weight of the lenses obviated,
still such an achromatic would be far below the six-feet in
quantity of light. From Amici’s experiment with an object
glass of two anda half inches it follows that it equals a New-
tonian when their acting surfaces are as six toten: this would
imply in the great one an aperture of fifty-six inches and a
focal length of eighty feet. But the absorption certainly in-
creases with the thickness of the medium, though neither the
law of this, nor the loss by the reflections at the four surfaces,
are accurately known. Mr. Potter found that a good object
glass by Dollond of four inches aperture and six feet focus
transmitted but 0.66 of the incident rays. This gives the ratio
of the equivalent surfaces 0.74, and it will be still greater where
the glass is three or four inches thick. It is said that the con-
struction of a reflector still larger than this is contemplated
by a northern Sovereign who has already shewn himself a
most munificent patron of Astronomy. If so, none will rejoice
more than Lord Rosse himself. It was not the mean desire
of possessing what no other possessed, or seeing what no other
had seen, that induced him to bestow so many precious years
on this pursuit: had such been his motives, he would have
kept to himself his methods, instead of opening his workshops
without reserve to all who had the slightest desire of following
his steps, and communicating in the most liberal manner the
fruits of long and painful experience. His sole object is to
_ extend the domain of astronomical knowledge: and the more
common such instruments become, the more perfectly wili it

be fulfilled.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1845. No. 51.

November 10, 1845.
GEORGE PETRIE, Esq., Vice-President, in the Chair.

Mr. Ball made a communication, the object of which was
to shew that the article called a crotal, of which there are three
_ Specimens in the Academy’s Museum, had properly but one
dise, and not two, as represented in Ledwich’s Antiquities
_ (plate xxiv. fig. 6), and Camden’s Britannia (Gough’s Ed.
vol. iii. plate xxxiv. fig. 1). He founded his arguments upon
the fact, that the three specimens in the Academy’s Museum
(Nos. 2, 3, 4, of the annexed cut) were each evidently per-
fect, while that figured by Ledwich and Camden, which still
exists in the University Museum, is a compound of two spe-
cimens, most rudely and recently rivetted together with a com-
mon copper rivet. (See No. 1, annexed cut).

Mr. Petrie stated, that of the six specimens said to have
been found at Slane, he had seen three which were certainly
double, though he would not undertake to say that they had
not been compounded, as that in the University Museum
quite evidently is. A gentleman who had been recently in
Persia, on seeing the specimens in the Academy Museum,
stated, that in that country, at the present day, they were
used in the manner of castanets for keeping time, and that

VOL. III, N

136 _

they were not provided with double discs. The manner in
which boys here hold and beat time with long bits of slate,
may be a specimen of the practice of using crotals.

St aE a
a f ij ~S
Se
ie ‘x
f \
/ \
{ \
\ i
\ i
\
N
Ni
~ :
SSS ie “
i a
hf) i OERE
\ If \
\ i er
RC 2

= 4G)

—

The Secretary of the Academy read a notice of an Ogham
Stone found by Mr. Nevins in the County of Wexford. A
rubbing of the inscription was also exhibited; but it was so
imperfect, from defects in the stone, that its publication in a
wood-cut would answer no end.

137

DONATIONS.

Statistical Return of the Dublin Metropolitan Police,
Jor 1844. Presented by the Commissioners.

Comptes Rendus hebdomadaires des Seances de l’ Academie
des Sciences. No.3. (21 Juillet, 1845.) Presented by the
Academy.

Memorie di Matematica e di Fisica della Societa Italiana
della Scienza residente in Modena. Tome XXIII. (Parte
Fisica). Presented by the Society.

A Sermon, preached in the Chapel of Trinity College,
Dublin, on 25th May, 1845. By the Rev. Charles W.
Wall, D.D. Presented by the Author.

Memoirs of Francis Baily, Esq., F.R.S., §c. &c. By
Sir John F. W. Herschell, Bart., &c. Presented by the
Author.

Poems in Irish and English (MSS.) By Carolan. Pre-
sented by Robert Ball, Esq.

The Coinage of Scotland. By John Lindsay, Esq. Pre-
sented by the Author.

The Eneis (Books I. and II.) rendered into English blank
Lambic, with Notes, §c. §c. By James Henry, M.D. Pre-
sented by the Author.

Journal of the Franklin Institute. Vols. VII. and VIII.
Third Series. 1844. Presented by the Institute.

Three Reports, upon improved Methods of constructing and
working Atmospheric Railways. By Robert Mallet, Esq.
Presented by the Author.

Resultats des Observations Magnetiques faites a Geneve
dans les Annés 1842 et 1843. By Mons. E. Planta. Pre-
sented by the Author.

_ Proceedings of the Geological Society of London, for
Session 1843-44. Presented by the Society.
N 2

138

Archives du Museum d Histoire Naturelle. ‘Tome lme
et 2me Livraison. Presented by the Governors.

Archeologia Cambrensis. No. I. Presented by the
Editor.

A Gold Fibula. _ Presented by the Marquis of Kildare.

An ancient Cannon Ball, made of Sandstone, found in an
Excavation made near the Castle of Dalkey. YPresented by
Frederick W. Porter, Esq.

A Heel-ball Rubbing from a brass Plate in the Cathedral
of Amiens. Also, a Rubbing from an Inscription on an Oak
Rood-screen in the old Church of Llanfair, near Kneighton.
Presented by Dr. Todd.

An ancient Wooden Tray, found at Hilltown, Co. West-
meath. By Arthur Webb, Esq.

November 29, 1845. (Stated Meeting.)

GEORGE PETRIE, Esgq., Vice-President, in the Chair.

William Wordsworth, Esq., was elected an Honorary
Member of the Academy.

It was resolved, on the recommendation of Council,

‘*That the sum of £50 be placed at the disposal of the
Committee of Antiquities, for the purchase of articles of
antiquarian interest for the Museum.”

The following letter, from Edward J. Cooper, Esq.,on the

Zodiacal Light, was read :
Markree Castle, 13th Nov. 1845.

**S1r,—The phenomenon of the Zodiacal Light being
but very rarely visible in these countries, I am induced to
trouble you with this communication, to inform you of its ap-
pearance here this month. At ten minutes past four o’ clock,
a.M., on the 4th instant, a strong light, convex in its upper
limits, was observed by me, and one of my assistants, at my
observatory, in the horizon east by south. It was very similar

oe

139

to that of low Aurore Boreales. We could not believe that
it was crepuscular, as it was too early, nor that it was of the
nature of what are commonly called the ‘*‘ Northern Lights.”
We watched it for a considerable time, during which it ap-
peared to vary in brilliancy. However, it branched out to
Regulus, and also towards Coma Berenicis, the edge of low
fog, towards the south, being also illuminated. It faded first
in the branch towards Coma Berenicis; and, lastly, under the
advancing twilight, in that towards Regulus. Gamma Virginis
was in the axis, near the horizon, and Kappa Crateris on
the azimuthal limits towards the south. From east, through
the north to west, stars were visible to the horizon, which
but very seldom is the case here. A considerable number of
shooting stars were streaming about this morning. Having
little doubt that the branch of elliptic ight which extended
towards Regulus was the zodiacal light, although I had ne-
ver before seen it in the morning (and, indeed, in Italy alone
in the evenings of the months of March and April), I re-
solved to look out again for it. The weather was unpropi-
tious until the morning of the 10th, when it was seen from
the observatory, at ten minutes before four o’clock, and for
some time afterwards, by my assistant, Mr. Magrath. I saw
it from my house at a few minutes before five o'clock, when
it shewed, with very tolerable definition, the elliptic outline
which I have so often remarked in Italy in the spring
evenings. There was no trace, on this occasion, of a branch
of light towards Coma Berenicis. In less than a quarter of
an hour it was almost entirely lost behind a rising fog,
which left a sharp white frost upon the ground. The re-
markable features of the phenomena we witnessed seem to
be these, viz., Ist, that on the morning of the 4th there
was a second branch of light, and also an illuminated edge
to the fog in horizon; neither of which were visible on the
morning of the 10th, nor have I ever previously observed
any thing similar to accompany the evening exhibitions of

140

zodiacal light. 2ndly, That there was on.that morning a
flux and reflux of the light. I cannot attempt to account for
the former; but I suspect that the latter appearance arose
from a rising and sinking of the imperceptible terrestrial
vapour.

‘“¢Kpwarp J. Cooper.

« To the Secretary of
“ The Royal Irish Academy, &c. §c.”

Mr. William Hogan read the following notice of the storm
of Sunday, 6th July, 1845:

«< was in Leamington at the time, and, though it did not
rage there, I had an opportunity of witnessing the atmos-
pheric phenomena, as the thunder-cloud passed at a small dis-
tance to the north, and I observed its course for an hour anda
half.

«¢ To shew what its aspect was to those over whom it passed,
I extract the following particulars of its history twenty miles
to the north of Leamington, from the published account of
Mr. Onion, of the Philosophie Institution at Birmingham.
After alluding to a violent storm of the preceding Thursday,
he says: ‘ Birmingham has again been visited by a thunder-
storm more terrible, and in its consequences more disastrous,
than the former. On Saturday afternoon the thermometer
varied at different times from 70° to 78°; not a breath of
air stirring, the barometer being moderately high. About
eight o’clock, Pp. M., a few heavy drops of rain fell, which were
shortly afterwards followed by a complete deluge of water; the
lightning was grand and awful in the highest degree, flash
succeeding flash in rapid succession, and of that beautiful
purple tint which betokens a large quantity of free electricity
in the atmosphere. The thunder in the mean time rolled in
nearly one continued peal; the wind, which had been varying
from S. E. to E., suddenly shifted to S., and about the middle

141

of the storm the vane veered suddenly and with great rapidity
through the whole points of the compass, again setting in the
south. For the space of three or four hours afterwards it con-
tinued very inconstant, changing in all directions, and even-
tually settling in the S.W. In the short space of half an
hour 1.945 inches of rain fell.’

‘* Such were the phenomena at Birmingham as the thunder-
cloud passed over it. Its arrival was preceded by oppressive
heat and a dead calm, while a fresh breeze blew at Leamington.
Its passage was marked by a whirlwind, with constant light-
ing, and the fall of nearly two inches of rain in half an hour.

« Particular circumstances led me to be an attentive observer
of the state of the atmosphere from seven to half-past eight on
the evening of the 6th of July. Isaw the thunder-cloud appear
in the south-west, and pass over Birmingham in its course to-
wards the north-east ; it was of great extent, and I should think
very high; a rapid current of air in the same direction carried a
light seud under the cloud, or at least between me and it, so as
toappear under it. The heat was intense thewhole evening,
but previous to and during the storm we had a constant fresh
breeze from the south-east; thecloud came from south-west. The
lightning was very brilliant and constant, but I heard very
little thunder, perhaps owing to the state of the wind. In shape
and appearance the cloud might be represented by the map of
Africa, from the Bight of Benin southwards, laid on its side,
with the eastern coast and the island of Madagascar upper-
most. A cloud of the relative size and position of this island
kept constantly and steadily in advance of the larger one, and
all the lightning which I saw until the cloud passed was from
the upper surface, and generally played round the cloud repre-
sented by Madagascar, though it sometimes darted out from
the latter in every direction. It was forked lightning, but its
appearance was not that of bars of light, but such as one
would observe were the electric current sent along a zig-zag
chain in a darkened room.

142

‘« As the cloud passed on to the north-east, and I looked after
it, the end next me had the appearance ofa vast crater, emitting
forked lightning and flashes of light; and it was from this
crater-like opening that I suppose the lightning was emitted
which was visible at Birmingham, after the storm had ceased
and the cloud passed on towards Nottingham.

« All accounts say that meteors and lightning were observed
at the rear of the cloud for an hour or two after the tempest.
When the cloud had nearly passed over Birmingham, the
quantity of ozone which saturated the air at Leamington was
so great as to be very unpleasant, and I was obliged to close
the window to exclude it. It is to be observed that no rain
fell in Leamington at that time, and consequently there was
no moisture to absorb the ozone and prevent its accumulation.
The lightning always broke from the upper surface of the
cloud while it passed before me; when I looked after it, it
came from the inside of the crater-like opening in the rear, but
never from the surface next the earth. The unpleasant effects
of the storm on the invalids of my party soon afterwards occu-
pied all my attention.

‘* This immense cloud, so heavily charged with water, ap-
peared to be completely isolated; it did not attract the flying
scud, nor did it break into masses; and the sky became serene
and blue when it had passed. I observed its approach from the
south-west; at eight it had reached Birmingham, and at nine
it had passed. I traced it in the local newspapers in a straight
line from Hereford to Nottingham, where it caused prodigious
floods, passing over Kidderminster, Dudley, and Birming-
ham, in a direction from south-west to north-east. All the
newspapers agreed in their general description of brilliant, con-
stant lightning, and heavy rain; some also spoke of hail.

‘* About twenty miles to the south-west of Birmingham the
storm began at seven P.M., and ceased about eight P.m.;
at that time it had reached Birmingham, where it raged
shont an hour. I therefore conclude that the cloud was

143

twenty miles long, and that it passed over its own length in
an hour; or, in other words, that it only moved at the rate of
twenty miles an hour, carrying the whirlwind along with it ;
for that the whirlwind was caused by the cloud, and had no
connexion with the tranquil current of air which bore it, was
evident.

‘«¢ Where this immense cloud was formed, and charged with
materials for such prodigious torrents of rain, and by what
means that immense weight was supported, are problems for
the meteorologist. Supposing that the rain fell as heavily
in other places as in Birmingham—and every account makes
the supposition probable—every square superficial foot of the
under surface of the cloud must have given out two inches of
water per hour; and calculating six gallons to the cubic foot,
every superficial square foot must have deposited one gallon
per hour during its course; and if that course only lasted six
hours, each superficial foot must have given out 50lbs. of
water in that time.

“ Whether the cloud actually carried this weight of 50]b. on
each square foot, and if it did, what was the sustaining power

which enabled it to do so, would not be easily told; but another

question suggests itself, was all, or the greater part of the
water deposited during its course, generated from time to time in
the cloud? One thing seems clear, constant lightning accom-
panied the release of the water from its aerial carriage, and a
whirlwind seems to have been necessary to supply the con-
sumption of atmospheric air.

“The great accumulation of heat for two or three days
before such violent thunder-storms, seems to indicate that
they are preceded by a cessation of some ordinary heat-absorb-
ing atmospheric processes over the places where the storm
afterwards passes. In the case of this storm Mr. Onion says,
that the barometer had been in a very unsettled state for some
days previously, often in the course of twenty-four hours rising
or falling to a considerable amount, although not followed by

144

a corresponding change in the weather. Perhaps the pheno-
mena of a thunder-storm are due as much to the state of the
atmosphere in each locality, as to the ominous black cloud
which passes over it at the time of their appearance.

‘“‘ A few days after the storm of the 6th of J uly, I had an
opportunity of observing some of the effects of the whirlwind
which accompanied the cloud, and thus tracing a portion of its
course. It was at Hilhampton, adjoining Whitley Court, the
residence of her Majesty the Queen Dowager; which lies on
the direct line between Hereford and Birmingham—several
large, full-grown elms, standing in the middle of a field, were
torn up by the roots; other trees were stripped of their branches
at one side only, while the stem and remaining branches had
not been touched; a low brick wall, not a foot high, which
supported some paling, was torn up. It did not proceed in a
straight line, but in a zig-zag or curve, running in the direc-
tion of the course of the cloud; and what is a little remarkable,
the dwelling-house, which was not injured, lay in one of the
bends of the curve; a large fir tree in the front had all the
branches on one side twisted off, and a walnut tree imme-
diately behind the house suffered in the same way; neither
tree was ten feet from the house which was between them,
and it was in its course round the house that the low brick
wall was torn up; it then passed amongst some hay-cocks,
which it carried off and scattered.”

Colonel Harry D. Jones gave the following account of
recent excavations which he made in the Round Towers of
Clonmacnoise:

‘* As some time must necessarily have elapsed before the
vegetable material in the large tower could be removed to the
level of the lower floor, it was determined to employ another
party in sinking below the foundations of the smaller tower,
called ‘Teampull; the ground in the interior was level with
the sill of the door and with the ground outside.

145

** Upon sinking nine inches, vegetable mould only was
found, then sand mixed with small stones and mould, which
became more compact as the excavation proceeded. At the
depth of three feet nine inches the workmen discovered the
ribs of a skeleton; they were then directed to proceed very
carefully in their operation: it should be observed that the
pieces of bone taken up would scarcely bear to be handled,
falling into small fragments; upon clearing the earth away,
the skull of a human body was found in a perfect state, firmly
imbedded in the earth and gravel. Upon removing the earth
to bare the skeleton, a second was found, one foot above that
first discovered. Every endeavour was then made to lay bare
this second skeleton, which was to a great extent effected,
but no skull could be found; the legs were buried consi-
derably under the foundation-walls of the tower; the bones
found were very perfect until we attempted to raise them,
when they were found to be very brittle, falling to pieces with
the least pressure or strain. Having removed the upper skele-
ton, the intervening layer of earth was carefully raised, and
thus the second or lower skeleton, with the exception of the
ribs, which had been disturbed upon first finding it, upon being
laid bare, were found as perfect as the day the body was placed
in the grave; the bones of one leg were taken out uninjured,
which measured one foot two inches, but not so the skull,
which broke into several pieces upon the attempt to raise it from
the soil, which was very firmly attached to it; the formation of
the head appeared to be remarkable; the fragments have been
carefully preserved. Having removed the bones of the lower
skeleton, the excavation was then proceeded with, until the
natural ground was found, which was coarse limestone gravel,
mixed with boulder-stones of a middling size, rendering the
progress of the work very difficult, and evidently shewing
that it had never been disturbed. The lower of the two
skeletons was laid upon the surface of the limestone gravel,
apparently in a naked state, as there was not the slightest

146

appearance of wood or linen, or anything to indicate that the
body had been enveloped by a covering of any description.

‘‘From the position of the two bodies, it would appear
evident that they had been buried subsequent to the erection
of the tower, inasmuch as the lower, and most perfect of the
two, and the one on which any reasoning that may be made
should be applied, was placed with the head two feet from
the interior face of the tower, in consequence of the rubble-
work of the foundation projecting that distance within the
upright walls of the tower, and the feet were inserted under
the foundation on the opposite side. The direction of the
body was W. N. W. and E. S. E., the head at the west, and
which appears to be the general direction of the graves in the
adjoining yard.

‘‘ Upon commencing operations, it became necessary to
remove the great quantity of vegetable matter, which was
composed of pieces of wood, twigs, &c., evidently the debris
of bird’s nests, mixed with stones thrown in by idle persons.

«¢ Upon entering the large tower by the doorway, which is
eleven feet six inches above the upper footing-course of the
foundation, the interior was found to be filled with decayed
vegetable matter, bones of birds, sheep, pigs, &c., with a few
human bones, all intermixed to the height of five feet above
the level of the footing-course, or, as was subsequently ascer-
tained, above the level of the lower floor of the tower. The
first thing to be accomplished was the removal of such a large
mass of material; this was done by fixing staging of planks
across the interior, and hoisting it up and discharging it out-
side; this was a long and tedious operation; when accom-
plished, it was ascertained that the dressed stone was eleven feet
six inches below the sill of the doorway, corresponding with the
height measured outside. Upon sinking eight feet, the vege-
table mould, &c., was found lying upon a rubble stone paving
of about one foot six inches in thickness. The material next to
be removed was gravel and sand mixed, about nine inches; then

less ee

147

yellow clay, three inches; and lastly, four feet six inches gravel
mixed with boulder-stones of moderate size, and evidently, by
the seams of fine sand, shewing that the excavation was then

_ in the natural ground; and as one of the workmen observed,

when throwing it out, ‘that has not been moved since the
morning of the flood.’ The total depth sunk below the sill of
the doorway was eighteen feet seven inches, viz. :
1 ft. 7 in. from sill to under side of the projection of floor,
8 ,, 0 ,, to the level of bottom floor or commencement of
dressed ashlar work,
Begs! Gigs rubble masonry—foundation of floor and
loose stones with earth,
Sy gravelly sand,
yellow clay,

a a)
mw wo

»» gravel, sand, and boulder stones,

18 5, 7 55

being seven feet one inch below the ground-floor of the tower.
Considering the nature of the materials, and the depth in which
the men were working, it appeared conclusive that the ground
beneath had never been disturbed, and consequently the
object for which the work had been undertaken had been
fully and satisfactorily executed, not leaving a doubt upon
the minds of any present, that prosecuting the work any longer
would be useless waste of time and labour. Mr. Molloy, a
respectable farmer, who is seventy years of age, states, that for
fifty-six years, that his memory serves him, no excavation
similar to the present had been made within that period.

“Mr. Long, C. E., Mr. C. Mayne, and Mr. Molloy,
farmer, were present during the entire operation. After
having satisfied myself as to the result of the excavation, the
material taken out was thrown back into the tower.”

Colonel Jones also exhibited rubbings from a rock at
Drumlish, of which he read the following account :

148

** This rock, which it appears has engaged the attention
of the curious for many years, is situate in a small pasture-
field, in the parish of Killoe, townland of Clernaugh, barony
of Granard, county of Longford.

‘* The field is now in the possession of Thomas M‘Cann,
who lives on the spot. Itis on the west side, and within fifty
yards of the high road, and about three quarters ofa mile
from Drumlish, on the way to Longford. ‘The spot is more
particularly shewn in the sketch plan accompanying this
paper.

‘* At the upper corner of the field there is a large irregular
patch of the scalp of a rock bare; it is about eight yards in
length, and its greatest breadth is about three. The rock is
laminated perpendicularly, and appears to be of clay slate, but
accidentally discoloured, nearly all of it being deep red (the
country people call it the Red Flag), but there is a small por-
tion of it grey.

“The whole of this surface is more or less occupied with
indented marks, all apparently without connexion, arrange-
ment, or method; and perhaps there are more of these marks
to be found, if more of the rock was uncovered, for upon each
of the three little separated patches (see the plan which
accompanies this Number) I find there are similar marks; but
yet, in the adjoining lane, where there are two more patches
of the rock bare, I found more of these marks.

‘¢ The surface being so large, I made transcripts of por-
tions only, which accompany this notice. These were made
by laying the paper on the rock, and rubbing it with heel
ball; and as this gave a confused appearance from the rough-
ness of the rock, I used a tint afterwards to make the spaces
more solid, and thus the indentions appear white; and as this
tinting was not done upon the spot, perhaps there may be
some slight deviations from the original.

‘I have shewn upon one of the papers the character of
these marks; they are all angular; there are none of them

149

sunk or cut square; they are deeply indented in the mid-
dle, and decrease in depth to the surface; at the ends they
appear, therefore, like marks or scratches made with a nail or
some pointed instrument, when the rock was in a soft state;
for instance, like a gash made in the dough ofa loaf, and
when baked, this gash would become an angular furrow.

“ The people of the neighbourhood do not speak Irish,
and that renders it difficult to obtain from them any thing
like satisfactory evidence upon the subject, but M‘Cann says
that many people have come (even from England) to exa-
mine this rock: he also recollects a preacher, named M‘Quig,
who examined it between twenty and thirty years ago, and
who said he could understand parts of it, and that an account
of it would be found in O’Halloran’s History. He also says
that it is mentioned in a book published about seven years
ago—a book about which there were many law-suits. (‘This
must be Lewis’s Topographical Dictionary.)*

‘‘ The people have a saying, that great troubles are to
come, and that the finishing battle is to be fought in the ad-
joining valley, and the ratification or settlement will be signed
upon this rock.”

DONATIONS.

Two ancient Iron Swords and a Spear Head, found near
Kilmainham. Presented by the Directors of the Great
Southern and Western Railroad.

Rubbings from an inscribed Stone, with Characters, sup-
posed to have been Ogham, at Drumlish, near Granard.
[Engraved to accompany the foregoing description.] Also a
Lithograph of a ruined Temple in Malta. Presented by
Colonel H. D. Jones, C, E.

* It is not mentioned under Drumlish, in Lewis’s Typogr. Dictionary.

150

December 8, 1845.
SIR Wm. R. HAMILTON, LL.D., President, in the
Chair.
The President made a communication on some new appli-
cations of Quaternions.—See Appendix, No. V.

DONATIONS.

Registrum Prioratus Omnium Sanctorum juxta Dublin.
Edited, for the Irish Archeological Society, by the Rev.
Richard Butler. Presented by the Society.

Transactions of the Institution of Civil Engineers of Ire-
land. Vol. I. Presented by the Secretary, Thomas Old-
ham, Esq.

Memoires de ’ Academie Imperiale des Sciences de St.
Petersbourg. 6me serie, viz.: Science Naturelles. ‘Tome
IVme, 6me Livraison. Divers Savans. Tome IVme, 6me
Livraison. Recueil des Actes de la Seance Publique de l Aca-
demie Imperiale des Sciences de St. Petersbourg; tenue le 29
Dec. 1844; et Science Politique. Tome V., Livr. 5. Pre-
‘sented by the Academy. ;

Memorie de la Reale Academia delle Scienze di Torino.
Tome XX XIX. (1836). Presented by the Academy.

Proceedings of the Geological Society of London. Vol. 1V.
Part 3, No. 104. Presented by the Society.

Flora Batava. Nos. 137, 138. Presented by the King
of Holland.

Several Iron Swords, and other Weapons, found near
Kilmainham. Presented by the Directors of the Great South-
ern and Western Railroad.

A large Collection of Iron Swords, Bosses of Shields,
Spears, and other Weapons, some Fibule made of Bronze and
Silver, all found in the Cuttings of the Great Southern and
Western Railroad, near Kilmainham. Presented by Colonel
Napier, Deputy Adjutant-General.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846. No. 52.

January 12, 1846.
GEORGE PETRIE, Esq, Vice-President, in the Chair.

The Earl of Enniskillen, William Lloyd, M.D., The Ven.
Henry Cotton, D.C. L., Archdeacon of Cashel, Rev. John
Connell, John C. Deane, Rickard Deasy, Conyngham Ellis,
Arthur Nugent, Edward King Tenison, John Tyrrell, and T.
Jolliffe Tuffnell, Esquires, were elected Members of the
Academy.

ReEsotvep,—* That the recommendation of the Council,
to place £50 11s. at their disposal, for the purchase of a con-
voluted Gold Bracelet, be adopted.”

The Rev. Professor Graves read a paper on the discussion
of Algebraic Curves and Surfaces, with special references to
the theory of Curves of the third degree.

The general equation of an algebraic curve or surface of
the n degree being written in the form

Un+Un-1+ Un-ofeeeees + U.+U,+U)=0, (1)
where uv, stands for a homogeneous function of the n' degree
of the rectilinear coordinates, any equation such as
AmUm-- Am—1Um—1-+ Am—2Um—2+ «++ + AgUg+A,U + AgUy = 0 (2)
in which m is not greater than ”, and Ao, Aj, Ag, -.. Am are con-

VOL. III. Oo

152

stants, represents a curve or surface derived from the former
by means of the following geometrical construction.

Draw from the origin o any right line meeting the surface
(1) in the 2 points Nj, No, N3,.----- Ny 3 and assume on it m
points My, Mg, M3,....+« .Mmy 80 as to satisfy the m conditions

m03( Sn) =52(5y)
ms ss pase home)
=m

:(——— 1
ON}-ON5.0N3

AGS
OM;.0My.0M;

EN

1
= Amz :
ON,-ON».ON3..00% ON»,

Then the points M), My, M3, ..-..- Mn Will lie on the surface (2).

If we suppose now that the coefficients Ao, 41, Ag, --» Am are
formed according to any assumed law ; for instance, if they are
given functions of m and n, we shall have, as m takes different
integer values from 1 up to x, a series of curves or surfaces,
derived from the original one, and related in a particular man-
ner to it and to each other.

By making the coefficients Ao, Aj, Ao) --- Am, all equal to
unity, we form a series of curves or surfaces most easily de-

1
Ay | —————
OM).OM.0M3.....-OMm

rived from any given one; and the consideration of them sug-
gests some interesting results.
The problem of drawing a tangent geometrically ata given

point on a curve of the third degree has been elegantly solved .

by M. Poncelet; but we are now in a condition to solve it
generally for any algebraic curve.

Having drawn any right line from the given point o,
meeting the curve in m—1 other points N,N, N3....Nn—y, let
us assume on it a point m such that

=a(ch) ®

153

the locus of the point m will be a conic having a three point
osculation with the curve ato. The tangent and osculating
circle of this conic belong therefore likewise to the given curve.
So also, in the case of a point o given on any algebraic sur-
face, the surface of the second order, which is the locus of a
point m determined in the same way, will have its lines of
greatest and least curvature coincident with those of the given
surface at o. All this is obvious, since if

Un + Unit... +-U.+U,=0 (4)
be the equation of the given curve or surface, referred to axes
passing through the given point 0,

U. -U,;=0 (5)
will be the equation of the curve or surface of the second
order, constructed in the manner described above.

Let us suppose = 3, and (4) to be the equation of a
plane curve of the third degree; its intersections with the
conic (5)* determine the three right lines represented by the
equation

Uz = 6

which are obviously parallel to the asymptots. The directions
of the asymptots being thus ascertained, we may readily deter-
mine their actual position. For this purpose draw tangents
to the curve of the third order at the extremities of any one of
the chords common to it and the conic; they will meet the
curve in two points ; and the line joining these points will cut
the curve in the point through which the asymptot parallel to
that chord passes.

Of course the results here stated are subject to modifica-
tions when o is a singular point.

* As we are accustomed to regard the curve as generated by the motion
of the tangent, whose equation is u,; = 0, it seems natural to extend this
conception, and to call the conic u, + 0, = 0 the generating conic: the curve
U,+ 0, + u,=0 the generating curve of the third degree, and so on.

Ones:

154

If we draw from o two right lines parallel to the asymptots
of the generating conic, in virtue of the equation (3), they
will each meet the curve of the third degree in two points
equidistant from o. It follows, therefore, that the two recti-
linear diameters of the curve, conjugate to these right lines,

must pass through o. Hence we know how to construct —

these diameters. Again, as there are plainly but two diame-
ters passing through 0, the curve enveloped by all the diame-
ters of the curve must be of the second class, that is to say,
it must be a conic section.

If o be a conjugate point, the conic and its asymptots are
imaginary ; consequently o must lie within the envelope.

If o be a cusp, the conic degenerates into two coincident
right lines. The diameters of the curve conjugate to them
must, therefore, be coincident likewise. Hence o lies on the
envelope.

If o be a double point, the conic is replaced by two inter-
secting right lines; and it is easy to see that, as we can draw
from o two diameters of the curve, conjugate to the two systems
of respectively parallel chords, o must lie outside the envelope.

The preceding theorems, relative to the envelope of the
rectilinear diameters of a curve of the third order, and to the
positions of singular points of the curve with respect to it, are
due to Professor Pliicker of Bonn, who obtained them by ana-
lytical methods. ‘They are here presented as consequences,
derived by purely geometrical considerations from the proper-
ties of the generating conic ; in order to illustrate the impor-
tance of the place which it holds in the theory of curves of the
third order.

Perhaps the most interesting class of derived curves or
surfaces is that of the Successive Polars of a given curve or
surface of the n’ order. The geometric mode of generating
them is as follows:

Draw from any point o a right line meeting the surface in
m points, Nj, No, N3.s++++.Nn, and assume on it m points,

155

Mj, Mo) M3..... Mm, Such that

1 m 1
=(u)=a()
OM, n” \ON,
1 _ m(m—1) ( l
3 (Siren) = n(n —1) % ave

1 _ _m(m—1).....2.1 <3 1 );

OM}.0M.....0Mm 2(n—1)..(n—m-+1)” \ON}.0N9....0Np/”

the curve or surface which is the locus of the points M,, My,
M3...-+My Will be the m polar of the point o with relation
to the given curve or surface. It is plain that, so far as re-
gards this method of geometrical generation, the polars are
successive: that is to say, the (m + 1)" polar is derived from
the m‘” in the same manner as the m'* from the (m— 1)". In
every case the products of the distances 0M), OM)...OMn,
taken r by r, have the same harmonic mean as the products of
ON), ON,... ON,, also taken r by 7: and ‘his for all integer
values of 7 from unity to m inclusive.
It follows from what has been already said, that if

Un FUni+t..-+U,.+0,+0U,=—0
be the equation of the given curve or surface, referred to rec-
tilinear axes passing through o,

__m(m—1)...2.1 m(m—1)..
n(n—1).. (n— ml)” ey ee Um—1 +
m(m — 1) m 18
ane e). ar ities U,;=0

will be the equation of the m polar of the point 0, with rela-
tion to the given curve or surface. By making’m, in this
formula, successively equal to the integer numbers from 1 up
to n—1 inclusive, we obtain the equations of all the succes-
sive polars of the origin. For instance, the equation of the
first polar is

U,; + 2U, = O

156

which involves in it the celebrated theorem of Cotes, so
successfully used by Maclaurin. And the equation of the
(n— 1) polar is
Una + 2Un—2 + 3Un-3 + +--+ (m — 1)U,; + nUy = 9,

an equation which we recognize as belonging to the curve or
surface of the (n— 1)" order, which passes through the points
of contact of all the tangents drawn from the origin to the
given curve or surface. It is by this geometrical property
that M. Bobillier, who first directed attention to these suc-
cessive polars,* has chosen to characterise them.

5 ail z f
By substituting iy - 7 for x, y, Zz, in the general equa-

tion of the surface, and in the equations of its polars, Profes-
sor Graves shews that, when the point o recedes to an infinite
distance, the whole series of successive polars become diame-
tral lines or surfaces of the different orders belonging to the
given curve or surface. This had, in fact, been observed, in
the case of the first polar, by M. Poncelet, who has shewn
that the theorem of Cotes is an extension of Newton’s propo-
sition relative to the rectilinear diameters of plane curves.{

This theory of polars enables us to give a geometrical
construction of the problem, ‘“‘ From a given point in its
plane to draw all the possible tangents toa curve of the third
order.”

We have only to construct the second polar of the given
point, which will be a conic section, and its intersection with
the curve will give the points of contact. Here we see the
advantage of adopting the geometrical definition of polars
employed in this paper.

In connexion with the present subject, Professor Graves
announced an extension of a theorem deduced by Maclaurin

* See a Series of Articles contained in the eighteenth and nineteenth
volumes of Gergonne’s Annales de Mathématique.
{ See Chasles’ Histotre de Geometrie, p. 147.

157

from the theorem of Cotes. Maclaurin’s theorem is: ‘¢ If
any transversal be drawn through a fixed point o, in the
plane of a curve of the n" order, so as to meet the curve in
n points, the tangents drawn at these points will cut off upon
any fixed right line passing through 0, segments OT), OT)...
oT, the sum of whose reciprocals is constant.”

The following is a more general theorem for plane curves :
“<< Tf any two transversals be drawn through a fixed point o,
in the plane of a curve of the n order, so that one meets the
curve in n points My, Mg... Mn, and the other in n points M’,,
M95... M'n3 the right lines M\M’;, MoM’y,..-MnM’n, will cut
off, upon any fixed right line passing through 0, segments o7,,
OTs, - +. OT», the sum of whose reciprocals is constant.”

And we have an analogous one for surfaces: ‘* If any
three transversals be drawn through a fixed point o, the first
meeting a surface of the n order in n points, My, Mz, ..- Mn 3 the
second meeting it inM’), M’,,...M’,; the thirdin mM), M"o,...
My”; the planes M\M’\M’,, MjM’/,M"o, «+» MnM/nM”, will cut off;
upon any fixed right line passing through 0, segments, the sum
of whose reciprocals is constant.

The Rev. Dr. Drummond read a paper on the authorship
of the poem entitled “* The Exile of Erin.”

This subject was taken up in consequence of a provincial
newspaper having been sent to Sir William Hamilton, accom-
panied by a letter setting forth the claims of George Nugent
Reynolds, Esq., to the authorship of that poem, and request-
ing that the matter might be brought under the consideration
of the Royal Irish Academy. This task was at first declined,
as unworthy of serious attention ; but the claims of Reynolds
continuing to be urged in several publications, and Thomas
Campbell, the reputed author, represented as a plagiarist,
Dr. Drummond, lest the silence of the Academy should
be construed into an admission of the validity of Reynolds’

(158

e

claims, thought it an act of justice to both parties, to
subject those claims to a strict scrutiny.

It is admitted by the friends of Reynolds, that Campbell’s
account of the poem has been unvarying ; that he wrote it in
Altona in 1801 ; that it soon became universally known as his;
that it was published in various editions of his poems, and his
right to it never questioned till nearly thirty years after its
first appearance. He was then accused of having ‘‘ abstracted”
it from the library of the Marquis of Buckingham, though
there was no Marquis of that title. In a letter addressed to
the Editor of The Times, he indignantly repelled the charge
as a calumny; and affirmed, that never in his life had he access
to any papers of either Marquis or Duke of Buckingham ;
that he wrote the song in Altona, and sent it off immediately
from thence to London, where it was published by his friend
Mr. Perry in the Morning Chronicle. This statement of Camp-
bell’s was in perfect accordance with the account of the origin
of the poem communicated to Dr. Drummond in Edinburgh,
in the winter of 1811, by Dr. Robert Anderson, who had
been Campbell’s particular friend, viz., that it was written in
Altona, in consequence of Campbell’s having met with some
éxpatriated Irishmen in that city, for whose misfortunes he
felt a deep sympathy. This has been still farther corroborated
by George Petrie, Esq., who affirms that he heard the same
statement from certain of those very exiles whom he named,
and who were well known in Dublin prior to their banish-
ment. Campbell had spent the evening in their company,
and their conversation having naturally turned on their ruined
hopes and unfortunate country, he was greatly moved, and on
retiring gave vent to his feelings in the song of the Exile of
Krin. The following morning he gave them a copy of it, and
by them it was specdily transmitted to Ireland. It is possible
that one of those copies, or a transcript of one of them, may have
fallen into the hands of Reynolds, that he spoke of it to his
friends, and, as he wasknown to have had some propensity to

159

rhyming, that their partiality led them to imagine that he was
the author, though it does not appear that Reynolds himself
ever made any such assertion. Some of his particular friends and
near relatives, in lack of more conclusive evidence, swore before
a justice of the peace in Dublin, that it was their belief that
Reynolds was the real author; that the song was well known
in their circle in the year 1799; that one of them, a lady, had
given away a hundred copies of it among her friends, and that
it had been noticed as the composition of Reynolds in the
newspapers of the day. None of these newspapers, however,
had been produced or named ; and as to the belief or convic-
tion of any individual, however respectable and trustworthy, it
availed nothing in the determination of a question of this kind.
It was stated in favour of Reynolds, that a wandering harper,
called M‘Cluskey, had said that he had learned the song in
the Irish Harp Society of Belfast in 1799, and that G. N.
Reynolds was the author. This statement was treated as a
fabrication, for the following reasons. The principal founders
and supporters of the Irish Harp Society were Henry Joy,
Esq., of Belfast, and Edward Bunting, the well-known col-
lector of ancient Irish melodies, of which he published a
volume or ‘‘ General Collection,” in 1809. Mr. Joy wroté
the learned and elaborate History of Irish Music which is
prefixed to that volume. English songs appropriate to the
airs were collected from various sources. Among them were
three from Thomas Campbell, one of which is ‘‘ the Exile of
Erin.” Had that song been ascribed to any claimant but
Campbell, who gave it to Bunting as his own, Messrs. Joy
and Bunting must have known it ; and it is not for a moment
to be imagined that either of those honourable men would
have published the song as Campbell’s, had there been but a
breath of suspicion that he was not bond fide the real author ;
and as little is it to be imagined that Campbell, with the con-
sciousness of its not being his own, would have suffered it
to be sent forth with his name, in a volume to which public

160

attention had long been carefully solicited, and which was
about to pass into the hands of all readers of poetry, and all
admirers of Irish music.

What, it was asked, were the literary pretensions of Rey-
nolds, that he should be considered as the author of a lyric
poem, to which he had written nothing equal? As to
Campbell, no one acquainted with his poetry could doubt his
competency to the task. Moreover, the style, the senti-
ments, the versification, were all in perfect harmony with the
unquestioned productions of Campbell’s muse, and particu-
larly with the ‘* Lines written on a Visit to Ayrshire.” The
warm friendly feelings expressed by Campbell for Ireland,
entitle him to the gratitude of Irishmen; and it would ill be-
come any native of our country to pluck a single leaf from
the chaplet of fair renown that encircles the brow of Camp-
bell.

«* Non ego illi detrahere ausim
Herentem capiti multa cum laude coronam.”
Hor. Sat. x. 48.

W. R. Wilde, Esq., read the following Memoir of the
Dublin Philosophical Society of 1683 :

‘«¢ The year 1683 is memorable in the annals of scientific
literature in Ireland for the formation of the Dusiin Patio-
SOPHICAL SOCIETY, the great prototype of all our existing
learned bodies, but in particular of the Royal Irish Academy.
It was commenced in October in that year by William Moly-
neaux, ‘the friend of Locke,’ and the distinguished mathe-
matician and astronomer, who was the first secretary of this
society.

** As there is no detailed account of this body in print, and
as the notices. of it which have as yet appeared are always
exceedingly brief, and frequently incorrect, I have for some
years past endeavoured to collect as much of its history and
proceedings as the scanty records scattered through works
and libraries afford. With these materials—with the manu-

3

161

scripts and correspondence of both William and Thomas Moly-
neaux placed in my hands by Sir Henry Marsh—from a care-
ful examination of the documents belonging to it in the
Manuscript Library of our University—and from the Minute
Book still preserved in the British Museum, which has been
accurately noted for the purpose—I have made, through these
and other sources, some more memoranda of the history of the
Philosophical Society than the usual accounts afford, and
these I beg leave to offer to the Academy.

‘< In the manuscript correspondence of the Molyneaux’s just
alluded to, we find in a letter from William to his brother
Thomas, then in Leyden, and dated 30th October, 1683, N.S.,
the following :—‘ I have also here promoted the rudiments of
a society, for which I have drawn up rules, and called it Con-
ventio Philosophica. About half a score or a dozen of us have
met about twelve or fifteen times, and we have very regular
discourses concerning philosophical, medical, and mathemati-
eal matters. Our convention is regulated by one chief, who
is chosen by the votes of the rest, and is called Arbiter Con-
ventionis, at present Dr. Willoughby (the name ‘ President’
being yet a little too great for us). What this may come to I
know not; but we have hopes of bringing it to a more settled
society. The event you shall know. Sir W. Petty and_all
the virtuosi of this place favour it much, and have at some
times given us their company.’

‘‘ From this it would appear that Dr. Willoughby was vir-
tually, though not in name, the first President, and W. Moly-
neaux the original Secretary, although the former honour has
been generally conferred on Sir William Petty, who, how-
ever, was not elected till the Ist of November, 1684.*

* «At this election Sir W. Petty and Dr. Willoughby had equal marks
for President, but upon a second election Sir William carried it by four
votes, so he stood. Afterwards we had a handsome dinner at a tavern, so
finished the day.” —Molyneaua Correspondence, Dublin University Magazine,
vol. xviii., p. 489.

162 q

‘« The first meeting took place on the 15th of October, 1683,
when papers were read by Mr. William Molyneaux, Dr.
Narcissus Marsh, afterwards Archbishop of Dublin, Mr. Foley,
and Mr. St. George Ashe. It is remarkable, that although
Ware, Birch, and Whitelaw have agreed in dating the origin
of this society in 1683, Mr. Halliwell has, in a “ Collection
of Notes on the early History of Science in Ireland,” pub-
lished in the Proceedings of this Academy for 1841, stated
that its first meeting took place on the 28th of January, 1684.
In the winter of 1683, writes Archbishop Marsh in his Diary,
‘was set up the Philosophical Meeting in Dublin, that met
and formed itself into a society, in the Provost’s lodgings.
There, at the first opening of it, as a prelude to what we were
to do, I in three or four days’ time, composed An Introductory
Discourse to the Doctrine of Sounds, which was sent to the
Society in Oxford, and oe printed in the Philosophical
Transactions.’ *

‘* Not having facilities for publishing their proceedings in
Ireland, it appears that they determined upon offering them
to the Royal Society ; accordingly, on the 18th of December,
1683, the Provost, Dr. Robert Huntingdon, wrote a letter to
Dr. Plot, of the Royal Society, giving an account of ‘a
weekly meeting of several ingenious men about philosophical
subjects in Dublin.’ This notice, which is recorded in the
letter book of the Royal Society (vol. ix, p. 103), informs us
that W. Molyneaux, then residing near Ormond’s Gate (now
Wormwood Gate), and who was at that period engaged in
writing an ‘ Atlas for this Country,’ was Secretary :—‘ And
since,’ he writes, ‘you so generously, as well as charitably,
offer your assistance, I think this will be the best method of
conveyance, to transmit our notices to the Secretary of the

* The Diary of Archbishop Marsh, from a transcript in Marsh’s Li-
brary, Dublin, published by the Rev. Dr. Todd in the British meagre
for July and August, 1845.

163

Royal Society, who, after he has perused them, can send them
to Oxford’ (where a similar society, under the care of Mr.
Musgrave, had just been established), ‘as you likewise by
him may send hither. After Christmas that we next meet,
our Secretary will pursue that course ; you smoothing our
way at London once again, as it seems you have already
done.—After awhile we may perchance ease ourselves of that
expense, and have our intelligence for nothing.* However,
you may be sure we shall never grudge to defray all manner
of charges that shall be incident to our correspondences, and
we have raised a fund out of which to doit. By Moses Pit,t
ifnot before, you may expect one or two of their discourses at
large: for the way is for particular subjects mentioned in the
foregoing meeting to be treated on by particular persons the
next, and when they have done, every one that has anything
to add or object has his time to express it. I don’t give you
the names of our society, because you know few of them,
except the Bishop of Ferns and Leighlin, Sir William Petty,
and Dr. Willoughby, and besides you will receive it more
authentic from the Secretary. Several of the number meet
on Sunday nights, as the whole company does on Mondays,
to discourse theologically, of God, suppose, and His attributes,
and how to establish religion and confute atheism by reason,
evidence, and demonstration.’

‘* Having complimented Dr. Plot, and conveyed to him the
thanks and acknowledgments of this ‘ young society for the
promotion of philosophy, on account of the advantageous cor-
respondence offered to it by the Royal Society,’ he encloses
him an account of some previous meetings tending to its
‘better regulation, settlement, and future transactions,’ and
also the Minutes for October 15, 1683.

- * The Royal Society charged only half payment to the Members of the
Dublin Society, (see Minutes for 4th July, 1685).

+ Moses Pit, a celebrated London bookseller, and publisher of ‘‘ The
Atlas.”

164

** When I first commenced this inquiry some years ago, I
was under the impression that the Transactions of this society
were still in existence, and would one day or another be dis-
covered, and acknowledged by some of the public libraries or
private collections in these kingdoms. I have since, however,
convinced myself of the contrary being the fact, and feel as-
sured that no manuscript volume of the Transactions of the
Dublin Philosophical Society is, or perhaps ever was, in
being.

‘¢ The Minute Book of this Society, from 1683 to No-
vember, 1686, with its revival in 1693, and again in 1707,
is still preserved in the British Museum (Addit. MSS.,
4811). In the Manuscript collection in the Library of Tri-
nity College we find among some scattered papers lately
collected by the Rev. Dr. Todd, rough drafts of the minutes
of the Dublin Philosophical Society, in the handwriting of
William Molyneaux, from January the 28th to June the 9th,
1684, all of which accord with the notices of this body still.
existing in the papers of the Royal Society. On the first of
these dates we find the officers for that year were appointed,
and the ‘obligation subscribed.’ At that time there was
no President (as already stated in the Molyneaux correspond-
ence); Dr. Willoughby was appointed Director, and William
Molyneaux Secretary and Treasurer. ‘The members present
were Dr. Narcissus Marsh, Sir William Petty, and Messrs.
Bulkeley, Cuff, Foley, Baynard, Ash, Mullen, Follet, Bag-
got, and Mr. Keogh, who was represented by proxy. At
this meeting Sir William Petty read a paper on Concentric
Circles.

«‘ On the 18th of February the Minutes closed with this
notice :—‘ Nicholas Hudson, our operator, attended on us.’
(MS., T.C.D., Cl. I. Tab. 4, No. 18, p. 11).

“«‘ The unpublished Letter Books of the Royal Society, and
Birch’s History of that body, likewise contain the Minutes of
the Dublin Philosophical Society from its first meeting on the

165

15th of October, 1683, to the end of 1687, after which we
have not been able to discover any record of its proceedings
from these sources.

‘«¢ The principal papers read to this body, all of which are
enumerated in the Minutes, were either printed in the Philo-
sophical Transactions, or formed the material for distinct
works or monographs, which were published by their respec-
tive authors, and many of the communications were delivered
in form of vivd voce discourses at one sitting, and debated at
the next.

‘* There are two manuscript volumes of county histories in
the library of the University of Dublin (from which the His-
tory of West Connaught is now about to be printed by the
Irish Archzological Society), which have generally been
supposed to have formed part of the Transactions of the
Philosophical Society ; but as some of the papers in these are
dated in 1682, prior to the creation of that body, and as we
have no notice or allusion made to any of them in the Minutes
of the Society, which are in every other respect so full and
explicit, we feel assured that they were written and intended
for the general survey of Ireland under Sir William Petty.

‘¢ Dr. Plot was desired to acquaint the Provost of Trinity
College that the Royal Society very willingly embraced the
correspondence of the Society in Dublin, and had ordered
their secretary to write to themin the manner proposed ; ac-
cordingly, Mr. Aston wrote to Mr. Molyneaux to that effect, a
letter, dated the 26th of February, 1684, which is inserted in the
unpublished Letter Book of the Royal Society, (vol. ix. p. 111).

‘¢ This courtesy of the Royal Society is alluded to in one of
the letters of William Molyneaux to his brother Thomas, then
residing in Holland, a portion of which I extract from the
interesting correspondence of those gentlemen, which I pub-
lished some years ago in the University Magazine.-—‘I know,’
says William Molyneaux, ‘you would willingly hear what
has become of our meeting here in Dublin, of which take this

166

following account. Since my last to you concerning this
particular, we have constantly every Monday had a meeting,
at which one or other would produce discourses no ways con-
temptible, till about a week before Christmas, we received a
letter from Dr. Plot, directed particularly to the Provost, Dr.
Huntingdon, but designed in general for us all, in which he
takes notice of our design here on foot, for Dr. Huntingdon
had formally given him an account thereof, and encourages
us to go on vigorously therewith, promising us all the assis-
tance we can desire, as, likewise, the favourable countenance
and encouragement of the Royal Society, as also of such ano-
ther philosophical meeting as our own, begun within these
three months at Oxford : assuring us also of the constant cor-
respondence of them, and that we may at any time command
whatever we may please to hear communicated from them.
This encouragement from so great a man, as he is secretary
both to the Royal and Oxford Societies, made us think upon
modelling ourselves into better form; and, accordingly, the
Bishop of Ferns, Sir Wm. Petty, Dr. Willoughby, and I, were
pitched upon to draw up rules, to be presented to the consi-
deration of the rest after the holidays; so that yesterday (Jan.
7, 1684) our rules were presented, and are ordered to be read
at three several meetings before they pass. The rules are
much the same as those of the Royal Society, and we have
entrance money, and a weekly contribution, but what it will
yet come to, God knows.’

*¢ On the 10th of May, William Molyneaux wrote to his
brother, then at Leyden, the following notice of the young So-
ciety :—‘ Our Society goes on; we have a fair room in Crow’s
Nest’ (off Dame-street), ‘ which now belongs to one We-
therel, an apothecary, where we have a fair garden for plants,’
where they first met in April of that year. And again, upon
the 14th of June we read: ‘ Our society has built a laboratory
by Dr. Mullen’s directions, in the same house where we have
taken a large room for our meeting, and a small repository.’

167

*¢ Subsequent to the general meeting in November, 1684,
a list of the members of the Philosophical Society was for-
warded to Mr. Aston, to which I have added the names of
some seven or eight others, who, either prior or subsequent to
the publication of this list, were, I have positive assurance,
connected with this society, prior to 1688.

President, Sir William Petty, Knt., M.D.
Director, Charles Willoughby, M.D.
Treasurer, William Pleydall, Esq.
Secretary, William Molyneaux, Esq.

MEMBERS.

Narcissus Marsh, Bishop of
Leighlin and Ferns.

William Lord Viscount Mountjoy.

Robert Huntingdon, D.D , Pro-
vost of Trinity College.

John Worth, D.D., Dean of St.
Patrick’s..

John Baynard, A.M., Archdea-
con of Connor.

Sir Robert Redding, Bart.

Sir Cyril Wyche, Knt., P.R.S.

Richard Bulkeley, F.T.C.D., af-
terwards Knt. and Bart.

Patk. Dun, M.D., afterwards Knt.

Henry Fenerly, Esq.

J. Finglass, M.A.

Samuel Foley, F.T.C.D., after-
wards Bishop of Down and
Connor.

Daniel Houlaghan, M.D.

John Keogh, M.A.

Dudley Loftus, afterwards Judge
of the Prerogative Court.

George Tollet, Professor of Ma-
thematics.

—— Patterson, Surgeon.

John Maden, M.D.*

Allen Mullen, M.D.

* The name of Madden (or Maden, as it is written in the Minutes of the

Philosophical Society) is intimately connected with the rise of science, litera-
ture, and medicine in this country. The John Maden, M.D., here alluded
to, was son of Thomas of Maddenton, and died in 1703. His family were
connected with, and he himself was the intimate friend of the Molyneaux.
His son, the Rey. Samuel Madden, commonly called ‘‘Premium Madden,”
was the founder of the Royal Dublin Society in 1731. See ‘“‘ The Tribes and
Customs of Hy-Many,” by John O'Donovan, printed for the Irish Archzeolo-
gical Society.
VOL. Il. P

168

William King,Sch.T.C.D., after- William Palliser, F.'T.C.D., Pro-

wards Archbishop of Dublin. fessor of Divinity, and after-
Richard Acton, B.D., F.T.C.D. wards Archbishop of Cashel.
St. George Ashe, F.T.C.D., after- Edward Smith, F.T.C.D., Pro-
wards Bishop of Cloyne. fessor of Mathematics, and af-
Mark Baggot, Esq. terwards Bishop of Down and
John Bulkeley, Esq. Connor.
Paul Chamberlain, M.D. John Stanley, M.A.
Robert Clements, Esq. Jacobus Silvius, M.D.
Francis Cuff, Esq. Walkington, Esq.*
Christopher Dominick, M.D. Sir Paul Ricaut,
Corresponding Member—Doctor, afterwards Sir Thomas Molyneaux,

Bart.

‘* These men formed the stelle majores of Irish literature
and science at this period; and nearly every one of those of
whom we have any subsequent account attained to considerable
eminence either here or in England.

<¢ At this time Sir William Petty designed to remodel the
society, and drew up a code of laws for its future regulation
and government, which were deemed worthy of being referred
to the Council of the Royal Society, to see how far they might
be useful to that body. We here find from authentic docu-
ments that some of the principal men of learning and science
at that time in Great Britain, and even on the Continent,
looked with a favourable eye on our Philosophical Society,
and addressed to it, through its Secretary, several letters and
papers upon scientific subjects, some of which are still pre-
served in the original Minute Book in the British Museum,
and abstracts of which are to be found in the records of the
Royal Society. At the end of the first year we find its pro-
gress thus recorded by William Molyneaux. ‘ Our society

* IT have not been able to discover the Christian name of this gentleman,
as the name was common in the University at that period. It was probably
Samuel Walkington, who was a Scholar in 1680, for Edward Walkington,
who was a Fellow in 1676, Archdeacon of Ossory in 1683, and afterwards

Bishop of Down and Connor, in 1695, was elected into the Philosophical
Society on its revival in 1693.

Cp oe er oe

169

has been complimented in the philosophical acts, as you will
find by the paper Mr. Ashe will send you, wherein for curious
subjects (invented by our learned and ingenious Provost) I
think we may vie with any Oxford ever had, and truly most
of the poems and speeches therein were excellent. Thus,
Tom., you see that learning begins to peep out amongst us.
The tidings, that our name is in the journals of Amsterdam,
was very pleasing to me, and really, without vanity, I think
our city and nation may be herein something beholding to
us, for I believe the name Dublin has hardly ever before been
printed or heard of amongst foreigners on a learned account.’
The Minutes of the Oxford Society were likewise regularly
transmitted and read at the meetings of the Philosophical
Society of Dublin.

‘© On the 11th of May, 1685, ‘ Mr. Molyneaux going for
England, Mr. Ashe was chosen Secretary; and Mr. Tollet
was then nominated Treasurer in Mr. Pleydell’s place.’ These
gentlemen were continued in office at the November meeting
of that year, and Lord Mountjoy was elected President. In
June, 1686, Mr. Edward Smith* was chosen Secretary, and
the other officers of the Society were re-elected at the general
meeting, together with the following council:—Sir R. Red-
ding, Sir Paul Ricaut, the Provost, Dr. Willoughby, and Mr.
W. Molyneaux. They then adjourned to the 5th of Novem-
ber. The last notice of the Society at this period which we
have been able to discover, is in the minute-book of the Royal
Society, in which, according to Birch, we read, that on the
13th of July, 1687, ‘the minutes of the Dublin Society for
several months past were read ;’ but there is no detail of their

* In the minutes for 21st July, 1684, we read as follows:—‘‘ Ordered,

That the thanks of this society be returned to Mr. Smith, for the honour he

-did us in the public act in the College on this lemma paradozon vetus Aigyp-

tiacum, quod sol nonnunquam oritur in occidente. Demonstratur de Societate

ad promovendam scientiam naturalem Dublinii nuper instituta.”—Birch’s His-
tory of the Royal Society, vol. iv. p. car
PZ

170

proceedings given. Whether the Society actually ceased to
exist at that period is not precisely known, but Dr. Hutton
and other authorities are of opinion that it did not till 1688.*
The minute-book in the British Museum has no entry after
the 6th November, 1686. For some time, both previously
and subsequently to the last note in the minute-book, it would
appear from the letters and other communications made by
several of its members directly to the Royal Society, that its
meetings were few and irregular: even so early as the 10th of
August, 1685, we read thus in the Secretary’s letter to the
Royal Society enclosing the minutes :—* Our company of
late has been very thin, and people’s heads so much dulled
with politics, that next meeting, I believe, we shall adjourn
till the term.’

‘¢ The unsettled state of this country in 1687 and 1688
caused a complete rupture of all society, public as well as pri-
vate, and several of the principal members of the Philosophi-
cal Society removed from Dublin.

‘¢ The subjects entertained by this Society, during the first
four years after its establishment, may be considered under the
following heads: Mathematics and Physics; Polite Litera-
ture; History and Antiquities; and Medical Science, includ-
ing Anatomy, Zoology, Physiology, and Chemistry, And

with some pains we have arranged, under their respective

denominations, the following list of the principal subjects,
together with the names of their authors, as recorded by the

Dublin Philosophical Society during the early years of its
existence :

‘* MATHEMATICS AND PHYSICS.

“ Mr. W. Motyngaux.—Deapparente Magnitudine Solis.—Ex-
planation of the Volution of Concentric Circles—On Telescopic
Sights.—On the viewing of Pictures in Miniature with the Tele-
scope.—Calculations on the Solar Eclipse.—An Essay on Crysta-

* Hutton’s Mathematical Dictionary, vol. ii. p. 61.

ee

171

lography.—Experiments on Hydrostatics—On the Hydroscope,
and the variations of the Barometer.
’ Dr. T. Monynzaux.—Account of the Astronomer Huygens.

Dr. Munien.—Magnetical Experiments (several papers).

Lord Mountsoy.—On the Air Gun.

Sir W. Perry.—Magnetical Observations.—On Weather Regis-
tries—Ship-building.—On the Construction of Carriages——On
Concentric Circles.

Mr. St. G. Asuz.—Review of De Chasles’ Book on Motion.—
On the Evidence of Mathematical Demonstration.—On the Solar
Eclipse—On the Weather Registry, T.C.D.—Experiments on
Freezing.

Mr. BuLkeLEy.—On Wind Gauges.—A new Pump for Ships.—
The Mechanism of Carriages.

Dr. Smrtu.—De Angulo Contactus.

Mr. Stantey.—Discourse on the Motion of Water.

Mr. Totuet.—On the Longitude.—On Gunnery.

Mr. Watxincton.—Observations on Archimedes.—Observa-
tions on Algebra.

Dr. Fotey.—Objections against ‘ipebrate Calculations.—Com-
putatio Universalis.

Mr. Kinc.—On the Difference in Size between the horizontal
and Meridional Sun.—On the Acceleration of Descending Weights,
and the Force of Percussion.—On Hydraulics.—On the Trisection
of an Angle.

Dr. Narcissus Marsu.—De Radiis Reflectis et Refractis.—
Magnetical Observations.

Dr. Wittovensy.—On the Mirage seen at Rhegium in Italy :
and on Winds.—On the Lines of Latitude and Longitude.

POLITE LITERATURE, HISTORY, AND ANTIQUITIES.

Aychdeacon Baynarp.—Concerning the Instruction of Youth
for the- Universities.

Dr. Lorrus.—Concerning Pere Simon’s Histoire Critique.

Dr. Huntinepon.—On the Obelisks and Pillars of Egypt.

Dr. Forzy.—On the contagious Communication of a strong
Imagination.

Mr. Krng—On the Bogs and Loughs of Ireland.

172

Dr. Mutten—On fifteen cinerary Urns, and Bones found toge-
ther, at Dontrilegue, County Cork, three feet deep, each covered
with a small Stone, and varying in size from a Pottle to a Pint,

Dr. SmitH—On cinerary Urns, found in the Caves at Warrings-
town, and at Loughbrickland, in the County of Down.

MEDICAL SCIENCE,—INCLUDING ANATOMY, ZOOLOGY, PHY-
SIOLOGY, AND CHEMISTRY, ETC.

Dr. AnLEN Mouzen [or Movin |—On the human and compara-
tive Anatomy, and the Structure of the Ear (several papers).—
Experiments, consisting of injecting Fluids into the Thorax of
Animals.—Experiments on the Blood.—On Digestion.—On the
Mineral Waters of Chapelizod.—On Poisons.—On Runnet and
Coagulum.—On the Organs of Respiration and Circulation, by
removing a Portion of a Dog’s Lung, &c.—Dissection of a Mon-
strous Kitten ; and a Chicken with two Bills.—Dissection of a Man
who died of Consumption.—Observations on the Serum.—On the
Peculiarities of the Pulse.—Dissection of Hydatids attached to the
Diaphragm.—De Alkali et Acido.—On Ligature of the Jugular Vein
in a Dog.—On various Chemical Phenomena.—On Ovarian Disease.
—On Ague.—Observations on Scurvy Grass.*

Mr. W. Motyneavx.—On the Phenomenon of Double Vision,
—On the petrifying Qualities of Lough Neagh.—Report on the
Sirones or Acari.—The Dissection and microscopic Investigation of
a Water Newt.—On the Circulation.—On the Pulvis Fulminans.—
On the Connaught Worm.

Dr. T. Motyngavx.—On the Anatomy of the Bat.

Lord Mountsoy.—On the Mode of Bleaching in Holland.

Sir W. Perry.—Observations on Consumption.—On the Mode
of examining Mineral Waters.

* Mr. Dalrymple, in his admirable ‘‘ Anatomy of the Human Eye,” in
writing of the vascularity of the lens and its capsule, says, that ‘‘ Haller, in
his Description of the Eye, quotes an Englishman of the name of Allen
Moulin, as the first observer, and in fact the discoverer of these long-denied
vessels.” Mullen, or Moulin, was, however, an Irishman, and the diseases
referred to are published along with his Dissection of the Elephant burned
in Dublin in 1681, and entitled ‘“‘ New Anatomical Discourses on the Eyes of
Animals.”

173

Mr. St. George Asnx.—On the Fossils and Petrifactions of
Londonderry.—On a remarkable Case of Heemorrhage.*—On Her-
maphrodism.—Account of a Man in Galway who suckled his Child,
and had Pendulous Mamme.

Mr. R. Burxetey—Experiments on venous and arterial Blood.
_Discourse on Mr. Boyle’s Book on Human Blood.—On Divers
Alkalies and Acids.—On the Dissection of a Bat.

Mr. Parrerson.—Various Dissections of the Human Subject.
—On Stone in the Bladder—On Menstrua for dissolving the
human Calculus.—On Cohesion between the Liver and Diaphragm.

Sir R. Reppinc.—On the Lampreys of the River Barrow.

Dr. Suity.—On the Waters of Lough Neagh.

Dr. Wittovensy.—On Hermaphrodism.

Dr. Forry.—Explanation of the Theory of Vision.—Experi-
ments on Vegetation.—On Fossils.

Dr. Hovnacuan.—On the Mode of Discovering the Acidity of
Liquors.—Description of a Human Kidney weighing forty-two
Ounces.—On the Tests for Acids.—On the Dissection of a Mon-
strous Child with two Heads and three Arms.

Mr. Kinc.—On the Mineral Waters of Clontarf and Edenderry.

Dr. Dun.—On the Analysis of Mineral Waters.

Dr. Narcissus Marse—On Sounds and Hearing.—-On the
History and Classification of Insects.

Dr. Sirvius.—De Acido et Urinoso.

Mr. Acton.—On the Scoter Duck found at Ireland’s Eye.

* We are not quite certain with regard to the author of this paper.
Birch merely says, ‘“‘Mr. Ashe.” The Minutes of the British Museum, how-
ever, state that this paper was contributed by Thomas Ashe, Esq. We
know not who this gentleman was—if a member of the Philosophical Society
he would increase the number to 40.

+ Human dissections were very rare in Dublin at that period. Mr. Pat-
terson’s communications to the Philosophical Society were founded upon the
examination of the body of a malefactor procured by Dr., afterwards Sir P.
Dun, to make a skeleton of. Mr. W Molyneaux says he ‘‘was constant at

_ the dissection, and nothing curious was done, but only the chirurgeons and
physicians that were present spoke at random as the parts presented them-
selves.” This is the first notice of a dissection in Ireland that we have seen
recorded. See University Magazine, vol. xviii. p. 479.

174

*« During the remaining years of the seventeenth centary,
the unsettled state of Ireland precluded the possibility of lite-
rary enterprise or scientific investigation. From the following
paragraph in the Diary of Archbishop Marsh, it would appear
that an attempt was made to revive the Society in 1693; on
the 26th of April in which year he writes, ‘ This evening, at
six of the clock, we met at the Provost’s lodgings in Trinity
College, Dublin, in order to the renewal of our philosophical
meeting, where Sir Richard Cox (one of the Justices of the
King’s Bench), read a geographical description of the City and
County of Derry, and of the County.of Antrim, being part of
an entire geographical description of the whole kingdom of
Ireland, that is designed to be perfected by him; wherein also
will be contained a natural history of Ireland, containing the
most remarkable things therein to be found, that are the pro-
ducts of nature. Upon his reading this essay he was admitted
a fellow of this Society, together with Dr. John Vesey, Lord
Archbishop of Tuam; Francis Roberts, Esq., younger son
to the Earl of Radnor, some time Lord Lieutenant of Ireland :
O Lord, grant that in studying thy works, we may also study
to promote thy glory, (which is the true end of all our studies),
and prosper, oh Lord, our undertaking, for thy name’s
sake.* The manuscript volume in the British Museum re-
commences at this date, and informs us that the members of
the old Society who met on this evening, or, as they are styled,
‘the members before the warre,’ were the Archbishop of
Cashel, the Provost, Dr. Willoughby, and Sir Cyril Wyche.
At the meeting of the 3rd of May, Mr. Cuff and the Bishop
of Cork rejoined the body, and papers were read by Sir R.
Cox, describing Judland, and by Sir Cyril Wyche, on Varro’s
Book, ‘ De Lingua Latina.—Dr. Thomas Molyneaux, Mr.
Edward Walkington, and Mr. Bartholomew Van Homrigh,

* The Diary of Archbishop Marsh, already cited.—British Magazine, for
August, 1845,

175

were proposed at this meeting, and admitted on that of the
10th, when Sir. R. Cox finished his History of Judland; read
some papers on Ireland, and on the bringing of the Society
into its ancient model, &c. On this evening the Hon. Francis
Roberts was elected President; Dr. Charles Willoughby,
Secretary, and Francis Cuff, Esq., ‘Treasurer.

‘«¢ Bound up with this minute book are several copies of a
letter, which I judge to be of the same date, and of which the
following is a copy:

«‘¢ Strn,—The Dublin Society is again revived, and they
have ordered me to give you notice of it, and desire me to
renew their correspondence with you. Weare as yett but very
young, and therefor cannot hope to make any suitable returne,
but must have a little time to settle, after the disorder the
warr has put every thing into here. Mr. Roberts is chosen
President, and our Society increases by new elections, so that
we may expect it may be considerable, and then there may be
something fit to be communicated from,

«¢¢ Sir, your most humble Servant,
«¢<¢ Owen Lioypn,’—F.T.C.D.

«¢ A considerable hiatus occurs after this entry ; but it ap-
pears that in the year 1707, an attempt was made to re-esta-
blish the Society ; but its success was not of any long duration,
and this MS. contains a register of the philosophical papers
read before the Society, from August 5th, 1707, to March
11th, 1708. The Earl of Pembroke, then Lord Lieutenant
of Ireland, presided over the Society at this revival. Addit.
MSS. 4812.

‘¢ The Minutes do not inform us who the members were
that attended this re-union, but the following is a list of the
papers read during that period :—

The Bisnor or CLocuEer.—A Letter from, to Dr. Molyneaux, con-
cerning an odd Hare’s Tooth; afterwards accounted for by Dr.
Molyneaux,

Mr. Dernam.—On the Spots on the Sun,

176

The ArcugisHop oF Dusiin.—A Discourse on Measuring Land.—
A Letter on a fiery Eruption from the Bowels of a dead Cow.—
Thoughts for Improving the Harbour of Dublin.—Scenography of
an Engine to force Water out of a Quarry, &c.

Dr. Tuomas Motyneavx.—On Mines and Minerals within the
Kingdom of Ireland.—Account of a petrified Honey Comb, and
an Essay on Antiquities.

Mr. W. Motyneaux.—On Mercurial Phosphorus.

Dr. Rozryson.—Concerning the Density of the Atmosphere.

Mr. Warinc.—Account of the Occurrences of a Storm.—Letter to
Dr. Molyneaux concerning the Cross-Bills.

Mr. E. Crow.—Account of Lightning near Tuam.

Mr.(afterwards Bishop) BERKELEY.—A Discourse on Infinities—An
Inquiry whether the Figure of the Earth be spheroid.

Mr. Norman.—A Letter on Barnacles.

«¢ These Minutes appear to have been in the possession of

Sir H. Sloane, and were by him presented tothe British Museum.

«¢ Subsequently the Philosophical Transactions continued
to be the medium of communication between the medical
profession in Ireland and the public.”

Mr. George Yeates presented returns of observations,
made by himself, with thermometer, barometer, and rain and
wine guages, from January to December, 1845, inclusive —

(See Appendix, No. V1.)

DONATIONS.
An Astrolabe, made in Florence in the 16th Century.

Presented by Sir William Betham.

A Small Bronze Ink- Bottle, found in the Excavation made
by the Great Southern and Western Railway Company near
Kilmainham. Presented by W. Ogilby, Esq.

Three Bracteate Coins, found in the Round Tower of
Kildare, and figured in Mr. Petrie’s Essay on the Round
Towers, p. 209. Presented by Rev. Mr. Brown of Kildare.

A Beautiful Bronze Dirk, found near Tullamore. Pre-
sented by Anthony Molloy, Esq.

January 26, 1846.
GEORGE PETRIE, Esa., Vice-President, in the Chair.

The Rev. Samuel Butcher, F.T.C. D., read the first part
of a paper by the Rev. Dr. Hincks, on Hieroglyphics.

This paper commences with a review of the progress made
in Egyptian learning, from the first discoveries of Drs. Young
and Champollion to the present day. It was alleged, that very
little progress had been made since the death of Champollion,
the only point established since that event being the principle
of peculiar letters and their complements, discovered by Dr.
Lepsius. The causes of the want of progress since this disco-
very were affirmed to be two: Ist, ignorance of another prin-
ciple, in some measure antagonistic to this, which was exten-
sively applied in Egyptian writing; and, 2nd, an erroneous
mode of investigating the phonetic powers of the letters. This
consideration was postponed till the second part of the paper:
the third part to contain the results, as far as yet known, ofan
inyestigation into the powers of the letters, conducted in the
manner that would be shewn, in the second part, to be most
likely to lead to the truth.

The present part was devoted to the establishment of the
new principle above referred to. The principle is this: “the
phonoglyphs which compose the proper Egyptian alphabet
had names, which consisted of themselves with the addition
of certain expletive characters: and these names might be,
and often were, used in place of the single phonoglyphs. If,
then, a phonoglyph belonging to the alphabet be followed by
the expletive character which appertains to it, that expletive
may be, and, for the most part, should be, altogether neglected.”
It was added, that the single characters were occasionally,
though not frequently, used for their names, and the name
‘“‘ Ptulmius” occurring so frequently on monuments of the

178

Greek age, was given as an example; the two feathers in this
word representing, not, as has been heretofore supposed, an I
singly, but LU, the name of that letter ; while, on the other
hand, in the name “ Philipus,” the name IU is twice written
for the single vowel I.

In order to establish this principle, it was first shewn that
it was adopted in transcribing foreign words, when written in
Egyptian characters, in the papyri published in fac-simile by
the Trustees of the British Museum, and mostly dated in
the reign of Rameses the Great, and his grandson. A num-
ber of such transcripts were produced. Some of them were
shewn not to represent the words that corresponded to
them, which were preserved in Hebrew characters in the
Old Testament, unless a quantity of, apparently, superfluous
characters ‘were removed ; such were Ma-ru-ka-bu-ta for
both singular and plural of the name of a chariot, Mirkeveth;
I-u-ma for Yam, a sea; and Pu-ha-ru-ta for Phrat, the river
Euphrates. Others were shewn to be written at times with
those, apparently, superfluous characters, and at other times
without them, as Astaruta and Astart, the name of the Syrian
goddess; K-sh, Kash and Kshi, varieties of the name of a
country which we know was Kush, the supplied vowel being
wand not a. It was observed, as an essential point in the
proof, that the vowel which was introduced in this seemingly

“unnecessary manner, was always the same after each letter;
some letters, however, take for their expletives ideagraphic
signs, which determine their pronunciation, and are thus equi-
valent to vowels. It was remarked that the letter may, in
such cases, have for its expletive either the ideagraphic
character, or the letter which it suggests or implies. This is
an apparent but not a real exception to the law proposed.

It was shewn, secondly, that this principle was not con-
fined to foreign words, though applied to them more systema-
tically; but that several pure Egyptian words were written
with superfluous characters. In order to meet the cavils
which it was anticipated would be raised against this position,

Pe

179

it was necessary to bring forward words, in which the alleged
expletive could not be pretended to be properly a part of the
word, there being no room for it either in the place where it
was found, nor in any other part of the word, to which, accord-
ing to the pretended law of transposition of vowels, it might be
removed. Such were the instances of Ru-u-i-ha, for Ruha,
“evening,” the Coptic Ruhe; and Aahu, for Aah, ‘ the
moon,” which the Greeks have transcribed by the single vowel
A. Instances were also adduced, in which an ideagraphic
character, or a consonant, appeared as an expletive in a pure
Egyptian word; and also, an instance of two homophonous
letters, which took different expletives, being interchanged,
namely Tu and Ta, as formatives of the past participle,
both of which, it was affirmed, should be read without the final

vowel.
The principle having been thus established in the age of

the papyri, it was shewn, in the third place, that it was not
confined to that age, but was recognised in the time of the
twelfth dynasty, and even previously thereto. This was
shewn by a collation of texts, which were repeated in dif-
ferent steles, or in different parts of the same slab. It was
shewn, in a variety of instances, that the same word was
written sometimes with, and sometimes without, a vowel;
which vowel was, according to the practice of the age of the
papyri, the known expletive of the preceding consonant. It
was argued that, if a vowel so circumstanced should be re-
jected as an expletive in the age of the papyri, it should be
so also in the early ages to which the monuments now under
consideration belonged.

In order to explain the origin of this practice, it was
affirmed that all the Egyptian phonoglyphs originally repre-
sented syllables; and that, when a limited number of them
was selected to represent the initial sounds in the respective
syllables, they still retained their old names, as the sounds
now appropriated to them could not be uttered alone. The

180

five different modes used for completing the syllabie charac-
ters, by the addition of letters, were briefly explained ; and it
was then stated, that the old syllabic powers or names of the
letters of the alphabet, were completed by the addition of
another alphabetic character, representing the final sound in
the syllable. This additional character is the expletive of
the letter, and for it, as has been already noticed, an idea-
graph, determining the pronunciation of the syllable, and thus
equivalent to the first letter, may be obtained.

The reason why the practice of using expletives was re-
tained, especially in foreign words, was the readiness with
which some letters were confounded in the Hieratic texts.
These letters had always different expletives, and a distinc-
tion was thus established between them, which would not
exist if the expletives were omitted. The hieroglyphic texts
in which expletives are chiefly found, were stated to be those
which were copied from Hieratic, or, as they are called here,
hieroglyphic originals.

Mr, Huband Smith read a paper descriptive of an ancient
Wayside Cross, situate in the townland of Nevinstown, on the
northern bank of the river Blackwater, about two miles from
the town of Navan, in the county of Meath. One side bears
an inscription ; the opposite has a shield, with armorial bear-
ings, party per pale, nearly effaced. Beneath the dexter side
are the initial letters M.C., and, under the sinister, M.D.
The height of the shaft is at present three feet six inches
above the slab, in which a socket is cut to receive the tenon
upon the lower end of the shaft. This slab stands on a low
grassy hillock, the remains, doubtless, of an ascent of three or
four stone steps, which, when complete, the cross surmounted.

Mr. Smith exhibited to the Academy a “rubbing,” taken
from the shaft, which shewed the present state of the inscrip-
tion on the front, the shield on the back, and an ornamental
pattern on each of the sides. He also produced a restoration

181

of the entire, which shewed that the upper part of the shaft
had been broken off, and with it the first line of the inscrip-
tion. Of what remains the first line is illegible, but the rest is
tolerably distinct. Itis in the black-letter character of the six-
teenth century, the letters being beautifully formed; and (fill-
ing up the contractions) it runs thus:

falas eae Armigert, et (Margarete Werter uroris efus ac
Heredum eorum qui Hanc crucem fececunt anno Womini 1588
quorum animabus propicietur Deus, Amen.”

This inscription leaves little doubt that this memorial was
one of the Wayside Crosses so generally erected by the piety
of individuals about the sixteenth and the preceding centuries,
but which the ill-directed zeal of a subsequent period so
unsparingly mutilated, and often wholly destroyed. Upon
inquiry it proved that a road, leading from Navan to Rath-
aldron Castle, long the residence of one of the principal
branches of the ancient family of the Cusacks, once passed
close in front of this cross.

The name of the husband of “ Margaret Dexter’ Mr.
Smith soon after learned from a manuscript in the possession
of Mr. Henry T’. Cusack. This MS. is written in French, and
entitled “* An Historical Memoir and Genealogy of the ancient
and illustrious House of Cusack, of the Kingdom of Ireland.”
It appears to have been compiled by the Chevalier O’Gorman
in the year 1767. It states that ** Michael de Cusack, lord
of Portrane and Rathaldron, married Margaret Dexter, who
brought him, as a marriage portion, the castle, town, and
lands of Rathaldron. He was ‘ Greffier’ [a term which Boyer
translates ‘ Registrar,’ or Keeper of the Rolls] of Westmeath
and of Louth in 1553, one of the Barons of the Exchequer in
1580, and died in 1589.” From this it may be safely con-
-cluded that the initials ** M.C.,” upon the cross, are those of
** Michael Cusack,” and that his was the name sculptured on
the upper part of the cross, now lost.

182

In conclusion, Mr. Smith submitted that it would be
desirable to have careful drawings, and, where practicable,
rubbings also, made of all such existing monuments, in order
that these most interesting memorials, which contain valuable
confirmations of written documents, as well as curious illus-
trations of the manners and customs of bygone times, may be
preserved from oblivion; and stated that he would be much
gratified by receiving any communications on the subject,
though they went no further than to state the existence of
such crosses, in order to complete the materials for a general
history of these Christian memorials, so deeply interesting,
even in an historical point of view alone.

Rev. Charles Graves, F.T.C. D., read a Memoir, by Mr.
George Boole, of Lincoln, on Discontinuous Functions.

The author deduces in succession three theorems for the
expression of the discontinuous function, f(x). ‘The first
theorem, which is free from signs of integration, implies that
between the limits 2 = a, and z=a-+ Aa,

fla) = — (tan EAE — tan — —*) fe), (1)

provided that we suppose & a positive ee and take the
limit to which the second member approaches, as k approxi-
mates to0. When «=a, or a+ Aa, the first member of the
above equation must be divided by 2; and when a transcends
those limits, the first member is to be replaced by 0. From
this formula, the author deduces his second theorem, involving
one sign of integration, viz.:

] kda f(a)

R= eee 2)
in the second member of which the fo —o and may be
replaced by any other real limits, p and g, when all the values
of z, for which f(x) does not vanish, lie between the limits
pandg. This theorem is subject to the same conditions,

183

with reference to the interpretation of the second member, and
to the changes of value which it undergoes in passing the
limits, as the preceding one.

By an integral transformation, Mr. Boole then deduces
the third, or Fourier’s theorem, involving two signs of inte-
gration, viz. :

Jet) = =e a dadve aan (av— av) f(a). (3)

TT

He remarks, that when this theorem is written in the
form,

102 eo
8 Ce Wem a) ) da dv cos (av — av) f(a),
TT —2 ~0
@
we must attach to the symbol a meaning different from its
0
ioe)
ordinary one, and understand by ) dv ¢(v), the limit of
0

2
dv bea); for decreasing positive value of k. Mr. Boole
0

proposes to designate an integral of this kind as taken in a
limiting sense, and he observes that some anomalous results
have been obtained by writers who have neglected the distine-
tion here implied. Thus, from the equations

[e.@) (oa) f
y dx cos xz = 0, ) dzsng = 1,
0 0

a
in which the sign ) has been used in its limiting sense, have
0

been deduced, by taking that symbol in its ordinary sense,
and integrating without reference to the factor understood,

=, the incompatible conclusions,
cos co = 0, sino = 0.

~ Mr. Boole remarks that, by a converse error, other writers
have been led to infer the incorrectness of Fourier’s theorem,
VOL. Ill. Q

184

From Fourier’s theorem the author finally deduces a

J)

theorem for the discontinuous expression of apr viz.

J = — a ‘er i ‘i dadv dw cos (@ —a)v—tw + “2 ‘ea, (4)

ee)
in which the symbols | are both used in a limiting sense.
0

This theorem, it is observed, is susceptible of important appli-
cations, in the theory of definite multiple integrals.

As respects the expression of discontinuity, the formule
(1), (2), (8), are shewn to be equivalent, The advantage
which the second possesses over the first is, that # enters into
the second member in arational form; and the advantage of
the third, or Fourier’s theorem, over them both, is, that x
enters into the second member exponentially, which affords
facilities for both the direct and the inverse processes of the
differential calculus.

In the fourth theorem the author remarks that both « and
¢ enter exponentially.

Sir William R. Hamilton made some observations on Mr.
Boole’s communication.

Professor Harrison made some remarks on the peculiarities
of the anatomy of the Emu. [This paper, not haying been
received in proper time for insertion here, will be printed in

the Appendix, No. VII.]

Professor Allman announced the addition of Deotis Mari-
tima to the Irish Fauna. This plant he had observed during
the latter part of the summer of 1845, in the sand-hills in the
neighbourhood of Dungarvan, county of Wexford.

ae ae,

DONATIONS.
Memorie della Reale Academia della Scienza di To-
renzo. Serie Secunda. Tome. VI. Presented by the Academy.

185

Proceedings of the Philosophical Society of Glasgow,
1842, 1843, 1844, 1845. Presented by the Society.

Astronomical Observations made at the Radcliffe Obser-
vatory, Oxford, in the Year 1842. Vol. III. Presented by
the Radcliffe Trustees.

Astronomical Observations made at the Observatory of
Cambridge. Presented by the Rev. James Chatto, M.A.

Journal of the Asiatic Society of Bengal. No. CLV.
1844. Presented by the Society.

Index and Appendix to the Minutes of Evidence taken be-
Sore the Commissioners of Inquiry into the State of the Law
and Practice in respect to the Occupation of Land in Ireland.
Parts IV. and V. Presented by the Lord Lieutenant.

Facts from Gweedore, with Hints to Tourists in Donegal.
By Lord George A. Hill, M.R.LA. Presented by the
Author.

On the right Ascensions of the principal fixed Stars, de-
duced from the Observations made at the Cape of Good Hope,
im the Years 1832 and 1833. By Thomas Hudson, Esq.
Presented by the Lords Commissioners of the Admiralty.

Proceedings of the Zoological Society of London. Part
XII.—1844, Presented by the Society.

Letter on the Irish Colleges Bill. By John D’ Alton,
Esq. Presented by the Author.

Annual Report of the Royal Cornwall Polytechnic So-
ciety. 1844, Presented by the Author.

Facts connected with the social and sanitary Condition
of the Working Classes of Ireland. By Thomas Willis,
F.L.S. Presented by the Author.

Manual of writing and printing Characters. By B. P.
Welme. Presented by the Author.

An ancient Bronze Bit, found at Ballinaminton, King’s
County. Presented by George Marsh, Esq.

Q2

186

February 9th.

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

Richard Cane, Robert Franks, Charles W. Levinge,
James Corry Sherrard, Pierce Morton, and Stephen O’ Meagher,
Esqrs., were elected Members of the Academy.

Mr. Robert Mallet read part of his paper on the Me-
chanics of Earthquakes.

The author first notices the various instances recorded of
an apparently vorticose motion having occurred in earth-
quakes, as evidenced by the twisting displacement of objects,
such as the superimposed stones of obelisks, &c., and then
proceeds to demonstrate that the conclusion adopted by Mr.
Lyell and other authors, that such a vorticose motion actually
takes place, does not follow from the premises, and is incon-
ceivable and impossible in many respects.

He proves that the twisting displacement is due to a mere
alternate, straight-line motion, given by the earthquake-
shock to the base upon which the displaced body rests. The
insistent body is moved by the adhesion of its base, and its
inertia, acting through its centre of gravity, will cause the
body to twist whenever the point in the base, at which all
the adhesion may be supposed to act, and which the author
calls “the centre of adherence,” lies either to one side or
the other of a vertical plane, passing through the centre of
gravity of the body twisted, and being on the line of motion
of the base.

The alternate, straight-line motion having such great ve-
locity, yet within narrow limits, as thus to move heavy bodies
by their inertia, and which constitutes the earthquake-shock,
the author defines as the passage of a wave of elastic com-

187

pression though the solid crust of the earth, produced at any
distant points, by any original sufficient impulse, such as the
sudden bending, by elevation or depression, or the rupture of
a portion of the earth’s crust.

From this single principle, viz., that the true earthquake-
shock consists simply in the transit through the solid crust of
the earth of a wave of elastic compression, which the author
believes to be now, by him, for the first time, enunciated,
he proceeds to develope and account for, in detail, all the
more important recorded phenomena of earthquakes, as _ well
as many of the more perplexing secondary phenomena.

The original impulse, or origin of an earthquake, may be
either under the sea, or on land, at a distance from the sea.
In the former case, at the moment of originating the impulse,
whether by bending or fracture, several distinct sets of waves
set out from the same points, and at the same moment of
time, but they move with very different velocities,

The wave of elastic compression, or great earth-wave of
the author, makes its transit through the solid crust, outwards,
in all directions, from the point or points of impulse, and
moving at a speed proportionate to the specific elasticity and
density of the formations through which it passes. This,
the author shews, may be as much as 11,000 feet per second.
This wave constitutes a real undulation of the surface through
which it is passing, and may be also (if there is fracture at
the origin) heard as a sound-wave in the solid, moving at
the same rate. A sound-wave also travels through the water
of the sea, and, moving more slowly than in the solid, is heard
upon land after the shock has passed. Lastly, a rolling wave
of translation, or great sea-wave of the author, is formed by
the movement of the bottom, directly above the originating
disturbance. This sea-wave, though setting out at the same
‘moment as the shock or earth-wave, is rapidly outstripped by
the latter—because its motion is dependent upon its own form
and magnitude, and upon the depth of the sea upon and

188

through which it moves. The great sea-wave, therefore,
comes to land long after the shock has passed, and may be
followed by several in succession, into which the original
great sea-wave has broken, where the form of the soundings
in-shore are suitable. ;

The apparent recession of the sea just at the moment of
the earthquake-shock reaching the land, the author shows, is
to be accounted for by a small undulation of the sea, carried,
as it were, upon the back of the earth-wave, and moved along
at its speed, and which he has called the ‘forced sea-wave.”
Such are the usual train of circumstances when the centre of
disturbance is under the sea, accompanied, in addition, by a
sound-wave through the air, when rupture of the crust has
occurred.

When the centre of disturbance is far inland, the “ great
earth-wave” and sound-wave through the solid, with the
sound-wave through the air, and the ‘‘ forced-wave” upon the
shore, are the only ones that can occur.

Dr. Apjohn observed, that Mr. Mallet appeared to him not
only to state very correctly how the onward motion of the
earth’s crust, produced by an earthquake, might cause the
upper stones of a pillar of masonry to be deranged from their
position in the line of such motion, but also to have sug-
gested, for the first time, the true cause of their partial rota-
tion, or displacement in azimuth. In endeavouring, however,
to remove the obvious objection to this explanation, viz., that
the returning movement should restore such disturbed masses
to their original position, he (Dr. Apjohn) could not but think
that Mr. Mallet had introduced speculations as to the mecha-
nism of terrestrial wave-motion, which, though very ingenious,
appeared somewhat far-fetched and obscure, and, unless he
(Dr. Apjohn) was much mistaken, certainly not necessary to the
solution of the difficulty in question. In fact, it is impossible
that the displacement produced by the forward motion could
be undone by the returning stroke, unless upon a hypothesis

189

almost infinitely improbable, viz., that, after the displacement,
what Mr. Mallet calls the centre of adhesion shall have, in rela-
tion to the centre of gravity, such a position, that the moment
of the weight of the displaced masses, referred to the centre
of adhesion, shall have its original value, and tend, at the same
time, to produce a motion of rotation opposite to that which
has already occurred. Now, in order to this, the centre of
adhesion must continue at the same side of the line of direc-
tion of the earthquake-movement passing through thecentre of
gravity of the displaced materials, and we must also have
dxsin 6’=d' x sin 6’, d and d’ being the distance between
centre of gravity and centre of adhesion before and after the
first displacement, and 9 and @’ the angles made by the direc-
tion of earthquake-movement with the lines connecting centre
of gravity with centre of adhesion. It is scarcely necessary
to say, that the fulfilment of such conditions in any particular
case must be in the highest degree improbable.

The Secretary of the Academy read the second part of the
Rev. Dr. Hincks’ paper on Phonetic Hieroglyphics :

The object of the second part is to shew what data are
most to be relied on for determining the exact powers of the
Egyptian letters; the existence of an approximate alphabet is
assumed, and the knowledge of facts grounded on the general
correctness of this is to be applied to determine the exact al-
phabet. Itis remarked, in the first place, that, as the powers of
the letters probably varied at different times and in different
parts of Egypt, it is necessary to assume a particular place
and time, the alphabet of which is to be investigated. The
place chosen is Thebes, and the time the interval between the
deaths of the first and third kings of the name of Rameses,
during which the principal sculptures at Thebes were exe-
cuted, and the papyri in the British Museum, of which fac-
similes have been published, were written. The data which

190

are considered the most valuable are transcriptions of foreign
words occurring in the papyri and on the monuments of this
period; while the words themselves, or transcriptions of them
into Hebrew letters, are preserved in the Hebrew Scriptures,
and in many cases transcriptions into Greek letters are also
met with. As the alphabet, which, we previously found,
was formed from transcriptions of Greek and Roman proper
names into Egyptian characters made in the later ages, so it
is by similar transcription, made in the time and at the place
chosen for a standard, that this alphabet must be corrected and
completed. Transcriptions of Egyptian words into Hebrew
letters are a useful auxiliary to the other kind of transcrip-
tions, especially when they contain the peculiar Hebrew let-
ters which represent sounds unknown to the Greeks. Against
these, however, the objection lies, that they probably repre-
sent the pronunciation of Lower Egypt, which may have dif-
fered from that of Thebes. The transcription of Egyptian
words into Greek characters in Theban papyri of the Ptole-
maic period, and in the names of kings, are also to be taken
into consideration, chiefly, however, to supply the proper
sounds of those letters, the Hebrew representative of which
were ambiguous; the Maronetic points, by which a certain
value was affixed to these letters, being shewn to be of no
authority. In the case of S and SH, where the two sounds
are expressed by the same letters in Greek as well as in
Hebrew, we are compelled to seek a distinction in the Coptic
equivalents of the ancient Egyptian words. It is maintained,
however, that, owing to the Coptic representing the Egyptian
language in its latest form, when many words had been cor-
rupted, it should not be admitted as evidence in opposition to
clear indications of the powers of the letters found in ancient
transcriptions. Interchanges of letters, if habitually made in
texts of the standard period, are admitted to be good evidence
of the identity in power of the letters interchanged. But it is
observed that the number of letters thus exchanged is very

ye

191

limited, and a caution is given against depending too much
on manuscripts, the writers of which were often very careless,
and committed gross mistakes. This is especially the case
with funeral MSS., on which no dependence whatever should
be placed in reference to the present object. An opinion is
expressed that all these MSS. are of a late age, and that the
famous one at Turin, of which Dr. Lepsius has published a
copy, is not earlier than the second century before Christ.
It is shewn, too, that it was transcribed from a hieratic origi-
nal, or from a hieroglyphic one which had been copied from a
hieratic one. At the end of this part suggestions are given as
to the aid which may be derived from the Indo-Germanic
languages in determining the powers of Egyptian characters
in some particular instances. The whole of this part is pre-
paratory to the third, in which the principles laid down here
will be applied to the practical determination of the powers of
the letters.

Mr. Mallet presented his Translation of the Report of the
Institute of France upon M. Arnollet’s System of Atmos-
pheric Railways.

February 23, 1846.
GEORGE PETRIE, Esq., Vice-President, in the Chair.

Thomas Butler, Esq., John T. Evans, M.D., Richard R.
Madden, M.D., Robert C. Williams, M.D., and Henry W.
Massy, Esq., were elected Members of the Academy.

The Secretary of the Council having read to the Academy
the following Resolution of the Council of the 16th of Febru-
ary,

‘¢ That the Council are of opinion, that itis not expedient
that the same person should be elected to the office of Presi-
dent more than five times in succession :”

192

Ivy was Resotvep,— That the Academy do concur in the
preceding opinion expressed by the Council.

Mr. Robert Mallet completed the reading of his paper on
the ‘* Mechanics of Earthquakes.”

The author pointed out the correspondence of his theory
with the actual velocity of earthquake-shocks, so far as these
have been observed, and by numerous quotations shewed how
completely his theory accounts for the complex phenomena
often detailed, and many of which have been heretofore inex-
plicable.

He shewed that an exact knowledge of the velocity of
earthquake-waves passing under the bed of the ocean, would
enable us to ascertain, with considerable certainty, what the
geological formations are, which, constituting this bed, form
more than two-thirds the whole surface of our globe, which
hitherto has been a geological blank. He also indicated the
means of experimentally determining the velocity of waves of
elastic compression in the crust of the earth, and proposed the
establishment of geological observatories, both separate and in
connexion with the magnetic observatories scattered over the
face of the globe, for the purpose of registering and recording
with suitable instruments, all the motions of the water of
earthquake-waves which occur; and he has shewn reason to
believe that these (though so small as to be inappreciable
without the aid of proper instruments) are much more fre-
quent than has been hitherto supposed; in fact, Arago has
actually observed an earthquake-shock at his magnetic obser-
vatory at Paris, which was imperceptible there without the aid
of instruments, and the origin of which lay in the south of
France.

Dr. Lloyd took this occasion to mention that he had fre-
quently observed certain abnormal movements of the magnets
in the Dublin Observatory, which, like that noticed by M.
Arago, and referred to by Mr. Mallet, he was inclined to

193

\

ascribe to earth-tremors, propagated from remote centres of
disturbance. These movements were vertical oscillations of
the magnets, which came on suddenly, and by which all the
instruments were, in general, simultaneously affected. That
they were not due to any sudden change in the direction or
intensity of the magnetic force, is evident from the fact that they
were in general unaccompanied by any changes in the mean
position of the magnetometers, such as would result from a
sudden magnetic disturbance. It appeared equally evident
that they were not the result of any ordinary extraneous dis-
turbing causes, such as currents of air; for, besides that the
instruments are well protected from such influences, they fre-
quently occurred at times of perfect calm, and when there was
no movement within the Observatory. Under these circum-
stances it was difficult to avoid the conclusion that they were
the effects of mechanical movements of the earth’s crust itself,
which were too slight to affect the senses directly. Under
this supposition, Dr. Lloyd stated that he had given instruc-
tions to his assistants to keep a record of these movements ;
and that he was now in possession of a registry of them for the
last two years, the times of which he hoped soon to compare
with those of recorded earthquake-shocks, and thus to estab-
lish or disprove the conjecture respecting their origin which

he entertained.

The Chairman read some extracts from a letter he had
received from Dr. Lappenburg, and presented to the Aca-
demy, on the part of Dr. Lappenburg, of Hamburg, the volume
of the Encyclopedia in which his Essay on Ireland is printed.

DONATIONS.
On some Roman Vestigia, recently found at Kirkley
Shore, in Westmoreland. By Captain W. H. Smith, R.N.,
“&e. Presented by the Author.
Vestiyes of the Natural History of Creation. 5th Edition.
Presented by Anonymous.
Twenty-four Maps of the Geological Survey of Great

194

Britain. From No. 19 to 33, and from 35 to 43, inclusive.
Presented by the Earl of Lincoln, Chief Commissioner of
Woods, Works, and Land Revenues.

Natural History of New York. In 10 vols. 4to, with a
geological Map accompanying each set. Presented by the
Legislature of New York. -

Transactions of the American Philosophical Society, held
at Philadelphia for promoting useful Knowledge. Vol. IX.
New Series. Part 2. Presented by the Society.

Transactions of the historical and literary Committee of
the American Philosophical Society. Vol. III. Part 1. Pre-
sented by the Society.

Proceedings of the American Philosophical Society for
January and April, Mayand August. Presented by the Society.

A Cast in Plaster of the ancient Harp, called Brien
Borws Harp, in the Museum of Trinity College, Dublin.
Presented by the Provost and Senior Fellows.

Two heads of Fossil Elks, found at Castleknock. Pre-
sented by Algernon Preston, Esq.

March 16. (Stated Meeting.)

Sir WILLIAM R. HAMILTON, LL.D., President, in
the Chair.
The following Report from the Council was read and re-
ceived, and ordered to be entered in the Minutes :

During the past year the twentieth volume of the Transactions of
the Academy, containmg Mr. Petrie’s long expected paper on the
Round Towers of Ireland, was published, and delivered to such members
as were entitled to it.

The great beauty of this volume, the laborious and extensive re-
search which it displays, and the approbation with which it has been
received by the public, will, it is hoped, prove ample compensation to the
Academy for the delay that unavoidably took place in its publication.

Although it contains only a portion of Mr. Petrie’s essay, the
Council have recommended, and the recommendation has been adopted

195

by the Academy, that in consideration of its bulk and value, and the
numerous and beautiful wood-cuts which adorn it, the volume be re-
ceived as acquitting Mr. Petrie of his engagement; hut they have de-
clined entering into any further agreement with him, as to the publication
of the remainder of the essay.

# In this resolution the Council have also had the concurrence of the
Academy ; and they may add, that the twentieth volume of the Trans-
actions has been received with such favour by the members, that it was
found necessary to order fifty additional copies, over and above the usual
number which the Academy had originally agreed to take from
Mr. Petrie, in order to meet the demand of those, not otherwise en-
titled to it, who desired to obtain it by purchase.

The twenty-first volume of the Transactions is in progress; four
sheets have been printed off in the department of Science, and eleven in
the department of Polite Literature.

In the publication of the Proceedings much delay and difficulty
have been experienced. Two additional parts, however, are ready, and
are now laid on the table; but they extend only to July of last year,
leaving the proceedings of the present session still in arrear.

One great cause of this delay has been the difficulty of obtaining in
proper time, from those.who read papers before the Academy, the neces-
sary abstracts of such papers. This throws an immensity of unnecessary
labour and trouble upon the Editor of the Proceedings; but the Coun-
cil have now made a rule, which will in a great measure remedy this
evil; and they hope that in future there will be nothing to complain of
on this head.

During the past year a great number of most important and interest-
ing papers have been read before the Academy; and on one occasion
his Excellency the Lord Lieutenant was pleased to honour us with his
presence, when the Rev. Dr. Robinson gave an account of the first
observations made with Lord Rosse’s six-foot reflector.

The Museum has been fitted up in a manner which has given great
satisfaction, and has attracted a great number of visiters to the Academy.

_ An inventory of its contents has also been commenced, on a plan sug-
gested by Mr. Clibborn, and is in progress.

Of the donations to the Museum during the year, may be noticed the
singularly interesting specimen of an ancient Irish waxed wooden tablet

196

presented by the Rev. James Spencer Knox ; the valuable collection of an-
cient Swords, and other antiquities, found in the works of the Dublin and
Cashel Railway, near Kilmainham, presented by Colonel J. Ei. Napier
and the directors of that railway; and the donation of ancient weapons,
by the Shannon Commissioners, which are also of very great interest
and value. The importance of this class of donations, possessing #
peculiar value from their authenticity, can scarcely be too highly estima-
ted; and the Council therefore thought it right to address a circular to
the Directors of the railways new in progress in Ireland, calling their
attention to this subject, and requesting their co-operation with the
Academy in the attempt that has been made to establish here a
public museum of Irish Antiquities.

The increase of our collection of MSS. has made it necessary to
provide for their security; the Council have therefore made rules pre-
scribing the conditions upon which access to the MSS. is to be hence-
forth permitted, with a view to the exclusion of such persons as would
be likely to injure them, or to make an improper or dishonest use of
their contents. Under this head should be noticed the recovery of two
of the missing leaves of the Leabhar Breac, which were presented to
the Academy by Messrs. Hodges and Smith, having been purchased by
them, along with some other volumes in MS. which they have also
presented to our library.*

During the past year friendly communications have been opened
with the Literary and Scientific Society of Toronto, the Irish Society of
London, the Archeological Institute of Great Britain and Ireland, and
the Belfast Library and Society for promoting knowledge.

The Council have now to notice, with regret, the retirement from
the office of President, of the distinguished gentleman who has for the
last eight years presided over the Academy. Sir William Hamilton’s
determination to resign a place whose duties he has so long discharged
with honour to himself and to the Academy, is already well known to
every member; it was communicated to the Council by a letter received
by them on the 17th of November, which contained also a suggestion
that the voluntary resignation of the President afforded a favourable
opportunity for considering, without the infringement of delicacy

* See their letter in the Proceedings, vol. iii. p. 73.

Foy

towards an existing President, the expediency of introducing any rules
of practice with respect to the election of the President, which, in the
judgment of the Council, might seem desirable.

The President being by our charter an annual officer, it is of course
the undoubted right of the Academy to re-elect the same individual as

+ often as they think fit; and with this right, as it is a chartered right,
perhaps not even the Academy itself, could directly interfere. But asa
majority of the Council were in favour of some limitation, the following
resolution was communicated to the Academy, on the 23rd ult. :—

« RESOLVED,—That the Council are of opinion, that it is not
expedient that the same person should be elected to the office of Presi-
dent more than five times in succession.”’

In this opinion the Academy at the same meeting expressed their
concurrence.

During the past year the distinguished name of William W ordsworth
was added to our list of Honorary Members; and forty ordinary members
have been elected during the same period, whose names are as follows :

J. A. Galbraith, Esq.
J. Jameson, Esq.

John F. Waller, Esq.
C. Bournes, Esq.

W. C. Dobbs, Esq.
W. Henn, Esq.

Digby P. Starkey, sq.
B. Wilme, Esq.

J. Clarridge, Esq.
Adolphus Cooke, Esq.
Wyndham Goold, Esq.
C. K. King, M.D.

C. W. Williams, Esq.
James S. Close, Esq.
D. Conolly, Esq.
David Moore, esq.
Rev. Classon Porter,
James Talbot, Esq.
The Earl of Enniskillen.

Rev. John Connell.

John C. Deane, Esq.
Richard Deasy, Esq.
Conyngham Ellis, Esq.
W. Lloyd, M.D.

A. R. Nugent, Esq.

E. K. Tenison, Esq.

F. J. Tyrrell, Esq.

J. Tuffnell, Esq.

Richard Cane, Esq.

R. Franks, Esq.

Charles W. Levinge, Esq.
Pierce Moreton, Esq.
James C. Sherrard, Esq.
Stephen O’Meagher, Esq.
Thomas Butler, Esq.
John T. Evans, M. D.
Richard R. Madden, Esq.
Robert C. Williams, M.D.

The Ven. Henry Cotton, D.C.L. Henry W. Massey, Esq.

198

The painful task now remains of recording the names of those who
have been lost to the Academy during the past yearby death; amongst
them will be found two of the oldest Members of the Academy:
Dr. Whitley Stokes, elected a Member in 1787; and the Hon, Justice
Johnston, who was elected a Member in 1790.

Of Dr. Stokes, whose distinguished career is so well known, it will .

be unnecessary to say much. The philanthropic and practical objects
to which his useful life was devoted, left him but little time for purely
literary or scientific pursuits, and consequently his nme oceurs but
seldom in the Minutes of the Proceedings of this Academy. But the
Council cannot permit that name to pass away from the list of Members
of the Academy, without expressing their respect for the memory of
one to whose zeal and energy‘is very mainly to be attributed the
present flourishing and progressing state of the practical sciences of
Botany, Mineralogy, Geology, and Zoology, in Dublin and in the
University.*

We have also lost our late excellent and active Treasurer,
Dr. Thomas Herbert Orpen, whose useful life was passed inthe constant
discharge of those benevolent virtues which leave little of incident to be
recorded in a biographical notice. He commenced practice as a physician
in Dublin, in 1803, about which period he took the regular medical
degrees in the University, having previously studied at Edinburgh; and
the charitable institutions of Dublin engaged a great portion of his time
and attention. For a great part of his life he kept a diary of the
weather, noting the heights of the barometer and thermometer, and the
direction and intensity of the wind, twice every day. These observa-
tions, which extend through a period of thirty-five years, are now in the
Academy’s library.

The names of the remaining deceased Members, with the dates of

their elections, are as follows:—

1816, George Kiernan, Esq.
1824, Hugh Ferguson, M. D.
1829, John Houston, M.B.
1836, Thomas Arthur, Esq.

* A brief Memoir of Dr. Stokes has appeared in the Dublin University
Magazine, for August, 1845.

_—e a

199

1844, The Most Noble the Marquis of Downshire.
1845, Robert S. Bradshaw, Esq.
» Thomas Davis, Esq.
» Sir Richard Franklin,
There are therefore now on the books of the Academy, 162 life
Members, and 203 annual Members.

The President delivered the following Address :

. “My Lorps anp GENTLEMEN OF THE Royat Iris ACADEMY,—
Although it is, I believe, well known to most, perhaps to all, of you,
that it has been for a considerable time my wish and intention to retire
this evening from the Chair to which, in 1837, your kindness called me,
on the still lamented event of the death of my distinguished predecessor,
the late admirable Doctor Lloyd, and in which your continuing confi-
dence has since replaced me on eight successive occasions, yet a few
parting words from me may be allowed, perhaps expected; and I
should wish to offer them, were it only to guard against the possibility
of any one’s supposing that I look upon my thus retiring from your
Chair as a step unimportant to myself, or as one which might be taken
by me with indifference, or without deliberation. It was under no
hasty impulse that I resolved to retire from the office of your President
into the ranks of your private members, nor was it lightly that I deter-
mined to lay down the highest honour of my life.

“« My reasons have been stated in an Address delivered in another
place, at a meeting of some members of your body. They are, briefly,
these: that after the expiration of several years, I have found the duties of
the office press too heavily upon my energies, indeed, of late, upon my
health, when combined with other duties; and that I have felt the anxieties
of a concentrated responsibility—exaggerated, perhaps, by an ardent or
excitable temperament—tend more to distract my thoughts from the calm
pursuits of study, than I can judge to be desirable or right in itself, or
consistent with the full redeeming of those pledges which I may be con-
sidered to have long since given, as an early Contributor to your
Transactions.

“ When I look back on the aspirations with which first I entered

VOL. II. R

200

on that office from which I am now about to retire, it humbles me to
reflect how far short I have come of realizing my own ideal; but it
cheers me to remember how greatly beyond what I could then have
ventured to anticipate, the Academy itself has flourished. Of this result
I may speak with little fear, because little is attributable to myself.
Gladly do I acknowledge that it has been my good fortune, rather than
my merit, to have presided over your body during a period in which,
through the exertions of others much more than through my own
(though mine, too, have not been withheld), the Academy is generally
felt to have prospered in all its departments. The original papers
which have been read; the volumes of Transactions which have been
published; the closer communication which has been established with
kindred societies of our own and of foreign countries; the enhanced
value of our Library and Museum, which have been, at least, as much
enriched in the quality as in the quantity of their contents; the improved
state (as it is represented to me) of our finances, combined with an
increased strength of our claims on public and parliamentary support ;
the heightened interest of members and visiters in our meetings, which
have been honoured on four occasions, during my presidency, by the pre-
sence of representatives of Royalty; even the convenience and appropriate
adornment of the rooms in which we assemble ;—all these are things, and
others might be named, in which, however small may have been the
share of him who now addresses you, the progress of the Academy has
not been small, and of which the recollection tends to console one who
may, at least, be allowed to call himself an attached member of the
body, under the sense, very deeply felt by him, of his own personal
and official deficiencies.

“« Whoever may be the member elected by your suffrages, this
evening, to occupy that important and honourable post which I am now
about to resign, it will, of course, become my duty to give to that future
President my faithful and cordial support, by any means within the
compass of my humble power. But if it be true, as J collect it to be,
that your unanimous choice will fall upon the very member whom, out
of all others, I should have myself selected, if it could have been mine
to make the selection—with whom J have been long connected by the
closest ties of college friendship, strengthened by the earnest sympathy

201

which we have felt in our aspirations for the welfare of this Academy
which has already benefited by his exertions in many and important
ways—then will that course, which would have been in any event my
duty, be in an eminent degree my pleasure also.

“« And now, my Lords and Gentlemen, understanding that an old
and respected member is prepared to propose for your votes, as my
successor, the friend to whom I have ventured to allude—very inade-
quately, as regards my opinion of his merits, yet, perhaps, more pointedly
than his modesty will entirely forgive or approve of,—I shall detain you
no longer from that stage of the proceedings of the evening which must
be the most interesting to all of us, but shall conclude these words of
farewell from this Chair, by expressing a hope that my future exertions,
though in a less conspicuous position, shall manifest, at least in some
degree, that grateful and affectionate sense which I must ever retain of
the constant confidence and favour which you have, at all times, shewn

towards me.”

Reso_vep,—That the thanks of the Academy be given
to Sir William R. Hamilton, and that the Academy desire to
express their entire sense of the value of his services as Presi-
dent, of his high and impartial bearing in the Chair, and of his
untiring efforts to advance the interests of the body ; and they
also wish to record their satisfaction that he has determined to
remain in the Council of the Academy.

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—Rev. Humphrey Lloyd, D.D.

Treasurer—Robert Ball, Esq.

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

Clerk and Assistant Librarian—Edward Clibborn.

Committee of Science.

Rev. Frane Sadleir, D.D., Provost; James Apjohn,
M.D.; James Mac Cullagh, LL.D.; Robert Ball, Esq. ;
R 2

202

Sir Robert Kane, M.D.; G. J. Allman, M.B.; Sir William
R. Hamilton, LL. D.

Committee of Polite Literature.

Samuel Litton, M.D.; Rev. William H. Drummond,
D.D.; Rev. Charles W. Wall, D.D.; John Anster, LL.D. ;
Rev. Charles Graves, A. M.; Rev. Samuel Butcher, A. M.,
F.T.C.D.; Rev. James Wilson, D. D.

Committee of Antiquities.

George Petrie, Esq., R.H.A.; Rev. James H. Todd,
D.D.; Henry J. Monck Mason, LL.D.; J. Huband Smith,
A.M.; Captain Larcom, R.E.; William R. Wilde, Esq.;
F. W. Burton, Esq., R. H. A.

DONATIONS.

_ Journal of the Asiatic Society, Nos. 69, 70, 72, 73, 14,
77. New Series. Presented by the Society.
Journal of the Royal Asiatic Society of Great Britain
and Ireland. No.26. Part II. Presented by the Society.
Observations des Phenomeénes periodiques de l Academie
Royale des Bruxelles. Extrait du Tome X VIII. des Memoirs.
Resume des Observations magnetiques et meteorologiques faites
a des Epoques determinées. Academie Royal de Bruzelles.
Extrait du Tome XVIII. des Memoirs. Presented by the
Academy.
Annales de L’ Observatoire Royal de Bruxelles. Tome
IV. By A. Quetelet. Presented by the Academy.
Nouveau Memoires de Academie Royale des Sciences et
Belles Letters du Bruxelles. Tome XVII., 1844, et Tome
XVIII., 1845. Memoires Couronnés et Memoires des Sa-
vants Etrangers par 0 Academie Royale des Sciences et Belles
Lettres de Bruxelles. Tome X XII.,:1844, et Tome X XIII.,
1845. Presented by the Academy.

203

Bulletin de la Sceance du 5 October, 1844, No. 9,
Tome XI.; 2nd Nov., 1844, No. 10, Tome XI.; 15th Dec.
and 30th Dec., Nos. 11 and 12, Tome XI.; No. 1, 11th
Jan., 1845; No.2, Ist Feb., 1845; No. 3, lst March, 1845;
No. 6, 7th June, 1845,-Tome XII. Presented by the Aca-
demy.

Annuaire de 1 Academie Royale des Sciences et Belles
Lettres de Bruxelles. Onzieme Annuare, 1845. Presented by
the Academy.

Memoir of Simon Stevin. By A. Quetelet. Presented
by the Author.

Catalogue of Stars of the British Association for the Ad-
vancement of Science. Presented by the Association.

Flora Batava. Nos. 139 and 140. Presented by the
King of Holland.

Geological Map of the State of New York. By Legis-
lative Authority. Presented by the State of New York.

13th April, 1846.
Rev. HUMPHREY LLOYD, D.D., President, in the
Chair.

John Alcorn, Esq., Abraham W. Baker, Esq., Philip
Bevan, M.D., John Oliver Curran, M.B., Matthew D’ Arey,
Esq., James Birch Kennedy, Esq., Michael H. Stapleton,
M.B., and the Hon. and Rey. William Wingfield, were
elected Members of the Academy.

The President, on taking the Chair, delivered the follow-
ing Inaugural Address:

“ GENTLEMEN,—My first—my most urgent duty—on this, to me
most solemn occasion, is to thank you for the high distinction you
have conferred. It would be idle to attempt to express how highly I
esteem the honour: the thought that I had been deemed worthy to

204

occupy the chair which has been filled by Kirwan, by Brinkley, and by
Hamilton, might indeed well nigh overwhelm me, did I not know that
there were other merits, more humble than theirs, upon which you set a
value—other qualities less dazzling, which may find here their employ-
ment and their use. Aninstitution such as this has been compared to the
House of Solomon, in Bacon’s philosophical fiction, the New Atlantis,
in which the investigation of Truth is carried on by labourers of various
kinds, to each of which he has assigned a separate task. We have had,
m this Academy, the representatives of each of these classes: we,
too, have had our ‘Miners,’ our ‘ Lamps,’ and our ‘Interpreters of
Nature.’ I am content to enrol myself in the lowest class; or if, by
reason of the high trust which you have now reposed in me, other tasks
should fall to my lot, I am proud to accept a new station among the
Intellectual Workmen, and to perform the part of one whose office
it is to harmonize and give effect to the labours of all.

“‘ There is another personal consideration, to which I cannot refrain
from alluding ; and yet it is one upon which IJ hardly trust myself to
speak. Among my predecessors in this high office, was one whom
Tam still more proud to follow :—my nearest relative filled this chair. I
know how he was valued here; and I cannot but feel that much of
the indulgent estimation which you have formed of my fitness for the
same station, has come to me reflected from his memory, and that you
hope to find in the son some of these qualities for which the father
was loved and honoured.

“ But, Gentlemen, whatever qualifications I may want, there is one
to which I lay claim: I mean that of deep interest in the welfare of
this Body, and zeal for its service. Here I will yield to none; and I
console myself with the hope that it may make some amends in your
estimation for the many wants which you will hereafter have occasion
to observe.

“GENTLEMEN,—My predecessor in this chair, upon an occasion
similar to the present, laid before you some of his views respecting the
constitution of the Academy, and the means by which its future interests
might be promoted. I am sure that you will permit me to follow this ,
precedent, and to offer a few remarks—/irsily, upon the mixed nature

205

of that constitution under which we are here united for the Pursuit of
Truth,—and, secondly, upon the progress that has been made, or that
may hereafter be made, in that high object of our incorporation. It
is of the fudure that it is important to speak : the precept

< Te, peev omiow extdavbcevopeevos, Tors Oe gumgorbey emexresvapesvas”

holds good in the pursuit of knowledge, no less than in the advance in
piety. But still our hopes of the Future, if they are to be more than
dreamy visions, must be based upon the history of the Past.

“The first thing that must strike every one, in considering the con-
stitution of this Academy, is the comprehensiveness of its scheme, and
the wide scope of its labours; and we are inclined to ask, whether a con-
stitution so large and so varied,—so opposed to modern precedent,—can
be sound and healthful ? When we look into the recent history of Asso-
ciations for the advancement of knowledge, we see that each division of
the wide domain of truth, as it has arisen into prominent view, by the
labours of those engaged in its cultivation, has claimed for itself the
concentrated energy, and the undivided resources, of an exclusive
Society. In this manner the Royal Society of London, which included
originally, and still includes, representatives. from every department of
Philosophy, has seen Society after Society spring up, manned by its
own Members, and claiming to perform, in a more complete and
effective manner, the separated portions of its work.

“ Such a state of things is the natural result of increased acti-
vity in any department, and of the consequent demand which it makes
of a larger portion of time, and of the other appliances of labour, than can
be devoted to it in a body of mixed constitution and more comprehensive
plan. Nor can it be doubted that such a multiplication of the instru-
ments, by which Intellectual Force is concentrated and applied, is
attended with the many advantages which arise from the divéston of
labour, or that it has actually tended, and in a very important degree,
to push forward and to extend the boundary which divides the known
from the unknown.

“But perhaps these advantages, great as they are, have not been
wholly unbalanced. Have we not reason to apprehend that Phz/oso-
phy has suffered, while the portions of her mighty empire have asserted
their independence, and erected themselves into separate kingdoms ?

206

So far as we insulate any portion of Truth from the rest, by an exclu-
sive devotion to its pursuit (and there can be no doubt that such exclu-
siveness tends to insulation,) so far we mutilate the fair proportions of
Truth itself, and injure and impair the Philosophie Spirit, whose vital
power should animate and pervade the whole. And the injury, great
as it is, does not end here. There is an evil partaking of a Moral nature
obviously springing from this exclusiveness, and which unhappily we see
too often realized, unless where some counteracting power is brought
in to check it. I mean its effect in narrowing our views, in rendering
us bigots in Philosophy, and in causing us to undervalue that which we
do not understand. x

“ Now, the mixed constitution of our Society has a manifest ten-
dency to overcome, or, at least, to mitigate, these evils. I do not mean
to say that these evils, and these means of combatting them, were dis-
tinctly perceived by the first founders of this Body. It is an humbling
lesson, that Human Institutions, in which we have learned to find
wisdom, have often had their origin in circumstance, and their growth
amid the adjustments of conflicting interests. The plan of this
Academy took its rise, I believe, in the union of two small Societies, eall-
ing themselves the Palwosophers and the Neosophers, starting originally
from opposite extremities of the field of Truth. But, whatever may have
been its origin, we may now derive from it lessons not only of mutual
forbearance, but of mutual instruction. The Mathematician may imbibe
from the Antiquarian the taste which will lead him to explore, with reve-
rence, the early history of the efforts of those master-minds in Science,
whose very failures are fraught with philosophic interest, and to trace
the progress of discovery up to the first dawn of thought; and he will
return from the investigation with clearer views of the Human Mind
itself, and of the means by which it attains Truth. The Antiquarian
may Jearn from the man of Science those habits of precise thought, and
exact reasoning, which, in the mysterious twilight that surrounds the
fascinating objects of his pursuit, he is apt to think inapplicable; and
both may learn from the cultivator of Literature to value and to acquire
that magic power which Language confers upon Thought.

“‘ Having said thus much in vindication of the constitution of the
Academy, suffer me, in the next place, to consider how far it has been

207

effective in attaining the ends proposed. For this purpose, it will be
requisite to take a brief survey of the recent advancement of knowledge
in this country, so far as it has been influenced by this Academy. And
if, in the brevity with which the necessary limits of this Address compel
me to glance over the subject, I should appear to have overlooked, or
not to have assigned its due weight to any portion of our labours, you
will, I trust, attribute this to its true cause.

«The prominent place which the Mathematical Sciences have occu-
pied in our Transactions, may be dated from the time when Brinkley
was enrolled amongst our Members. But it is to the labours of your
late President, and your late Secretary, in this department, that the
Academy, in a great measure, owes the high place which it holds
among the Scientific Bodies of Europe. Of these labours, it might,
perhaps, be rash to single out any portion as preeminent, had not the
Academy itself, and the Royal Society of London, by the awards of
their highest honours, marked out the researches of Sir William Hamil-
ton, and Professor Mac Cullagh, in connexion with the wave-theory of
light, as of especial value. The theoretical discovery of Conical
Refraction, by Sir William Hamilton, the theory of Crystalline Re-
flexion and Refraction, by Professor Mac Cullagh, and the general
Dynamical Theory of Light by the same author, mark an era in this
branch of science not inferior to that of Fresnel.

“Time will not permit me to do more than allude to the new
branch of Analysis, which has recently engaged so much of the atten-
tion of Mathematicians, and which originated in the Theory of Qua-
ternions of Sir William Hamilton, and has received an important
modification and development in the Triplet theory of Professor
Graves. Asa member of the University, I rejoice to be able to add,
that worthy successors, even to such men as I have named, are arising
there ; and that the recent union of the mathematical strength of Cam-
bridge and of Dublin, in the Mathematical Journal which was so
long and so ably supported by the former University, is likely to give a
new impulse to this branch of science amongst us. And long may
these scienees continue to flourish in the University and in this Academy!
Independently of the magnitude and sublimity of their own proper
objects,—independently of their direct value in Physical Science, as

208

instruments of research,—they confer a no less important, but indirect
service, in disciplining the Mind, and correcting those tendencies of
other portions of our mental constitution, which, when unbalanced, are
sure to mislead.

“Turning from the Mathematical to the Physical Sciences,—and first
of all to Astronomy, which stands upon the confines of both,—we
cannot fail to be struck by the fact, that in this one Island, with
all its disadvantages of climate, there are no fewer than four Astro-
nomical Observatories, each claiming a high place in the history of
European Science; and that while, in other countries, these costly
institutions have been, with but few exceptions, founded and endowed
by their respective Governments, in Ireland (a country not certainly
among the foremost in pecuniary resources) they have been erected,
equipped, and, with but one partial exception, maintained by the
munificence and public spirit of Individuals. The names of Mr.
Cooper, and of the Earl of Rosse, will henceforward be added to those
of Provost Andrews and Primate Robinson, as benefactors. of science
in this country; and Markree and Birr be united to Armagh and Dub-
lin in the future history of Astronomy.

“The Dublin Observatory is the eldest of this noble sisterhood.
As respects its connexion with this Academy, I need not remind you
that its chair has been filled by two of your Presidents. With the
labours of Brinkley the Dublin Observatory will always stand con-
nected in the history of Science. I am sure that it is unnecessary for me
to remind you of his researches connected with the problem of the
“Stellar Parallax,’ of which your Transactions contain the first results—
that great problem, whose final solution has at length been placed beyond
question by the observations of Bessel. Of the other and better known
énequalities, which affect the apparent places of the stars, all have been
illustrated by the observations made with the Meridional Circle of the
Dublin Observatory. In this important class of astronomical inves-
tigations, the able Director of the Armagh Observatory has had a dis-
tinguished share; and the labours of Dr. Robinson have conferred, as
might have been expected, increased accuracy upon the resulting
values of the Constants.

“ And here, Gentlemen, you will permit me to pause for a moment,

209

and, having named the name of Bessel, to offer a passing tribute to his
memory. He, who but afew months since occupied the foremost place
in the ranks of living Astronomers, is now no more! He died on the
day which followed the last meeting and Anniversary of this Body; and
those among us who had the happiness to form his acquaintance, during
his short visit to England, and to the British Association, four years
ago, will be able to sympathize with his personal friends, no less than
with the world of science, in deploring his loss.

‘‘ Of the Astronomical and Optical labours of the Earl of Rosse, and
of his great reflector—the marvel of astronomical science—it is needless
for me to speak. No one who was present when the account of its con-
struction, and of its first achievements, was given in this room by Dr.
Robinson, can readily forget it; and for others, the printed notice of
that aecount, in the last Number of our Proceedings, will give the fullest
information we yet possess respecting it. Even from this statement of
its earliest trials, it is manifest that the astronomical history of the
nebule will, ere long, be re-made; and it must be satisfactory to us
to know, that the noble artist has arranged a plan of systematic obser-
vation, directed to these remote and mysterious portions of the universe,
which promises to reveal all that can be known, until a still higher
optical power (if such be practically possible) shall be applied to their
examination. The imagination is bewildered when it seeks to grasp
the possible future, which may be opened to this and other depart-
ments of Astronomical Science by the application of such means: I
will mention but one amongst the many anticipations which press for
utterance. The observations of Bessel have detected proper motions
in the fixed stars, Siréws and Procyon, which appear to establish the ©
existence of invisible companions, of vast magnitude, about which
they revolve. Is the invisibility of these great bodies relative only?
and if so, may it not be dispelled before the optical power which Lord
Rosse has brought to bear upon the Heavens ?

“¢ Astronomy, however,’ to use the words of one whose philosophic
mind, and varied and profound acquirements, well entitle him to
legislate for science, ‘is only one out of many sciences, which can be
advanced by a combined system of observation and calculation, car-

* * #

ried on uninterruptedly. * * * * ina utilitarian point

210

of view, the Globe which we inhabit is quite as important a subject of
scientific inquiry as the Stars. We depend for our bread of life, and
every comfort, on its climates and seasons, on the movements of its
winds and waters. We guide ourselves over the ocean, when Astrono-
mical observations fail, by our knowledge of the laws of its Magnetism;
we learn the sublimest lessons from the records of its Geological history ;
and the great facts which its figure, magnitude, and attraction offer to
mathematical inquiry, form the very basis of Astronomy itself. ‘Terres-
trial Physics, therefore, form a subject every way worthy to be associ-
ated with Astronomy as a matter of universal interest and public
support, and one which cannot adequately be studied except in the
way in which Astronomy itself has been—by permanent establishments
keeping up an unbroken series of observation.’

“ T'wo of the leading branches of Terrestrial Physics—the sciences of
Meteorology and Magnetism—have now, as you know, for the last six
years, been investigated after one uniform and comprehensive scheme,
in more than thirty observing stations scattered over the entire globe ;
-and the very bounds of civilization itself have been overleaped in order
to give a wider development to the system. In order to realize the view
which Sir John Herschel has so often and so ably advocated, it is only
necessary to give permanence to the more important of these Observa-
tories, and to enlarge somewhat their sphere of labour. All the phe-
nomena of which our Earth, its Ocean, or its Atmosphere, is the seat;
the Tides and the Oceanic Currents, no less than the Winds ;_ the tem-
perature of the Earth and of the Sea, as well as that of the Air; the
movements of the earth’s crust, whether calm or convulsive, no less than
the changes of the mysterious power which animates and pervades its
mass ; all these, and more which might be easily added, are the proper
subjects for continued and systematic observation. We have arrived
‘at a period in the history of these branches of science, when the more
obvious phenomena have revealed themselves to our desultory efforts,
and when the precise laws, and the quantitative measurements, which
must form the basis of exact theory, can be reached only by sustained
and systematic exertion.

“In these researches, no less than in those of Astronomy, this country
has taken its part. The Meteorological Observatory at the Ordnance

211

Survey office in the Phoenix Park, planned and directed by Captain
Larcom, has now been upwards of ten years in active operation,
and may be taken as a model for similar establishments. Of the Mag-
netical and Meteorological Observatory of Dublin, founded in the year
1838 by the University, I have already had frequent occasion to speak
at these meetings, and I hope before long to communicate some of the
ultimate results.

“ Of the Geology of Ireland I have, perhaps, less right to speak, as
the subject-has been appropriated by another and a younger Society,
Yet there are two facts in its recent history of such importance, that it is
impossible not to refer to them in noticing the labours of the members of
this Academy. Imean the completion of the Geological Map of Ireland
by Mr. Griffith, which, as the work of one man, is certainly one of ex-
traordinary merit; and the recent arrangements for the continuation of
ihe Geological Survey of this country, the first fruits of which are before
the world in Captain Portlock’s able and elaborate Report on the
Geology of Londonderry. .

« Passing now from the sciences of Odservation to those of Experi-
ment, we here also meet with labourers of our own Body, and our
Transactions are enriched with the results of their successful toil. Here
are to he found the hygrometric researches of Dr. Apjohn, which have
solved one of the most intricate problems in Meteorology ; and the still
more refined researches of the same author upon the Specific Heats of
the Gases, to which you have awarded your medal. Here too are to be
found most of the Chemical researches of Sir Robert Kane, upon the
chief of which you have conferred a similar reward ; and to this body
were communicated the first investigations of Dr. Andrews, upon the
Heat developed in Chemical Combination, which have recently been
honoured with the Royal Medal.

«To remind you of the progress which Natural History has made,
and is yet likely to make in this country, I have only to mention the names
of Ball, of Thompson, of Mackay, and Harvey, and Allman, whose con-
tributions to the history of the Fauna and the Flora of Ireland are too
well known to need any comment here. The researches of Dr. Har-
vey, indeed, have embraced a wider range; and his latest work, the
Phycologia Brittanica, now in course of publication, cannot fail to

212

sustain his high character as a descriptive botanist. As a member of
the University, I rejoice to be able to add that, of the distinguished
Naturalists just mentioned, four are now connected with her teaching ;
and that a large portion of the plan contemplated by her late head, with
reference to the advancement of these branches of science within her
walls, has now been realized.

“The contributions to the department of Polite Literature, which in
the early volumes of our Transactions occupied a large and conspicuous
place, have, I regret to say, been of late years less numerous. To what-
ever cause this may be ascribed, we are the more indebted to such men
as Dr. Wall, Dr. Hincks, and Dr. Kennedy Bailie, who have enriched
our volumes with the results of their learning and their research. But
it would not be difficult to name others, fellow-countrymen and fellow-
members, who are qualified to share with them the honour and the
toil. The latest communication that we have received in this department,
—the paper by Dr. Hincks upon Egyptian Hieroglyphics, the first part of
which was recently read,—promises to throw much light upon the deci-
phering of these ancient and mysterious records, and, if the author be
right in his theory, to add considerably to the discoveries of Young and
Champollion.

“The study of Antiquities, on the other hand,—and especially of the
Antiquities of Ireland,—has never been, and, I hope, never will be, out
of fashion here. From the time of Molyneux, and of the Dublin Philoso-
phical Society, the earliest of the learned Societies in Ireland from which
we can trace our descent, the pursuit of Irish Antiquities has been a
favourite one. Of the researches of our living Antiquaries, the most
conspicuous, undoubtedly, is the important work of Mr. Petrie, on
the Ecclesiastical Architecture of Ireland, which has been referred to
in the recent Report of your Council, and which forms, as you know, the
last volume of your Transactions. Of the value of that work we should
Judge inadequately, were we to confine our view to the light which it
has thrown upon the subject discussed; it is, perhaps, still more
valuable as an example of the mode of dealing with Antiquarian
questions, and of the evidences which may be brought to bear in their
investigation.

“The study of Irish Antiquities will, there can be no doubt, receive

213

both aid and impul sefrom the institution of your Museum, a collection
well worthy of this Academy, and of this Country. It may be rash_in
one wholly unacquainted with the subject, as lam, to offer any suggestion
respecting it; yet I cannot but think that much more may be done, in
advancing our knowledge of Antiquities generally, and especially of that
higher department of it which borders so closely upon History,—the dis-
tribution of the early races of mankind,—by the comparison of our own
Monuments, and other relics of early civilization, with those of other coun-
tries. ‘The information we gather from a Cairn, a Torque, or a Spear-
head, will thenno longer be limited to the light which they may throw upon
the arts and mannersof our Celtic ancestors. We may obtain from them a
knowledge of the geographical distribution of their various tribes, much
in the same manner as the geologist recognizes the fragments of one of
the great formations which compose the earth’s crust by the comparison
of their imbedded fossils; —we may approach the history of their families,
and trace them up to the parent stock. Studied with this reference,
Antiquities may, perhaps in an important degree, tend to advance the
science of Ethnology; and be combined with the study of Language,
and of Physiological characters, as a new instrument in its research.

“ GENTLEMEN,—I fear I have already trespassed too long upon
your time. But I desire, before I conclude, to offer a few remarks
upon the future advancement of the objects of the Academy, and upon
some of the modes by which it may be accelerated.

“The first and chief of these, beyond all question, is rapzd publica-
tion. It is not to be expected that men, who find a reward for their
toils in the sympathy with which they are hailed by those engaged
elsewhere in the same pursuits—it is not to be expected that they will
communicate to us the fruits of those toils, if they should be long with-
held from public view. Already there are indications that researches,
which should naturally find their place in our Transactions, are about to
reach the public through other channels. I.trust that this evil may be
stayed. The injury that it inflicts is not merely the loss of so much
that should add to our credit and our character as a public body, but
this very loss itself reacts upon, and augments the evil from which it has
sprung. Nor is it necessary for me to urge, that publication is the first,—
the main and essential duty of such a body as ours. No matter what

214

may be the interest of our Meetings,—no matter how far the study of
Science, Literature, or Antiquities, may be aided by our Library and our
Museum,—it is by our published works that we shall be judged, and
by which we must stand or fall. Ihave only to add, that your
Council are duly impressed with this feeling; and that your Officers are
at present engaged in the consideration of some measures, which
promise to give not only a speedy, but also an increased publicity to
our Proceedings. ,

« Another instrument of progress, to whose efficacy I'will advert,
and which this Academy may, I think, effectively wield, is the dérecting
power which it may reasonably assume, in pointing out to its Members
problems of local interest remaining to be solved, and encouraging
them to the task by the proposal of Honorary Rewards. The practice of
proposing subjects for investigation, and of honouring them by Prizes,
has existed, you must be aware, from the very origin of the Academy ;
and it has tended to elicit researches of considerable interest and value.
Some years since, indeed, it was generally felt that the system had failed;
and that opinion (in which at the time I shared) led to an alteration
in the system of honorary rewards, with which you are of course
acquainted. It may be doubted, however, whether this failure was the
necessary result of the system itself, and not rather of the nature of
some of the topics selected and proposed. It must be manifest, I think,
that no encouragement which such a Society as this can bestow, will be
likely to stimulate a man of genius to the investigation of an. abstruse
question, to which he feels no predisposing movement,—that no Reward
can usurp the place of Inspiration itself. But there are problems of a
different stamp, whose solutions may be expected as the certain result
of well-directed labour; to such problems as these, especially when their
local character invests them with additional interest, and in some
degree prepares men’s minds for the research,—to such problems the
recommendation of a learned Society may, with full assurance of the
result, direct the attention of its Members. We know how much our
knowledge of the Antiquities of this country has benefited by the pro-
posal of such questions. Allow me to suggest one or two of a similar
‘character connected with Physical science, as examples of what may
be done in other departments. oils

215

“Tn an interesting paper recently printed in the Philosophical
Magazine, Colonel Sabine has suggested that the almost unparalleled
mildness of the late winter may possibly be explained by an unusual
extension of the Gulf-stream, bathing the shores of these Islands, and
carrying with it a portion of the high temperature of the tropical
region from which it flows. And the probability of this explanation has
been augmented by the fact, that in the winter of 1821-2, a winter in
many respects resembling the last, this great oceanic current, whose
force is usually spent when it reaches the Azores, was actually observed in
the neighbourhood of our shores. I have long speculated upon the proba-
ble influence of the Gulf-stream upon the Irish winters generally, which
appear to be much milder, in comparison with those of England, than can
be well accounted for upon the principles of insular climate alone ;
and I was glad to see, from Colonel Sabine’s paper, that my conjectures
had some real foundation. Whether or not they will account for the
fact, may, I think, be easily tested by a series of observations of the
temperature of the sea on the Hastern and Western coasts of the Island,
and under the same parallel ; and I cannot but think that such a result,
throwing so great a light upon the Climatology of this country, would,
if established, well reward the labour bestowed in the investigation.

“The Climate of Ireland, indeed, engaged a large share of the
attention of the Academy during the life-time of Kirwan; and several
papers on the subject, by himself and others, are to be found in the early
volumes of our Transactions. Should the Royal Irish Academy, as I
think it ought, take that subject again under its peculiar care, the
knowledge of it might be extended and improved, by the observation of
the times of the leafing and flowering of certain plants, after the plan
suggested and carried out by M. Quetelet of Brussells, and now
extensively followed in many parts of Europe. Such observations fur-
nish us with a simple but admirable measure of the otal effects of all
the influential causes in their combination and union.

“ Another subject of special inquiry, which might be fitly urged by
‘this Society, is the History of the Tides on the coasts of Ireland. On
this subject much has been already done; but probably much yet
remains to be accomplished. Of the observations made in the sum-
mer of 1842, by the non-commissioned officers of the Ordnance Survey,

VOL, III. s

216

under the direction of Colonel Colby, Mr. Airy, by whom they
have been ably discussed in a paper recently printed in the Phzloso-
phical Transactions, observes, that ‘extent of time alone appears
wanting to render them the most important series of tide-observations
that has ever been made.’ Among the results to which Mr. Airy has
arrived, is the remarkable one, that in the harbour of Courtown, on the
coast of Wexford—‘ the only place on the earth in which such a result
has been distinctly obtained,’—the Solar Tide exceeds the Lunar.
Such a result as this, affords not only encouragement to fresh exertion,
but also direction as to its application.

“Another, and most interesting subject of research, which this
Academy might direct, if not undertake, is that to which attention has
been recently drawn by Mr. Mallet,—the movements of the Earth’s
crust, whether convulsive and paroxysmal, or gentle and regular. The
phenomena of Earthquake shocks in Scotland have been systematically
observed for the last five years, at the instance of the British Association,
and yearly reports of the results have been made, and published in its
Proceedings. Although there appears to be nothing in this country
analogous to the local movements at Comrie, in Perthshire, still there is
no doubt that Earthquake shocks have been fé/¢t here; and that more
refined methods of observation would detect numberless others, which
wholly escape the cognizance of the unaided senses.

‘These, and many other investigations, connected with the Physical,
the Physiological, and the Monumental history of Ireland, appear to be
fitting subjects, if not for the direct labours of this Academy, at least
for its encouragement. Science has a right to demand such histories of
local phenomena from the representatives of Science in each portion of
the civilized globe, and shall this Academy be deaf to the call?

“‘ GENTLEMEN,—I have, at the outset of these remarks, noticed
the moral, as well as the intellectual benefits, which result from the
union of different mental powers, such as this Academy presents,
combined in the investigation of different portions of Truth. But
there is a yet higher principle, to which this union may lead us—a yet
holier temper which it may inculcate; I mean the contemplation of
Truth itself as essentially ONE, under its many and diversified forms,
and the habit of tracing all its varied and refracted rays to its One

217

and Kternal Source. Strengthened by this high thought,—our feel-
ings raised and spiritualized by this habit,—there is no danger that
we shall give place to the weak apprehension (which is but a subtle
form of unbelief itself), that any portion of Truth can ever prove
inconsistent with any other. And the same principle, while it saves us
from slavish fear, will also guard us from presumption. Standing in
thepresence of confessed and established truth, we shall feel that we
are treading upon holy ground; and we shall demean ourselves, not
with the elation and pride of conquest, but with the devotion of wor-
ship and of love.”’

Ir was REesotvep,—That the President be requested to
permit his Address to be printed in the Proceedings of the
Academy.

The Rev. Charles Graves read a paper by Mr. George
Boole, of Lincoln, on a Certain Definite Multiple Integral.

It has for some time been known that the evolution of
definite multiple integrals can, in many cases, be effected by
the employment of discontinuous functions. In illustration
of this fact, the author notices the researches of M. Lejeune
Dirichlet, founded on the properties of the discontinuous in-

tegral ‘a “emgenre, and those of Mr. Ellis based on
0

Fourier’s theorem. In his own investigations he employs the
formula of triple integration,

f@) = 3 fu \ { dadv dw cos (ce —x)v—twt+ ns) w"—! f(a),

tt aT(n)

by the aid of which he deduces the value of the multiple defi-
nite integral,
vaf.. de, dty..dinf Gat zat + fa)

the limits of the integrations being given by the condition

218 ©

ee eee
The result of his me is
nee unin
i—"hhy..haw? = (=) S(e)

Ee ey t Og aly, Ree Synsnaceatus

oe ge §(s+h,) (s+hz”) ..(s$hn)}”
in which

An?
enim ee eS pe

and f(c) is a discontinuous function, which is supposed to
vanish when o Z 1.

As particular examples of this result, the author deduces
the attraction of an ellipsoid on an external or internal point,
when the force varies as the inverse square and as the inverse
fourth power of the distance. In the latter case some re-
markable consequences are seen to flow from the discontinuous
character of the function f(c). When the density is uniform,
and the point external, all the elements of the integral which
precede or follow the break in that function vanish, while at
the break a single finite element occurs. This gives a finite
algebraic expression for this case of an ellipsoid’s attraction.
When the ellipsoid is of variable density, and the point exter-
nal, the attraction is given partly by a finite algebraic expres-
sion, and partly by a definite single integral.

Similar remarks apply to all inverse even powers of the
distance, except the square.

Dr. Allman read a paper on the larva state of Plumatella,
and on the anatomy of Polycera quadrilineata.

In this paper the author described the occurrence in Plu-
matella fruticosa, Allm., of a larva state presenting a very
different form from that assumed by the mature animal. This
Jarva was discovered in a glass of water containing specimens

219

of the adult Bryozoon, and when first observed was enclosed
in a delicate, transparent, egg-shaped sac, through which the
various parts of the contained embryo might be seen with
ease.

Within this external sac the embryo is suspended in a
transparent cell, the rudiment of the future polypedom, and
presents distinct traces of tentacula, stomach, and intestines.
‘The rudimentary muscles may also be plainly seen. The
tentacula are as yet very imperfect, they are short and thick,
when compared with the same organs in the adult animal,
and strongly suggest the idea of having been formed by the
longitudinal division of what had been, in a still earlier stage,
a continuous infundibuliform membrane. The cell or rudi-
mental polypedom is of an oval figure, densely ciliated
posteriorly. Where the cilia terminate, the membranous
walls of the cell present an invagination to a considera-
ble extent, and are again reflected outwards to undergo a still
further invagination, by which a sheath is formed for the
rudimental tentacula, and the digestive organs suspended in
the visceral cavity.

When the embryo Plumatella is released from the external
egg-shaped envelope, its locomotive powers being now no
longer restrained, it soon becomes evident how active a crea-
ture it is, for withdrawing the anterior portion of its cell,
which, as we have already seen, is deprived of cilia, within
the posterior ciliated portion, the latter is completely closed
around the anterior end, and the little embryo thus becomes
closely wrapped in a natatory mantle, through whose agency
it is carried through the surrounding fluid in endless and
elegant gyrations.

Beyond this point in the development of Plumatella, Dr.
“Allman was unable to adduce any observations; the little
larva, however, now described, presenting as it does all the
essential elements of bryozoal structure, belongs undoubtedly

220

to a phase considerably in advance of the well-known locomo-
tive gemmules of the marine bryozoa.

Dr. Allman also made some observations on the Anatomy
of Polycera quadrilineata.

In this mollusk the buccal mass is furnished with two pow-
erful corneous jaws, acted on by distinct muscles, and con-
tains a spinous tongue of very complex structure. ‘The eso-
phagus leads to a stomach, which is imbedded in the anterior
extremity of the liver, and from which an intestine first passes
forward and then curves backwards, to terminate at the anal
outlet, which is situated between the two posterior leaflets of
the bronchial tuft. Two pair of glands are connected with
the buccal mass. The liver, though in its natural condition
it is compact, like that of Doris and its allies, may yet be
unravelled so as to display its minute structure ; and it is then
seen to consist essentially of a ramified tube, whose branches
end in slightly dilated cuds de sac, and are furnished along
their sides with closely-set spheroidal divertacula, which
would seem to be the essential secreting portion of the organ.

The heart consists of an auricle and ventricle, and occu-
pies the back of the animal immediately in front of the bran-
chial tuft; it is furnished with auriculo-ventricular and aortic
valves.

The brain consists of six supra-cesophageal ganglia, and
the nervous collar is completed below by a band of nervous
matter, which passes from the most external ganglion of one
side, round the ventral aspect of the cesophagus, to the corres-
ponding ganglion of the other side; the nerves which supply
the dorsal laminated tentacula are furnished at their base with
large ganglionic dilations; and two small pharyngeal ganglia
are placed upon the ventral aspect of the cesophagus just as
this tube leaves the buccal mass.

The eyes are almost sessile upon the anterior ganglia of

221

the brain, having the whole thickness of the integumentary
structures intervening between them and the external world.
They consist of a spherical lens, imbedded in the anterior
extremity of a pigment cup, which is penetrated posteriorly
by the very short optic nerve, and the whole surrounded by a
delicate capsule.

The auditory capsules, with their otolites, are easily de-
monstrable.

The generative apparatus is complex. It is hermaphro-
dite ; the male organs consist of testis vas deferens and penis,
and the female of ovary, oveduct, uterus (?), and certain acces-
sory glands.

The President appointed, under his hand and seal, the fol-
lowing Vice-Presidents :
George Petrie, Esq.
Captain Larcom, R. E.
Sir William R. Hamilton, LL.D.
Rev. Frane Sadleir, D.D., Provost.

DONATIONS.

Famine and Fever in Ireland. By J. Corrigan, M.D.
Presented by the Author.

Annual Report of the Leeds Philosophical Society, jor
1844-5. Presented by the Society.

London University Calendar, for 1846. Presented by the
University.

Memoirs of the Astronomical Society. Vol. XV. Pro-
ceedings of the Royal Astronomical Society, from Novem-
ber 8th, 1844, to January 9th, 1846. Presented by the
Society.

_ Journal of the Asiatic Society of Bengal. Nos. 75 and
76 (for 1845). Presented by the Society.

Transactions of the Linnean Society of London.

Vol. XIX. P.4. Proceedings of the Linnean Society of

-

222

London, from p. 237 to 268, for the year 1845. List of the
Members of the Linnean Society of London, for 1845.
Presented by the Society.

The Quarterly Journal of the Geological Society of
London. Vol. 1. Presented by the Society.

Reduction of the Greenwich Observations of Planets, from
1750 t0 1830. Greenwich astronomical Observations, 1843.
Greenwich magnetical and meteorological Observations, for
1843. Presented by the Royal Astronomical Society.

Geological Survey of the United Kingdom of Great
Britain and Ireland. Horizontal Sheets, coloured, Nos. 1
to 17, inclusive. Vertical Sections, 1 to 8, and 10 to 15,
inclusive. Index Sheet of Colours. Presented by the Earl
of Lincoln, Chief Commissioner of Woods, Works, and Land
Revenues.

Philosophical Transactions of the Royal Society of
London, for 1845. Part II, Proceedings of the Royal
Society. Nos. 61 and 62. List of Members of the Royal
Society. 30 Nos. 1845. . Greenwich magnetical and
meteorological Observations, for 1843. Presented by the
Royal Society.

Report of the Secretary of the Navy of the United States,
communicating a Report of the Plan and Construction of the
Depét of Charts and Instruments, §c. February 18, 1845.
Third Bulletin of the Proceedings of the National Institute
Sor the Promotion of Science at Washington. Presented by
the President of the United States.

Practice of the Court of Record of the Borough of Dublin.
By William P. Pike, Esq. Presented by the Author.

Some Account of the Dominions of Furney. By Evelyn
P. Shirley, Esq. Presented by the Author.

Etudes sur la Mortalité dans les Bagnes, et dans les Mai-
sons centrales de Force et de Correction, depuis 1822 jusqu’a
1837, inclustvement. Par M. Ravoul Chassinat. Presented by
the Author,

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846. No. 53.
April 27.
REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Dr. Todd gave an account of an Irish Manuscript pre-
served in the Royal Library, Paris. Ancien Fond. No. 8175.

After refuting the conjecture of M. Champollion Figeac,
that this is the identical volume which was sent from Bre-
tagne by M. de Robien to Paris, for the use of the Benedic-
tine authors of the Nouveau Traité de Diplomatique, Dr.
Todd proceeded to give an account of the contents of the ma-
nuscript.

It is a parchment volume, containing now 117 leaves small
folio, or what modern booksellers would perhaps call imperial
octavo size. It was found by the Revolutionary Commis-
sioners, during the French Republic, in some house in Paris,
and by them deposited in the National Library, as is attested
by a curious note inserted in the volume, in the handwriting
of M. Villebrune, then Librarian or Conservator of that Insti-
tution. Of its previous history nothing is known, except what
may be gathered from a few entries made by the original scribes
and some of its possessors.

The volume may be divided into seven portions, which
are, in fact, different works, having been written by different
scribes, and at different times, although now bound together.
These are:

VOL. III. T

224

I, A book written by William Mac an Legha, some sheets
of which are misplaced by the binder. The book, however,
when this error is corrected, will be found to be quite perfect,
and contains ten tracts, viz. :

1. The History of the Children of Israel. A note at the
end tells us, that this work was transcribed in the year 1473,
in the space of two summer days; and that it was written by
William Mac an Legha, at Cluan Lorg, in the house of Cor-
mac O’Betnachan.

2. The History of King Solomon.

3. A Tract against defiling or profaning Churches.

4, A Legend of Hell and its Torments, entitled Cenga bie
nua, ** The Eternal new Tongue.”

5. A Legend describing the Condition of Enoch and Elias
in Heaven, entitled, Oa. bpon plaéa nme, “ The two sorrowful
ones of the Kingdom of Heaven.”

6. A Legend of a holy Monk and a Woman who went to
him for Confession.

7. A Legend of two Children, one Jewish, the other Chris-
tian.

8. A Legend of an Eastern Woman and her Child.

9. A Legend of St. Brendan.

10. The Reasons for making Friday a Day of Fasting,

II. The second book bound up in the volume is stated to
have been written by Flathri (who calls himself m cpuag, ‘‘ the
wretch, or miserable”) for Donogh, son of Brien Mac Conor
O’Brien, who must have been the same as Brien Duff, son
of Brien O’Brien of the battle of Nenagh, who was the first
of that branch of the O’Brien family who settled in the Castle
of Carrig O’Gonnell, County Limerick, about 1449; and,
therefore, it follows that this portion of the MS. must have
been transcribed after that year. The Book of Flathri con-
tains the following tracts :

1. Charta humani Generis, seu Speculum Peccatoris.

2. A Tract entitled Spud gnada Oe, “Stimulus amoris Dei.”

3. A Tract on Alms.

225

4. A Dialogue between the Body and the Soul. It is at
the end of this that Flathri gives us the information above
stated, from which we learn that he was the writer of the vo-
lume. And the following tracts seem to be also in his hand:

5. A Legend of the Virgin Mary. This is imperfect,
some leaves being lost between what are now fols. 14 and 15
of the MS.

6. A Tract entitled Oo peip ppocepena, “* Of the Rule of
Preaching.”

7. A curious Tract on the institution of the Festival of
All Saint’s Day.

8. On the Miracles attending the birth of our Saviour.

9.A Sermon on the Text, “ Intrate per angustam por-
tam.”

10. The history of the Right of spiritual Direction of the
Men of Ireland.

11. On the Virtues of Faith, Chastity, Humility, Charity,
Fortitude, and Temperance.

At the end of this are notes in Irish, in different hands,
giving two different calculations of the number of leaves in
the volume. One of these states that it contains six score
(which is corrected by another hand to seven score) leaves
and one. But a later entry makes the number seven score,
and astill later note adds, ‘‘ and three leaves over.”

We gain but little information from this note : because it
must always be uncertain whether it refers to the whole
volume, or only to that part of it which was written by Flathri
for Donogh O Brien. If it refers to the whole volume, the
loss sustained since the seventeenth century, when the note
appears to have been written, will amount to twenty-three
leaves. Ifonly to the book of Flathri, the loss will be 130
leaves. Let us hope, therefore, that the note related to the
entire volume, which is, perhaps, the more probable supposi-
tion. There is also another uncertainty attaching itself to
the Irish mode of counting by scores, for it was very common

T2

226

to count six score to the hundred ; and it is curious that if we
count the volume so, the number of leaves it now contains
will be exactly seven score and one; so that, on this supposi-
tion, the volume has remained uninjured for the last two hun-
dred years. ;

III. The next part is a collection of the Lives of Saints,
not all in the same hand. The name of the scribe is not given,
but the great mass of this part of the manuscript appears to
be in the hand of William Mac an Legha. It contains the
following tracts : '

1. Life of St. Maighnen, Abbot and Founder of Kilmain-
ham, near Dublin.

2. Life of St. Mochua, founder of the Church of Timohue,
in the Queen’s County. :

3. Life of St. Senan, of Scattery Island, in the mouth of
the Shannon.

4. Life of St. George.

5. Life of St. Gregory the Great.

6. Life of St. Longinus, who pierced our Saviour’s side on
the Cross, and became blind in consequence, but was converted
to Christianity.

7. Life of St. Juliana.

8. Life of the four Donalds. A Legend, which begins by
telling us of three students who came from the diocese of Con-
nor to be educated by Maolsuthan O Carroll, of the Eogha-
nacht of Loch Lein, and abbot of Inisfallen in the Lake of
Killarney. This Maolsuthan, the story tells us, was spiritual
director to Brien, son of Kennedy, i. e. to Brien Boru.

9. A Legend of Nicomedes, or Joseph of Arimathea.

10. Life of St. Columba or Columbkille. Followed by
the curious legend of the saint, whilst he resided in the
island of Aran in the bay of Galway: a tract of which we
know no other copy.

11. The Legend of the Seven Sleepers. This tract ends
imperfect, some leaves being lost, between fol. 57 and 58 of
the manuscript.

227

IV. The next portion of the volume contains three theolo-
gical treatises :

1. A Sermon on the verse Novet in principio vigoris met.
The initial letter N (which M. Champollion has mistaken
_ for F) is illuminated in red and ornamented, shewing that here
began a distinct book, which afterwards came to be bound
up with the rest, but has no other connexion with it. A fac-
simile of the beginning of this Sermon is given by MM. Cham-
pollion and Silvestre, in the Paleographie Universelle.

2. Some Letters (apparently of Pope Innocent III.),
translated into Irish.

3. A Dialogue between the Body and the Soul. This is
the same tract of which another copy occurs also in this
volume, in the portion of it written by Flathri for Donogh
O Brien. This is probably the original; for a note at the
beginning of it tells us that it was translated into lrish by
William Maguibhne [Mac Gawney], and that Daniel O’Con-
nell induced him to do so in the year of our Lord 1443. The
tract is imperfect, some leaves being lost between fol. 73 and
fol. 74.

V. Then follows another collection of Lives of Saints, con-
taining three lives: this is the oldest portion of the MS. and
is unfortunately imperfect at the beginning. It appears from
the handwriting (for no other means remain of determining its
age), to have been written in the 14th, or beginning of the
15th century. It contains—

1. A fragment of the Life of St. Patrick, imperfect at the
beginning.

2. The Life of St. Bridgit.

3. The Life of St. Brendan, imperfect in the middle ; the
defect is supplied, however, by a more recent hand: so that
the tract is complete, although not in its original state.

VI. Next follow two tracts, written, as appears from a
note at the end, by Mailechlain, son of Ilan Mac an Legha,
for Donogh, son of Brien Duff O’Brien, “the head of the

228

hospitality and munificence of the English and Irish of Ireland
(Gall 7 Gardel nEpeno), the year in which the son of the Earl
of Ormond was treacherously killed by the Butlers.” The
son of the Earl of Ormond here mentioned, was probably
James,. commonly called Black James, natural son of James,
fifth Earl of Ormond, who was slain by Sir Pierce Butler,
between Dunmore and Kilkenny, March 17, 1518. The
tracts are—

1. An ancient Exposition of the Lord’s Prayer.

2. An Account of the Destruction of Jerusalem, entitled
‘¢ The Avenging of the Blood of Christ.”

VII. A miscellaneous collection of Theological Tracts,
containing .

1. The Vision of St. Adamnan.

2. An Account of the King of the Medes and Persians.

3. Liber Sententiarum. A fac simile of part of this Trea-
tise is given by M. Champollion in his Paleographie Univer-
selle. It consists of nineteen chapters.

4, A Treatise on Repentance.

5. A Tract entitled, 6leo Michil ler in beipz, “ Michael’s
Combat with the Monster.”

6. A Tract entitled, ‘‘ The Ambition of the Angel, and the
banishment of Adam out of Paradise.”

7. A very short Tract, without title, on the same subject.
On the lower margin the transcriber has written in Irish, “I
have not found any more of this narrative to write;” so that
it is probably incomplete.

8. A Tract entitled, «* Words on the Sacrament :” This is
a sermon or theological discourse on the Lord’s Supper. At
the end is this note: ‘‘ I, John, son of the Earl of Desmond,
wrote this at Carrig o Gonnell (a Cappaig o Comnell) in order
to assist my companion, and faithful tutor, Mailechloin Mac
Illion:’ This was probably John, son of Thomas, Earl of
Desmond, who died 1536.

9. A Tract entitled, ‘“‘ History of the Monks of Egypt.”

229

The remaining pages of the volume contain only some
scribbling of no importance or interest.

Mr. Huband Smith exhibited to the Academy a ‘‘rub-
bing” taken from the tombstone of William O’ Byrne (a. p.,
1569), in the cathedral of Old Leighlin, county of Carlow.

This tombstone has been noticed but slightly in the
‘‘ History and Antiquities of the County of Carlow,” by
John Ryan, Esq., published in 1833, from which Mr. Smith
read a passage (pp. 344 and 345), in which a few words of the
inscription are given, so as to identify the stone, which is said
to be ‘‘generally reputed, even by men of education, to be
that ofa Bishop Kavanagh,” but the writer professes his
‘inability to decipher the entire,” and adds, that he ‘could
not discover the exact year inscribed on the tomb.”

The rubbing, now exhibited by Mr. Smith, was made by
Mr. Robert J. Gabbett, of Cahirmoyle, County of Limerick,
and the inscription, as deciphered from this rubbing, is as
follows :

Wit facet GAillelHmus obrin filius inominati flit Wail.
lelmt fltt Dabdid rufl Grenerosus de Corraloske et ballenebre-
nagh ac burgensis Weteris Leqhleniensis——obit xbif. die
mensis Yunti A, vt. SO. cecee®. Inix. et efus Cxoris WHinna
Bewanagh filia (Maurict filii Donati ( ) monens gui
obit... . Die mensis... . A%. OY, $B, cece... . . Quorum
animabus propicietur deus. Amen.

Several contractions occur in the inscription, which, how-
ever, are easily filled up; a few letters also are wanting on
the edge of the stone, which Mr. Smith had little doubt he
supplied correctly from the context. The only word he was
unable to read was the title, or designation, as he supposed,
following the name of Donatus, or Donogh Kavanagh, and
ending in the dissyllable “‘monens.” Blanks are left on the
stone for the exact date of the decease of Winna Kavanagh,

230

from which Mr. Smith stated his conjecture that she was still
living when the stone was placed over her husband’s grave.
The name ‘‘inominatus,’ Mr. Smith suggested, might be a
latinization of the Irish Christian name ‘* Fearganonym”
(literally “a man without a name”), which appears frequently
in the Patent Rolls and other historical documents of this pe-
riod, as one commonly in use among various septs and families
of Irish descent. He read an extract from the Patent Roll of
the 28th, 29th, and 30th Henry VIII. (dorso, Ixxi. 3.) of the
enrollment of an ‘* Indenture between Lord Leonard Gray,
Viscount Grane, the King’s Deputy, and Fergynanym Roe
O’Byrne, whereby it is agreed that the said Fergynanym
shall be the king’s faithful subject, and serve at hostings with
his power, at his own expense ; that he shall pay to the King’s
use four-pence Ir. yearly, for every horse, mare, cow, bull
and ox, being in future in the town of Ballihorsy, Cowlyth,
Dwly, Dromor, and Kilparke. And the Deputy shall main-
tain and defend said Fergynanym, and his tenants, &c., and
the possessions in the towns aforesaid, against all men, as
well English as Irish.”—17 Sep. 1536.

The O’Byrne mentioned in this indenture, Mr. Smith sup-
poses was the same whose tomb remains in the Cathedral of
Old Leighlin.

In conclusion, he suggested that careful rubbings of the
tombstones which yet remain in the various churches and
abbeys, especially in Kilkenny and Cork, and other places
in the south of Ireland, and which are every day fast disap-
pearing under the hand of time, would preserve a vast deal
of curious information, of no inconsiderable value to the topo-
grapher, the genealogist, and the historian.

Mr. Ball brought under the notice of the Academy, as an
unobserved fact, a beautiful provision in the foetus of the
spined dog-fish (Acanthias vulgaris), by which the mother is
protected from being lacerated by the spines of the young

231

before birth. He exhibited two perfectly developed young,
which he had taken from the mother on the 30th of Novem-
ber last ; in these the spines were each covered at the point
with a small knob of cartilage, fastened by straps of the same
material, passing down one on each of the three sides of
each spine, in such a manner as evidently to become easily
detached at birth, thus allowing the little animal to commence
life effectively armed. He mentioned that the female in
question contained a large number of eggs, in various states
of development, in addition to the two fully-formed young ;
and he took oceasion to remark, that this fish is so destructive
to herrings that fishermen look on it with abhorence: in this
he thought they were wrong, for he considers that some of
the success of fishing with driving nets is to be attributed
to the headlong haste with which shoals of herrings go along
when pursued by enormous packs of dog-fishes, and that thus
they serve man rather than injure him. Fishermen, however,
destroy the dog-fish whenever it falls into their power, as they
did the specimen which gave occasion to this notice.

Dr. Allman mentioned an analogous fact in the ova of
Cristatella mucedo.

Rev. N. J. Halpin commenced the reading of a paper on
some passages in the life of Shakspere.

Rev. Dr. Drummond presented to the Museum an ancient
Ogham inscription, on the part of FrancisW. Jennings, Esq.

Mr. Robert Mallet presented a drawing of a silver antique
ring found in Ireland, and presented to the British Museum
by Lord Enniskillen, containing an inscription in characters
_ resembling Chinese.

DONATIONS.
Proceedings connected with the magnetical and meteoro-
gical Conference, held at Cambridge, in June, 1845. Pre-
sented by the Association.

232

The Laws of the Tides on the Coast of Ireland, as
inferred from observations made in connexion with the
Ordnance Survey of Ireland. By G. B. Airy, Esq. F.R.S. &c.
Presented by the Author.

Transactions of the Geological Society. of London.
Second Series, Vol. VII. Parts 1 and2. Presented by the
Society.

On the Heat of Vapours. By Sir J. W., Lubbock.
Presented by the Author.

Philosophical Transactions for the Year 1845. Part 1.
Presented by the Royal Society.

Reduction of the Greenwich Observations of Planets, from
1750 to 1830. Greenwich Astronomical Observations, for
1843. Presented by the Royal Society.

Journal of the Royal Asiatic Society. No. XVI.
Part 1. 1845. Presented by the Society.

Dramatic Sketches, and other Poems. By the Rev.
James Wills, M.R.I.A. Presented by the Author.

Eleventh Annual Report of the Poor Law Commissioners,
with Appendices, for 1845. Presented by the Commissioners.

The Repeal Dictionary. Part 1. By John O’Connell,
Esq. M.P. Presented by the Author.

Inaugural Address to the Members of the Temperance
Institute in Cork. By Edward Kinnealy, Esq. Presented
by the Author.

An old Dutch Tobacco Box, found near Newmarket,
County of Clare. Presented by Sir Lucius O’ Brien, Bart.

Vertical Sections of the Geological Survey of Great Bri-
tain. Sheet No.9. Presented by the Chief Commissioners
of Woods and Land Revenues, on the part of Her Majesty’s
Government.

Results of the Mackerstoun Observations. No. I. Pre-
sented by J. Allan Broun, Esq.

233

May 11.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

John Aldridge, M. D., and George Lefroy, Esq., were
elected Members of the Academy.

The reading of the Rev. N. J. Halpin’s Paper, on some
passages in the lifeof Shakspere, was resumed and concluded.

The object of this paper is to vindicate the poet’s memory
from aspersions thrown upon his character, as a father and a
husband, by Malone, Drake, De Quincey, Moore, &c.

Those aspersions—unfounded in either fact or tradition—
are chiefly inferences, rashly drawn, from the poet’s last will
and testament, and consist of two charges, viz.: favouritism
towards one of his daughters, and neglect of his wife: which
Drake lays down as ‘the most striking features” of that do-
cument. To these are added, from other sources, calumnies
respecting the education of his children, and jealousy of his
wife ; all of which it is the object of the paper to refute.

The inference of favouritism towards his eldest daughter,
deduced from the unequal division of his property, is shown to
be false, by proving that the inequality was the result of the
undutiful conduct of the younger, who had married a person of
inferior station, who was either unable or unwilling to make a
settlement upon her or her issue; whereas the elder had made
a match to her father’s entire satisfaction. Malone, Drake, &c.
assert that, at the time of making his will, the poet was igno-
rant of his second daughter’s marriage, and still spoke of her
as an unmarried woman; whereas the reverse is the fact. He
was aware of the marriage, and thereupon made the final dis-
position of his property ; and though his resentment prevented
him from mentioning the husband’s name, he still indirectly
recognizes the marriage, by including him as the husband

234

with whom, at the end of three years, his daughter may be
found united in wedlock. The clauses of the will (from which
these facts are elicited) are fully discussed, and the memory
of Shakspere rescued from the charge of ‘ favouritism” or
unjust partiality.

The charge respecting his supposed neglect of his wife is
next examined. It rests upon three points: the omission of
her name in the first draft of his will; the neglect of any
ostensible provision for her support; and the interlineation
which conveys to her his “‘second best bed.” Malone, fol-
lowed by Drake and others, interprets these facts into proofs
of the unhappiness of the marriage through life, and the un-
friendly feeling with which it closed in death. The last
point, in particular, Malone construes into ‘‘ cutting her off,”
not with a shilling, but an old piece of furniture; and Moore
translates it into ‘‘a bitter sarcasm.”

With reference to the first, Mr. Halpin argues that the
poet’s omission of his wife’s name in the first draft of the will,
and the subsequent interlineation, no more imply the absence
of conjugal love, than the similar omission and interlineation of
his friends’ and fellows’ names (Burbage, Hemings, and Con-
dell) intimate his want of friendship for them—an interence
which, in their case, the biographers never thought of drawing.

With reference to the second, Mr. H. concurs, to a certain
extent, with Mr. Charles Knight’s solution of the point,
namely, the provision already made by law,—the widow being
entitled to dower, or the third of all her husband’s freehold
property during her life; and further suggests, from other
provisions of the will, the extreme probability that she and
her children had been, previous to her marriage with the
poet, provided for by a marriage settlement, and that she
consequently had brought him a fortune.

With respect to the third, the vindication which Stevens
suggested is confirmed by reference to the testamentary habits
of the times ; and the bequest is proved, by parallel with a

235

similar bequest of William Herbert, first Earl of Pembroke, to
Queen Elizabeth, to have conveyed, not ‘a bitter sarcasm,”
but the tender memorial of a love and attachment surviving
the grave.

The calumnies derived from the will being thus disposed
of, Mr. Halpin next adverts to the poet’s alleged neglect of the
duty of a father in the education of his children. Drake as-
serts that neither of his daughters had been taught to write ;
and sustains his assertion on the evidence of a legal document
still existing, attested, as he thinks, by the mark of his daugh-
ter Judith.

This calumny the author treats as a superfetation of the
similar degrading ignorance ascribed to the father of the poet,
but without the shadow of evidence in the document on which
it is founded. A fac-simile of the signatures to the entry on
the books of the corporation of Stratford-upon-Avon (pub-
lished by Mr. Knight), amongst which John Shakspere
is said to have figured as a marksman, exhibits the name
of that worthy corporator without any mark ; proves that
the mark assigned to him belongs, in reality, to George
Whately, the high bailiff for the current year; and leads to
the juster inference that, so far from not being able to write
at all, John Shakspere probably wrote the best hand of any
man in the corporation.

With reference to the daughters, the assertion as to both
is disproved by the production of a fuc-simile of the signature
of the elder (Susanna) affixed, with her seal, to a legal instru-
ment still existing ; and with reference to the younger, it is
shewn to rest on an ignorant or wilful mistranslation of the
word signum into mark, instead of seal, &c.

The paper goes on to argue, from the nearness of their
births, that both daughters were educated together; that
whatever instructions or accomplishments the one had re-
ceived, the other had at least the same opportunities of
acquiring ; and that, as Susanna is recorded to have been a

236

woman of high attainments, it may be justly inferred that
Judith was not deficient.

The character of Susanna Shakspere is then discussed, and
her moral, intellectual, and poetical faculties asserted on the
evidence of a contemporary. ‘That her education embraced
the Latin language, at least, is proved by the production of
one indisputable, and several probable, pieces of her composi-
tion in Latin, as well as English metres; and the whole is
brought to a conclusion by a vindication of her mother’s me-
mory, on the testimony to her virtues furnished in the monu-
mental inscription placed over her remains by the piety and
love of this exemplary daughter.

Edward J. Cooper, Esq., made some remarks upon the
four Comets which were lately visible, and which were all
observed in one night at Markree—namely, Biela’s double
comet, the two comets of De Vico, and Brorson’s comet.
He likewise read a communication from Professor Schuma-
cher respecting a fifth comet, which has just been discovered.

The President commenced the reading of a paper ‘‘ On
the Variations of the Magnetic Declination at Dublin, as
deduced from four years’ observations.”

DONATIONS.

Abhandlungen der Kéniglichen Gessellschaft der Wissens-
chaften zu Gottingen. 11%" Band von den Jahren 1842-4.
Presented by the Society.

Bericht tiber die zur Bekanntmachung guigneiten Ver-
handlungen der Koniglichen Preuss. Akademie der Wissens-
chaften zu Berlin. From July, 1843, to June, 1845.

Abhandlungen der Kéniglichen Akademie der Wissens-
chaften zu Berlin. Yor 1842 and 1843. Presented by the
Academy.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846. No. 54.

May 25.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

It was resolved, on the recommendation of Council, that
a subscription be opened for the purchase of the Domnach
Airgid, and that the Academy do subscribe fifty pounds.

The President resumed and concluded the reading of his
paper ‘‘ On the Variations of the Magnetic Declination.”

The observations at stated hours, in the Magnetical Ob-
servatory of Dublin, commenced November 1, 1838, the
hours of observation being at first limited to the day. _ In the
beginning of the year 1840, the observations were taken every
alternate hour, night and day, according to the more compre-
hensive scheme which received the sanction of the Royal
Society, and which, under the recommendation of that body,
has been followed in more than thirty observing stations
scattered over the whole globe. This plan has been in ope-
ration at the Dublin Observatory until January 1, 1844,
when it was discontinued, four years’ observations having
been found fully sufficient for the determination of all the

238

phenomena connected with the diurnal movements. The
results now laid before the Academy are chiefly those of the
four years just mentioned. The observations have since been
continued upon a different and reduced scale, and with a view
to other classes of phenomena.

The changes which the magnetic declination undergoes,
at a given place, may be reduced to three classes, namely, 1.
periodical variations; 2. secular variations, which are either
continually progressive, or else return to their former values
in long and unknown periods; and 3. trregular variations,
which observe, apparently, no law. The periodical variations
hitherto noticed are those which depend upon the position of
* the Sun with respect to the horizon, or with respect to the
equator, and which, therefore, complete their course in a day,
or ina year. The author commences with the first of these.

Diurnal Variation.

In order to determine the laws of the diurnal changes, the
observations of each month are combined separately, and the
means of the results corresponding to the same hour taken.
The observations having been continued for four successive
years, there are thus four groups of mean results for each
month, the means of which are then taken. And, finally,
the mean values for the separate months are grouped toge-
ther, so as to obtain the mean yearly, as well as the mean
summer and winter course of the variation. The total num-
ber of individual observations thus combined exceeds 14,000.

When the mean results at each hour of observation, for
the whole year, are examined, it is found that the course of
the diurnal variation is regulated by the following laws:

1. About 7h. 30m. a.m., the north pole of the magnet
begins to move to the wesiward, and, therefore, the declina-
tion increases. This increase continues until about 1 P.m.,
when the declination attains its maximum.

2. The north pole of the magnet then moves to the east,

~ ee

239

.
and the declination diminishes, but at a slower rate than
it has increased. ‘This diminution continues until about
10 p.m., when the declination is a maximum. Vhe whole
diurnal range, between 1 p.m. and 10 p.M., is about 9.4
minutes.

3. During this increase, and subsequent decrease, the de-
clination twice reaches its mean value, as deduced from the
results of the entire day. ‘The epochs of the mean declination
are 9h. 30m. a.M., and 6h. p.m. nearly.

4. There isa second, but much smaller oscillation of the
magnet during the night and morning, the north pole moving
slowly to the west, from 10 p.m. until 3 a.m., nearly, when
there is a second maximum, and then returning to the east
until 7 a.m., when there is a second minimum.

When the means corresponding to the several hours of
observation, taken for the six summer months, and the six
winter months, separately, are examined, it is found that the
course of the diurnal variation is very different in the two sea-
sons. The following are the distinguishing circumstances :

1, The range is much greater in summer than in winter.
The mean summer range amounts to 12-2 minutes; the mean
winter range to 9-0 minutes.

2. In summer, the morning minimum is greater than the
evening minimum, which is not the case in the curve for the
entire year; and, consequently, the greatest range is between
7a.M.and1vp.m. In winter, on the other hand, the morn-
ing minimum, and the small preceding maximum, disappear
altogether; and the course of the diurnal change presents
only a single oscillation.

If now the inquiry be extended from the seasons to the
separate months, it is found that the course of the diurnal
change, in each of the six months from April to September
inclusive, has all the characters of the mean summer variation,
both as respects the Jaw of the change and its amount. In like
manner the diurnal variation, in each of the six winter months,

VOL. Ill. U

240

corresponds with the mean variation for the whole period ; the
nocturnal oscillation vanishing, and the course of the repre-
sentative curve, from 10 p.m. to 9 a.M., being in all nearly
a straight line. Thus the curves for the separate months ap-
pear to distribute themselves into two groups, depending upon
the position of the sun to the north or south of the equator;
and it is remarkable that the transition from one to the other
system appears to take place abruptly, and almost per saltum.

The whole range is nearly the same in each of the six
summer months. The maximum range occurs in April, and
its amount is 13’.3 ; this maximum is followed by a secondary
minimum in July, which is succeeded by a secondary maxi-
mum in August. There is a sudden change in the mag-
nitude of the range from February to March, and again
from October to November. The minimum range occurs in
December, and its amount is 7’.0.

The physical dependence of the phenomena of the changes
of the declination upon the sun is evident from the fact, that
they observe a diurnal and an annual period. In addition to
this fundamental fact, it has been long ago observed, with
respect to the diurnal change, that the time of the maximum
of westerly declination follows the sun’s meridian passage at
a nearly constant interval, and that the morning and evening
minima are in like manner connected (although not so closely)
with the hours of sunrise and sunset; and another point of
connexion between the cause and effect has been established
by the fact, long since observed, of the greater magnitude of
the range in summer than in winter.

Dr. Lloyd proposes to show that the sun acts by means of .
its heating power (as, in fact, is assumed both in the hypo-
thesis of Canton and that of Christie) ; and that the connexion
between the changes of declination and those of temperature
is more intimate than has been hitherto supposed.

The force which produces the deviation of the magnet
from its mean position, at any moment of the day, is mea-

241

sured by the sine of that deviation,—or, since the deviation is
small, by the angle of deviation itself, or by the ordinate
of the diurnal curve; and the sum _ of all these forces
throughout the day, or the integral of the diurnal action, is
measured by the area of the diurnal curve. Dr. Lloyd has
computed this area for the several months of the year; and,
on comparing it with the corresponding area of the diurnal
curve of temperature, he finds that there is a marked agreement
in the course of the two functions. The slight dissimilarities
which exist between them may be accounted for by the cir-
cumstance, that it is to the heating power of the sun, exerted
upon the earth’s surface, and not upon its atmosphere, that
we must ascribe the changes of declination; and the author
feels assured, that as soon as we are in possession of data, re-
specting the diurnal changes of temperature of the earth’s
surface, sufficient to institute a comparison similar to that
now made with the temperature of the air, the agreement of
the laws will be found to be still more complete.

Annual Variation.

The annual variation of the declination was discovered by
Cassini, in 1786. It appeared from the observations of Cas-
sini, that the north pole of the magnet moved to the east
during three months, viz., from the vernal equinox to the
summer solstice ; and, consequently, the declination dimi-
nished. During the remaining nine months, viz., from the
summer solstice to the vernal equinox, it moved to the west,
and the declination increased. The increase, during the nine
months, preponderated over the decrease, which took place
during the remaining three; and thus the declination was
greater at the close of the year than at the commencement.
This excess is the yearly amount of the secular change,
which was then additive.

Although the law of the annual variation may be traced

u2

242

in the subsequent observations of Gilpin and Bowditch, it has,
nevertheless, escaped the attention of more recent observers.
There is but a faint indication of its existence in the Gottin-
gen observations, which were made at the hours of 8 a. mM. and
1 p.m. ; and Professor Gauss finds, in the mean results de-
duced from these hours, no ‘‘ important fluctuation dependent
on season.” A similar negative result is deduced by Dr.
Lamont from the Munich observations, which were made
twelve times in the day.

It will be easily understood, that the determination of
the annual variation is much more difficult than that of the
diurnal change; both on account of the much smaller fre-
quency of the period itself, and the difficulty of preserving
the instrument in the same unchanged condition during the
much longer time, or of determining and allowing for its
changes when they do occur. The Dublin observations
appear to possess a peculiar value for this determination.
Since the spring of 1841, the magnet of the declinometer has
remained absolutely untouched ; and the suspension thread
(which elsewhere has frequently broken) has continued per-
fect since the instrument was first mounted.

The course of the annual variation in Dublin, as deduced
from the results of the years 1841-4, is as follows:

1. During the first three months of the year, the mean
daily declination is nearly constant.

2. In the month of April the declination begins to in-
crease; and it continues to increase until the beginning of
August, when it attains its maximum. 3

3. From the beginning of August it decreases ; and the
decrease continues, with rapidity, until the end of the year,
when the declination is about five minutes less than at the
commencement.

4. The increase, from the beginning of April to the be-
ginning of August, is four minutes. The decrease, from the
beginning of August to the beginning of January, is nine mi-

243

nutes; thus leaving a total decrease, from year to year, of
five minutes.

When we compare the course of these changes with those
observed by Cassini, we find that the directions of the move-
ments are precisely opposite,—as, indeed, we might have been
led a priori to expect from the opposition in the directions of
the secular changes ; and we are led to generalize the law as
follows :

<‘ From the beginning of the year to the beginning or
middle of April, the mean declination undergoes little or no
change. Thence, to the beginning of August, its movement
is retrograde (or opposite in direction to the secular change) ;
and from the beginning of August to the end of the year, it
is direct.”

The phenomena just described are, it is manifest, the
resultants of two distinct changes, namely, the annual varia-
tion properly so called, and the progressive or secular change.
If the latter be subtracted, at the rate of 5.0 per annum, or
0./4 per month, the remaining numbers give the true annual
period. When thus considered, the annual variation exhibits
an increase of the declination during the first seven months of
the year, and a decrease during the remaining five months ;
the apparently stationary condition of the declination, during
the first three months, arising from the mutual compensation
of the periodical and the progressive changes.

It appears, then, that the annual variation (unlike the diur-
nal in this respect) is a single oscillation. The minimum
oceurs near the end of January, and the mazimum in the
beginning of August ; and the whole range of the change is
6.6 minutes.

The laws of the annual variations of the declination and
of the temperature, present the most complete accordance
in the epochs of maxima and minima, as well as those of the
mean values. The maximum of temperature occurs about
August 1,—that of declination about August 8. The mini-
mum of temperature takes place about January 15,—the mini-

244

mum of declination about January 25. Finally, the annual
curve of temperature crosses the axis of abscisse in two
points, which correspond to May 1, and October 10,—the
corresponding epochs in the curve of declination are May 10,
and October 15.

Secular Variation.

The westerly declination is at present diminishing from
year to year in these countries, and has been so since the year
1818, which was the time of the maximum. The present
rate of the secular decrease in Dublin, as deduced from four
years’ observations, is 5.0 minutes annually.

With respect to the physical cause of the secular change,
Dr. Lloyd said that he had been led to form an opinion very
different from any of those heretofore held. From the re-
markable relation which had been shown to exist between the
annual and the secular changes, he was driven to conclude
that they depended (ultimately at least) upon a common cause;
and that thus the sun was the cause of the secular, no less than
of the periodical changes, although not only the magnitude,
but even the direction of the effect were different in different
times.

Disturbances.

Having examined the periodical and the secular variations
of the declination, as deduced from the observations made at
the Dublin Observatory, it now remains to consider those
which, from our ignorance of their laws, we have been accus-
tomed to call *¢ trregular.”

Professor Kreil seems to have been the first to notify the
remarkable fact, that magnetic disturbances occur more fre-
quently at certain hours than at others; and, that the direc-
tion, as well as the frequency, of these movements, has a
dependence upon the time of the day. Colonel Sabine has
since made a more complete and elaborate examination of this

215

question, in his able discussion of the Toronto observations,
and has arrived at conclusions for the most part confirmatory
of those obtained by Professor Kreil.

In these investigations, however, those disturbances only
are taken into account which exceed a certain arbitrary limit ;
and, even of these, the frequency is considered without any
reference to their magnitude. In examining the question of
the periodicity of disturbances, Dr. Lloyd has thought it ne-
cessary to pursue a different course. His method consists in
taking the differences between each individual result, and the
monthly mean corresponding to the same hour, and combining
these differences in the same manner as the errors of observa-
tion (to which they are analogous) are combined in the caleu-
lus of probabilities. The square root of the mean of the squares
of these differences is, in fact, a quantity analogous to the mean
error, and which he therefore proposes to call the mean distur-
bance ; andit is evident that its values, at the several hours of
the day, and at the several seasons of the year, are measures
of the probable disturbance to be expected at the corresponding
times.

The values of this function have been deduced for the
several hours of observation, in each month of the year
1843; and those for the entire year are obtained from
them by a repetition of the same process. ‘These numbers
show that the mean disturbance follows a law of remarkable
regularity in dependence upon the hour. During the day,
i.e. from 6 a.M. to 6 P.M., it is nearly constant ; at 6 P.M.

it begins to increase, and arrives at a maximum a little after
10 p.m.: it then decreases with the same regularity, and
_arrives at its constant day-value about 6 a.m.

The preceding results are independent of the direction
of the disturbance. If, however, we take the sum of the
squares of the easterly and westerly deviations separately, we
find that the easterly disturbances preponderate during the
night, and the westerly during the day; the former being,

246

however, much more considerable than the latter, and the
difference reaching a maximum about 10 p. M.

It thus appears that the mean daily disturbance observes
a regular period, both in magnitude and direction ; and this
period, itis worthy of remark, is precisely the reverse of that
of the regular diurnal movement,—the mean position of the
magnet being nearly constant during the night, the mean dis-
turbance during the day ;—the principal oscillation of the
magnet, in the regular movement, being to the west during
the day, while that of the irregular movement is to the east
during the night. From these remarkable relations it seems
evident that the two classes of phenomena are physically con-
nected ; and Dr. Lloyd is led to regard the disturbance which
prevails about 10 p.m., as an trregular reaction from the
regular day movement, and dependent upon it both for its
periodical character and for its amount.

If this hypothesis be a just one, it will, of course, follow
that the magnitude of the mean disturbance will vary, in some
direct proportion to the daily range, and should, therefore,
be greater in summer than in winter. This (which is con-
trary to the results deduced by Professor Kreil and Colonel
Sabine, with reference to the frequency of disturbances ex-
ceeding a certain limit) appears to be the fact. The mean
disturbance, deduced from the observations of 1843, is, for
the summer six months, 2’.9, and for the winter 2’.2; so that
it observes an annual as well as a diurnal period.

It by no means necessarily follows, from the results now
stated, that all disturbances have a periodical character.
There probably are two classes of disturbances, the results
of distinct physical causes, of which one observes a period, -
while the other is wholly irregular; and it is manifest that,
in such a case, the period of the former will necessarily be
impressed upon the resultant mean disturbance. Dr. Lloyd
stated that he had instituted, during the last year, a series of
observations at short intervals, which seem to afford the means

247

of testing this hypothesis, and of distinguishing the two classes
of disturbances, if they really co-exist. The inspection of
these observations has nearly satisfied him of the truth of this
view ; and he believes that it will be found, upon a more minute
examination, that there are two classes of disturbances, one
periodical and local, the other irregular and universal. Of
the former, the principal (if not the only one) is that which
- occurs about 10 p. M., and which causes the north pole of the
magnet to deviate to the east. The magnitude of this dis-
turbance is on the average 10’.0; and its mean duration is an
hour and a half. The epoch of the maximum of easterly deflec-
tion varies from 73 Pp. M., to 13 a.m., the mean epoch being a
few minutes before 10 P.m.; and, hence, it is evident, that its
effect on the monthly mean curve is to produce a general in-
crease of the negative ordinate between these limits of time,
as well as the minimum which occurs at 10 P.M.

It seems to follow also, from these facts, that the ordinary
mode of grouping the observations, by taking the mean of all
the results at the same hour,—although it truly gives the
mean diurnal curve for the period embraced by the observa-
tions,—does not represent the actual course of the movement
during any one day. In order to obtain the representative,
or fype curve, as it may be called, it seems necessary to com-
bine the results in a different manner, of which the author
hopes to speak more fully upon a future occasion.

Mr. Ball exhibited a specimen of Apteryx Australis, recently
purchased for the University Museum, and made some obser-
vations on the species, referring to the elaborate papers of
Yarrell and Owen in the Transactions of the Zoological So-
ciety of London. He noticed the adaptation of the position
of the nostrils of the bird to its wants; being placed at the
end of the bill, it is enabled, by its powerful olfactory appa-
ratus, to detect the burrowing larvee on which it feeds. This
is accomplished by snipes, woodcocks, &c., by means of ex-

248

traordinary development of nerves on the end of the bill.
They obtain their food by the delicacy of their power of feel-
ing, as the Apteryx does by its powers of smelling.

Professor Graves read the following memorandum in re-
ference to the discovery of the remains of a cedar ship, near
Tyrella, in the county of Down, by George A. Hamilton,
Esq., M. P.:

«¢ About the year 1796, the late Mr. Hamilton, in pulling
down some old buildings at Tyrella, found, to his surprise,
that the beams, lintels, &c., were composed of cedar. On in-
quiry, he was informed that there was a tradition (for even
then it was but a tradition) that a large ship, from the coast of
Guinea, laden with slaves, ivory, and gold dust, had been
wrecked, a great many years previously, in the Bay of Dun-
drum, and a considerable portion of her swallowed up in the
sands near Tyrella; and though the shore, in the lapse of so
many years, had undergone considerable changes, there was
still a mark known by the country people under the name of
‘The Cedar Ship.’ I remember this well when a child.
There were two pieces of wood, covered with sea-weed, to be
seen at very low tides, sticking up in the sand.

‘* About the year 1815, my father, having collected a num-
ber of men, and having made an excavation in the sands,
discovered the upper works of the ship, and succeeded in ob-
taining six elephants’ tusks, a considerable quantity of cedar,
a silver goblet, and the remains of chains supposed to be those
with which the slaves had been confined.

‘‘ The situation of the wreck being under the level of low
water, and the soft oozy nature of the sand rendering the
work extremely difficult, prevented his proceeding further
with the excavation.

*¢ On the 10th of November, 1829, it occurred to me to
make a similar attempt. ‘The marks of the ship had been
long effaced, and I found some difficulty in discovering the
place. I succeeded, however, and in one tide I obtained six-

249

teen elephants’ tusks, a large quantity of cedar, four cannons,
the remains of a number of swords, muskets, and chains, a
number of small shells, some coral, a piece of metal, nearly
in the shape of a horse-shoe, which, at the time, we supposed
to be the handle of a trunk, and several pieces of a heavy me-
tallic substance.

<¢ Sir Charles Giesecke stated this substance to be a kind of
iron dross, probably of voleanic production, which is abundant
on the coast of Guinea, and the shells have been classified as of
that description which the inhabitants there use for money.”

Professor Graves exhibited specimens of the shells, coral,
&c.; and mentioned that the piece of metal, supposed to have
been the handle ofa trunk, was one of the maniille, or bracelets,
used to this day for the purpose of barter by merchants trading
on the coast of Africa, and identical in shape with the massive
gold ornaments frequently found in Ireland.

Professor Graves also read the following memorandum,
by Mr. Hamilton, relative to the discovery of what is termed
by the country people ‘‘a North House,” in the demesne of
Hampton, and the opening of a tumulus near Knockingen:

‘¢In the month of September, 1840, my brother-in-law,
Mr. Rowland Burdon, of Castle Eden, in the county of Dur-
ham, being on a visit at Hampton Hall, it occurred to me
one morning to ask him to examine two hillocks near Barna-
geera, in this neighbourhood, in order to ascertain whether
they were artificial mounds, or whether they were some of
those natural heaps of gravel called Eskers, which are found
so frequently across Ireland.

‘¢ Mr. Burdon had satisfied himself that the first which he
examined was natural, when his attention was attracted by a
large stone in the face of a ditch, which had been made re-
cently, traversing the hillock; he found it to be a flag, and,
when pulled down, it proved the head-stone of a rude stone
coffin, with a skeleton encased. ‘There was no weapon or
coin, or anything to indicate the date or circumstances of the

250

interment. On learning this, we proceeded to make an ex-
cavation in the second mound, and found there also some _
bones, and a broken pipe, of a very large size, but in shape
resembling the common tobacco pipes of the country.

‘‘ While thus engaged, an old man, one of my tenants,
came up to me, and inquired whether I had ever seen ‘the
North House,’ that had been found on my property, not far
from the place where we then were. I had never heard the
term ‘ North House’ before, and asked him what he meant,
‘ Oh,’ he said, ‘a kind of house under ground, made of large
flags and stones, with a passage like a large sewer lead-
ing to it.’ The North House, to which he referred, proved
to have been completely destroyed ; the stones had been car-
ried away for building some years previously. But one of the
fields in my demesne at Hampton, having been usually called
‘The North House meadow,’ although the origin of the
name had never before suggested itself, it occurred to me as
not unlikely that the name might have been given to it in
consequence of one of these North Houses having been at
some time discovered in it.

“¢ With the view of ascertaining this, we proceeded to make
excavations in different parts of the field, and at length we
happened upon the top stone of just such a chamber as the
old man had described.

“‘ It was constructed with large stones, in the rudest man-
ner; the one stone projecting beyond that immediately below
it, till a kind of bee-hive arch was formed: its height might
have been six feet, and its diameter perhaps the same. There
was a winding passage, or sewer, about three feet in height,
and the same in breadth, constructed also of large flags and
stones, and probably twenty yards in length, leading into it,
and a small funnel, not more than one foot in its dimensions,
at the opposite side of the chamber: the passage and the fun-
nel were probably much larger, but they had been broken
into as they approached the surface of the hill. We traced
the side walls for a considerable distance. There was no

251

cement used in the construction of this North House. We
found in it bones of oxen and swine, and some sea shells ;
also the bones of birds, brought there, probably, by foxes.

«< There was a larger and better defined mound than those
I have mentioned, on the edge of the sea-cliff, near Knock-
ingen, or Knocknagen, just where the little river Delvin,
dividing the counties of Dublin and Meath, falls into the
sea, and forms a small sandy bay. A portion of this mound
had been already washed away, and the remainder seemed
destined soon to share the same fate. On the beach imme-
diately below there were several immense stones, which ap-
parently had fallen from the mound. There was also, perhaps
a hundred yards to seaward, a considerable number of similar
stones, I could not help thinking that they had formerly
formed a part of two North Houses.

“The mound at the edge of the cliff afforded so favourable
an opportunity for examination, that, having obtained permis-
sion from Lord Gormanstown, on whose estate it was situate,
we proceeded to dig it away. It was composed of small
round stones, or shingle, from the shore. Our work was soon
interrupted by huge stones, similar to those on the shore, and
which appeared placed in a circle, buried in sand and shingle,
around, but at some distance from the centre of the mound.
Within this outer circle of stones we found, on what appeared
to have been a floor of beaten clay, alarge quantity of burned
human bones, apparently of persons of different ages: we
found amongst them the bones of very young children. In
the centre of this circle there was a chamber constructed of
immense flags, some of them more than six feet in height;
and within this a rude stone basin, or rather a large stone of
_ sandstone grit, with a cavity or hollow formed in it. This
stone bore evident marks of fire; and around it, on all sides,
were remains of charcoal or burned wood, and a quantity of
burned human bones. Amongst these bones we found some
beads, made of polished stone, in shape conical, with a hole
through each, near the apex of the cone.

252

‘¢ A portion of the mound may still be seen overhanging
the cliff, and if the section of it next the cliff be examined,
the bones and charcoal may be easily observed.

‘I gave the particulars of this discovery to Mr. D’ Alton
when he was about to publish his Memoir of Drogheda, and
it is referred to in the first volume of his History of Drog-
heda. I stated to Mr. D’Alton that there was no tradition
of the origin of this vast funereéal pile, but he quotes a passage
from Dr. Hanmer’s Chronicles of Ireland, from which it
would appear that a battle was fought between an army of
marauders and Dermott Lamhdearg, King of Leinster,
about the commencement of the fifth century, at Knock-na-
cean, 7. e., the Hill of Heads, the marauders having landed
at the ‘ Follesse of Skerries.’

‘« Rude stone coffins, composed of the common flag-stones
of the country placed together in the form of a coffin, with
skeletons, are found very frequently in this neighbourhood.

‘* Although it is unconnected with the foregoing, I may as
well state, as a matter of curiosity, that Mr. Burdon, about
the same time, when visiting the Hill of Tara, discovered
and brought home to me a regular joint of a basaltic column,
brought, no doubt, in the days of Tara’s greatness from the
Giant’s Causeway. He discovered it accidentally; it was
covered by the sod, and was not far from the pillar supposed
to be the Lia Fail.’

Rev. Samuel Haughton, Fellow of Trinity College, read
a paper on ‘“‘ The Equilibrium and Motion of elastic solid,
and fluid Bodies.”

The object of the paper is to deduce, by the method of the
‘ Mecanique Analytique’ of Lagrange, the laws of solid and
fluid bodies from the same physical principles, and to discover
by the same method the conditions at the limits,

The principle from which Mr. Haughton deduces the
equations is, that the molecules of solid and fluid bodies act on
each other in the direction of the line joining them, with a

253

force which is a function of the distance; and in the case of
crystalline structure, also of the direction of the line joining
the molecules.

The general equation of equilibrium of a system is,

SS(xSE + v8n + 28Z) dm = WSSvdadydz. (1)

Mr. Haughton shows from the definition of the medium, that
v=Vt+t+VM,
where v, is a homogeneous function of the first degree of
the six quantities,
@evon do. aq dG dc. de de. dn
dx’ dy’ dz’ dz* dy dy’ de ae ae
and v, a homogeneous function of the second order of the same
quantities. The function vo is zero in a solid body, and not in
a fluid ; which is equivalent to saying that in a solid body the
molecular forces equilibrate each other without the aid of ex-
ternal forces, but that in fluids this is not the case, and that
consequently a fluid left to itself would be dissipated by the
action of its own molecular forces; this Mr. Haughton con-
ceives to be true of all fluids, whether gaseous or liquid. It
should be understood that the mutual gravitations of the par-
ticles are not included among the molecular forces, but among

the external forces.
The values of v, and v, are shewn to be finally

PP dE KOs OG
w= ata =) (2)

a= a( + off + Bt a

of an %, de aE an
42.9. © MT, tN aa’ a+ 2(ayvw + Bouw + yur)

+231 ulate +Bigh +7 vg) +? (as 4 Bigttyae)

de
iE w(age i Bag im rE) }

254
where,

tig aca _ dé dn
z

dy’ aa IT MOI ph

It may be observed that the function v cannot be the
same as the function used by Professor MacCullagh for light,
which is a function of the quantities,

dn dc dZ dé dé dy

de ap page ay a
and that, consequently, if the latter represent light, that the
molecules of the luminous ether cannot act on each other in
the line joining them; in fact, the two functions mutually
exclude each other.

From (2) is deduced
WS§(xdE + v¥dn + 282) dm= (4)
(Sp o& dydz + Wpendadz + Sp 82 dady

a (2 o& + - on + — Bn da dy dz,
which will give the well-known equations of hydrostatics, and
the conditions at the limits of the fluid.

If the function v, be transformed by changing the direc-
tions of the axes of coordinates, it can be shown that the
transformation is the same as the transformation of the sur-
face

ax! + By* + cz* + 6(Ly?z? + Ma’2* + nay?) (5)
+ dy2z(3aa? + Bry? + y12*) + 4ez(ag2® ++ SBay? + 22")
+ Aay(asa? + B3y? + 3y32*) = 1.

This surface may be called the characteristic surface of the
function vj, as, ifit possesses any geometrical properties which
simplify its equation, a corresponding simplification will take
place in the function vj.

255

It is then shown, by the aid of the auxiliary ellipsoid, whose
equation is
(A—L)a? + (B—M)y? + (c—N)2 + 2a, + Pi + iY?

+ 2(a, + Bz + yo)? + 2(a3 + Bs + ys)ay = 1, (6)
that the function v, and the surface (5), may be referred to a sys-
tem of rectangularaxes, for which the following relations exist :°
8423,4+3=0; S$2,4+3,.=0:; 8,42,413,=0; (7)
the Hebrew letters denoting what the Greek become after
transformation of coordinates. The possibility of these equa-
tions in every case amounts to a proof of the existence of three
axes at each point of a body, which are intimately connected
with the molecular constitution of the body round the point.

The equation of equilibrium of a solid body is then shown
to be
WSS(x0E + ¥ dy +-28Z)dm= a —(Vh(P0E + a,6n+ R82 )dadydz, (8)
where

Bare aE BE aE Pe ae
* i uy ay aM a +2 (a7: dz ae “Teay)

dyn
. “Ee c Pp + vt 2 ar Dae en Bes Porras)

&Z LS
+ wre + Ma a raat "oa 7 age ee)

an

Q) oe

< tN z +287
a o(

* Pl tress as See

Boards “tf ley +P Ee)
aoe PE FS
p: “Hedy * " dydz a a

aE dé DE
+ Bigg t gat eget ot Pai evans * "edy)
& &L az BL
Ce aa? ™ fe a ap tat Ht ae ae Lae
at PE
ee as “ie 2 + Bayt * avait . nat “aay
9 he n a n
+72 2 a an at Be 20 ee ae Patedy ee
VOL. Ifl. x

256

A consists of double integrals, and gives the conditions at the
limits.

The differential equations of motion derived from (8) are
(no external forces x, ¥, z acting) :

a? a P?
ae = Pj; ian = Q) oa = R). (9)

These equations will admit of the particular integral

E = cosa. f(w), n=cosB.fiw), C=cosy.f(w),
w = le + my + nz — vt,

provided it is possible to satisfy with real values of (a, , y, 2)
the equations of condition resulting from the substitution of
these values in the equations of motion.

These equations of condition lead to the following con-
struction for the directions of the possible vibrations of mole-
cules, and the corresponding velocities of wave-planes.

Construct the six fixed ellipsoids,

P= Av?+ ny + M2? + 2ayyz + 2aoaz + 2a,2y = 1,
Qa BY + Le + Na? + 23,y2 + 23.024 2B,0y= 1,
R= C2? 4 Ma? + Ly + 2y,y24 2yo.xz 4 2y,2y = 1,
Foaat Py + y2+ 2Lyz 4+ 2y302 + 2B,.2y =1,
G age? + Bay? + yor’ + 2y3yz + 2Maz + 2azy = 1,
H = a3" + By + y32 + 2B.yz + 2qyaz + 2Nay = },

(10)

and from their common centre draw the normal to the wave-
plane, this will pierce the surfaces in six points ; let the corres-
ponding radii vectores be p,p,, Py 7,773 With these con-
struct the ellipsoid

2, Qyz , uz | ay

+ 2

2 2
P, Pu Pa a ri, Pun

The axes of this ellipsoid will be the three possible directions

Zot

of molecular vibration, and the corresponding velocities of
waves will be inversely as the lengths of these axes.” ’

The six ellipsoids just mentioned perform a very impor-
tant part in the problem of elastic solids, as they reappear in
the conditions at the limits, and afford a geometrical meaning
for many of the results.

Mr. Haughton then determines from simple considerations
the equation of the Sphero-Reciprocal-Polar of the Wave-
surface, or the Surface of Wave-slowness of elastic Solids,
which occupies a position in this subject, analogous to that
held by the index-surface in light. This surface, and the im-
portant results it leads to, are, as faras Mr. Haughton is aware,
given by him for the first time; it is of the sixth degree, and
has three sheets, and by means of it, the direction of a vibra-
tion passing from one medium into another may be determined.

The paper then proceeds to the discussion of three parti-
cular cases of elastic solids: 1. The case where the molecules
are arranged symmetrically round three rectangular planes.
2. Round one axis. 3. The case of a homogeneous uncrys-
talline body.

In the first case, the following results are deduced: The
traces of the surface of wave-slowness on the planes of sym-
metry, consist of an ellipse and a curve of the fourth degree.
The surface possesses four nodes in one of its principal planes,
where the tangent plane becomes a cone of the second degree,
and the existence of these points will give rise to a conical
refraction in acoustics, similar to what has been established in
physical optics.

In general, for a given direction of wave-plane, three

* After Mr. Haughton had obtained this construction, he found that M.
Cauchy has given analytically, and for a particular case, a solution which
involves an analogous ellipsoid ; but M. Cauchy has not followed out the con-
sequences of his analysis in the right direction, and has been misled in his
attempt to apply his equations to the problem of light.

x2

258

waves will be possible, the corresponding vibrations of the
molecules being in three directions, at right angles to each
other, though not, in general, parallel or normal to the wave-
plane. Mr. Haughton ‘investigates the possibility of the
vibrations being normal and transversal, and finds . that for
particular directions of wave (given in the paper), the vibra-
tions are, two in the wave-plane, and the third perpendicular
to it. He discusses also at length the other two cases, toge-
ther with the equations of condition which hold in general at
the limits, and the geometrical interpretation of these condi-
tions by means of the fixed ellipsoids (10).

The President read a note from Edward Cooper, Esq.,
giving the place of the new Comet, as observed at Markree,
May 18d. 12h. 6m. Greenwich mean time.

DONATIONS.

Report of the Commissioners appointed to take the Census
of Ireland for the Year 1841. Presented by W. R. Wilde,
Esq.

Transactions of the Botanical Society of Edinburgh.
Vol. II. Parts 1 & 2. Presented by the Society.

Lettres a S. A. R. le Duc Regnant de Saxe Coburg et
Gotha, sur la Theorie des Probabilites appliquée aux Sciences
morales et politiques. Par A. Quetelet. Presented by the
Author.

Annales des Sciences Physiques et Naturelles, d Agricul-
ture et d’ Industrie, publieés par la Société Royale d Agricul-
ture, &c., de Lyon. Tome VII. Annee 1844. Presented by
the Society.

Popery unmasked. By John Ryan, Esq. Presented by
the Author.

The thirteenth Annual Report of the Royal Cornwall
Polytechnic Society. 1845. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846. No. 55.
June 8th.
REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Thomas John Beasly, Esq., Thomas Percy Boyd, Esq.,
and Rey. Robert J. M‘Ghee, were elected Members of the
Academy.

The President announced to the Academy, that Arthur R.
Nugent, Esq., M. R.I. A., on the part of the Rev. Francis
Brownlow, had deposited the ancient MS. called the Book
of Armagh, in the Museum of the Academy, and that he had
given to Mr. Nugent the following receipt for the same, sub-
ject to the approval of the Academy : :

* Royal Irish Academy,
‘¢ Dublin, 4th June, 1846.

** Arthur R. Nugent, Esq., M. R. I. A., has this day de-
posited in the Museum of the Royal Irish Academy, on the
part of the Rev. Francis Brownlow, that ancient Irish MS.
called the Book of Armagh, the property of the said Rev.
Francis Brownlow, with the understanding that the Academy
will take the same care of the said book that they do of the
best article in their Museum; and that the Academy will at
any time return the said book to the said Rey. Francis Brown-

260

low, ,or his heirs or representatives, on his or their demand,
and without any delay, charge, or hindrance whatever.
‘¢ Signed, subject to the approbation of the Academy,
‘¢H. Luoyp, President.”

Ir was Resotvep,—That the deposit of the Book of
Armagh be accepted by the Academy, on the conditions
named ; and that the thanks of the Academy be voted to the
Rev. Francis Brownlow, and to Arthur R. Nugent, Esq.

W. R. Wilde, Esq., exhibited and described the ‘* Mias
> an ancient Irish shrine, from the barony of
Tyrawley, County of Mayo, which had been lent to him by
Annesley Knox, Esq., for that purpose.

Ir was Resotvep,—That the thanks of the Academy be
presented to Mr. Knox, by whose permission the Mias Tigher-
nain has been exhibited to the Academy.

i 5
Tighearnain,

Mr. Wilde presented a collection of Celtic antiquities,
weapons, ornaments, domestic implements, sepulchral urns,
and some animal remains, found in ancient tumuli, from Arthur
R. Nugent, Esq., Portaferry, from whom Mr. Wilde made a
communication in 1844. These interesting relics consisted of
a very large stone celt, eight inches long; several flint arrow-
heads, among which is one of the most beautiful, both in form
and execution, which the Academy has yet received; three flint
knives, two very rude and apparently in the process of forma-
tion ; a small sharpening stone; and four small circular stone
discs, perforated in the centre, and probably used for the dis-
taff ;—all discovered in the County of Down, a locality re-
markably rich in antiquities of this description. He also
presented some silver pieces, among which was a shilling of
Elizabeth and one of James I.

The sepulchral urns, two in number, one very perfect,
the other in fragments, but capable of being restored, were dis-
covered along with some incinerated bones, charred wood, and

ee

261

a quantity of the remains of some of the lower domesticanimals,
at Donaghanie, in the County of Donegal ; and Mr, Wilde
stated that he had received a communication on the subject
from Mr. John Bell of Dungannon, informing him that they
were found on opening a cairn contained “ within a circle of
large stones, measuring seventy yards in circumference. One
of the Rev. John Davis’s tenants requiring building materials,
thoroughly laid open the tumulus, uncovering numerous se-
pulchral cells. These were replete with such rudely sculp-
tured ornaments as are frequently found in cairn chambers.
The vertical columns supporting large flags, shortening
inwards, one over the other, are about six feetin height, and
the roof-stones are kept in their places by the pressure of the
heap or cairn on their extremities. This structure is similar
to those near Drogheda and in Rosshire, and to that which
once stood on the banks of the Carron in Stirlingshire.”
From this description, the similarity of the cairn at Do-
naghanie to the great tumulus at New Grange will be at once
recognised by the Academy; and the sculptured ornaments
found in both these localities, and consisting of volutes, circles,
and zig-zag characters, Mr. Wilde considered to be purely cha-
racteristic of the ancient Pagan burial places in Ireland, and per-
fectly distinct from that denominated Ogham writing. Of this
sepulchral character a fine ex-
ample is found upon the inte-
rior of one of the stones forming ~
the upright pillars in the open
kistvaen at Knockmany, in the
County Tyrone, and of which
the accompanying is a rude
- sketch. The animal remains
found at Donaghanie consisted
of the bones of several domes-~
tic animals, oxen, swine, cats, _
dogs, sheep, together with those
of geese, and other domestic fowl; and it is interesting to dis-

262

cover such traces of the distribution of these animals in the
British Isles at a period’so remote as the date of this tumulus
points to. ?

Mr. Wilde recorded the discovery of a smal] tumulus on the
western side of the great mound of New Grange, which had
been opened by Lieutenant Newenham two years ago: it was
abouteight feetlong,.and consisted of a small stone passage lead-
ing into a little chamber, formed on the type of the great barrow
in that vicinity. In this was discovered a vast collection of the
remains of domestic animals, as well as several human bones,
some perfect and others in a half-burned state. What gave
particular interest to this excavation was the fact of the stones

‘which lined the floor having” been vitrified on the external face,

which would lead to the conclusion that the cremation had
taken place in the grave : and one of these vitrified stones Mr.
Wilde presented to the Academy.

It is much to be lamented that ignorant persons, or those
actuated by mere curiosity, should be allowed to open, and, as
is very often the case, destroy those interesting monuments
throughout the country, many of which possess an historical
as well as an antiquarian and ethnological interest, and are
alluded to in the ancient annals.*

* The following communication has been made to the Secretary by Mr.
Wilde. ‘‘Some time ago, Arthur R. Nugent, Esq., opened a large sepul-
chral mound in the townland of Kintagh, in the neighbourhood of Porta-
ferry, whence he writes to me: ‘ There was a circle of large stones con-
taining an area of about a rood. Between each of these flat stones there
was a facing of flat ones, similar to the building of our modern fences.
The outer covering was coated with white pebbles, averaging the size of
a goose-egg, of which there were several cart-loads,—although it would
be difficult to collect even a small quantity at present along the beach.
After this was taken away, we came to a confused heap of rubbish, stones,
and clay, and then some large flag stones on their end, the tumulus still pre-
serving a cone-shape. In the centre we came to a chamber about six feet long,
formed by eight very large upright stones, with a large flag-stone at the bot-
tom, on which lay, in one heap of equal thickness, a mixture of black mould
and bones.’ ‘These bones, seyeral of which are now in the Museum 0 {the

263

.Resotvep,—That the thanks of the Academy be given to
Mr. Nugent.

The Secretary announced to the meeting, that the Com-
missioners for the Improvement of the Shannon had for-
warded a further donation of antiquities found in the bed of
that river to the Museum; together with a section and plans ©
of the small tower at Clonmacnoise.

ReEsoLtveD,— That the thanks of the Academy be given
to the Commissioners.

Dr. Allman exhibited a remarkable form of Saxifraga
Leucanthemifolia, presenting the retrograde metamorphosis
of flowers into bulbs, which were thickly scattered over the
inflorescence, occupying the position of the leafy tufts de-
scribed by Robert Brown in his Saxifraga Foliosa.

Rev. Samuel Butcher read a paper by the Rev. Edward
Hincks, D. D., ‘<* On Persepolitan Writing.”

In this paper various rectifications of the received mode
of reading the first kind of Persepolitan, writing were pro-
posed; and an alphabet, or rather a combined alphabet and
syllabary for the second was given, differing in some important
respects from that of Westergaard.

Academy, are all human, and consist of the ribs, vertebre, and the ends of
the long bones, together with pieces of the skull, and some joints of the fingers
of a full-grown person, and also several bones of a very young child, none of
which hadbeen subject to the action of fire. But among the parcel forwarded
to me by Mr. Nugent, are several fragments of incinerated human bones.
Either these latter were portions of the same bodies burned, or they belonged
to an individual sacrificed to the manes of the person whose grave this was ;
and I am inclined to think the latter is the more probable, from the circum-
“stances in which similar remains have been discovered in other localities.
There were no urns, weapons, or ornaments of any description discovered in
connexion with this tumulus; but Mr. Nugent states, that in the field where
it was opened, small stone chambers, or kistvaens, have at various times
been dug up, and in one of these a long, flat, and narrow skull was some time
since discovered.” W.R. W.

264

The changes proposed with respect to the first kind were
these :

1. The vowel a might be inserted after any primary letter,
before a vowel, either as a distinct syllable, or as a guna to the
vowel, as well as before a consonant.

2. W after u, and y after ¢, are in general, both in the

‘middle and at the end of words, absolutely mute. When not
so, they are to be sounded as a, which they implicitly con-
tain.

3. Secondary consonants, which are only used before par-
ticular vowels, are to be sounded in the same manner as the
corresponding primary ones; and if a secondary consonant
exist proper to any vowel, and the corresponding primary
consonant appears to precede that vowel, an a is always to be
supplied. Ifa secondary consonant be used without its pro-
per vowel after it, that vowel must be supplied ; 7 is here con-

’ sidered as a vowel. Thus the combination of the letters which
Lassen calls mz would be mi; while his mz would be me, for
mai. His fr would be pr; while his pr would be par.

4, Besides his mistake in giving values to the secon-
dary consonants generally, different from those of their cor-
responding primary ones, Lassen has erroneously considered
the secondary consonant corresponding to d before z to cor-
respond to &’, i. e. ch; and he has given to three primary
consonants the values d, z, and 2’, i.e. zh ; the true values of
which Dr. Hincks maintains were z, zh, andj, or dzh.

The second Persepolitan alphabet, it is here maintained,
consisted of characters representing nine elementary sounds :
viz., four vowels, a, z, w, and er, and five consonants p, R, ¢, s,
and n: and various combinations of these nine elements. In
most cases, two or more characters, phonetically equivalent,
represented the same element or combination.

Westergaard supposes a much larger proportion of the
characters to represent elementary sounds than Dr, Hincks ;
and he supposes that an a might be inserted, as in the first

265

kind of writing. Dr. Hincks maintains that every vowel
is expressed at least once; but that both vowels and conso-
nants might be expressed twice, at the end of one character
and at the beginning of the next.

In addition to the correction made in Westergaard’s al-
phabet by the addition of vowels to the consonants, which he
supposed the complete representations of certain characters,
and by the substitution of different vowels for those which he
used, entirely new values are given by Dr. Hincks to five cha-
racters which Westergaard had improperly valued, and to five
more which he had not valued at all.

Specimens of the inscriptions in this kind of writing, as
read and translated, were added. The language was said to
agree with the Indo-Germanic languages in having inflections ;
but to have inflections completely different from those of all
these languages.

In a postscript to the paper it was stated, that the Babylo-
nian and Assyrian alphabets were both of the same nature as
this ; so far as that some of the characters represented syl-
lables and some elementary sounds; that the same sound was
represented by two or more characters; that no vowel was
omitted ; and that vowels and consonants were habitually re-
presented twice, when only to be sounded once. The number
of elementary sounds in the Babylonian, or third kind of Per-
sepolitan writing, was greater than in the second kind, as was
the number of characters in use. Both the Babylonian and
Assyrian had something in common with the second Persepo-
litan language ; but they had also affinities with the Semitic
languages.

Rev. T. R. Robinson made some observations on Dr.
Hincks’s paper, referring to researches on the same subject
by Mr. Norris and Colonel Rawlinson.

Rev. S. Butcher read the third part of Dr. Hincks’s paper
on Egyptian hicroglyphics.

266

In it the principles established in the preceding parts were
applied to ascertain the exact power of each of the letters of the
Egyptian alphabet. Those contained in the alphabet lately pub-
lished by Chev. Bunsen were first examined; and then the other
characters alleged to be alphabetic: some of which were classed,
in Chev. Bunsen’s arrangement, among thesyllabic signs, while
others were altogether omitted. A new class of letters having
the power of ch, and corresponding to the Hebrew ¥, is esta-
blished, to which the long serpent belongs, occurring in the
word chat, signifying ever.

Robert Ball, Esq., exhibited various anatomical prepara-
tions of marine animals made by Mr. Goadby of London.

June 22.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Mr. Oldham, on the part of Mr. R. Mallet, who was
unavoidably absent, described the objects, construction, and
use of certain new instruments devised by the latter for self-
registration of the passage of earthquake shocks.

Instruments previously intended for this purpose have not
possessed the power of self-registration ; they have consisted
either in the trace left by the motionyof a viscid fluid on the
containing vessel, or they have been upon the principle of the
inverted pendulum, or watchmaker’s noddy. Instruments so
constructed are objectionable, because having themselves
times of vibration of their own, which may conflict with those
of the earthquake shock, they are liable to fail in point of
delicacy. They also possess several inconveniences of a me-
chanical kind in being adapted to self-registration.

The objects to be attained in the instruments which the
author has had in view, are:

267

The self-registration—

Ist. Of the time of transit, at a given point of the earth’s
surface, of an earthquake shock, or earth-wave, noting same
to a small decimal of a second of time.

2nd. Of the vertical element, or altitude, of the earth-
wave, at the moment of its transit, whether the wave be a po-
sitive or a negative one.

3rd. Of the horizontal element, or amplitude of the wave,
at the same moment.

4th. Of the direction, as to azimuth, of the wave transit.

The principle adopted, as the means by which the wave, or
shock, shall act upon the instrument, consists in availing our-
selves of the oscillation of a column of mercury, in two verti-
cal, and in four horizontal glass tubes, of peculiar construction.
One end of the column of mercury in each tube is so adjusted
in contact with one pole of a constant galvanic battery, that
the oscillation produced in the mercurial column by the wave,
in passing, breaks contact. The time during which the con-
tact remains broken is proportionate to the amount of the ver-
- tical and horizontal elements of the wave. The breach of
contact releases one or more of six pencils at the instant of its
occurrence, and until contact is restored. Either of these
continues to describe a trace upon a ruled sheet, placed upon
a cylindrical barrel, carried round by the astronomical clock.
The length of this trace is, therefore, a graphic representa-
tion of the amount of the respective element of the wave, and
the pencil which mark it indicates the direction of the oscil-
lation, whether vertically positive or negative, or horizon-
tally from any point of the compass.

A somewhat similar arrangement marks, upon four dials,
the hour, minute, second, and fraction of a second, at which
the crest of the wave has passed the point of the observa-
tory, or locus of the instrument. This is of peculiar im-
portance for ascertaining the rate of progress of the wave
between two distant observatories. The instrument cannot

268

be understood in its details, without the aid of diagrams, as
exhibited to the Academy.

The instrument is designed to register, by itself, for
twelve hours at a time, and at such an interval its registra-
tions require to be read off and noted.

Dr. Todd read a letter from C. T. Barnwell, Esq., con-
taining some observations on two passages of Archimedes,
De Sphera et Cylindro, where commentators appear to have
been strangely misled.

The first occurs in the Demonstration of Proposition I. of
the first book.

In the demonstration of this proposition it is assumed that
the triangles ABA, BIA are together greater than the tri-
angle AAT’ (fig. pag. 79, Oxf. ed. fol. 1792).

Dr. Barrow (in whose edition this is Prop. XII.) says,
“‘liquet.... quia AB+BI'> AT, et altitudo communis est,”
which is evidently not true, unless the triangle ABI’ were
equilateral.

In the German edition of J. C. Sturm (where this is
Prop. IX.) the following most extraordinary inference is
drawn from Euc. I. 24, viz., that, since (fig. in p. 80)
AZ> AE, TA common, and the angle TAZ > the angle TAE,
the triangle TAZ > the triangle TAE.

In the Oxford edition, the demonstration of Eutocius is
condemned as invalid; but the editor, without stating the na-
ture of his objection, contents himself with adding ‘sed res
ipsa satis patet.”

Flauti, of Naples (Corso, vol. I.) observes, and rightly,
that the line AZ should have been directed to be drawn in the
plane of the triangle AAT, and states what he considers to
be the objection of the Oxford editor, viz., that the triangle
TAZ will not include the triangle [AE in the case of
the angle AAB > the angle AAT, and that it cannot, there-
fore, be inferred generally, that the first of these triangles >
the second, He then subjoins a different demonstration.

269

Hauber, in his excellent edition of this treatise (Tubin-
gen, 1798), appears also to admit the objection; for he gives
another demenstration of the assumption in question, which
is, perhaps, preferable to Flauti’s. Peyrard does not attempt
any explanation or demonstration.

It is, however, very remarkable, that not one of the edi-
tors seems to have observed that, in the subsequent applica-
tion of Prop. X. (see the Corollaries at the end of Prop. XIII.
p. 86) the triangle AAT is composed with the lesser of the
two conical surfaces intercepted between the lines AA, AT;
and consequently, that the lesser of the two segments, into
which the circle is divided by the line AT’, is the one which
should have been bisected in B.

The figure in p. 80, when corrected accordingly, will be
this :

where, since the angle TAZ (=the angle TAB) is >1AE,
and < T'AA (since TB < TA), the triangle TAZ will evidently
include the triangle. CAE, and the demonstration given by
Eutocius will be valid. The only objection now to be made
to it is, that it is unnecessary ; for, since (B+BA > I'A, and
the perpendicular on IB or BA is also > that on T'A, it at
_once follows that the triangle TAB + the triangle BAA >
triangle TAA.
In every edition, the point Z appears to be in the circum-
ference of the circle (BA, which seems to have misled Sturm
and, perhaps, the Oxford editor also.

270

In a modern German edition of the whole of Archimedes,
by Nirze (Stralsund, 1824), Hauber’s demonstration is adopted,
but in a less advantageous form, and with an erroneous figure.

The second occurs in the Demonstration of Proposition V.
of the second Book.

At the foot of page 157, Oxford edition, it is said: ** Since
the ratio of AA to AX is given, as well as that of PA to
AX, the ratio of PA to AA is also given.” But this is untrue
with respect to the first of these ratios, which is not given.
Indeed, if it were, the analysis would here be at an end; for,
since (p. 157, lin. penult.) AA: AX :: BZ:ZX, the ratio of
BX:ZX would be given, as also ZX (since BZ is given) and
the point X.

But it is remarkable that this corruption is as old as the
time of Eutocius; for he has been led into an error so gross,
that it is hardly possible to imagine how so able a commenta-
tor could have fallen into it. This error is no less than the as-
sertion (page 160, line 25) that BX is given, because its
extremities are given ; whereas the whole object of the analy-
sis is to find the point X.

This corruption of the text has been allowed to pass unno-
ticed into the Oxford edition, though it had been corrected in
the old Latin translation, in the edition of 1544, as well as in
the Greek text of that edition, except that in this latter there
is an error of AA for PX.

Sturm, who does not give a regular translation of his au-
thor, has avoided the error in the text, but it is retained in
Nizre and Peyrard.

Hauber has adopted the correction of the old translation,
which is, undoubtedly, just; ‘* since the ratio of PX to AX is
given, that of PA to AX is also given.”

The President described certain improvements in the
construction of the Anemometer, and exhibited to the Aca-
demy the improved instrument.

271

The Anemometer of Osler, which is that employed in the
Dublin Magnetical and Meteorological Observatory, regis-
ters, as is well’ known, both the direction and the pressure of
the wind at every instant. The improvements which Mr.
Osler has lately introduced into the construction of the instru-
ment seem to leave nothing to be desired, so far as relates to
the former part of its office. The place of the directing vane is
now supplied by a vertical wheel with oblique vanes, which,
by the intervention of wheel-work, is made to work round
upon a fixed horizontal toothed wheel, and thus to maintain
itself always in the vertical plane passing through the direc-
tion of the wind. This plan, which is that of the small direct-
ing wheel of the ordinary wind-mill, is found to answer its
purpose admirably, and to avoid altogether the inconvenience
which arose from the oscillations of the vane in the old con-
struction. ‘The only change which Dr. Lloyd has adopted
in this part of the instrument, consists in placing this wheel
centrally, instead of excentrically, with respect to the whole
apparatus.

In the portion of the instrument destined to measure and
register the pressure of the wind, which had always been
found the least satisfactory, Dr. Lloyd employs a smaller
vane-wheel, connected with the former by means of the frame-
work of the instrument, and maintained by it always per-
pendicular to the direction of the wind. The pressure of
the wind acts, through this wheel, upon a spiral spring coiled
in a box, the vane-wheel and the spring being connected by
an intermediate wheel and pinion. The axle of the vane-wheel
carries an endless screw, which works upon a toothed wheel ;
and upon an arbor, attached to the axle of the latter, is coiled
the chain which communicates with the registering apparatus
below. The chain is kept tended, when the pressure of the
wind is relaxed, by means of a small spring attached to the
registering table.

The objects proposed to be attained by this arrangement

VOL. I. Y

272

are: 1. ‘To augment the sensibility of the instrument, and to
render it available for the registry of light gales, no less than
high winds; and 2. To diminish, by means of the inertia of
the wheel, the oscillatory movement of the registering pencil,
occasioned by the unsteady action of the wind.

Mr. Petrie exhibited several ancient bells—the bell of St.
Cuanna, of the county Clare, and the bell of St. Ruadhan, of
Lorha, and some others. He also exhibited some bells sup-
posed to be of pagan age.

The thanks of the Academy were given to Mr. Cake
for permitting the Bearnan Cullain to be exhibited to the
Academy.

DONATIONS.

An ancient Bronze Bit and Flint Knife, part of the collec-
tion of the late John Echlin, Esq. Presented by Miss Echlin.

July 20. (Extraordinary Meeting.)
REV. HUMPHREY LLOYD, President, in the Chair.

RESOLVED, on the recommendation of the Council,— That
a congratulatory Address be presented to His Excellency the
Lord Lieutenant.

ResoLtvep,—That the President and Secretaries (or offi-
cers) be a Sub-Committee to prepare a draft of an Address,
which, having been agreed to by the Sub-Committee, was
presented to the Meeting, whereupon

Ir was Reso_vep,—That the Address now presented be
adopted, and that the President shall summon the Academy,
as soon as His Excellency’s pleasure is declared, as to the

time when it would be convenient to him to receive the
Address.

et,

273

During the absence of the Sub-Committee, the Chair
was taken, pro tem., by George Petrie, Esq., V. P., when

Sir William R. Hamilton read a paper on the expression
and proof of Pascal’s theorem by means of quaternions; and
on some other connected subjects.

This proof of the theorem of Pascal depends on the fol-
lowing form of the general equation of cones of the second
degree :

8. BP’ B" = 0; (1)
in which
B SSN (v ° aa’. View al’ a”),
B! = -wiev natal wid” a”); (2)
Bra eva ale: a’ a),

a, a’, a’, a’, a’", a", being any six homoconice vectors, and
s, v, being characteristics of the operations of taking sepa-
rately the scalar and vector parts of a quaternion.

In all these geometrical applications of quaternions, it is
to be remembered that the product of two opposite vectors is
a positive number, namely, the product of the numbers ex-
pressing the lengths of the two factors ; and that the product
of two rectangular vectors is a third vector rectangular to
both, and such that the rotation round it, from the multiplier
to the multiplicand, is positive. These conceptions, or defi-
nitions, of geometrical multiplication, are essential in the
theory of quaternions, and are hitherto (so far as Sir William
Hamilton knows) peculiar to it. If they be adopted, they
oblige us to regard the product (or the quotient) of two in-
clined vectors (neither parallel nor perpendicular to each
other), as being partly a number and partly a line ; on which
account a quaternion, generally, as being always, in its

geometrical aspect, a product (or quotient) of two lines, may

perhaps not improperly be also called aGRaMMaRITHM (by a

combination of the two Greek words. ypayyh and apOude,

which signify respectively a dine and a number). In this
¥ 2

274

phraseology, the scalar part of a quaternion would be the
arithmic part of a grammarithm ; and the vector part of a
quaternion would be the grammic part of a grammarithm.
In the form given above, of the general equation of cones of
the second degree, the six symbols, a, ...a”, denote six edges
of a hexahedral angle inscribed in such a cone; the six
binary products aa’,...a”a, of those lines taken in their order,
are grammarithms, of which the symbols v.aa’, &c., denote
the grammic parts, namely, certain lines perpendicular re-
spectively to the six plane faces of the angle; the three pro-

ducts
v.aa.vV.a” a”, &e.,

of normals to opposite faces, are again grammarithms, of
which the grammic parts are the three lines 6, 9’, 8”, situ-
ated respectively in the intersections of the three pairs of
opposite faces of the angle inscribed in the cone; and the
equation (1) of that cone, which expresses that the arithmic
part of the product of these three lines vanishes, shows also,
by the principles of this theory, that these lines themselves
are coplanar: which is a form of the theorem of Pascal. _

The rules of this calculus of grammarithms, or of qua-
ternions, give, generally, for the arithmic or scalar part of
the product of the vector parts of the three products of any
six lines or vectors aa’, 33’, yy’, taken two by two, the fol-
lowing transformed expression:

s(v. aa’.v. 3 P/.v. vy’) Se ayy’: Ss. a 3/3’ —s. ayy’: S. aS’; (3)

and by applying this general transformation to the recent
results, we find easily, that the equation (1), under the con-
ditions (2), may be put under the form:

1 WY ot IV hv Vio IV

S.aaa S.aaea S.aaa S.aaa (4)
——, » — a = ooo ooo:
s.aa’a”’ s.a’a‘al” s.ada” ~~ s.a“a'al’”

which is another mode of expressing by quaternions the ge-
neral condition required, in order that six vectors a,...a", ©

275

diverging from one common origin, may all be sides of one
common cone of the second degree. ‘The summit of this cone,
or the common initial point of each of these six vectors, being
ealled o, let the six final points be ancpsc’: the transformed
equation of homoconicism (4) expresses that the ratio com-
pounded of the two ratios of the two pyramids OABC, OCDE, to
the two other pyramids oavC, OCBE, does not change when we
pass from the point c to any other point c’ on the same cone
of the second degree: which is a form of the theorem of M.
Chasles, respecting the constancy of the anharmonic ratio.
An intimate connexion between this theorem and that ot
Pascal is thus exhibited, by this symbolical process of trans-
formation.

As the equation (1) expresses that the three vectors
B PB’ B” are coplanar, or that they are contained on one com-
mon plane, if they diverge from one common origin, and as
the equation (4) expresses that the six vectors a,...a" are
homoconic, so does this other equation,

s.p(p— vy) (y—B)(B —a)a=0, (5)

express that the four vectors a, (3, y, p are homospheric, or
that they may be regarded as representing, in length and in
direction, four diverging chords of one common sphere. Thus,
the arithmic part of the continued product of the five succes-
sive sides of any rectilinear (but not necessarily plane) pen-
tagon, inscribed in a sphere, is zero; and conversely, if in
any investigation respecting any rectilinear, but, generally,
uneven, pentagon aBCDE in space, the product aB x BC X CD
x DEXEA of five successive sides, when determined by the
rules of the present calculus, is found to be a pure vector, or
ean be entirely constructed by a dine, so that in a notation
already submitted to the Academy (see account of the com-
munication made in last December) the equation

S.ABCDEA — 0, (6)

276

is found to be satisfied, we may then infer that the five cor-
ners A, B,C, D, E, of this pentagon, are situated on the surface
of one common sphere. This equation of homosphericism
(5) or (6), appears to the present author to be very fertile
in its consequences. To leave no doubt respecting its meaning,
and to present it under a form under which it may be easily
understood by those who have not yet made themselves mas-
ters of the whole of the theory, it may be stated thus: if we
write for abridgment,

ai i (a — 2) +) (Yi — Yo) + (Zi — 2)s
ay = 1 (#2 — U3) + J (Yo — Y3) +k (22 — 2s),
a3; = 1 (23 — #4) +) (ys — ys) +R (23 — 24) (7)
a, = 1 (%4— 25) +9 (Ys — Ys) +B (Zs — 2s)s
a, = 2 (a — 2) +7 (Ys—%") + h(25 — 2),

and then develope the continued product of these five expres-
sions, using the distributive, but not (so far as relates to 77k)
the commutative property of multiplication, and reducing the
result to the form of a quaternion,

Q, Ag a3 Ag as = W + 1 + yy + kz, (8)

by the fundamental symbolical relations between the three
coordinate characteristics ijk, which were communicated to
the Academy by Sir William Hamilton in November, 1843,
and which may be thus concisely stated :

Sy =e ae = V; (Cae)

and if we find, as the result of this calculation, that the term

* These fundamental equations between the author’s symbols i, j, £, appeared,
under a slightly more developed form, inthe number of the London, Edinburgh,
and Dublin Philosophical Magazine for July, 1844; in which Magazine the
author has continued to publish, from time to time, some articles of a Paper on
Quaternions; reserving, however, for the Transactions of the Royal Irish
Academy, a more complete and systematic account of his researches on this

extensive subject.

277

w, or the part of the quaternion (8) which is independent of
the characteristics 77k, vanishes, so that we have the following
equation, which is entirely freed from those symbolic factors,

1 20; (9)
we shall then know that the points, of which the rectangular.
coordinates are respectively (2Y12,) (@2Y222) (#34323) (@4YsZa)
(t5Y525), are five homospheric points, or that one common
spheric surface will contain them all.

The actual process of this multiplication and reduction
would be tedious, nor is it offered as the easiest, but only as
one way of forming the equation in rectangular coordinates,
which is here denoted by (9). A much easier way would be
to prepare the equation (5) by a previous development, so as
to put it under the following form :

o’S.aBy =a’s.Byp + B's. yap + y’S. ap; (10)
which also admits of a simple geometrical interpretation. For,
by comparing it with the following equation, which is in this
calculus an édentical one, or is satisfied for any four vectors,
a, B, ep

pS.apy = as. Byp + BS.yap + yS-afp, (11)
we find that the form (10) gives

p= aa’ + BP’ + yy’, (12)
if a’, 3’, y’ denote three diverging edges of a parallelepiped,
of which the intermediate diagonal (or their symbolic sum) is
the chord p of a sphere, while af y are three other chords of
the same sphere, in the directions of the three edges, and
coinitial with them and with p; so that the square upon the
diagonal p is equal to the sum of the three rectangles under
the three edges a' [3 y' and the three chords ay, with
which, in direction, those edges respectively coincide. This
theorem is only mentioned here, as a simple example of the
interpretation of the formule to which the present method con-
ducts ; since the same result may be obtained very simply

278

from a more ordinary form of the equation of the sphere, re-
ferred to the edges a’ [3’y’ as oblique coordinates ; and, doubt-
less, has been already obtained in that or in some other
way. An analogous theorem for the ellipsoid may be ob-
tained with little difficulty.

If we suppose in the formula (6), that the point & of the
pentagon approaches to the point A, the side Ea tends to be-
come an infinitely small tangent to the sphere; and thus we
find that v.aBcpa, or that the vector part of the continued
product AB X BC XCD XDa, of the four sides of an uneven (or.
gauche) quadrilateral ancy, if determined by the rules of
multiplication proper to this calculus, 7s normal to the cir-
cumscribed sphere at the point a, where the first and fourth
sides are supposed to meet. By the non-commutative cha-
racter of quaternion multiplication, we should get a different
product, if we took the factors in the order Bc x CD x Da X AB;
and accordingly the vector or grammic part v. BCDAB of this
new quaternion product would represent a new line in space,
namely, a normal to the same sphere at B: and similarly may
the normals be found at the two other corners of the quadri-
lateral, by two other arrangements of the four sides as factors.
To determine the lengths of the normal lines thus assigned, we
may observe that. if a’, B’,c’, p’ be the four points on the
same sphere, which are diametrically opposite to the four
given points A, B, C, D, then the four diameters a’A, B’B, C’c, D’D
are given by four expressions, of which it may be sufficient to

write one, namely :
,. __V.ABCDA

‘A= : (13)
S.ABCD

The denominator of this expression denotes (as was re-

marked in a former communication) the sextuple volume of —

the pyramid, or tetrahedron, aBcp; it vanishes, therefore,

when the four points a, B,C, D are in one plane: so that we

have for any plane quadrilateral the equation,

S.ABCD = 0, (14)

279

If the sphere is then to become only indeterminate, and
not necessarily infinite, we must suppose that the numerator
of the same expression (13) also vanishes; that is, we must
have in this case the condition

v.aBcpa = 0. (15)

In words, as the product of the five successive sides of an
uneven but rectilinear pentagon inscribed in a sphere, has
been seen to be purely a line, so we now see that the product
of the four successive sides of a quadrilateral inscribed in a
circle is (in this system) purely a number: whereas, for every
other rectilinear quadrilateral,. whether plane or gauche, the
grammarithm obtained as the product of four successive sides
involves a grammic part, which does not vanish. This
condition (15), for a quadrilateral inscribable in a circle,
could not be always satisfied, when p approached to a,
and tended to coincide with it, unless the following theorem
were also true, which can accordingly be otherwise proved :
the product ABCA, or AB X BC X CA, Of three successive sides of
any triangle aBc, is a pure vector, in the direction of the tan-
gent to the circumscribed circle, at the point a, where the
sides whick are assumed as first and third factors of the pro-
duct meet each other. If a, be the point upon this cireum-
scribed circle which is diametrically opposite to a, we find for
the length and direction of the diameter aa, in this notation,
that is, for the straight line to a from a,, the expression : *

ABCA

AA = ——3
: Vv. ABC

(16)

the denominator denoting a line which is in direction perpen-

* With respect to the notation of division, in this theory, the author pro-

poses to distinguish between the two symbols

Q
qq’ and ae

280

dicular to the plane of the triangle, and in magnitude repre-
sents the double of its area; while the numerator is, as we
have just seen, in direction tangential to the circle at a, and its
length represents the product of the lengths of the three sides,
or the volume of the solid constructed with those sides as
rectangular edges. We may add, that this tangential line
ABCA is distinguished from the equally long but opposite tan-
gent acBa to the same circle aBc at the same point a, by the
condition that the former is intermediate in direction between
AB (prolonged through a) and ca, while the latter in like
manner lies between ac (prolonged) and Ba: or we may say
that the line anca touches, at a, the segment alternate to that
segment of the circle anc which has ac for base, and contains
the point B; while the opposite line acBa touches, at the
same point, the last mentioned segment itself. The condition
for the diameter aa, becoming infinite, or for the three points
ABC being situated on one common straight line, is

v.aBc = 0. (17)

This formula (17) is therefore, in this notation, the general
equation of a straight line in space; (15) is the general
equation of a circle ; (14) of a plane; and (6) of a sphere.*

which he inadvertently used as interchangeable in his first communication to the
Academy: and to make them satisfy the two separate equations,
exegid=a;

,

- Xe=da.

He proposes to confine the symbol 9’ — q to the signification thus assigned
for the latter of the two symbols which have been thus defined, and which, on
account of the non-commutative property of multiplication of quaternions,
ought not to be confounded with each other.

* The simpler equation of scalar form, s. anc = 0, also represents a spheric
surface, if B be regarded as the variable point; but a plane, if B be fixed, and

either A or c alone variable.

a |

281

It may seem strange that the line and circle should here be
represented each by only one equation; but these equations
are of vector forms, and decompose themselves each into three
equations, equivalent, however, only to two distinct ones,
when we pass to rectangular coordinates, for the sake of com-
parison with known results.

In the same notation of capitals, whatever five distinct
points may be denoted by a, 8, Cc, D, E, we have the general
transformation,

ABCDEA = ABCA X ACDA X ADEA — ACADA, (18)

in which the divisor acaba, or AcA X aDA, is the product of
two positive scalars; if then we had otherwise established
the interpretation lately assigned to the symbol aBca, as de-
noting a line which touches at a the circle anc, we might
have in that way deduced the equation (6) of a sphere, as the
condition of the coplanarity of the three tangents at a, to the
three circles, ABC, ACD, ADE. And we see that when this
condition is satisfied, so that the points a, B, c, D, E are homo-
spheric, and that, therefore, the symbol aBcpza represents a
vector, we can construct the direction of this vector by draw-
ing in the plane which touches the sphere at a, a line A, Ag
parallel to the line acpa which touches the circle acp at a,
and cutting, in the points a, and a,, the two lines aBca and
ADEA, which are drawn at a to touch the circles aBc, ADE;
for then the vector aBcDEA, which is thus seen to be a tan-
gent to the sphere, will touch, at the same point a, the circle
A Aj Ag, described on the tangent plane. In the more general
case, when the condition (6) is noé¢ satisfied, and when, there-
fore, the rectilinear pentagon aBcpE, which we shall suppose
to be uneven, cannot be inscribed in a sphere, the scalar symbol
S.ABCDEA which has been seen to vanish when the pentagon
can be so inscribed, represents the continued product of the
lengths of the five sides AB, BC, CD, DE, EA, multiplied by the
sextuple volume of that triangular pyramid which is con-

282

structed with three conterminous edges, each equal to the
unit of length, and touching at the vertex a the three circles
ABC, ACD, ADE, Which have respectively for chords the three
remote sides of the pentagon, and are not now homospheric
circles. And because, in general, in this notation, the equa-
tion

S.ABCDEA = S. BCDEAB (19)
holds good, it follows that for any rectilinear pentagon (in
space) the five triangular pyramids constructed on the fore-
going plan, with the five corners of the pentagon for their
respective vertices, have equal volumes.

Besides the characteristics s and vy, which serve to de-
compose a quaternion Q into two parts, of distinct and deter-
mined kinds, the author frequently finds it to be convenient
to use two other characteristics of operation, tT and v, which
serve to decompose the same quaternion into two factors, of
kinds equally distinct and equally determinate; in such a
manner that we may write generally, with these character-
istics, for any quaternion q,

Q=se+va=rTe X va. (20)

The factor Tq is always a positive, or rather an absolute
(or signiess) number; it is what was called by the author,
in his first communication on this subject to the Academy,
' the modulus, but he has since come to prefer to call it the
TENSOR of the quaternion q: and he calls the other factor ve
the versor of the same quaternion. As the scalar of a sum
is the sum of the scalars, and the vector of a sum is the sum
of the vectors, so the tensor of a product is the product of the
tensors, and the versor of a product is the product of the ver-
sors; relations or properties which may be concisely expressed
by the formule :
Spates Ie Vl Sv; (21)

API aye uL=Tv. (22)

i a a a i i

283

When we operate by the characteristics + and u on a
straight line, regarded as a vector, we obtain as the tensor of
this line a signless number expressing its length ; and, as the
versor of the same line, an imaginary unit, determining its
direction. When we operate on the product aBc = AB X BC
of two successive lines, regarded as a quaternion, we obtain
for the tensor, T. aBc, the product of the lengths of the two
lines, or the area of the rectangle under them; and for the
versor of the same product of two successive sides of a triangle
(or polygon), we obtain an expression of the form

U.ABC = cosB + Y— 1 sinB; (23)

the symbol B in the second member denoting the internal
angle of the figure at the point denoted by the same letter,
which angle is thus the amplitude of the versor, and at the
same time (in the sense of the author’s first communication)
the amplitude of the quaternion itself, which quaternion is
here denoted by the symbol asc. In this theory (as was
shown by the author to the Academy in that first communi-
cation), there are infinitely many different square roots of
negative unity, constructed by lines equal to each other, and
to the unit of length, but distinguishable by their directional
(or polar) coordinates: the particular s/—1 which enters
into the expression (23) is perpendicular to the plane of the
triangle asc. It is the versur of the vector of that quaternion
which is denoted by the same symbol azc ; and it may, there-
fore, be replaced by the symbol uv.asc, which we may
agree to abridge to w. aBc, so that we may establish the sym-
bolic equation :

uva@ = we, orsimply, uv = w; (24)

we ee also call wa the vector unit of the quaternion a. The
‘expression (23) suggests also the denoting the amplitude of
any quaternion by the geometrical mark for an angle, which
notation will also agree with the original conception of such

284

an amplitude; and thus we are led to write, generally, as a
transformed expression for a versor,

vga=cos2Q+ wa.sinZa. (25)

The amplitude of a vector is in this theory a quadrant;
that of a positive number being, as usual, zero, and that of a
negative number two right angles. Applying the same prin-
ciples and notation to the case of the continued product
ABCDA of the four successive sides of an uneven quadrilateral
ABCD, we find that the amplitude Z ascpa of this quaternion
product is equal to the angle of the lunule ancpa, if we em-
ploy this term ‘‘lunule” to denote a portion of a spherical
surface bounded by two ares (which may be greater than
halves) of smai/ circles, namely, here, the portion of the sur-
face of the sphere circumscribed about the quadrilateral ancp,
which portion is bounded by the two arcs that go from the
corner A of that quadrilateral to the opposite corner c, and
which pass respectively through the two other corners B and
p. The tensor and scalar of the continued product of the
four sides of the quadrilateral do not change when the sides
are taken in the order, second, third, fourth, first; and gene-
rally,

cos Z Q = SQ +7Q; (26)

so that we have the equation,
Z ABCDA = Z BCDAB; (27)

hence the two lunules ascpa and BcpaB, which have for
their diagonals ac and BD the two diagonals of the quadri-
lateral, and with which the lunules cpaBc and paBeD re-
spectively coincide, are mutually equiangular at a and B.
Thus, generally, for any four points, aBcD, the two circles
ABC, ADC cross each other at a and c (in space, or on oné
plane), under the same angles as the two other circles, Bcp,
BAD, at B and D.

;
;

285

Again, it may be remarked, that the condition for a fifth
point E being contained on the plane which touches, at a, the
sphere circumscribed about the tetrahedron aBcp, is expressed

by the equation
S.ABCDAE = 0; (28)

this equation, therefore, ought not to be compatible with the
equation (6), which expressed that the point & was on the sphere
itself, except by supposing that the point & coincides with the
point of contact a; and accordingly the principles and rules of
this notation give, generally,

S.ABCDEA + S.ABCDAE = S. ABCD. AEA, (29)

in which by (14) the first factor s.apcp of the second
member does not vanish if the sphere be finite, that is, if the
volume of the tetrahedron do not vanish, while the second
factor may be thus transformed,

AEA = — (#A)?, (30)

so that the coexistence of the two equations (6) and (28) of a
sphere and its tangent plane, is thus seen to require that we

shall have

ra = 0; (31)
which is, relatively to the sought position of E, the equation
of the point of contact. ‘These examples, though not the
most important that might be selected, may suffice to show
that there already exists a calculus, which may deserve to be
further developed, for combining and transforming geometrical
expressions of this sort. Several of the elements of such a
calculus, especially as regards geometrical addition and sub-
traction, have been contributed by other, and (as the author
willingly believes) by better geometers; what Sir William
Hamilton considers to be peculiarly his own contribution to
this department of mathematical and symbolical science con-
sists in the introduction and development of those conceptions

286

of GEOMETRICAL MULTIPLICATION (and division), which were
embodied by him (in 1843) in his fundamental formule for the
symbolic squares and products of the three coordinate charac-
teristics (or algebraically imaginary units) ¢, 7,4, which entered
into his original expression of a QUATERNION (w+7z+Jy +2),
and by which he succeeded in representing, symmetrically,
that is, without any selection of one direction as eminent, the
three dimensions of space.

It is, however, convenient, in many researches, to retain
the notation in which Greek letters denote vectors, instead of
employing that other notation, in which capital letters (a few
characteristics excepted), denote points. In the former nota-
tion it was shown to the Academy in last December (see
formula (21) of the abstract of the author’s communication of
that date), that the equation of an ellipsoid, with three unequal
axes, referred to its centre as the origin of vectors, may be put
under the form :

(ap + pa)’ — (Be — eB) = 15"

p being the variable vector of the ellipsoid, and ( and a being
two constant vectors, in the directions respectively of the axes
of one of the two circumscribed cylinders of revolution, and
of a normal to the plane of the corresponding ellipse of con-
tact. Decomposing the first member of that equation of an
ellipsoid into two factors of the first degree, or writing the
equation as follows:

(ap + pa+ Be — pf) (ap + pa— Bp + pB) =1, (82)

we may observe that these two factors, which are thus sepa-
rately linear with respect to the variable vector p, are at the
same time conjugate quaternions; if we call two quaternions,
Q and KQ, conJuGATE, when they have equal scalars but
have opposite vectors, so that generally,

* Appendix, No. V., page lviii.

:

287
KQ = SQ — VQ, or, more concisely, K=s-—vy. (33)

And if we further observe, that in general the product of
two conjugate quaternions is equal to the square of their
common tensor,

Q X Ka= (sa)’— (va)? = (Ta)’, (34)
we shall perceive that the equation (32) of an ellipsoid may

be put, by extraction of a square root, under this simpler, but
not less general form :

T (ap + pat Bp — pB) = 1. (35)

Again, by employing the principle, that TI] = Ilr, we

may again decompose the first member of (35) into two fac-
tors, and may write the equation of an ellipsoid thus :

Tiat+B+o).tp=1, (36)
if we introduce an auxiliary vector, o, connected with the vec-
tor p by the relation

¢=p(a—P) e's (37)
which gives, by the same principle respecting the tensor of a
product,
To = T(a—f); (38)
so that the auxiliary vector o has a constant length, although
it has by (37) a variable direction, depending on, and in its
turn assisting to determine or construct the direction of the
vector p of theellipsoid ; for the same equation (37) gives for
the versor of that vector the expression

up = +u(a—B+o). (39)
Hence, by the second general decomposition (20), and by
the equation (36), the last mentioned vector p itself may be
expressed as follows :
u(a—B +9)
=e ; 40
p T (a+ B +o) ( )
making then, in the notation of capital letters for points,
VOL, III. Z

288

a+P=cB, a—P=ca, c=vc, p=e#A, (41)
so that a is the centre of the ellipsoid, & a variable point on
its surface, c the fixed centre of an auxiliary sphere, of which
the surface passes through the fixed point a, and also through
the auxiliary and variable point p, while B is another fixed
point, we obtain the equation:

EA= + U.DA~+T.DB; (42)
which gives

(cA)-'= = U.DA.T.DB, (43)
and shows, therefore, that the proximity (ua)—' of a variable
point E, on the surface of an ellipsoid, to the centre a of that
ellipsoid, is represented in direction by a variable chord pa
ofa fixed sphere, of which one extremity a is fixed, while
the magnitude of the same proximity, or the degree of near-
ness (increasing as E approaches to the centre a, and dimi-
nishing as it recedes), is represented by the distance DB of
the other extremity v of the same chord pa from another fixed
point B, which may be supposed to be external to the sphere.
This use of the word ‘‘ proximity,” which appears to be a
very convenient one, is borrowed from Sir John Herschel :
the construction for the ellipsoid is perhaps new, and may be
also thus enunciated :—From a fixed point a on the surface
of a sphere, draw a variable chord pa; let p’ be the second
point of intersection of the spheric surface with the secant pz,
drawn to the variable extremity p of this chord from a fixed
external point B; take the radius vector Ea equal in length
to p’s, and in direction either coincident with, or opposite to,
the chord pa ; the locus of the point ©, thus constructed, will

‘be an ellipsoid, which will pass through the point s. This

fixed point B (one of four known points uponthe principal
ellipse) may, perhaps, be fitly called a Pox, and the line BE
a polar chord, of the ellipsoid; and in the construction just
stated, the two variable points p, p’ may be said to be conju-
gate guide-points, at the extremities of coinitial and conju-

j

289

gate guide-chords pa, v’a of a fixed guide-sphere, which
passes through the centre a of the ellipsoid.

We may also say, that if of a quadrilateral (aBED’) of
which one side (AaB) ts given in length and in position, the
two diagonals (AE, BD’) be equal to each other in length, and
intersect (in D) on the surface of a given sphere (with centre
c), of which a chord (av’) isa side of the quadrilateral adjacent
to the given side (aB), then the other side (BE), adjacent to the
same given side, is a (polar) chord of a given ellipsoid: of which
last surface, the form, position, and magnitude, are thus seen
to depend on the form, position, and magnitude, of what may,
therefore, be called the generating triangle anc. ‘Two sides
of this triangle, namely, Bc and ca, are perpendicular to the
two planes of circular section; and the third side aB is per-
pendicular to one of the two planes of circular projection of
the ellipsoid, being the axis of revolution of a circumscribed
circular cylinder. Many fundamental properties of the ellip-
soid may be deduced with extreme facility, as geometrical*
consequences of this, mode of generation; for example, the
well-known proportionality of the difference of the squares of
the reciprocals of the semi-axes of a diametral section to the
product of the sines of the inclinations of its plane to the two
planes of circular section, presents itself under the form of a
proportionality of the same difference of squares to the rec-
tangle under the projections of the two sides Bc and ca of the
generating triangle on the plane of the elliptic section.

If we put the equation (35) of an ellipsoid under the form

T(ip + px) = K—v, (44)
the constant vectors . and x will be in the directions of the
normals to the planes of circular section, and may represent

* For the following geometrical corollary, from the construction assigned
above, the author is indebted to the Rev. J.W. Stubbs, Fellow of Trinity College.
If the auxiliary point p describe, on the sphere, a circle of which the plane is

perpendicular to Bc, the point £ on the ellipsoid will describe a spherical conic.

290

the two sides Bc and ac of the triangle, while t—«will be
one value of the variable vector p or Ea, namely, the remain-
ing side of the same triangle, or the semi-diameter Ba in the
last mentioned construction of the surface; and by applying
to this equation (44) the general methods which the author
has established for investigating by quaternions the tangent
planes and curvatures of surfaces, it is found that the vector
of proximity v of the tangent plane to the centre of the ellip-
soid (that is, the reciprocal of the perpendicular let fall on this
plane from this centre), is determined in length and in di-
rection by the equation,

(2 —?Yv=H(e+ ep tpt «pr; (45)

while the two rectangular directions of a vector 7, tangential
to a line of curvature, at the extremity of the vector p, are de-
termined by the system of equations :

vr trv=O03~) ovtirk — Ktitrv = 0; (46)
which may also be thus written :
s.v7 = 03,.S pte = 0. (47)

Of these two equations (46) or (47), the former expresses
merely that the tangential vector 7 is perpendicular to the
normal vector »; while the latter is found to express that the
tangent to either line of curvature of an ellipsoid is equally
inclined to the two traces of the planes of circular section
on the tangent plane, and therefore bisects one pair of the
angles formed by the two circular sections themselves, which
pass through the given point of contact. Indeed, it is easy to
prove this relation of bisection otherwise, not only for the
ellipsoid, but for the hyperboloids, by considering the common
sphere which contains the circular sections last mentioned ;
the author believes that the result has been given in one of
the excellent geometrical works of M. Chasles; it may also
be derived without difficulty from principles stated in the mas-

291

terly Memoir on Surfaces of the Second Order, which has
been published by Professor Mac Cullagh in the Proceedings
of this Academy. (See Part VIII., page 484.)

The length to which the present abstract has already ex-
tended, prevents Sir William Hamilton from offering on the
present occasion any details respecting the processes (analo-
gous in some respects to the calculi of variations and partial
differentials) by which he applies the principles of his own
method to investigations respecting surfaces and curves in
space, or to physical problems connected therewith ; he de-
sires, however, to mention here that, in investigations respect-
ing normals to surfaces, he finds it convenient to employ a
new characteristic of operation of the form

(S doy. d= a, _ . (48)

in order to obtain from a scalar function of a variable vector
p, a new variable vector » which shall be normal to the locus
for which that scalar function is constant ; and that the fol-
lowing more general characteristic of operation,
d d d

p— + 7—+k—=<J 4

ae ay dz i (49)
in which zg, y, z are ordinary rectangular coordinates, while
i,j,k are his own coordinate imaginary units, appears to him
to be one of great importance in many researches. ‘This will

be felt (he thinks) as soon as it is perceived that with this
meaning of <| the equation

kag) Nagata? A Ss OO

is satisfied in virtue of the fundamental relations between his
symbols 7, 7,2; which relations give also, as another result of
operating with the same characteristic, this other important
symbolic expression, which presents itself under the form of
a quaternion :

292

. dé du dv
a (it tjut be) =— (T+ 4 F)

vie al
TJ dz dz

+h (S2— 3): (51)

The President having taken the Chair,

The Rev. Charles Graves read a paper by Mr. George
Boole, of Lincoln, containing investigations supplementary
to his former papers on Discontinuous Functions and Definite
Multiple Integrals.

The author commences his observations by pointing out
a distinction among integrals which constitute the limits of
more general forms, according as they are supposed to be
obtained by the vanishing of one or of more constants. The

D
integral \ dz cos (qx) x", n being positive, considered as
D
the limit of i, dxe—** cos (qx) a"—', he designates a limiting

integral of the first class, because it involves the consideration
of one vanishing constant. The same integral, when m is
negative, he regards as the limit of the more general form.

" dxe—** cos qu cos (n tan— 2)
t) (R? Ma a?)
two constants & and 2’ vanishing"; and designates it a limiting

integral of the second class. Under this assumption he
assigns as its value

*dzcosge — 7(+q)""
\, Fela iy i ats)

293

the upper or lower sign being taken, according as q is posi-
tive or negative. Assuming as the definition of I'(z), the
equation

a
n(2) = y dx cos (x) x"—",
0

whether 7 is positive or negative, and regarding the integral
in the second member as a limiting integral of the first or
second class, according as 7 is positive or negative, the author
shews that, universally,

I'(n) T1—2) =

sina
a theorem which is known to be true of I" in its ordinary de-
finition when z lies between 0 and 1, but not otherwise. This
theory is further applied to explain the discontinuity of form
which is apparent in integrals, the subjects of which become
infinite within the limits of integration, with some other con-
nected points.

The paper concludes with an application of Fourier’s
theorem to the solution of equations. It is proved that the
value v of the definite integral

1
ia —\" bie da dv e"—)’V—' F(a, vy —1)
2a J-ax J—x ;

is symbolically expressed by the equation
d

d\@
ous 8
v=(-—) SF (#1 €)s
provided that @=0, from which the following theorem is
deduced :

If f(u) = x and ¢(z) be any function of x which makes
F [9 (#)] real, then

: |
d\O" stone!
ru) = —(—S) MOM Lge] 9)

which may be expanded in the form

294

F(w) = F[9 (a)] + xF’[o(@)] 9'( nto

wherein

mare be PVE) p ee

x=a—f[p(@)].

From this result the author deduces the theorems of
Laplace and Lagrange for the expansion of implicit functions;
and he shews that, through the arbitrary character of ¢(2),
they are particular cases of a class of theorems, infinite in
number. Applied to the solution of the equation f(u) = 2,
by making F(w) = w, this method gives that root which will
be represented by ¢(v), in which v is the least root of the

equation
Sle @)] = 2.

The President read the following letter from Mr. Cooper:—

*¢ Markree Castle, July 3, 1846.
‘¢ My pear Sir,—I now beg to transmit to you, for the
favourable consideration of the Academy, the observations we
-have been able to make on comets at this Observatory,
during the first six months of this year. They are preceded
by the places of some stars with which we compared the
comets, and which we were forced to determine, as they were
not included in any catalogue we possess. The results of
observations, made by Mr. Graham principally, for polar
point on circle, are also added. ‘The dates without places,
signify that we have the observation, but not yet the stars of
comparison.
** Believe me, my dear Sir,
“* Your’s very sincerely,
‘* EpwarpD Cooper.
“¢ The Rev. H. Lloyd, D. D.

&c. &c. Fe.”

295

DONATIONS.

Report of the Fifteenth Meeting of the British Associ-
ation for the Advancement of Science, held at Cambridge in
June. Presented by the Association.

Recueil de l Academie des Jeux Floraux. Presented by
Viscount De Mac Carthy, M.R.I.A.

Memoire sur deux Balances a Reflexion. Presented by
Professor Wartman.

Journal of the Royal Asiatic Society. No. XXII.
Part I. Presented by the Society.

Journal of the Asiatic Society of Bengal. No. CLXIV.
Part I. Presented by the Society.

De la Methode dans [ Electricitie et le Magnetisme, &c.
Presented by Professor Wartman.

Akademischer Almanach auf das Jahr, 1845. Presented
by the Society.

Bulletins des Séances de la Societe Vaudoise, des Sci-
ences Naturelles. Presented by the Society.

Proceedings of the Royal Asiatic Society of Great Britain
and Ireland. Presented by the Society.

Magnetische und Geographische Ortsbestimmungen in
Béhmen in den Jahren, 1843-1845. Von Karl Kreil. Pre-
sented by the Author.

Magnetische und Meteorologische Beobachtungen zu Prag,
vom 1. Jdnner bis 31 Decr. 1845. Von Karl Kreil. Pre-
sented by the Author.

Bulletins des Séances de la Societe Vaudoise des Sciences
Naturelles. Tom. I. Années 1842-1845. Presented by the
Society.

VOL Iit.

tS
+>

v
Dok ed sy ie

ae

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-47. No. 56.

November 9th, 1846.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The following Address, which was presented to the Lord
Lieutenant on the 2nd September last, together with His Ex-
cellency’s Answer, was ordered to be entered on the Minutes:

“* To His Excellency the Right Honourable John William
Earl of Bessborough, Lord Lieutenant General and
General Governor of Ireland, &c.

«¢ May IT PLEASE your EXxcELLENCY,

** We, the President and Members of the Royal Irish
Academy, beg leave to offer to your Excellency our respectful
congratulations on your acceptance of the high office of Re-
: presentative of our Most Gracious Sovereign in this country.
‘¢ In virtue of the Charter under which we have been incor-
porated by our Royal Founder, for the Promotion of Science,
Polite Literature, and Antiquities, the duties of Visitor of this
Academy have devolved upon your Excellency, as Lord Lieu-
tenant of Ireland.
** We cannot but rejoice that we are thus placed, in the
present instance, in official dependence upon one who is both
VOL, IIl. 2B

298

a native and a resident of this country, and to whose sympa-
thies a Society such as our’s, founded for the advancement of
knowledge in Ireland, may confidently appeal.

** Composed, as our body is, of men conscientiously dif-
fering upon questions of the first importance, and united by
the sole bond of kindred intellectual pursuits, we have had the
satisfaction to know that, while the immediate objects of our
incorporation have been successfully forwarded, the advance
has been hallowed by those feelings of mutual good-will which
are not less valuable than knowledge itself.

«‘ That such feelings may take root and spread in this
country, under your Excellency’s Government, is our earnest
hope and prayer.”

ANSWER.
‘¢ Mr. PresIDENT AND GENTLEMEN,

“‘ Tt is most gratifying to me to receive your congratula-
tions on my acceptance of the high office to which Her Ma-
jesty has been pleased to appoint me; and I learn with great
pleasure that, by virtue of the Charter under which you were
incorporated, I am associated with your distinguished body
as Visitor of the Royal Irish Academy.

“As a resident of Ireland I feel peculiar interest in a
Society founded more particularly for the advancement. of
Science in this country; and it is most satisfactory to me to
receive an Address from persons who, differing on questions
of great importance, have done me the honour of concurring
in their approval of my appointment.”

Sir W. R. Hamilton having taken the Chair pro tempore,
the President described a new instrument for observing the
Magnetic Dip.

This instrument is similar to one furnished to the late
Arctic Expedition under Sir John Franklin, and which was -
constructed by Mr. Barrow under the direction of Dr. Lloyd.

299

It is formed on the principle suggested by Gauss, of separat-
ing the needle altogether from the circle by which its position
is determined ; the moveable arms of the divided circle being
furnished with compound microscopes, by means of which the
extremities of the needle are observed. The circle is divided
to 10’; and the readings are made to single minutes by the
help of verniers.

By a simple modification in the construction of the in-
strument, it is capable of being used with needles of various
lengths, not exceeding the diameter of the measuring circle ;
and it is hoped that it will thus serve to determine the ques-
tion, not yet solved, as to the most advantageous dimensions
of the dip needle.

Another, and more important, peculiarity in this instru-
ment, is its adaptation to the determination of the intensity in
absolute measure. In the received method, the horizontal
component of the intensity is determined by a double observa-
tion, and the ¢otal intensity thence inferred by multiplying it
by the secant of the inclination. Hence, in the high mag-
netic latitudes, where the inclination is considerable, any error
in it will induce a large error in the inferred intensity; and
in the neighbourhood of the magnetic pole the method fails
altogether. The present instrument is adapted to measure the
total intensity directly ; and it is easily shewn that the result
thus obtained is, in the high magnetic latitudes, much more
accurate than that deduced in the ordinary way. The instru-
ment may be employed, also, for the measurement of the hori-
zontal and of the vertical components of the intensity.

Mr. Clibborn read a notice of certain Bronze Antiquities
in the Museum of the Academy. :

Mr. Clibborn stated that he had lately detected iron
cores in the centre of the bronze composing the mouth-
pieces of several ancient horse-bits in the Museum. The
fact was interesting, as it appeared to prove that, at the time

300

these bits were manufactured, iron was a cheaper metal than
bronze, it being used to save so much of that metal. It might,
however, have been used for the purpose of chilling the bronze
which composed the lateral rings, when their material in the
molten state flowed through the openings in the mouth-pieces
and formed these rings, which would otherwise have adhered
to the mouth-pieces. In the Museum are many specimens of
bronze castings, united by a process of this kind, yet there
is no example of hard soldering, which appears to be a more
modern invention.

The principle of covering iron with bronze, in the fluid
state, is exhibited in the fabrication of the folded or lapped
iron bells in the Museum, which are, in several instances,
covered with bronze or brass, perfectly adhering to the iron
surface. The bronze fills up the folds and joints, thus pre-
venting any false vibration, and the bell sounds as if it were
composed of one piece of metal.

He also directed the attention of the Meeting to the
resemblance between the patterns on some curious antique
plates in the Museum, and the details of a certain ornament
very common in the initial letters in the manuscript Books of
Kells, in the College Library, and the Book of Armagh, now
deposited in the Museum of the Academy. He was disposed
to infer, that these plates were of the same time as the MSS.,
or even earlier; for Mr. Westwood, who was the first to notice
the resemblance, considered the pattern on them to be the
type or original of the designs in the illuminations. This
would support the conjecture that these plates were intended
for Christian purposes, as pattens, or communion plates, pro-
bably ; though the designs differ so very much from those of
a later period.

The size and materials of these plates are the same as
those of the Mias Tighernain, which may have been used as a
patten also. This is rendered probable by the fact, commu-
nicated by the Rev. Dr. Kelly of Maynooth, that he had seen

301

pattens of the same size, also made of copper, in use in the
south of France. One of the plates in the Museum forms a
cover for another, and is pierced with an opening, which is over
a hollowed part of the under plate. The arrangements and
proportions of the parts are such as to lead us to suspect that
these plates, when placed together, may have formed a sort of
poor-box, the alms having been dropped through the opening
into the cupped part of the lower plate. It may be also
observed that, on the most perfectly finished portion of one
of these plates, there is the evident wear or impression of the
thumb of a person who had, for a considerable time, handled
it in the way a mendicant would, who might present it for alms.
The back of this plate, and one of the others, has marks of fire
on it. Mr. Clibborn also stated that a visitor to the Academy
lately recognized these plates, as being very similar to two
others, also composed of copper, which had been recently
found in Armagh, and which he hoped would be soon depo-
* sited in the Museum, as they had been freely offered to our
collection. Some light may thus be thrown on the use of
these curious articles, which have hitherto been called shields ;
there being no evidence as to their original use, nor until
lately was there any suspicion entertained of their belonging
to the Christian period. From the perfection of the work-
manship, and from some analogies in it and in the designs, it
was also inferred that the large trumpets in the Museum
might have been fabricated by artists of the same school as
those who constructed the pattens.

The Secretary of Council read a translation ofa letter from
Professor Encke to M. Schumacher relative to Le Verrier’s
Planet. He also laid before the Academy the following note
of observations made by E.J. Cooper, Esq., of Markree Castle,
with his transit circle :

No. 1.

5.

z

302

STARS OF COMPARISON.

Capricorni.

. 7451 Brit. Assoc. Cat.

- 7487
42 Capricorni.
6

do.

do.

do.

No, 6. i Aquarii.
7. 39 do.
8. 45 do.
9. 50 do.

10. o do.

The following observations must hereafter undergo some
modification, particularly those involving a comparison with
39 Aquarii, the declination of that star being lower than that
assigned to it in the British Association Catalogue by about
four seconds of space.

Apparent Places deduced from Mean Places, as given in the
British Association Catalogue.

Mean Time,
Greenwich.

1846.
Oct. 3.401067
6.392739

12.376121

14.370345

17.362062

19.356785

24,343014

16.365063 |

!
26.337522

Right Ascens.

h.
21 52 32.54

Apparent

m. 5.
20.74

0.27

51

Apparent
Declination.

| o é “
—13 28 10.40

29 13.93

30 53.67

31 24.57

53.54

32 2.03

36.65

33 19.78

13 33 38.88

Compared Stars, &e. |

No. 7.

No. 7. Bisection satisfactory,
though blowing hard.

No. 7. Hurried observation
of Planet. Cannot depend
on it. An opening only mo-
mentary in the clouds, which
were general at the time.

Nos. 1, 2, 8, 4,5, 6. Got
only the three first wires of
the Planet, which was faint
even at these.

Nos. 1, 3, 4, 6, 7, 8, 9, 10.
Good observation.

\Nos. 1, 2, 4, 6, 7, 8, 9, 10.

Got only the three first

| wires of the Planet.

Nos. 4, 5, 6, 7, 8. Good ob-
servation.

Nos. 1, 2, 3, 5, 6, 7, 8, 9.
Blowing hard, so that the
clock was heard with diffi-
culty ; at some wires not at
all.

Nos. 5, 6, 7, 8, 9,10. Satis-

factory observation. Night

had been very unpromising.

303

Sir W. R. Hamilton gave an account of the first observa-
tions of the new Planet made by him at the Observatory of
Trinity College, Dublin.

DONATIONS.

Archeologia. Vol. XX XI. Presented by the Society
of Antiquaries of London.

A Geographical Description of West or Hiar-Connaught,
by Roderick O’ Flaherty. Edited by J. Hardiman, M.R.I. A.
Presented by the Irish Archeological Society.

Transactions of the Royal Society of Edinburgh. Vol.
XVI. -: Part 2.

Proceedings of the Royal Society of Edinburgh.- Vol. II.
1845-46, Nos. 27 and 28. Presented by the Society.

Address to the British Association for the Advancement of
Science. Southampton, 1846. Presented by the Association.

Det Kongelige Danske Videnskabernes Selskabs Historiske
og Philosophiske Afhandlinger. 7 Deel.

Det Kongelige Danske Videnskabernes Selskabs Naturvi-
denskabelige og Mathematiske Afhandlinger. 11 Deel.

Oversigt over det Kongelige Danske Videnskabernes Sel-
skabs Ferhandlinger og dets Midlemmers Arbeider. 1 Aaret,
1844 and 1845. Presented by the Royal Society of Copen-
hagen.

Reports of the Council and Auditors of the Zoological So-
ciety of London. Read April 29th, 1844. Proceedings of
the Zoological Society of London. Part 13. 1845. Presented
by the Society.

Memoirs of the Geological Survey of Great Britain and
the Museum of Economic Geology in London. Vol. 1. Pre-
‘sented by the Commissioners of Woods and Forests.

On the Supply of printed Books from the Library to the
Reading-Room of the British Museum. By A. Pannizzi,
Esq. Presented by the Author.

Animadversions on the Library and Caletonies of the

304

British Museum. By Sir Harris Nicolas. Presented by the
Author.

History of the Mace given to the Royal Society by King
Charles II. By Richard Weld, Esq. Presented by the
Author.

Two curious Blocks of Wood, with Mortices, found in a
small Land-lake at Montayh, County Fermanagh. Presented
to the Museum by the Earl of Enniskillen.

Proceedings of the Royal Society. Nos. 62 to 64.

List of Members of the Royal Society. Nov. 30, 1845.

Presented by the Society.

The Quarterly Journal of the Geological Society of Lon-
don. No.7. Presented by the Society.

Memoires de la Societe de Physique et d Histoire Natu-
relle de Geneve. Tome XI. Ire Partie. 1846. Presented
by the Society.

Journal of the Statistical Society of London. Vol. 1X.
Part 3. Oct. 1846. Presented by the Society.

Seals of Archbishop Broderick and Archbishop Lawrence.
Presented to the Museum by the Rev. Mr. Mayne.

=

ee

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 57.

November 30th, 1846. (Stated Meeting.)

REV. HUMPHREY LLOYD, D. D., President, in the
r Chair.

Thomas Moore, Esq., having been specially recommended
by the Council, was elected an Honorary Member.

The Rev. William Roberts, F.T.C.D., read a paper on
the definite integral

Ne log(1 + sin’)

o ¥(1 — A? sin’g)

It is clear that the only admissible values of m (real) are those
of the parameter of an elliptic function of the third kind, to
the modulus 2, namely, cot?0, —1-+ k?sin®0, and — h?sin?0,
where ’ is the complement of k. The value of the definite
integral may, in each of these cases, be expressed by elliptic
functions of the first and second kinds, and by the remarkable
7a Oa) by the aid of which func-
tions of the third species, with a logarithmic parameter, can be
VOL. Ill. 2c

transcendant Y (

306

calculated by tables of double entry. In fact, we have the
following formule,

*log(1 + cot? sin *®) 4
\, V (1 — FR sin’) debe ()
oF (h!, 0) — 2(k) ¥ (#’, 0) — { E(k) — F(A} {7(R’, 0) }?
— drr(k’) — ¥(R) log (4 sin?6)

*log(l — (1 — b?sin®6) sin’) 1 _
y coy CL oma) i

m¥(h’,0) — 2e(h) Y(k’,0) — {0(k) — F(A) } fr(R’, 8) }2
— $F (h’) + log al F(R).
\" log (1 — k? sin?@ sin?o) ,
of Vein
2(h) § F(R, 0) 32 — 2r(h) Y(h, 8). (3)

In equation (3) if we put 0 = $7, we will have, recollect-
ing that

Y(3m) = 3r(2) w() — Blog &,

dor
log (I — A? sin’) 4 _ LOY
0 VC — sin’) dp = log(k’) F(z). (4)

Again, 0, being the amplitude of the semi-complete function,
we have
1
ae pase
sin 70, = Ter
and,
Qh! / ki
fi oes a\e
—¥0,) = bx) w(t) — Flog (2 =a)
so that

log(cos2p + k’sin *®) 4

Qh! o/ ki
0 (1 — # sino) Ci blog (>

=) r(k). (5)

The values of the definite integrals (4) and (5) have been

307

already deduced by Mr. Roberts from entirely different consi-
derations, and published in Liouville’s Journal de Mathema-
tiques, May, 1846.

Some other interesting results may be obtained from our
general formule. Thus, if in (2) we put 0 = 0, we will have

in l d k’
J aoe ig (f) atts

from which we may deduce, by an easy transformation,

Bu 1 é d , i
\ Vv —— ae migaog (;) r(k) — gmr(k') 5 (7)

and, consequently,

*" log (tang) do : 1 |
\ Fae Beate (a) r(h). (8)

If we suppose & to vanish in formule (6) and (7), we ob-
tain the well-known results, originally given by Euler,

a0 wir
. log (cosp) dp = A log (sing) dp = 37 log 3.

Denoting (1 — k?sin?p) by A, we can also derive from
the above the value of the definite integral

\" log (1 = « sin) dp

0 Aa

(9)
For, the sum of the integrals

log (1 + aA sin@) dg bees (, ee (1 — a sin@) d
0 A 0 A p

may be found from (1), and their difference from the formula
eb lytA ant 8 de th ;
J, tog {ES yf oe = we

which Mr. Roberts has demonstrated in the Journal de Ma-
thematiques, May, 1846.
2c 2

308

In conclusion it may be observed, that the particular re-
sults, (4), (6), (7), (8), are nothing more than immediate con-
sequences of Mr. Jacobi’s factorial developments of the trigo-
nometrical functions of the amplitude of an elliptic function,
in terms of the function itself.— Traité des Fonctions Ellip-
tiques, tom. ili. page 97. It may be seen that they follow at
once from these expansions, if we remember that

. log (1 + 2acosx + a’) dx =0
0

when a is less than unity; a theorem proved by Poisson in
the seventeenth cahier of the Journal de [ Ecole Polytech-
nique. _

- Sir William R. Hamilton stated the following theorems of
central forces, which he had proved by his calculus of quater-
nions, but which, as he remarked, might be also deduced from
principles more elementary.

If a body be attracted to a fixed point, with a force which
varies directly as the distance from that point, and inversely
as the cube of the distance from a fixed plane, the body will
describe a conic section, of which the plane intersects the fixed
plane in a straight line, which is the polar of the fixed point
with respect to the conic section.

And in like manner, if a material point be obliged to re-
main upon the surface of a given sphere, and be acted on by
a force, of which the tangential component is constantly di-
rected (along the surface) towards a fixed point or pole upon
that surface, and varies directly as the sine of the arcual dis-
tance from that pole, and inversely as the cube of the sine of
the arcual distance from a fixed great circle; then the material
point will describe a spherical conic, with respect to which the
fixed great circle will be the polar of the fixed point.

Thus, a spherical conic would be described by a heavy
point upon a sphere, if the vertical accelerating force were to

309 :

vary inversely as the cube of the perpendicular and linear dis-
tance from a fixed plane passing through the centre.

The first theorem had been suggested to Sir W. Hamilton
by a recently resumed study of a part of Sir Isaac Newton’s
Principia; and he had been encouraged to seek for the second
theorem, by a recollection of a result respecting motion in a
spherical conic, which was stated some years ago to the Aca-
demy by the Rev. C. Graves. In that result of Mr. Graves,
the fixed pole was a focus of the conic, and the polar was
therefore the director arc; consequently, the sine of the dis-
tance from the polar was proportional to the sine of the distance
from the pole, and, instead of the law now mentioned to the
Academy, there was the simpler law of proportionality to the
inverse square of the sine of the distance from the fixed pole

or focus.

Professor Graves observed, that he had that morning, in
conversation with the President, stated the theorem just an-
nounced, respecting the motion of a material point on the sur-
face of asphere. Sir William Hamilton having, at the last
meeting of the Academy, kindly communicated to him his
theorem of plane central forces, it occurred to Professor
Graves to inquire whether two theorems, which he had stated
in January, 1842,* relating to the motion of a point in a sphe-
rical conic, might not be included in a more general one, ana-
logous to that first mentioned by Sir William Hamilton. This
inquiry led him to perceive the truth of Sir William Hamil-
ton’s second theorem.

The mode of proof employed by Professor Graves rests,
so far as regards the dynamical part of the question, on the
two following elementary propositions :

If a material point, Pp, constrained to move on the surface
of a sphere, be urged by a force acting along a great circle
passing through a fixed point, s;

* See Proceedings of the Academy, vol. ii. p. 209.

310

1. Its velocity will vary inversely as the sine of the per-
pendicular are let fall from s on the great circle which isa tan-
gent at P to the trajectory described by the point.

2. The force in the direction of the are sp is equal to
ve
tany sind
osculating circle, and @ the angle between sp and the tangent

, v being the velocity of the point, y the radius of the

are.

The proposition may be readily proved by means of these
principles, taken in conjunction with the following property
of spherical conics :

A tangent arc being drawn at any point on a spherical
conic, if a perpendicular be let fall upon it from a fixed point,
and if a second perpendicular be let fall from the point of con-
tact on the polar of the fixed point, the quotient of the sines
of these two perpendiculars will always be proportional to the
tangent of the normal arc at the point of contact.

This very general theorem is its own polar reciprocal.

Mr. J. J. A. Worsaae, of Copenhagen, being requested to
give an account of the formation of the Museum of Antiqui-
ties in that city, made a communication to the following effect :

** It is a very well known fact, that but few countries in
the north of Europe escaped invasion or conquest by the Ro-
mans. Among those few, however, Ireland and Denmark
are specially to be named ; and on that account it is certainly
more than a mere accident that these two countries are in
possession of some of the best collections of national antiqui-
ties in Europe. I have had the opportunity of repeatedly in-
specting the very interesting collection of the Academy, and it
has been told me, that the comparatively large number of Irish
antiquities there assembled has been brought together in a
short time, but under circumstances of considerable difficulty.
Our collection of national antiquities in Denmark has like-
wise been founded under great disadvantages ; and perhaps it

311

will not be without interest to the Academy, if only in that
respect, to get a short history of its foundation, progress, and
present state.

‘¢ About forty years ago, the general character of scientific
pursuits was, in our country, much the same as in most other
parts of Europe: great pains were spent in collecting all sorts
of objects illustrating the changes of the globe upon which
we live, and the distribution and habits of animals and plants, in
short, all the departments of natural history ; whilst, strange
to say, people for the most part neglected éraces of men, the
remains, not only of their own ancestors, but also of all the
different races who have been spread over the world. The
antiquities, with the exception of those of Roman and Greek
origin, were regarded as mere curiosities, without any scien-
tific value ; and they were generally found in collections mixed
up with petrifactions and other objects, with which they had
little or no connexion. It was not until after the French Re-
volution, that the value of ethnology, as a most important
branch of science, was seen in its proper light. With a greater
respect for the political rights of the people, there awakened
in the nations themselves a deeper interest in their own
history, language, and nationality. Since that time there
have been formed antiquarian societies, and collections of na-
tional antiquities, in most European countries; in Germany
alone there exist at present more than eighty societies, formed
for the preservation and collection of national antiquities,
which, as I hope, is sufficient to show that an earnest effort
is now being made to do what undoubtedly has been too long
neglected.

«‘ Denmark was one of the first countries in which a col-

lection of national antiquities was founded, and no wonder,
because the olden time was that in which Denmark, together
with the two other Scandinavian countries, Norway and Swe-
den, was in its greatest power. I shall only reeall to your
memory, that the weapons of the Scandinavian warriors had

312

at that time conquered the coasts of the Baltic, a great part
of the British islands, of France, and some parts of Spain and
Italy ; that, crossing the Atlantic so early as in the ninth and
tenth century, they colonized Iceland and Greenland, and put
their foot upon the mainland of America. It was immediately
aiter great national calamities, that the attention of the Danish
people was turned to that early period of their history, as a
time from the contemplation of which their spirit of nationa-
lity might gain support, and in whose memories they found
the hope of a new and equally glorious era again. The North,
too, has this great advantage, that a complete picture of the
life of the old time has been preserved in the remarkable Ice-
landic sagas, which, certainly, compared with other literary
remains of that time, in regard to style and representation of
character, are almost unique. In the year 1807, the Danish
government, in compliance with the request of several lite-
rary men, appointed a Royal Committee for the Preservation
and Collection of National Antiquities, but the unfortunate
war with England hindered the Committee, for the first seven
or eight years, from making much progress. After the resto-
ration of peace, it happened that a young man, a merchant’s
son in Copenhagen, who, from his earliest childhood, had felt
a great interest in all sorts of antiquities, was appointed Se-
cretary of this Royal Committee. He found a few antiquities,
mixed up with the most curious things, in a small room in the
library of the University. He commenced with exceedingly
small grants, and under very great difficulties. He had not
only to contend with the prejudices of the unlearned, but
also with the conflicting opinions and baseless theories of
the learned men. Some believed that the antiquities of iron
were the oldest, because they were most corroded; others
believed that the antiquities of brass were older than the an-
tiquities of stone; others, again, supposed, that the wealthy
men had used iron, the middle classes brass, and the poor
stone, However, he opened his small collection for public

313

inspection ; was always present on the public days for the
purpose of showing and explaining the antiquities; and when
peasants happened to visit the collection, he paid particular
attention to them, ‘ because,’ as he said, ‘it is by them we
shall have our collection enlarged.’ For many years he con-
tinued to show the collection, and to diffuse an interest in the
old remains throughout the country, and all this without re-
ceiving any pecuniary emolument, I ought rather to say, at
very considerable expense to himself. At last, the collection
became so large, that the room in the library was far from fur-
nishing sufficient accommodation ; and the constantly increas-
ing interest in the collection, and fresh donations of antiquities,
made its removal necessary. After many difficulties, he made a
great step in advance, by getting rooms in the royal palace,
‘Christiansborg,’in Copenhagen. He then fully carried out his
idea of arranging the Pagan antiquities into three periods, the
stone, brass, and tron periods, which he was the first to point out
to antiquaries. It was not long before the collection acquired a
great name on the Continent; all foreigners spoke about it as
one of the most remarkable collections in the north of Europe.
The Government evinced more and more interest in the Mu-
seum, and the public began to regard it as a national treasure.
In the mean time, the Royal Society of Northern Antiquaries
in Copenhagen had published many of the remarkable Icelandic
sagas, through which the people got more knowledge of the
importance of the olden time, than they had hitherto possessed.
The Society published in its Annals descriptions of the anti-
quities of the Museum, and published separately popular
tracts, illustrated with woodcuts, on the value and importance
of preserving the antiquities, many thousands copies of which
were spread over the country, among clergymen, schoolmasters,
and peasants. From all sides and all parts of the country an-
tiquities were presented to the Museum; and it has now been
enlarged to such an extent, that when the new arrangement,
which is now going on, is finished, it will occupy about ten

314

rooms of the royal palace. His Majesty the present King of
Denmark, whose great zeal for the promotion of literature and
science is well known, and His Royal Highness the Crown
Prince, are both most anxious to make this collection still
larger and more important. The real founder of the Museum,
about whom I spoke above, the present Councillor of State,
C. J. Thomsen, has had the gratification of seeing his extra-
ordinarily energetic efforts crowned with the most signal suc-
cess. In order to give some idea of the extent of the Museum,
I shall only mention, that it contains more than three thousand
specimens of implements of stone; a very large room is filled
with antiquities of brass, among which are complete shields,
and several large trumpets of war, between two and three
hundred complete swords and daggers of brass, several hun-
dred celts and brass hatchets, lance-heads, ornaments, &e. As
many specimens as possible, even of the most common things,
are collected, because true historical results can be deduced
only from a long series, showing that the various articles were
in common use. Among the antiquities of the bronze and iron
periods are to be seen a great number of rings, and other or-
naments of silver and gold, I should say a larger number than
I have found in any other collection. It was formerly a law
in our country, that all antiquities of silver and gold, which
were found in the earth, must be surrendered to the Crown,
without any recompense to the finder, the effect of which was,
that most of those things were melted and made away with.
The King, therefore, ordered, that the finders of antiquities of
silver and gold should receive the full value of the articles,
when they sent them into the Royal Collection ; and that they
should get more than the real value when the specimens were
uncommonly rare, or when particular pains had been taken to
find or preserve them, 1am happy to say, that the Museum
now gets very nearly all the antiquities of silver and gold
which are found in our country, particularly as they are paid
for by the Government out of a peculiar fund.

315

** | have thought that it would not be without interest to
the Academy, to see how a large collection has been formed,
in about thirty years, by energetic exertions, continued in spite
of great difficulties; and how the collection, after those diffi-
culties have been overcome, now stands as a national monu-
ment, supported alike by the Government and by the people.
I doubt not that the Collection of this Academy, which in a
few years has attained such magnitude, will, if carried on with
the same energy, be soon of so much importance, and gain so
great a name in Europe, that it will receive that strong sup-
port, both from the Government and the inhabitants of Ireland,
which it at present wants.

*< If you will allow me I shall, at another meeting, insti-
tute a short comparison between the antiquities in the Irish
and Danish collections. It is only through such a comparison
of the antiquities in different countries, that a new light will
be thrown over the many dark periods of the early history of
Europe; and I hope that the connexion, which in ancient times
existed between Ireland and Scandinavia, will give me a pe-
culiar advantage in illustrating the origin and use of some
antiquities in the collection of the Academy.”

Rev. Samuel Butcher read a paper by Rev. Dr. Hincks,
in continuation of his researches in the Persepolitan writing.

In this paper Dr. Hincks shows, that the general principles
respecting the Persian writing, which he had laid down in his
former communication on this subject,* are borne out by the
Bisitun inscriptions, recently published by Major Rawlinson.
The values which, in his former paper, Dr. Hincks had assigned
to four of the characters, he admits to be erroneous, and, ac-
cordingly, now corrects them; but maintains that the values
assigned by him to the remaining characters are the true ones,
and adduces the new inscriptions in proof thereof. With re-

* «On the first and second kinds of Persepolitan writing,” by the Rey.
E. Hincks, D. D. (Vid. Proceedings, vol. iii. p. 262).

316

spect also to the author’s Median Alphabet, as given in the
same paper, he now makes a few slight corrections, which,
however, do not affect the general views there stated regarding
that language. Dr. Hincks further gives a Babylonian alpha-
bet or syllabary, exhibiting the values of sixty-five characters
of the third Persepolitan writing, and of one hundred and
twenty-eight of the Babylonian lapidary characters: placing
the Babylonian characters in juxtaposition with the corres-
ponding Persepolitan ones. He adds an analysis of fourteen
proper names written in the latter character, and of two in the
former; and he points out the mode of reading them in the
different forms under which they appear in the inscriptions.
Dr. Hincks moreover states, that, with the exception of a few
letters, to which correct values had been assigned by Professor
Grotefend, and a few others to which the same author had
approximated, nothing in the right direction had hitherto been
published concerning these two last-mentioned kinds of writing.

The Rev. Charles Graves read a paper on the date of the
manuscript commonly called the Book of Armagh.*

Shortly after the Book of Armagh had been deposited in
the Museum of the Royal Irish Academy, Mr. Graves ob-
served, on a careful examination, that numerous erasures had
been made in it. These occur at the end of the following
writings contained in the volume:

1. The Confession of St. Patrick, fol. 24, b.

2. The Gospel of St. Matthew, fol. 52, db.

3. The Gospel of St. Mark, fol. 67, b.

4. The Gospel of St. Luke, fol. 89, db.

5. The Revelation of St. John, fol. 170, a.

6. The Acts of the Apostles, fol. 190, a.

7. The second Book of the Life of St. Martin of Tours,
fol. 214, a. .

8. A letter of Sulpicius Severus, fol. 220, a.

“ For an account of this manuscript see Transactions, vol. xx. p. 329.

317

So effectually had the original writing been effaced in these
places, that, in the first instance, Mr. Graves gave up the
attempt to decipher it as utterly hopeless. But his attention
was again urgently drawn to the subject by Mr. Eugene
Curry, who had independently noticed the same fact. Being
aware that it was usual for Irish scribes to insert, at the end of
books written by them, their own names, and some notices of
the date or occasion of the writing, he had been looking at
these very places in the hope of finding such entries, and, to
his disappointment, he had ascertained that they had been

_erased. Still he did not despair of their being ultimately read :
and as he thought it probable that, like the body of the work,
they were written in Latin, a language with which he is not well
acquainted, he requested Mr. Graves to endeavour to make
them out. One of the erasures to which he particularly
directed attention was the one marked 7 in the list given
above, and to this Mr. Graves first applied himself. He reads
it as follows :

Pro Ferdomnacho ores.

A well-executed fac simile is subjoined, for the purpose of
enabling those who have access to the manuscript to judge
whether his reading be correct.

Pyerronmacho one

On turning to erasures 3, 4, and 8, he satisfied himself that
the same words had been written in those places also. It is
thus established that the whole volume was executed by the
same scribe, as, indeed, the uniformity of the handwriting suf-
ficiently proves. Erasures 6 and 7 are considerable ones ; and
there is good reason to apprehend that, in both these instances,
we have to deplore the loss of much information respecting
the manuscript.

At all events, we know that it was written by a scribe
named Ferdomnach. But it yet remains to be ascertained who
this Ferdomnach was, and at what time he lived.

318

The Annals of the Four Masters contain entries respecting
two persons of this name, both of them scribes.

A. C. 726. Ffpoomnach pspib- A. D. 727. Ferdomnach, Scribe

nfoip Apnoa Maca o’ecc. of Armagh, died.

A, C. 844. Feapoomnach eag- | <A. D. 845. Ferdomnach, a sage
nae 7 pspibnid cogaide do and choice scribe of the church
muinzin Apoa Maca v’ece. of Armagh, died.

The fact that both these persons were scribes of Armagh,
where this manuscript was preserved for so many centuries,
renders it in the highest degree probable that one or other
was the writer. The names of between thirty and forty per-
sons, who held the office of Scriba or Scholasticus in Armagh,
are enumerated in the Annals of that see, given by Colgan
in his Trias Thaumaturga. But of all these there were only
two Ferdomnachs, the two already mentioned.

Assuming, then, as it seems safe to do, that one or other of
these persons was the scribe of the manuscript, Mr. Graves
proceeds to fix the actual year in which it was written. He
thinks that he has effected this by partly deciphering the writing
in the erasure No.2. This erasure consists of four short lines ;
and the original writing was in a semi-Greek character, the
nature of which is exhibited in the following passages, con-
taining nearly all the letters of the Roman alphabet. The
first is one of the petitions of the Lord’s Prayer, as given in
St. Matthew’s Gospel, fol. 36, a. The second is a memoran-
dum occurring in the very column at the foot of which is the
erasure under consideration.

16 PANEM
WocTyyoc-foTiM kaye - DK NOSTRUM + COTIDIANUM - DA
Minbié- fodtf. NOBIS + HODIE +
611. iar: MEV AMrVe EXPLICIT » AEVANGVE
Aum: HATH -yrcar LION - KATA + MAT
THyvnac - pri ty TEVM - SCRIPTVM:
aT Ave bismtyorc: ATQVE FINITVM -

1m Sapir weattTH:: IN FERIA - MATTEL - -

319

After the latter passage comes a Collect appropriate to the
Festival of St. Matthew, and then, at the bottom of the page,
is the erasure.

By the use of a weak solution of gallic acid in spirits of
wine, Mr. Graves revived the traces of the original writing a
good deal ; and, aided by a magnifying glass, he succeeded,
at the expense of much time and labour, in deciphering the
greater part of the erased writing. The following fac simile
exhibits as much as can be read with any certainty :

Mek kyu *

+0 €& Atktdyte
+ 3] gate: FHptaAn tar
pki cKpimcT —

Now, as the Heres Patricii undoubtedly meant the succes-
sor of St. Patrick in the see of Armagh, we at once gain this
additional and positive information, that the scribe who wrote
the book was contemporary with some Archbishop of Armagh
whose name ended with ach: and this cannot be said of the
earlier Ferdomnach, who died A. D. 727. It appears, from a
passage in fol. 18, 5, that Flann Febla had attained the pri-
macy before this book was written, and he was succeeded by
Suibne, who outlived this Ferdomnach. Nay, more, if we
may trust the list of the Archbishops of Armagh contained in
the Leabhar Breac, fol.99,6, or that given by Colgan from
the Psalter of Cashel, there had been no Archbishop of Ar-
magh, whose name terminated thus, for more than a hundred
years previous to the death of the first Ferdomnach. On the
other hand, we know that, in the time of the second Ferdom-
nach, there were three Archbishops of Armagh whose names.
ended in ach, Foendelach, Connmach, and Torbach. But fur-
ther, enough remains of the letter preceding the final ach to
indicate that it was a 6, certainly enough to show that it could
not have been either an / or an m. Moreover, in the space

320

occupied by the name, there is not room for more than seven
or eight letters. On these grounds Mr. Graves concludes
that the name was that of Torbach, whose death is thus
recorded in the Annals of the Four Masters :

C1. C. 807. Copbach mac §op- | A. D.808. Torbach, son of Gor-

main Scpibnid, Ceszoip, 4 man, Scribe, Lecturer, and
abb Cpoa Maca epide, v0 Abbot of Armagh was he, of
cenel Topbamg, eadon, O the Kinel Torbaigh, i. e. of
Ceallang Speas. Hy-Kelly of Bregia.

Introducing then the name of Torbach, Mr. Graves pro-
poses to restore the whole passage thus:

F pomnacu- HvNC - LIB

E RVM- E DICTANTE

R TORBACH - HEREDE ~- PAT
RICII - SCRIPSIT

Torbach held the primacy, according to the catalogues of
the Psalter of Cashel and the Leabhar Breac, for a single year;
and his death took place on the 16th of July ; “* colitur 16°
Julii,” says Colgan, 'T. T. p. 294. Since, then, the writing of
the Gospel of St. Matthew in the Book of Armagh was
finished on St. Matthew’s festival day, the 21st of September,
and during Torbach’s primacy, it must have been in the year
807.

If we could be quite sure that the half-erased name ter-
minated in bach, there would remain no reasonable ground for
doubting the conclusion at which Mr. Graves has arrived.
For the satisfaction, however, of those who may not partici-
pate in the certainty which he feels as regards this point, he
thinks it right to notice the following circumstances, which,
although not deserving the name of proofs, tend in some de-
gree to confirm the probability of his conjecture.

The Torbach abovementioned having been himself a scribe
of Armagh, the copying of the precious manuscripts of the

321

see was such a work as we might expect to find undertaken
during his primacy : and of the second Ferdomnach we are
informed, not only that he was a scribe of Armagh in Tor-
bach’s time, but that he was pembnio cogaide, a choice scribe,
a fit person to be intrusted with so important a work. Cer-
tainly the penmanship of the Book of Armagh is of the most
consummate excellence. The whole of the writing is remark-
able for its distinctness and uniformity. All the letters are
elegantly shaped, and many of the initials are executed with
great artistic skill. The last verses of St. John’s Gospel, fol.
103 a, may be especially referred to, as exhibiting a specimen
of penmanship which no scrivener of the present day could
attempt to rival.

It is also worthy of notice, that, about the time of Tor-
bach’s primacy, the inroads of the Danes in the north of Ire-
land, and the adjoining islands, were becoming so frequent
and serious, that the ecclesiastics of Armagh might well have
been anxious to take measures for the preservation of their
records. In the year 802 the Scandinavian pirates plundered
the monastery of Hy, on which occasion many of the inmates,
both laymen and monks, perished. They again attacked it
in 806, and put to death no less than sixty-eight of the monks.
In 807 they effected a landing on the Irish coast, and, pene-
trating as far as Roscommon, destroyed it, and laid waste the
surrounding country. But it was not till 831 that they entered
Armagh. In that year, as we learn from the Annals of the
Four Masters, they plundered it three times in the course of
one month. It had never before been taken possession of by
foreigners.

Mr. Graves stated that, on mentioning to his friend Mr.
Petrie the fact of his having ascertained the name of the scribe
of the Book of Armagh to be Ferdomnach, Mr. Petrie at once
informed him, that he had, many years ago, made a drawing
of a tombstone at Clonmacnoise, on which that name ap-

VOL. III. 2D

322

peared. By his kind permission Mr. Graves is enabled to
lay the following outline of it before the Academy :

'

The character of the inscription, and the style of the cross,
belong, as Mr. Petrie thinks, to the ninth century. It is not
unlikely that this may be the tombstone of the very person by
whom the Book of Armagh was transcribed. His having been
buried at Clonmacnoise rather than at Armagh, furnishes no
argument to the contrary. We know that many distinguished
ecclesiastics and learned men came from remote places to pass
their last days as pilgrims at Clonmacnoise. It might be that
Ferdomnach retired to that place when Armagh was plundered
by the Danes in 831.

It is not a little remarkable, that the Book of Lecan, in
the library of the Royal Irish Academy, furnishes us with the

323

pedigree of a Ferdomnach, twenty-third in descent from Co-
nary More, Monarch of Ireland, whose reign commenced A. D.
158. Allowing thirty years to a generation, we should bring
the time of this Ferdomnach just down to the middle of the
ninth century. For the discovery of this curious coincidence
Mr. Graves is indebted to Mr. Eugene Curry, who, at his
request, most kindly undertook the laborious task of making
the necessary searches.

Sir William Betham, in his account of this manuscript, *
has assigned to it an earlier date, assuming it to have been
written by Aidus, Bishop of Sletty, who died A. D. 699.
And in this he has been followed by Mr. Westwood, in his
recently published Paleographia Sacra. Sir William Be-
tham, wanting the positive evidences now brought forward,
appears to have been led to that conclusion by a passage in the
Life of St. Patrick, fol. 20,5: ‘‘ Hecpauca de Sancti Patri-
cii peritia et virtutibus Mupchu Mace vu Machchem dictante
Aiduo Slebtiensis civitatis episcopo conscripsit.” But it would
seem that these words were only intended to convey that the
memoir of St. Patrick was originally drawn up at the desire
or command of Aidus, just as the Gospel of St. Matthew, and
probably the whole Book of Armagh, was transcribed by Fer-
domnach dictante herede Patricii, at the bidding of the then
Archbishop of Armagh.

The original Life of St. Patrick, by Muirchu, together
with the annotations of Tirechan, were evidently becoming il-
legible at the time that Ferdomnach’s copy of them was made.
This is sufficiently indicated by notes in the margin, which
show that the scribe found it difficult, in many places, to
read the manuscript from which he was transcribing. What-
ever abatement, therefore, has been made from the supposed
age of the Book of Armagh, is fully compensated for by the
knowledge that it is a copy from documents which were them-
selves old in the year 807.

* Trish Antiquarian Researches, vol. i. pp. 257, 270.

Y 324

It is not easy to conjecture at what time the erasures now
noticed were made in the manuscript. They seem not only
to have concealed the name of the scribe from those scholars
through whose hands the manuscript has passed at different
times, but to have escaped their observation. At all events,
they are not mentioned by those antiquaries who have hitherto
published descriptions of the Book of Armagh. It is hardly
possible to conceive how so intelligent a scholar as Lhwyd
could have spoken as he does of the commonly received belief,
that it was in the handwriting of St. Patrick, if the name of
the real scribe, Ferdomnach, had appeared in eight or more
places. And if he had not himself observed the signature of
the real scribe, it could scarcely have passed unnoticed by Mr.
Arthur Brownlow, who, on purchasing the book, after it had
been left in pledge for £5 by Florentine Mac Moyre, carefully
arranged and numbered the folios, and marked in the margin
the beginnings of the chapters of the several books of the New
Testament, a task, in the execution of which he must necessa-
rily have examined every single page of the book. On these
grounds Mr. Graves is inclined to believe, that the erasures
were made before the manuscript came into the possession of
Mr. Brownlow, that is to say, about the year 1680.

DONATIONS.

1. Dictionary of the Roots of the Latin, according to the
Method of A. F. Yazvenskago. Presented by the Author.

2. Memoirs of the American Academy of Arts and Sciences.
New Series. Vol. II. Presented by the Academy.

3. Natuurkundige Verhandelingen van de Hollandsche
Maatschappy der Wetenschappen te Haarlem. 2e Verzamel-
ing. 3e Deel. leStuk. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 58.

December 14th, 1846.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The Rev. William Reeves, M. B., was elected a Member
of the Academy.

The Rev. Charles Graves made some observations on the
use of distributive signs of operation, both real and imaginary,
in the construction of systems of algebra.

1. An algebra with two distributive signs, one real and the
other imaginary, might be framed in the following manner:

We might define the sign + as standing for a distributive
operation, such that the repetition of it any integer number of
times is still equivalent merely to +. We might suppose the
nature of this operation known, and, on that account, call any
quantity affected with the sign +a real quantity. Along
with this symbol we might employ a second, +*, defining it
as being the symbol of another distributive operation, such,
that the twofold execution of it is equivalent to +. And the
nature of this operation, denoted by +-*, might be supposed

VOL, III. 25

326

unknown, or in some sense transcendental as compared with
+, so that it would be impossible to express a term affected

withthe sign +? by means of any combination of terms affected
with the sign +. With this understanding we might call
terms affected with +-* imaginary, and the importance of the
distinction between reals and imaginaries consists in this: that
when we have an equation, u = 0, involving quantities of
both kinds, we may put the real and imaginary parts of u
respectively equal to 0.

The following example will show the advantage of employ-

ing such asymbol. If we put +* in place of + ¢ in the

development of e*, we find

+3, Sie
e * =cosd +? sing (1)
where cog@ and ging respectively stand for the series

e ~° #
Lt Joh ae 8 Ae os

¢° ¢°
apo aoa a ae ae

multiplying equation (1) by the similar one
ay
et ® = cogg’ +? ging’
we have
eines o = cosp cosp’ + sing sing’ +* [cose ging’ + sing cosp’].
But again, from (1) we have
+3, |
eT 9 = cos(o + 9’) +4ain( + 9’).
And since we are entitled to compare the real and imaginary
parts in the two last equations, we conclude that
£08(% + o’) = cos cosg’ + sing sing’
sin(d + ’) = cos sing’ + sind cos¢’.

327

These are the fundamental equations for the comparison
of hyperbolic sines and cosines.

2. The distributive symbols +*, +?, +?, +, enable us
to construct the ordinary double algebra. The equation
+*1+4 1=0 makes +* real aswell as +. But + and +
are both imaginary, as compared with + and +3, though

they admit of being compared together because of their rela-
tion

+71 471= 0,
which is a consequence of
+714+1=0.

3. With the distributive symbols +*, +3, +, supposed
to be heterogeneous, we might construct an algebra of one
real and two imaginary symbols. This algebra would be vir-
tually equivalent to the triple system discussed by Mr. Graves
in former communications to the Academy. !

4, Stating with the primary symbol +5 we might frame
an algebra with two imaginaries, viz., + and +4, and three
reals, +3, +3, +, related to one another by the condition

Pye? 1] rae

1
Developing ¢'”? we find it equal to
1 2
3 3
r, + ft + Ue 5
Ay fi,» and y, representing series in which the signs of the

terms are successively +, +7, +3,4+, +3, +4 &c. Between
these series and the ordinary trigonometric series, expressing
the sine and cosine in terms of the arc, there exist many
remarkable analogies.

Mr. J. J. A. Worsaae, of Copenhagen, in continuation of
his former communication to the Academy, gave a review of the -
different descriptions of Danish and Irish antiquities, and of

242

328

several historical events connected with the invasion of Ire-
land by the Danes.

Mr. Worsaae commenced by observing, that all the anti-
quities found in Ireland, as well as in other countries, are to
be divided into two large classes. Those of the first are of
the greater importance, being all of a time in reference to
which we have no historical records. 'The monuments of the
second class, belonging to a later period, could not give infor-
mation of so much value, because we have from written re-
cords a certain degree of knowledge as to the civilization of
the time ; but it is a remarkable fact, that the antiquities of
the second class were, until lately, regarded with the greatest
interest, because of the prevailing inclination to combine the
study of antiquities with that of written records. It was long
before archeologists could bring themselves to relinquish that
mode of research, and come back to a critical examination of
the monuments, without being influenced by written records ;
but the time seems at length to have arrived, when it has
become possible to enter upon an entirely new inquiry into
the history of the earliest state of the European nations, by
means of the antiquities alone.

§ 1. The Stone Period.

With regard to the existing collections of different kinds
of stone implements, found in nearly all parts of Europe, it
is interesting to compare those implements with the stone
hatchets, knives, &c., found in America and Africa, and still
used by the natives of the South Sea islands. Such a compa-
rison indicates that they have been used by tribes which sub-
sisted by fishing and hunting; and the striking resemblance
of the forms is a direct proof that different people, in the
same uncivilized state, use weapons and implements of ex-
actly the same description for killing animals and_build-
ing houses. It is well known that a great number of stone
hatchets, arrow-heads, and lance-heads, have been found in Ive-

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land, and particularly articles formed of flint, in the northern
counties ; but in Denmark there occurs a greater number and
variety of implements of flint, probably because that stone is ex-
ceedingly common in that country. Most of these implements
of stone seem to belong to a time before all history—to an
aboriginal people, who lived by fishing and hunting upon the
sea-coasts and along the large rivers of Europe. The tombs
of these people give the best information on this point. There
are in Ireland and England a number of stone structures
ealled Cromlechs, Druidical altars, &c., which are generally
regarded as religious monuments belonging to a historical
time ; but excavations in Ireland (in the Phoenix Park), in
Jersey, Guernsey, and several other places, have shewn that
they were tombs, containing skeletons, implements of stone or
bone, vases of clay, and rude ornaments of amber and bone.
Exactly similar monuments in Denmark and France contain,
without ;exception, the same objects, and, like the Irish
and English cromlechs, they differ from all other tombs.
They are only found on the coasts of the Baltie and the
German ocean, in Holland, France, Portugal, and on the
coasts of the Mediterranean, but never in the interior parts of
Germany, Austria, or Hungary. There is every reason to
believe that those remarkable monuments were raised by a
people who had no metal, and therefore were unable to pe-
netrate into the interior of Europe, which was then covered
with forests and morasses of an immense extent. It is only
through a careful examination and comparison of the skeletons
andiskulls found in the tumuli just mentioned, that we can
get information concerning the races to which this aboriginal
people belonged. ‘This discovery of a stone period, in the
-history of Europe, was the first important result arrived at
by the study of antiquities alone.

§ 2. The Bronze Period.

Mr. Worsaae remarked further, that, in looking over

330

the European collections of national antiquities, we next
observe a great number of implements, weapons, and ornaments
of bronze, together with ornaments of gold. It is impossible
that all these could have belonged to the aboriginal people
who built the cromlechs ; first, because the tombs are quite dif-
ferent ; and secondly, we do not find any sufficient transition
from the antiquities of stone to the antiquities of bronze. The
latter are of a mixed metal, and are so beautiful in their
forms, and of such fine workmanship, that they must have be-
longed to a new people, who invaded Europe, followed the
large rivers into the interior parts, where, with their imple-
ments of metal, they were now able to make their way through
the thick forests. ‘They began to drain the bogs and cul-
tivate the soil, no longer living merely by fishing and hunting,
as the people before them. ‘There have been, however, diffe-
rent opinions about the origin of these implements and wea-
pons of bronze. Some said they were all of Pheenician or
Roman workmanship ; some contended that they all belonged
to an early Celtic population of Europe; but a comparison
of the Irish and Danish antiquities will clearly shew that
these opinions are not to be relied upon. There is cer-
tainly a general resemblance in the forms of the bronze anti-
quities, but many differences in details, which prove that the
Irish antiquities of bronze were not brought from Ireland to
Denmark, or from Denmark to Ireland. The handles of the
Irish bronze swords were very nearly all of wood or horn:
while in Denmark a great many had handles of bronze, orna-
mented with a peculiar sort of pattern, which in no instance
appears on the Irish antiquities, and sometimes inlaid with
gold. In Denmark there are several antiquities which are not
to be found in Ireland ; and in Irelandsome have been found,
which either did not exist at all in Denmark, or assumed another
shape. The Danish antiquities of bronze are again different
from the remains of the same period in the southern part of
Germany, in Greece, in Italy, and France, which in their turn

a es

331

differ from the English and Irish antiquities; in all those
countries moulds have also been found in which the imple-
ments and weapons of bronze were cast. ‘This shews that dif-
ferent people in Europe, in the same state of civilization, had
used the same implements of the same metal, only in slightly
varying forms. ‘The oldest accounts of Greek and Roman
authors confirm this important result, which is principally
due to the antiquities.

§ 3. The Iron Period.

It seems that the implements and weapons of bronze
completely disappeared when the Romans had overrun the
northern or north-western part of Europe; but Ireland and
Denmark, the two countries which were never conquered
by the Romans, continued longer to make use of them,
and thus are peculiarly rich in antiquities of bronze, though
poor in Roman remains. When the Roman empire fell,
upon its ruins arose a new civilization, which commenced
by imitating the Roman models; it is no wonder, therefore,
that the same ornaments which appear on the oldest Irish
ecclesiastical remains are also to be seen on remains from
the iron period in Denmark, Sweden, Norway, France,
Germany, &c. They were all barbarized imitations of Ro-
man designs, and resembled one another, inasmuch as they
were derived from a common archetype. It was only re-
cently that Irish weapons belonging to the iron period were
found, for the first time, in the course of excavations in the
Shannon and at Dunshaughlin. In exhibiting some of these
Mr. Worsaae remarked, that they were very small, compared
with the large and heavy swords which were found, a short
-time ago, in cutting the railway at Kilmainham, and which,
undoubtedly, were Danish, or rather Norwegian swords. The
contrast between these Irish and Norse swords gives quite
a picture of the time. It is a fact that not only Ireland,
but other countries, England, France, Germany, &c., were,
from about the eighth until the twelfth century, exceedingly

332

weak, in consequence of internal wars; which accounts for
the remarkable circumstance, that a small number of vikings
from Scandinavia were able to take possession of large tracts
of Jand in those remote countries, and keep them under their
control for several centuries.

The swords which were found at Kilmainham are so like
the Norse swords, that if they were mixed with the swords
found in Norwegian, Swedish, and Danish tombs, and now in
the collections of Christiana, of Stockholm, and of Copenhagen,
it would be difficult to distinguish one from the other. ‘The form
of the handle, and particularly of the knob at the end of the han-
dle, is quite characteristic of the Norse swords. Along with
the swords foundat Kilmainham, some other antiquities of un-
doubtedly Scandinavian origin were also discovered. Mr. Wor-
saae here exhibited a number of old draughtsmen of bone, of a
hemispherical shape, and with a hole in the flat bottom, which
were so constructed, that they could not tumble off the table if
itwas shaken. Great quantities of these draughtsmen are found
in Norway,’ along with tesseree, buried with the warrior in the
grave. It might, perhaps, confirm what Tacitus said of the
«¢Germanni,” that they were exceedingly fond of gambling,
so much so, that at last they staked their personal liberty, and
thus sometimes became slaves. At Kilmainham were also
found, besides the swords, large brooches of a peculiar sort,
of a convex form, with a pin of iron, and ornamented with
serpent-like devices; such brooches had never been found in
other countries than in Scandinavia, or where Scandinavian
people were settled ; in Norway and Sweden they are most
common. The existence of these brooches at Kilmainham
along with the swords, would, therefore, furnish the strongest
argument in favour of the Scandinavian origin of their buried
owners. Similar brooches and weapons have been repeatedly
found in the Phoenix Park and in College-green, memorials
of the influence which the Norsemen had in Ireland, and
particularly in Dublin; and it is a remarkable circumstance,

333

that we should have in our hands, after so many centuries
had elapsed, the swords by which a foreign people once ruled

over Ireland, perhaps the very weapons by which Norsemen
had shed Irish blood.

§ 4. Early Civilization and Literature of the Northmen
and Irish.

It has often been said, and it is very well known, that
the predatory attacks of the Danes or Norsemen on the Eng-
lish, Scotch, and Irish coasts, were attended with much blood-
shed. There is scarcely a monument in the country which
has not been attributed, by some at least, to the Danes; and
Mr. Worsaae stated that he was well aware that in Ireland there
still remains a traditional recollection of the plunderings of
the Northmen ; nor would he deny, what both the Irish an-
nals and the Icelandic sagas often asserted, that the Northmen
in their plunderings treated the Irish very ill, taking them pri-
soners, and carrying away both males and females from the
country to be sold elsewhere as slaves. To illustrate these ad-
ventures he would endeavour to give, from memory, a story
preserved in one of the Icelandic sagas. ‘There was an Ice-
lander of the name of Hoskuld, who, at a fair in Halland (now a
part of Sweden), bought Melkorka, the daughter of an Irish
king, Myrkjartan, who had been made a prisoner in one of the
Norse expeditions to Ireland. He took her to Iceland, where a
son, Olaf, was the issue of their union. The Irish mother taught
her son to speak Irish, and when he was grown up he fitted
out a vessel, which was well manned, to go upon an expe-
dition. The vessel was wrecked upon the coast of Ireland,
and the crew were attacked and killed by the natives; but
when Olaf spoke to them in their own language they spared
his life; and, upon his telling them that his mother was the
daughter of King Myrkjartan, they brought him to the king,
who received him with the greatest kindness as his daughter’s
son. The king kept him at his court for some time, and when
Olaf left, he gave him a new vessel, Afterwards, when Olaf

334

returned to Iceland, and married there, he gave his son the
name of Kjartan, after his grandfather. Several names in
Iceland, as Niall and Kjallak, are also said to have been
brought over from Ireland.

The Irish annals contain many accounts of the Pagan
Danes and Norwegians having burned or plundered churches
and monasteries, and killed the monks, in Ireland. It has,
therefore, been often said, that the Christian Irish were
much more civilized than the Pagan Norsemen, and that
before the. invasion of the latter, a high state of civili-
zation had prevailed in Ireland, which their barbarism inter-
rupted and defaced. Mr. Worsaae quite agrees with his
friend Mr. Petrie and the other Irish antiquaries, who say
that many of the monuments in Ireland, such as the round
towers, which had often been referred to as proving the
civilization of the Danes or Norsemen, were in reality not of
North origin at all. But he thinks, on the other hand, thatsome
antiquaries have now and then detracted too much from the
Northmen, making them out—according to the tradition of
the country—to be only rude robbers and plunderers. Being
convinced that these opinions were not founded upon histori-
cal truth, he would not omit this opportunity of trying to
demonstrate their unsoundness.

It cannot be denied that Ireland was christianized at a
very early period, and several centuries before Scandinavia.
The Icelandic sagas show traces of that, and of the influence
Ireland exercised in the christianizing of the North. When
the Norsemen went first to Iceland in the latter half of the
ninth century, they found no traces of inhabitants there, except
of Irish monks, who had left croziers, bells, and Irish books.
This account, in the sagas, of Irish monks in Iceland, is con-
firmed by the statement of an Irish monk, Dicuil, who wrote
in the ninth century, and who mentions, that monks from
Ireland had visited the Fero islands, before these were yet
inhabited, and also Iceland, where the monks had stopped

339

from the first of February until the frst of August. (Dicuil’s
work was found in Paris, and published there in the years 1807
and 1814). The Norsemen called monks ‘ Pape,” and
thence they called the islands, where they found monks,
‘¢ Papey” and ‘* Papeyar.” In the western isles of Scotland,
in Orkney and Shetland, several islands bear that name;
thus shewing, that monks had resided there at an early
period. It is also curious to observe, that in Iceland there
existed in the olden time a church which had been built
in honour of St. Columba; and mention is made of an Ice-
lander who was said to have been educated by an abbot
named Patrick, in the western isles of Scotland or Ireland.
The King of Norway, Olaf Tryggveson, who first tried to
introduce Christianity there, was converted and baptized on
an island near Ireland, or, as some sagas say, ‘‘ west over in
Ireland.” Be that as it may, he was married to a sister
of king Olaf Kvaran in Dublin, where he stopped for some
time, and where, undoubtedly, the Christianity of Ireland must
have influenced him. An Irish princess named Sunnifva is
also said to have come to Norway, where she died, being per-
secuted by the Pagans. Her body, according to the legend,
being afterwards found in a perfect state of preservation, she
was canonized ; and on the 8th of July the Norsemen after-
wards had a mass in honour of her.

Such is the testimony borne by the Icelandic sagas to the
fact of there having been an early Christian civilization in Ire-
land. But + the question remains, whether this civilization
was not limited, for the most part, to the clergy, and whether
the mass of the people were not still very rude. From all the
accounts in the Irish annals, it appears, as Mr. Worsaae
thinks, that the people of Ireland, with the exception of the
clergy, were at that time really not more civilized than the
Northmen, perhaps even less so. It is true that the North-
men robbed and plundered, burned and killed ; but the people
of that remote period ought not to be judged according to

336

the standard of modern usages and feelings. | What is now
regarded as a shame was then accounted an honour. ‘The
Northman who went upon an expedition in his vessel, acquired
a large tract of land, or returned with gold and silver, after
having killed many warriors in battle, was quite sure
that the daughters of the highest nobles in the land would
gladly give him their hand; but they never liked to marry a
man who remained at home all his life. There is a curious
story in one of the old Icelandic sagas which affords a very
good idea of the state of society in the olden time. When
King Olaf Tryggveson was stopping in England, after having
been converted to Christianity, he bought a beautiful shield
from a clergyman of the name Thangbrand. The clergyman,
instead of purchasing holy books with the money, bought a
handsome Irish girl, who some time before had been taken
prisoner and made a slave. Not long afterwards the clergy-
man was obliged to leave England and proceed to Germany
in company with a bishop Adelbert ; nevertheless he carried
the Irish girl along with him. In Germany, one of the fol-
lowers of the Emperor becoming enamoured of her, attempted
to take her from the priest, upon which the latter drew his
sword and killed his rival. The priest, being expelled by the
Emperor from his dominions, returned to England, where
King Olaf Tryggveson received him with great kindness, and
made him his chaplain.

When this was tolerated among the clergy, what was to be
expected from the common people? It is true enough, that
the Danes robbed and killed Irishmen, but they were, perhaps,
not so much to blame as the native Irish, who constantly
assailed each other, each tribe making incursions into the terri-
tory of its neighbour. If we take a view of the different coun-
tries of Europe, France, Germany, Spain, and Italy, we shall
find that people of the same era called Christian were addicted
to plunder and assassination as well as the Pagan Norsemen;
nor were such practices considered in the least degree extra-

337

ordinary. It would, however, be a great mistake to suppose
that the Danes or Norsemen came to Ireland only to plunder
and commit murder. The fact that the Norsemen in Ireland
had their principal settlements in towns, as in Dublin, Limerick,
Waterford, and Cork, is sufficient to shew that they must
have carried on trade and commerce. The Icelandic sagas
contain frequent accounts of men going, with their vessels,
for trade to Dublin; and one saga adds, ‘“‘as many now” (in
the tenth century) ‘‘do.” The Irish annals give some infor-
mation relating to the Danish or Norse merchants in Dub-
lin, where some families, supposed to be descendants of the
old Norse merchants, still exist, and where a part of the town,
called Oxmantown, or originally Ostmantown (in old docu-
ments, Villa Ostmannorum), to this day records the influence
which they once possessed. The Norsemen were called by the
Irish *‘ Ostmen,” and the Norsemen in return gave to the
Irish the name of ‘* Westmen.” Some islands to the south of
Iceland retain the name ‘‘ Westmannaeyar,” originally given
because some Irish slaves, nearly a thousand years ago, were
killed there.
It is often, though incorrectly, asserted, that ‘* the Danes”
were so completely defeated at the battle of Clontarf, that
they never ventured to Ireland after that defeat. It is true
that after that engagement the Danes, or rather Northmen,
came less frequently to the shores of Ireland; but the reason
was, not so much that they had been defeated at the battle of
Clontarf, as that they became Christians, and their predatory
excursions to the country became, on that account, less fre-
quent. The battle was fought in the year 1014; at that time the
Anglo-Danish king, Canute, succeeded his father, and com-
‘pletely introduced Christianity into Denmark. Norway also
was Christianized about the same time. And it was the natural
effect of Christianity to put an end to all single expeditions
of vikings. In the year 1038, twenty-four years after the
battle at Clontarf, the Ostmen appointed a bishop, Dona-

338

tus, in Dublin, and Christ Church was founded by Sitrie Mac
Olaf, King of Dublin. The Ostmen continued to have bishops
in Dublin until the English invasion; they had also bishops
in Waterford and Limerick. The Bishops of Dublin and Wa-
terford were, as an effect of the connexion between the Ost-
men and their relatives in Kent, consecrated by the Arch-
bishop of Canterbury; and that, perhaps, may have been a
reason why the Archbishop of Armagh continued to hold the
station of Lord Primate of all Ireland, rather than the Arch-
bishop of Dublin, the metropolis of the country. There is no
doubt but that the Norsemen possessed considerable influence
in the towns above-mentioned, and in Cork, until the English
invasion. In the year 1095, Godfrid Meranagh, King of the
Ostmen, had ninety ships in the harbour of Dublin; and men-
tion ismadein the Irish annals of a meeting at Athboy of Tlactga,
in the year 1167, when as many as 1000 of the Danes of Dublin
were present. Both in Dublin and Cork they resisted the
English; and in the year 1171, more than a century and a half
after the battle of Clontarf, the Norse Prince of Dublin, Has-
culf, who was expelled by the English Earl Strongbow, returned
to Dublin with sixty ships, and tried to regain possession of
the city. Even in the year 1263, the Irish applied to the
Norse king, Hakon Hakonson, then on an expedition to the
western islands of Scotland, to assist them against the English,
which it is not probable they would have done, if there had not
been remnants of the Ostmen in Ireland. Giraldus Cambrensis
mentions a remarkable fact, that after the occupation of Dub-
lin by the English, 400 of the Danes of Dublin were taken
into the English army. One may well ask, how could the
Ostmen have kept up their influence in the towns of Ireland
after the expeditions from Scandinavia to Ireland had ceased,
if they had not carried on trade and commerce, and been of
great use to the Irish, whose daughters the Ostmen very often
married ?

Partiality might be imputed to Mr. Worsaae, because he

339

was a Dane, but the ancient coins which have been discovered in
this country fully bear him out in what he has stated. We do
not find any particular Irish coins before the invasion of the
Norsemen; but immediately after that event we see a great
number of ‘“* Hiberno- Danish” coins, which were imitations of
Saxon and other coins. A number of Arabian or Cufic coins
have also been found in Ireland, a circumstance which could
only be accounted for by the commerce with the Northmen.
Arabian coins of the same kind have been found, with silver
ornaments, in great abundance in Scandinavia, particularly in
Sweden, on. the island Gotland, upon the shores of the Baltic,
and in Russia along the rivers as far as the Caspian sea, which
shewed the course of trade with the East at that remote time.
There is every reason to believe that the Norsemen, who
were the only sailing people at that period, and who had con-
nexions not only with Scandinavia, but with Russia, Scotland,
England, Holland, Germany, and France, had highly im-
proved the trade of Ireland. When we consider, moreover,
that the Northmen had beautiful ornaments and well-made
swords, inlaid with silver and gold,—that they could build
vessels, in which, several centuries before Columbus, they
sailed across the Atlantic,—we find strong arguments support-
ing the assertion, that the Northmen at that time were not so
rude or so injurious to the civilization of Ireland as is generally
supposed.

But what most sustains Mr. Worsaae’s opinion is the old Ice-
landic literature. The Irish and Icelandic literature are so far
alike, that they were written in the native tongue, the reason of
which probably was, that Ireland and Iceland, in their re-
moteness, were unaffected by the many movements of Europe.
But between them there was this great difference, that theIrish
literature, and especially the historical part of it, was, for the
most part, written by the clergy ; but the Icelandic sagas or his-
torical works are more characteristic monuments of the spirit
of the people in the Pagan time. They preserve all the old re-

340

collections which the clergy in other countries succeeded in
destroying. The Irish annals, therefore, differ only in regard
to language from the Latin annals of other countries ; whilst the
Icelandic sagas, like historical novels, are quite descriptive of
the state, the manners, and the habits of the people at the
periods to which they referred.

Mr. Worsaae here read a scene of the saga of King Ha-
rald Haardraade (cap. 99), which gives an idea of the origin
of the sagas. It shewed that in Iceland there were men whose
principal business it was to learn sagas and tell them to the
people ; such men were called sagamen, and they were very
often bards (Skjalde). These bards accompanied kings on
their expeditions, or lived at their courts, both in Scandinavia
and in foreign countries. Several bards are known to have
been in Ireland with the Norse Kings of Dublin. They had
thus the best means of obtaining information respecting all
events of importance. Both the bards, the vikings, and the
merchants, after they had returned to their home, amused the
people in the long winter evenings by describing the battles
and other events they had been present at. This was an amuse-
ment in the house of the yeoman and in the hall of the king,
The scene of the saga just quoted furnishes a proof that the
sagamen and bards did not think it necessary to flatter the
kings. On the other hand, the old Danish and Norse kings
themselves were not very fond of flattery: the well-known
story of the Anglo-Danish king, Canute, and the flatterers on
the sea-shore, presents a striking example of this. We have
thus an assurance of the general truth of the old sagas.

A few other extracts from the sagas, particularly illustrating
the connexion between Ireland and Scandinavia, were read by
Mr. Worsaae. The first was a dialogue between Eistein and
Sigurd the Crusader, both Kings of Norway in the twelfth
century, and sons of the Norse King Magnus Barfod or Bare-
foot (so called because he wore the Highland dress), who was
killed in Ulster, a.p.1103. Sigurd had been married, as the sagas

341

relate, to Biadmynja, a daughter of Myrjartak, King of Con-
naught, or, as the Norsemen called it, ‘* Kunnaktir.” King
Myrjartak was consequently an ally of King Magnus Bare-
foot on the occasion of his expedition to Ireland. But when
Magnus was killed, Sigurd left his wife in Ireland, and after-
wards sent an ambassador thither, requiring the Irish to pay
him a large sum of money as a fine for the murder of his
father, else he would again invade the country. It is said
that the Irish, at a numerous meeting, when the ambassador
delivered his message, resolved to pay the money.

The saga introduces the two kings comparing themselves
(vid. Laing’s Translation of Snorre Sturleson’s History of the
Kings of Norway, vol. iii. pag. 176, sq.), and gives in the two
characters an admirable picture of the old and new time in
Norway. Sigurd is the old viking, who cares only for war-
like achievements, and viking expeditions, and looks with con-
tempt upon the man who sits at home. Listein has in the
mean time been building churches, fishing villages, and light-
houses; he has made roads over the mountains, and restored
peace in the country; and he says that the state of Norway
has perhaps been more benefited by these domestic services
than by his brother’s victories over the infidels in the Holy
Land.

The last fragment of the sagas read was a part of the his-
tory of an Irishman named Gillekrist or Harald Gille, who is
said to have been a son of King Magnus Barefoot, and who,
to satisfy King Sigurd the Crusader, proved his descent by
undergoing the ordeal of treading over nine red-hot plough-
shares ; he afterwards became King of Norway, and left his
sons as kings after him. The saga describes some quarrels
between Harald and Magnus the son of King Sigurd, and
gives a very spirited account of a race between Harald, who
was on foot, and Magnus on horseback. The saga says :
** Harald Gille was a tall, slender man, with a long neck and
face, black eyes and dark hair, brisk and quick, and generally

VOL. IfI. 2F

342

wore the Irish dress of short, light clothes. ‘The Norse lan-
guage was difficult for Harald, and he used expressions which
many laughed at, but King Sigurd did not permit this when
he was present.” At the race Harald wore ‘an Irish hat,”
and he ran so swiftly, that Magnus was not able to follow him
on his Gotland horse—“ a beautiful animal, and very swift.” —
(Vid. Laing’s Translation of Snorre Sturleson’s History of
the Kings of Norway, vol. ili. p. 193, sq.)

Mr. Worsaae pointed attention to the beautiful, simple,
and lively descriptions in the sagas, which are full of the
most entertaining accounts, representing the time, with all its
favourable and unfavourable features. In the sagas one sees the
family round the fire, the viking on board his vessel, the Par-
liaments at their meetings, the King and his retainers in his hall.
When it is remembered that those sagas were written down
immediately after the introduction of Christianity into Iceland
in the twelfth and thirteenth centuries, so that the Christian
element of civilization could have exercised but little influence
upon them; and when those sagas are compared with the Irish
historical works, what has been already said about the in-
fluence of the Northmen in Ireland being also borne in mind,
Mr. Worsaae will, perhaps, be acquitted of the charge of par-
tiality, when he contends, that the Pagan Northmen in the
ninth, tenth, and eleventh centuries, were not less civilized
than the Christian Irishmen, perhaps even a little more.

In conclusion, Mr. Worsaae made the following observa-
tions : :

‘© T should be very sorry if any’ one should think that it
was my intention, by these remarks on the Icelandic and
Irish literature, to deny the worth of the latter; on the con-
trary, I have had the opportunity of seeing how many inter-
esting and most important old manuscripts still exist in the
collections of the Academy and Trinity College, and I have
felt the greatest pleasure in observing with what energy the
Irish Archeological Society has continued to print hitherto

343

unpublished Irish manuscripts, which can scarcely be too
highly valued. I must, at the same time, express my regret,
that in Great Britain and Ireland public support is given in
most instances to societies which publish their books privately
for the use of their members, in consequence of which system
the books are very little or not at all known on the Continent.
I think it would be of great importance, if the old Irish literary
remains could be more generally known in Europe than has
hitherto been the case. Ireland has an immense advantage
over Scotland, England, and all other countries, which are
now partly, and were once completely inhabited by a Celtic
people, in that it has preserved an entire literature, whilst
other countries have preserved little or none at all. All
nations of Celtic descent will, therefore, be obliged to turn
their eyes to Ireland, when seeking information concerning:
the ancient manners and institutions of the genuine Celtic
people. I have also learned, with the greatest surprise, that
the most interesting and most important documents from the
Celtic time—I should say the most remarkable documents in
existence in Ireland—I mean, the old Brehon laws—have never
been published. The Irish annals, and all the other exist-
ing Celtic remains, will scarcely throw so much light upon
the real state of the institutions of Ireland and other Celtic
countries, as those venerable laws; and I think now is the
time to publish them, while the Celtic is still a spoken lan-
guage, which it probably will not long continue to be, and
while there are still men alive who are competent to do it.
It is said that the publication of these laws will be a very
expensive work: but if the British Government will not do
for Ireland, what it has done for England, Scotland and
Wales, by publishing their old institutions,—if Trinity Col-
lege, in possession of which the manuscripts are, cannot do
it,—then I hope that there are in Ireland men who will do
honour to themselves and their native country, by publishing
its most remarkable literary remains; and I hope that they will
2F2

344

publish them in such a way, that literary men on the Continent
also, will have the opportunity of becoming acquainted with
them.

‘¢ T should be most happy, if my remarks could in any de-
gree increase the interest which aiready exists in Ireland, for
its remains, both literary and monumeptal ; and if they also
could shew how important it is that the antiquaries of the
different countries should work together; that the Irish and
Scandinavian, in particular, should unite their efforts more
than they have hitherto done. I have tried to shew that
our antiquities and sagas have an interest connected with
Irish history. And I know now, better than before, how much
light the Irish annals and other remains throw upon the in-
vasions of the Danes and Norsemen in this country.

*¢ The archeologists have not yet their general meetings
like the naturalists. But Lhope that the easy communication
which now exists between Ireland and Denmark will soon
bring an Irish antiquary over to us, who, addressing our Royal
Society of Northern Antiquaries, may impart to us some por-
tion of the rich store of information which not only we, but
the whole of Europe, have every reason to expect from the
unique Celtic National Museum, and the unique Celtic Lite-
rature of Ireland.”

The President communicated to the Academy the result
of the further researches of Dr. Hincks, in connexion with
the third Persepolitan Writing, in which the Author has ex-
tended the number of ascertained characters from sixty-five to
seventy-six.

Sir William R. Hamilton made a communication respect-
ing anew mode of geometrically conceiving, and of expressing
in symbolical language, the Newtonian law of attraction, and
the mathematical problem of determining the orbits and pertur-
bations of bodies which are governed in their motions by that
law.

345

Whatever may be the complication of the accelerating forces
which act on any moving body, regarded as a moving point, and,
therefore, however complex may be its orbit, we may always
imagine a succession of straight lines, or vectors, to be drawn
from some one point, as from a common origin, in such a man-
ner as to represent, by their directions and lengths, the varying
directions and degrees(or quantities) of the velocity of the mov-
ing point: and the curve which is the locus of the ends of the
straight lines so drawn may be called the hodograph of the
body, or of its motion, by a combination of the two Greek
words, 60dc, a way, and ypadw, towrite or describe; because the
vector of this hodograph, which may also be said to be the vector
of velocity of the body, and which is always parallel to the tan-
gent at the corresponding point of the orbit, marks out or in-
dicates at once the direction of the momentary path or way in
which the body is moving, and the rapidity with which the
body, at that moment, is moving in that path or way. This
hodographie curve is even more immediately connected than
the orbit, with the forces which act upon the body, or with
the varying resultant of those forces, for the tangent to the
hodograph is always parallel to the direction of this resultant ;
and if the element of the hodograph be divided by the element
of the time, the quotient of this division represents (to the
usual units) the intensity of the same resultant force ; so that
the whole accelerating force which acts on the body at any
one instant is represented, both in direction and in magnitude,
by the element of the hodograph, divided by the element of the
time. We have also the general proportion, that the force is
to the velocity, in any varied motion of a point, as the element
of the hodograph is to the corresponding element of the orbit.

These general remarks respecting varied motion, under
the influence of any accelerating forces whatever, having been
premised, let it be now supposed that the force is constantly
directed towards some one fixed point or centre, which it will
then be natural to choose for the origin of the vectors of the

346

hodograph. The straight nines drawn to the moving body
from the centre of force being called, in like manner, the vectors
of the orbit, or the vectors of position of the body, we see that
each such vector of position is now parallel to the tangent of
the hodograph drawn at the extremity of the vector of velocity,
as the latter vector was seen to be parallel to the tangent of
the orbit, drawn at the extremity of the vector of position; so
that the two vectors, and the two tangents drawn at their ex-
tremities, enclose at each moment a parallelogram, of which it
is easily seen that the plane and area are constant, although
its position and its shape are generally variable from one
moment to another, in the motion thus performed under the
influence of a central force. If, therefore, this constant area
be given, and if either the hodograph or the orbit be known,
the other of these two curves can be deduced, by a simple and
‘uniform process, on which account the two curves themselves
may be called reciprocal hodographs.

The opposite angles of a parallelogram being equal, it is
evident, that if the central force be attractive, any one vector
of position is inclined to the next following element of the
orbit, at the same angle as that at which the corresponding
vector of velocity is inclined to the next preceding element of
the hodograph. Also, if from either extremity of any small
element of any curve, a chord of the circle which osculates to
that curve along that element be drawn and bisected, the ele-
ment subtends, at the middle point of this chord, an angle
equal to the angle between the two tangents drawn at the two
extremities of the element ; that is, here, if the curve be the
hodograph, to the angle between the two near vectors of posi-
tion, which are parallel to the two extreme tangents of its
element. We have, therefore, two small and similar triangles,

from which results the following proportion, that the half

chord of curvature of the hodograph (passing through, or
tending towards the fixed centre of force) is to the radius vec-

tor of the orbit as the element of the hodograph is to the ele-

—

347

ment of the orbit, that is, by what was lately seen, as the
Sorce is to the velocity.*

But also, the radius of curvature of the hodograph is to
the half chord of curvature of the same curve, as the radius
vector of the orbit is to the perpendicular let fall from the
fixed centre on the tangent to the same orbit; therefore, by
compounding equal ratios, we obtain this other proportion:
the radius of curvature of the hodograph is to the radius vec-
tor of the orbit, as the rectangle under the same radius vector
and the force is to the rectangle under the velocity and the
perpendicular, or to the constant parallelogram under the vec-
tors of position and velocity. If, therefore, the law of the in-
verse square hold good, so that the second and third terms of
this last proportion vary inversely as each other, while the
fourth term remains unchanged, the first term must be also
constant; that is, with Newton’s law of force (supposed here
to act towards a fixed centre), the curvature of the hodograph
is constant: and, consequently, this curve, having been already
seen to be plane, is now perceived to be a circle, of which the
radius is equal to the attracting mass divided by the constant
double areal velocity in the orbit. Reciprocally, we see, that
no other law of force would conduct to the same result: so
that the Newtonian law may be characterized as being the
Law of the Circular Hodograph.

Another mode of arriving at the same simple but impor-
tant result, is to observe, that because the radius of curvature of
the hodograph is equal to the element of that curve, divided
by the angle between the tangents at its extremities, or (in
the case of a central force) by the angle between the two cor-
responding vectors of the orbit, which angle is equal to the

* By an exactly similar reasoning, the following known proportion may
be proved anew, namely, that the force is to the velocity as that velocity is
to the half chord of curvature of the orbit, whatever the law of central force

may be.

348

double of the elementary area divided by the square of the
distance (of the body from the centre of force), while the ele-
ment of the hodograph has been seen to be equal to the force
multiplied by the element of time, or multiplied by the same
double element of orbital area, and divided by the constant of
double areal velocity, therefore this radius of curvature of the
hodograph must, for any central force, be equal to the force
multiplied by the square of the distance, and divided by the
double areal velocity.

The point on the hodograph which is the termination of
any one vector of velocity may be called the hodographic re-
presentative of the moving body, and the foregoing principles
show, that with a central force varying as the inverse square of
the distance, this representative point describes, in any proposed
interval of time, a circular arc, which contains the same num-
ber of degrees, minutes, and seconds, as the angle contempo-
raneously described round the centre of force by the body itself
in its orbit, or by the revolving vector of position ; because,
whatever that angle may be, an equal angle is described in
the same time by the revolving tangent to the hodograph.
Thus, with the law of Newton, the angular motion of a body
in tts orbit is exactly represented, with all its variations, by
the circular motion on the hodograph; and this remarkable re-
sult may be accepted, perhaps, as an additional motive for the
use of the new term which it is here proposed to introduce.

Whatever the law of central force may be, if the square of
the velocity in the orbit be subtracted from the double rectan-
gle under the force and distance, which has been seen to be
equal to the rectangle under the same velocity and the chord
of curvature of the hodograph, the remainder is the rectangle
under the segments into which that chord is cut by the centre
of force, being positive when this section takes place inter-
nally, but negative when the section is external, that is, when
the centre of force is outside the osculating circle of the hodo-
graph. In the case of the law of the inverse square, this latter

349

curve is its own osculating circle, and the rectangle under the
segments of the chord is, therefore, constant, by an elemen-
tary theorem of geometry contained in the third book of Eu-
clid ; if, then, the square of the velocity be subtracted from
the double of the attracting mass, divided by the distance of
the body from the eentre of force, at which that mass is con-
ceived to be placed, the remainder is a constant quantity,
which is positive if the orbit be a closed curve, that is, if the
centre of force be situated in the znterior of the circular hodo-
graph.

In this case of a closed orbit, the positive constant, which
is thus equal to the product of the segments of a hodographic
chord, or the constant product of any two opposite velocities
of the body, is easily seen, by the foregoing principles, to be
equal to the attracting mass divided by the semisum of the two
corresponding distances of the body, which semisum is, there-
fore, seen to be constant, and may be called (as in fact it is)
the mean distance. ‘The law of living force, involving this
mean distance, may, therefore, be deduced as an elementary
consequence of this mode of hodographic representation, for
the case of a closed orbit; together with the corresponding
forms of the law, involving a null or a negative constant, in-
stead of the reciprocal of the mean distance, for the two cases
of an orbit which is not closed, namely, when the centre of
force is on, or is outside the circumference of the hodographic
circle.

Whichever of these situations the centre of force may have,
we may call the straight /éne drawn from it to the centre of
the hodograph, the hodographic vector of eccentricity ; and
the number which expresses the ratio of the length of this
vector to the radius of the hodograph will represent, if the
orbit be closed, the ratio of the semidifference to the semisum
of the two extreme distances of the body from the centre of
force, and may be called generally the numerical eccentricity

350

of the hodograph, or of the orbit (without violating the re-
ceived meaning of the term).

Whatever the value of this numerical eccentricity may be,
the constant area of the parallelogram under the vectors of
position and velocity may always be treated as the sum or
difference of two other parallelograms, of which one is equal
to the rectangle under the constant radius of the hodographie
circle and the varying radius vector of the orbit, while the
other is equal to the parallelogram under the vectors of posi-
tion and eccentricity ; and hence it is not difficult to infer,
that the length of the vector of position, or of the radius vec-
tor of the orbit, varies in a constant ratio, expressed by the
numerical eccentricity, to the perpendicular let fall from its
extremity, that is, from the position of the body, on a constant
straight line or directrix, which is situated in the plane of the
orbit, and is parallel to the hodographic vector of eccentricity.
The orbit, therefore, whether it be closed or not, is always
(with the law of the inverse square) a conic section, having
the centre of force for a focus—a theorem which has, indeed,
been known since the time of Newton, but has not, perhaps,
been proved before from principles so very elementary.*

Conceive a diameter of the hodograph to be drawn in a
direction perpendicular to the vector of excentricity ; the ex-
tremities of this diameter correspond to the extremities of that
chord of the orbit which is perpendicular to the shortest radius

* The hodograph of the earth’s annual motion may be considered to be ex-
hibited to observation in astronomy, as the curve of aberration of a star; and
it is known that this aberratic curve is a circle, notwithstanding the eccen-
tricity of the earth’s orbit ; but the author is not aware that this circularity
of the aberratic curve (for a star near the pole of the ecliptic) has ever been
shewn before to be a consequence of the law of thé inverse square, except by the
help of the properties of the elliptic orbit; whereas the spirit of the present
communication is to derive that orbit from the circle, and to regard that circle
itself as a sort of geometrical picture of Newton’s law, instead of being only
one of many corollaries from the laws of Kepler.

351

vector, and which is called the parameter ; from which it fol-
lows, that the semiparameter of the orbit is equal to the con-
stant area of the parallelogram under distance and velocity,
divided by the radius of the hodograph, and, consequently, that
it is equal to the square of the constant double areal velocity,
divided by the attracting mass.

It is evident that these results agree with and illustrate
those by which Newton shewed that Kepler’s laws were ma-
thematical consequences of his own great law of attraction.
In applying them to the undisturbed motion of any binary
system of bodies, attracting each other according to that law,
we have only to substitute the sum of the two masses for the
single attracting mass already considered, and to treat one of
the two bodies as if it were the fixed origin of the vectors of a
relative hodograph, which will still be circular as before. And
even if we consider a ternary, or a multiple system, we may
still regard each body as tending, by its attraction, to cause
every other to describe an orbit of which the hodographic
representative would be a perfect circle.

When there is one predominant mass, as in the case of the
solar system, we may in general regard each other body of the
system as moving in an orbit about it, which is, on the same plan,
represented by a varying circular hodograph. For if, at any
one moment, we know the two heliocentric vectors of position
and velocity of a planet, we know the plane and area of the
parallelogram under those two vectors, and can conceive a
parallelepiped constructed, of which this momentary paral-
lelogram shall be the base, while the volume of the solid
shall represent the sum of the masses of the sun and planet;
and then the height of the same solid will be equal to the
radius of the momentary hodograph ; so that, in order to con-
struct this hodograph, we shall only have to describe, in the
plane, and with the radius determined as above, a circle which
shall touch the side parallel to the heliocentric vector of posi-
tion, at the extremity of the vector of velocity, and shall have

352

its concavity, at the point of contact, turned towards the sun.
The moon, or any other satellite, may also be regarded as
describing, about its primary, an orbit, of which the hodogra-
phic representative shall still be a varying circle.

As formule which may assist in symbolically tracing out
the consequences of this geometrical conception, Sir William
Hamilton offers the following transformations of certain gene-
ral equations, for the motion of a system of bodies attracting
each other according to Newton’s law, which he communi-
cated to the Royal Irish Academy in July, 1845. (See Pro-
ceedings, vol. II], part 2, Appendix III. and V.)

The new forms of the equations are these :

m’

= a a t= BfodU(p'p);
V.(p —p)(r’—7) T So (p p)

p= (rdt; co
in which p and 7 are the vectors of position and velocity of the
mass m at the time ¢; p’ and 7’ the two corresponding vectors
of another mass m’ at the same time ; o is another vector, per-
pendicular to the plane, and equal in length to the radius of
the momentary relative hodograph, representing the momentary
relative orbit, which the attraction of the mass m/ tends to cause
the body m to describe; d, §, 3, are marks of differentiation,
integration, and summation, and V, U, are the characteristics
of the operations of taking respectively the vector and versor
of a quaternion. Or, eliminating p and o, but retaining the
hodographic vector r, and using A as the mark of differencing,
the conditions of the question may be included in the follow-
ing formula, which the author hopes on a future occasion to
develope:

(m +-Am)dU (GArdeé)
PSS a)
V (Ar.§Arde)
Meanwhile it is conceived that any such attempt as the
foregoing, to simplify or even to transform the important and
difficult problem of investigating the mathematical conse-

quences of the Newtonian law of attraction, is likely to be re-

353

ceived at the present time with peculiar indulgence and interest,
in consequence not only of the brilliant deductive discovery
lately made of the new planet exterior to Uranus, but also
of the extraordinary and exciting intelligence which has just
arrived from Dorpat, of the presumed discovery, by Pro-
fessor Madler, of a central cluster (the Pleiades), and of a
central sun (Alcinoe, called also Eta Tauri) : around which
cluster, and which sun or star, it is believed by Madler that
our own sun and all the other stars of our sidereal system, in-
cluding the milky way, but exclusive of the more distant
nebule, are moving in enormous orbits, under the combined
influences of their own mutual attractions, all regulated by
the same great law.

Sir William Hamilton exhibited Professor Miidler’s work,
Die Centralsonne, Dorpat, 1846, in which, as a first provi-
sional attempt to determine the orbit of our own sun, with the
help of the proper motions of a great number of stars, com-
bined with Bessel’s parallax of 61 Cygni, Madler assigns to
what he regards as the Central Sun, Alcinoe, a distance
amounting to thirty-four million times the distance of our
sun from us; concluding, also, but still only as first approxi-
mations, that the period of our sun’s revolution is about
eighteen millions of years, and that its orbit has now an in-
clination to the ecliptic of about 84 degrees, with an ascend-
ing node, of which the present longitude is nearly 237°.

A chart of observed places of Le Verrier’s Planet was also
exhibited by Sir William Hamilton; and was illustrated by

- comparison with Bremiker’s Star-Map, which also was laid

upon the table.

354

DONATIONS.

Mémoires présentés a l Académie Impériale des Sciences
de Saint Pétersbourg. Par divers Savans. Tom. 5me, Livs.
1-6 ; et Tome 6me, Liv. Ire.

Mémoires de l Académie Impériale des Sciences de Saint
Pétersbourg. 6me Serie. Sciences Naturelles. "Tome 5me,
Livs. 3me et 4me. Sciences Mathématiques et Physiques.
Tome 4me, Liv. 2me. Presented by the Academy.

Introduction to Zoology, for the Use of Schools. Part I.
By Robert Patterson, Esq. Presented by the Author.

Labour on Land, containing a plan for the Employment of
the destitute Poor in Ireland. By Major S. W. Blackall.
Presented by the Author.

Memorie della Societa Italiana delle Scienze residente in
Modena. Tomo X XIII.—Matematica. Presented by the
Society.

An old Watch, found in the Bog of Allen, made in Paris
by M. Gavdron. Presented to the Museum by John Len-
taigne, M. D.

A Model of an ancient Frame or Vat, found in the Town-
land of Templemoyle, Parish of Banagher, County Derry,
and also a number of the more portable parts of the structure
discovered during the excavation.

A Model of an ancient Wooden Frame House, found in
Drumkelin Bog, in the Parish of Inver, County Donegal,
twenty-five feet below the surface. Presented to the Museum
by Captain Larcom.

The Ordnance Survey of the County 9° Kerry, in 113
sheets, including the Title and Index. Presented by His
Kxceellency the Lord Lieutenant.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 59.

January 11th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

William Brooke, Esq., Q.C.; Dominick Corrigan, M. D.;
Leonard Dobbin, Esq.; Michael Donovan, Esq. ; Charles Hali-
day, Esq. ; William Neilson Hancock, Esq.; John Kells In-
gram, Esq., F.T.C.D.; Charles P. Mac Donnell, Esq.; Right
Hon. Louis Perrin; and Frederick John Sidney, Esq., were
elected Members of the Academy.

On the recommendation of Council the following By-laws
were adopted by the Academy :

“1, That the number of Honorary Members of the
Academy shall be limited to sixty.

«2. That there shall be three Sections of Honorary
‘Members, corresponding to the threefold objects of the Aca-
demy, and that the numbers in each Section shall be limited
as follows:

‘* Section of Science, 30; of Literature, 15; of Antiqui-
ties, 15; = 60.

VOL. III. 2G

356

‘¢3. That the number of Honorary Members in each
Section, natives of Great Britain and Ireland, shall not ex-
ceed one-half of the total number in that Section.

«© 4, That the election of Honorary Members shall take
place only at the Stated Meeting in November.

‘© 5, That none shall be eligible as Honorary Members
unless previously recommended by the Council, and that the
choice of the Council shall be determined by Ballot.

«© 6. That the former By-laws of the Academy relating
to Honorary Members be repealed, and the foregoing substi-
tuted in their place.

On the recommendation of Council, it was RESOLVED,—
That the Committee of Antiquities be authorized to make a
selection of specimens from the purchased articles in the Mu-
seum of the Academy, to be presented to the Royal Museum
of Copenhagen, by the hands of Mr. Worsaae; and that this
donation be accompanied by drawings of other antiquities.

The Rev. Charles Graves made a communication supple-
mentary to his paper on the date of the Book of Armagh.

On the margin of fol. 64, b., and opposite to that part of
the text which contains the twenty-first verse of the thirteenth
chapter of St. Mark’s Gospel, the proper name Cellach occurs,
written in the peculiar Greek character of which examples
have been already given.* As it was an ordinary thing for a
scribe to make in the margin of a page a memorandum relat-
ing to some circumstance which took place at the time he
was writing it, there is reason to suppose that the name
Cellach, written here, was intended to record some event in
which a person of that name bore a principal part. Unfor-
tunately, as the name was a very common one amongst Irish
ecclesiastics, we cannot, with any certainty, fix upon the in-

* Proceedings of the Academy, vol. iii, p. 318.

357

dividual here referred to, and so obtain grounds for determin-
ing the date of the manuscript a priort. On the other hand,
if we are permitted to assume that it was written A. D. 807,
good reasons for this conclusion having been already shewn,
we are enabled to account in a satisfactory manner for the
appearance of the name in question.

In the twenty-fourth chapter of Sir James Ware’s Anti-
quitates Hibernice, where he gives an account of the acts of
the Ostmen in Ireland, we find the following passage :

** Anno 807, Dani et Norwegi in Hiberniam appulerunt,
et Roscomaniam, regionemque adjacentem ferro flammaque
vastarunt. Eodem tempore Cellacus Abbas cenobii S. Co-
lumbe Huensis, multis e suis, Norwegorum crudelitate, inter-
fectis, in Hiberniam profugit, et Kenanuse, alias Kenlise in
Midia, monasterium inhonorem 8S. Columbe sive condidit, sive
restauravit. Cum vero annos circiter septem ibi preefuisset
Abbas, Dermitio quodam in dicto cenobio Abbate relicto, in
Ionam sive insulam Huensem reversus est, ubi, post annum
unum vel alterum mortem obiit.”

Ware does not indicate the sources from whence he has
derived this account. It is confirmed, however, as regards
the date and the history of Cellach, by the Manuscript An-
nals in the Library of Trinity College, H.1,7, commonly called
the Annals of Innisfallen; and mention is made in the Annals
of Ulster, ad. ann. 806 (A. D. 807), of the building of the
monastery at Kells.

To the history of this Abbot of Iona it is by no means
improbable that allusion may have been intended by the scribe
who wrote the name of Cedlach in the margin: and perhaps he
may have thought that our Lord’s descriptive prediction of
‘the miseries attending the destruction of Jerusalem ( Mark xiii.
14—23) was not inapplicable to the sad visitation which had re-
cently fallen upon Iona.

With respect to the practice of writing Latin in Greek
characters, of which so many instances occur in the Book of

358

Armagh, it is to be observed that it does not necessarily indi-
cate a greater antiquity than Mr. Graves has assigned to this
manuscript. A decisive example of this kind occurs in the
case of the great Bible of the Abbey of St. Germain des Prés,
which, according to a note contained in it, was written in the
eighth year of the reign of Louis le Débonaire, that is, A. D.
822. The scribe of that manuscript has inserted in it two
Latin memoranda, which refer to the fact of its having been
executed by him, employing in both a Greek character, similar
to that used in the Book of Armagh.

His reason for doing so seems, in one case, to have been
the desire to vindicate his right to the credit, of which some
other scribe was depriving him. ‘*‘ Obsecro te lector,” he says,
*‘ ne laborem manuum mearum despicias; sed queso deprecor
mellifluam charitatem tuam ut pro me Domini misericordiam
exores. Evio idem fero laborem, alius tollit honorem.” It must
be inferred that the alius here spoken of was unacquainted
with the Greek character, in which these words were writ-
ten. In the other note the object of the scribe was plainly to
exhibit his own skill and learning, and, at the same time, to
test the intelligence of the reader. The passage, of which
the first part is written in a strangely elongated cursive hand,
and the last four words in Greek letters, runs as follows:
“© Supplicamus omnibus in Christo fidelibus qui hunc libellum
ad volvendum ad legendum accipitis meam ne reprehendito
insipientiam ;” which is immediately followed by the penta-
meter,

‘« Me quicunque capit rusticitate caret,”
written in the ordinary hand.

Nor was it only in the use of Greek characters that the
scribes of those times displayed their pedantry. Sylvestre, in
his Paléographie Universelle, vol. iv., describes a manuscript

* Fac-similes of these two passages are given in the Nouveau Traité de
Diplomatique of the Benedictines, vol. iii., pp. 186-437.

359

of the ninth century, in the Royal Library at Munich, in
which the Scribe has written the following sentence in Anglo-
Saxon runes: ‘* Omnis labor finem habet, premium ejus non
habet finem. Madalfrid scripsit istam partem. Deo gratias
quod ego perfect opus meum.” Thus recording his name,
which he may not have been allowed to do without resorting
to this artifice, and at the same time giving a proof of his
learning.

Mr. Graves insists much upon the importance of deter-
mining, with precision, the date ofa manuscript so ancient,
and of so much interest, as the Book of Armagh. By effect-
ing this, a great advance is made towards the establishment
of principles of paleography, by which we may estimate the
age of Irish manuscripts in general; and we are furnished
with the means of refuting the assertion, still repeated, that
Ireland has no manuscripts of a date more ancient than the
close of the ninth century.*

The Secretary of Council read the abstract of a paper by
the Rev. Dr. Hincks, on the third Persepolitan Writing, and
on the Mode of expressing Numerals in Cuneatie Characters.

** When I laid before the Academy, at its last sitting, my
alphabet of the third Persepolitan writing, with the corre-
sponding lapidary characters, I by no means expected that it
would prove perfectly correct ; no first attempt at the alphabet
of an unknown language has been so. I considered it, how-
ever, an approximation, and probably as near a one as could
be attained by means of the data in my possession; and I
looked forward to its being amended by those who had the
command of more numerous inscriptions. There were some
circumstances which left no doubt on my mind that error ex-
isted somewhere in it, though I could not discover where,
The number of dentals was too small ; there was no character

* See Moore’s History of Ireland, vol. i. p. 310.

360

for the word corresponding to the compound epithet, wysada-
hyésh, in Du, were only in part legible; and the manner of
writing the name Ormusd in the inscription H, and that of
Artaxerxes on the vase at Venice, could only be explained by
supposing the sculptors to have committed errors. All these
for tu or du; thename in NRu, answering to Harautish, and
difficulties, and others connected with the first inscription of the
East India Company, have been removed by an important rec-
tification, or series of rectifications, which I have made during
the past fortnight; and the language has, moreover, been
brought to exhibit a much greater similarity to the other Se-
mitic ones than I had at first supposed. I have, therefore, to
request leave to substitute the alphabet which I now send for
that in my last paper. As the correspondence between the
cursive and lapidary characters in the plate to that paper is
correctly given, though the values of many of the characters
are erroneous, and as the plate is, I believe, partly engraved,
I propose to let it stand, with so much of the paper as is neces-
sary for understanding it; but the transcriptions of Babylo-
nian words into Roman characters, and the catalogue of
Babylonian words, will be superseded by those which follow,
which are much more correct. In the plate which I now
send I give no lapidary characters, but instead thereof I give
many additional Persepolitan ones; and at the foot of it I
give a series of numbers from the rock inscription at Van, ex-
hibiting the mode of expressing numbers in Cuneatic charac-
ters on to 100,000. These are so arranged as to require no
comment; but it may be proper to state that the large num-
bers are those of men belonging to different nations which are
named ; and I presume they refer to the deportation of these
nations, according to the Assyrian practice. The historic
character of these inscriptions, of which I received a copy
very recently, is obvious.”

The President made a few remarks upon the present state
of the researches connected with Persepolitan writing, and

301

upon the position occupied by Dr. Hincks in these investiga-
tions.

The President presented to the Academy a set of coloured
drawings of celts and other antiquities, found in Cornwall,
which he had procured through the kindness of a friend re-
siding in that country. It appeared from a comparison of
them with the corresponding objects in the Museum of the
Academy, that there was an exact resemblance of form. The
Cornish antiquities of this kind are, however, comparatively
rare.

DONATIONS.

Runamo og Braavalleslaget, med fem lithographerede
Tavler, af J. J. A. Worsaae. Presented by the Author.

Tilleg til ‘“* Runamo og Braavalleslaget.” 1845.

Giornale dell? I. R. Istituto Lombardo di Scienze, Let-
tere ed Arti. Tom. 1V.e V. 1844 and 1845.

Memorie dell’ I. R. Istituto Lombardo di Scienze, Lettere
ed Arti. Vol. 2do. 1845.

Elogio di Bonaventura Cavalieri da Gabrio Piola. Pre-
sented by the Institute.

Philosophical Transactions of the Royal Society of
London for 1846. Parts 1, 2, and 3.

Proceedings of the Royal Society. 1845. Nos. 62-65.
Presented by the Society.

The Transactions of the Microscopical Society of London.
Vol. I., Parts 1 and 2; Vol. II., Part 1. Presented by the
Society.

- Journal of the Asiatic Society of Bengal. Nos. 166, 167.
1845. Presented by the Society.

Bulletin des Séances de la Société Vaudoise des Sciences
Naturelles. No. 12. 1846. Presented by the Society.

Oversigt over det Kongelige danske Videnskabernes Selshabs

302
Forhandlinger og dets Medlemmers Arbeider i Aaret 1842.
Presented by the Society.

Quarterly Journal of the Geological Society of London.
No. 8. Nov. 1, 1846. Presented by the Society.

Twenty-five School-books, published by direction of the
Commissioners of National Education in Ireland. Presented
by the Commissioners.

Proceedings of the Archeological Institute, Winchester.
Presented by the Institute.

Archeological Journal. Vols. I. and 11. Presented by
the British Archeological Association.

Abhandlungen der Fiirstlich Jablonowskischen Gesell-
schaft. Presented by the Society.

Det Kongelige Danske Videnskabernes Selskabs. Natur-
videnshabelige og Mathematiske Afhandlinger. Niende deel.
Presented by the Society.

Magnetical, Meteorological, and Astronomical Observa-
tions made at Washington. By Lieutenant J. M. Gilliss, U.S.
Navy. Presented by the Author.

An Explanation of the Observed Irregularities of the Motion
of Uranus on the Hypothesis of Disturbances caused by a
more distant Planet. By J.C. Adams, Esq. Presented by
the Author.

A long Sword, with four Guards, found in Malta ; and
a brass Puzzle Box, found in Ireland. Presented to the
Museum by Major-General R. H. Birch, Royal Artillery.

a

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 60.

January 25th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The Secretary of Council read a letter from Edward J.
Cooper, Esq., containing some recent observations of Le
Verrier’s planet, made with the meridian circle at Markree.

** Merville, Stillorgan,
** Dec. 28th, 1846.

“¢On the 9th of November my observations on the Le
Verrier planet, made during the month of October, were pre-
sented to the Academy ; I have now the pleasure to subjoin
those which have been since obtained with the Markree me-
ridian circle. My first Assistant, Mr. Graham, has annexed,
in Table II., corrections of the British Association Catalogue
places of those stars selected for comparison with the planet ;
and in Table III. corrections of the right ascensions and de-
clinations of the planet as given in my former comunication,
and in Table I. of the present.

‘¢ EpwarD J. Cooper.”

VOL. Ill. 2H

364

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365

TABLE IL.

CORRECTIONS OF BRITISH ASSOCIATION CATALOGUE
PLACES OF STARS.

sta, | A RIEM | Ober Destine | Ops

vations. vations.
1 | ¢ Capricorni,. | — 0.034 | 15 | — i.65 14
2 | 7451 B. A. C. | — 0.355 12 — 0.43 12
SHAPMA GIO at ete nett —— 0:021 12 —) #27 12
4 | 42 Capricorni, | + 0.161 17 — 0.41 17
Breil Drrstde: aaa + 0.074 | 17 | — 0-69 17
Pe ee eee — 0.026 Dl (agen Tay 2
6 | ¢ Aquarii, — 0.007 17 + 1,12 17
MOOS ees eae + 0.030 15 + 5.57 15
Beales, Soa wicca — 0.072 14 Ss DE 14
OT HOO! sous ste Ws. + 0.102 13 + 0.87 13
VOUS isaer tia ie . + 0.035 13 — 1.66 13

These corrections were obtained by subtracting each result from the mean
of all the results for each night, and then by combining the remainders according
to the weights of the determinations.
sign, to the Right Ascension and Declination of the Planet; the South Declina-

They are to be applied, with the proper

tion being, as usual, regarded as negative. On the night of November 9th, a mis-
take was made in reading the level attached to the declination circle in the instance
of¢ Capricorni. In reducing the observations, what was, very probably, the read-
ing was used instead of that given in the observing book. An anomaly still,
however, appearing in the result ; it has been thought better wholly to reject the
observation of declination of this star for that night. The correction of decli-
nation for November 9th will consequently be + 0”.9, instead of what would be
obtained from the Table given above ; or November, 9th 6 = — 13° 34’ 11".4.

Since the corrections given in the Table are mutual, any more accurate deter-
mination which may hereafter be obtained for one star will be applicable to all.
—ANDREW GRAHAM.

2H 2

366

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367

The following note by Professor Mac Cullagh, on the
attraction of ellipsoids, was read.

‘“* The object of the present note is to show how the final
integrations by which the attraction of a homogeneous elli psoid
is found, when the force varies inversely as the square of the
distance, may be performed geometrically ; and thus to com-
plete the synthetic solution of a celebrated problem. It has
been always supposed that the utmost geometry can do is
to arrive in a simple way at the differential expressions on
which the attraction depends, leaving the further treatment of
the question to the integral calculus ; but we shall see that, by
putting the differential of the attraction under a certain form,
the integral is at once obtained, and that in a very elegant
shape, by geometry.

‘* To avoid useless generality, we shall suppose the attracted
point to be at the extremity of an axis of the ellipsoid, as it is
well known that the solution of this particular case enables us
find the attraction wherever the point is placed. Let O be the
centre of the ellipsoid, and A, B, C the extremities of its semi-
axes, the lengths of which are denoted by a, b, ¢ respectively,
a being the greatest, and c the least. And first, suppose the
attracted point to be at C, the extremity of the least semiaxis.
Let two right lines passing through C, and making respec-
tively the angles @ and ¢ + dg with OC, revolve within the
ellipsoid, describing two right cones, of which OC is the com-
mon axis, and which include between their surfaces a differen-
tial portion dM of the volume of the ellipsoid. The attrac-
tion of the matter contained in dM is evidently in the direction
of OC.

‘* Now let us consider the focal ellipse having its centre at
O, and lying in the principal plane which is at right angles
to OC. Let E be the extremity of the major axis of this
ellipse ; and putting

eee Ve pi VTE (a2) oO

368

take in OE produced a point P such that OP shall be to OE
asp toc. Then, if a right line drawn from P touch the focal
ellipse in the point T, and if the angle OPT be denoted by 6,
it will be found that

2 2

ee
cos 6 = ——
P

; cos ¢.

Suppose that the point P moves to p, when ¢ is changed into
¢ +d. Then it may be easily shown that the attraction of
dM upon the point C is proportional to the interval Pp mul-
tiplied by the cosine of @. In this form the differential of the
attraction is immediately integrable. For if from p we draw
a right line pt touching the ellipse in ¢, and if s denote the
difference between the tangent PT and the elliptic are ET,
while s + ds denotes the difference between the tangent pt and
the are Et, it will appear, by a lemma which I have fre-
quently had occasion to use (see the Proceedings of the Aca-
demy, vol. ii. p. 508), that ds is equal to Pp multiplied by
cos 9. The integral, beginning when ¢ = 90°, or p =¢, is
therefore proportional to s. At the other limit we have ¢ = 0,
and p= b, which determines the extreme position of the point
T. The difference between the tangent PT and the elliptic
are ET, corresponding to this position, is to be multiplied by
a certain function of the semiaxes, in order to get the whole
attraction of the ellipsoid on the point C.

«* When the attracted point is at B, the extremity of the
mean axis, we proceed exactly as before; but instead of the
focal ellipse we make use of the focal hyperbola, whose plane
is at right angles to OB. Putting now

p=VP—(P—e)cos’, p'=Vb + (a — 2) cos *4,

and calling E the extremity of the primary axis of the hyper-
bola, we take in OE a point P (which will lie between O and
E) such that OP shall be to OE asp tod. Then, drawing

369

from P the right line PT, touching the hyperbola in T, and
denoting the angle EPT by 0, we have

Ve ren COS @ 5

cos 6 =

whence it may be shown that if p be the point to which P
moves when @ becomes ¢ + dg, the interval Pp multiplied by
cos @ will be proportional to the attraction of the matter dM
contained between the surfaces of two right cones having B
for their vertex and OB for their common axis, provided
and + d@ be the angles which the sides of these cones make
with OB. The whole attraction is therefore proportiona.
to the difference between the tangent PT and the hyperbolic
are E'T, the position of T being that which corresponds to the
supposition ¢ = 0, orp =e.

‘¢ When the attracted point is at the extremity of the great-
est axis of the ellipsoid, we’ cannot employ a similar method,
because there is no focal curve perpendicular to that axis.
But if a, B, c be the attractions at A, B, C respectively, we
have the known relation

Lphh Sach
poh Ae ie

of which a geometrical proof will be found in the Proceedings,
vol. ii. p. 525; and from this relation we can find a in terms
of B and c.

‘¢ The preceding method of treating the question of the
attraction of ellipsoids was given at my lectures in Trinity Col-
lege, in the beginning of last year. I have since observed
that the same results may be obtained, and perhaps more rea-
dily, by dividing the ellipsoid into concentric and similar shells.
For the attraction of dM is equal, in each case, to the attrac-
tion of the shell bounded by the surfaces of two! ellipsoids
whose semiaxes are acosp, bcos, ccos¢, and acos(p + dp),
beos(¢ + do), ccos(p + d®), these ellipsoids having O for their

370

centre, and OA, OB, OC for the directions of their semiaxes.
And the attraction of such a shell on an external point may be
simply expressed by means of the semiaxes of a confocal ellip-
soid passing through the point. (See a Memoir by M. Chasles
in Liouville’s Journal, vol. v.) The quantities which we have
called p and p’ are, in fact, semiaxes of an ellipsoid described
through the attracted point (that is, through C in the first
case, and through B in the second) so as to be confocal to the
surface of which the semiaxes are acos¢, bcos¢, ccos¢.”

A note by Professor Mac Cullagh, on the rotation of a
solid body, was read.

Let a solid body be made to revolve round a fixed point
O, and be afterwards free from any external forces; and
through O conceive a right line OI to be drawn perpendicu-
lar to the invariable plane (the plane passing through O and
the direction of the primitive impulse). If O be the centre
of an ellipsoid whose semiaxes are in the directions of the
principal axes belonging to that point, and of such lengths
that the square of each semiaxisis equal to the corresponding
moment of inertia divided by the mass of the body, the motion
will take place in such a way that the point I, in which the
right line OI intersects the surface of the ellipsoid, will be
fixed in space; and therefore OI will describe within the
body a cone of the second order, condirective with the ellip-
soid (that is, having its circular sections parallel to those of
the ellipsoid), while the point I describes on the surface of the
ellipsoid a certain spherical conic. In a former number of the
Proceedings (vol. ii. p. 542), the author had alluded to a theo-
rem for determining the time at which the point I occupies
any given position on the spherical conic, and he now gave a
particular statement of it as follows :

Conceiving a plane of circular section of the ellipsoid to
be drawn through its mean axis, and the spherical conic to be
projected on this plane, first by right lines parallel to the

371

greatest axis of the ellipsoid, and next by right lines parallel
to its least axis, each projection of the conic will be a circle
having its centre at O. The two projections P and Q of the
same point I will always be ina right line perpendicular to the
mean axis; let this right line cut the mean axis in M. Then,
while the point I describes the spherical conic, the points P
and Q will move in their respective circles, in such a way,
that the velocity of P will vary as the ordinate MQ, and the
velocity of Q will vary as the ordinate MP.

From this theorem we immediately obtain the elliptic in-
tegral which represents the time. For, supposing the greater
circle to be that described by Q, and taking its radius for unity,
if we put c for the radius of the other circle, and denote by ¢
the complement of the angle which OP, in any position of
P, makes with the mean axis of the ellipsoid, we have
MQ= V1 — esin’4, and therefore

a= rs 5
VY 1 — c’sin’¢

where dt is the element of the time, and & is a constant quan-
tity. Hence, the time at which the point P attains any given
position in its circle, and therefore the time at which the point
I attains any given position in the spherical conic which it
describes, is determined by an elliptic function of the first kind,
the modulus and amplitude of which are exhibited geometri-
cally. The modulus c of the function is obviously the ratio
of the two moduli of the cone which the right line OI describes
within the body; for the radius of each circle is found by
dividing the distance OI by one of the moduli of the cone.

The preceding method of determining the time in the pro-
blem of rotation occurred to the author in the year 1831, and
has since been given at his lectures in Trinity College.

It may be observed, that the motion of the axis of rotation
within the body is known when that of the right line OI is
known; for that axis is always perpendicular to the plane
which touches the ellipsoid in the point I.

372

Mr. Donovan read the first part of a paper ‘* on the sup-
posed identity of the agent in the phenomena of ordinary elec-
tricity, voltaic electricity, electro-magnetism, magneto-elec-
tricity, and thermo-electricity.” This part was introductory
to the subject of the remaining portions, which will be de-
voted to an attempt to prove that the hypothesis at present
accredited by philosophers, as adequate to explain the pheno-
mena of the electric fluid, under its various aspects, does not
accord with well-observed facts.

Its object was to render it probable that what is called
the electric fluid, is not a simple element, as it is generally
believed to be, but that it consists of several constituent ele-
ments, each exercising a separate function; and many facts
were referred to in support of the opinion. Reasons were
assigned for believing that this hypothesis is more consonant
with the general analogy of nature, than the supposition that
electricity is a homogeneous fluid. References were also given
to the opinions of those who coincide in this view.

After a full consideration of the facts and arguments, Mr.
Donovan summed up as his conclusion, that the electric fluid,
in the comprehensive sense of the word, including frictional,
voltaic, electro-magnetic, magneto-electric, and thermo-elec-
tric, does not consist of one homogeneous element, but of
several, viz., heat, light, magnetism, electricity proper, che-
mical attraction, the physiological agent, and the deflecting
agent: that the difference between the various exhibitions of
it just mentioned depends on the proportions or energy of the
constituent elements, or the influence of the modifications
which, under different circumstances, they are capable of ex-
erting on each other. This influence is probably of the same
character as that which the forces of nature exercise on each
other, on the great scale of creation, controlling, antagonizing,
and modifying each other’s effects, thus producing the diver-
sified phenomena of the universe, but rarely acting indepen-
dently.

373

Considerations were then adduced, with a view of render-
ing it probable that the electric fluid is matter in some extra-
ordinary state of constitution. Ifit be matter, its constituents
are probably endowed with chemical attraction, a property of
which no known kind of matter is destitute: a kind of chemi-
cal combination of all the constituent elements would be the
result. The affinity of the elements would keep them toge-
ther, and this would explain the ready passage of all the con-
stituents through conductors; one constituent, namely the
‘electricity proper,” conveying the other constituents, some
of which may not possess the same ready conductibility.
Thus the electric fluid, either in its state of frictional, voltaic,
or any other electricity, ought to pass with its known facility
through the same bodies, and be intercepted by the same
bodies, and so we find it.

In assuming that chemical affinity is thus transported to a
distance, Mr. Donovan stated, that there is no innovation on
opinions at present entertained by philosophers; and he re-
ferred to statements by Sir H. Davy, Faraday, Berzelius, Am-
pere, Schoénbein, and others, in support of that statement.
That a distinct constituent element, possessing chemical
powers, should exist in the compound called the electric
fluid, associated with heat, prismatic rays, and magnetism, is
neither less intelligible nor more improbable than that the
very same elements should be found associated in the sun’s
rays. With regard to the existence of magnetism in the sun’s
rays, the author conceived that such a number of witnesses
as Morichini, Carpi, Rodolfi, Davy, Playfair, Somerville,
Baumgartner, and the Messrs. Knox, could not all have been
deceived.

Admitting the agents in common and voltaic electricity to
be compounds of certain constituent elements, the same in
number and nature, but very different in proportions, or per-
haps differently combined, they may be considered as fluids
perfectly different; in the same way as chemists pronounce

374

bodies composed of common matter to be different, when the
constituents are similarly circumstanced.

The paper (first part) thus concluded : ‘* Aware that the
identity of the agent, in all the phenomena called electric, is
firmly established in the minds of the scientific, and that ex-
periments of apparently so convincing a nature have been
brought to bear upon the subject, that doubts seem to be no
longer entertained, I scarcely know how to declare, in terms
that shall protect me from the imputation of presumption, that
I have never been able to view the matter in the same light.
I have long hesitated to repeat, in advanced life, an opinion
which, in my early days, I ventured to promulgate within the
walls of this house, namely, that the agents in electricity and
galvanism are different, and that the laws of one do not ex-
plain the phenomena of the other. Believing, however, that
useful results have often sprung from humble causes; that
moral cowardice is as little to be esteemed as moral rash-
ness; that the influence of public opinion ought to have its
limits in promoting and restraining human actions; I deter-
mined to bring my reasons for dissenting from the views of
the philosophical world before a tribunal so competent to
judge of their pretensions.”

The Rev. J. H. Todd, D. D., gave an account of a frag-
ment ofan ancient purple manuscript of the Gospels, in Latin,
which he supposes to have been written in the fourth, or early
in the fifth century, and which he had purchased some years
ago in Dublin.

The fragment is but a single leaf, containing a portion of
the Gospel according to St. Matthew. It is written in double
columns. Each column begins with a large capital letter,
although in the middle of a sentence, or even (as in the case of
the third and fourth columns) in the middle of a word. Capital
letters are also used at the beginning of sections, which, how-
ever, do not always coincide with the ancient Ammonian sec-
tions, or kepaAaa, employed in the Eusebian canons; nor are

ay a eee

a ae ee

ee ti

375

any traces of the Eusebian numbers to be found in this manu-
script. Dr. Todd, having exhibited the manuscript to the
Academy, proceeded to adduce some of the proofs of its great
antiquity. ‘These were derived,

1. From the character in which it is written, and the form
of the letters, which agrees exactly with those manuscripts
that are known to be of the fourth or beginning of the fifth
century as, for example, the Codex Vercellensis and the
Codex Veronensis, as also from the absence of all stops, divi-
sions of the words, or ortyou.

The following wood-cut is an accurate representation of
the first five lines of the first column:

2. From its text, which is the ancient Italic version prior
to St. Jerome’s revision. This will appear from the following
“Table, in which the first column exhibits the text of Dr.
Todd’s fragment, divided exactly as in the original; the re-
maining columns exhibit the text, divided in a corresponding
manner, of the Codex Vercellensis, the Codex Veronensis, and
the modern Vulgate.

376

uNIeIpne 104
-IABIS SHQIING
ga ‘snfny tndod
100 WINS 489
TIN} BssV1OUT,
“SI}IQOpIA WOU
4@ STIZIQOPTA Soy
-UdpIA 49 ‘sTJOS
-I]J9}UI WOM 49
SIL gh

sty
-U99IP BIVsy vTy
-eydoad sto ut my
-ojdumpe 471

“yunsttjeyur enb
-oU JUNIpne
UoU soqyusIpne 49

“VNUFIGOH VLVITO A

JU.IOIpNe 104
-IARIS sIns snqiime
yo snf{ny tpndod
100 wWIIUe 489
TWN} VssvISUyT
styiqepmn wou

42 SIJIqepmM soy
-uepin 4a styos
-9][0}UT MoT 49
SIJOIPNV or

-ne omy opndod
oIp 38 open sty
-usorp ovyoydoard
OULIOS SII] Ur
oun} VT
INJURYIOA

-u00 opuenb ott
quevsoaT[oyUT Wom
yo yueIpne
soyUoTpne 49

‘NOUTA XAAOO

sorne
snf{ny tpndod
100

esse1ouy

stjo5

-9]]0}UI WoT 4a
STJOIPNV 1

-ne ony oyndod
DIP OpvA sTy
-W90IP OBIASe BI}
-aydord 1my

-oy duit oun} 44h

quvIpne wou
SoJUIPNV 4d

“ITHOUT A XAOS

LINAUSICAVUaL
INVUDSNGIUAV
LaSnInHitaAdod
UOOWINALSA
WOLVSSV YONI
SILISUCINNON
LasiLiggainsaL
NAGINLASILID
TITALNINONLA
SILGIGAVALIA
NVOINHOTONAOd
OIGLAIGVASAL
NOOIGAVIGSAVIL
IAOUdMSTIANIUVAL
Ida TAAUONALLT
GSLNVLUGA
NOOOGNVNDEN
LINVSATTALNIGN
INVIGQVNON
SHINGICAVL

377

-10A 4yrpne mb sta

-WQ ‘styUeUTUL

as wBpoqvied

aIPNV 08.19 SOA.

‘JUNIETpuY Ou

yo syipne enb

aITpne 4a

“UNIOpIA WOU 49 Sty

-opia enb a.zop

-TA qunasordno

ysnfl yo ayoyd

-ord 1yynUt

emnb stqoa oorp

oddinb uaury ‘yuntpne emb
#1j89A some yo “Wuoapra vimnb
TTN00 Tyvaq

WO}NB 1.1489 A

‘soo WlouRs 19
INjJUB{IOATON 49 4URS

-I][9JUTopr0o yo “QueIpnesnqrine yo

‘sI[00 yuvepra opuenbeu
“{UNIOSNB]O SO
-ns so[noo 4a

“VNUAIGOH VLVOTO A

-10A yrpne mb sia

-W1O ST}UBUTUT

-9s umvjoqvaed

aJTPNVB O81 SOA

qunserpne wou

42 Sttpne soa oenb

dIIpNe 4o

qUNIOPIA WOU 4a ST}

-SIpta oenb o1op

-TA yunzetdno

ysnf yo ovyoyd

-oid 1yynUT

ponb stqoa oorp

uouy “jyuntpne oenb

sone yo yuepta mb

T]N90 1yeaq

ToyNe 11489 A.

SNUTULO(] JLOTp soy{I WoURs 4a
InjuejIeAuo. opuenb ou vavis wan.109
SoTN00 49 onI4sqo wUN.A09 saine yo sn{ny
tTndod 109 wus 4s0 wNyessvroUT

soo mous 49 In4

-1UBq.10A TOO

42 JUBSOT[O}UT OpIOo 4o “yueIpNe snqrane 4d
gUBEPIA st[n00 opuenb ou
JUN.IOGVABIS SO

-ns soynoo 4a

‘NOUTA XAACOD

-19A Jipne nb sia
-M0 sty ueUTUL

-08 Wivpoqvaed
d}IPNB OS. SOA
qunJEIpne tou

4a styrpne ovnb
apne 49

qUN.AOIpNe WOU 4 ST}
-opra avnb asop

-1A gunserdno

tysnf yo ovyoyd

-ord yynUT

ponb stqoa oorp
uomy 4yuntpne oenb
soine yo yueprA mb
T[no0o Tyeaq

W9yNv 114s9A.

s09 MOUS 40 In}

-UejIeAu0d Opuenb ou
VABIC TUNE
-09 soTNoo 40

"TIHOULA XACOC

AANA LIGOVINDSIN
WOSILLNVNIKA
USsVTIOUVUVd
GLIGAVNALAVS oA
INNUGIGAVNON
LASILIGAVAVND

TUICAVLASLL
aqainavadauaa
ININONaIaNO
ILSAILAAY Lad
OUdLL TAWWVIN
ondsIson001a
NONWVLNGGIAIND
INLSHAITONOLA
SauAVaVLVaS
watavavaiss |

SOANANVSLYGS

INVLUGnNOoaN
VOVUONINOAYD
OusOTAIOL

378

-rad 49 auoT}eTKq

-I1} WO} Ne By{ORT
:sTperodue, 4s

pes ‘uteo

-Iped 08 UT WeyNne yoqey
tou $pnqyt yid

-1008 OIpnes

WMd ONnUT}UO0D 49

qIpne wangsea mb

4so OI “4So snyvu

-1UI08 880.14

-od redns

WojNe N~) “4se snyvuTues
WBIA snoes nb 4so o1y
tsnfo op.zoo ut

480 UN, vUTUeS

ponb qidea 4a

SN[VUL JIUDA ‘419

-I[[2}UI wou 4a

Tus wang

“VNUGIGOH VIVOTN A

7

-aod aA auoTyeyNq

-11} WIOyNB BLOB
‘stperodue} 480

pes m9

-Iptd 08 UL yoqey

tou pes ‘pnqit ytd
-1008 oIpnes

tnd onuUT}UOD 40
qipne ungszea mb

489 OIY 4so snyeu
-IULOS BOOT BSOTY

-od vidns

woejne mb 4so snyvurues
weIA snoes mb 4so ory
*SNI][I OpL09 UL

qso UINZeUTULES

ponb y1dea 40

SNIVUI JIUOA 41d
-9]]2}UI Uou 49

Tuser ung

‘NOUPA XAGOD

-ded JOA ouoTyeTNG

-11} Wen vpOBT
“styeroduiay 489

g ' -pes u180
-Iptl 98 UL JoqeyT

uou pos ‘tanyyr 41d

-1008 OIpnes

wd ONUT}U0d 49

4ipne wmqies mb

480 O1Y 4So sngvu

-TU1OS BI}

-od vadns

qwoyne mb 4s9 snyeurutes
WRIA snoes mb 4so ory
{SNI][I opLo0o UL

4so WUN}eUTUES

ponb 41dex 4a

sn[Bu IUeA 41d

-9][9}UI wou 49

Tuser Ung

“IIHOUT A XIAOD

utadLAVVILSAD
NyWwaLavvLovH
SYIVUOdNALLsa
GasasNINGdO
IGVUSNAAVH
NONLAWATINLId
1osasolanava
WNOLaWad
UGA LIGAVIND
LSHOINSALVN
INUSNVSOUL
TaAWILAVuad
ASSALVNIWGAS
nvinvixarisaor
SQITACUOONI
LSAWOLVNINGS
doadLidvuLge
SO TYNLINGALID
aTIGLNINONLE
inpwuwaG]

379

qlovy JO “y1oTye
wangonigy 4o “419
-T][9}UL 49 WONG
-I0A yIpne mb

‘480 OI, “Qso snyeu
118s WIBUO0g
WICIL0} UL OL0A TY)
“In{IOyyo

nyondy ours 40
‘TUNGIOA 4BO0F

-Jus “WUMIBIYLATp
BIOV][RT 40

‘Sniyst T[Moes opnyTo
GRINS ee eats
wnq.10a mb 489 ory
studs ur 40 snyvu
-TuOs THE4NB IN?)
“IMYUBZT[Bp

-uvos ONUT}U0D
wnq10a 104dord
auOTjNdesS

“VNUAIGOH VLIVOTO A

4ovy 4a Joraype
uInyondf ouNy 419
-9] [07 Ur Yo UNG
-I0A yIpne mb

489 O1y 4so snyeu
-Tuas TARO,
WII0} UI 010A Tm)
“IM LOWyo

nyonsy ours 40
WING.19A 4 BOOT

-JNs WINIVTyLATp
soyeydnjoa yo
snfny Ipnooes tmourpnyto
-T]jos red yo y1pne
wmnqi0a mb 4s ory
480 SNYBUTUIOS STU
-ids ur woyne me
InpuURzIpep

-UBOS ONUITIOD
twunq.t0a 103dord
auoTJNoes

‘NOULA XTaD

FORT 49 Joroype
wnjon.sy. ouny 418
-oT]yUI 49 TaN
-10A yrpne mb

489 OL] 489 snyvu
-Tules wietOd
WVIIO} UT 010A Thy
4

snsonjonszjur 49
WINC.10A 7B00F

-jJus WHEY MIP
$o]BJUNTOA 40
T[Moovs ourpnyto
SEG Re eh pINe
winqioa tb 4s ory
INpeuLmMes STU
-1ds Ur Woyne me
Inyeztpep

-Weds ONUT}U0O
wunqsoa 103dord
ouoT}Noes

“TTHOUA A XAAOD

LIOVAONOLLID
TTIAINILAW AS
ULALIGAVIAD
*LSMOIHLSASALVN
INASINDVNOS

WALAVNVAUAEN |
OL
OMULAINISLIAL
WATUAOLVOOT
TOSsVINOTON
WAUVILIAIGLS
TINOAVSOaALIO
TITOSLEWAGIAN.
LIGAVIND LSaOIn
UO.LVNIVASSIN
IdSNINDLOVIO
UALVZLIVG
NVOSOMNIZNOO
WATUAAUTLAOU

WANOILADAS

Lo

N

VOL. III.

380

The Codex Vercellensis is shown by Blanchini, and gene-
rally believed, to be the autograph of Eusebius, first bishop
of Vercelli, in the diocese of Milan, who died in the year 371.
Having been banished from his see by the Arians, he em-
ployed his retirement, at the suggestion of Pope Julius, in
the revision of the Latin versions then in use, which were, for
the most part, full of errors, interpolations, and solecisms ;
and his recension became afterwards very generally received
throughout the West, having been adopted by St. Hilary of
Poictiers as the text from which he quotes in all his writings.

The Codex Veronensis is a purple manuscript, written
in letters of gold and silver, and is assigned by Blanchini to
the beginning of the fifth century: its text is generally con-
sidered to belong to the Eusebian recension, but it has mani-
festly been corrected by the Greek text of Hesychius, and is
no where indebted to Jerome’s revision.

An examination of the foregoing table, in which these two
very ancient specimens of the Vetus Itala, or old italic Latin
version, are compared with the fragment, will prove that Dr.
Todd’s fragment is also a manuscript of that version; and many
of its peculiarities are such as would naturally be expected in a
manuscript of the same age. It is curious that in all the three
manuscripts the word intelligo is uniformly spelt intellego,
showing that this variation from the usual spelling was not
the mistake of a copyist, but the spelling of the same period
and locality.

Again, it will be seen that the fragment sometimes agrees
with the Verona manuscript and differs from the Vercelli ma-
nuscript; sometimes agrees with the Vercelli manuscript and
differs from the Verona manuscript ; and, in some cases, even
where the two other manuscripts agree with the modern Vul-
gate, it differs from them all.

The conclusion, therefore, is inevitable, that this is a leaf
of a purple manuscript of the fourth or early part of the fifth
century, of the Eusebian revision,—one of those which were

—————

381

in use before the Hieronymian Vulgate, and from which Je-
rome made the recension now known as the Latin Vulgate.
It was probably written, like the Vercelli manuscript, in gold
or silver letters, but the metallic surface, if what are called
gold and silver letters in this class of manuscripts be metallic,
has long since been rubbed away, and nothing now remains
but the traces of the original ink with which the letters were
described before the golden substance was applied to them. Of
this, however, we have no certain proof.

It will be observed that this fragment is full of solecisms,
mistakes of the scribe, and misspellings, a circumstance very
common in the more magnificent manuscripts of the class to
which Dr. Todd supposes it to belong; for the artists who
excelled in penmanship and decorative skill were often very
incompetent as biblical scholars ; and the very costliness of
the material, and elegance of the writing, were obstacles to
correctness, for the scribe preferred leaving a mistake to spoil-
ing the beauty of his penmanship by attempting to correct it
Thus we find dicentes for dicentis; parabolas for parabolam ;
éllum for illud; persecutionem for persecutione ; bona for
bonam.

DONATIONS.

Antiquities from Dunshaughlin, viz.: A fragment of an
Iron Chain, consisting of twenty-seven double-looped links,
one Ring, and part of a Staple. A large Steel Knife or
Dagger. A Draughtsman made of Bone, mounted with
Bronze Pin. A Bronze Spear-head with double Blade, and
two lateral loops. Three Boar Tusks. The Bone of @
Cock’s foot.

A Stone Celt, from the county Antrim.

A similar Stone Celt, found near the Falls of Niagara.

A Steel Spear and Ferule, from the Gambia.

A similar Spear, but larger, with small Trowel for Foot
of Shaft, used by the Mandingees, from the Gambia.

382

A Steel Spear and Ferule, from the Gold Coast.

A pair of Slave Shackles from the Gold Coast, supposed
to be of African manufacture.

Two Scarabei ; three small Mummy Figures ; one large
Mummy Figure ; two Copper Coins, with Arabic Inscrip-
tions ; from Egypt.

Three African Idols in Brass or Bronze, viz.

1. Sitting Figure, from Bight of Benin.
2. Ornamented Head, with Spirals, from Gold Coast.
3. Ichneumon, from Mandingo Country.

Ingot of Bronze.

All the foregoing antiquities were presented by Dr.
Madden.

Miscellany of the Irish Archeological Society. Vol. I.
Presented by the Society. :

Ancient Iron Hatchet found in the Bed of the River
Boyne. Presented by Charles Cheyne, Esq.

Legal Education. By Henry Holmes Joy, Esq.,.M.R.1.A.
Presented by the Author.

Medicines, their Uses, and Mode of Administration. By
J. Moore Neligan, M.D., M.R.I. A. Presented by the
Author.

Memoir of the Family of French. By John D’ Alton,
Esq., Barrister, M. R.1I.A. Presented by the Author.

A Copy of a Document preserved in the Chapter House,
Westminster, with impressions of the Seals attached to it.
Presented by Sir William Betham.

Errata.—Page 353, lines 7 and 19, for “ Alcinoe” read “ Alcyone.”

PROCEEDINGS

or

THE ROYAL IRISH ACADEMY.

1846_7. No. 61.

February 8th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The Rev. Henry Tibbs and John O’ Donovan, Esq., were
elected members of the Academy.

A paper by the Rev. M. Roberts, on the lines of curva-
ture on the surface of the Ellipsoid, was read by Mr. Ingram.
The analogy between the lines of curvature on an ellip-
soid, and a system of homofocal plane or spherical conics,
was first remarked by Mr. M. Roberts, in a note communi-
eated by M. Liouville to the French Academy of Sciences,
where he has shewn, among other things, that the sum (or
difference) of the geodetic distances from the umbilics to any
point of the same line of curvature is constant. The follow-
ing properties, which he has recently obtained by assigning
a significant geometrical meaning to the constant introduced
by M. Jacobi in the integral of the differential equation of
the geodetic line, appear worthy of the attention of geometers:
1. Assuming the distance between the umbilics (interior)
as the base of a system of triangles, whose sides are geodetic
VOL. III. 2K

384

lines, and of which the product of the tangents of the semi-
angles at the base is constant, the locus of the vertex will be a
line of curvature.

2. And if the ratio of the tangents of the aforesaid angles
be constant, the locus of the vertex will be a line of curvature
of the orthogonal system.

3. As the arc s of a plane curve is expressed in polar co-
ordinates by the equation

ds? = dp” + p dw’,
and the arc of a spherical curve by the equation

ds? = dp? + sin’pdw’,
so let the are of a curve on the surface of an ellipsoid, referred
to the geodetic distance (p) from one of the umbilics, and the
angle (w) made by p with the section containing the umbilics,
be given by the equation

ds? = dp” + P*dw’,
and, as Mr. Roberts has demonstrated,
Psinw

will be the perpendicular distance of the point (p, w) from the
plane of the umbilics. Hence, P’, w’ denoting the same things
“for the contiguous umbilic, we have

= /
eee VS Ae P _ sinw
w = P’sinw’, or = =

P

sinw’

which may be regarded as an extension, to the surface of an
ellipsoid, of the fundamental property of plane and spherical
triangles, that the sides (or the sines of the sides) are propor-
tional to the sines of the opposite angles.

4. Let w be a right angle, and the corresponding geodetic
vector will pass through the vertex of the mean axis, and its
length comprised between this point and the origin (the um-
bilie) will be equal to the quadrant of the elliptic section con-
taining the umbilics. The function p of this are will be equal
to the mean semiaxis of the surface, in the same way as the
sine of the quadrant is the radius.

385

5. Let geodetic lines issuing from the same point upon a
line of curvature, and passing through the umbilics 0, 0’, meet
the line of curvature again in the points Pp, p’.. Then will the
locus of the point of concourse of the geodetic lines op’, o’P,
be a line of curvature of the same species as the given one.

The following note, by Mr. M. Roberts, on a theorem
relating to the Hyperbola, was also read :

Let s denote the difference between the infinite are and
the asymptote of the hyperbola, whose equation is

9
ited 2

Y é
@ p's
and let s’ be the length of the quadrant of the curve which is
the locus of the feet of perpendiculars dropped from the centre
upon its tangents; also, let =, =’ denote the same things in
reference to the conjugate hyperbola

2
—— LE ==(b,
b? a
and we shall have

a aay
ss’ + 33/= inf a bs}

where we suppose a >, and denote by s an arc of the first
hyperbola, measured from the vertex to the point whose coor-
dinates (2’, y’) are

w= SX, yf = a &.
If a = b the hyperbola is equilateral ; the derived curve is the
common lemniscate, s = 3, s‘= »’; and

ss’ = ira’,

a theorem proposed by Mr. W. H. Talbot, and proved by M.
Sturm, in vol. xiv. of Gergonne’s Annales de Mathematiques,
page 17.

Professor Harrison read the following paper on the ana-
tomy of the elephant :
** Having had, within the last few weeks, an opportunity of
examining the body of an elephant which died in this city,
2K 2

386

I have dissected different portions of it with some care, and
shall lay before the Academy, at the present Meeting, a sec-
tion of the recent skull, also the brain, and a minute dissec-
tion of the nerves of the proboscis on one side. As my time
has been limited, and much engaged with other matters, I
shall not enter into a minute examination of these parts, but
merely exhibit such striking characters and peculiarities as
are likely to engage the attention of those who are not fully
acquainted with the subject. I may observe that, in the
course of my dissections, I have ascertained some points which
I do not find noticed by preceding writers, and others which
have been stated differently from what I have found. ‘Thus,
among the ocular appendages, the membrana nictitans, or third
eye-lid, presents some interesting relations ; in the orbit I do
not find any retrahens oculi muscle, as is to be inferred from the
descriptions in books; I also observe a second external rectus
muscle. In the ear also I find a peculiar arrangement of the
muscles of the ossicula auditus ; and I see no evidence of the
muscular structure of the membrana tympani, so accurately
described by Sir E. Home in the Philosophical Transactions,
and mentioned by subsequent writers, who seem to have
adopted his opinions, rather than to have examined the organ
for themselves. In the thorax I have remarked the absence
of the pleural or serous membranes; and I find the lungs are
connected to the parietes by a great quantity of filamentous
and yellow tissue, yielding and elastic. I have also discovered
aremarkable muscle extending from the back part of the
trachea to the cesophagus, near its passage through the dia-
phragm, of which I can find no previous notice. The rudi-
mentary condition of the gall bladder in the abdomen, as well
as the mucous membrane of the small intestines, and. the re-
productive male organs, present certain peculiarities, which do
not appear to me to have received sufficient attention. I shall
not allude further to any of these points at present, but as time
permits me to complete their examination, and to prepare
suitable illustrations, I hope to place some additional remarks

—

387

before the Academy, which may tend to enlarge our knowledge
of the anatomy of this very interesting animal.

‘* One of the earliest dissections of the elephant on record
is that which was made in Dublin, in 1682, by A. Moulin, a
medical graduate of Trinity College. This animal was destroyed
by a fire which accidentally occurred in the city. In the
volumes of the Philosophical Transactions several papers have
been published on the anatomy of particular parts of this animal.
Camper’s description and plates have added much to our know-
ledge; but the most complete and concise description is to be
found in the Encyclop. Method. vol. ili. p. 173. In Cuvier’s
system of comparative anatomy several of its peculiarities are
noticed ; and in his splendid work, Ossemens Fossiles, tom. i.
p- 12, its osteology has been minutely and carefully described.

“The subject of this examination was an Indian or Asiatic
elephant, one of the family of the Pachydermata, which may
be regarded as a distinct genus, under the name of probosci-
dean, as no other animal possesses the true and perfect pro-
boscis or trunk. Of this genus there are only two living
species, the Asiatic and the African, which are distinguished
by certain well-marked differences: the head of the Asiatic is
large and oblong, the forehead concave, the external ears
small, and the molar teeth present undulating transverse
ridges of enamel, which are the separations of the lamine
which compose them, worn down by trituration; the head of
the African is round and smaller, the forehead convex, and the
ears very large, and the molar teeth are marked with lozenge-
shaped ridges of enamel.

‘¢ The present animal was not full grown; he was supposed
to be nine or ten years of age, was about six feet high, and
‘six and a half from the top of the head to the root of the tail ;
he had latterly increased considerably in height and size, had
always enjoyed perfect health until within a few days of his
death, which was the result of an acute fever. No organic
disease could be detected in any part of his system.

‘* The large expanse of forehead, the peculiar expression of

388

countenance of the elephant, together with his well-known
docility, lead to the presumption that this animal must possess
a brain of considerable magnitude. Although this is really
the case in a remarkable degree, yet the external skull is by
no means a measure of the organ within. I now place before
you a horizontal section of the cranium of this animal ; and it
exhibits two remarkable facts, first, the small space occupied
by the brain, and secondly, the beautiful and curious structure
of the bones of the head. To the latter we may first direct our
attention. ‘The two tables of all these bones, except the oc-
cipital, are separated by rows of large cells, some from four
to five inches in size, others very small, irregular, and honey-
comb-like; these all communicate with each other, and through
the frontal sinuses with the cavity of the nose, also with the
tympanum or drum of each ear; consequently, as in some
birds, they are filled with air, and thus, while the skull attains
a great size, in order to afford an extensive surface for the
attachment of muscles, and a mechanical support for the tusks
or the enormous incisor teeth, it is at the same time very
light and buoyant in. proportion to its bulk ; a property the
more valuable, as the animal is fond of the water, and fre-
quently takes to it, and swims and bathes in deep rivers. All
these cells are lined by a delicate mucous membrane of a light
rose colour, being slightly vascular, like that in the frontal
sinuses, of which cavities these cells may be considered as an
extension, rather than as analogous to the diploe in other ani-
mals. The septa between the cells are vertical, and pass from
the euter table to the inner; they are very hard and vitreous,
whereas the outer table is of a coarse and porous texture.
These septa strengthen the whole fabric, the outer table abut-
ting against them ; some rows are separated from others by
horizontal shelves. This structure also extends into some of
the bones of the face, and into those at the base of the cra-
nium, the pterygoid processes, and the condyles of the occipi-
tal; but all the superior part of the last-named bone is devoid
of them, the two tables being close and thin, and the bone

389

diaphanous. A deep depression exists in this region, at the
bottom of which is a slightly prominent crest, and on either
side a very rugged surface for the attachment of the ligamen-
tum nuchez, which substance I now also place before you; it is
a yellow, elastic tissue of immense strength, attached by thick
roots to the spinous processes of the vertebra ; ascending
thence it divides into two thick vertical and diverging plates,
which are inserted into the rough surfaces of the occipital bone
already alluded to, and it is worthy of remark, that each fasci-
culus or lamina of these plates of yellow tissue first ends
obliquely in a round tendinous cord, and it is through the me-
dium of an infinite number of these tendons the attachment to
the skull takes place. This peculiar structure is well seen in
the preparation on the table; its design, most probably, is to
effect a more intimate union with the bone than the elastic
tissue could obtain. The internal table of the cranium is
thin, but very hard and vitreous, and the base is rough and
irregular ; the cribriform plate is very broad and deeply
depressed, with numerous foramina for the passage of the
olfactory nerves, which are also numerous and large; the
foramen for the nasal branch of the opthalmic is also very
large; the optic holes are small ; there is little or no sella
Turcica, and there is no distinct pituitary body attached to
the brain; some vascular and fibro-cellular tissue corresponds
to its situation: the foramen rotundum is very large, to trans-
mit the superior maxillary nerve, which is of prodigious size.

«<T next place before you the cast of the encephalon, and two
drawings, one of its upper, the other of its under surface, both
of the full size ; also portions of the organ hardened in spirits.
The brain, though very large, forms a diminutive contrast to
the immense cranium. On examining the three divisions of
the encephalon, I found the anterior lobes of the cerebrum
to be but of moderate size, narrow anteriorly, and arched a little
downwards ; beneath each is the olfactory lobe, of considerable
size; its rounded oval ganglion was so depressed into the
ethmoidal recesses, that it was necessary to cut through each

390

of them in removing the brain; each of these lobules or gan-
glions contained a large ventricle with smooth surface, and
communicating with the lateral ventricle. ‘The middle lobes of
the cerebrum are very large and of great transverse breadth,
like those of the cetacea, as may be seen by comparing them
with the brain of the porpoise upon the table: there are no
posterior lobes. The cerebellum is of considerable extent,
both transversely and vertically, and abuts against the posterior
inferior margin of the cerebrum; the mesocephale or cerebral
protuberance is very large and broad, and the crura cerebri
on leaving it are of great thickness ; the medulla oblongata is
highly developed, and not only the anterior pyramids, but
also the olives, are of great size; the tubercula quadrigemina
and pineal body are small, not much larger than the human;
the optic nerves also are small, and the fourth pair are about
the same size as in man; the fifth nerves are of prodigious
size; the seventh also are rather large. The weight of the
encephalon was eleven pounds ten ounces, but, allowing for
the loss of some portions of the surface injured in the removal,
also for the olfactory lobes, and the empty state of the vessels,
it may be fairly stated as twelve pounds, Troy weight. On
weighing each part separately, the cerebrum was seven pounds
and a half, the cerebellum was four pounds, and the mesoce-
phale and medulla oblongata half a pound.

‘Thus the brain of this young elephant weighs twelve
pounds, while that of the full-grown horse does not exceed
two pounds, and that of man seldom equals four pounds.
From an examination of the brains of 150 men, the average
weight of this organ was found to be about three pounds eight
ounces, but exceptions occasionally occur, thus the brains of
Cuvier and Dupuytren are recorded as nearly five pounds
Troy weight. From an examination of ninety females, the
average weight of the brain was three pounds four ounces,
that is, about four ounces lighter than that of man. The
brain of the idiot is seldom more than one pound and a half.
These are the general results of the observations of Tiede-

391

mann, * and of the extended series of inquiries of Sir W. Hamil-
ton} of Edinburgh, Mr. Sims,t and Dr. Reid.§ In considering
the brain, however, in relation to the nervous function, many
other circumstances are to be attended to beside the actual size
or weight of the organ, namely, its weight compared with that
of the body, the relative proportion of one part of the organ to
another, as the cerebellum to the cerebrum, the relative size
of the brain to that of the nerves connected to its base, and,
above all, the structure of the organ, the size, number, and
depth of the convolutions, and the extent and thickness of the
encrusting lamina of the vascular, or grey vesicular neurine,
which there are good reasons for believing to be the essential
dynamic agent in the function of innervation. The weight
of the human brain, compared to the weight of the whole
body, is as one to forty-five or fitty, supposing the former to
be about four pounds, and the latter to vary from 180 to 200
pounds; whereas, the proportion in the elephant will be as one
to 400 or 500, supposing the former to be twelve pounds, and
the weight of the body to be only from two to three tons.
The weight of the present specimen, which was by no means
full grown, was about two tons. ‘Therefore, the human body
is only forty-five to fifty times heavier than the brain, whereas
the elephant’s body is four or five hundred times as heavy as
its brain: then again the human cerebellum is much smaller
than the cerebrum, being in the proportion of one to eight or
nine, but in the elephant, the proportion is as one to two:
therefore, the human cerebrum is eight or nine times larger
than the cerebellum, whereas the cerebrum of the elephant is
only twice as large as his cerebellum. These relative propor-
tions are interesting and important, if, as we believe to be the
‘ease, the cerebellum be connected with the functions of the
general muscular system, and the cerebrum with the manifes-
tations of the mental principle. It must be admitted, however,

“Phil. Trans. 1836. + Munroe’s Anat. of Brain, 1831, p. 4.
t Med. Chir. Trans. vol. xix. p. 359.

§ Lond. and Edinb. Monthly Journal of Med. Sci., April, 1843.

392

that conclusions drawn from the relative weight of the brain
and of the body are open to many objections ; as the weight
of the latter must be influenced by the previous state of health,
of fulness or of emaciation; the weight of the brain too must
be materially affected by the amount of fluid it contains, or
which may have escaped during the operations of removal and
of weighing. Attention to the relative structure of the brain,
therefore, is also necessary. The convolutions of the elephant’s
cerebrum are very numerous, but rather small, and but few of
the sulci are deep; the fissure of Sylvius is closed, and there-
fore that numerous group of convolutions forming the ‘‘island
of Reil” are absent; the grey neurine is not so thick as in
man: on the whole, the cerebrum bears more analogy to that
of the porpoise than to that of man, in whom the convolu-
tions are large and numerous, the sulci deep, and many of
them involuted over and over again. In man, too, the fissure
of Sylvius is very deep, and when opened out presents a pro-
digious number of convolutions ; his posterior cerebral lobes
are extensive, and overlap the cerebellum; the grey neurine
forms a thick investing lamina, the superficial extent of which
is increased to a wonderful extent, and to a degree superior to
what it is in any other animal.

‘<I shall next place before this meeting a dissection of the
proboscis or trunk of the elephant, the organ which forms
the striking and characteristic feature of this group of ani-
mals, no other possessing it in a perfect state, though in
many it is rudimentary, as in the tapir and in the pig. It
is essential to the existence of this animal, as the instrument
for taking its food, and hence its name (zpo, Bookw). Its
length varies from four to six feet, according to the height of
the animal ; it is of a conical form, the base is attached to the
nose, of which it may be regarded as a continuation, and is
about two feet in circumference ; the apex is from four to six
inches; the fore-part and sides are convex, and marked by
rugged, transverse folds, which admit of extension and change
of form; the posterior surface is flat and rough, and bounded

393

on each side by a row of rough tubercles : the whole is covered
by a coarse, hard skin; this being removed, the proper struc-
ture comes into view. ‘The proboscis consists of two long
tubes separated by a median septum ; these tubes open above
into the nose, and below at the extremity of the trunk; they
are somewhat contracted at each of their extremities ; they are
composed of a whitish membrane, not very vascular or sensi-
tive, covered by a dense elastic tissue, which preserves their
calibre ; inferiorly the skin is continuous with the lining mem-
brane. ‘The point of the proboscis is worthy of attention, a
thick lip surrounds it, with a groove below, and a thumb-like
projection above; this little conical appendix enjoys free mo-
tion, and can be brought into contact with every part of the
border. The skin being removed from the proboscis, the
muscular tissue which composes the principal portion of the
entire mass is exposed ; this is arranged, partly in superficial
strata, and partly in deeper seated, radiating, and decussating
fasciculi. The first layer consists of strong, red, longitudinal
fasciculi, which extend, from the frontal and nasal bones, the
entire length of the organ; some of the fasciculi are short,
and end between two others; some are intersected by tendi-
nous lines, which adhere to the integuments: on each side of
the trunk also are seen longitudinal muscles extending down-
wards from the superior maxillary bones and commissures of
the lips. As these fasciculi descend they spread out obliquely,
some forwards, others backwards, or to the under surface;
some intermingle with the other superficial muscles, others
are inserted into the tendinous interlacements of the deeper
muscles, and some into the skin; the posterior or flat surface
also is covered by muscular fibres, which take a decided oblique
-course, attached above to the intermaxillary bones in front of
the mouth ; they descend in different laminz, some obliquely
inwards, and join those of opposite sides, in a median tendi-
nous raphe, which extends the whole length of this flat surface
of the trunk ; this muscular lamina is not so red or longitudi-
nal as those on the front and sides; this lamina may also he

394

partially divided into two layers, the fibres of the deeper layer
passing obliquely downwards and outwards, and decussating
the former. All these investing muscles which you now see
exposed on one side, must have the effect of moving, bending,
and curling this organ in every direction ; the animal can thus
bend it upwards over his head, or downwards between his legs,
or on either side along his neck.

** Qn one side we haveraised these longitudinal muscles, and
in doing so we perceive some of the principal nerves descend-
ing in tendinous sheaths or canals. ‘To these nerves we shall
more particularly allude directly. These sheaths are con-
nected to the muscular fibres on either side, and resemble the
tendons of digastric muscles ; there are several laminee of these,
through and between which the principal nerves descend, and
are thereby protected ftom the pressure of the contracting
muscles, as, during the action of the latter, these canals will
be enlarged rather than diminished. Beneath all these long
muscles, but intimately united to them, we meet another por-
tion of muscular structure, which extends from the longitudi-
nal fibres, and from these tendinous canals obliquely inwards,
to be inserted into the parietes of the tubes. If we look at the
upper extremity of the proboscis, which has been cut off from
the skull, the course of these fleshy fibres is evident; they pre-
sent a radiated appearance, as they pass from the central tubes
outwards to be inserted, some into the longitudinal fibres,
others into the tendinous canals for the nerves just mentioned,
and others pass between the longitudinal fasciculi to the sub-
cutaneous aponeurosis. Some have attempted to count the
number of these muscles, but such an attempt is totally use-
less. These radiated fibres, by their contraction, can approxi-
mate the parietes of the tubes to the skin, and at the same
time compress the general structure of the trunk, and thus
tend to its general elongation, when the longitudinal fibres are
relaxed ; while by this arrangement, also, circular compres-
sion or constriction of the tubes is avoided, which must have
been the effect if the fibres pursued.a circular course. At the

ae

395

upper or cranial extremity, however, some strong fasciculi
take a semicircular course around its anterior and lateral sur-
faces, and are attached to the bones on either side ; and around
the lower end also are some oblique and partly annular fibres,
which are attached to the central appendix and to the border
on either side.

‘¢ T shall next allude to the nerves which are distributed to
the proboscis, and which extend its entire length: they are
four in number, that is, two on each side, and, like the muscles,
are symmetrically arranged ; these nerves are the facial, or
the portio dura of the seventh and the infra-orbital or supra-
maxillary division of the fifth cerebral nerves. These nerves
are remarkable for their size and length, and for the numerous
plexuses they form with one another. The portio dura, or the
seventh, is about the size of the little finger, and between the
point of its exit from the stylo-mastoid foramen in the base of
the skull, and its entrance into the proboscis, pursues a curved
course about two feet in length ; in this course it sends many
branches to the glands and muscles on the side of the face, and
then enters the upper and lateral part of the proboscis between
the anterior and lateral longitudinal muscular fasciculi, and is
joined in this situation by the superior maxillary nerve, the
second division of the fifth pair ; this great nerve, fully the
size of the middle finger, escapes from the infra-orbital fora-
men, gives off a few branches to the lower eye-lid and to the
integuments, and then descends into the same sulcus in the
proboscis with the seventh. The two nerves now unite, butthey
soon separate and divide, the divisions reuniting so as to forma
most intricate nervous plexus; and, as you may observe in the
dissection before you, these nerves pursue a similar arrange-
- ment during their long course down the trunk, until within a
few inches of the extremity. This chain of plexuses resembles
a thickly tangled skein of silk extending from one end to the
other. When the dissection is carried deeper, the same plexi-
form appearance is observed, the nerves running in the ten-
dinous sheaths, already described, in courses one beneath the

396

other. From the larger nerves innumerable fibrillze cross in
every direction to supply the surrounding muscular fasciculi.
Language can convey no adequate idea of the number and
plexiform arrangement of these proboscidean nerves; and,
although in this dissection many hundred are brought into
view, I have no doubt as many more could be displayed, if
sufficient time could be afforded to the tedious process of ex-
posing them. The plexiform arrangement of the seventh and
fifth nerves on the human face, though anatomically and phy-
siologically analogous to these, yet bears no comparison as to
size, number, or complexity. From the intimate union between
the seventh, which is the nerve of motion, and the fifth, the
nerve of sensation, the greater number of the branches derived
from these plexuses must be compound filaments, and, there-
fore, supply the parts to which they are distributed with the
two endowments, motion and sensation. In this dissection,
however, I have in several situations unravelled the nerves in
the plexus to their respective sources, and traced fine filaments
from the fifth or sentient nerve, inwards to the lining mem-
brane ; and have also pursued some very large branches of the
same nerve, undivided, down to within two or three inches of
the proboscis, where they separate into fine hair-like branches,
about twenty of which are exposed in one situation, all de-
scending in parallel lines to the very border of the opening,
where they branch off into minute filaments, and terminate in
the subcutaneous tissue.

‘*T shall not delay you with any minute account of the
blood-vessels of this organ, and shall only observe, that they are
very large and very numerous. Some of the principal trunks
accompany the nerves, but many others run in channels
through the muscular substance, and distribute their branches
to it in every direction.

** T shall next place before you a dissection of the cartilages
of the true nose, which are connected above to the nasal bones,
and below to the proboscis. These cartilages present a long,
curved tube, which is convex forwards, and divided into two

397

tubes by a median cartilaginous septum. The tubes of the pro-
boscis communicate with these, and so with the nares and
throat. The lateral cartilages are very elastic, and lie so close
to the septum as partially, but not completely, to close this
communication ; but between the lower border of each carti-
lage and the proboscis are some strong muscular fibres, which
- can compress the connecting membrane, and thereby perfectly
close the upper end of each proboscidean tube, and so prevent
the fluid which the animal draws into these from rising into
the nose and flowing through the nares into the throat.

‘< The lining membrane of these cartilaginous nasal tubes is
somewhat of the same nature as that which lines the nares,
which is thick, soft, and vascular, and very superior in organi-
zation to that which lines the proboscidean canals. In the lat-
ter there are no olfactory nerves, and no sense of smell; this
sense resides, as in other animals, in the true nose.

‘¢ From the anatomical examination of the complex struc-
ture of this very curious appendix, we can understand the
powers it displays, and the purposes it effects in the economy
of the animal to which it appertains. Its muscularity and
its pliancy render it, as a weapon of offence and defence, pow-
erful and effective. With it he can strike down an animal, or
can raise it into the air and dash it to the earth; or he can
bend it round its body or its neck, and crush it by- powerful
compression. It can tear down large branches of trees, and
raise and propel great weights; hence the great value of the
elephant in warfare, and in marshy countries, as a beast of
burden, for the transport of heavy guns and cumbrous bag-
gage. In such services his exertions are well-known, and have
often excited admiration and surprise; the more so, as the

-docility and intelligence of the animal enable him to direct his
physical strength with the degree of energy and skill exactly
suited to accomplish the desired object.

‘‘ For the prehension of food the proboscis is indispensable
to his existence; by its means he plucks off branches and
leaves, blossoms and fruits, and tears away the herbage, gathers

398

all into a mass, and, as with a hand, places it within his mouth.
With it he sucks up a large draught of fluid, closes the com-
munication with the nose, and then turns its spout-like extre-
mity into the mouth, the anterior part of the latter being so
shaped as accurately to receive the contents.

‘¢ As the prehensile organs for food in other animals possess
the sense of touch, whether they be lips or anterior extremi-
ties, so the tapering end of this organ enjoys exquisite sensi-
bility and delicate motor power. By its thumb-like appendix
he can pick up the smallest substance from the ground, hold
it, and turn it in every direction, to examine it with accuracy
before he commits it to his mouth. He can also execute
(especially in his captive state, when taught and encouraged
by kindness) a variety of delicate manipulations with astonish-
ing dexterity.

‘* This organ also enables him to remain in deep water, his
whole body immersed and concealed from view, except the
point of the proboscis, which appears just over the surface,
and through which respiration is conducted, occasionally draw-
ing in a little fluid, and then ejecting it with force, not unlike
the ‘jet d’eau” from the blow-hole on the head of the ceta-
cea. By it also, when on land, he can dash water, sand, and
mud all over his body, so as to cool and refresh the surface,
_and remove any source of irritation. Finally, by this instru-
ment he can modify his voice, and increase its tone, so as to
cause it to be heard at a distance of one or two miles, and,
according to some, still more.. Through it he can send forth
trumpet sounds, loud, harsh, and discordant, but varying ac-
cording as they are indicative of social or sexual feeling, or of
terror, anger, or satisfaction.”’*

* Since the above went to press I have found, in the library of Trinity Col-
lege, A. Moulin’s pamphlet on the dissection of an elephant, published in the
form of a letter to Sir William Petty, Lond. 1682. He has correctly noticed
the absence of pleurz or pulmonary serous membranes. The brain, in his
specimen, which was older and larger than mine, weighed ten pounds (I pre-
sume avoirdupois), or between thirteen and fourteen pounds Troy weight.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846_7. No. 62.

February 22nd, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The President read the following letter from Mr. Cooper :

“¢ Merville, February 19th, 1847.

«¢ My pear Liuoyp,—On Saturday last I received a letter
from my First Assistant at Markree Observatory, Mr. A.
Graham, dated 11th inst., in which he states, that having on
the previous day heard from Mr. Hind of his discovery of a
new comet on-the 6th, he had the night before observed it ,
thus:

Feb. 10.49768, G. M. T. a= 2h. 42m. 39.4s. 6= 69° 1’ 44”.

‘* Mr. Hind’s place on

Feb. 7th. 6h. 54m. 5s. a = 2lh, 16m. 58.8s. S—=70° 56’ 42”.

** Again, on the 15th, I heard from Mr. Graham, under
date the 12th, stating that he had attempted an orbit from
the observations of Mr. Hind of the 6th and 7th, and his own
of the 10th, which, he conceived, could not be worth much,
as the heliocentric arc was only 0° 38’ 20” between the ex-
treme observations. The result he obtained was:

VOL. III. 20

400

Perih. Passage, 1847, March 30th, 9h. G. M. T.
Long. Perihel. . 284° 42’
Ase. Node. . . 34 53
Inclination. . . 49 40
Log. Per. Dist. = 8.4087
Motion direct.

‘* A letter has reached me this morning from Mr. Graham,
dated yesterday, in which he states that he has been fortunate
enough to obtain, with the circle, the place of a second star,
with which he had compared the comet on the 10th, and which
was not in any of the catalogues. It is:

a= 2lh. 44m. 16.42s. 6 = 69° 26’ 51” .5.

The other star of comparison on the 10th was 7610, B. A.
Catalogue. On the 15th he was enabled to compare the
place of the comet with the stars 7786, B. A. C., and 7810,
B. A.C. Result:

Feb. 15.45391,G.M.T, a= 22h. 16m. 26.9s. 6 = 65° 36’ 42”.

‘¢ The elements deduced by him from Mr. Hind’s observa-
tions of the 6th, and his own of the 10th and 15th, are:

Perihel. Passage, 1847, March 30.3483 G. M. T.

Long. Perih. . . 276° 50’ 32’) To app. Equinox,

Ase. Node. . . 22 38 16 Feb. 10th.

Inclination. . . 48 44 2

Log. Perih. Dist. = 8.60520

Motion direct.
These agree near enough with the middle observation. He
says that he can find no former comet that comes near this
orbit : that of 1680 is the most similar, but still wide. His
first set of elements seems to have been by no means bad. It
strikes me, from the short perihelion distance, that this comet
may prove ere long a very fine one.
‘* Ever sincerely your's,

‘* EpwarpD CoopeEr.”

401

The President also exhibited to the Academy a diagram,
representing the diurnal changes of temperature during the late
remarkable depression, which occurred in the week commenc-
ing February 7. The observations from which it is taken
are those made at the Magnetical Observatory of Trinity Col-
lege, at six stated hours during the day, together with those
of the maximum and minimum temperature, furnished by self-
registering thermometers. The following Table exhibits the
mean temperature for each day ; the maximum and minimum
of temperature ; and the difference of the latter, or the diurnal
range. ‘The mean temperature is deduced from the observa-
tions at 10 a.m. and 10 Pp. M., except on the two Sundays,
when it is inferred from the maximum and minimum tempera-
tures. The Table includes the day preceding and that follow-
ing the depression :

Day of Month ... | 6th. | 7th. | 8th. | 9th. | 10th.| 11th.| 12th.| 13th.| 14th.
Mean Temp. . . | 45.0 | 33.8 | 29.6 | 28.4 | 30.8 | 31.9 | 24.2 | 35.6 45.5.
Maximum ... . | 50.5 | 34.5 | 34.8 | 33.2 | 35.5 | 34.6 | 30.3 | 47.5 | 51.2
Minimum ... . | 40.0 | 33.0 | 26.0 | 25.2 | 25.7 | 24.7 | 21.5 | 16.7 | 39.8
Mange 6)... 0, 10.5} 1.5} 88] 8.0) 9.8) 9.9| 8.8) 30.8} 11.4

The greatest depression took place on the morning of the
13th, the minimum temperature being 16°.7.* A registering
thermometer, exposed to radiation towards the sky, exhibited
at the same time the temperature 12°.0. Temperatures so low
as these, although not uncommon in England, have not oc-
curred for many years in this country. The range of tempe-
rature, otherwise pretty constant, was remarkably affected on
the first and last days of the depression (the 7th and 13th),
the decrease of temperature on the former day reducing it to
1°.5, while the increase on the latter raised its amount to 30°.8.
In fact, on this day (the 13th), the rise of temperature was so
rapid, and so continuous, that the day maximum was entirely

* At Mr. Yeates’ house, on the south side of Dublin, the minimum ther-
mometer registered 11°.

402

obliterated, the absolute maximum occurring during the night.
In six hours, namely, from 7 a. M. to 1 p. M., the increase
amounted to nineteen degrees.

Michael Donovan, Esq., read a continuation of his paper
‘‘ on the supposed identity of the agent in the phenomena of
ordinary electricity, voltaic electricity, electro-magnetism,
magneto-electricity, and thermo-electricity.”

After briefly noticing the circumstances of the discovery
of galvanism, the author remarked, that as soon as even a few
of the facts were discovered, an hypothesis was invented to
account for them ; they were at once attributed to the agency
of an animal electricity secreted by the brain, of which the
muscles are the depositories, and the nerves the conductors.
Volta admitted that the agent is electricity, but maintained
that it is generated by the contact of the conductors concerned ;
the contraction being produced by the restoration of the equi-
librium throngh the animal. Hundreds of facts have been
since discovered, but, wonderful to say, the hypothesis in-
vented before they were known has been adhered to, and is
still used for their explanation.

‘The vast difference of properties observable in electric and
voltaic phenomena has been conceived to be explicable on the
supposition that in the former the quantity of electricity is
small, and the intensity great, while in the latter the quantity
is great and the intensity low. Several quotations from autho-
rities were adduced to this effect, and also with a view of
determining the exact meaning of quantity and intensity.

It was then argued, that the efficiency of great quantity,
at a low intensity, to account for the difference between com-
mon and voltaic electricity, has been received upon grounds
which have not been sufficiently canvassed; that we know
nothing of quantity of electricity but by its intensity ; that
the two terms represent ideas which are inseparable; that in-
tensity is the only significant condition of electricity of which

403

our senses take cognizance ; that the expression ‘‘ quantity of
electricity” aims at conveying to the mind a condition which
cannot be comprehended, and that, therefore, no clear idea of
any explanation founded on the notion of ** quantity” can be
attained. Several considerations, in support of these positions,
and an experiment to the same effect, were adduced. In fine,
it was concluded, that there is not a known phenomenon the
explanation of which receives any real assistance from the
assumed agency of quantity. M. Biot, probably perceiving
this defect in its alleged operation, has substituted the influence
of ** velocity.”

Those who sought to establish identity of the different
forms of electricity had long been embarrassed by the failure
of all efforts to produce deviation of the galvanometer needle
by means of common electricity, although it is so easily effected
by voltaic. M. Colladon, imagining that this want of success
was occasioned by an insufficient quantity or supply of the
electric fluid, or by imperfect insulation of the coil of the gal-
vanometer, employed one in which particular precautions were
taken to insure insulation. With this instrument, placed in the
circuit of a very large Leyden battery, a deviation of twenty-
three degrees was obtained; the deviation increased with the
intensity of the charge; it sometimes amounted to forty degrees.
When the galvanometer was made part of the circuit between
the conductors of a Nairne’s electrical machine, the deviation
was three or four degrees only ; but when a coil of 500 turns,
of the same construction, was substituted, a maximum deflec-
tion of thirty-five degrees was produced, provided the cylinder
was made to revolve three times in a second.

Mr. Donovan then stated an experiment of his own in
relation to this subject, the object of which was to prove, that
in Colladon’s experiments it was intensity and not quantity
that acted. Other experiments were adduced to prove that,
when the electricity is of the voltaic kind, the most feeble in-
tensities are far more efficient in causing deflection of the

404

needle than the most powerful intensities of common electri-
city; showing, as it was suggested, that in the latter case the
agent was electricity, which, being evolved by chemical ac-
tion, contained much of the deflecting constituent element ;
and that in the former the agent was electricity, with its natu-
ral minimum of the deflecting constituent, because it was de-
veloped without chemical action, by mere friction ; and hence
the necessity of the presence of such electricity in considera-
ble abundance to produce the required effect.

The same thing was stated to be evidenced by an experi-
ment, in which two voltaic apparatuses were made to act sepa-
rately on a differential gold-leaf electrometer, one of them pro-
ducing divergence, the other none; yet the effect of the latter
on the galvanometer needle was powerful, that of the former null.

Professor Faraday’s repetition of Colladon’s experiments
on deflection by common electricity were then reviewed, and
the remarkable circumstance was adverted to, that one of his
deflections was produced by one pole, contrarily to the laws
of voltaic electricity, in which the operation of two poles is
indispensable. If it be admitted as proved, that common elec-
tricity does not require a twofold polar arrangement in order
to produce deflections, it becomes a question, what is the use
of the two poles used in Colladon’s and Faraday’s experiments
with the Leyden battery ? One of them must be superfluous.
If this be so, we arrive at this general proposition, that voltaic
electricity is composed of elements existing in such ratio, and
so combined and modified, that it must be brought to bear
upon the subject of its action by means of two poles simulta-
neously and equally energetic; while the proportions and mode
of combination in the common electric fluid are such, that it
produces the same effect with one pole only. Thus a diffe-
rence, instead of an identity, would be proved by these expe-
riments.

It was further observed, on Faraday’s deflection of the gal-
vanometer needle by common electricity, that no less than

405

2000 one-inch sparks were required to produce a deviation of
forty degrees, while, in an experiment with a minute pair of
zine and platinum plates, the zine not weighing more than the
head of a pin, and probably not the thousandth part of a grain
dissolved during the action of an acid on it, the needle, never-
theless, whirled round the circle twice. Thus, a chemical ac-
tion, almost inconceivably small, produced an effect eighteen
times greater than 2000 sparks of electricity from a powerful
plate-machine. The inference drawn was, that the agents
could not be the same in both.

In furtherance of the objects above detailed, Professor
Faraday has made experiments to determine the quantity of
electricity associated with the particles or atoms of matter; from
which it may be calculated, that to decompose a single grain
weight of water, 800,000 discharges of an electric battery, each
discharge consisting of 300 one-inch sparks, would be required ;
which Faraday conceives is equal to a powerful flash of light-
ning : and he estimates that the electricity, that is the affinity,
which maintains the oxygen and hydrogen of the grain of water
in combination, is of the same amount. Thus, according to
him, there is the electricity of a flash of lightning in every
grain or drop of water, that is, if the electricity of a drop of
water could be collected in one spark, it would be 454545
miles in length.

But Faraday neglected to compare his results with those
of MM. Paets Van Troostwick and Deiman, and also with
those of Dr. Pearson. These philosophers, who made expe-
riments with the greatest care, represent the matter very diffe-
rently. Many calculations were entered into, which proved
that, according to the experiments of the Dutch chemists, the
quantity of electricity necessary to decompose a grain of water
is thirty-eight times less than Faraday’s estimate, and, accord-
ing to those of Pearson, forty-two times less. The vast diffe-
rence of Faraday’s estimate leads to some suspicions of the uni-
versality of the law as laid down by that philosopher, namely,

406

that if water be subjected to the influence of the electric cur-
rent, no matter what the intensity or acting surface, the quan-
tity decomposed will be exactly proportionate to the quantity
of electricity which has passed. All this may be very true,
when applied to the voltaic influence, but, if so, the law seems
to individualize common electricity, and to dissever it from its
alleged identity with voltaic electricity. When we find two
estimates of an effect to agree pretty well, while a third is forty-

two times greater than one, and thirty-eight times greater than

the other, it is plain there is a monstrous error somewhere ;
and hence, before we venture to draw any conclusion, it will
be necessary to investigate the grounds on which the discor-
dant opinion has been formed. This becomes the more neces-
sary, when it is recollected that the stronghold of those who
maintain the identity of the voltaic and electric agents is the
almost unlimited supply of the latter at a low intensity, which,
they affirm, can be brought into action during the exhibition
of any phenomenon caused by the former.

Faraday has affirmed, as already observed, that one grain
of water, decomposed by four grains of zine, can evolve elec-
tricity to an enormous amount, no less than 240 millions of
one-inch sparks. ‘To test this, an experiment was made, in
which diluted sulphuric acid was made to act on a voltaic pair
consisting of four grains of zine foil and a plate of platinum,
the metals being separately connected with a differential elec-
trometer with insulated, detached, and moveable gold leaves.
The solution of the zine occupied one minute and a half, and
during this period the gold leaves were rapidly approached
until they touched, and then rapidly withdrawn; there was
not the slightest attraction or repulsion, although, according

to Faraday’s estimate, the equivalent of 240 millions of one- .

inch sparks was passing between them at the time. Yet, when
the same electrometer was subjected to the action of a voltaic
series, consisting of twenty pairs of three-quarter-inch plates,
both attraction and adhesion took place.

:

407

Lest it should be supposed that this quantity had been
really evolved, but was lost by dissipation, an experiment was
made, in which a voltaic pair, the zine weighing four grains,
was made to act as above described, the whole being contained
in a hermetically sealed glass vessel, with an electrometer so
constructed that it would indicate the smallest quantity of
dissipated electricity ; but there was not the slightest appear-
ance of such.

Should it be affirmed that the alleged enormous quantity
of electricity was produced, but, being in the positive and nega-
tive states, they neutralized and destroyed each other, the fol-
lowing experiment was opposed to the supposition. A plate
of zine was connected with a plate of platinum, by means of
an inch of platinum wire +35 inch thick : this was included in
a glass sphere with dilute sulphuric acid, the glass being her-
metically sealed. When the acid was made to act on the zinc,
there was not the least appearance of heat in the platinum
wire, resulting from the neutralization of the alleged enormous
quantity of the two states of electricity ; nor were any traces
of electrical action on the electrometer discoverable. If, ac-
cording to the hypothesis, the equivalent of 240 millions of
positive and negative one-inch sparks had passed through the
platinum wire, at the rate of 1,600,000 per second, need it be
inquired what would have become of the wire and the whole
apparatus. Van Marum, with one discharge of his battery,
melted forty feet of thin iron wire.

The supporters of the doctrine here objected to may
maintain that the alleged quantity of electricity was really in
operation, but that it was retained and concealed in the con-
stitution of the resulting gases; and this also seems to be the
opinion of Faraday, by his adoption of the electro-chemical
theory of Berzelius, wherein he expresses his belief that the
light and heat evolved during combination are produced by the
discharge of positive and negative electricity which at that
moment takes place. If in the seven or eight cubic inches of

VOL. III. 2M

408

mixed oxygen and hydrogen, which result from the decompo-
sition of a grain of water, there be electricity concealed equal
to 240 millions of one-inch sparks, when the mixture is de-
tonated, so as to recompose water, a flash of lightning and
clap of thunder ought to be the consequence, instead of the
little bright flame and the trivial crack which occur.

But it is not merely this immense quantity of electricity
that is unaccounted for. Professor Faraday conceives that the
electricity which holds the elements of a grain of water in com-
bination, enormous as its quantity is affirmed to be, can only
be overcome, during decomposition, by an equal quantity of
electricity. What then becomes of this second portion?
What has become of the first? We have not been able to
discover traces of either. No less than 480 millions of one-
inch sparks are concerned in the decomposition of one grain or
drop of water, and we can find no account of any portion of
them.

Mr. Donovan thus concludes this portion of his paper :
** | conceive that the rules of discussion warrant my running
this hypothesis as closely to the impossible as I can. The
higher the authority, the stronger must be the argument to
give it any chance ofsuccess. It is on this account that I
take the liberty of reasoning thus freely on the opinions of so
celebrated a philosopher.”

The President and Dr. Apjohn made some remarks on
Mr. Donovan’s communication, in opposition to his views,
and confirmatory of the received doctrine of the identity of
electricity from different sources.

DONATIONS.
A Silver Hiberno-Danish Coin and a Bronze Celt, found at
Newington, County Kildare. Presented by James Forbes, Esq.
The Twenty-sizth Report of the Leeds Philosophical So-
ciety, for 1845-6. Presented by the Society.

a

409

The Head of a Cow and the Horn of a Bull ; two portions
of Deer Horn and two Bones ; fragments of an ancient Iron
Spear ; a Hammer and Ring ; fragment of a Crucible ; from
a Rath in the townland of Cullanagh, parish of Ballyroan,
Queen's County. Presented by Joseph Ferguson, Esq.

Nieuwe Verhandelingen der eerste Klasse van het Konink-
lijk-Nederlandsche Instituut van Wetenschappen, Letterkunde
en Schoone kunsten te Amsterdam. 12 vols.

Précis Historique des Opérations Géodesiques et Astro-
nomiques, faites en Hollande.

Beschrijving van eenen Toestel ter Verwarming van een
Uitgestrekt Gebouw ; door A. Van Beek.

Verhandeling over eene nieuwe wijze om Afstanden te
Meten, door wijlen den heere Hendrik Aeneae. 1812.

Over de meethundige bepalingen ; door J. F. Schréder.

Onderzoekingen aangaande het Zwart in de Melisbrooden ;
door C. M. van Dijk en A. van Beek. 1829.

Verhandeling over het verschil tusschen de Algemeene
grondkrachten der Natuur en de Levenskracht ; door C. G.
Ontijd.

Nadere waarnemingen en proeven over de onlangs ge-
heerscht hebbende ziekte der aardappelen ; door G. Vrolik.
(Parts I. and IL., 1845 and 1846).

Presented by the Royal Institute of Sciences, Belles
Lettres, and Arts, of the Low Countries.

A Silver Reliquary. Presented by Dr. A. Smith.

An ancient Irish War Axe, made of Iron, found in the
bed of the River Boyne, near Castle Rickard. Presented by
General Birch, R. A.

; Fragments of an old Irish Folio Manuscript, on Paper ;
part of a larger Work in the Library of the Academy, de-
scribed at page 157 in the Catalogue of the Collection of
Irish Manuscripts lately purchased from Messrs. Hodges §
Smith.

‘“* The fifteen unpaged loose leaves at the end of this

410

volume appear to be part of a translation into Irish, from
some other language, of the ancient history of the Greeks,
Romans, Persians, &c. These leaves are not in the same
handwriting as the preceding treatise on medicine, nor do
they appear to have been at any time part of the volume.
The second page is marked Chapter III., between which and
Chapter VI., on the fifth page following, no other chapter
intervenes, so the leaves are not consecutive. ‘The style of
the translation is that of the early part of the sixteenth cen-
tury.”

The fragment now presented begins with the end of
Chapter I. It contains the whole of Chapter II., and the
beginning of Chapter IIT.

The following is a translation of the heading of Chapter II.:

‘¢ The second chapter, in which Belus, Ninus, and Semi-
ramis, are spoken of, and of their successors in the kingdom
of Babilon, until the fifth year of the reign of Sethos.”

The chapter then opens in words to this effect: ‘‘ Syn-
cellus says, following the opinions of Halanicus, Ctesias,
Halicarnassus, and Hephalion, that Abraham was fourteen
years dwelling in the country of Canaan, when Belus came
to conquer Babilon.” :

Page 7 contains a list of the Judges and Chiefs of the
Children of Israel, and of the contemporary kings of Egypt.

The third chapter: ‘‘ Of the kings of Asiria from the
time of Laostines to the nineteenth year of the reign of Nabu-
chadonosor, who plundered and destroyed the Temple.”

Presented by Eugene Curry, Esq.

ERRATA IN PRECEDING NUMBER.

Page 383, line 3, for “ the Rev. M. Roberts” read “ Mr. M. Roberts.”
» 9385, ,, 6, for “Mr. M. Roberts” read “the Rev. W. Roberts.”

2 2 2 2
ees cen 15, for = —* =1, read — — = — 1.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. Wiech gs No. 63.

March 16th, 1847. (Stated Meeting.)

REV. HUMPHREY LLOYD, D. D., President, in the
Chair.

The Secretary of the Academy read the following Report :

The Council, on the expiration of their year of office, are happy
to be able to express their satisfaction at the continued prosperity
of the Academy.

During the past year the first part of the twenty-first volume of
the Transa€tions has been published, containing some valuable
papers in the departments of Science and Polite Literature. The
second Part is in the press, and is considerably advanced.

The Proceedings have been published with great regularity. The
Council are happy to be able to state, that the strict enforcement of
the rule which requires a complete abstract of each paper to be
furnished before leave to read it can be obtained, has enabled the
Secretary of Council to bring out the Proceedings after each meeting
without delay. It would be unjust, however, to that gentleman, not
to admit, that this success is also very much due to the zealous
manner in which he has carried out the intention and spirit of the
regulation, as well as to the willing co-operation he has received
from the authors of papers.

VOL. III. 2N

412

The Proceedings, therefore, being now in the hands of all
Members up to the present date, render unnecessary any minute
recapitulation of what has occurred at our public meetings; it must
suffice to observe, that there has been no lack of important and
valuable communications in any of the three departments of the
Academy’s labours.

The formation of a Museum of Irish Antiquities is an object to
which the attention of the Academy has been directed for the last
seven years ; and the Council have great pleasure in being able to
report, that, during the past year, this important department has
not been neglected. The value of such a Museum is now recognised
by every Member of the Academy, and continues to be regarded
with great interest by the public.

The Council are most anxious that the Museum should be
thrown open to public inspection as fully as is consistent with its
safe preservation. But they are impeded in this desire by the nar-
row accommodation afforded by our present rooms, and also still
more by want of funds; for it is obvious that a greatly increased
staff of attendants would be necessary if the public were admitted
to the Museum as fully as is desirable. For these reasons, admis-
sions have hitherto been restricted to parties accompanied by
Members, or bearing their orders, although it is the wish of the
Council that no respectable person who applies for admission should
be excluded.

The Museum, as is well known, is deeply indebted to the libe-
rality of Members, and other friends, who have, from time to time,
by private subscription, raised large funds for the purchase of anti-
quities. About £800 have also been contributed in various sums at
different periods, during the last seven years, from the funds of the
Academy, for the promotion of this object, and donations of anti-
quities of great interest and value have been, from time to time,
received. It would be very desirable that a full and exact account
of all these purchases and donations should be placed on record ;
and the Council would, therefore, strongly recommend it to their
successors to have a brief historical account of the formation of
the Museum drawn up, and presented in the form of a Report to the
Academy.

413

During the past year a subscription has been set on foot for the
purchase of the Domhnach Airgid, a most interesting relic, whose
history is well known to the Academy from Mr. Petrie’s paper,
which has appeared in our Transactions. The purchase-money
agreed upon was £300, and the sum of £285 7s., including £50
subscribed by the Academy, has already been received, leaving a
balance of about £15 (exclusive of some costs for printing, &c.),
which, it is hoped, will without difficulty be collected.

During the past year very little progress has been made in the
Catalogue of the Museum, which must necessarily be a work of
time, and of considerable expense ; but the Pictorial Catalogue has
been continued, and every article added to the Museum has been
drawn as it was obtained, so that the Academy will at all times
possess the means of ascertaining the identity of every thing that
now forms a part of the Collection.

Some few articles of interest and value have been purchased and
added tothe Museum during the past year, at a cost to the Academy
of £22 in all. Several donations have also been received, which
have been acknowledged from time to time in the Proceedings, and
it is, therefore, unnecessary to give a list of them here.

Next to the donors who have presented to the Museum articles
of interest and value, the thanks of the Academy are due to those
who have deposited there, for the inspection of the Members and of
the public, such valuable relics as they do not wish to part with. It
will be in the recollection of the Academy that, some time ago, Sir
Richard O’Donnell deposited in the Museum, under the safe keeping
of the Academy, the Cathach of St. Columbkille, and Dr. William
Stokes deposited the Fiachall Phadruig.

During the past year the Rev. Francis Brownlow has deposited,
in the same way, the celebrated Book of Armagh, a manuscript
of great antiquity, and of the utmost importance to the ancient
-Church History of Ireland.

The Council would beg leave to call the attention of the Aca-
demy, and of the public generally, to the example set by these gen-
tlemen. Those who are in possession of such relics of antiquity,
by depositing them in the safe keeping of the Academy, retain the
full power of recalling them whenever they think fit, whilst, at the

414

same time, they give an opportunity to those who are best qualified,
of discussing and investigating their claims to antiquity; and thus,
in the end, the value of these curious relics is greatly enhanced, by
the light that is thus thrown on their history, and the additional
evidence that is collected in confirmation of their genuineness.

The sum expended on additions to the Library during the past
year has necessarily been very small. The funds of the Academy
are so nearly absorbed in the unavoidable expenses of the House.
and Officers, and in the publication of our Transactions and Pro-
ceedings, that the expenses of binding, together with the annual
subscription to periodical publications, generally exhaust almost all
that can be spared for the support of the Library.

The Library, however, has received several valuable donations
during the past year, which have been acknowledged from time to
time in the Proceedings.

We have also added the following to the list of Societies with
whom we are to exchange Transactions :

. The Society of Zurich.

. The Society of Agriculture, Lyons.

Academia della Crusca of Florence.

. Societé des Sciences Naturelles du Canton de Vaud.

. The Imperial Observatory, Pulkova.

. L'Institut Royal des Pays Bas, Amsterdam.

. The Library of the Museum of Economic Geology, London.

IDF OD

No changes have been made during the past year in the by-
laws or rules for the management of the affairs of the Academy,
except in the mode of electing Honorary Members. It was found
that some inconvenience was experienced from the vagueness of the
former rules, and that a somewhat too great facility was given by
them for the admission of Honorary Members ; and, as this tended
to the injury of the Academy, by diminishing the value of that dis-
tinction, the Council submitted to the Academy the regulations
which received your approbation on the 11th of January last, and
which will be found in the Proceedings under that date. The prin-
ciple of these new regulations, which, it is hoped, will prove satis-
factory in practice, is twofold ; first, to limit the number of Honorary

415

Members; and secondly, to divide them into sections corresponding
to the threefold objects of the Academy, so that the respective
branches of Science, Polite Literature, and Antiquities, may be
fairly represented among the Honorary Members.

During the past year an opportunity presented itself, from the
visit of an intelligent Danish antiquary to this city, of opening a
communication between the Academy and the: Royal Museum of
Northern Antiquities of Copenhagen, from which we may reasonably
expect the most beneficial consequences. From the connexion
which subsisted in ancient times between the Norsemen and this
country, a comparison of Scandinavian and Irish antiquities has long
been a great desideratum. The Academy, therefore, in accordance
with the recommendation of Council, requested Mr. Worsaae to be
the bearer of some drawings of the objects which seemed most
likely to be interesting to Northern antiquarians in our Collection,
to be presented, in the name of the Academy, to the Royal Museum
of Copenhagen. They selected also, for the same purpose, under
the superintendence of the Committee of Antiquities, a few dupli-
cates from the Museum, which, it is hoped, may be regarded at
Copenhagen as worthy of a place in the Royal Museum. They will,
at all events, serve as a testimony of our good-will, and as an ex-
pression of our desire to establish a friendly intercourse between
the learned men of two countries, whose early history was once so
closely and so singularly united.

During the past year the Academy has to lament the death of
the following Members :

Abraham Palmer, Esq... . - + + elected 1838.
George Digges La Touche, Esq.,. . a hOde.
Goddard Richards, Esq., . . - - 4 1843.
Maxwell M‘Master, Esq., . . . » » 1844.

- The death of George Downes, Esq., also occurred during the year.
He died on Sunday, August 23, 1846 ; and although, from the state
of his health, he had, a short time before, ceased to be a Member
of the Academy, the Council cannot refrain from paying this brief
tribute to his memory. His attainments in Polite Literature were
of a high order ; and his extensive knowledge of the northern lan-

416

guages was favourably displayed in his valuable paper on the Norse
Geography of Ireland, which has appeared in the Transactions of
the Academy.

Thomas Moore, Esq., the distinguished Lyric Poet of Ireland,
a gentleman whose name is too well known to need any eulogy on
this occasion, was the only Honorary Member elected during the
past year.

The Academy has also been increased by the election of twenty-
six ordinary Members, whose names are as follows:

1. John Alcorn, Esq. 15. William Brooke, Esq.

2. Abraham W. Baker, Esq. 16. D. J. Corrigan, M. D.

3. Philip Bevan, M. D. 17. Leonard Dobbin, Esq.

4, J. O. Curran, M. D. 18. Michael Donovan, Esq.

5. Matthew D’Arcy, Esq. 19. Charles Haliday, Esq.

6. James Birch Kennedy, Esq. 20. W. Neilson Hancock, Esq.
7. M. H. Stapleton, M. B. 21. John Kells Ingram, Esq.

8. Hon. and Rev. W. Wingfield. 22. Charles P. M‘Donnell, Esq.
9. John Aldridge, Esq. 23. Right Hon. Louis Perrin, Jus-
10. George Lefroy, Esq. tice, Queen’s Bench.
11. Thomas John Beasly, Esq. 24. Frederick John Sidney, Esq.

_
nw

. Thomas Percy Boyd, Esq. 25. Rev. Henry Tibbs.
. Rev. Robert J. M‘Ghee. 26. John O’Donovan, Esq.
. Rev. William Reeves, M. B.

Ll ot
me CO

It was resolved, that the Report of the Council be adopted,
and printed in the Proceedings.

The ballot for the annual election having closed, the Seru-
tineers reported that the following Gentlemen were elected
Officers and Council for the ensuing year :

President.— Rev. Humphrey Lloyd, D. D.

Treasurer.— Robert Ball, Esq.

Secretary to the Academy.—Rev. James H. Todd, D. D.

Secretary to the Council.— Rey. Charles Graves, A. M.

Secretary of Foreign Correspondence.—Rey. Samuel
Butcher, A. M.

417

Librarian.— Rev. William H. Drummond, D. D.
Clerk and Assistant Librarian.—Edward Clibborn.

Committee of Science.

Rey. Frane Sadleir, D. D., Provost of Trinity College ;
James Apjohn, M.D.; James Mac Cullagh, LL. D.; Robert
Ball, Esq.; Sir Robert Kane, M.D.; GeorgeJ. Allman, M.D.;
Sir William R. Hamilton, LL. D.

Committee of Polite Literature.

Samuel Litton, M.D.; Rev. William H. Drummond, D. D.;
Rey. Charles W. Wall, D. D.; John Anster, LL. D.; Rev.
Charles Graves, A. M.; Rev. Samuel Butcher, A. M.; Rev.
James Wilson, D. D.

Committee of Antiquities.

George Petrie, Esq., R. H. A.; Rev. James H. Todd, D.D.;
J. Huband Smith, Esq., A. M.; Captain Larcom, R. E.;
William R. Wilde, M.D.; F. W. Burton, Esq.; Samuel Fer-
guson, Esq.

The President then appointed, under his hand and seal,
the following Vice-Presidents :

Captain Larcom, R. E.; Sir William R. Hamilton, LL. D.;
Rev. Frane Sadleir, D. D., Provost, Trinity College; Rev.
Charles W. Wall, D. D.

The following note by Sir W. R. Hamilton, announcing a
theorem of hodographic isochronism, was read :

If two circular hodographs, having acommon chord, which
passes through, or tends towards a common centre of force, be
cut perpendicularly by a third circle, the times of hodographi-
eally describing the intercepted ares will be equal.

DONATIONS.

Abhandlungen der Kéniglichen Akademie der Wissen-
schaften zu Berlin. Aus dem Jahre 1844.

418

Bericht iiber die zur Behanntmachung geeigneten Verhand-
lungen der '‘Kéniglichen Preussischen Akademie der Wissen-
schaften zu Berlin. From July, 1845, to June, 1846.

Specimens in Silver and Copper of a Medal struck in
honour of Leibnitz. Presented by the Academy of Sciences
of Berlin.

The Seal of the Right Rev. Dr. Sandes, late Bishop of
Cashel. Presented by the Rev. Charles Mayne, M. R. I. A.

Three Lectures on Political Economy. By W. Neilson
Hancock, Esq., LL. B., Whateley Professor of Political Eco-
nomy. Presented by the Author.

Extracts from the Introduction to the Observations made
at General Sir T. M. Brisbane’s Observatory in the Year
1843. By J. Allan Brown, Esq. Presented by General T.
M. Brisbane.

Comptes rendus Hebdomadaires des Séances de 1 Académie
des Sciences. From 16 Novem. 1846, to Feb. 1, 1847. Pre-
sented by the Academy.

Transactions of the Geological Society of London. Se-
cond series. Vol. VII., Part 2. Presented by the Society.

Journal of the Asiatic Society of Bengal. No. CLXIX.
1846. Presented by the Society.

Journal of the Royal Asiatic Society of Great Britain
and Ireland. No. XVII., Part 2. Presented by the Society.

The Quarterly Journal of the Geological Society of Lon-
don; for February 1, 1847. Presented by the Society.

Memoires de la Société Géologique de France. 2me Serie.
Tome II. Ire partie. Presented by the Society.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846_7. septh agiiGide

April 12th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Abraham Whyte Baker, Esq. ; James W. M. Berry, Esq. ;
Richard V. Boyle, Esq.; Sir Thomas Esmonde, Bart. ; Na-
thaniel Hone, Esq.; and Philip Jones, Esq. ; were elected
Members of the Academy.

Dr. Allman made a communication on the Structure of
the Fruit and Mechanism of Dehiscence in some of the Hepa-
tice, and on the probable Origin of the Organs known by the
name of Elaters in these Plants.

In this paper the author demonstrated the existence, in the
sporangia of Jungermannia, Marchantia, and Fegatella, of
spiral cells similar to those found in the lining membrane of
the anthers of flowering plants. The sporangium of these
genera is composed of a single layer of such cells immediately
enclosing the spores and elaters. The author described the
circumstances which he had observed to attend the phenome-
non of dehiscence in Fegatella conica. In this plant the pe-
duncle of the sporangium is connected with the fundus of the

VOL. III. 20

420

calyptra by a mass of loose, succulent, cellular tissue. At the
period of dehiscence this mass becomes rapidly enlarged, appa-
rently by engorgment of fluid, and, by acting against the more
resisting receptacle, forces the sporangium with its pedicle
through the mouth of the calyptra, beyond the margin of the
receptacle. The peculiar spiral cellular tissue of the sporan-
gium is thus brought into direct contact with the atmosphere,
and the hygroscopic properties of this tissue placed in a con-
dition for manifesting themselves. The result of this is the
dehiscence which takes place in the exposed portion of the
sporangium, in consequence of the balance of tension in the
opposite walls of the cells being disturbed. The author was,
moreover, of opinion that the presence of elaters in the hepaticz
might be accounted for by supposing the separation, in an early
period, of certain cells from the sporangium walls ; that these,
falling into the cavity, retain for a certain time their inde-
pendent vitality, and become developed into the peculiar or-
gans in question, lying at last free among the spores. He could
not assent to the doctrine so generally promulgated, that the
elaters assist in the dispersion of the spores.

Dr. Allman also read a paper on the external anatomy of
Chelurus, Phil., a genus of Amphipodous Crustacea, destruc-
tive to submarine timber works.

In this communication the author. gives a detailed descrip-
tion of the external anatomy and zoological relations of an
amphipodous crustacean, recently discovered by Mr. Mullins,
C.E., in the timber jetty at Kingstown Harbour, where it has
been doing a vast amount of mischief by destroying the timber
of the submarine works in that locality. It proves, on inves-
tigation, to be referable to a genus established by Philippi,
under the name of Chelurus, for a crustacean discovered by this
naturalist at Trieste.* The Irish specimens, however, differ

* See Wiegmann’s Archiv. fiir Naturgesch., 1839.

421

in certain points from the animal as described by Philippi; and
Dr. Allman thought it not impossible that these differences
would indicate a distinct species, which might be noted under
the name of C. destructor, as distinguished from the C. tere-
brans of Philippi. As, however, it is by no means improbable
that the differences in question are referable to slight inaccu-
racies in the memoir of the continental zoologist, the proposed
distinction was considered purely provisional, to be confirmed
or rejected according as actual comparison of specimens shall
decide. The following summary of the generic characters of
Chelurus, more condensed than that given in the memoir of
Philippi, was proposed by Dr. Allman :

CueLurus, Philippi.

Gen. Cha.— Body not compressed; head distinct ; superior
antenneé shorter and more slender than the inferior, and con-
sisting of a peduncular portion, which supports two unequally
developed rami.* Inferior antenne large, not divisible into a
distinct peduncle and ramus. Mandibles strong, palpigerous ;
furnished with a molar tubercle, with transverse ridges. First
pair of maxille strong, pyramidal, palpigerous ; second pair
lamelliform. Mazillary feet large, bearing a palp-like stem,
and united at their origin, so as to constitute a great opercular
lip, covering all the other organs of the mouth. Thorax com-
posed of seven distinct segments, with the epimerz distinct,
and moderately developed. First two pairs of thoracic legs,
didactyle; five remaining pairs terminated by a small, unop-

* Philippi takes no notice of this character of the superior antennz, and
simply describes them as setaceous, with seven articulations; whereas the
number of articulations, in the animal I have examined, are three in the pe-
duncular portion, and six in the larger ramus. I cannot, however, help be-
lieving that this excellent naturalist has, in the hurry of examination, over-
looked the real form of these antennze; otherwise I would feel well inclined to
consider the character in question as affording sufficient grounds to separate
generically the Irish from the Mediterranean amphipod.

202

422

posable articulation. First three segments of abdomen, each
bearing a pair of biramous, natatory feet; remainder of abdo-
men consisting of one very large trunk, supporting anteriorly a
pair of large, foliaceous, lobed appendages, and a pair of cylin-
drical false feet, and terminated posteriorly by two lamellar
leaping organs, and an intermediate leaf-like lobe.

1. C. terebrans, Philippi.— Last three pairs of thoracic feet
with the terminal joint foliaceous. Hab.—Coast of Trieste.

2. C. destructor, Mihi (provisional species).—All the tho-
racic feet, except the first two, terminated by a small hooked
claw. Hab.—lIrish coast.

The author, after entering into the details of the external
anatomy of Chelurus, maintains the necessity of considering
this genus as the type of a distinct family among the amphi-
poda, assuming as the grounds of the assigned rank the remark-
able condition of the posterior region of the abdomen, the first,
second, and third ring of this region being consolidated into
one great trunk, bearing three pairs of heteromorphous appen-
dages. Availing himself, therefore, of the characters derived
from these considerations, the families of amphipodous crusta-
cea were analytically arranged as follows :

Fourth and fifth abdominal segments conflu- }
ent ; abdominal appendages of the fourth and S Family.

4 fifth pair very different in form (heteromor- f CueLurip4.
< phous). - J ;
BS | (Mouth con-
= J cealed by G :
t+ } Fourth and fifth abdominal the maxil- pce
= segment distinct; abdomi- lary feet.
a nal appendages of the fourth ) Mouth _ not}
| and fifth pair nearly similar concealed | yy
in form (isomorphous). by the nae eee
L L illary feet.

Dr. Allman also read a paper on a new Genusand Species
of Entomostraca.

The little animal which formed the subject of this commu-
nication inhabits the branchial sac of Ascidia communis, in

423

which it may be observed swimming freely during, perhaps, all
seasons of the year. ‘The author describes it under the name
ot Notodelphys ascidicola, and assigns to it the following ge-
neric characters :

Notrope.puys,* Mihi.

Gen. Cha.— Body elongated ; head scutiform, and bearing
in front a solitary median eye; antenne two, filiform, multi-
articulate ; mouth with a pair of mandibles, and surrounded
by five additional pairs of appendages, of which the anterior,
as well as the last two pairs, are prehensile ; thorax having
but two rings distinct, the anterior one being confounded with
the head. Female with a large dorsal ovigerous receptacle
immediately behind the last distinct thoracic ring. Locomo-
tive feet, four pairs; biramous natatory, each pair having an
intermediate plate ; abdomen with about five rings, the last of
which is terminated by two setigerous appendages.

Species unica.—WN. ascidicola. Hab.—swimming freely
in the branchial sac of Ascidia communis, Irish and English
coasts.

The author, after entering into numerous details relative to
the anatomy of the new entomostracon, and describing four
distinct phases in its development, maintained that the ovige-
rous receptacle was formed by a peculiar development of the
dorsal arches of a certain number of posterior thoracic rings,
and that it was the true representative of the singular, elytroid,
dorsal appendages of the thorax in Anthosoma, Cecrops, and cer-
tain other suctorial crustacea. He was, moreover, of opinion,
that the genus Notodelphys presents us with a most interesting
_ transitional form between the true entomostraca and the suc-
torial crustacea. Its perfect mandibulate mouth will at once
place it with the former,—a position, indeed, which its highly
developed natatory feet and active habits, as well as its general

* From vwroe, tergum, and dehpic, matrix.

424

physiognomy, would, in the first instance, suggest. The form,
on the other hand, of the accessory oral organs, or maxillary
feet, which are here constructed so as to constitute organs of
attachment, as well as the singular development of the dorsal
arch of the posterior thoracic ring, and the connexion of the
feet of opposite sides, through the intervention of a large in-
tercoxal plate,—a striking feature in the greater number of the
suctorial crustacea, but not found in the true entomostraca,—
unite with the semi-parasitical habits of Notodelphys in indi-
cating an affinity not to be mistaken with the true suctorial
tribes.

Dr. Allman read another paper on a new Genus and Spe-
cies of T'racheary Arachnidans.

In this paper the author described a Tracheary arachnidan
discovered by Dr. O’Brien Bellingham in the posterior nares
ofa seal (Halicherus gryphus). It turns out, on examination,
to be generally distinct from all the forms hitherto on record,
and Dr. Allman assigned to it the appellation of Halarachne
Halicheri, with the following generic characters :

HaLaRacuHne,* Mihi.

Gen. Cha.—FPalps free, filiform; mandibles didactyle ;
sternal dip, bifid ; degs with the last joint terminated by two
hooks, and an intermediate three-lobed caruncle; body entire,
elongated, sub-cylindrical, furnished anteriorly with a dorsal
plate; eyes, none.

Species unica.—H.. Halicheri. Hab.— Infesting the pos-
terior nares of Halicherus gryphus, Irish coast.

H. Halicheri possesses a very distinct tracheary system,
opening externally by means of two spiracles, which are placed
one at each side of the anterior extremity of the abdomen.
The alimentary canal, just before its termination at the pos-

“From dXc, mare, and apaxyn, aranea.

425

terior extremity of the abdomen, receives two long ceca, which
may be traced forwards, one at either side of the body, till
they terminate anteriorly by entering the basal joint of the
first pair oflegs. A large central nervous mass may be easily
demonstrated. It is placed near the middle of the cephalotho-
rax, of a somewhat stellate figure, with four pyriform lobes,
from which nervous filaments pass off to the surrounding parts.

The reproductive system is very obscure ; to it, however,
may probably be referred a pair of tubular organs, placed in
the anterior part of the abdomen, terminating at one end in a
cul de sac, which contains a striated, curved body, and appa-
rently opening at the other upon the surface. The larva is
hexapod. The structure of the oral organs is similar to what
occurs in Gamasus.

Sir Robert Kane read a paper on the composition of the
essential Oil of the Laurus Sassafras, and of certain compounds
derived from it.

This oil, which has a specific gravity of 1087, boils at
438° Fahr. By fusion with potash it is not acidified. Its com-
position was found to be expressed by the formula Coy Hip O4,
the same as that obtained by Saint Evre for the stearopten,
with which it is consequently isomeric.

When this oil is treated with chlorine, a great deal of
muriatic acid gas is produced and given off, and finally a very
thick liquid is produced, which requires to be kept for a long
time at a temperature of boiling water to free it from the ex-
cess of muriatic acid gas; the same may be done by washing
with a small quantity of water of ammonia, and then expo-
-sure to a moderate temperature, when the chlorine com-
pound can be obtained again, quite anhydrous. Its formula
is found to be Cay Hy Oy Cly. When this body is heated to
about 350° of Fahr., it suddenly and violently decomposes,
gives off much muriatic acid, and deposits a large quantity of

charcoal.
-

426

When the oil of sassafras is put into contact with bromine,
great heat is evolved, much hydrobromic acid is evolved, and
a solid product obtained, which, washed with alcohol until
the excess of bromine and some secondary products are re-
moved, is a brilliant white, crystalline powder. If this be
gently heated it becomes yellowish pink. It fuses at about
300°, and soon after decomposes, giving off hydrobromic acid,
and depositing charcoal. It is moderately soluble in ether,
and by the cooling, or the evaporation of its ethereal solution,
it can be obtained in brilliant oblique rhombs. The formula
of this body is Cy) H, O, Br;.

When oil of sassafras is treated with nitric acid, very vio-
lent action is produced, and a large quantity of oxalic acid is
formed ; but by diluting the acid, and avoiding much eleva-
tion of temperature, a resinoid substance is obtained, of a pale
yellow colour, soluble in alcohol and ether, slightly soluble
in boiling water, and depositing on cooling. This body is
quite destitute of acid characters, but it dissolves in alkalies,
and may be precipitated by solutions of earthy or metallic
salts, with the bases of which it forms definite compounds.
The formula of this substance, which I term nitro-sassafras, is
Cis Hg Og N, and it is evidently formed by the action of

259 Cp Hig O4. + Na Ono
giving
C, O,.+ H, O, and N, O,,
besides
Cis H; Og N.

When oil of vitriol is put in contact with oil of sassafras,
an intense and beautiful crimson colour is produced. This is
so remarkable as to constitute a very decisive means of recog-
nising this essential oil. On studying this reaction more
minutely, it is found that the oil of sassafras enters into a
direct compound with oil of vitriol, and there is produced an
intensely deep purple resinoid body, soluble in alcohol and
ether, a little soluble in water, destitute of acid reaction, yet
dissolving in alkalies, and being precipitated by the alkaline

427
and earthy salts. On analysis this substance gives the formula

Cao Hyg Or S.,
corresponding to
Cy Hip Os + S. O6 + He Oc.

That the sulphuric acid exists in this body, as such, is
shown by the fact that, on treating it with pure potash, the
whole of the sulphur separates as sulphate of potash. This sub-
stance is denominated sulpho-sassafras by Sir Robert Kane.

During the reaction of the sulphuric acid and oil of sassa-
fras, in order to produce this body, very small quantities should
be operated on, and the mixture kept perfectly cool, so that
no effervescence, or violent reaction, should take place. If
there be the slightest elevation of temperature, the substance
in question ig decomposed, sulphurous acid is evolved, and a
resinoid black material is produced, which does not contain
sulphuric acid, but for which, from the complexity of the re-
action accompanying its formation, and the great difficulty of
obtaining it absolutely pure, Sir Robert Kane does not at pre-
sent wish to propose a formula.

M. Donovan, Esq., continued the reading of his paper on
the Nature of the Agency which produces the Effects called
Galvanic, Electro-magnetic, Magneto-electric, and Thermo-
electric.

To support the opinion of identity, and to effect other ob-
jects, one of the chief of which is to show the absolute quan-
tity of electricity with which matter is associated, Professor
Faraday makes use of the following law, viz.: ‘* If the same
absolute quantity of electricity pass through the galvanometer,
whatever may be its intensity, the deflecting force upon the
magnetic needle is the same.” The general method of proof
of the truth of this law was to charge a Leyden battery witha
certain number of turns of a powerful plate electric machine,
varying the number of jars employed from eight to fifteen ; to
transmit the charge through a galvanometer, and to note the

428

deflection. The charge was transmitted through various me-
dia, all intended to retard it more or less, and thus to affect the
galvanometer with various intensities of electricity. In all
cases the deflection of the needle was the same, no matter what
the intensity: hence Faraday concluded that his law was proved.

To invalidate the inferences and proofs thus drawn, Mr.
Donovan brought forward a number of considerations to show
that, in all Faraday’s experiments, the intensity of the elec-
trical discharges employed was the same or commensurate with
the deflection of the needle; and that it is the intensity of the
electricity which passes through the galvanometer, and not its
quantity, that determines the degree of deflection, the highest
intensities producing the greatest deflection.

We should be cautious, therefore, Mr. Donovan observed,
in applying Faraday’s law : and if the law fail, the comparison
drawn by him between the quantity of electricity produced
during chemical action, to be immediately noticed, and that
discharged from an electric machine, cannot be considered as
proved. The comparison is this: Faraday found that by
connecting a galvanometer with a wire of platinum and a wire
of zine, each being ;', inch in diameter, and plunging their
other ends 4 inch deep in a mixture of four ounces of water
and one drop of sulphuric acid, during 85 of a minute, the
deflection of the galvanometer amounted to exactly the same
degree as when, in a former experiment, he passed a charge of
common electricity through the galvanometer, amounting to
thirty turns of the large plate-machine received in fifteen jars.
Each turn of the machine afforded 300 or 360 dense sparks.
Hence, according to the law, Professor Faraday inferred the
equality of the two ‘‘ absolute quantities” of electricity from
the equal deflection of the needle in both cases. The double
purpose of this experiment was still further to support the in-
ferred identity of voltaic and frictional electricity, and to estab-
lish the estimate, already alluded to, of the enormous quantity
of electricity with which matter is naturally associated.

ee ee

429

In order to discover how far the experiment supports either
of these positions, Mr. Donovan adduced counter-experiments,
in which combinations of zine and copper were acted on by di-
lute acid of different strengths until dissolved. The solution
took place in different periods of time, and, consequently, the
electricity evolved during any given period was unequal in
quantity, in some cases very much so; yet in all of them the
effect on the galvanometer was the same.

These experiments appear incompatible with Faraday’s law
of equal quantities of electricity producing equal deflections,
irrespectively of other circumstances. Support is, consequently,
withdrawn by them from his estimate of the enormous quantity
of electricity naturally associated with matter.

The following note by Professor Mac Cullagh was read.
Let a surface A of the second order be represented by the
equation

its primary axis being that of z. Through a given point S,
whose coordinates are 2’, y’, 2’, conceive three surfaces conto-
cal with A to be described, and let p, P’, p” be the squares of
their primary semiaxes. Then, if normals drawn to these sur-
faces respectively at the point S be the axes of a new system
of coordinates &, », 2, and if we put

P—P,=Af, Pp’ — PP =k, BY = Pek,

the equation of the surface A, referred to the new coordinates,
will be

a Eo& non Cos 2
Sg (f— 1) (27 + 4 1), (a)

where & , 1) Zo are the coordinates of its centre.

430

From the form of this equation it is evident, that if the
surface be intersected by the plane whose equation is
aa MOM os 0 Un
ai ar ef = fragt l, (6)
it will be touched along the curve of intersection by the cone
whose equation is
£? (ae
seni ra se (c)
This mode of deducing, in its simplest form, the equation of
a cone circumscribing a surface of the second order, is much
easier than the direct investigation by which the equation (c)
was originally obtained.

Let a right line passing through S intersect the plane
expressed by the equation (0), in a point whose distance from
S is equal to a, while it intersects the surface A in two points,
Pand P’, the distance of either of which from S is denoted by
p. Let the surface B, represented by the equation

£7) Mae Se

i Wage oe ee (d@)
be intersected by the same right line in a point whose distance
from S is equal to r, the distance being, of course, a semidia-
meter of this surface. Then it is obvious that the equation (a)
may be written

so that, if p and p’ represent the distances SP = SP’ respec-
tively, we have

1
mae (e)
and therefore

oy Ss (Sf)

431

This result is useful in questions relating to attraction.
For if A be an ellipsoid, every point of which attracts an ex-
ternal point S with a force varying inversely as the fourth
power of the distance, and if the point S be the vertex of a
pyramid, one of whose sides is the right line SPP’, and whose
transverse section, at the distance unity from its vertex, is the
indefinitely small area w, the portion PP’ of the pyramid will
attract the point S, in the direction of its length, with a force
expressed by the quantity

ae a
soa) 0 on 3
pe ?

and, putting 6 for the angle which the right line SP makes
with the axis of &, the attraction in the direction of € will be

2weos
re (9)

Now, supposing the axis of & to be normal to the confocal
ellipsoid described through S, it will be the primary axis of
the surface B, which will be a hyperboloid of two sheets ; and,
the surface being symmetrical round this axis, it is easy to see,
from the expression for the elementary attraction, that the
whole attraction of the ellipsoid will be in the direction of E.
Therefore, when the force is inversely as the fourth power of
the distance, the attraction of an ellipsoid on an external point
is normal to the confocal ellipsoid passing through that point.

Hence we infer, that if u be thesum of the quotients found
by dividing every element of the volume of an ellipsoid by the
cube of its distance from an external point, the value of vu will
remain the same, wherever that point is taken on the surface
of an ellipsoid confocal with the given one.

The question of the attraction of an ellipsoid, when the
law of force is that of the inverse square of the distance, has
been treated by Poisson, in an elegant but very elaborate
memoir, presented to the Academy of Sciences in 1833 (Mé-

432

moires de U’ Institut, tom. xiii.) In the preceding year I had
obtained the theorems just mentioned, by considering the law
of the inverse fourth power ; and, as well as I remember, they
were deduced exactly as above, by setting out from the equa-
tion (a). But I did not then succeed in applying the same
method to the case where the law of force is that of nature,
probably from not perceiving that, in this case, the ellipsoid
ought to be divided (as Poisson has divided it) into concentric
and similar shells. This application requires the following
theorem, which is easily proved :

Supposing A’ to be another ellipsoid, concentric, similar,
and similarly placed with A, let the right line SPP’ intersect
it in the points p and p’, respectively adjacent to P and P’;
then, if the direction of that right line be conceived to vary,
the rectangle under Pp and P’p (or under Pp’ and P’p’) will
be to the rectangle under SP and SP’ in a constant ratio.

Denoting the constant ratio by m, and combining this
theorem with the formula (f), we have

Pp x Pp _ mr

po ape: ue.
Now let the two surfaces A and A’ be supposed to approach
indefinitely near each other, so as to form a very thin shell,
then ultimately P’p will be equal to PP’, and we shall have

Ot Er,
Pp = P’p =a

where m is indefinitely small. Therefore, if the point S, ex-
ternal to the shell, be the vertex of a pyramid whose side is
the right line SP, and whose section, at the unit of distance
from the vertex, is w, the attraction of the two portions Pp and
P’p’ of this pyramid, which form part of the shell, will be equal
to mrw. Hence it appears, as before, on account of the symme-
try of the surface B round the axis of &, that the whole attrac-
tion of the shell on the point S is in the direction of that axis,
and consequently (as was found by Poisson) in the direction

a

433

of the internal axis of the cone whose vertex is S, and which
circumscribes the shell.
To find the whole attraction of the shell, the expression

mrw cos 0 (2)

must be integrated. Let ¢ be the angle which a plane, pass-
ing through SP and the axis of £, makes with the plane &y;
then
w = sin 0d0d¢,
en Gx sin’@ cos" ua 1
ge (Seg)

When these values are substituted in (7), that expression may
be readily integrated, first with respect to 0, and then with
respect to ¢.

It is evident that, by the same substitutions, the expres-
sion (g) may be twice integrated.

An investigation similar to the preceding has been given
by M. Chasles, for the case in which the force varies inversely
as the square of the distance (Mémoires des Savants Etran-
gers, tom. ix.) He uses a theorem equivalent to the formula
(f), but deduces it in a different way.

From what has been proved it follows that, if v be the
sum of the quotients found by dividing every element of the
shell by its distance from an external point 8, the value of v
will be the same wherever that point is taken on the surface =
of an ellipsoid confocal with the surface A of the shell.

Let >’ be another ellipsoid confocal with A, and indefi-
nitely near the surface 3. The normal interval between the
two surfaces & and 3’, at any point S on the former, will be
inversely as the perpendicular dropped from the common cen-
tre of the ellipsoids on the plane which touches & at S. Hence,
supposing the point S to move over the surface =, that per-
pendicular will vary as the attraction exerted by the shell on
the point S, when the force is inversely as the square of the

434

distance, or as the attraction exerted by the whole ellipsoid
A on the point S, when the force is inversely as the fourth
power of the distance.

When the point S is on the focal hyperbola, the integra-
tions, by which the actual attraction is found in either case,
are simplified, for the surface B is then one of revolution
round the axis of €, and its semidiameter r is independent of
the angle ¢.

From the expression for the attraction of a shell we can
find, by another integration, the attraction of the entire ellip-
soid, when the law of force is that of nature. And thus the
well-known problem of the integral calculus, in which it is
proposed to determine directly the attraction of an ellipsoid on
an external point, without employing the theorem of Ivory to
evade the difficulty, is solved in what appears to be the sim-
plest manner.

The preceding note having been read, Mr. Graves observed
that the mention therein made, of the equation which repre-
sents so simply a cone circumscribing a given surface of the
second order, reminded him of a circumstance which he thought
it right to state ; as that remarkable equation had been in cir-
culation among geometers long before it appeared in print, and
thus its origin, though generally known, was sometimes mis-
taken. Mr. Graves stated that he still retains a large part of
the memoranda, in which he set down, from day to day, the
substance of Professor Mac Cullagh’s lectures, delivered in
Hilary Term, 1836, and that the part preserved contains the
equation in question (the equation (c) of the preceding note).
In the memoranda it is deduced directly ; that is, the equation
of the cone is first given in the usual form, and is then reduced
to the form (c) by a transformation of coordinates.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 65.

April 26th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

The Rev. Dr. Robinson presented an autograph of Euler.

Dr. Apjohn drew the attention of the Academy to some
researches in Thermo-chemistry, with which he has been
recently occupied.

‘¢ It is well known” (he observed) ‘* to chemists, that muri-
atic acid gas and ammoniacal gas are absorbed by water in large
quantity, and that during their absorption much heat is deve-
loped. ‘The experiments which I have undertaken had for
object, to submit to exact estimation the heat so evolved ; and
the results being, as far as my information extends, quite novel,
and, I think I may add, theoretically and practically interest-
ing, I am anxious to present them to the public with as little
delay as possible.

' The apparatus employed in these experiments, though
necessarily somewhat complex, proved admirably adapted to
the purpose to which it was applied. It consisted of a flask,
in which the gas was developed, of an exsiccation tube, and
of a pair of tubes of small bore attached to the latter, by one
VOL. Ill. 2P

436

of which the gas, when dried, could be conveyed into a cup
containing mercury covered with a stratum of water, and, by
the other, into a small cylinder of very thin copper containing
the liquid to be heated. The cylinder was furnished with two
necks, into one of which a very delicate thermometer was fitted
by means of a cork, while the second received the tube by
which the gas was to be introduced. By turning a stopcock
attached to the latter tube, the gas could at any instant be
conveyed into the copper cylinder, or excluded from it, an
assistant at the same moment raising or depressing the vessel
containing the mercury, so as to prevent or permit of the issue
of the gas at this part of the apparatus. The temperature of
the air at the instant of the admission of the gas, and the tem-
perature of the liquid in the cylinder, having been accurately
noted, and, in addition, the time m, which elapsed between the
introduction and exclusion of the gas, as also the time m’,
which intervened between the latter manipulation and the
second reading of the thermometer, data were obtained for cal-
culating the total rise of temperature, and hence, for estimating
the heat evolved by the gas as a consequence of its absorption.
Thus, if x be the number of degrees by which w grains of

water are heated, by the absorption of G grains of gas, —
G

will be the heat extricated, i. e., the number of degrees that
the caloric given out by the gas would heat an equal weight
of water.

‘* Such is an outline of the general course pursued. The
experiments required the greatest attention, with a view to the
management of the apparatus, and the accurate mensuration
of time and temperature; and I am not a little indebted to my
scientific friend, Dr. Head, for the valuable assistance which
he has rendered to me.

‘* The observations being made, other difficulties remained
to be overcome. How, it will be asked, is the true value
of n to be determined ? For the observation of temperature

437

made at the close of the experiment is obviously less than the
truth, for two reasons: Ist. Because it was not taken until mm/
minutes after the gas was cut off. 2nd. Because, during the
m minutes that the gas was being absorbed, the copper cylin-
der was hotter than the surrounding air, and, therefore, con-
stantly losing heat. After a good deal of reflection on the
subject, it finally occurred to me to adopt the following method
of calculating the necessary corrections.

Having introduced into the copper cylinder, furnished with
its thermometer, 4.66 cubic inches of water, very nearly the
quantity used in all the experiments, and raised the whole to
93.4° (the air being 53.7°), the temperatures were noted at
intervals of a minute, until the thermometer indicated 66.5°.
To those I then applied the expression for the velocity of
cooling, deducible from the Newtonian law, viz. :

et Age eb
t b)

a being the excess of temperature of the cylinder over the air
at any instant, and 1 the excess after ¢ minutes, and thus
obtained the velocities of cooling corresponding to the succes-
sive values of T separated by intervals of a minute. These
being reduced to a tabular form, furnish, by mere inspection,
the means of applying the first of the two corrections already
indicated, or of ascertaining the temperature which the ther-
mometer would show, had it been read at the instant the gas
was cut off, or m/ minutes previous to the actual time of

observation.
‘¢ But the rise of temperature actually produced is less than
that which we are in search of, in consequence of the cooling
‘power exercised by the joint influence of radiation and atmos-
pheric contact during the time m. The method I have adopted
of determining the effect of refrigeration, and which, as far as
I am aware, has not been previously used, I shall now explain.
“¢ The velocity of cooling at any instant while the gas is

2P 2

438

passing in, is, adopting the Newtonian law, proportional to
the rise of temperature at such instant. But the gas having
been always introduced in my experiments at a uniform rate,
the rise of temperature is proportional to the time. Hence
the velocity of cooling at any instant is proportional to the
time. Such being the case, the well-known theorems, which
relate to the motion of a material point actuated by a constant
force, are here strictly applicable; and, amongst the rest, that
the space (number of degrees) through which the cylinder
cools in the time m, is equal to half the rectangle under the
time and the last acquired velocity. This theorem, in fact,
immediately gives the correction in question, not, I may ob-
serve, in an approximate, but in a complete manner, and, in
practice, I have every reason to be satisfied with it.

‘¢ In what precedes it will be seen, that I have employed
the Newtonian law of cooling, which the researches of Dulong
and Petit have shown not to represent observations with rigour,
except when the excesses of temperature are small. My results,
however, are not on this account appreciably less accurate, for
the thermometer which I employed only read to tenths, and
the divergence of the Newtonian law from the truth, within
the range of my experiments, is only observable in the second
decimal place.

‘¢ Having explained every thing necessary to enable the
Academy to judge of the accuracy of my results, I shall now
state the numbers at which I have arrived:

o ‘ Equal weights. An atom.
Ammoniacal gas passed into water, 940° 940°

Muriatic acid gas passed into water, 885° 1900°
Weight for weight, then, ammonia gives out more heat than mu-
riatic acid; but an atom of the latter gives out almost exactly
the double of the heat evolved by an atom of the former.

<¢ The number for ammonia, it’ will have been observed,
does not materially differ from that for aqueous vapour of maxi-
mum density at 212°, the latter having been fixed, by the

439

recent experiments of Brix, at 972°. The numbers, however,
are not strictly comparable. For, the heat evolved by the
steam is truly its latent heat, or is due solely to its change of
state, while the caloric evolved by ammoniacal gas, or muriatic
acid gas, undoubtedly consists of two distinct parts, viz., of
the heat of compression of these gases, and of that due to the
chemical action exerted between them, supposed in the liquid
condition, and water.

‘¢ Though I did not entertain any doubts as to the accu-
racy of the results just stated, it was obviously desirable to
resort to some experiments, if any such could be devised, by
which they could be tested; and none appeared better suited
to the purpose, than to pass ammoniacal gas into liquid muria-
tic acid, and muriatic acid gas into liquid ammonia, and deter-
mine, by the means already explained, the heat developed in
each case. Such experiments were accordingly performed, care
being taken that the gas introduced did not in amount. exceed
what would be necessary for saturating the opposite principle
contained in the liquid, and subjoined are the numbers to which
they have conducted :

Heat of ammoniacal gas passed into liquid muriatic acid, 2523°
Heat of muriatic acid passed into liquid ammonia, . . 1527°

' Deducting from the former 940°, and from the latter 885°, the
remainders are 1583° and 642°. Now, according to Andrews
(Transactions, Royal Irish Academy, vol. xix. part 2), .129 of
a gramme of ammonia, in the form of aqua ammonia, in com-
bining with liquid muriatic acid, evolves sufficient heat to raise
31.09 grammes of water 5.58°, from which it is easy to calcu-
late that it would raise an equal weight of water 1344°. But
- the heat evolved by equal weights of ammonia and muriatic
acid, in combining with each other, are obviously reciprocally
proportional to their atomic weights, so that, 1344 being the

number for ammonia, 1344 X — = 626 will be the number

440

for muriatic acid. The following, therefore, are the compara-
tive results, the numbers in first column being the differences ;
those in the second, the heat of the chemical action between
aqueous ammonia and muriatic acid, as inferred from the ex-
periments of Andrews; and those in the third, the excesses of
the former over the latter:

Differences. Andrews

Ammoniacal gas into aqueous acid, . 153d° 1344° 239°
Muriatic acid gas into aqueous ammonia, 642° 626° 16°

‘«* A glance at these numbers is sufficient to show that,
when muriatic acid gas is passed into aqueous ammonia, the
heat extricated exceeds that obtained when the gas is passed
into water, by almost exactly the heat of the chemical action of
aqueous muriatic acid and ammonia; while, as respects the
case of ammoniacal gas passed into water and aqueous acid,
this equality is wanting, the estimate by difference exceeding
the direct determination by 239°.

‘¢ This is a very curious result, and I was so startled by it,
that it was not my intention to give publicity to these experi-
ments until I had more frequently repeated them, and exe-
cuted others, which I had planned with the view of throwing
additional light upon the subject of my inquiry. In entering,
however, upon this new investigation, I had the misfortune to
lose, by an accident, both my thermometers, and as I do not
anticipate being able to return to it for a considerable time, I
gladly avail myself of the permission of the Council, to submit
these researches, in their present state, to the judgment of the
Academy. I entertain, indeed, a very confident hope, that the
numbers at which I have arrived will eventually be found to
be very close approximations to the truth. Assuming such,
for a moment, to be the case, and, in addition, that the results
of Dr. Andrews, in relation to the heat arising from the che-
mical action of aqueous ammonia and aqueous muriatic acid,
are rigorously correct, it has occurred to me that my results
admit of the following interpretation :

441

“‘ Let a + b= heat given out by ammoniacal gas when
absorbed by water, a representing the heat of compression, and
b that of the chemical action between compressed or liquid
ammonia and water. When ammoniacal gas is passed into
liquid muriatic acid, the heat represented by 6 will be wanting,
and that actually developed will be a +c, c being the chemi-
cal heat determined by Andrews. The difference of these,
therefore, ora-+c — (a+), willbec—d. But this dif-
ference we have actually found to be greater than c. 6 must,
therefore, have a negative sign ; or, in other words, when com-
pressed ammonia is brought into contact with water, cold, not
heat, is the result.

‘“‘ This may appear a very paradoxical supposition, but I
am not aware of any fact which would prevent us from enter-
taining it; and the great expansion which water experiences
when absorbing ammoniacal gas, even confers upon it some
degree of probability. I may add, that this view of the mat-
ter gives us 239° as the value of 6, and suggests an experi-
ment, which, though difficult, it would not be impossible to
perform, and the result of which would at once elucidate com-
pletely the subject under consideration.”

The Rev. Dr. Todd exhibited an ancient Irish brooch, be-
longing to the Rev. Richard Butler, of Trim.

Mr. Petrie having been called on for his opinion respect-
ing the style, workmanship, and age of this beautiful relic
of antiquity, stated, that he considered it as the most elegant
specimen of Irish workmanship in silver which he had hi-
therto seen, but believed its age to be not so great as that of
most, or perhaps any, of the brooches in the Museum of the
Academy, or the other collections in Dublin ; its minor orna-
ments being peculiarly those characteristic of the early portion
of the twelfth century, to which period he referred it; though

442

the type of many of its general forms might be found in earlier
examples.

Mr. Petrie then proposed that the thanks of the Academy
should be given to the Rev. Richard Butler, for his kindness
in sending this brooch for the inspection of the Meeting.
The thanks of the Academy were accordingly voted to Mr.
Butler.

Mr. Ingram read the following note on certain Properties
of the Surfaces of the Second Degree.

«¢ Mr. Salmon, Fellow of Trinity College, has given a
mode of generating certain of the surfaces of the second degree,
which is in a remarkable way supplementary to the modular
method of Professor Mac Cullagh, and which has been called,
for distinction’s sake, the umbilicar method. In it the surface
is had as the locus of a point moving so that the square of its:
distance from a fixed point is proportional to the rectangle un-
der its distances from two fixed planes. Out of this generation |
arise many highly interesting properties of the surfaces in
question, to some of which it is the object of the present com-
munication to call the attention of the Academy.

‘¢ 'The fixed point is called the Focus of the surface, the
two fixed planes the Directive Planes, and their line of inter-
section the Directrix.

‘<¢ 1. Two right lines, reciprocal-polars with relation to the
surface, meet a directive plane in two points such that the
vectors drawn to them from the focus are at right angles.

««2. A similar theorem holds for two conjugate tangents at
any point of the surface.

<3. Two right lines, reciprocal-polars with relation to the
surface, seen from the pole of a directive plane, appear to cut
at right angles.

** 4, Let a cone be described, passing through two plane
sections of the surface ; it will intersect a directive plane in a
certain conic : let a second cone be described, passing through

443

this conic, and having its vertex at the focus ; the cyclic planes
of this latter cone will pass respectively through the two right
lines in which the planes of the two sections meet the directive
plane.

«© 5. Hence, through a right line, situated in a directive
plane, draw two planes cutting the surface in two conics; a
cone passing through these two curves intersects that directive
plane in a certain conic : now let acone be described, passing
through this conic, and having its vertex at the focus; this
latter cone will be one of revolution, and its principal plane
will pass through the right line assumed in the directive plane.

«¢ 6, Hence, a cone enveloping the surface intersects a di-
rective plane in a certain conic; a cone passing through this
conic, and having its vertex at the focus, is one of revolution ;
and its principal plane passes through the right line in which
the plane of contact of the enveloping cone meets the direc-
tive plane.

«7, A plane curve is traced on the surface, and through it
a cone is described, having its vertex at the pole of a directive
plane; this cone cuts the directive plane in a certain conic :
now let a second cone be described, passing through this conic,
and having its vertex at the focus; the latter cone is one of re-
volution, and its principal plane passes through the right line
in which the plane of the original curve intersects the directive
plane.

“©. If a cone be described, having its vertex at the focus,
and passing through a plane section of the surface, the cyclic
planes of this cone will pass respectively through the two
right lines in which the plane of the section meets the two
directive planes ; and the directive axis of the cone will there-
fore be the right line drawn from its vertex to the point where
the directrix is cut by the plane of the section.

«9, Hence, any plane passing through the directrix inter-
sects the surface in acurve such that the cone passing through
it, and having its vertex at the focus, is one of revolution ;

444

and the principal plane of that cone passes through the direc-
trix.
‘«‘ The above properties are true for every point on the um-
bilicar focal of the surface, with the directive planes and direc-
trix corresponding to that point. When the two directive planes
coincide, these theorems, suitably modified, reduce to known
properties of the non-modular surfaces of revolution. For that
particular case they have been demonstrated by M. Chasles,
in the Transactions of the Royal Academy of Brussels (Nouw-
veaux Mémoires, tom. v.) In the general shape in which
they are, I believe, now for the first time* given, they appear
to me of sufficient elegance to merit the attention of geome-
ters.”

* «Since the above note was read, my attention has been directed toa paper
‘ On the Focal Properties of Surfaces of the Second Order,’ by Dr. Booth,
in the Philosophical Magazine for December, 1840. In that paper he consi-
ders as analogous to the foci in conic sections four points, which he calls the,
foci of the surface, situated, two by two, on the umbilical diameters, at dis-
tances from the centre equal to each other and to we, where wu is the length of
a—ec?

the umbilical semi-diameter, and «? = (a>b6>c.) The polar planes

az
of these points he terms the ‘ directrix planes’ of the surface, and of these
planes the two which intersect in a directrix of the principal section (a, 5) are
‘ conjugate directrix planes.’ The foci of the same section (a, 5) he calls
the ‘focal centres’ of the surface. These definitions being premised, he
states the theorem, that if from any point of the surface perpendiculars be
let fall on two conjugate directrix planes, the rectangle under those perpen-
diculars is to the square of the distance of the point from the corresponding
focal centre in a constantratio. But he does not observe the fact which gives
the umbilicar generation its chief interest and value, namely, that the ‘focal
centre’ may traverse the focal curve on which it lies, the ‘ directrix planes’
changing along with it, while the generated surface remains unaltered. He
then proceeds to state several properties of his ‘ focal centres’ and ‘ direc-
trix planes,’ and among them I find those which I have marked (1), (2), (8),
and (9). But these theorems are given by him only for his two ‘ focal cen-
tres’ and his four ‘ directrix planes ;’ whereas they are really properties of
every point on the umbilicar focal of the surface, and the directive planes
corresponding to such point.”

445

The following memorandum respecting some ancient In-
scriptions in Scotland, by Mr. John Ramsay, of Heading Hill,
Aberdeen, was read.

«¢ Towards the end of January last, my attention was di-
rected to an inscription on a portion of what was once the cross
of St. Vigean, a parish of Forfarshire, contiguous to that of the
town of Arbroath. Through the medium of a friend, I was
permitted to inspect a handsome lithograph of this interesting
monument of antiquity, executed, I understand, under the
auspices of Patrick Chalmers, Esq., of Auldbar, a gentleman
not less skilled than zealous in archeological pursuits. The
cross referred to is thus mentioned in the Statistical Account
of the Parish of St. Vigean (1845), written by the parochial
clergyman, the Rev. John Muir: ‘ In the churchyard there
formerly stood a large cross over the grave of some person
of eminence, richly carved in hieroglyphical figures of the kind
found on sepulchral stones in some other places of Scotland.
The cross has been long ago demolished, but the stalk re-
mains, with characters at the base hitherto undeciphered.

‘¢ I entirely concur in the opinion of the reverend writer,
that the cross in question was monumental. Such sepulchral
monuments were common about the period to which the cross
of St. Vigean seems to belong. A comparison of some of its
ornaments with those of other crosses of the same kind, sug-
gests that it was the production of the latter part of the tenth
century. The peculiar and beautiful interlacery in the com-
partment immediately above the inscription, and on one of the
faces of the cross, is of kindred character with that which is
exhibited in similar monuments of the same era, sketches of
which are given in Mr. Petrie’s valuable Essay on the Eccle-
siastical Architecture of Ireland. I observe that it is stated, in
the Account of the parish already referred to, that St. Vigean
lived in the latter part of the tenth century ; and that he had
his residence in the neighbourhood of the spot where the cross
formerly stood. ‘ His original chapel and hermitage were at

446

Grange of Conan, where there are a small grove, and founda-
tions of a chapel, and also a most copious fountain, which pre-
serves his name. Three or four acres of land contiguous to
these are by tradition held as belonging to the chapel.’

‘‘ May it not, then, be not unreasonably inferred, that this
monument marked the place of St. Vigean’s sepulture? This,
of course, is merely a conjectural suggestion,—at all events the
cross is evidently the monument of some person of distinction.
Of the personal history of this saint I know nothing ; but I
think it not improbable, that he was of Irish origin or con-
nexion. From the similarity to like monuments in Ireland,
of the cross referred to, and of others in Forfarshire, and the
adjoining districts, not to mention the round towers at Aber-
nethy and Brechin, it is evident that Irish missionaries were
intimately connected with those parts. ‘The inscription, ac-
cording to my copy of it is as follows :

CEROTTEM**
YpEuUORET
CTTEO R «x x x
CORO Bi Gee ainsi get as

‘« The above inscription appears to be partly in the old Irish,
and partly in the Roman character. 1 take the alphabet of
the former from Armstrong’s Gaelic Dictionary. This mixed
character of the inscription is quite common in monuments be-
longing to a period prior to the distinctive fixation of alphabets,
established in later times, particularly after the introduction of
printing. Supposing, as is not improbable, that the aboriginal
alphabets of Britain and Ireland had been lost sight of in the
darkness attendant on social convulsion, so remarkably coin-
cident either with the extermination of the order, or the decay
of the influence, of the pagan priesthood; a renewed acquaint-
ance with the use of letters was only to be derived from éwo
sources, either from the Romans, or from the early Christian
missionaries.

447

‘« Hence, I believe, it comes to pass, that the most ancient
native inscriptions in Britain (see Borlase) are in the Roman
character. Subsequently, some letters were borrowed from the
Greek, by the Christian missionaries, owing to their acquaint-
ance with the original language of the New Testament. In all
writings and inscriptions, then, of the earlier medizval times,
we may naturally expect a mixture of Roman and Greek
characters. Hence, the strong similarity of the old Irish to
the old Anglo-Saxon.

«¢ This premised, I proceed further to observe, that the
inscription above noted seems to be only part of that which
originally belonged to the cross of St.Vigean. I conjecture,
for reasons which will afterwards more clearly appear, that the
first part must have been cut on the top of the cross, above the
interlacery, which is now lost. It was not unusual to divide
such inscriptions into two parts. An instance of such arrange-
ment is to be found in Borlase’s Antiquities of Cornwall,
pp- 399, 400. Further, in monuments of the age to which the
cross of St. Vigean belongs, the beginning of the inscription was
usually prefixed with a small cross, either so (+), or so (®);
but this is wanting in the portion of the inscription referred to.
Taking all these circumstances into account, I venture to re-
store the inscription (for it has evidently suffered) as follows :

Cli-kwO1_G €M 2
YPEUORET
ETTEORPRO
CULELANIMA;

that is, using Roman capitals:
CHROS. TEMPTU
Ss. DEVORET
ET. TE. OR PRO
CU. AN fit.

‘* I do not pretend to give the original letters or contrac-
tions, which time or accident seems to have effaced from the

448

inscription. It is impossible to determine what selection the
stone-cutter may have made in his drafts on the Roman and
Irish alphabets. At all events, he must have so managed
matters, as to confine his work within the prescribed limits.

‘¢ T translate the above as follows :

‘“©¢O! Cross! Time may destroy thee, too! Pray for his
(the person named in the first part of the inscription) soul /’

‘«‘ Now, there is a singularity in this inscription: the first
word (Chros) is Gelic, and the rest are Latin. How may this
be accounted for ? The ancient Geelic term for a cross is cros.
The vocative is formed by aspirating the nominative into
chros. To write the Latin crux with the Jrish character was
impossible. ‘The alphabet has no z, and the sound of this let-
ter is foreign to the Gelic language. Hence, instead of Saze-
nach, we have Sassenach. Thus there was an obvious neces-
sity for using the vocative of the Gelie word, cros.

‘* I conjecture that, as was usual in such cases, the first part
of the inscription contained the name of the person to whose
memory the cross was erected. Thus, the part above deci-
phered would be a very natural sequence. It is marked by
all that touching simplicity which is characteristic of inscrip-
tions on monuments of the same era, noticed by Mr. Petrie,
whose accurate and tasteful researches have thrown so much
light on some of the darkest and most interesting points of

* Gelic antiquities.

‘¢ Of the devices, animals, &c., on the back of the cross, I
shall not here speak, as my present business is with the in-
scriptions. Suffice it to say, that I think I could prove that
some of these devices are borrowed from monuments, still ex-
tant in Scotland, the age of which exceeds that of the cross by
many centuries.

‘“‘ The next inscription which I shall notice is that on an
ancient monument in the Church of Fordun. Fordun is a
parish of Kincardineshire, the county immediately north of
Forfarshire. Kincardineshire is sometimes called the Mearns,

449

and its people, ‘the men of the Mearns.’ In the old Irish
Annals they are called ‘Viri na Moerne. There are many
interesting particulars connected with the parish of Fordun.
John de Fordun, author of the Scotichronicon, was either a
native of it, or resided there, when he wrote his History of
Scotland. It was the native parish of George Wishart the
Scottish martyr; of the eccentric Lord Monboddo; and of
Beattie, author of ‘ the Minstrel.’ Further, it was the locale
of the famous shrine of St. Palladius. The remains of Paldy
Chapel are still standing ; there is still Paldy, or Pady Fair ;
and there is a well in the minister’s garden, called St. Palla-
dius’ Well. Some will have it, that the famous Saint actually
lived, died, and was buried here. I am not sufficiently ac-
quainted with our early ecclesiastical history to give any
opinion on the subject ; but I am disposed to agree with those
who think that Pady Chapel was built, not by the Saint, but
by some of his Irish disciples, who came to this part of Scot-
land, probably with some of his relics. His mission certainly
was to Ireland, ‘ ad Scotos in Christum credentes. The
earlier Christian churches in this quarter were certainly Co-
lumban ; but some may have been of Ninian, or Palladian
origin. Even at the early period referred to, the spirit of ec-
clesiastical rivalry seems to have been at work. At all events
the chapel of St. Palladius was always accounted the anene
church of the Mearns.

‘‘ But to come to the matter in hand: the ancient monument
to which I refer (some account of which was first given by the
late Professor Stuart, of Marischal College, Aberdeen), was
first observed upon taking down the old church of Fordun,
some sixty years ago. ‘ It had been placed horizontally as a
base for the pulpit to rest on, and was considered of so little
consequence, as to be thrown aside for many years into the old
chapel of St. Palladius, hard by.’ This old church of Fordun
was so old, that it was new roofed about 360 years ago. After
lying neglected for a long time, the old stone attracted the

450

attention of the parish minister, who had it cleaned, and a
drawing of it taken. ‘The material is a very coarse free-stone.
The dimensions, five feet one inch in length, by two feet eleven
inches broad, thickness fully four inches. It is carved on one
side only. The emblematical devices are three figures on horse-
back, a greyhound, a wild boar, a serpent, or dragon ; and the
peculiar spectacle device

like that on other old monuments in the north of Scotland.
To these I do not refer at present ; my business being with the
inscription. Professor Stuart makes it probable that this mo-
nument commemorates the assassination of King Kenneth III.,
in the year 994. His Majesty is said, by our historians, to
have been assassinated at the instigation of Finele, “daughter,”
says the Professor, ‘“‘ of Cruchné, Maormor of Angus.” This
should be the Cruithne (Pictish) Maormor of Angus. The
royal residence was at Kincardine. In the neighbourhood are
Strath-Finella and Den-Finella. In this case, history is con-
firmed by tradition and topographical etymology. A drawing
of the fragmentary inscription will be found in the Areheolo-
gia Scotica, vol. ii. p. 315.

‘‘ There has been another line, if not more, above what re-
mains, and I do not pretend to be able to decipher that with
certainty ; but it strikes me that it looks like Kenkardin or
Kinkardin, the name of the royal residence. It is to be ob-
served that the costume of the human figures on this monu-

451

ment is exactly the same as that of the only human figure on
the cross of St. Vigean, belonging, as I conjecture, to the same
period.

“< The next inscription which I shall notice is that on one
old monument which was found some years ago in the parish
of Insch, Aberdeenshire. ‘The dimensions of the stone are
six feet by one foot eight inches. The inscription runs along
the central length of the stone. It is—

ORAGEPR°RHKIARADVLFI? SACE RDOCIS:

This is evidently :
Orate pro Anima Radulphi Sacerdotis.
The characters shew the influence of Anglo-Saxonism at the
period when the monument was executed. There are good
grounds for believing, that it was placed over the grave of
Radulph, Bishop of Aberdeen, who died in 1247.

‘¢ [have been induced to give the above specimens of an-
cient inscriptions in Scotland, in the hope that they may incite
the able and zealous archeologists of Ireland to direct their at-
tention to the subject. There are other inscriptions in this
country of, perhaps, greater interest, to which I forbear to
refer; partly because I confess my entire ignorance of their
nature, and partly because I believe they have already at-
tracted the notice of members of your Academy, from whom,
if from any, the interpretation of those inscriptions may be
expected.

‘‘ Between the antiquities of Ireland, and those of the north
of Scotland, there are many points of interesting connexion.
The aborigines of both countries belonged to the same great
-family of the human race; both remained almost equally in-
tact by the ambition of ancient Rome; neither had to bow the
neck to the yoke of the old Saxons; both were harassed by
the Danes; and while the Picts were compelled, partially,
to succumb to warriors of Irish descent, it was to missionaries

VOL. III. 2a

452

of Irish origin that they owed their first acquaintance with
the Gospel of Peace! In both countries are still to be found
many memorials of aboriginal times, which had once their
resemblances in England, but which have there disappeared
under ‘‘ the tramplings of three conquests,” and the march
of modern improvement. I refer, particularly, to those re-
mote times when Druidism bore its mystic sway. Its usages
yet linger in customs of popular superstition, although obli-
vion has long since fallen on the meaning attached to them by
a crafty, powerful, and domineering hierarchy. Many an age
has passed since its oracles became dumb; but the nomencla-
ture of its religious creed is still employed to express, by the
unwitting Gael of the present day, some of the mysteries of
his purer faith! We have still the mysterious “‘ temple,” with
its massive ‘“ cromlech,” the poetry of the solitary moor, and
seldom-trodden height,—many of which have been protected
by our landed proprietors, with commendable feeling, disre-
garding not the protest against eviction of those adscripta
glebe, and refusing to abandon to

‘ Hands more rude than wintry winds,’

relics which have braved the buffetings of countless storms.”

Mr. Petrie remarked, that he thought the Academy
should feel great pleasure at every effort made by the Scottish
antiquarians to illustrate their antiquities, which were so
intimately connected with those of Ireland; and that they
should be grateful to Mr. Ramsay for communicating to their
Institution his very ingenious attempt to decipher and ex-
plain the remarkable inscription at St. Vigean’s.

Mr. Petrie regretted, however, being obliged to state, that
he could not, by any means, concur either in Mr. Ramsay’s
reading of this inscription, or his conclusions as to its age.
He did not believe that there were any abbreviations of words,
or varieties of language or alphabetic writing, in it, such as

453

Mr. Ramsay supposed ; or that the inscription was in any
way imperfect, or originally connected with another on the
same cross, now destroyed. Mr. Petrie further stated, that,
having been kindly supplied with two rubbings of this in-
scription, one from Mr. Chalmers of Auldbar, through his
friend Mr. Worsaae, and the other from Mr. C. Innes, the
able Secretary to the Royal Scottish Society of Antiquaries,
he had given a good deal of attention to them, and had been
so far successful as to read with certainty nearly one-half of it.
As he still hoped, however, to be able to master the whole,
and to present the results to the Academy, he would, on the
present occasion, content himself with remarking, that the
inscription was unquestionably one connected with the Pictish
history ; and that, as might be expected in a country where
the literature had been, confessedly, entirely in the hands of
Irish ecclesiastics, the letters of which it was composed were
wholly of that description usually called Jrish, though, in
reality, only the corrupt form of the Roman alphabet, general
in Europe during the fifth and some succeeding centuries.
In proof of these conclusions he exhibited a tracing from
the rubbing of the first line of the inscription (of which the
following is a copy), and which plainly gives the name
Drosten.

This, Mr. Petrie remarked, was peculiarly a Pictish name,
and was equally connected with the ecclesiastical as with the
regal history of Scotland. It was a diminutive of the name
Drust, so common in the list of the Pictish Kings, and was
that of a Pictish ecclesiastic who flourished in the sixth century,
and who was spoken of in St. Adamnan’s Life of St. Columba.
Whether, however, the St. Vigean’s monument or cross was
erected to this Drosten, or one of the others of later date re-

454
corded in Pictish and Irish authorities, Mr. Petrie would not
then offer an opinion, though he had no hesitation in stating
that, from the forms of the letters, he had no doubt that the
inscription was of an age some centuries earlier than that
ascribed to it by Mr. Ramsay.

An extract was read from a letter addressed to Sir William
Hamilton by Lieutenant Steevenson, on a mode of ascertaining
the general state of the weather for any spring and summer
from the general state of the preceding winter.

The writer is of opinion that the prevalence of westerly
winds and rain, during our wet summers, arises from the pre-
sence in the Atlantic Ocean of a greater quantity than usual of
ice, brought southwards by currents from the Arctic regions.

Robert Ball, Esq., Treasurer, read an abstract of the Ac-
counts of the Academy, for the Year ending 31st of March,
1847, which was ordered to be printed in the Proceedings.
(See Appendix, No. X.)

DONATIONS.

Comptes rendus Hebdomadaires des Séances del Académie
des Sciences. From 8 Feb. to 8 March, 1847. Presented by
the Academy.

Philosophical Transactions of the Royal Society of Lon-
don, for 1846. Part IV.

Proceedings of the Royal Society (1846). No. LX VI.

List of Members of the Royal Society. Nov. 30, 1846.
Presented by the Society.

Astronomical Observations made at the U. §. Naval Ob- -

servatory, Washington, during the Year 1845. By M. F.
Maury, Lieut. U. S. Navy. Presented by the Author.

i

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 66.

May 10th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Edward Barnes, Esq., and Henry Freke, Esq., were
elected Members of the Academy.

The Rev. Charles Graves read the following note on the
development of a function in factorials of the variable upon
which it depends.

The process of integration for factorials being simpler than
that for powers, in the inverse calculus of finite differences,
we sometimes have occasion to resolve a proposed function of
zx into a series of the form

Ag + A, & + Aga (a—1) +43” (a—1) (vx—2) 4 &e.;
and we may readily determine the coefficients Ay, Aj, Ag, A3)
&c., by making x successively equal to 0, 1, 2,3, &c. In
this way Sir John Herschel, in his Collection of Examples of
the Applications of the Calculus of finite Differences, has
solved the more general problem of developing a function F (2)
in a series of factorial terms of the form

Ay + A) (t—fi) + Ao (e—fi) (@ — ft) + &e.
F (x) being any function whatever of a, and fi, fi, &c., parti-
VOL. III. Aer DR

456

cular values of any other function f(x), corresponding to the
values 1, 2, &c., of x. The two methods of developing F (x)
in a series of factorials, which are here noticed, seem to have ad-
vantages over the method of indeterminate coefficients, in being
more simple and direct, andin manifesting more clearly the law
which the coefficients Ao, A1, Ao, Az) &¢., follow. They furnish,
at the same time, interesting examples of the use of separating
symbols of operations from their operands ; and it is for this
latter reason, rather than on account of any novelty in the re-
sults arrived at, that they are now submitted to the notice of
Members of the Academy.

I. Employing w* to denote the ouanen which changes
F (x) into F (+1) we are entitled to write

F(a +n) = wu" F (#) and F(n) = wu" F (0).
But wis known to be equivalent to 1+ A; we may there-
fore write
F(n)= (1 + A)"F(0);
or, with the right-hand member of the equation developed,

AF ©,

F(n) = F(o) + —— eal n(n—1) + &e. (1)

A particular case of this theorem is commonly given in
treatises on the calculus of finite differences, viz. :

n, 2 yn
oa oe + TF a (e-l) + &e.

And indeed the theorem itself may be derived from the
fundamental expression for u,4n by making x = 0.

* Arbogast, in his Calcul des Derivations, has appropriated the letter £
to this use, as being the initial of the word Etat; and in so doing he has been
followed by recent writers. But against this usage it may be objected that
the symbol £ is now devoted to a different office in the theory of elliptic func-
tions. And, on the other hand, there seems to be a peculiar fitness in denot-

ing by wu that operation which changes wu, into u eau

457

Il. If we take the differential coefficient of 2, and mul-
tiply it by x, the result will be 2” 2; that is to say,

“n= xrx— x";
cE

and as a consequence of this equation, we shall likewise have,

Bw (1) (22) a (2)

In the right-hand member of this equation, let us put

1+ 2—1 in place of x; and then expand by the binomial
theorem ; the result will be

z d d : 2
w=(a) = d : a (eZ )e—D (v= )(@—1) cc 1)
+ va) % i a cl

+ &e. (3)
The coefficient of n (n—1)...(n—m+1) in this deve-
lopment will be

—

1
12 a yone(n — ma"—'F(m—1)+ zl — 0" F(m— 2) — ae.

and, if we now suppose a = |, we shall have the development
of F (7) in the desired form ; the coefficient of the factorial
n(n—l)..... (n—m-+ 1) being

m Le

1 ian Ot awe ar
as (m) — m ¥ (am —1) + 12 F (m -2) &e.}

Comparing the two expressions (1) and (3) we find, as we
ought to do,

—1
A” ¥F (0) = ¥(m) —m x (m—1) + 2S

F (m—2)— &e.,
a formula which might be obtained directly by making 2=0
in the fundamental equation of the calculus of finite differences,
m (m —1)

A" uy, = Urtm— MUytm-1 ofé 1.2

Uxtm—2 &e.

458

By the aid of the symbol (25) we may obtain another

interesting development. In virtue of the equation (2) we
have

ee
e “gn = em a = (ea).
It is plain, then, that the symbol
d
hr—

e =

operates on any function of x by changing x into e"a; that
is to say,

haz
F(e'a) =e “ F(a);

whence, developing the right hand member, we get

d 2
F,(e"2) = ot, Ca) 76

As Taylor’s theorem gives the altered state of F (x), after
x has received an increment h, so the theorem just announced
exhibits the new value of F (x) after x has been multiplied by
a number whose logarithm is h ; the series in both cases being
arranged according to ascending powers of h.

In executing the operations indicated in the development

- aNe.. :
(4) it must be remembered that (o<) is not. equiieat to

ait dvigd
oe —; but toe ie ae and so on for the other powers of the

symbol. Neglecting to make this distinction we should get the
development of r («+ xh) instead of r (e'x). The actual re-

lation Wee the symbols a” = and oo i is obtained immedi-

ately from the equation (2) which gives us

ie = (a lege—!) oe eZ
eras oa eke abia Goc ra —n+1).

459

Sir John Herschel has given the following theorem, which
enables us to develope F (e) in a series of ascending powers
of A when such a development is possible :—

I i?
F(e) =r (I+7r (1+ Ao+5r(I + A)o? + &e.

Comparing this with the one given above, we obtain the
following theorem :

Gal F(x) = F[a(1+A)]o’,

by the help of which we arrive at a still more general one,

f(eG) © =e + 17)

Sir William R. Hamilton wished to be allowed to remind
the Academy that he had communicated to them, in 1831,
another extension of Herschel’s Theorem, which was pub-
lished in the seventeenth volume of the Transactions (page
236), namely, the following :

V SEO) =SU +A) V' (HO)?

where the accents in the first member might have been omitted,
and where vy’ denoted any combination of differencings and dif-
ferentiatings, performed with respect to o’, and generally any
operation with respect to that accented zero, of which the sym-
bol might indifferently follow or precede f(1 + A), as a sym-
bolic factor. By making ~ (0’) =<”, and y’ = v’, where
pi = the theorem of Herschel is obtained. A much less
general formula was cited as ** Hamilton’s theorem,” in the
last Number of the Cambridge and Dublin Mathematical
Journal, namely, the following :

S (2) =f + A)2;
which had, however, been also given in the same short paper
of 1831.

_

460

The Rev. Charles Graves exhibited an ancient gold orna-
ment, belonging to the Earl of Leitrim, of which the follow-
ing description is given in Vallancey’s Collectanea, Vol. V.,
p- 90:

‘‘ Mr. Burton Conyngham has now in his possession one of
those double cupped patera, described and engraved in the 13th
Number of the Collectanea. The instrument is of gold, was found
in the county of Mayo, and weighs about six guineas. On the out-
side of one cup is .an Ogham inscription; on the outside of the
other an inscription in the Pheenician or Estrangelo character.—
See Pl. I1I.,—where the cups are reversed to show the inscription.
The Pheenician word is composed of the din, Lamed, Tau, Aleph,
i.e. NV9Y, i.e. Alta or Olia, signifying an holocaust. This con-
firms my former opinion, that these instruments were used in sacri-
fices. ‘The Ogham characters are UOSER, Uoser, Osir, or Usar,
the Sun, the principal deity of the pagan Irish. The names desar,
Aosar, frequently occur in ancient Irish MSS., which are always
translated God.”

Mr. Graves stated that, whilst he recognised the gold
ornament itself as being a genuine and a very fine specimen
of the ancient manillz,* of which many are preserved in the
Museum of the Academy, he was forced, after a careful exami-
nation of it, to pronounce the inscription to be a forgery of com-
paratively recent date. For this conclusion he assigned the
following reasons :

Faint tracings of all the characters scratched upon the sur-
face, as if to serve as a pattern to be copied by the engraver,
are still quite visible. There can hardly be a doubt but that
casual attrition, and the action of the atmosphere or earth for
a thousand years or more, would have effaced such marks.

The inscribed characters have a sharpness which is not
to be seen in ancient work, even though executed in gold. All
the original devices which appear on ancient gold articles

* See Sir William Betham’s papers on Ring Money, in the Transactions
of the Academy, vol. xvii.

461

possess a peculiar mellowness, from the action of the causes
just alluded to.

These characters, moreover, have plainly been cut with
a graver, such as is employed at the present day. But no
traces appear, on genuine antique Irish ornaments, of the
use of such an instrument. The lines and patterns on them
seem to have been laboriously scratched with a point rather
than cut in. The conclusiveness of these reasons is main-
tained by the judgment of Mr. West, the eminent jeweller, to
whom Mr. Graves applied for his opinion on the subject. So
many valuable relics of antiquity have passed through his
hands, at different times, that his opinion on a point of this
kind ought to be nearly decisive.

Mr. Graves further remarked, that the characters said by
Vallancey to be ‘* Phoenician or Estrangelo,” are neither the
one nor the other; and, what is more, in the scanty remains of
Pheenician literature, which have been collected by Gesenius
and Hammaker, we meet with no such word as Olta, meaning
a holocaust. As for the word Aesar, which Vallancey pro-
fesses to find, though somewhat deformed, in the Ogham in-
scription, Mr. Graves asserts that it does not frequently occur
in ancient Irish MSS. ; on the contrary, it is so rare that, with
the aid of the most accomplished Irish scholars, Mr. Graves
has not yet succeeded in finding a single instance of its use,
except as it occurs in O’ Reilly’s and Shaw’s Dictionaries. It
certainly is an Etruscan word, meaning God, and it may have
found its way into Irish glossaries, though not belonging to
the Irish language.

In order to show how unsafe a guide Vallancey is in what
relates to Ogham writing, or, it might be added, in any mat-
ter of Irish archeology or philology, Mr. Graves referred to
a passage which occurs in the tract on Oghams, preserved in
the Book of Ballymote. This passage stands thus in the
original (Book of Ballymote, f. 168) :

462

“(zain ogaim Ozma. Ma- ‘The father of Ogham was
tainogaim lam no pcianOgma. Ogma; the mother of Ogham was
Ipé po imoppo m céona m po _ the hand or knife of Ogma. This
pepibad tpi ogaim .1.” &e. indeed was the first thing that

was written through Ogham,
viz.,” &c. ’

The meaning, as is quite plain from the context, being,
that Ogma was the inventor of the Ogham character, and
- that the instrument with which he first executed it was his
own hand or knife. Vallancey, in his Essay on the Ogham
Writing of the Ancient Irish (Collectanea, vol. v. p. 79),
gives the following reading and version of the same words :

** Atair Ogaim, Ogma ; ma- ‘“‘ The father of Ogum was
thar Ogaim, Lam, no Scian Ogma, his mother’s name was
Ogma. Is sé Séminceadna: Lam, or Scian Ogma (the help-
sé ro scribtar tri Ogam,” &c. mate of Ogam). The same is

called S6m: he wrote his own
name in three Oghams,” &c.

Here it will be seen that Vallancey has introduced two
imaginary personages, Som and Lam, neither of whom were
thought of by the Irish writer; and he expends a vast quan-
tity of irrelevant erudition in making out this Som to bea

Theban (Egyptian) Hercules, and Lam to be the daughter of —

Belus and Libya. ‘* This helpmate” [of Ogam] he adds, “‘ was
named Lam, or Lamia, which signifies a horrid, dreadful mon-
ster; hence must have arisen the Grecian story of Hercules
having begotten Scythes, the progenitor of the Seythians, on
the body of a monster, half woman, half serpent. A fable
which gained ground wherever the Scythians went,—from
Seythia to Tartary, China, and Japan.”

It ought to be added that, by tampering with two other
passages in a like way, Vallancey has elsewhere educed the
name of his Theban Som (Collectanea, vol. v. pp. 63, 69).

Mr. Graves referred to another instance in which, by a

463

perverse ingenuity, additional darkness has been thrown upon
the obscure subject of Ogham writing.

Mr. Beauford contributed to the first volume of the Tran-
sactions of the Academy a paper in which he describes twelve
coins, on which he thinks he finds legends, in Ogham, Roman,
and Runic characters intermixed ; and he gives readings of
these, exhibiting various Irish names of persons and places.*
Any person, the least conversant with numismatics, will at once
recognise these coins as being all of them Hiberno-Danish.
By the kindness of Dr. Aquilla Smith, Mr. Graves was enabled
to exhibit to the Academy one of the actual coins figured by
Mr. Beauford, viz., that marked No.7 in the plate illustrating
his paper.

This coin, now in Dr. Smith’s collection, is appropriated
by Mr. Lindsay, who has studied this class of coins with most
attention, to Sihtric 1V., King of Dublin, A. D.1034, It
may, however, belong to Sihtric III., A. D. 989.

Mr. Beauford’s description of the coin is as follows :—

‘¢ Round the head, on the obverse, is the following inscription
in Latin, Runic, and Ogham Croabh characters :

u mearc readon
or,
U meare re a don, for O More Re I dun.

On the reverse, in one of the quarters of the cross, is a hand, with
the following inscription in Latin, Runic, and Ogham Croabh cha-
racters :
mac ghealach ofutla
or,

Mae Ghealach O Futla, for Magh Ghealach O Fodhla.”

Subjoined is a figure of the coin in question, executed from

* Still more absurd misrepresentations respecting Ogham characters and
writing may be seen in a paper by the same author, called Druidism Revived,
which is inserted in the second volume of Vallancey’s Collectanea.

VOL. Ill. 2s

464

a drawing by Dr. Smith, and also a fac simile of the (enlarged)
figure given in Mr. Beauford’s plate:

Mr. Graves concluded by apologising for having occupied
the time of the Academy in the discussion of matters of so little
intrinsic importance ; but pleaded the necessity of breaking
down the remnant of authority which still gives to the asser-
tions of Vallancey and his adherents the power of leading
students in Irish history and antiquities astray.

Practices like those now commented on once brought con-
tempt upon Irish archeology ; and philologists for a long while
shrank from entering upon the rich field of inquiry which the
study of the Celtic language and literature presents, through
fear of sharing in the ill repute of former labourers. But these
feelings are now happily dying away ; and it is to be hoped
that the Academy, encouraging such pursuits, when carried on
in a Scientific spirit, and vigilantly checking all attempts to
mislead, will have the satisfaction of seeing permanently estab-
lished amongst its members a sound and numerous school of
antiquaries and scholars, really conversant with the language
and antiquities of this country, and therefore able successfully
to prosecute that work of illustrating its history, which a few,
in recent times, have so well begun.

465

Sir William Betham exhibited two specimens of gold ring
money, found at Chiusi and Perugia, in Italy. He also pre-
sented to the Academy an ancient brass basin, found in the
King’s County ; and two antique metallic mirrors, found in

Italy.

Sir William R. Hamilton stated and illustrated a theorem
of anthodographic (or anthodic) isochronism, namely, that if
two circular anthodes, having a common chord, which passes
through or tends towards a common centre of force, be both
cut perpendicularly by any third circle, the times of anthodi-
cally describing the intercepted arcs will be equal :—the an-
thode of a planet being the circular locus of the extremities of
its vectors of slowness, or of straight lines representing, in
length and in direction, the reciprocals of its velocities, and
drawn from a common origin.

This theorem is intimately connected with the analogous
theorem respecting hodographic isochronism (or synchronism),
which was communicated to the Academy by Si» William
Hamilton, in a note read at the Meeting in last March. He
had been led to perceive that former theorem by combining
the principles of his first paper on a General Method in Dy-
namics, published in the second part of the Philosophical
Transactions for 1834, with those of his communication of last
December, since published in the Proceedings of the Aca-
demy, respecting the Law of the Circular Hodograph. This
-Hodograph was, for a planet or comet, the circular locus of
the extremities of its vectors of velocity, as the Anthode is the
locus of the extremities of the vectors of slowness; so that the
rectangular coordinates of the Hodograph are a’, y/’, 2’, if

dx , dy Lynne ds
hae apie. owes

=

466
while those of the Anthode may be denoted as follows :
a= ua y = — vy’, z, = — 072;
where v? = a’? + y/?4 2”",

He had effected the passage from the theorem respecting
hodographic to that respecting anthodic isochronism, by the
help of his calculus of quaternions; but had since been able
to prove both theorems by means of certain elementary proper-
ties of the circle.

For a hyperbolic comet, the Anthode is a circular are,
convex to the sun; for a parabolic comet, the Anthode is a
straight line. And for comets of this latter class the theorem
of isochronism takes this curiously simple form: ‘* Any two
diameters of any one circle (or sphere) in space, are anthodi-
cally described in equal times, with reference to any one point,
regarded as acommon centre of force.” By this last theorem, -
the general problem of determining the time of orbital descrip-
tion of a finite arc of a parabola, is reduced to that of determin-
ing the time of anthodical description of a finite straight line
directed fo the sun; and thus it is found that ‘* the interval
of time between any two positions of a parabolic comet, divi-
ded by the mass of the sun, is equal to the sixth part of the
difference of the cubes of the sum and difference of the diago-
nals of the parallelogram, constructed with the initial and final
vectors of slowness, as two adjacent sides.” Another very
simple expression for the time of description of a parabolic
are, to which Sir William Hamilton is conducted by his own
method, but which he sees to admit of easy proof from known
principles (though he does not remember meeting the expres-
sion itself), is given by the following formula:

é= 37 tan (0 —tan— J tan} 6);
where 6 is the trué anomaly, and ¢ is the time from perihelion,
while rT is the time of describing the first quadrant of true

anomaly.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846-7. No. 67.

May 24th, 1847.

REV.WILLIAM HAMILTON DRUMMOND, D.D.,
Librarian, in the Chair.

M. Donovan, Esq., continued the reading of his paper on
the Nature of the Agency which produces the Effects called
Galvanic, Electro-magnetic, Magneto-electric, and Thermo-
electric.

The next. subject to which Mr. Donovan called the atten-
tion of the Academy was the instantaneous charge which a
Leyden battery receives by a momentary contact with an ex-
tensive voltaic series. This has been always adduced as an
argument in support of the affirmed enormous quantity of
electricity which constitutes the voltaic current. Van Marum
charged a Leyden battery of twenty-five jars by a momentary
connexion with a pile consisting of silver coins and zine discs,
one inch and a half in diameter. The battery and pile were
thus charged to the same intensity, so feebly, however, as to
produce divergence in a gold leaf electrometer to the extent
of five-eighths of an inch; but the shock from the battery was
only equivalent to half that of the pile. Facts and calcula-
tions were adduced to show that the charge of electricity in
this Leyden battery, when thus charged, could not have ex-
ceeded the quantity of two or three one-inch sparks. Sir H.

VOL. III. 2T

468

Davy charged a Leyden battery with 2000 pairs of zine and
copper plates, each plate exposing thirty-two superficial inches
of metal to the exciting liquid ; the total surface being 128,000
square inches. On making the proper connexions, with the
Leyden battery, ‘‘ either a shock or a spark could be per-
ceived.” Thus the shock was barely perceptible ; and to this
Mr. Donovan added his own testimony of the shock from a
Leyden battery, charged by 1000 pairs of plates, which he re-
presented as exceedingly feeble.

In support of the inference drawn of the trifling nature of
the shock, and the inconsiderable quantity of electricity which
a Leyden battery is capable of communicating, when charged
by a voltaic series, Mr. Donovan detailed an experiment made
by Professor E. Davy and himself, in which twenty Wedg-
wood ware troughs, each containing ten cells, were employed,
with a total number of 200 pairs of plates excited by dilute
acids. When charcoal points, fixed to the polar wires, were
brought into contact, an instantaneous burst of light, of
dazzling splendour, announced that the series was in high ac-
tion. On attempting to charge a Leyden battery of twelve or
thirteen square feet of coated surface with this voltaic series,
neither shock nor spark could be obtained. Yet it was proved
that the charge communicated to the Leyden battery by three
turns of a very small electric machine was sufficient to enable
the battery to give a spark visible in day-light, the three turns
producing three weak sparks of one inch in length. Six turns
of the cylinder, that is six one-inch sparks, enabled the Ley-
den battery to give a sensible shock. This failure was sup-
posed to be explicable by the small size of the Leyden battery
compared with that of Van Marum, the ratio being as 123 to
1372.

So far as all the experiments, whether these last, or those
of Van Marum or Davy, are concerned, there seems to be no
evidence of great quantity of electricity in the voltaic series.
But, even if there were, it was stated that none of the fore-

469

going cases are applicable to the doctrine, and that no sup-
port can be derived from them. A series of arguments was
then made use of, which cannot be abridged, to prove that a
Leyden battery has never yet been really charged by the vol-
taic current ; that the circumstances under which the charge
has been supposed to have been communicated are such as
to render the thing impossible ; and that hence the so-called
charge of a Leyden battery by a voltaic current does not prove
the circulation of an enormous quantity of electricity in a vol-
taic series, but-rather shows that the agent which gives the
voltaic shock is not the same as that which acts in the pheno-
mena of ordinary electricity. The shock of the coil apparatus
was adduced as an evidence to the same effect; and, finally,
it was observed that the sensation which constitutes the shock.
ought not to be received as evidence on either side of the ques-
tion, since sensations depend more on the organ acted on than
on the agent; and in support of this opinion a number of in-
stances were adduced.

Whatever difference of opinion may exist relative to the
nature of positive and negative electricity, it appears to be a
position universally agreed to, that, when equal to each other,
and at liberty to act, they mutually neutralize and destroy
each other’s properties ; all symptoms of both disappear; a
condition of absolute quiescence results; that of equilibrium
is induced ; and this state manifests no electrical properties.
The poles ofa voltaic battery, being in the positive and negative
states, conform to the general law: when unconnected, they
manifest their electrical condition ; but as soon as they are con-
nected by a good conductor, all symptoms of electricity vanish.
This has been proved in a remarkable manner by Mr. Gas-
siott with a water battery consisting of 3520 pairs, exhibiting
great power over even a distant gold-leaf electrometer while
the poles were unconnected, but losing all energy when they
were united.

Yet it is at the moment when the poles are united, and

272

470

when all symptoms of electricity vanish, that the connecting
wire of the voltaic series becomes magnetic. Is there not in
this fact something repugnant to the idea that electricity is
the agent. To admit that the two states of electricity, after
having neutralized and virtually annihilated each other’s pro-
perties, should at that moment be more active in calling into
operation the magnetic power, would be to declare that in the
natural state of the equilibrium of the electric fluid the mag-
netic influence must be perpetually active ; that is, that all the
bodies in nature are magnets. ‘This objection applies to the
opinion of those who maintain that electricity, considered as
a simple element, is the cause of, or is identical with, or ex-
cites magnetism; but not, as Mr. Donovan conceived, to his
own view, stated in the beginning of this Essay, relative to
the supposed compound nature of the electric fluid.

The boldest of all the hypotheses of magnetism, and the
most ingeniously supported, was described to be that of Am-
pere, who denies the existence of any magnetic agent called
into action by electricity, but affirms the identity of both
powers. Some experiments were described which cannot be
here detailed, the object of which was to show that magnet-
ism and electricity observe different laws, and that one my
exist when the other is not present.

A word has of late years come into common use, which,
while it explains nothing, conceals the solecism contained in
the notion of neutralized electricities retaining their energies :
the new term is the ‘“‘ current.” The counter-current is thus
kept out of view, which is the grand difficulty, because it must
antagonize and destroy the current. This new current, con-
sisting of both electricities, instead of being powerless, as was
formerly the nature of such, is now said to be capable of ex-
erting peculiar power ; but it no longer harmonizes with those
facts from which our knowledge of the true current was derived.
Faraday’s views of the current were examined, and the con-
clusion drawn that they are inconsistent with each other, and

ee

471

with facts. Mr. Donovan terminated this part of the inquiry
with the following observations :

‘* T have thus freely expressed my opinions relative to the
eurrent, fearing that the old legitimate sense has been lost
sight of; that many have understood it to mean something
more than is warranted by proved properties; and that the
universally admitted identity of the agent in electric and vol-
taic phenomena has emboldened philosophers to attribute qua-
lities to the former which belong only to the latter. On the
whole, I conceive that the current, in its modern acceptation,
instead of explaining voltaic phenomena, is calculated to
mislead ; and that it is of no avail in obviating the difficulties
which beset the alleged simultaneous operations of the two
states of electricity, when present in a state of commixture,
and which, instead of being at that moment in their condition
of greatest energy, should be destitute of all sensible proper-
ties.”

Sir Robert Kane read a communication from the Rey. Dr.
Callan, Professor of Natural Philosophy in the College at
Maynooth, on some improvements in the construction and use
of the Galvanic Battery.

<< Some time ago, whilst I was reflecting on the principle
of action of Grove’s and Bunsen’s batteries, it occurred to me
that lead might be substituted for the platina of Grove’s and
the carbon of Bunsen’s. I put into the porous cell of a Grove’s
battery a plate of lead about one-sixteenth of an inch thick,
two inches broad, and six inches long. I found that the voltaic
current produced by the lead, excited by a mixture of concen-
trated nitric and sulphuric acid, was very powerful. I after-
wards compared the power of the leaden battery with that of
a Grove’s battery of the same size, by sending at the same
time, but in opposite directions, through the helix of a galva-
nometer, the current produced by the two batteries. Both
batteries were charged with the same acids. The voltaic eur-

472

rent from the platina battery destroyed the deflection of the
needle produced by the current from the leaden one, and caused
an opposite deflection, which indicated that the former current
was nearly twice as strong as the latter. ‘The two batteries
were allowed to work for three hours anda half. At the end
of that time the current from the lead was more than twice as
strong as the current from the platina. ‘The quantity of lead
dissolved during these three hours and a half was very small.

‘¢ It struck me that, by diminishing the action of the acids
on the lead, I might increase the power of the battery. I there-
fore covered a plate of lead with gold-leaf, and coated another
of the same size with chloride of gold, in the same way in
which sheet silver is platinized for Smee’s battery. ‘These
two, and a platina plate of the same size, were put successively
into a porous cell of a Grove’s battery, and the voltaic cur-
rent was sent through the helix of our large electro-magnet,
in which the iron bar is about thirteen feet long, and two and
a half inches thick, the copper wire is about 500 feet long, and
one-sixth of an inch in diameter. The magnetic power given
to the electro-magnet by the leaden plate coated with chloride
of gold, appeared to be fully equal to that produced by the pla-
tina plate : the magnetic effect of the current from the leaden
plate covered with gold-leaf was not so great. Platinized lead
produced as strong a current as platina, or as lead coated with
chloride of gold.

‘On last Friday week, a leaden and platina battery of equal
size were left working for four hours and a half. At the end
of that time the plate of lead acted fully as well as the platina
plate. When the nitric acid was so much exhausted that the
lead was barely capable of magnetizing the large electro-
magnet, so as to sustain a certain weight, the leaden plate was
taken out of the porous cell, and a platina plate of the same
size put in its place. The platina plate was not able to make

the electro-magnet sustain the weight which the lead caused
it to sustain,

473

‘«* When a zine plate is put into the porous cell, and aleaden
one coated with gold powder is placed on each side of it, in
the exterior cell, the effect of the voltaic current on the elec-
tro-magnet appears to be greater than that which is produced
by a single platina and double zine. The voltaic current from
a leaden or platina battery is about fifteen times as great as
that of a Wollaston battery of the same size. In all the ex-
periments which I have described, the lead and platina plates
were about two inches by six. The lead and platina were ex-
cited by a mixture of concentrated nitric and sulphuric acid,
and the zine by diluted sulphuric acid. The acids employed
in some of the experiments had been previously used.

«¢ When a platinized or gilded leaden plate is taken out of
the cell, and afterwards immersed in the acid, it does not pro-
duce its full effect until it has acted for about a minute. The
lead plate, after being used for a long time, requires to be again
coated with platina or gold powder.

‘* Seeing that the concentrated acids, by dissolving a small
quantity of the lead, gradually removed the powder of gold or
of platina, and that the nitric acid was very expensive, I en-
deavoured to find a cheap substitute for it, which would not
act on the lead. The first that occurred to me was common
nitre, I dissolved about the eighth of an ounce of it: in sul-
phurie acid, which I diluted with about an equal bulk of water.
I poured the mixture into a porous cell of a Grove’s battery ;
after putting into the cell a platina plate, I sent the current
from the battery through the helix of the large electro-magnet.
The magnetic power given to the electro-magnet appeared to
be about equal to that which the same battery produced when
the platina was excited by a mixture of equal parts of concen-
trated nitric and sulphuric acid. The platina plate was taken
out of the cell, anda platinized leaden one of the same size put
in its stead. ‘The magnetic power given to the electro-magnet
by this battery was greater than that which was given to it by
the platina battery when the platina was excited either by the

474
concentrated acids, or by the solution of nitre. The battery
was kept working for nearly an hour. During that time there
was very little diminution of its power, and apparently no ac-
tion on the lead or platina powder.

‘* T afterwards tried the power of the leaden battery when
the lead was excited first by the nitre dissolved in water with-
out acid, and then by the diluted sulphuric acid without nitre.
The voltaic current was feeble in both cases. When a few
crystals of nitre were put into the cell containing the diluted
sulphuric acid, the power of the battery increased as the nitre
was dissolved. The power, then, must be ascribed to both:
to the nitre and sulphuric acid.

‘* T have compared the power of platinized or gilded lead,
excited by dilute sulphuric acid, with that of platinized silver,
and have found the former fully equal to, and as constant as
the latter.

‘* From the experiments which have been described, I in-
fer, first, that a battery equal in power to that of Professor
Grove may be made by exciting platina with a solution of
nitre in dilute sulphuric acid, or by exciting gilded or plati-
nized lead with concentrated nitro-sulphuric acid, or with
common nitre dissolved in sulphuric acid diluted with about
an equal bulk of water ; secondly, that platinized or gilded lead
may be substituted for platinized silver in Smee’s battery.

** The advantages of what I may call the nitre platina .

battery over Professor Grove’s nitric acid battery, are, first;
that the expense of the nitre necessary for working the former
for a given time, is only about the thirtieth part of the cost of
the nitric acid required to work the latter: the diminution of
expense in working the voltaic battery will contribute very
much to make electro-magnetism a more economical prime
mover than steam ; secondly, that from the nitre battery there
are no noxious or disagreeable fumes.

“« The advantages of the nitre leaden battery over Pro-
fessor Grove’s platina battery, are, first, that the former is

pai ee core

475

very cheap compared with the latter: a plate of platinized or
gilded lead, one foot square, may be made for a shilling, but
a platina plate of the same size will cost nearly three pounds;
secondly, the expense of working the former for any time is
much less than the expense of working the latter for the same
time ; thirdly, the nitre leaden battery does not emit fumes of
nitrous gas.

‘<¢ The leaden battery, when charged with nitro-sulphuric
acid, appears not to exhaust the nitric acid so rapidly as the
platina battery ; probably, a good deal of the hydrogen, which
would otherwise unite with the oxygen of the nitric acid, is
dissipated by the gold or platina powder on the surface of the
lead,

«<The advantage of the platinized or gilded leaden battery
over Smee’s battery, is, that platinized or gilded lead costs far
less than platinized silver. A plate of the former, six inches
square, will not cost more than three-pence, whilst a plate of
the latter of the same size, will cost about three shillings.

‘‘ 1 shall now mention a few more experiments which I have
made with the leaden and platina batteries. I compared their
power in magnetizing our large electro-magnet, and in pro-
ducing heat. The magnetic power and heat produced by the
platina, excited by concentrated nitric and sulphuric acid, was
equal to that produced by the platinized lead excited by a
mixture of nitre and sulphuric acid diluted with an equal bulk
of water. Each of the batteries fused the thinner of the two
wires which I enclose. In each battery there was but a sin-
gle voltaic circle. The platina and leaden plates contained
each about ten square inches; they were about five inches
_long and two broad. Neither of these batteries was able to
fuse the thick wire; but when about a tea-spoonful of nitric
acid was poured. into the cell containing the leaden plate, and
the current sent through the thick wire, it was fused. The
platina battery only raised the thick wire to a white heat.
Hence, I infer that platinized lead, excited by a mixture of

476

dilute nitro-sulphuric acid and nitre, produces a more powerful
voltaic current than platina does when excited by nitric and
sulphuric acid. In consequence of the small quantity of acid
contained in the lead cell, its power declined sooner than that
of the platina. From the results of several experiments made
with the platina and lead batteries, I have come to the con-
clusion that the expense of doing a given amount of work by
the former, excited by nitric and sulphuric acid, would be
about three times as great as if the work were done by the
latter, excited by a mixture of nitre and sulphuric acid. I have
tried a mixture containing one part of sulphuric acid and three
parts of water, in which a little sulphate of soda and nitre was
dissolved. When the platinized lead was excited by this mix-
ture, the power of the battery was very great, but not so great
as when the mixture contained as much sulphuric acid as
water. I have not as yet tried any other sulphate as a sub-
stitute for the sulphuric acid. When the platinized or gilded
lead is taken out of the cell, it should be rinsed in water, and
dipped into a weak solution of chloride of gold or platina. By
this means, and by amalgamating the lead plates with mer-
cury, before they are gilded or platinized, the platina or gold
powder may be kept on them for a long time.

‘‘’ The reason why the platinized or gilded lead produces so
powerful a voltaic current is, that the acting metals are not lead
and zine, but platina or gold powder and zinc. It appears to
me that the current produced by zine and platina, or gold
powder, is more powerful than that which is produced by zine
and platina, or gold. Perhaps by depositing on lead a powder
of some of the metals, such as tungsten, arsenic, &c., which
are more negative, compared with zinc, than platina or gold
is, a battery may be yet made which will be more powerful
than the platina or platinized lead battery. I have tried an-
timony, but it did not answer.”

47

The Rev. Dr. Todd gave an account of the formation of
the following Catalogue, by Mr. Bindon, of MSS. in the
Irish, English, French, and Latin languages, forming part of
the Burgundian Library at Brussels, and serving as materials
for Irish history.

The first volume having reference to Ireland, which will
be found in the ‘* Inventaire’* of this celebrated collection,
is numbered 471. This MS. isa large vellumf folio in the Latin
language, consisting of 205 leaves; it is entitled, ‘* Dialogus
Richardi Episcopi Armacanit contra Errores Armenorum.”
The initial letter (B) is about two inches in length, and beau-
tifully illuminated in purple and gold ; the initials commencing
paragraphs are also ornamented, but they are small. At the
conclusion of the text and the commencement of the index, or
rather table of contents, which occupies six folios, there is a
short note, stating that the MS. was finished upon the
day of November, A. D. 1410. At the end of this table of
contents there is another short note also, which is as follows :
« Liber Mésterii sii Pauli i Zonia seu Rubeevallis.” ‘This
note, as well as the other alluded to, are in the same hand as
the text. The monastery spoken of was that of the “* Red

* The ‘‘Inventaire” is the first volume of the printed catalogue. In it
the MSS. are enumerated without reference to subject ; the second volume,
or ‘* Repertoire.” is a ‘* Catalogue Methodique.”

+ All the MSS are upon paper, except when the contrary is stated.

} Richard Fitzrauph or Fitzralph. This individual was one of the most
celebrated ecclesiastics of his age. He is said to have been born at Dundalk,
and was advanced to the see of Armagh, A. D. 1347, by Clement VI. He
died at Avignon in 1360; and ten years afterwards his body was removed

_ to the place of his birth, by Stephen de Valle, Bishop of Meath, and a mo-
nument raised to his memory, which was remaining in 1624. This Prelate
is said to have been the first who possessed an Irish translation of the New
Testament made by himself. His canonization was proposed, but never
effected. Some of his works, in manuscript, will be found in Trinity Col-
lege Library, and others were printed at Paris so early as A. D. 1496.—
See Ware’s Bishops, p. 81; Ware’s Writers, p. 84, and the authorities there
quoted.

478

”

Cross,” in the forest of Soigny. There are no notes in the
Irish character or language, nor do any figures of animals,
which are so commonly found in Irish MSS., form any part
of the illuminations. The MS. is in good preservation, and
the text commences thus: ‘‘Joannes qui ex literali.” The name
of the scribe has not been discovered in any part of the volume.

Vol. II. containing the Nos. 1160, 1161, 1162, and 1163,
is a middle-sized folio also in the Latin language, bound in
wood covered with calf-skin, and ornamented with brass clasps.
This volume is entitled, in the classing of the old library, to
which it belonged, as follows: ‘* Navigatio S. Brendani ad va-
rias Insulas cum aliis.— Beth. Louv. 48 F.” At the com-
mencement and also at the end of the MS. may be found the
following note: ‘* Pertinet Mésterio Canénor. Reglarm. in
Bethleem ppe. Lovanium.” The contents of the volume are
given upon the first fly-leaf, and are as follows:

1160. It navigatio S. Brendani abbatis ad diversas insulas.

1161. It visio Tungdoli militis valde admirabilis.*

1162. It epistola Presbiteri Joannis imperatoris majoris.

1163, It itinerarium Joannis de Mandeville militis.

The initial letters of the four different pieces are about
two inches in diameter, and ornamented in vermilion and pink
colours, but not very neatly executed, and the same observation
applies to the penmanship. The first leaf of this MS. is vel-
lum, then follow four of paper, and then two of vellum, and so
on until the eightieth, which is of vellum also, and which is the
Jast in the volume. Mandeville and Tungdolus.are in the text
styled ‘‘ milites.” ‘he date, or the name of the scribe, could
not be found in the MS.; but, by comparison with MSS. of
a known date, it appears as old as the ‘ Inventaire” states,
namely, the close of the fifteenth century.t No note in the

* There are three copies of this tract in the Library of Trinity College,
Dublin. They are marked as follows: C. 4. 23.; E. 1. 29.; and E. 4, 12,

t Nos. 1161 and 1163 have short prologues; for other copies of these
MSS, see Nos. 4531 et 7960.

479

Irish language or character appears ; and the different pieces
commence as follows:
1160. ‘‘ Sanctus Brendanus filius Finlothe.”
1161. “* Hibernia igitur insula est.”
1162. ‘* Presbiter Joannes potentia Dei.”’
~ 1163. ‘Qui de Anglia Hibernia.”

Vol. III. (2159-2167). ‘This volume, which is a thick
quarto, belonged to the ‘‘ Domus probationis” of the Jesuits
at Mechlin, and contains some interesting papers in reference
to Irish history ; among: them I-may mention ‘‘.Magna sup-
plicia et persecutiones in Hibernia,” commencing thus: ‘‘Anno
1599, Guillielmus Drurius ;” and No. 2167, which is a collec-
tanea, entitled ‘* De Rebus Hibernicis ;” in the latter will be
found a letter or memorandum in Latin, signed «© Thomas
Fleming,” and dated 1612.

This compilation was written between the years 1602 and
1616, and is in the Latin language: the name of the scribe
does not appear. The volume contains some short pieces re-
lative to English history.

Vol. LV. (2324-2340). This is a thick quarto volume,
divided into two parts, the first containing 105 and the second
246 pages, written upon both sides. The contents of the first
part are given in an alphabetical table, which is at the begin-
ning of the volume, and of which the following is an abstract :

EeriamuaniOanones, ts he Ie el en eB
S. Adamnanus de Scrinio . . TUES lteh ate as MeO
Apli duodecim Hib. in Convivio det oun na x ngs, ties Geet now
Apli duodecim Hib. in Schola Cluainerardensi,. . . . . 73

S. becc mec. dé. prophetia hujus quam primum ac natus fuit, 68
_S. Brendanus éx Schola praaiectariepel ivit quesitum Ter-
RAMP TOMMISSIOIS So Bit eae ek Ms es den val ie ings oho
S. Brigidz Vita, .°. 9...” i ee aera vats ee
Colmdnus Fil. Obeonz ‘de vitiis slatentibus me ambos bono-
rum operum, . .- Rhee OE UBL ah a a A pe Ne cae OY
S. Columbe Kille Lanes ER ee aS ae ae ce en eke LO

480

Convivium de vun nangfo per Donaldum, . .... . 56

S. Cormaci fil. Culennani tria vota, . . . ...... #77
5: Cumini Longi wits. ig ue joe eet eee ee
S. Ercus eps. Slanensis seu verius comorbanus ejus, . . . 56
S. Finchuonis de Brighobhan Vita, . . . ..... =. 35
S. Finnianus Maighbile, . .te-5 «ours +s, 8 ot Gapped See
Si'Rieranus Ce... 9... 5 ee ape ee eis cee OOF
8. Kierani Oonfessio; Os '. 2 2. Reo = ee ee 6G
S. Macrecii Vita, . . . , oad ag + ei a89
Ministri provinciales ord. Minotis i in Hib. ab initio vefhasite
tionis, . . yrs a alpen Wid rage 7
Monasteria frim Maa in Hib. Peter carts 2 ae 1
S. Molingo Jesus Christus apparuit in forma Benen ope 67
S» Patricii Vita,:, .,: *.. xn jr yeaa teed Ue
S. Ronani fil. Berachi Vite pede &x bate ae ot oy sees oe
Scriptores antiqui Hib. . . . . ree dn abe id

Vitze SS™ quee habentur apd. Dnm. Simovlent Barnewell, | AGE 17:

In this abstract two or three entries are omitted, which are
quite illegible in the original, in other respects the copy is
substantially correct.

At the end of the volume is a table of contents for the se-
cond part, of which the following is an exact copy :

Vita mochua balla. Hibernice, 1
Fragmentum vite S. Baitheni. Hib., 28219010 gaa eee
Frag. Vite 8. Donati ui bnuin. Hib, . .. . 2... 6
Vita S. Finchonis Brigovan. Hib., . Ree ere 7
Vita S. Batri Corcagicny, 21s 05 cic he. yo, oe, oe
Nita S. Creunate: Virgins. Be 6 nea yee eo eee
Vita S. Moliigi. Hibertitees fo. op xe. egos ol eee
Mita\S. Finan Coifese. (GMb. os ne eau
Wita Sancti Alyer. Fb. Ce an 5 ee ee!
Vita'S. Abbam. Hibs a. er
Nita S. Cavthagi. “Hibermess (Se i). 0 ice te ee
Nita So Purse, Hiberniegs 27% if.) dots age (ee «eee
Bigot. Vitos Maram: FED a ok See ce pe
Vata S. Cellaci Ep.jet: Martyr. Hibs... 26.) a2 a. axcc' suum

481

Vita S. Medoci Fernensis. Hib, . . . . . . . . . ~~ 60
Mata SCalmant Blozy Tibi) «<.- od) i eausedyas syoie bea hdd
Vita S. Senani. Hibernice, . . Gb ics Aa AeA ode LS
Miracula S. Senani post mortem. a Ee re are . 233
Pocmata diversa S. Senani, 8. Brendani, et aliorum. Hib., 142
Poemata plur. S. Columbe Kille et aliorum. Hib, . . . 154
Vita S. Caimini Metro-hibernice,. . . . ..... . 156
Vita S. Coemgheni. Hibernice, . . . MF Ty eet ROG
Vita ejusdem aliter tradita. Asean deste STS ee
fate 5: sMochevor.”* Hibermice, fs Peo er te hae
Vita S. Callini. Hibernice, . . . sien Me eros

Ejusdem poemata et Prophetia de statu Hib. idssaalibids
nec non plura alia de diversis rebus, quz in ejus vita et
in ceteris usque ad finem, . . . . . . +... . 244

The contents of this volume are entirely in the Irish cha-
racter and language, except the list of the Franciscan Provin-
cials, which is in Latin.

The paper upon which this MS. is written is very coarse,
and some of the writing not well executed, in comparison with
other MSS. written by Michael O’Clery, whose name ap-
pears at folio 75, and also at the end of the first part of the
volume, where it is stated that the MS. was finished at Done-
gal, upon the 7th of August, 1631, by ‘“ Brother Michael
O’Clery.” The name of this individual appears in several
places of the second part also, with various dates in the year
1629. See pp. 7, 22. From these dates it appears that the
second portion of the work was written before the first ; and
from the appearance of the binding it may be concluded that
the collection was bound after being written, as the paper of
the first half of the volume does not correspond with that in
‘the remainder.

Vol. V. (2542, 2543) is a thin, quarto volume, bound
in vellum, and not entirely written upon. ‘The first piece in
this volume is an Irish poem, of 250 stanzas, with four verses

to each stanza; and the following is its title : ‘‘Shof Oall §ul-

482

ban mic neil ;” it is accompanied with a gloss and notes. The
second piece commences thus: ‘‘ Cea ingean luiweach,” and
the penmanship of this is not so neatly executed as that of the
other, than which nothing can be more beautiful. Upon the
cover of this volume the following note, or rather title, will be
found: ‘Genelaé na naom a nodn, Cum opusculis de uxoribus
et matribus filiorum Milesii et successorum.” This MS. was
finished January, 1642, and although, judging by the hand-
writing, I am almost certain it was written by Michael O’ Clery,
I was unable to find his name in the volume.

Vol. VI. (2569, 2572). This is a small quarto, con-
taining poems in the Irish character and language, some in the
handwriting of Michael O’Clery, others,—the greater part, I
may say,—in another hand, with the corrections, or rather an-
notations, of O’Clery, appearing here and there through them.
The heading of some of the poems is as follows: ‘ giolla na
naom ua ouin,” “ giolla caomam ce.” Fol. 23, ¢* mic vapig Cc.”
At the conclusion of these poems is a continuous prose piece
in Irish, ee thus :

“Gar vocive, 1ongzi aobalmon ap efi yle.”

This is in the handwriting of Michael O’Clery, and was
finished by him at the convent of Donegal, in November, 1635.

This latter piece is styled in the ‘“‘ Inventaire” ‘* Guerres
des Irlandais et des Danois.”

Vol. VII. (3195). ‘This MS. is a large folio, canine
104 leaves, closely written on both sides. It is a History of
the Franciscan Order in Ireland. Upon the fly-leaf is written
the following note, first in red and again in black ink :

. «FE Antonius Purcell compegit hunc librum
jussu Rdi. admodum P. Fratris Donah Mooney
ordinis minor. Regular. observantiz
- Ministri Provincialis, afio domini 1617, die Novembris
2°. in collegio Fratrum Hybernorum Lovanii
_pro quo pius Lector ex charitate
oret.”

483

At the commencement of the volume is the following head-
ing or title: ‘* Tractatum sequentem de Provincia Hiberniz
concinnavit, R. adm. P. Donatus Moneus, dum esset Provin-
cialis et hue ex Hibernia ad res hujus collegij S. Anthonii or-
dinandas advenisset.”” It may be remarked that this appears
an interesting and valuable historical document, and, together
with the papers before mentioned upon the Irish Franciscans,
must be of great value in preparing a correct ‘* Monasticon
Hibernicum.” Of course, their value is much increased when
we remember that they were compiled under the directions of
the heads of the Irish college of St. Anthony. The text of
this history commences thus: ‘* Provincia ordinis 8. Fran-
cisci in Regno Hyberniz.”

Vol. VIII. (3201). This volume, which is a large folio,
appears to be a ‘* Collectanea” of the Lives and Acts of
Saints for the month of March; probably it formed part of the
Bollandist collection, although it has not their library mark.
The above number is stated im the * Inventaire” to be “* Vita
S. Patricii,” and under this title will be found four different
lives of the Saint. The second life bears date 1641, and the
third is extracted from Camden. There are also two copies
of the ‘‘Purgatory;” the first, ‘ex MS. Hiber. Min. Lova-
nii ;” and the other, **ex MS. Maximini Treveris;”’ besides
these there is a life of St. Senan, ‘‘ ex MS. Hibern. Seminar.
Salamaticensis Soc. Jesu,* coll. cum MS. R. P. Ward ;” and
also a long poem and hymn to this Saint; some of the other
lives appear to have been extracted ‘ex MS. F*. J. Colgani.”
This volume has been recently bound, and I was unable to
discover any name or date, &c., indicating the compiler, or
where it was written.

W eVol/ 1X: (3824, 3825). The first part of this volume,
which is a large, thin quarto, is occupied with the correspon-

* This MS. is now in the Burgundian Library. See vol. xxii. in this Cata-
logue.
VOL. III, 2uU

484

dence of some Irish Jesuits and the heads of a college at Rome,
called in the correspondence the ‘‘ English College.” Much of
this correspondence is between Louis Newman, for some time
a prisoner in Dublin Castle, and Mr. Thomas Roberts, of the
aforesaid College, and bears various dates, from the years 1634
to 1639. There are also letters signed by Edward Blake and
Robert Spreul, with memoirs of F. Slingisbey by the said Spreul,
and also by William Moloney. The correspondence appears to
be entirely about Slingisbey, and some of his letters are also
given, signed, ‘ F. H. Slingisbey, Kilkenny, this St. Joseph’s
day, 1640,” and directed to Mr. John Thompson, of Rome.
This person was also of the English College; one letter is
signed ** Franciscus Perszus,* alias Slingisbeus, propria manu,
Rome, 14th February, 1639.” The letters are in the Latin,
Italian, and English languages.

At the end of the volume is a complete memoir of this
person, entitled, ‘‘ Relatio brevis de Vita et Moribus Rdi. P.
Francisci Slingisbeii Societatis’ Jesu pro eo tempore quo
vitam Scecularem egit in Hibernia, postquam fuisset ad Fidem
Catholicam conversus. P. Mauritij Wardcei Sacerdotis Hi-

]

berni.” This latter is written upon duodecimo, in a very
legible hand, and if it was printed the correspondence would
make a necessary appendix.

Vol. X. (3944) is a very thin quarto volume, in the Latin
language, bound in calf, and is the Obituary of the Irish Col-
lege of St. Anthony of Padua, at Louvain, from 1614 to the

year 1716. A couple of leaves are devoted to each month, and

* In Mr. Burke’s Heraldic Dictionary of the Peerage and Baronetage of
the British Empire, vol. ii. p. 297, the following will be found: ‘‘ Henry
Piers, Esq., of Tristernagh. This gentleman conformed to the Church of
Rome, and prevailed upon some of his children to embrace the same creed; of
whom Thomas, his third son, became a Franciscan Friar; and Henry, his
fourth son, left a son, John, who took orders in the Catholic Church.” Very
probably the ‘‘ Franciscus Perszeus,” above alluded to, was a member of
this family.

485

the names of the brothers are entered in the order of the calendar,
opposite the dates upon which they died. The entries con-
tain short notices of the labours, &c., of the fraternity, and
indeed no Franciscan college has maintained with more zeal
than this the character of the order, as expressed in their
motto, *‘ Doctrina et sanctitate.” The obits of the benefac-
tors of the college follow those of the brethren.

Vol. XI. (4190-4200) isa thick quarto, bound in vellum :
the paper is very coarse, and the penmanship rudely executed.
The contents of this volume are all in the Irish character and
language, except one of the two lives of St. Molingus which
is Latin.

1, A life of St. Brigid,. . . . Sat fy iol sty
2. The Hymns, Life, and Vision of St. Waalanad: BIW wi ea

Se theslife of Sts Molingus, | sua) to ve ont 2 4,) 48
4 iy SE, J eKACHUS V4 mtr eray, cyt. dalalevm tins 1st tay 666
o. ‘a St. Grellanus, ot, atte teh bea eliger BES
6. A St Worsiiamisy Sea LS ly Seen Mle gel Oe
7 = St. Molassius Daimhinis, . oy Co ak GE
8 ie Si Weagsara VECO S | ot oth a! iin oni). Suincebsmaelle
9. a MSIEINAUILLI Seay tap ecu rates Dace | ect. eats alta SRM
10. 5 St. Kieranus Saigir, », 139
rh. s St. Kieranus Cluanensis, . . . . . . ,, 149
12. ae Sta Declanusy wards te eet ak, Siento i LOU
13. B St. Ruanus; 2°. . a Senta ety atte ee TOG
14. is St. Finianus Gidea, bint, avast ete hea) SOG
15. at St. Benignus, Meee ttl pial ets rise ee DUS
16. ey St. Aireranus seu Aileranus,. . . . . ,, 212
17. Sapientes precationes ejusdem, . . . - . « - « 4, 217
18. The Life of St. Brendanus Cluanfert,. . . . . . 4, 259
19. ss St. Mochudda seu Carthaci, .. . . 4, 2695

20. De St. Suanachi filiis et de St. Mochudda, . . . . ,, 268
21. Fragment of the Life of St. Senan, and the poems of
Dallanus upon that saint, 2 £06 6 ee ee gp
Judging from the writing of this volume, one would not
suppose it to be a compilation of Michael O’Clery’s ; how-
ever, his name appears as the scribe in several places ; for in-
2u2

486

stance, at folios 121,131, and183. ‘The volume appears to have
been written in the years 1628 and 1629; it contains 270 folios.

Vol. XII. (4241). This is a thick quarto, composed of dif-
ferent sized paper, and contains about 270 leaves, with short
memoirs and notices of Irish saints in the Latin language;
the arrangement is alphabetical, and the volume appears to
be a note-book of some hagiographer. I was unable to
discover a name or date in the book. At page 99 is a pedi-
gree of ‘“* SS. Furseus, Foilanus, et Ultanus,” the sons of
Giltanus, ‘* Rex Hiberniz.”

Vol. XIII. (4531) isa second copy, and I believe the oldest
in the library, of the Visio, &c.; see Vol. II. (1162), and Vol.
XXIV. (7960), in this catalogue. The MS. is written upon
vellum, and beautifully executed; the sheet is small octavo,
and there are eighteen of them occupied with the piece. It
has no illumination, nor any trace of the Irish character, or
the name of the scribe. It is attributed to the close of the
thirteenth century.

Vol. XIV. (4639). This is a small duodecimo volume
bound in calf; upon the fly-leaf is the following title : i

‘*¢ Martyrologium
Sanctorum Hiberniz collegit et digessit
Michael O’Clerij
ord. S. Francisci
Duaii in Flandria Gallica 1629.” .
After this follow four pages in Irish, in the hand-writ-
ing of Michael O’Clery, and dated from Donegal, 1628.
After this a short paragraph or testimonial in Irish, dated
Nov. 1, 1636, and signed

Fina’ Ae a

pak Sadek

This paragaph appears upon the next page also, and is
signed ‘* Connep Mac Opavp,” bearing date Nov. 11, 1636.

487

The testimonials, in the Latin language, of Thomas Flem-
ing, Archbishop of Dublin and ‘‘ Primate of Ireland,” dated
from Kildare, February 1, 1636, and from Father Roche of
Kildare, dated from his convent, 8th January, 1637,* next fol-
low, and then the Martyrology, first arranged according to
the calendar, and then alphabetically. This MS. is in the
Irish language, and can be read without any difficulty: it
contains about 250 pages.

Vol. XV. (5057, 5058, 5059). Thisis a thin quarto, rudely
stitched together, and in bad condition. It contains, first, a
fragment of a catalogue of saints, then some poems by
‘© Kogan mac an Bhaird,” and by ‘* Moel Patric,” &c. &c.,
and ends with a fragment in prose, commencing ‘‘ Gloriosus

’

Episcopus Carthagus qui vulgo vocatur Mochuoa.” The con-
tents are all in the Irish language, and I was unable to disco-
ver the name of the scribe or date of the compilation ; how-
ever, I believe it belonged to the Louvain collection, and is
justly attributed in the catalogue to the seventeenth cen-
tury.

Vol. X VI. (5095, 5096) is a small, quarto volume, bound
in vellum, in the Irish character and language; and is another
copyt of the‘ Martyrologium Dungalense” of Michael O’ Clery.
It contains a preface by the author, in which he states that the
work was finished at Donegal, 19th April, 1630, and then a
short paragraph, signed Flan Mac Aodhagan as above.

Upon the following page this paragraph again occurs, signed
“ Connep M‘Gpaop,” Then follow the approbations, in Latin,

* Flann Mac Aodhagan, whose autograph is here given, was a famous
antiquary, from the village of Bally Mac Aodhagan, in the county of Tippe-
rary. It may be remarked that the individuals whose names are here given
are the same who have given approbation to the Annals of the Four Masters ;
as may be seen in the autograph copy belonging to Trinity College Library.
Rerum Hib. Scriptores, vol. iii. p. xv. The same observation applies to the
other copy of this Martyrology. See vol. xvi. in this Catalogue.

+ See vol. xiv. No, 4639.

488

of Malachy, Archbishop of Tuam, dated from Galway, fifteenth
of the kalends of December, 1636; that of

yibey ely es

dated 27th December, 1636; that of F. Thomas Fleming,
‘‘Archiepiscopus Dubliniensis, Hib. Primas,” dated from
Kildare, February 6, 1636; also that of ‘Frater Rochus
Kildarii,” dated from his convent, 8th January, 1637, in
which it is stated that “Fr. Florentius Keegan” and “ D.
Cornelius Bruodyn” examined the Martyrology.

The Martyrology is first arranged according to the calen-
dar, and then alphabetically ; the writing is clear and beauti-
fully executed ; some short notes in the Irish and Latin cha-
racter are scattered through its pages.

eat

At the commencement of the volume will be found a
sketch of a shield with some armorial bearings as above,

489

Possibly the readers of the ‘‘ Unkinde Deserter” may be able
to conjecture the purpose of this composition, and assign some
reason for finding the Lion of Belgium, the Harp, and crowns
of Ireland quartered together.

Vol. XVII., containing Nos. 5101, 5102, 5103, and 5104,
is a thin quarto volume; the first part is occupied with a col-
lection of religious poems in the Irish language; some upon
Columbanus, and others attributed to him and to St. Mo-
ling, also the rules of the Irish saints, commencing with St.
Columbanus. This collection was finished in 1630, as may be
seen at page 45, where it ends. Then commences * Festilo-
gium S. Engussii Keledei,” also in Irish, and beautifully writ-
ten, unquestionably in the handwriting of Michael O’Clery ;
the accompanying gloss and notes are very full, and the ‘* Fes-
tilogium” occupies fifty-one pages.

The next piece is entitled ‘* Mariani Gormani Sancti de
quibus dubito, an sint Hiberni an alij, quid non reperiantur in
aliis Martyrologiis iis quibus denotantur diebus.” It is in the
Irish language, as well as a testimonial which precedes it,
bearing date ‘18. aug. 1633,” and signed Feapfearra o maoil-
conaine and Cucoiccnice o Cleims.

This Martyrology is in short metre, and contains 141
pages.

After this there is a third Martyrology, that of Tallaght,
occupying about twenty-seven pages, and then the following
testimonials :—

Nos infra scripti fidem facimus, et per presentes testa-
mur has annexas duas copias transumptas fuisse per fratrem
Michaelem Clery ex duobus codicibus manuscriptis, quibus
a lingue Hybernice peritioribus hucusque fides adhibebatur,
uno nimirum vetustissimo codice pertinente ad Clann y Mul-
choner, et altero qui est vera copia celeberrimi et vetustissimi
codicis nunc Dublinij reservati; easdemque copias de verbo ad
verbum sine styli ordinis aut substantiz rerum inversione aut
corruptione cum eisdem suis prothotypis per omnia concor-

490

dare. In cujus rei fidem et testimonium his subscripsimus in
deserto nostra mansionis die 29 Aprilis, 1636.”
Fr. Bernardinus Clery.
Guardianus Dung.
Fr. Mauritius Ultanus.
Fr. Mauritius Ultanus.

Upon the opposite side will be seen a fac simile of this
testimonial ; I have thought it worth presenting to the reader,
that it might be compared with the signatures of the same three
individuals as attached to the testimonial upon vellum, in the
Annals of the Four Masters, now in the Library of the Royal
Irish Academy, as well as with their handwriting, which may
be seen in another copy of the same work in Trinity College
Library.

Then follows another testimonial to the same effect, signed
‘¢ Joannes Culenanus. Epus Rapotensis,”’ with his episcopal
seal. There is also one in Irish, signed by Conell Mac
Geoghegan, dated October, 1636, and some short historical
pieces, finished at the Convent of Donegal, 28 April, 1636.

Upon the outside of this volume will be found the follow-
ing note, in a hand apparently as old as that of the text or
testimonials: ‘* Continens Martyrologia Cingussei, Mariani
Gormani et Tamlactense et Genealogias SS" et plura alia
opuscula.” We may add, that the binding of this valuable
volume is of vellum, with a piece of calf-skin rudely stitched
upon its back.

Vol. XVIIL., containing Nos. 5301 to 5320, inclusive, is
a very thick quarto paper volume, bound, or rather stitched
together, with a piece of calf-skin as a cover. Its contents
are very varied, and, it is presumed, are of much historical
interest; they are as follows :—

No. 5301. ‘‘ Fragmenta tria Annalium Hiberniz extracta
ex codice membraneo Nehemie mac Aigan Senis, Hibernici
juris peritissimi, in Ormonia, per Ferbissium ad usum R. D.
Joannis Lynch. ‘Ab anno Xti circiter 571 ad annum plus

491

minus,” * * * * and commences thus: ‘ Rt. caé pfimm,” ‘in
quo victus est Colman,” &c.

These extracts extend to seventy-one pages, and are well
and closely written. At the end is an index, and an accom-
panying collation with the Annals of Donegal.

No. 5302 is a little fragment upon Irish hagiography,
commencing ‘* Notanda in opere fratris Jacobi,” &c., consist-
ing of four small leaves.

No. 5303 consists of sixty-five pages; the first twenty-six
are entitled ‘“‘ Adversaria Rerum Hibernie excerptaex mutila
Historia’ D. Cantwelly,” and commences thus: ‘* Hoe anno
ante diluvium.” At page 25 commences “ Annales Ros-
creenses.” The initial line is ‘‘ Patricius Archiepus in Hi-
berniam venit atque Scotos baptizare inchoat, nono anno
Theodos. minoris,’ &c. These Annals, as wellas the ** Ad-
versaria,” are in Latin and Irish, and very badly written,

No. 5304 is a very long alphabetical Index of the Annals
of Roscrea, made by ‘“ Frater Brendanus Conorus,” accom-
panied by marginal references to the Annals of Donegal.

No. 5305 is ** Familia, seu Monachi S. Fintanisive Munn
Abbatis, numero 233, quos non uret ignis judicii: ex Mart,
Taml. pergameno, 21 Octob.” The names are alphabetically
arranged, and this fragment is but four leaves in extent.

No. 5306 is very closely written, and is entitled, ‘* De
Multiplici Naturee bono ad Hybernos in terrestri elemento

>

istius regni,” and commencing ‘‘ Authores qui volunt re-
gionem.”

No. 5307. ‘ Itenerarium in Hibernia,” by ‘‘ Frater [d-
mundus Mac Cana,” and commencing “ Monasterium de Kill
Snabha.”

No. 5308 is a ‘* Descriptio Insule Sande,” by the same
author, and commences ‘‘ Insula Sanda est.”

No. 5309 is an extract from Joannes Major, ‘ de historica
Britannica antiqua,” commencing ‘* Ab Albina Regina.”

No. 5310 is another extract, ‘‘de regibus Scotiz,” from

492

Hector Boetius, and commencing “ Primus imperat Scotis ;”
these extracts are only a few pages in length.

Nos. 5311, 5312, 5317, 5318, are, respectively, bulls by
Popes Urban VIII. and Alexander VII.; and letters to the
Irish bishops from Popes Zacharias and Gregory.

No. 5313 is ‘de Monasterio St. Jacobi Herbipolensis”
(Wurtzburg) ; and commencing, ‘ Circa hoc tempus multi in
Scotia.”

In 5314 is an extract from Marianus Scotus upon Ireland,
very short, and commencing, ‘‘ Hac quoque tempestate.”
There are also extracts from the ‘“* Annales Suevici” of Mar-
tinus Crucis concerning Ireland; and a collection upon the
‘*‘ Trish Apostles,” with their labours in Belgium and Ger-
many.

To the historical student wishing to pursue his researches
in reference to the seminaries established on the Continent
by these missionaries, the contents of the volume we are
speaking of would be indeed an acquisition. In it he has
the names of many authors with which, very possibly, he has
hitherto been unacquainted, with references to their writings
already arranged, which would give him considerable trouble
even to make out.

Vol. XIX. (6131, 6132, 6133) is a large quarto, bound
in vellum, containing a collection of Irish poems and pieces
in prose, upon the O’ Donnell family, and has been evidently
left in an unfinished state; a good number of the poems are
headed ‘‘ €oghan puad mc an Shaipo ce.” Upon the outside
of the volume its title is written in Irish and Latin as fol-

lows:
“¢Gebhap ipipin i COomhnailt.

Liber poematum O’Donnellij.”’
Upon the inside of the cover I found a note scarcely legible.
I was able to decipher with difficulty the following words at
the conclusion: ‘* O’Donnell a dall fall. ... Brukelles,
xiii. September, 1622.” The writing in this volume is not

493

well executed ; and in the note I have just spoken of some of
the words are in the Flemish language.

Vol. XX. containing No. 7299, is merely an extract from
the theological works of Richard Archdekin, of Kilkenny,
which are highly prized abroad, and have, consequently, gone
through eleven editions.

Vol. X XI. containing Nos. 7658, 7659, 7660, 7661. This
volume is a very large paper folio, bound in vellum; and ap-

pears by the class-mark a to have belonged to the

Jesuits. The title or heading occupies half the first page, and
has the following note written across it, in an old hand differing
from the text: ‘‘ Authore N. P. Stephano Vito, soc*. Jesu
Hiberno, Clonmeliensi.” The title is as follows:

‘‘ Vindicize Scotorum veterum, et Sanctorum indigenarum
Iberniz oceani magne Insule, que olim ab immemora
bili tempore, passim per Europam usque ad annum
Christi saltem 1000 audiebat Scotia, deinde
vero per 200 et amplius annos dicebatur
Scotia major sive vetus, ad discrimen Scotize primoris et nove,
que ante per plurima
secula audiebat Patria Pictorum Britannie.

In tres libros distribute
ADVERSUS
Graves crebrosque errores novorum de rebus Scoticis his
toricorum Hectoris Boetii, Georgii Buccanani,
Georgij Tomsoni, Roberti Turneri sub nomine
Joannis Leslei, et asseclarum ipsorum qui [ber
norum nationem et patriam prisco nomine proprio
christianorum Scotorum et Scotiz una cum
ingenti numero Sanctorum Iberniz Scotorum
veterum immerito privant et transformant
in Neoscotos Britanniz Insulz posteros
prise Pictorum ac Dalreudinorum Gentis
Candido Lectori memorabilium antiquitatum amanti. S.”

494

The preface, or rather the address to the reader, which com-
mences thus: ‘ Frons operis futuri Vindicias pro Patria pre-
terat,” &c. &c., occupies about six pages, and endsas follows :
‘6 si tibi lector ero. Vale, Fave, et fruere labore nostro.”
Next follow ‘‘ Generales Censurz variorum Authorum de fide
Catholica et Libris Hectoris Boetii atque asseclarum ipsius ;”
including those of Polydore Virgil, Carolus Sigenijus, Tho-
mas Boygus, Joannes Lelandus Londinensis, Luidyus, Cam-
denus, Petrus Berteyus Belgeus, Buccananus, Richard Stani-
hurst. After these Censure there follows something like
a table of contents, divided into eleven chapters, and headed
thus: ‘* Referuntur capita potissima historicorum errorum
qui in Vindiciis nostris refutantur.”

The body of the work commences at page 14, and to it
there is a short heading, thus: “ Brevis descriptio Iberniz
Insule,” &c. &c., and then a little prologue commencing :
‘‘ Inter multos exteros nostri szculi qui geographiam,” &c.,
which occupies half a page; at the end of this, cap. i. com-
mences, and is entitled: “ Situs, magnitudo, celum, solum,
salubritas, feecunditas aliaque commoda, ac dotes Ibernie In-
sule.” And the text of the work begins thus: ‘* Vernaculo
vocabulo Erin,” which is then continued in 202 folios written
upon both sides, when a different character of hand appears,
which continues until page 309, written very closely, and also
upon both sides.

After this a second part commences, with different paging,
headed thus: ‘ Ihesus Maria Deo gratias. Apologia pro —
Ibernia adversus Cambri calumnias, sive Fabularum et Famo-
sorum libellorum Silvestri Gyraldi Cambrensis, sub vocabu-
lis, ‘Topographia sive de mirabilibus Iberniz, et Historia Vati-
cinalis sive expugnationis ejusdem insule, refutatio.’ With
an address to the reader commencing—‘* Benevo. lectori S.
In contumeliam multorum cum Sanctorum.” After this, and
a table of contents, follows cap. i. headed thus: ** Quid Sta-
nihurst et alii senserint universim de intemperie et mordaci-

495

tate Sylvestri Geraldi Cambrensis,” and commencing, ‘* Preter
Hereticos tres.” Cap. xix. is headed: ‘ Fictitium aut surrep-
titium fuisse Diploma Adriani,” &c. The last, or chapter
Xxvi., commences, “ Audisti Lector Cambrensem,” &c.*

At the end of the volume will be found a detached folio
tract, entitled, upon the cover,

*« Apologia pro Sanctis Scotiz, sed Infirma videtur saltem ‘si
conferatur
cum Vindiciis P. Step. Viti pro Scotia an
tiqua Seu Hibernia.”

The text of this is preceded by the following heading :
** Apologia pro gente Scotica hodierna contra Hibernos ;” and
commences, ‘* Dedimus in Lucem aliquando,” &c. This also
formed a part of the Jesuit Collection, and contains twenty
folios written upon both sides ; and it is accompanied by a few
leaves of detached Irish MS. upon quarto paper, and very
badly written, and of no importance.

The contents of this volume, that is to say, the part fas-
tened within the binding, amount in all to about 1000 closely
written pages, and it was evidently a copy, made perhaps for
the author, by four, or, at all events, three different scribes. As
for its contents as a valuable historical document, the writer
has merely to mention that he has never seen a work upon
Ireland, from which information appears to have been drawn
from so many or such high authorities: one need only look at
a single page of it, when he will at once perceive the immense
amount of learning with which the author was gifted, and the
facility of arrangement with which he has used it.

* Dr. Todd has just called my attention to a manuscript fragment in the
Latin language, forming part of the Ussher Collection, in the Library of
Trinity College, Dublin (E. 3. 19). Upon inspection, we have discovered
that it is a part of this work of-Stephen White, which is above described.

t Since the above was written, Mr. Charles P. Mac Donnell, M. R. I. A.,
has been kind enough to place in my hands the Rev. Dr. Oliver’s “ Collec-

496

Vol. XXII., containing Nos. 7672, 7673, and 7674, is
perhaps one of the most valuable Irish MSS. in existence, be-
ing the second volume of a collection of lives of Irish saints,
in the Latin language, and written in the fifteenth century.
It consists of 177 large folios of parchment; the first is num-

tions towards illustrating the Biography of the Scotch, English, and Irish
Members of the Society of Jesus.” Quoting from page 269, of this very in-
teresting work, I find a confirmation of the opinions upon the merits of this
MS. which I have just ventured to express.

‘* Stephen White. This Irish Father deserves a fuller eulogium than I
am able to supply. He was the author of some historical pieces relating to
Treland, in confutation of the assertions of Giraldus Cambrensis. The Rey.
John Lynch, who had the custody of this valuable MS., mentions it in chapters
i. and xiv. of his Cambrensis Eversus, printed in 1662, and expresses his deep
regret that a considerable part of it was lost during the civil wars. Arch-
bishop Ussher, an excellent judge of these matters, in page 400 of his Pri-
mordia, gives F. White the character of being ‘ a man of exquisite knowledge
in the antiquities, not only of Ireland, but also of other nations.’ In a letter
of Robert Nugent, superior of his brethren in Ireland, and addressed from
Kilkenny, January 10, 1646, to F. Charles Sangri, I read what follows:

“*«T have given the commission to four of our fathers diligently to exa-
mine the works of F. Stephen White, and to forward their judgment to your
paternity, conformably to the directions you have recently sent us. His
works are various, and as our fathers live in places very distant from each
other ; and notwithstanding the most Reverend Bishops (who are ready to
defray the expenses of the printing), as also the supreme council, very ear-
nestly insist, that a certain work of his “‘ De Sanctis et Antiquitate Iberniz,”
be instantly sent to the press, I find it difficult, and next to impossible, to
resist their reasonable demand, since the MS. itself has been perused by seve-
ral amongst them, and has been pronounced not only worthy of being printed,
but highly necessary for the credit and advantage of this kingdom. There-
fore, [have written again to the examiners, that each would privately report
their opinions on this work as soon as possible to your paternity ; though all
in their letters to me greatly extol it, and declare it most worthy to issue
from the press. But I am unwilling to allow any work to be printed that
can give just cause of offence to any person: and yet here is less cause of
apprehension in this case, as this book merely treats on the Saints and An-
tiquity of the Kingdom of Ireland.’ ”

Dr. Nicholson, in his Irish Historical Library, p. 90, calls Stephen White
the friend of Archbishop Ussher ; and the passage referred to in Cambrensis

497

bered 48, consequently the forty-seven first leaves are want-
ing; and the MS. is written in double columns, of thirty-nine
lines each, ornamented with small illuminated letters scattered
through the volume. Between folios 128 and 129 is a semi-
longitudinal page, upon which is found the following note in

the Irish language :*

Dennatend :
Sennak oan aculnoemanw
ict a le
im 2 oNchUC ilerhuh-4- 14s Johns
Mikerti-oe ergallia, 02 oF
siirde. Lem diencharerede ere 7
pace am

Eversus, alluding to White, is as follows: ‘‘ Pater Stephanus Vitus e Societate
Jesu, sacre Theologiz doctor, et professor emeritus, lucubrationem elabo-
rayit accuratissimam, que infamiam Hibernie a Giraldo impactam luculen-
ter amovit. Ejus operis exiguum fragmentum penes me habeo, quod relique
partis prestantiam, tanquam unguis leonem indicat; sed integrum alicui
mutuo pridem traditum, proh dolor, in latebras aliquas reconditas abditum
est, ut ex iis erui, ac in lucem, hominumque conspectum proferri exinde non
potuerit.”—Cambrensis Eversus, p. 1.
* [It would seem that these lines ought to be read and translated as fol-

lows :

Sennacz cuanna agur (na) noem capo-

ul a cazcach ppp, ap amma in zi cuc

a Zaeoaile illaom in bechura «1. ppp Tohip

mac kepuill. oe epgallia, .

Anima quoque fratris Dermitii i Dhunchadha requiescat in
pace Amen.

‘« The blessing of Cuanna, and (of the) saints who were in communion
with him, be upon the soul of him who translated this life from the Irish into
Latin, viz., Brother John Mac Keruill of Oriel.”—-EpDIToR oF THE PROCEED-
INGS. ]

498

This is the only trace of the Irish language that I was ena-
bled to find in the volume; the two last pages are also semi-
pages, neither of which are written upon both sides, although
all the others are; upon the back of the volume may be seen
the following title: ‘¢ MS. Salmantic. de SS. Hibernis 11.”
A table of contents upon paper will be found in the commence-
ment of the volume, apparently laid there by some person who
had possession of the book, and of which the. following is a
copy: :

~~ 6 Codicem hune Rector Collegij Salmanticensis Hibernici
Sostis Jesu dono dedit nostro Patri Cigidio de Smidt qui
eundem donavit P. Heriberto Boswaydo.”

INDEX VITARUM.

FOL. | FOL.

S. Brigida acephala,. . - 48 . Cronani, efor 147
S. Fursei, . . Hi SOD . Malachie, . . . . . 149
S. Brendani Baie, . 69 et 192 | S. Laurentii Dublinien, . 167
S. Kierani abbatis, . . - 77 » Flannaniz’.| ieee ros
Catalogus SS. Hiberniz, or- - Katherine, "928 To
dinis triplicis, . . . - 78 | 5.Semani, . . . . . . 186
S. Monymna cogn. Darerca, 79 | S. Brendani, . . . . . 197
Seeiintanie |. 2 oS" he. Cemiedliy oa eee teed
S. Tygernachi, .. . 86 8. Mac Curtini acephala, . 190
De S. Columba et Brokdaee, &9 | Kaerani,) > 3)ge 97,

SHAME. Cpiey' 2 atria Anatom . Molingi, °.) 3.2) ya een oO
Semi, et tenn cai 94 .Colmani E. Drum, . . 201
S. Fintani cluan iedkinech, 101 | S. Cucaragius ab., . . . 203
S. Rodani, . . . . + . 106 | S. Columbe abbatis, . . 205
S. Aid, ep, >... a LOSS S. Baythint, |. ee
S.epintami, oe oy ese LO Molua, 0. eee
Ss Kamechi,i) ctr e-em let Doga,. oaths sae
S. Fintanl, bis <i cn atnntaoel20 Mochei, . .. . . 213

op)

. Colmani, Elo, . . . 123
. Columbi Tyredaglas, . 129
, Addani alias Mcedoci, . 133”
. Muni abbatis, . . . . 137)
Al banter es ees LAO

. Eoganii, ep., - . . . 216
. Meenissi,”) 3-.:.«inaietatt O17
- Cuone acephala,. . . 218
. Mochelloci acephala, . 219

™M

we

mM

o2

499

Upon the back of this table of contents is a portion of a
letter in Latin, without any signature, referring the reader of
it to Colgan and Speed for information as to the places men-
tioned in the book. The heading of the chapters is not in
the same handwriting as the body of the work, but in the
smaller hand which will be seen in the last couple of lines of
the fac simile. The book itself is about the size of the Book
of Ballymote, and has been cut down too closely in the binding,
which is also of vellum. A map of Ireland, without any name,
I think that of Speed, is laid into the volume, and I suppose
was made by the individual who wrote the index, the paper
of both being the same.

Vol. X XIII. (7806). The last piece in this volume is a
copy of the ‘* Purgatory of St. Patrick,” commencing thus :
** Patri suo peroptato in Christo.” The volume itself is a large
vellum folio, bound in wood, and attributed to the pen of °
‘* Henricus Saltereyensis,” and said to be written at the com-
mencement of the fourteenth century. It has no illumina-
tions, nor could I find any trace of the Irish character or
language.

Vol. XXIV. In this volume will be found No. 7960,
which is another copy of the ** Visio cujusdam militis Hibfnen-
sis ad edificationé multo¥ conscripta.” It commences thus:
** Incipit plogus Marci ad abbatissam quandam ;” and after this
prologue, commences, “ Ibernia igitur Insula.” The volume
itself is a very ancient vellum folio MS., in double columns,
attributed, and I believe justly, to the fourteenth century.
The vision occupies twenty folios, written upon both sides.
Upon the first folio of the volume may be found the following
note about this piece :

‘* Visio Tungdali militis Hiberni, an. 1148, auctore
Marco in qua mentio fit SS. Patricii apli Hiberni
Malachie ep. Dun. Ruadani Nenniz ep. Cluan
Ccelestini ep. Armach. Chaini ep. Lundinen.”

VOL. III. 2x

500

This MS. is without any illuminations, nor could I find
in it any trace of the Irish language.

Vol. XXV., containing Nos. 8530-8534, is a ‘collec-
tanea” which belonged to some Jesuit library, and contains a
tract entitled ** De Sanctis Hibernia Item de Hibernize His-
toria et quod qui Scoti appellantur usque ad annum fere 900
patria Hiberni fuerunt.”

The first part of this tract is a long alphabetical index to
the Irish saints, with references to notices, &c., of them. The
next part is a very interesting tract upon Irish history, being
a collection of notices by the most ancient writers upon the
country, arranged according to the subject. This tract is
- rather long. At the conclusion will be found a poem entitled
‘«¢ Sancti Ibernize in Belgio,” of fifty-two verses. The con-
tents of this volume are entirely in Latin. The second part
of the MS. is upon the Scotch saints. No date is to be
found in this volume ; Bossy it formed part of the Bollan-
dist collection.

Vol. XX VI. (8597) is a collectanea of hagiography, con-
taining the offices of some Irish saints, written in the same
hand as the last MSS. spoken of, and also belonging to some
Jesuit library. No name or date appear in it.

Vol. XX VII. In this volume will be found No. 9035,
which is a French translation of the Purgatory of St. Patrick,
and begins, ‘“‘ Moult de fois allant demander.” The com-
mencement of this is ornamented with a drawing of the Pur-
gatory, representing the souls in torment, the dimensions of
which drawing are about four inches by two and a half: it is
rather well executed, but presents nothing remarkable. The
MS. is of the fifteenth century.

Vol. XXVIII. This volume contains, among other
writings of St. Bernard, No, 9648, which is his sermon upon
the death of St. Malachy, ‘‘ Sermo in transitu Malachiz,”
commencing, ‘ De celo nobis, dilectissimi.” This MS. is
attributed to the twelfth century, and is perhaps the oldest

501

copy of the writings of this Father. ‘The initial letter is
ornamented with a portrait, said to be that of St. Malachy, and
of which the following is a fac simile.

This little portrait is of interest, representing, as is sup-
posed, the features of St. Malachy, and at all events exhibiting
the episcopal costume of the times; with this view I thought
it worthy of being presented to the reader, and, consequently,
made an accurate copy.

Vol. X XIX. containing Nos. 11976-11980, which are,
in the first place, ‘* Memorabilis promotio Dni Joannis Scoti
Canonici Dni Augustini prioris ecclesize de Busco dii Isaac in
eancellarium ordinis aurei velleris pr. fr. Hubertum Scotum.”
No. 11979 is ‘* Oratio habita in Capitulo gen. Ord. Velleris
Aur.,” and bears date the 5th of the Kalends of Ap. 1532.
They are both written upon paper of small quarto size; and

_at the end of the last piece (No. 11980) is the following
epitaph :
‘* Epitaphium Dni Johannis Scoti
Prioris Ecclesiz de Bosco Dmni Isaac”

“* Que cameratus in hanc protexit lucem Joannis
Scoti sub saxo hoc ossa sepulta jacent
Si quis erat procerum clarorum insignia doctus
Artifices inter gloria prima fuit
Ordinis enituit proin Cancellarius Aurei

| eee

502

Velleris Augusto Cesare sub Carolo
Hujus Cznobii tenuit moderamina pastor é
Terdenis annis pervigil atque tribus.”

This also bears date a. D. 1531.

Vol. XXX. In this volume, which is an historical col-
lection upon the governors of the ** Low Countries,” will be
found No. 16367, being the order of battle as given by Mar-
shal Saxe before the celebrated battle of Fontenoy. It was

‘printed at Gand, ‘* par ordre,” and is on official paper, some-
thing like a placard: it’bears date Ist May, 1746.

It may be mentioned, that the order of battle, as presented
in this paper, was not the one observed, as it differs materially
from a plan of the engagement which is in the possession of
the writer, and which was copied from that sent to the King
of Prussia after the battle; a copy of this latter plan was
also published at Lille in 1745, attached to Voltaire’s Poem
on Fontenoy, and had it not been correct it would not have
been attached to the writings of a court poet. However, the
discrepancy is easily accounted for; the Marshal may have
changed his mind, and countermanded his orders as first issued.

“Vol. XXXI. is a small portfolio, containing, among
other numbers, 17056; this is entitled ‘“‘ Anecdotes a la vie de
St. Dympna,” and is merely a short notice of that saint, not
differing from the ordinary memoir of her; it occupies but one
sheet of foolscap. ~

Mr. Ingram read the following note on certain Properties
of Curves and Surfaces of the Second Degree.

‘¢ The object of the present communication is to show that
several large classes of the properties of curves and surfaces of
the second degree, most of which, though of considerable in-
terest for their generality and elegance, have hitherto been
little studied by geometers, may, with advantage, be regarded
as results of that simplest form of the polar transformation, in
which a circle or a sphere (according as we are studying the

503
geometry of two or of three dimensions) is used as our auai-
liary.

** Beginning with curves of the second degree, we may
assume the properties of the circle as known. Then,

«<1. If we operate on the circle by the cyclo-polar method,
we arrive at the modular generation of the conic sections, and
are enabled to discover and prove almost all the properties re-
lating to their foci and directrices. This mode of proceeding
has been explained and practised by Poncelet, Gergonne, and
others, and is familiar to all students of geometry.

© 2, Let us next place the centre of our auxiliary circle at
the centre of the conic, and perform a second transformation ;
and we shall thus deduce from the already proved focal pro-
perties a series of theorems relating to two remarkable lines,
which may be termed the secondary directrices of the conic.
These lines have already been the subject of some researches
of Dr. Booth ; but he has obscured the simplicity of their
theory, by presenting their properties as results of a peculiar
and somewhat intricate analytic method. I have already no-
ticed, in another place,* the striking analogy which exists be-
tween these lines and the cyclic ares in the spherical conics. —

«© 3. But, instead of placing the origin of transformation -
at the centre of the conic, we may suppose it situated anywhere
in the same plane ; and in this way we shall be led to consider
a conic section as the locus of a point which moves so that the
square of its distance from a given point is constantly propor- -
tional to the rectangle under its distances from two fixed right
lines. The transformation at the same time indicates a class of :
new properties, which might be called guasi-focal properties,
inasmuch as in a particular case they reduce to the ordinary
focal properties, and they are in all cases analogous to those of
umbilicar foci in surfaces of the second degree. The generation
of the conic sections with which these properties are connected

* Philosophical Magazine for September, 1844.

504

was originally given by Chasles, but the properties themselves
to which I allude, have been overlooked both by him, and by
Cauchy, who has since discussed analytically the generation
in question in his well-known Report on M. Amyot’s Memoir,

‘* Similar considerations will apply to surfaces of the second
degree. .

«¢ We assume the properties of the sphere as known, Then,

‘¢ 1, From these the properties of the non-modular surfaces
of revolution are deduced by means of a sphero-polar transfor-
mation. This conception has been completely elaborated by
M. Chasles, in the Memoirs of the Royal Academy of Brussels.
(Nouv. Mem. tom. v.)

«© 2, Let us now take a non-modular surface of revolution,
and make its centre the origin of a second transformation ; and
from its properties, discovered in the way just mentioned, we
shall infer a great number of the properties of the modular
surfaces of revolution, especially those belonging to two planes
connected with them by remarkable relations. This idea also
M. Chasles has suggested, though he has not developed the
results of it to any considerable extent. (See Liouville’s
Journal de Math. tom. i. p. 187.)}

‘¢ 3. If, instead of placing the origin of transformation at
the centre of the non-modular surface, we assume it arbitrarily
in space, and then operate on the surface as before, we shall
light on the wmbilicar method, and we shall be enabled to de-
duce, by a uniform process, all the properties of the directive
planes and their poles, which arise out of that method. In
this way we are led to the theorems which | stated to the Aca-
demy on the last night of meeting, as well as to many others
of a similar kind. :

‘¢ 4. It is natural now to inquire what results we should
obtain by applying the sphero-polar transformation to the focal

* See also the Memoire de Geometrie, appended to the Apergu Historique.
§ xxii.

505

properties of surfaces of the second degree with three unequal
axes. And accordingly (in the Philosophical Magazine for
September, 1844), I have examined what are the results of
that process, when the centre of the surface is made the origin
of transformation, and in this way I have been led to discover
the properties of two cylinders, remarkably related to the sur-
faces of the second degree.

“5. But, more generally still, we may transform those
focal properties, placing the centre of our auxiliary sphere at
any point of space ; and thus the following leading problem is
suggested and solved :

** Given any surface of the second degree, and a point any-
where situated, to trace on the surface all the plane curves,
which, viewed from the given point, shall appear to be circles.

** The brief indications given in the present note will, of
course, require large developments; and these, with the per-
mission of the Academy, | shall endeavour to supply on some
future occasion. My object in what I have now said has been
merely to direct attention in a general way to several consider-
able groups of the properties of curves and surfaces of the
second degree, which may, with advantage, be studied as re-
sults of the Polar Transformation.”

DONATIONS.

Mémoires présentés par divers Savants al’ Académie Royale
des Sciences de (Institut de France. Tome IX. (Sciences
Mathématiques et Physiques.)

Mémoires de l Académie Royale des Sciences de Institut
de France. Tome XIX. Presented by the Institute.

On the Silurian Rocks and their Associates, in Parts of
Sweden.

A brief Review of the Classification of the sedimentary
Rocks of Cornwall. By Sir Roderick I. Murcheson. Pre-
sented by the Author.

506

Statistics of the Government Charitable Dispensaries of
India.

Statistics of Civil and Criminal Justice in India.

Statistics of the Educational Institutions of the East India
Company in India.

Mortality of the Madras Army, from official Records,
and A Catalogue of Chinese Buddhistical Works. By Col.
Sykes, H. M.R.I. A. Presented by the Author.

Memoirs of the Literary and Philosophical Society of
Manchester. Vol. VII. Part 3. New Series. Presented by
the Society.

Proceedings of the American Philosophical Society.
Vol. IV. Nos. 34 and 35.

Transactions of the American Philosophical Society.
Vol. 1X. New Series. Part 3. Presented by the Society.

An old Fiddle ; and an ancient Bronze Cheek-plate of a
Bit, anda small Celt. Presented by the Earl of Enniskillen.

Proceedings of the Royal Astronomical Society. Vol. X11.
Nos. 4-14.

Magnetical and Meteorological Observations made at the
Royal Observatory, Greenwich, in the Year 1844.

Astronomical Observations made at the Royal Observa-
tory, Greenwich, in the Year 1844. Presented by the Royal
Astronomical Society.

Astronomical Observations made at the Royal Observa-
tory, Edinburgh. Vol. VI. for the Year 1840. Printed by
the Observatory.

Transactions of the Royal Society of Edinburgh. Vol.
XVII. Part 2, containing the Makerstown Magnetical
and Meteorological Observations for 1843. Presented by
the Society.

A large Bronze Celt. Presented by the Rev. Dr. Sadleir,
Provost, T. C. D.

A Review of the Sanatory Condition of Dublin. By John
Aldridge, M. D. Presented by the Author.

a

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846_7. No. 68.

June 14th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

Arthur Sidney Ormsby, Esq., and John C. Egan, Esq.,
were elected Members of the Academy.

Ir was Resotvep,—That the Secretary of the Academy
be requested to prepare a draft of an Address to His Excel-
lency the Lord Lieutenant, to be submitted to the Academy
at its next Meeting.

Sir William Rowan Hamilton made a communication re-
specting the application of the Calculus of Quaternions to the
Theory of the Moon.

I. At two Meetings of the Royal Irish Academy, in the
month of July, 1845, Sir William Rowan Hamilton had exhi-
bited and illustrated the following general equation of motion
of a system of bodies, with masses m, m’, .., and with vec-
tors a, a’, .., and attracting each other according to New-
ton’s law: ti .

2a ;
Ta CIN CEN )
He had, at that time, deduced from this equation the known
VOL. III. 2Y

508

laws of the centre of gravity, of areas, and of living force, for
any such multiple system; and had shown that the corres-
ponding, but less general, equation of relative motion of a bi-
nary system, which (by changing a—a’ toa, and m+ m/ tom)
becomes

da M

de? ay (—a’)’ (7)

can be rigorously integrated by the processes of his new cal-
culus of quaternions, so as to conduct, with facility, when the
principles and plan have been caught, to the known laws of
elliptic, parabolic, or hyperbolic motion of one of the two at-
tracting bodies about the other. (See the Proceedings of July
14th and 21st, 1845, Appendix to Volume III., pp. xxxvii.,
&c.)

At a subsequent Meeting of the Academy, in December,
1845, Sir W. Hamilton had shown that the general differential
equation (1) might be put under this other form:

2 2 ’
0=43.m( 8a oat gata) +> Tirana (3)
and that it might, theoretically, be integrated by an adaptation
of that ‘* General Method in Dynamics” which he had pre-
viously published in the Philosophical Transactions of the
Royal Society of London, for the years 1834 and 1835; and
which depended on a peculiar combination of the principles of
variations and partial differentials, already illustrated by him,
in earlier years, for the case of mathematical optics, in the
Transactions of this Academy. (See Proceedings of Decem-
ber 8th, 1845, Appendix already cited, pp. lii., &c.)

At the same Meeting of December, 1845, Sir W. Hamilton
assigned the two following rigorous differential equations for
the internal motions of a system of three bodies, with masses
m, m’, m’’, and with vectors‘a, +a, y+a,—thatis, for the
motions of the two latter of these three bodies (regarded as

509

points) about the former,—as consequences of the general
equation (1) :

ay... Mm +m! ” (B—y)" y7
dé -By(—p)t” Toe a Hg roaats @)
SEM. stpienbaish th Bdeauibhe snfoe.

dé? Sa ae : eae cal (6)

It was remarked, that by regarding m, m’, m”, as repre-
senting respectively the masses of the earth, moon, and sun,
{3 and y become the geocentric vectors of the two latter bodies ;
and that thus the laws of the disturbed motion of our satellite
are contained in the two equations (4) and (5),—but especially
in the first of those equations (the second serving chiefly to
express the laws of the sun’s relative motion).

The part of this equation (4), which is independent of the
sun’s mass m”, is of the form (2), and contains the laws of the
undisturbed elliptic motion of the moon ; the remainder is the
disturbing part of the equation, and contains the laws of the
chief lunar perturbations. A commencement was made of the
development of this disturbing part, according to ascending
powers of the vector of the moon, and descending powers of
the vector of the sun; and an approximate expression was
thereby obtained, which may be written thus :

wnt} (E - ie it : ee ae 7 By) (6)
Vvi-(B-y)*} v7’) 2(—7'}

There was also given a geometrical interpretation of this
result, corresponding to a certain decomposition of the sun’s
disturbing force into two others, of which the greater is triple
of the less, while the angle between them is bisected by the
geocentric vector of the sun; and the lesser of these two com-
ponent forces is in the direction of the moon’s geocentric vec-
tor prolonged, so that it is an ablatitious force, which was
shown to be one of nearly constant amount.

Although the foregoing formulz may be found in the Appen-

2y2

510

dices already cited, to the Proceedings of the above-mentioned
dates, yet it is hoped that, in consideration of the importance
and difficulty of the subject, and the novelty of the processes
employed, the Academy will not be displeased at having had
this brief recapitulation laid before them, as preparatory to a
sketch of some additional developments and applications of
the same general view, which have since been made by the
author. It may, for the same reason, be not improper here to
state again, what was stated on former occasions, that all ex-
pressions involving vectors, a, a’, &c., such as are considered
in this new sort of algebraical geometry, and enter into the
foregoing equations, admit of being translated into others,
which shall involve, instead of those vectors, three times as
many rectangular coordinates, x, y, Z, x’, y’, 2’, &e., by means
of relations of the forms

axix+jythz, a’ =ta’+jy’+hk2’, &e. ; (7)
where 77 & are the three original and coordinate vector units

of Sir William Hamilton’s theory of quaternions, and satisfy
the fundamental equations

= jk = he |
Y=h jk st, ki=h;

(8)
jia=—h, hj = —i, n= —j;|

which were communicated to the Royal Irish Academy at the
Meeting of the 13th November, 1843. (See the Proceedings
of that date, and the author’s First Series of Researches re-
specting Quaternions, which Series has lately been printed in
the Transactions of the Academy, Vol. X XI. Part 2.)

II. It is evident, from inspection of the equations above re-
capitulated, that every transformation of the vector function,

o(a)=a7"(—a") (9)

which represents, in direction and amount, the attraction ex-
erted by one mass-unit, situated at the beginning of the vector

511

a, on another mass-unit situated at the end of that vector, must
be important in the theory of the Moon; and generally in
the investigation, by quaternions, of the mathematical conse-
quences of the Newtonian Law of Attraction. The integration
of the equation of motion (2) of a binary system was deduced,
in the communication of July, 1845, from a transformation of
that vector function, which may now be written thus:

as —a*),, = 2d .a(—a')* : (10)
where d is, as in former equations, the characteristic of diffe-
rentiation. And the hodographic theory of the motion of a
system of bodies, attracting each other according to the same
Newtonian law, so far as it was symbolically stated to the
Academy, at the meeting of the 14th of December, 1846, de-
pends essentially on the same transformation. In fact, if we
make

ada—daa

da=rdt, a= rdé; (11)
and if, by the use of notations explained in former communica-
tions, we employ the letters v and v as the characteristics of
the operations of taking the versor and the vector of a quater-
nion, writing, therefore,

U(a) =a(—a’)-; V.atT = —V.Ta= 3(at —Ta) : (12)
the equation (2) of the internal motion of a binary system be-
comes . P

a —mdu({rdé) .

ie v(r\rdé) sii

where the denominator in the second member is constant, by
the law of the equable description of areas. Hence, this second
member, like the first, is an exact differential; and an imme-
diate integration, introducing an arbitrary but constant vector
e, coplanar with a and 7, gives the law of the circular hodo-
graph, under the symbolical form

mee hy

v.r\rdé

512

the constant part of this expression (14) for the vector of the
velocity, r, being the vector of the centre of the hodograph,
drawn from that one of the two bodies which is regarded as
the centre of force; while the variable part of the same ex-
pression for represents the variable radius of the same hodo-
graphic circle, or the vector of a point on its circumference,
drawn from its own centre of figure as the origin.

Multiplying this integral equation (14) by §rdé, taking the
vector part of the product, dividing -by m, and multiplying
both members of the result into the constant denominator of
the second member of (13) or of (14), we find, by the rules of
the present calculus,

pease =s.e§rdé+7.(rde ; (15)

where s and 1 are the characteristics of the operations of taking
respectively the scalar and tensor of a quaternion, so’that, as
applied to the present question, they give the results,

t{rdt=Ta= ¥(—a’)=r; (16)
and
s.rdt = $(ea + as) = ercosv; (17)
where
€=Te= ¥ (—e’) =const. ; (18)

while v is the angle (of true anomaly) which the variable vec-
tor a of the orbit makes with the fixed vector —< in the plane
of that orbit ; and 7 denotes the length of a, or what is usually
called (and may still in this theory be named) the radius vec-
tor of the relative orbit. The first member of the equation
(15) is a positive and constant number, representing the quo-
tient which is obtained when the square of the double areal
velocity in the relative orbit is divided by the sum of the two
masses ; if then we denote, as usual, this constant quotient (or
semiparameter) by p, and observe that the constant e is also
numerical (expressing, as usual, the eccentricity of the orbit),
we shall obtain again, by this process, as by that of July,

513

1845, the polar equation of the orbit, under the well-known
form,

=— Pp .

1+ ecosv

(19)

This sketch of a process for employing the general transfor-
mation (10) in the theory of a binary system, may make it
easier, than it would otherwise be, to understand how the fol-
lowing equation for the motion of a multiple system,

(m+ Am)du(§Ardé)

v(ArSArdé) ”
(where m+ Am, 7+ Az, are the mass and the vector of velocity
of an attracting body, as m, 7 are those of an attracted one,

dr=>

(20)

which is analogous to, and includes, the equation (13) for the
motion of a binary one, and which agrees with a formula com-
municated to the Academy in December, 1846), was obtained
by the present author; and how it may hereafter be applied.

III. The vector function ¢(a) in (9) may be called the
TRACTOR corresponding to the vector of position a, or simply
the tractor of a; and another general transformation of this
tractor, which is more intimately connected than the foregoing
with the problem of perturbation, may be obtained by sup-
posing the vector a to receive any small but finite increment
B, representing a new but shorter vector, which begins, or is
conceived to be drawn, in any arbitrary direction, from the
point of space where the vector a ends; and, by then developing,
in conformity with the rules of quaternions, the new ¢ractor
$((3 +a), (answering to the new vector 3+a, which is drawn
from the beginning of a to the end of (3), according to the
ascending powers of this added vector 8. In this manner we
find
o(B+a)={—(B+a)} 4 (B+ay" =

§—a(1+a-'f) (1 + Pa) {a(l +a—')}-
= (14 Ba) (1 +a"p)# a "(—a") 4; (21)

p(B +a) = Zn, ni hn, ni (22).

that is,

514

if we make, for abridgment,

n,n = Mn, (Ba)” (aB)"a-"(— a) te (23)
where
1.3..(2n—1) _3.5..(2n’+1)
2.4.. (an) 24..Qn’) * es

Mn, ni —

The attraction ¢((3 +a) which a mass-unit, situated at the
beginning of the vector B-+a, exerts on another mass-unit
situated at the end of that vector, is thus decomposed into an
infinite but convergent series of other forces, gn, v, of which
the intensities are determined by the ¢ensors, and of which the
directions are determined by the versors, of the expressions
included in the formula (23) ; or by the following expressions,
which are derived from it by the rules of the calculus of qua-
ternions :

Tonw =m (x By (ways (25)
yu — Men n! 5 3

vbnn=(v.Ba)-" (va=(vB)"o(—a). (26)

Let a, 6, be the lengths (or tensors) of the vectors a, (3,
and let c be the angle between them, which angle we may
conceive to express the amount of the positive rotation, in
their common plane, from the direction of —a to the direction
of +3; then the positive or negative rotation in the same
plane, from the same direction of —a, to the direction of the
component force gn, n, is expressed as follows :

angle, from—a to force gn, v,=(n—’)C; (27)
and [

intensity of same component force = ina(Z) art (28)
The case n= 0, n’= 0, answers to the old tractor ¢(a), or toa
force of which the intensity is represented by a~®, while its
direction is the same as that of —a.

IV. Thus, if the vector a be conceived to begin at a point
-B, and to end at the point c, while the vector 9 shall be con-

515

ceived to begin at c, and to end at a; and if we conceive an
unit-mass at B to attract two other masses, regarded as col-
lected into points, and as situated respectively at c and at a;
this attraction of B will disturb the relative motion of a about
c, if a be supposed to be nearer than B is to c, by producing
a series of groups of smaller and smaller forces, of which
groups it may be sufficient here to consider the two following.

The first and principal group consists of the two disturb-
ing forces ¢)9 and ¢ ), and of these the first is purely ablati-
tious, or is directed along the prolongation of the side of the
triangle ABC, which is drawn from c to a, and it has its inten-.
sity denoted by the expression 34a—*, since we have for this
force, and for its tensor and versor, the expressions

dio=3B(—@)23 Toro=kba*; Udy=uP. (29)
The second disturbing force, of this first group, has for ex-
pression
dei 3aBa-"(—a’)= =3aBaa>; (30) ;
its intensity is exactly triple of that of the former force, being
represented by 3ba~*; and its direction is the same as that of
a straight line drawn from c to a’, if a’ be a point such that.
the line aa’ is perpendicularly bisected by the line Bc (pro-
longed through c if necessary). These two principal disturb-
ing forces evidently correspond to those which were considered
for the case of our own satellite in a communication above al-
luded to ; the second force being the one which was described
in that former communication as being directed to what was
there called the ‘‘ fictitious moon,” and was conceived to be
as far from the sun in the heavens on one side, as the actual
moon is on the other side, but in the same great circle.

If we now extend that mode of speaking so far as to con-
ceive a similar reflexion of the sun with respect to the moon,
and to call the point in the heavens so found the ‘ fictitious
sun,” the moon being thus imagined to be seen midway among
the stars between the actual and the fictitious sun: and if we

516

farther imagine a ‘ second fictitious sun,” so placed that the
actual sun shall appear to be midway between this and the first
fictitious sun; we shall then be able to describe in words the
directions of the three disturbing forces of the second group,
and to say that they tend respectively, for the case of our own
satellite, to these three (real or fictitious) suns. For these
three forces will have, for their respective expressions, the three
corresponding ¢erms of the development of the tractor (22),
namely, the following :

$2,0 = § Ba (—a°y =; +
gi = $P'a(—a’y (31)
« Goa = 2 aBaBar (—a)-#;
of which the intensities are respectively
gBa*; ga"; 12b'a; (32)

so that they are exactly proportional to the three whole num-
bers, 1, 2, 5; while they are directed, respectively, to the first
fictitious sun, the actual sun, and the second fictitious sun.
The disturbing force of a superior planet, exerted on an infe-
rior one, may be developed or decomposed into a series of
groups of lesser disturbing forces, the intensities of the several
forces in each group being constantly proportional to whole
numbers, in an exactly similar way ; nor does the application
of the principle and method of development thus employed
terminate here. In the applications to the lunar theory, a and
b, in therecent expressions, are to be regarded as denoting the
variable distances of the sun and moon from the earth; and
the expressions for the forces are to be multiplied by the mass
of the sun. Nothing depends, so far, on any smallness of ec-
centricities or inclinations.

V. The lunar theory is, very approximately, contained in
the differential equation (4), provided that we regard y as the
elliptic vector of the sun, drawn from the common centre of
gravity of the earth and moon; and the laws of the sun’s re-

517

lative elliptic motion, with respect to that centre of gravity,
are then contained in the following differential equation, which
takes the place of the equation (5) :

dy _ m-+m' +m”
LUG Gao i

Indeed, when we come to consider the small disturbing

(33)

forces which belong to the second group, and which depend on
the inverse fourth power of the sun’s distance, the correspond-
ing terms of the development of the first member of the formula
(6) are then, for greater accuracy, to be multiplied by the

. m—m’ ; : .
fraction Eran which expresses the ratio of the difference to

the sum of the masses of the earth and moon. But if we neglect,
for the present, those small disturbing terms, we may regard
that formula (6) as accurate, without as yet neglecting anything
on account of smallness of eccentricities or of inclinations ; and
even without assuming any knowledge of the smallness of the
moon’s mass, as compared with the mass of the earth; y still
denoting, as just stated, the elliptic vector of the sun. And
thus, if the moon’s geocentric vector SB be changed to the sum
(+86, where the term 6 is supposed to depend on the dis-
turbing force, and to give a product which may be neglected
when it is multiplied by or into the expression for that force,
we shall have the following approximate differential equation,
by developing the disturbed or altered tractor ¢((+ 3), and
confining ourselves to the first power of 6G :

acm al is OE

de dé? leibnlia %

| mt 3g 4 3-198 8) + (B+ By Br). (34)
2(— B*y? ramos
The disturbance 8B of the moon’s geocentric vector is thus
exhibited as giving rise to an alteration 6¢((3) in the corres-
ponding tractor (3), which alteration is analogous to a dis-

518

turbing force, and occasions the presence of the first of the
two parts of the second member of the equation (34): which
equation will be found to contain a considerable portion of
the theory of the moon.

VI. The author will only mention here two very simple
applications, which he has made of this equation (34), one to
the Lunar Variation, and the other to the Regression of the
Node. Treating here the sun’s relative orbit as exactly circu-
lar, and the moon’s as approximately such, neglecting the in-
clination, taking for units of their kinds the sum of the masses
of the earth and moon, and the moon’s mean distance and
mean angular velocity, and employing, as usual, the letter m
to denote (not now the earth’s mass, but) the ratio of the sun’s
mean angular motion to the corresponding motion of the moon,
the differential equation (34) becomes :

CoP = 4(88 +3838 B)+ (B+3y"By)s (8)

in which the laws of the circular revolutions of the vectors 3
and y give

d2R8° d2.
ce —B; Ta = —m*y. (36)

Assuming, from some general indications of this theory,

an expression for the perturbation of the moon’s vector, which
shall be of the form

oB=m*( AB + By "By + CB y" Byp); (37)
and neglecting all powers of m above the square, we find
as :
oP = —m"( AB + By"By +8°CB-y~"ByB); (38)
BSB.B =m" AB + Cy"By+ BB y'ByB); — (39)
so that the three numerical coefficients, 4, B, C, must satisfy
the three following equations of condition :

—A=2A+;_ giving dA=—1; (40)

and ; ‘
—B=}(B+3C)+3; —9C=3(C+3B); (41)

mal ae

giving
B=—-13; Cx=4+,%- (42)
Thus, if we neglect eccentricities and inclinations, and con-
fine ourselves to the first power of the disturbing force, or to
the second power of m, the perturbation of the moon’s vector,
produced by the sun’s attraction, is composed of the three fol-
lowing terms :

19m?

98 = — B—tBy + By ByB. (48)
The first of these three terms expresses that the sun’s abla-
titious force, by partially counteracting the earth’s attractive
force on the moon, allows our satellite to revolve in a some-
what smaller orbit than would otherwise be consistent with
the observed periodic time: the ratio of the diminished to the

Suleitiee : ; : m
undiminished radius of the orbit being that of 1— = to l.
The second term expresses a displacement of the moon, through
perturbation, from its diminished circular orbit, of which dis-

placement the constant magnitude or length bears to the radius
2

of the undiminished orbit the ratio of we to unity ; while

the direction of this displacement is always from that fictitious
moon, ¢o which it has been seen that one of the two principal
components of the sun’s disturbing force is directed : an oppo-
sition of sign which may at first surprise, but which is exactly
analogous to the contraction of the orbit produced by the ab-
latitious force (when the periodic time is given), and is to be
explained upon similar principles. Finally, the third term of
the formula (43) for 8, expresses that with the two foregoing
displacements a third is to be combined, which is, like them, of
constant amount, being equal to ;3,ths of the second displace-

ment, or bearing to the radius of the moon’s orbit the ratio of
m2
76 '° unity ; but being always directed to what, by an exten-

sion of a recently employed phraseology, might be called the.

520

second fictitious moon, being so placed that the actual moon
is midway in the heavens between this fictitious moon and the
one which was before considered. These two latter terms of
(43) contain the chief laws of the Lunar Variation ; and are
easily shown to give the known terms in the expressions of
the moon’s parallax and longitude, :
11m?
8

It may assist some readers to observe here, that when the in-

ds m?cos2()—®@); d=

sin2(D—@). (44)

clination of the orbit is neglected, the longitudes of the first
and second fictitious moons are, respectively,

2©—), and3)—20; (46)
while those of the first and second fictitious suns, mentioned
in a former section of this abstract, are, under the same con-
dition,

2) —©, and 3@©@—2). (47)

VII. The law and quantity of the regression of the Moon’s

Node may also be calculated on principles of the kind above
stated, but we must content ourselves with writing here the
formula for the angular velocity of a planet’s node generally,
considered as depending on the variable vector of position a,
da
de
and also on a vector unit A, supposed to be directed towards
the north pole of a fixed ecliptic. The formula thus referred
to is the following :

the vector of velocity and the vector of acceleration

"a
de”

dgettetesediana a, (48)
(v.Av.ada)?
where s and v are, as before, the characteristics of the opera-
tions of taking the scalar and vector of a quaternion. The
author proposes to give a fuller account of his investigations
on this class of dynamical questions, when the Third Series
of his Researches respecting Quaternions shall come to be
printed in the Transactions of the Academy: the Second Se-

=—

521

ries being devoted to subjects more purely geometrical ; as the
First Series (already printed) relates chiefly to others which
are of a more algebraical character.

Dr. Apjohn read a paper on the composition and optical
properties of a variety of hyalite, from Mexico.

‘¢ This mineral,” he observed, ‘*came into my possession as
Professor of Mineralogy to the University, having been pre-
sented, through Mr. Ball, tothe College Museum, by Profes-
sor Radice. It occurs in detached mammillary and wrinkled
masses, sometimes larger than a walnut, and pellucid ina
high degree. It is harder than glass, but is scratched by steel,
and, from an experiment very carefully made, was found to
have the specific gravity of 2.1016. It is much more frangi-
ble than quartz, but when broken exhibits something of the
conchoidal fracture.

‘* The different properties just enumerated belong also to
other well-known varieties of hyalite; and, notwithstanding
its occurring in detached glassy drops of unusual size, little
hope was entertained that a chemical examination of it would
conduct to any new result. Upon, however, subjecting it to
experiment, this anticipation was not verified, for it was found
to contain much less water than any variety of hyalite whose
composition has been recorded. Thus, as the mean of four
experiments scarcely differing from each other, it yielded,

Silex: WVer beet iog /essiagt.48
Waterss, dav! 20 srolsor2b2
results which correspond accurately with the formula
15SO;, 2HO.

‘* Beudant says, that in the case of the transparent opals,
by which he, of course, means the hyalites, the loss by calcina-
tion amounted always, in his experiments, to from eight to ten
per cent. ; while, in the case of the semiopaque opals, the vola-
tile matter expelled by heat varied from five to seven per cent.
And in two analyses of hyalite, the details of which he gives,

522

the water was in one 6.35, and in the other 8.68 parts in 100.
The Mexican hyalite, therefore, is quite peculiar as respects
the amount of its constituent water, this being not more than
two-fifths of what has been found in the least hydrated variety
of the mineral whose analysis has been published.

‘«¢ The most remarkable circumstance connected with this
mineral remains to be mentioned. ‘The hyalites are, in all
treatises on mineralogy, described as single refractors ; but,
upon transmitting through the Mexican hyalite a ray of plane-
polarized light, and examining it in the usual manner, with an
analyzing eye-piece, it was found to possess in a very marked
degree the property of depolarizing the ray. The action,
however, exerted by it, appeared of an anomalous kind ; for,
while in all doubly-refracting minerals, whether uniaxal or
biaxal, there are two positions of the crystal, in which, if inter-
posed (for example) between two tourmalines whose axes are
crossed, the light continues excluded, there is no position into
which a lamina of this hyalite can be brought, by revolving it
in its own plane, in which the light will not be restored.

‘“¢ The action, therefore, of this mineral on polarized light
is not of the ordinary kind, and can, as far as my knowledge
of this difficult subject extends, only be explained by suppos-
ing that, like rock crystal in one particular direction, and cer-
tain essential oils and aqueous solutions of sugar, dextrine, &c.,
it possesses the power of changing the position of the plane
of polarization of a plane polarized ray, or of causing it to
revolve through a greater or less angle. This view would
seem to be corroborated by the following experiments.

‘© 1, A ray of homogeneous red light was made to pass
through a lamina of the hyalite, on which nearly parallel
planes were cut and polished, this lamina being interposed
between a pair of crossed tourmalines. The light was thus
restored, and, by rotating the tourmaline next the eye to the
right, it was again very nearly extinguished.

««2. The preceding experiment was repeated with yellow

523

light, got from a spirit-lamp with salted wick, and with the
same results.

"© 3. Upon substituting for the light of the spirit that
transmitted through a window-blind of a yellowish colour, the
phenomena of the last experiment were very distinctly repro-
duced.

“<4, In operating, by aid of the apparatus used in the
preceding experiments, with heterogeneous or solar light, and
making the analyser revolve, a series of tints were produced,
much feebler than those exhibited by quartz, but following
apparently the same law. .

“* From these facts I think I am justified in concluding,
that this hyalite exercises the power denominated rotatory
polarization. This property, too, it possesses, no matter in
what direction it is traversed by the plane polarized ray, a cir-
cumstance which would seem to identify it with that exerted
by liquids, and distinguish it from the analogous influence of
quartz, which is manifested only in the direction of the optic
axis.

‘* Before concluding this paper I may be permitted to
give expression to an opinion, which is, I believe, shared by
most mineralogists, namely, that hyalite, opal, and calcedony,
have all had a similar origin, or were originally silex in the
gelatinous condition which it assumes when certain alkaline
silicates are dissolved in dilute acid, and their solutions are
slowly evaporated. All three include water, the hyalite in
greatest, and the calcedony in smallest quantity ; and in some
specimens that I have seen, these minerals may be observed
to pass by insensible gradations into each other. This is well
illustrated by some lumps of the Mexican hyalite which have
nodules of calcedony attached to them, the latter mineral dif-
fering in no respect from the former, save in being less trans-
parent, and containing a smaller quantity of water,—its amount
being about 0.53 per cent., according to a single experiment.
The water, too, in all, is, I believe, present, not in a state

VOL, III. 22

524

of chemical, but of mechanical union, and gives to these mine-
rals the different degrees of transparency which they exhibit,
just as water confers the same property upon specimens of
hydrophane or tabasheer, into whose pores it has been intro-
duced by capillary absorption.

‘* From the analogy as to chemical constitution between
hyalite and calcedony, one might be inclined to conclude that
both would modify light transmitted through them ina similar
manner. ‘This idea, however, would appear to be inconsistent
with experiment, for a plate of agate is said to polarize light
in the ordinary manner, or in a single plane; and Sir David
Brewster is of opinion that the action which it exerts is of the
same nature with that which belongs to tourmaline. These
statements are certainly not true of the mineral which I have
this evening brought under the notice of the Academy.

«¢ P.S.—Since the preceding remarks were put together,
I have found that a ray of light polarized by reflexion, and
made to disappear by the interposition of a Nicholl’s prism, was
restored when made to pass through a particle of hyalite from
Frankfort on the Maine. All varieties, therefore, of this mi-
neral may be concluded to possess the same optical proper-
ties.

“Tn respect to the experiments above detailed, I have found
that the results are somewhat different, according to the part
of the lamina of hyalite traversed by the light, the change in
the position of the plane of polarization not having always the
same direction or value, and being sometimes null. This fact
would seem to point to a different explanation of the pheno-
mena from that already suggested, and to identify the optical
characters of hyalite with those of rock crystal, the differences
being explicable upon the hypothesis of the former mineral
being composed of a multitude of minute crystals of the latter,
thrown together without any regular or symmetric arrange-
ment.”

525

Rev. T. R. Robinson, D. D., read a paper on the effect
of Heat in lessening the Affinity of the Elements of Water.

The author referred to the experiments of Mr. Grove on
the decomposition of water by the action of incandescent pla-
tinum; and, after noticing the objections which were urged
against its being caused by heat, detailed results which he
had obtained at a much lower temperature, and which ap-
peared to him to accord with that hypothesis.

Proceeding on the theory of the voltaic circuit, which
Ohm has given, he investigated the diminution of electric
intensity, which is caused by placing in the circuit a cell where
water is subjected to voltaic decomposition, and shewed that
it is equal to the affinity of platina for oxygen minus twice that
of hydrogen for oxygen, or

€ = op — 2ho.

This quantity e can be measured by the instruments and pro-
cesses described by Mr. Wheatstone in the Philosophical Trans-
actions for 1843, with some modifications, which, in the au-
‘thor’s opinion, increase their accuracy. After describing the
apparatus he used, he finds for the value of e,

At the temperature 61°. . . €=598.9 . . . 12 obs.
LOMA yi) ee 567.6... 13
2A) Os ea a HSU Crs sa

These give, for an increase of temperature of 100°, the decrease
of the affinity of the oxygen and hydrogen of water = 23.2. The
author applies to this result the theory of probabilities, which
has so much advanced astronomical and physical science ; and
finds the chances to be 10,000 to 1 that it is not all error of
observation.

It might be objected, that this diminution of e is due to
the expansion of the gases by heat enabling them to escape
more freely from the electrodes. This was tested by placing

526

the apparatus under the air-pump, and measuring the electro-
lytic resistance at a pressure of 1.1 inches. This gives

at 64°.6. . e= 589.6,
and it is shown, that the chances are 3 to 2 that the unexplained
difference is mere error of observation.. The mere escape of
the gas, therefore, does not change e.

This change of temperature produces no alteration of me-
tallic affinities, as is shown by the intensity of Daniell’s cell
being the same at 64° and 163°. The expression of this is
e=zo—2cu.o. That for a cell excited with dilute sulphu-
ric acid = zo — cu.o— ho, and it is found to decrease 27.9
for 100°. The mean of all gives 25.1; and, if we might sup-
pose this rate to be uniform through the thermometric scale,
it would give 2386°, midway between the melting points of
gold and cast-iron, for the temperature at which this affinity
would cease.

The author concludes by expressing his doubts, that the
combination of these gases is in any case produced by heat ;
and suggests that light is more probably the agent when the
combustion is rapid, and the capillary force of the surfaces in
contact with them, at lower temperatures, aided by some actinic
influence extricated by the heat. Finally, he points out as a
promising subject of mathematical research, the application
of the undulatory theory to the phenomena of conducted and
latent heat.

Sir William R. Hamilton read a paper by Professor Young,
of Belfast, on an extension of a theorem of Euler.

The object of the author is to extend and generalize the
theorem of Euler,—that the sum of four squares, multiplied by
the sum of four squares, produces the sum of four squares. He
commences by examining into the construction of the four-
square formula, with the view of ascertaining whether any
thing like a definite law or principle connects its component

527

parts together; and from which a formula for a greater num-
ber of squares might be suggested. Such a principle is found
to govern the generation of the four-square results, when these
are arrived at by a peculiar process, which the author exhibits.
The same process is then extended to the case of eight squares;
and it is found that
ee ee v2 + w? + 0? 4 y? 4 22)x
(9 +P 4V 4 4w+er +4 2)=
(ss’ + tt! + uu! + vv’ + ww’ + aa’ + yy! + 22’)?
+ (st’ — ts’ + uv’ — vw + wa’ — aw’ + y2’ — zy’)
+ (su’ — us’ + vl! — bv! + yw! — wy! + a2’ — 2za’P
+ (svo’ — vs’ + tu’ — ut’ + we! — zw’ + ay’ — yw’/y
+ (sw’ — ws’ + at! — ta’ + uy’ — yu! + 20! — v2’)?
+ (sa! — as’ + tw! — wt’ + yo’ — vy! + zu! — U2’)?
+ (sy — ys’ + 2t! — tz’ + va’ — av! + wi’— uw’)
+ (s2’ — zs’ + ty’ — yl + vw’ — we’ + ux’ — au’)’.

These results are verified by the actual development of the
several squares ; which development, by the mutual cancelling
of all the double products, reduces itself to the sixty-four
squares furnished by the product of the proposed factors, when
multiplied together in the ordinary way.

_ The author then enters into a more minute examination of
the constitution of the preceding polynomial ; and shows that
the cancelling of the aforesaid double products is a necessary
consequence of that constitution.

It is further shown that the product continues to be of the
same form as each of the factors, when the coefficients a°, a’,
a’, a®, &¢., are introduced in order, in connexion with the

squares entering those factors.

Sir William Rowan Hamilton stated also a theorem respect-
ing products of sums of eight squares, which does not essen-
tially differ from the foregoing, and was communicated to him
by John T. Graves, Esq., about the end of the year 1843.

528

One form of the theorem is the following:
(00’ — 11’ — 22’ — 33’ — 44’ — 55’ — 66’ — 77’)?
+ (10’ + 01’ — 32’ 4 23’ — 54’ + 45’ — 76’ + 67’)?
+ (20’ + 31’ + 02’ — 13’ — 74’ — 65’ + 56’ + 47’)?
+ (30/ — 21’ + 12’ + 03’ — 64’ 4+ 75’ + 46’ — 57’)?
+ (40’ + 51! + 72’ + 63’ 4 04’ — 15’ — 36’ — 27’)?
+ (50! — 41’ + 62’ — 73/ + 14! + 05’ — 26’ + 37’)?
+ (60! + 71! — 52’ — 43’ + 34’ 4 25’ + 06/ — 17’?
+ (70! — 61’ — 42’ + 53’ + 24’ — 35’ + 16’ + 07’?
= (0? + 1? + 224 3? + 424 5? + 6 + 7?) (02 +
12 4 Q/ 4 32 4 42 ke 5/2 + 62 + ie
In a letter dated January 18th, 1844, Mr. Graves commu-
nicated to Sir William Hamilton his theorem respecting sums
of eight squares under the form:
(P4+B04+C4P +e 4f?+9'? +h’) x
(a?+6?+4+c?+d? +e” +f? +9? +h”) =
AP 4+ 4 de pet frag? th?;

where a”. . h’’ denoted the following expressions;

a” =aa' — bb' — cc’ — dd’ — ee’ — ff’ —ggq' —hh’;

b’ = ba’ +ab’ — de’ + cd! — fe’ + ef’ +hg' — gh’;

ce” =ca' +db' + ac’ — bd’ —ge' —hf’ + eg’ + fl’;

ad!” = da! — cb! + bc! + ad’ — he’ + gf’ — fy’ + el’;

e’=ea' + fb +c’ +hd' + ae’ — bf’ — cg’ — dl’;

S' = fa — eb! +he' — gd! + be’ +-af" + dg’ — ch’;

g! = ga! — hb’ — ec’ + fa’ + ce’ — df’ +ag' + bh’;

h” =ha' +.g9b' — fc’ — ed’ + de’ + cf’ — bg’ + al’.
In a letter of somewhat earlier date, but evidently written
in haste, upon a journey, and dated December 26th, 1843,
analogous expressions had been given, containing, however,
some errors in the signs, which were soon afterwards corrected
as above. ‘That earlier letter also indicated an expectation
that a theory of octaves, including a new and extended system
of imaginaries, which had thus been suggested to the writer
(J. T. Graves, Esq.) by Sir William R. Hamilton’s theory of

529

quaternions, might itself be extended so as to form a theory of
what Mr. Graves at the time proposed to call 2”-¢ons : but in
a letter written shortly afterwards, doubts were expressed re-
specting the possibility of this additional extension, from oc-
taves to sets of sixteen.

The special thanks of the Academy were given to Lord
Farnham, for his Donation to the Museum of the following
Collection of Antiquities :

Two Gun Barrels, one Gun Lock, three Cannon Balls,
several fragments of Cannon Balls and Shells, four Leaden
Bullets, and one Sword, from Cloughoughter Castle.

Curious ancient Keys, from Newtownbarry, and Bally-
Jamesduff:

Fifty-five Flint Arrow- Heads.

Sia Flint Knives.

Twenty-four Bronze Celts, of different patterns.

An ancient Hand-mill, perfect ; the top Stone of another ;
and a round Grind Stone.

An old Glass Bottle, from Cavan.

A Sling Stone, from Dunshaughlin.

One perfect Bronze Sword, found at Corchor, Co. Cavan,
and fragments of another.

Five Blades of Bronze Daggers.

Two Bronze Spears.

Four Bronze Pins, with Rings.

Two Bronze Bosses.

A Brass Spoon.

A Brass Spur, found at Shaneloon, Co. Cavan.

A Brass Cross.

A Silver Cross.

A Brass Pistol.

A Snuff Box made from a Cannon used at the Siege of

Derry.
A Snuff Box found on the battle ground at Vinegar Hill.

530

A fragment of an ancient illuminated Breviary, found in
a bog at Myshal, Co. Carlow.

Two large BrassPots, and an Iron one, from the Lake of
Virginia. .

An ancient Bronze Bucket-shaped Pot.

Three Methers.

A small Wooden Cup.

Four Grey-beard Jars.

One beautiful cinerary Urn, found at Killinagh, “lying
in the centre of six large stones, placed perpendicularly, and
opposite to each other, three at either side. Near the spot was
a large, rough flag, supposed to have been originally covering
the stones. The urn was buried about two feet under ground,
and when found was nearly full of ashes, and the place about
bore evident marks of fire; no lid was found, nor any other
marks of its being a place of burial.”—Eztracted from the
Rev. C. S. Montgomery's Note to Lord Farnham.

Two Shoes found in a bog.

Ten Spindle Stones, and two Weights.

Two Stone Hammers.

One square perforated Stone.

One triangular Jet Ornament.

Two Flint and eighteen Stone Celts.

One Sharpening Stone.

A Stone shaped like a Cow’s Foot.

Two perfect Bronze Trumpets, and one imperfect, found
at Coracanway, Co. Cavan.

Three Iron Stirrups.

A fragment of shed Horn of the Irish Elk, found at Lis-
duff, Co. Cavan.

A Letter, found in the pocket of the Rev. Mr. Murphy,
who was killed at Arklow, on the 9th of June, 1798.

PROCEEDINGS

OF

THE ROYAL IRISH ACADEMY.

1846_7. No. 69.

June 28th, 1847.

REV. HUMPHREY LLOYD, D.D., President, in the
Chair.

His Grace the Archbishop of Dublin was elected a Mem-
ber of Council, on the Committee of Polite Literature.

Ir was Resotvep,—That the sum of £50 be placed at
the disposal of the Council, for the purchase of antiquities.

The Secretary read the draft of an Address to His Excel-
lency the Lord Lieutenant, which had been ordered at the
last Meeting.

ResotveD,—That the Address now read be adopted by
the Academy.

John Anster, LL.D., read a paper by the Rev. James
Wills, in continuation of his former papers on ‘ the Associa-
tion of Ideas.”

The author commenced by stating, that, according to the
view to which he had been led, the subject might be divi-
ded under three heads of inquiry :—the class of associations
formed by habits of action and perception, as described in his
first Essay; those from accidental association, explained in
the second ; and those next to be considered, originating in the
mind itself. From the first he had endeavoured to trace the

VOL. III. 3A

532

main stock of human ideas and capabilities of action ; to the
second he had traced the process of memory ; the third he
would show to be mainly instrumental in invention, and in
various ways operative in art and literature, as also upon human
character and conduct, and, lastly, upon the operations of judg-
ment and reasoning.

The formation of new ideas by the mind might, he ob-
served, be effected by means, not directly to be described as
single operations of thought; of this nature were purely ar-
tistic ideas, which might be framed by rules according to certain
models, and then become ideas of association or not, according
to circumstances. Such results were excluded from the author’s
inquiry, and were only mentioned to guard against any mis-
conception, and for the sake of a distinction, which would be
available in his illustrations.

The process at present to be considered by the author is
mainly distinguishable from that examined in his first Essay,
by the fact that, while the first class of associations were
framed gradually from the immediate repetition of acts or per-
ceptions, those now to be explained were instantaneously put
together from general analogies, which were, however, them-
selves framed from habitual experience, like the former. These
analogies are insensibly contracted through life, and are the
nearest approach to universal ideas, consisting of characters,
forms, colours, proportions, and properties, which are variously
combined throughout all known existence. Such are the ele-
ments of conceptual power, or the faculty of spontaneous as-
sociation, of which the action and exercise could be variously
determined by the habits and character of each individual.

The author briefly exemplified the mode of operation; and
went on to say that he would pursue the subject in relation
to literary composition and art,—to moral sentiment,—and,
lastly, to the operations of reasoning.

From this the author gave an explanation shewing the
justice of Mr. Locke’s distinction between wit and judgment.

533

The first head of this division might be regarded as coin-
cident with those mental operations commonly included under
the term imagination, which he would occasionally use, as a
convenient term, and of familiar use.

The author next proceeded to show that, as the ideas he
had described were essentially those of sensible properties, it
must be a consequence that their combination must be sensi-
ble associations, and therefore affecting the mind, in whatever
degree, in the same manner as the sensible presence of such
objects, had they any real or external existence. Such effects
would be very indistinct in some (probably in most) minds,
and very intense in others. It would be apparent from these
considerations, that in one class of writers, or artists, the mind
constructs a combination by mere rules, and in another from a -
distinct and sensible conception ; and further, that in the ana-
lysis of writings or works of art, some indications might be
discoverable of these two different modes of operation.

There was also another consideration, which, though
seemingly leading to a difficulty, would very much tend to aid
in the clear exemplification of this process. Its nature being
to produce effects similar to the known effects of present reality,
may be traced more clearly by comparison with them, The
author would, he said, avail himself of this inference as a
means of illustration.

He then proceeded to cite various examples from standard
poets, in which he traced the indications of distinct presence,
or conception of presence, which he severally contrasted with
conjectural cases of the opposite mode of artistic construction,
without those conceptions. -

The author next proceeded to notice other kinds of exam-
ples in the conception of characters, events, and in translation
of the thoughts of others, in which he showed that the differ-
ence of language could frequently be only remedied by equi-
valents supplied by the aid of the original conception. |

534

The Secretary read the following communication from Sir
William Betham, on a leaden seal of Herbert de la Mara, now
preserved in the Museum of the Academy :

«« This is a singular matrix, inasmuch as lead is a very
unusual material for a seal of any age, but especially of the
antiquity I take this to be.

‘* Considering the material of which it is made, it is very
perfect. Herbert is in armour on horseback, in full gallop, as
princes and great nobles of that day were represented ; on his
left arm is the triangular shield of the twelfth and thirteenth
centuries ; in his right, which is extended, is something like
a short club or mace. The bit of the bridle is very long and
severe. Round the circle is the following inscription:

+ SIGILLYM: HEREEBERTI DELAMARA.

‘¢ When Mr. Underwood first produced this seal to me, I
considered that it was the seal of Herbert Delamare, who lived
in the reign of Edward III.; at the same time, I thought the
shield indicated a higher antiquity, and further investigation
convinced me it was of the end of the twelfth or beginning
of the thirteenth century.

“ In a MS. in my possession I find the following notes
respecting the Delamares :

‘* ¢ Richard Delamara was witness to a charter of William
Rufus to the monastery of Bermondsey.

‘© ¢ Henry Delamare was huntsman to the King, 5 Ste-
phen.

‘¢ ¢ Richard Delamare, said to be son of Henry, was she-
riff of Oxfordshire, 34 Hen. II., and of Oxford and Bucks,
1 & 2 Rice. I.

‘* ¢ Geoffrey Delamare had lands in Berkshire, 10 John.

«¢ ¢ John Delamare, his grandson, was knighted 34 Edw. L,,
and summoned to the Parliament of England 6th February,
34 Edw. I. (1305), as Baron Delamare.’

530

‘¢ The name is evidently French, but as I do not find it in
Battle Abbey Roll, or in Brampton’s List, I should suppose
the first who came to England must have followed the Con-
queror after he was settled as King of England, or in the
reign of William Rufus.

“* In another MS. in my possession I find the following
passage, which I consider refers to the possessor of this
seal:

«© ¢ Herbert Delamare, of Norman French extraction, and
a leading man, came to Ireland on the first invasion thereof
by the English (with Hugh de Lacy, who obtained the grant
of the kingdom of Meath from King Henry I1., to be held in
as ample a manner as O’ Melaghlin held it ; in fact the King
granted him an honour, or Palatinate, as ample as it could be
granted: the words are ‘quod ibi habeo vel illi dare possum.”)
He obtained ample grants of great possessions in the western
parts of Meath, of which he was made governor, and from him
all the Delamers of Ireland were descended. From him this
family were called by the Irish Mac Erbert.

‘¢ ¢ William Delamer, son of Herbert, lived in the reign
of Henry the Third, and founded and endowed the Abbey of
Multifernam.

*¢ * John Delamer, a powerful nobleman, built the strong
castle of Maghbreacy, in the country of Annaly, now called
the county of Longford, and made it his chief seat in 1294,
which it continued until the family were deprived of their es-
tates by Cromwell. In that year he joined John Fitzgerald,
Baron of Ophaley, against Richard De Burgo, Earl of Ulster,
and took him prisoner, and confined him in the Castle of Leix,
This John was slain by the O’Ferralls of Annaly.

‘© ¢ Sir William Delamare, of Herbertstown, in the County
of Meath, was living in 1322, and was married to a lady named
Margery, and was father of

‘* « Herbert Delamare, who entered into recognizance for
the fealty of all his clan, 1347 ; his son was”

536

«© ¢ John Delamare, of Herbertstown, was living in 1354,
whose eldest son, William, died before his father, leaving a
son,

‘© < John Delamare, of Herbertstown, who succeeded his
grandfather, and was living 11 Richard II., 1387.

«¢ ¢ Herbert Delamare, of Herbertstown, was living 1419,
and was father of two sons,—Meyler, who left ason, Herbert,
who left a son, Herbert, who died 10th November, 1580, with-
out issue ;—and Walter, who was father of Theobald, whose
son, Walter, succeeded to the estate on the death of Herbert,
and died 1613, and was succeeded by his grandson, Richard,
who was twenty-six years of age, in 1613.’ ”

A note by the Rev. Charles Graves was read, ‘on the
Solution of linear differential Equations, and other Equations
of the same kind, by the Separation of Symbols.”

Mr. Graves gives two distinct developments, which furnish
solutions of the linear differential equations of the mth order.
The terms of one of these developments are obtained by suc-
cessive quadratures ; and the solution so arrived at is the gene-
ral solution of the proposed equation, containing » arbitrary
constants.

All the terms of the other development are obtained by
mere differentiation ; but the solution itself is only a particu-
lar integral.

The solution of the linear differential equation of the se-
cond order may be obtained in a sufficiently simple form by
this method, which applies itself with peculiar facility to the
treatment of equations of differences.

Rev. George Salmon read a note ‘‘on the Generation of
Surfaces of the Second Degree.”

‘« Mr. Ingram having, at a late Meeting of the Academy,
alluded to a mode of generating surfaces of the second degree
which IJ obtained a few years ago, I wish to state the method

i

eo eee ae

537

by which I arrived at it, as it involves a principle of very
useful application in the theory of reciprocal polars.

** Given a point and a plane,—if we take the reciprocal
plane and point with regard to any sphere, the ratio of the dis-
tances of the first point from the centre of the sphere, and from
the first plane, is equal to the ratio of the distances of the
second point from the centre of the sphere, and from the second
plane.

‘* Hence, since in a sphere the distance of any tangent
plane from the centre is constant, the reciprocal of asphere is a
surface such that the distance of any point from a fixed point
is to its distance from a fixed plane in a given ratio.

‘¢ Again, since in an ellipsoid of revolution round the axis
major the product of the distances of any tangent plane from
the foci is constant, the reciprocal of such an ellipsoid is
a surface such, that the square of the distance of any point
from a fixed point is in a constant ratio to the product of its
distances from two fixed planes. Or, more generally, if a sur-
face be such, that the product of the distances of a tangent
plane from 2 fixed points is constant, the reciprocal surface will
be such, that the ratio of the nth power of the distance of any
point from a fixed point, to the product of its distances from
fixed planes, will be constant.

I add one or two instances of transformations of plane
curves by the same principle.

In a conic section the product of the distances of any point
on the curve from two fixed tangents, is in a constant ratio
to the square of the line joining their points of contact.
Hence, the square of the distance of any tangent to a conic
section from a fixed point, is in a constant ratio to the product
of its distances from the two points of contact of tangents
drawn from the fixed point.

‘“* As a particular case of this, we derive the well-known
property,—any tangent to a conic will intercept, on two fixed
parallel tangents, segments whose rectangle will be constant.

338

‘¢ This theorem may be extended as follows: If a curve be
such that only three tangents can be drawn parallel to a given
line, any tangent will intercept, on three such tangents, seg-
ments whose product will bear a given ratio to the segment
intercepted on another fixed parallel.”

The Secretary read a communication from Mr. Bindon,
and presented a tracing from the original credentials which
Father Hugo de Burgo carried with him to Belgium in 1644.

‘¢ With the view of making my search as useful and com-
plete as possible, I thought it advisable, after having examined
the Burgundian Library, to visit the Archives du Royaume of
the Belgian government.

‘‘ In that collection the original document, a fac simile of
which is now presented to the reader, will be found. It is
the credential which Father Hugh de Burgo, a Franciscan
friar, carried with him when visiting Belgium, as the represen-
tative of the Irish Catholic Confederates assembled at Kilkenny
in the year 1644.

‘‘ It is presumed that this document is of some historical
interest, presenting as it does the signatures of several leading
members of the ‘“* Supreme Council,” including those of its
President, Richard Butler Viscount Mountgarret, and the se-
eretary, Sir Richard Belling. The other signatures are those of
Thomas Preston, the brother of Lord Gormanstown, and com-
mander of the confederate forces in Leinster ; ‘Thomas Walsh,
Archbishop of Cashel ; Malachy Quelly or O’Kelly, Arch-
bishop of Tuam, who was killed leading an attack upon Sligo;
Sir Daniel O’ Bryen, one of the Protestants who had joined the
Catholic Confederates; Robert Lynch, and Terence O’ Shaug-
nessy. The ninth name I have not been able to decipher.

‘¢ This mission of Father de Burgo to the Low Countries
has not been noticed, as far I can discover, by any historians
treating of the wars of 1641-1652. Carte, in his Life of the
Duke of Ormond, states that “ Father Hugh Burke” was sent

539

to Spain: and in the ‘“‘ Unkinde Deserter” we read of a Bishop
being sent to the Duke of Lorraine, in company with other
persons, in the year 1651: but in these authorities there is no
mention whatever of the embassy which this paper helps to
disclose. It is believed that Father de Burgo was afterwards
Bishop of ‘ Duacensisin Anglia.”—Hibernia Dominicana,
p- 490.

‘* Besides this document, a large collection of papers rela-
tive to the Stapleton foundation in the University of Louvain
will be found among the Archives. ‘They are not of general
interest, being principally the pedigrees of adverse claimants
to the many bourses which were bequeathed by the founder
to the Irish pastoral college of Louvain ; and as these bourses
are yet in existence, the documents may be of much use to the
different members of Dr. Stapleton’s family in proving their
respective claims. +

«A few letters giving an official account of the reception of
the Duke of Cumberland, after his landing in the Low Coun-
tries on the eve of the battle of Fontenoy, and a short memoir
of the Irish College of Lille, complete the collection as far as
Irish history is concerned.”

The special thanks of the Academy were given to William
R. Wilde, Esq., for his Donation of a large collection of the
remains of oxen, sheep, goats, dogs, &c., found at Dunshaugh-
lin, described by him to the Academy, April 27, 1840,* and.
since deposited for inspection in the Museum of the Academy.
Mr. Wilde also presented an ox head of the ancient short-
- horned variety, from Navan, similar to those found at Dun-
shaughlin ; and eleven specimens of Bronze Celts, and one

Brass Spur.

* See Proceedings, Vol. I. p. 420.

~

VOL. Ill. 3B

540

DONATIONS.

A Treatise on Atmospheric Phenomena. By Edward
Joseph Lowe, Esq. Presented by the Author.

A Reply to Mr. Babbage's Letter to the Times, on the
Planet Neptune, and the Royal Astronomical Society's Me-
dal. By the Rev. R. Sheepshanks, V. P. R.A. S., §e. Pre-
_ sented by the Author.

A Cannon Ball, found in the Townland of Baltrasna,
Mullingar. Presented by W. R. Wilde, Esq.

Comptes rendus Hebdomadaires des Séances de 0 Académie
des Sciences. From 5th to Tth June, 1847. Presented by the
Academy.

Report on Lunatic Asylums in Ireland, 1846. Presented
by Dr. White.

Address to the Geological Society. By Robert Mallet,
Esq., President. Presented by the Society.

Journal of the Geological Society of Dublin. Vol. III.
Parts 3 and 4, 1847. Presented by the Society.

The Traveller in the East. By Godfrey Levinge, Esq.
Presented by the Author.

Inventaire des Manuscrits de lancienne Bibliotheque Roy-
ale des Ducs de Bourgogne. - Nos. 1 to 18,000. Presented’
by S. H. Bindon, Esq.

A Stone Celt, from the vicinity of the Tumulus at Kil-
liney. Presented by the Rev. W. Wildbore.

Two Ivory Figures found at Balasore, East Tae by
Frederick Furnell, Esq. Presented by W. Furnell, Esq.

A Silver (cancelled) Seal of the Board of First Fruits in
Ireland; a Seal of the Right Rev. Nathaniel Alexander,
D.D., Bishop of Meath (1823) ; and a Seal of the Right
Rev. Nathaniel Alexander, D. D., Bishop of Down and Con-'
nor (1840).

An ancient Shoe, made of carved Leather. This shoe was
found in a turf bog at Ballym&comb, county of Derry, at the

541

depth of seven feet. It was discovered lying between the
branch and trunk of a fir tree. Presented by Miss Alexander.

Die Ueberbleibsel der Altigyptischen Menschenrace. Von
Dr. Franz Pruner. Presented by the Author.

Abhandlungen der Mathematisch-Physikalischen classe der
Koeniglich Bayerischen Akademie der Wissenschaften. Part 4,
Vol. III. of this class, or nineteenth Volume of the whole
series.

Gelehrte Anzeigen. Vols. XVI.— XXIII.

Bulletin der Kénigl. Akademie der Wissenschaften. For
the Year 1846. Nos. VI—LXXVII. Presented by the
Royal Academy of Munich.

A Copy of the Census of Ireland for 1841. Presented by
W. R. Wilde, Esq.

Ecclesiastical Antiquities of Down, Connor, and Dromore,
with Notes and Illustrations. By the Rev. William Reeves,
M. B., M. R.I. A., &c. Presented by the Author.

Journal of the Franklin Institute. Vol. XII. Third
series. Presented by the Institute.

Patent Rolls of James I. and Henry VIII. Presented by
Sir William Betham.

An Ancient Key. Presented by Aquilla Smith, M. D.

AaB hn

poet ERS os

APPENDIX.
No. I.

CORRESPONDENCE,

READ TO THE ACADEMY, JANUARY 271TH, anp FEBRUARY 241g, 1845,

FROM

THE MINUTES OF COUNCIL.

I.

“© Dublin Castle, 18th Jan., 1845.

“* GENTLEMEN,—I am directed by the Lord Lieutenant
to transmit the accompanying statement, which has been re-
ceived from Sir William Betham, for any observations the
Council of the Royal Irish Academy may wish to offer for
his Excellency’s information.

“Tam, Gentlemen, your obedient Servant,

‘¢ ELiorT.
‘¢ The Secretaries to the

Royal Irish Academy, Se. §c.”

‘© Dublin Castle, 15th Jan., 1845.

“My Lorp,—I take the liberty of drawing your lord-
-ship’s attention, and that of Her Majesty's Government, to
the following brief statement of facts.

“In the year 1830, the Council of the Royal Irish Aca-
demy put an advertisement into the public journals, offering
apremium of fifty pounds, with the Gold Medal, for the best
Essay on the Origin and Use of the Round Towers of Ireland.

** On the 17th December, 1832, they awarded the money
and Medal to Mr. George Petrie, one of the members of the
Council, for his Essay, as the best of those sent in. The

VOL. III. a

li

money was paid accordingly, and the medal was delivered.
Mr. Petrie was then permitted to take away the manuscript,
to prepare it for the Press; but he never returned it to the
Council for publication, though frequently urged to do so.
In the year 1840, eight years after the delivery and pay-
ment of this medal and prize, myself and other members of
the Academy called upon the Council to account why this
Essay, which had excited so much interest, had not as yet
appeared in the Transactions. In reply, we were assured
that it then was, or very shortly would be, in the Press.
“In July, 1844, we again inquired when the Essay was
to appear, and were told it would be published by the Ist
January, 1845. I, therefore, gave notice that I would move
at the next meeting of the Academy for certain returns
respecting the proceedings of the Council. On the 30th
November these returns were laid on the table of the Aca-
demy, in compliance with my notice, without motion. By
these returns it appears that the Council had permitted
Mr. Petrie to enlarge his Essay (which, when read and
adjudged, consisted of about fifty pages), so much as to
occupy an entire volume of the Transactions (about 500
pages), and had expended £144 in wood-cut engravings, to
illustrate it. They also appointed a committee to confer
with Mr. Petrie (himself a member of Council), relative to
the publication of his Essay on the Round Towers, who, on
the 29th June, 1840, reported the following proposition

from Mr. Petrie:
“© *99nd June, 1840

«I propose to supply the Academy with 400 or 450
copies of my Essay on the Round Towers, at thirty shillings
per copy, printed in the form of the Transactions.

«« « Signed, GerorGe Perris.’

And the Committee recommended the Council to adopt the
above proposal, and to request Mr. Petrie to send the work

to Press immediately.

ili

“The Council decided that the proposal was not suffi-
ciently explicit, and ‘Resolved, that Mr. Petrie be allowed
to substitute the following :

“620th June, 1840.

“«T propose to publish, at my own expense, my Essay on
the Round Towers, as the twentieth volume of the Transac-
tions, on condition that the Academy take from me 450
copies, at the rate of thirty shillings per copy ; the expense
already incurred by the Academy for engravings to be de-
ducted from the £675 to be paid for the 450 copies. It is,
of course, understood, that the blocks for woodcuts are my

property.
“* «Signed, GerorceE Perris.’
‘ Resolved, that the proposal in the latter form be adopted.’

* From this it appears, that the Council, in 1840, had
alienated to Mr. Petrie the copyright of the Essay for which
£50 had been paid, and a Gold Medal adjudged, in 1832!
And further, had allowed that gentleman to print the work
for his own benefit, virtually at the expense of the Academy ;
for by the acceptance of the proposal of 29th June, 1840,
the Council agreed to pay thirty shillings a copy for 450
copies of the volume, that being the selling price of the vo-
lumes of the Transactions, which amounts to £675, and in-
cludes the bookseller’s profit, which may be estimated at least
at thirty-five per cent., thus making Mr. Petrie a present of
£234 13s. 4d. of the Academy’s money, which would pay
for a considerable edition for his own benefit, and which
they might have saved, by printing the work themselves.
It should here be observed, first, that it is contrary to the
Jaws of the Academy to return the manuscripts even of un-
successful competitors for prizes and medals, while they
claim as property all Essays read at their ordinary meetings,
and ordered to be printed ; and secondly, that the Council
have no power to expend more than twenty pounds, without
the consent of the Academy at large.

a 2

IV

“In March, 1832, the Council inserted another adver-
tisement in the public journals, offering a premium of £50,
and a Gold Medal, for the best Essay on the Remains of
Ancient Military Architecture in Ireland.

‘In March, 1834, the Council awarded and paid the Gold
Medal and premium aforesaid to the same Mr. George Petrie,
himself a member of the Council, and the proposer of the
question, as he was also of that of the Round Towers; and,
as in that case, he took away the manuscript, to prepare it for
the Press; but, from 1834, to the present hour, no step ap-
pears to have been taken by Mr. Petrie for its publication.

“In the year 1838, Mr. Petrie read an Essay on Ancient
Bells before the Academy, which was referred to the Coun-
cil for publication ; for the embellishment of which, the sum
of £31 10s. appears to have been paid to one artist, and
£44 to another, for engraving copperplates to illustrate it;
which Essay has not appeared in the Transactions, nor does
it appear that the Council have taken any steps for its pub-
lication.

“In the year , another Gold Medal was awarded to
the same Mr. Petrie, for what was called an Essay on Tarah,
which was read before the Academy, as was alleged, by per-
mission of Colonel Colby, it having been prepared, under
the direction of the Ordnance Survey, by the persons em
ployed thereon, of whom, I believe, Mr. Petrie was one.
This work was certainly the production of several.

“Thave thought it right to lay these facts before your
Lordship, in consequence of having failed in prevailing on
the Council and the Academy to correct these deviations,
as I consider them, from the correct mode of conducting the
affairs, and disposing of the funds of the Academy intrusted
to the Council. Your Lordship’s letter to the Academy of
the 23rd November, 1843, calling for an account of ‘how
far the objects of the Academy have been attained, and the
circumstances under which the public grant to the Academy

Vv

has been made and continued to the Institution,’ renders it
necessary that Government should be in possession of cor-
rect information.

“The returns made to the Academy by the Council of
30th November, 1844, also contain statements of the assets,
debts, and engagements of the Academy.

‘‘T have the honour to be your Lordship’s
“ Obedient Servant,
“W.Betuam, M.R.I. A.
‘© To Right Honourable the
Lord Eliot, §c. &c.”

II.

‘¢ Royal Irish Academy,
°° 23rd Jan., |845.

“¢ My Lorp,—In compliance with the desire of the Lord
Lieutenant, as communicated to the Council of the Royal Irish
Academy, in your Lordship’s letter of the 18th of January,
I am directed by the Council to offer the following observa-
tions for the information of His Excellency, with regard to
the representations made by Sir William Betham to Her
Majesty’s Government, concerning the mode in which the
business of the Academy has been conducted.

“‘ The Council, in the first place, beg to say, that nothing
would give them greater pleasure than an inquiry, on the
part of the Government, into the management of the affairs
of the Academy ; that body, as is very well known, having
for some years back displayed a degree of energy and effi-

ciency, which has gained for it the entire confidence of the
public. But an inquiry of such a kind, on the part of Sir W.
Betham, is not a thing to be encouraged by the Council; and,
that it is not a thing which the Academy are disposed to coun-
tenance, Sir W. Betham was given to understand, by a vote
of the Academy, on the 13th of the present month, when he

vi

attempted to bring forward there those charges against the
Council, which he has since thought proper to carry before
the Government.

‘“‘In the next place, the Council have to express their
great, regret that the different Essays of Mr. Petrie, about
which Sir W. Betham shows so much concern, have not yet
been published ; but they beg to observe, that the peculiar
circumstances of the case have thrown entirely into the
author’s hands the publication of the Essay on the Round
Towers of Ireland,—and that, while he is employed uponthis,
which is a very large work, it would be useless to press upon
him the publication of the others, Mr. Petrie, however, has
addressed to the Council a statement of the causes which
have retarded the appearance of his Essays, and this state-
ment is herewith transmitted to your Lordship.

‘“* The Council also take leave to transmit two Estimates—
one from the Publishers of Mr. Petrie’s Essay on the Round
Towers, the other from the Printer of that work. By the
first of these it appears that the publishing price of the vo-
lume which Mr. Petrie has engaged to give to the Academy
for thirty shillings (and the printing of which is now greatly
advanced), cannot be less than two guineas, and is more
likely to be 24 guineas. By the second estimate it appears
that if the work were printed by the Academy, as a volume
of its Transactions, the impression being limited, as usual, to
500 copies, each copy would cost the Academy above three
pounds; that is, more than double the price for which
Mr. Petrie has undertaken to supplyit. Yet Sir W. Betham
has not hesitated to state, that the Council have allowed
Mr. Petrie ‘ to print the work for his own benefit, virtually
at the expense of the Academy ;’ and that, by agreeing to pay
him thirty shillings a copy for 450 copies, they have given
him ‘ booksellers’ profit’—and have ‘ made him a present of
£234 13s. 4d. of the Academy’s money, which would pay for

vil

a considerable. edition for his own benefit, and which they
might have saved by printing the work themselves.’

*«'To show the illegal nature of the agreement entered
into with Mr. Petrie, Sir W. Betham observes, ‘that the
Council have no power to expend more than £20, without
the consent of the Academy at large.’ But the Council have
power to contract liabilities to any amount that may be ne-
cessary for bringing out the volumes of the Transactions.
This is part of their office. They are not even obliged to bring
such engagements under the notice of the Academy, until a
grant of money is wanted to discharge them; but it so hap-
pens, that the agreement made with Mr. Petrie was laid be-
fore the Academy, along with other matters, at a stated
meeting on the 16th of March, 1841, in-a report which was
then adopted, and ordered to be entered on the minutes. In
this case no grant of money has been called for, as Mr. Petrie’s
part of the engagement is not yet fulfilled ; nor has any sum,
large or small, been expended in connexion with the Essay
on the Round Towers, except what had been paid for engra-
vings previously to the aforesaid agreement ; which sum, by
the terms of the agreement, isto be taken into account in the
final settlement. ;

“« Sir W. Betham further states, that ‘it is contrary to the
laws of the Academy, to return the manuscripts even of
unsuccessful candidates for prizes and medals, while they
claim as property all Essays read at their ordinary meetings
and ordered to be printed.’ Itis true that it is part of a law
of the Academy, that ‘all communications shall be deemed
the property of the Academy’ (Chap. VII. Sect. 5, of the

_ By-laws) ; but it is part of the same law, ‘that the author
of any communication may, by petition to Council, reclaim
such communication, which shall be restored to him on said
petition being granted.’ And this law applies to every
sort of communication. _

viii

“Sir W. Betham charges the Council with having ‘ alie-
nated to Mr. Petrie the copyright of the Essay on the Round
Towers.’ But it is apparent, from the foregoing statements,
that the most prudent course was to allow Mr. Petrie to
publish the work at his own risk. Besides, it is not usual,
nor does it seem very proper, in societies such as the Aca-
demy, to raise questions about copyright.

**' The Council do not find any other charges brought by
Sir W. Betham, of a kind proper to be noticed officially.
On the tone and manner of Sir W. Betham’s statements they
refrain altogether from making any comment.

‘1 have the honour to be, my Lord,
‘Your obedient Servant,
« J. Mac Cuntaeu,
** Secretary of the Academy.
“« To the Right Honorable
the Chief Secretary for Ireland.”

Il.

*¢ Dublin Castle, 3rd Feb., 1845.
“‘Sir,—I am desired by the Lord Lieutenant to acknow-
ledge the receipt of your letter of the 23rd ult., containing
observations with regard to representations made by Sir
William Betham, respecting the mode in which the business
of the Royal Irish Academy has been conducted.
‘Tam, Sir,
“Your most obedient humble Servant,
“C, Lucas.
‘© To James Mac Cullagh, Esq.,
* Secretary Royal Irish Academy.”

DOCUMENTS REFERRED TO IN THE REPLY OF COUNCIL.

i
[ Extract. |
“© To the President and Council of the Royal Irish Academy.

“‘GrnTLEMEN,—I have the honour to address you in
compliance with the request of the Secretaries of the Aca-
demy, that I would supply the Council with a statement of
the circumstances which have caused so much delay in the
publication of some Essays read by me at the Academy, as
well as to explain other matters charged against me, in a
letter addressed to Lord Eliot, Chief Secretary for Ireland,
in order that it may be appended to the answer of the
Council to that letter.

‘In the first place, then, I beg to acknowledge, that

_whatever blame may be attached to the delay in the publi-
cation of these papers, it should fall alone on me; for the
Academy has no power, either moral or legal, to force authors
to print papers in its Transactions, if it be contrary to their
wish or convenience to do so. The Academy, like all other
institutions of the kind, has been chartered chiefly for the
purpose of fostering science and literature, by giving facility
to the publication of Essays considered valuable, but which,
from their abstract or archeological nature, could not be
given to the world without great probability, if not certainty,
of pecuniary loss to their authors, by publishing them at
their own risk; and hence it becomes a high honour to an
author to be permitted to publish in its Transactions, if it be

- his wish or convenience to do so, but not an obligation on
him if otherwise, or that he should prefer publishing on his

own account. Such at least has been my impression on this
matter, and such also has been the opinion of Sir William

Betham, as often expressed while in friendship with me, and

urged with a view to persuade me to do as he said he was

x

determined to do with his own papers, whenever they were
of a sufficiently popular character to be likely to sell, namely,
to publish on my own account and at my own risk; and in
accordance with which, he sent in his Essay on the Gael
and Cimbri to the Academy, as an anonymous competition
paper for the prize and Gold Medal, printed as an octavo
volume, as it afterwards appeared, with only the addition of
a title-page, and, as I believe, a preface and index. With
this advice, however, being anxious to sustain and advance,
if in my power, the character of the Academy by my labours,
I never had any intention of complying; and the delay which
has occurred in the printing of my Essays has been entirely
caused by circumstances over which I had no sufficient
control.

“«‘ And first, as regards my Essay on the Round Towers.
This Essay did certainly, as Sir William Betham states, re-
ceive the reward of the Academy at the close of the year
1832; and I immediately afterwards applied myself to its
preparation for publication by improving its matter and in-
creasing its necessary illustrations, by every means in the
power of a man who had to sustain a large family solely by
the daily practice of his profession as an artist. But the
labour was a great and a tedious one, and having soon after,
perhaps imprudently for my own interests, accepted an em-
ployment as director under Captain Larcom of the orthogra-
phical and historical department of the Ordnance Survey of
Ireland, formed in part with a view to the publication of
memoirs to illustrate the map, its duties so entirely ab-
stracted me as to put it wholly out of my power, while thus
employed, to make the great number of drawings necessary
to the illustration of the work; nor was it possible to get
them done by others. The chagrin which this circumstance
necessarily caused me, was, however, considerably lessened
by the circumstance, that, in consequence of the Council
having, at the suggestion of Sir William Betham, and on the

Xi

score of economy, transferred the printing of its Transac-
tions to another printer, their succeeding volume was such
as to render it impossible for me, having a due regard to the
appearance of works so extensively illustrated, to put any of
my Essays into the volume of Transactions which followed.

** It is also true that I received the prize and Gold Medal
of the Academy, for an Essay on Irish Military Architec-
ture, in March, 1834; and I believe it true that I, a member
of the Council myself, was the proposer of this question, as
well as that on the origin of the Round Towers, as Sir
William Betham states with an obvious object. As ques-
tions for prize essays must originate with the Council, I had
as much right to suggest them for approbation as another,
and, in point of fact, I did, at the request of the Council,
draw up a list of themes for dissertations on Irish History
and Antiquities, from which they might select, similar to
those relative to the history of Scotland, suggested to the
learned of that country by the celebrated John Pinkerton,
who remarks, that ‘ Scotland is certainly that country in
Europe, if we except Ireland, in which national history and
antiquities are most neglected.’ But amongst those questions
there were many indeed, which I should never have thought
of treating of,—as, for instance, the question, ‘ who were the
Scoti?’ which Sir William Betham induced the Council to
propose, and in competition for the prize for which Sir
William Betham sent in his printed volume, entitled, ‘ the
Gael and Cimbri.’

“‘T may also remark, that though I may have suggested
to the Council the question on ‘ Irish Military Architecture,’
-I never seriously contemplated competing for the prize
offered, my time being occupied on the Ordnance Survey,
till one week precisely before the day appointed for deliver-
ing in the papers, when, at the earnest: solicitation of my
friend, Captain Larcom, R. E., I was induced to write an
Essay, as that gentleman will, I have no doubt, be ready to

Xli

testify. And with respect to the delay in the publication of
this Essay, I should state, that I was at all times ready to
undertake it, after the printing of the Transactions of the
Academy repassed into the original hands, not only because
it was an Essay of smaller size, and requiring fewer illustra-
tions, but that I was even anxious to do so, as it would have
been the proper precursor to my larger work, which relates
to a later class of antiquities. With this desire of mine, how-
ever, the Council showed the strongest indisposition to
comply ; and, consequently, I applied my mind, as much as
circumstances would permit, to the preparation for the Press,
of my Essay on the Round Towers. But being still em-
ployed on the Ordnance Survey, the time at my disposal
was very limited, and it was not till the department in which
I was employed, was finally broken up at the close of the
year 1842, that I was enabled to give nearly my whole time
and attention to the work, and commenced its printing.
Since that period, I may say, I have done little else than
labour at it. Ihave allowed myself no leisure for enjoyment
or for exercise. In my devotion to it, | have reduced myself
to poverty, and injured my constitution, perhaps irretriev-
ably. And yet, all these efforts have only enabled me to see
through the Press a volume of it, now on the eve of publica-
tion ; for the subjects treated of, in the copious manner which
I conceived that they merited, have run the work to the ex-
tent of two volumes.

“It is true, that many may say that they did not require
a work of so elaborate a character; but surely an author
himself should be considered the best judge of what was
necessary to his subject, at least till, by the publication of
his work, he has enabled others to prove that he was in
error.

“ With respect to the charge against the Council, for
having permitted me to enlarge my Essay, I have only to say,
that I am sure they did so from an anxious desire to promote,

xiil

to the best of their ability, one of the primary objects for
which the Academy was instituted. And with respect to
their agreement to take from me four hundred and fifty
copies of my Essay, at thirty shillings per copy, I can safely
state my conviction, that it was made solely with a view to the
financial interests of the Academy, and without any regard to
mine.

‘‘ T must also state, that it is my conviction that they were
driven to make this agreement with me, chiefly by Sir Wil-
liam Betham himself. When I commenced making the draw-
ings in wood to illustrate the work, it was on the understand-
ing with Council, that as the Academy did not publish with a
view to gain, they would allow me the use of the wood-cuts,
after the publication of their volume, to publish an edition of
my Essay for my own advantage. But Sir William Betham’s

_assertions before the Academy, that the publication of this
wgrk would reduce the institution to a state of bankruptcy,
and his threats that he would, by an application to the Go-
vernment, stop the payments to the wood-cutter, had the ef-
fect of inducing some members of the Council to propose,
contrary to the practice of the Academy and the spirit of its
institution, to publish such unlimited number of copies of my
work as would repay the Academy, by their sale, the expense
of its publication. To this proposal, which was nothing less
than to resign for ever nearly the labour of a whole life, and
which would still take me years of undivided attention to ac-
complish, I could not bring myself to agree, either as an in-
dividual whose interests were concerned, or as a member of
the Academy, who had its honour at heart. Hence I made
the proposal to supply the Academy with such a number of
copies as the Council desired, at the rate of thirty shillings
a copy; I, of course, obtaining thereby the copyright of my
work, and the management of its publication; and by this
agreement the Academy will get the work at considerably
less than half what it would cost them to bring out an edition

xiv
of it of their usual number of five hundred copies, and are
moreover saved from the expense of the paper and printing
of fifty copies, always given to authors who publish Essays
in the Transactions.

** With respect to the delay in the publication of my
Essay on the Ancient Irish Bells, which I wrote in compli-
ance with the wish of the Academy, as conveyed to me from
the Chair, by their former illustrious President, Bishop
Brinkley, I have only to state, that the cause of that delay is
solely attributable, since the plates were furnished, to my be-
ing wholly employed on the publication of my Essay on the
Round Towers.

“* And lastly, with respect to the charge that my paper on
the Antiquities of Tara Hill, was read by the permission of
Colonel Colby, it having been prepared under his direction,
for the Ordnance Survey, by the persons employed thereon,
I have only to remark, that it is certainly true that I wroteand
read the paper by permission of Colonel Colby, because, be-
ing employed in the Ordnance Survey at the time, I could
not, with propriety, have written or read it without such per-
mission ; but that it was my own work, assisted, as I have
constantly been, by more competent Irish scholars than my-
self, and written expressly for the Transactions of the Aca-
demy, I have already given the most unquestionable evidence,
namely, that of Colonel Colby and Captain Larcom, the di-
rectors of the Survey.

“7 have the honour to be, Gentlemen,
“© 21, Great Charles-st., “* Your obedient Servant,
“ Jan. 23rd, 1845.” ‘* GrorGE PETRIE.

“104, Grafton-street,
** 20th January, 1845.”
“ Hodges and Smith present their respects to the Secre-
tary of the Royal Irish Academy, and in reply to his note

XV

relative to the probable price of Mr. Petrie’s’ work on the
Round Towers, they beg to say, that it cannot, under any
circumstances, be less than 2 guineas, but they think it more
likely to be 23 guineas.”

“* University Press Office,

** Dublin, 20th January, 1845.

‘¢ Sir,—In answer to your question relative to the expense

of Mr. Petrie’s ‘ Round Towers,’ I beg in reply to state it is

my opinion, that if the Royal Irish Academy had to pay the

expense of the Drawings, and the Engravings from them of

the numerous and finely-executed wood-cuts, together with

the cost of printing and paper, and confined themselves to

the printing of an edition of 500 copies (their usual num-

ber), each copy of the work would stand them in a sum above
three pounds.

“Tam, Sir, respectfully,

** Your very obedient and humble Servant,

“M.H. Git.
“ James Mac Cullagh, Esq.”

mes {3 plat i is

FRAG sys) Canal CUA we Sef
. es

No. II.

METEOROLOGICAL JOURNAL,

COMMENCING
ist JANUARY, 1844, anp enpiInc 3lst DECEMBER, 1844,
BY

GEORGE YEATES.

TuE instruments employed, and the general circumstances
of the mode of observing, have been described in the prelimi-
nary observations to the Tables of the year 1843, in the
2nd volume of the Proceedings of the Academy, Appendix V.

“VOL. III. b

| |

Thermometer.

Max. Min
50° 3le
36 29
35 26
48 30
54 47
43 40
47 35
42 3l
47 36
51 38
46 36
47 39
45 3d
42 30
40 29
37 29
43 36
49 44
45 41
44 40
45 42
45 Al
46 32
57 53
50 4]
52 45
49 A)
50 45
A9 Al
52 Al
47 35

XVlil

JANUARY.

Barometer.

30.420
30.350
30.412
30.000
29.820
29,900
30.000

.004

.002

005

.045

010

.095

Wind.

x3

Ae

am

42m

2arosaaye
a 44!

a 244

an

COND & PP WS LO =

DD BD bO WO WO DN DO NOD NR
OON ATR WANFK TUAN OAH WON —& ©

Thermometer.

XiX

FEBRUARY.

Barometer.

Rain.

330

045
.090
046

045

010

.250
.200
.290
*045
.456
-120
045
-260
-046
030

Wind.

yiass
ZZzZ2%
4445

|

AAS 4
AAnAS

n 24
a" 8 as4e

eas
“244

245%

».@.4

MARCH.
Thermometer. Barometer. Rain. Wind,
Max. Min.

1 48° 37° 29.270 .170 W.S. W.

py) 47 35 29.250 .050 W.S. W.

3 A7 34 29.160 .050 Weck

4 48 33 - 29.500 025 N. W.

5 43 27 29.850 218 S. W.

6 492 29 29.950 Bere Mra N. E.

7 42 29 30.250 .010 W.

Sieh Oey | 38 30.050 010 S. W.

9 53 46 29.920 005 S. W.
10 53 38 29.900 .095 N. W.
1] 49 43 29.400 305 W.S. W.
12 49 35 29.709 .200 W.N. W.
13 47 393 29.060 025 W.N. W.
14 46) 40 29.700 -060 S. E.

15 48 34 29.420 .050 S. W.*
16 46 32 29.510 mle EK. N. E.f
17 38 34 30.120 ere baits E, N. E.t
18 45 31 30.200 .500 E. N. E.
Lowe leedou 16781 30.166 So ae N.N. W.
20 48 39 29.750 .060 N. W.
21 49 3l 30.600 .007 S. W.
22 57 39 29.550 015 N: N. W.
93 | 57 | 88 29.660 018 N.N. W.
24 49 4l 29.450 airy ee W.N. W.
25 55 42 29.360 .030 a Ss. W.
26 55 45 29.708 .020 W.

97 56 49 29.780 Bh do has W.S. W.
28 58 37 30.400 ate tale S. W.§
29 58 38 30.420 gett ie E,||

30 57 390 30.409 aca tis ET
31 56 40 30.150 ah genni E. S. E. |
* Stormy. + Very stormy. t Stormy.

§ Fine. || Very fine. { Very fine.

XXl

APRIL.
Thermometer. Barometer. Rain. Wind.
Max. Min.

1 59° 420° 29.200 Se gle W.

2 53 41 29.914 eee: Saw:

3 61 40 29.716 .265 S. W.-

4 50 42 29.552 Paiaen 2 cc S. S. E.

5 51 42 29.572 sac ea oe S. E.

6 50 44 29.930 010 W.

7 50 37 30.150 WwW. N. W

Bald) Gi: | 46 30.350 2 ae Ss. W.

9 70 5] 30.500 010 S. W.
10 71 4] 30.250 Spgiok ve S. W.
1] 64 42 29.900 .020 W.S. W.
12 06 42 29.750 oo ae S. W.
13 54 43 29.900 pee WANG: Wee
14 59 46 29.950 115 W.
15 59 90 29.900 -030 E.S. E.
16 57 40 30.116 .050 Ss. W.
ay, 61 45 30.100 S. W.
18 64 42 30.300 =a SMe N.W*
19 58 46 30.400 eee Ir W.
20 59 45 30.216 Bee e S. W.
21 60 51 30,250 .025 W.
22 | 61 | 49 30.200 020 S. W.
23 58 44 30.150 Ono. Ss. W.
24 58 45 30.200 N. W.
25 62 44 30.150 eee E.
26 65 47 30.100 Beanie 3 W..
27 56 39 30.250 fu Ya W. by N.
28 59 41 30.370 Sige N. E.
29 62 43 30.278 aries E. by N.
30 64 46 30.300 E. by N.

* Fine weather.

XXil

MAY.

Thermometer. Barometer. Rain. Wind.
Max. Min.
iL 65° 45° 30.410 E. by N
2 66 46 30.500 E by N.*
3 67 50 30.350 N. E.
4 68 56 30.350 E.N.E
5 63 44 30.178 4 E. by N.
6 67 45 29.900 E.byS
7 67 44 29.976 W.byS
8 64 43 30.000 Are E. by S
9 64 46 29.950 .005 E
10 61 42 80.100 205 N. W
11 61 44 30.150 W. by N.
12 64 47 30.350 W. by N.
13 71 50 30.460 3 W. by N.
14 68 57 30.462 N. W
15 68 43 30.462 pabbret (ts E.
16 69 43, 30.250 -106 N. W.T
17 57 44 30.200 oh | ee N.N. E.f
18 56 32 30.200 Bilge a) de N. N. E§
19 55 39 30.260 fe Gets N. N. E.
20 58 48 80.250 Pe eee te N.
21 63 46 380.250 2 N
22 | 65 | 50 30.290 N
23 69 48 30.300 N. E
24 | 70 50 30.180 of EEE N. E
25 68 55 30.200 othe vevalts N. E
26 64 47 30.450 N.E
27 60 42 30.400 N. E.
28 63 43 30.250 N. N. E
29 64 “44 30.112 N. E.
30 66 42 30.150 N. E.
31 60 44 30.160 N. E.

* Fine. } Cold. f Dry. § Very dry.

XXill

JUNE.

Thermometer. Barometer. Rain. Wind.
Max. Min
1 60° 440 30.150 N, E.
2 63 46 80.060 pe ene N. E.
3 60 51 30.150 nee een E. S.E.
4 63 52 30.100 ah dai ths S. W.
5 68 55 29.700 120 Ss. W.
6 69 54 29.620 .038 W.
7 68 55 29,540 ict Lyin S. W.
8 63 55 29.700 a or W. S. W.
9 69 53 29.900 105 NS)
10 63 47 30,000 .120 W.
ll 69 50 30.270 HSE ic S.
12 70 51 30.068 caer Ss. W.
13 71 55 29.840 .006 W.S. W.
14 68 51 30.060 W.
15 | 69 | 48 30.150 eo pa W. by N.
16 G7 |) 45 30.150 .010 W. by N.
17 64 50 80.050 .080 S. E.
18 58 52 29.860 .340 N. by W.
19 60 45 30.100 .080 N. by W.
20 67 52 29.900 215 W. by S.
21 70 58 29.818 015 S. by W.
99 68 56 29.680 .090 S.
23 70 57 29.700 .110 S.
94 69 56 29.600 .130 E. by S.
95 71 53 29.750 es fae S. by E.
96 73 57 29.850 .080 E.
97 60 53 29.950 hee E. by N.
28 67 47 30.100 Soho Ss W. by N.
29 70 50 30.150 Sr A W. by N.

30 70 30 30.050 ee caeh c E. S. E.

XXIV

S JULY.
Thermometer. Barometer. Rain. Wind.
1 29.950 E. S. E.
2 30.000 W. by N.
3 29.900 Roti inhig E.
4 29.700 .190 E. by N.
5 29.800 -002 N.
6 30.000 W. by N
7 30.050 N. by W.
8 30.000 W. by N
9 30.050 N. by W.
10 29.950 vere W. by N
11 29.950 .008 W. by N
12 30.000 ln eh S. by W.
13 29.650 .280 S. by E.
14 29.660 .070 N. W.
(15 29.900 .110 N. W.
16 30.100 W.
17 29.820 38 W.
18 29.800 095 W.
19 29.900 .310 W. by N.
20 30.160 .040 E.
oN 30.200 .170 S. by E.
92 30.124 so fore: E.
23 29,759 .110 E. by N.
24 30.000 .100 E. by N.
25 29.750 -030 E.
26 30.200 .250 W. by S.
27 _ 380.300 .004 Ww.
28 30.160 -020 S. E.
29 30.150 .074 S. E.
30 29.450 .090 W. by N.
31 29.760 .200 W. by N.

AUGUST.
Thermometer. Barometer. Rain. Wind.
Max. Min.

1 62° | 480 29.850 210 N. W.

2 67 -| 49 29.820 .027 S. W.

3 70 56 29.260 .250 N. E.

4 68 48 29.750 130 W. by N

5 | 66 | 46 29.796 '| . . W. by S

6 61 55 29.980 1.320 N. E.*

7 62 58 29.490 .600 W.

8 66 52 29.550 -100 W. by N

3) 66 52 29.700 .010 W. by N
10 65 51 29.600 .095 E. by N.
11 65 52 29.670 .012 S. W.
12 65 55 29.590 .120 E. by N
13 64 54 29.550 .095 E.
14 66 52 29.320 .210 W. by N
15 | 65 | 53 29.760 .129 W. by N
16 63 43 29.870 : E. by N
17 68 53 29.830 .045 W. by N
18 65 42 30.190 .020 W. by N.
19 66 44 30.170 S. W.
20 70 56 29.890 W. by N
21 | 65 | 46 29.880 W. by N
22 63 51 29.720 Sepa Fe W. by N
93 60 48 29.620 .100 W. by S
24 62 52 29.700 N. by W.
25 67 50 29.916 W.byN
26 65 53 30.100 W. by N
27 60 48 30.160 W. by N.
28 66 45 30.130 W.
29 66 50 30.050 E. by §
30 | 68 | 48 30.000 E. by S
3l 76 A8 30.430 E.

XXV

* Great rain,

XXVi

SEPTEMBER.
Thermometer. Barometer. Rain. Wind.
Max. Min. 2
1 | 74° | 50° | 30.300 E. by S,
2 76 53 30.230 ° E. by S
3 72 46 30.160 E. by S.
4 68 58 30.130 N. E.
5 69 60 29.990 N. E.
6 67 61 29.850 060 S. E.
7 70 58 29.730 200 108
8 69 55 29.860 070 Ww.
9 66 50 29.860 142 W. by N
10 58 50 29.840 By ie W. by N
11 63 55 30.000 S. by W
12 61 53 30.040 020 W. by S
13 64 51 30.100 090 W. by S
14 62 56 29.770 W.byS
15 70 61 29.640 .720 E. by S
16 66 55 29.750 .090 W. by S
17 66 55 29.700 .093 N. E
18 57 46 29.870 050 E
19 62 45 30.150 E. by S
20 | 60 | 51 B00) 2: Bae, N.E.
21 50 Ad 30.220 .210 N. E.
22 59 42 30.190 N.E
23 58 45 29.890 é N. E.
24 58 48 30.070 W. by N
25 58 38 30.200 W. by N
26 66 42 30.240 W. byS
27 63 52 30.180 W. by S
28 64 57 29.890 Pee a had W.byS
29 60 4l 30.190 .100 W. by N.

oe)
S
ox
©
eo
So
ot)
S
bo
ron
S
72)
x

|

Thermometer.

Max. Min.
1 60° 520°
2 60 49
3 61 55
4 63 46
5 63 48
6 61 43
7 59 38
8 55 38
9 57 51
10 59 49
1] 59 46
12 59 A9
13 60 52
14 60 48
15 59 39
16 58 36
17 55 43
18 53 33
19 51 ol
20 52 48
21 52 39
22 53 31
23 55 35
24 57 44
25 | 55 34
26 51 31
27 54 43
28 56 46
29 55 46
30 55 46
3l 57 50

* Storm, 12 o'clock, 28.500.

XXVIl

Barometer.

30.000
29.780
29.680
29.900
29.690
29.840
29.960
29.140
28.830
28.860
29.500
29.400
29.060
29.000
28.890
29.080
29.456
29.790
29.480
29.140
29.530
29.870
29.730
29.790
30.000
30.070
30.170
30.170
29.880
29.600
29.540

OCTOBER.

.100

Wind.

ND
4.43

<q
a

Zzn2 2s
4444244

XXVill

NOVEMBER.

Barometer.

—
NoreocowooaonrnnanrFr wn

NOK eB ee eS eS
owoomosat DO BB

SONNNNNN DY YL WD
SU ONDA WNW

120

005

.130

225

Wind.

*

Zn AZAzAAn mn
PE

Thermometer.
Max. Min.
55° 47°
54 42
52 42
52 42
53 40
52 48
50 49
51 43
52 AT
él 40
49 36
47 SM
56 42
55 40
58 43
57 41
52 45
63 45
59 50
55 49
55 29
ol 30
53 45
04 29
51 30
49 35
54 41
59 48
56 48
54 42
* Storm.

{+ Stormy.

OIBMAhwwe

XXix

DECEMBER. ©
Thermometer. Barometer. Rain. Wind.
Max. Min.
49° | 40° 30.160 .050 SBE
43 39 29.870 E. by S.
47 39 30.160 S. E.
48 28 30.270 S.E.
45 36 30.090 W.
44 30 30.120 N. W.
46 31 30.190 S. E.
49 30 30.160 E. by S.
43 29 30.120 Ss:
43 30 30.170 S. W.
44 30 29.850 Fy 0 E.
44 34 29.780 -100 N. E.
44 30 29.300 .086 N. E.
44 30 29.760 145 N. E.
45 34 29.400 .007 N.E.
47 40 29.240 an E.S. E.
49 44 29.230 .620 E. S. E.
50 44 29.480 .880 E. by N.
50 | 42 30.100 -100 E. by S.
48 35 30.350 S.E.
43 37 30.340 E. by S.
50 42 30.390 S. E.
44 34 30.180 E.
43 32 30.170 S. E.
45 32 30.080 S. E.
48 36 29.940 ee, S. E.
48 41 29.800 .160 S. E.
51 43 29.700 014 E. by S
51 35 29.800 .030 N. E.
50 35 29.990 E. by N
5 40 30.100 Ww.

XXX

GENERAL RESULTS.

Amount oF Rain.
Inches.

Samiarys. Bee We eis em eee leer

Bebruarys: 60 hess os) SO Ree eS
WMicinchitgcvea $< 2 (= Day saa qaiik Sag bee aE ce en Do
Arig as MMs. oe one as eh at Ol ieee ogee
WV Styg Te wepite ig ites, gens he eee Tals CeO

PUNE) paps Wis il he ete. deltbe Om Meee areeao
‘fr ie oa ea ede mC Rr Ra cy eae <.
ANGUISH, Pola SE Yel tia Ma eee ee Teale
Neptembery se.) 2 ek ete fe PEAS
October, 550 60 $a eB | E2530
November, . .. . ...- . - 34D
WDecembers. 92-52 25 6 pee os SS D9?

23.711

BAROMETER.

Greatest pressure, August 27,
Lowest point, January 13,

THERMOMETER.

Maximum, September 8,. . . .
Minimum, February 16, .

2, Grafton-street, Dublin.

Mean TEMP.

420
34
38
411
614
67, —
68
70
67
56
49
51.

30.660
28.100"

80°
21

Now ae

Tue Abstract of Sir William R. Hamilton’s Memoir on
Quaternions, read on February 10, 1845, and referred to in
page 64, has not been received for insertion in this Appendix.

Nor have the Abstracts of Sir William R. Hamilton’s
Memoirs on the New Imaginaries, read on July 14 and 21,
1845, and referred to in pages 111, 112, been received.

No. III.

February 10, 1845. (See page 64.)

The spirit of Sir William Hamilton’s communication, which
was designed as a further illustration from geometry of the
author’s theory of algebraic quaternions, consisted in re-
garding operations on such quaternions as admitting of being
ultimately interpreted as operations on straight lines ; each
line being considered as having not only a determinate length,

but also a determinate direction. The quotient > obtained by

the division. of one such line (b) by another (a), is, generally,
in the author’s view, a guaternion ; it depends, in general, on
Jour distinct elements, of which one, namely, the modulus, is
a positive or absolute number expressing the relative magni-
tude of the dividend and divisor lines, while the three other
elements serve jointly to express the relative direction of
those two lines. Of the three latter, one is the amplitude, and
marks the inclination of one line to the other, or the magni-
tude of the angle which they include; while the two others
determine the plane of that angle, and are what have been
called, in a former communication, the directional coordi-
nate, such as the longitude and colatitude of the quaternion.
In this comparatively geometrical view, as in the more alge-
braical view which was formerly stated to the Academy, the
consideration of these four elements, modulus, amplitude, lon-
gitude, and colatitude, presents itself, therefore, naturally. We
may also speak of the azis of a quaternion, meaning thereby
the axis perpendicular to the plane of the two straight lines of
which that quaternion is a quotient; and may say, that such
an axis is itself positive or negative, or that it is taken in the
c2

XXXil

positive or in the negative direction, according as it is the axis
of a positive or a negative rotation, from the divisor to the di-
vidend line. Quaternions may be said to be coazal when their
axes coincide, or only differ in sign. A quaternion is not
altered in value when the two lines of which it is the quotient
are transferred, without altering their directions, to any other
positions in space; or when their lengths are both changed
together in any common ratio; or when they are both made
to revolve together, through any common amount of rotation,
round the axis of the quaternion, without ceasing to be still
in (or parallel to) the same common plane as before. It is,
therefore, always possible to prepare any two proposed’ qua-
ternions, or geometrical quotients or fractions of the kind
above described, so as to have one common denominator or
divisor line ; and then the addition or subtraction of those
two quaternions is effected, by retaining that common line as
the denominator or divisor of the new. quaternion, and by
adding or subtracting the numerator lines, in order to obtain
the new numerator of the same new quaternion, that is to say,
of the sum or difference of the two old quaternions ; addition
and subtraction of straight lines (when those lines are supposed
to have not only lengths but also directions) being performed
according to the rules which have already been proposed by
several writers, and which correspond to compositions and
decompositions of rectilinear motions (or of forces). Multipli-
cation of two quaternions may be effected by preparing them
so, that the denominator (b) of the multiplier; may be equal
to, or the same line with, the numerator (b) of the multi-
plicand (lines being equal when their directions as well as their
lengths are the same), and by then treating the numerator (c)
of the multiplier as the numerator of the product, and the de-
nominator (a) of the multiplicand as the denominator of the
product: and division may be regarded as the return to the
multiplier, from a given product and multiplicand.

With this view of multiplication, it is evident that the pro-

XXxiil

duct of the moduli of the two factors is equal to the modulus
of the product. It is clear also, that if we construct a spherical
triangle aBc, of which the three corners, or the radii drawn to
them from the centre of the sphere, represent the directions of
the three lines a, b, c, then the are, or side of the triangle,
AB, will represent the amplitude of the multiplicand quater-
nion ; the are or side Be will represent the amplitude of the
multiplier; and the remaining are or side ac the amplitude of
the produet, so that the spherical triangle will be constructed
with these three amplitudes for its three sides. And we see
that in the triangle thus constructed, the spherical angles at
4 and c, which are respectively opposite to the amplitudes of
the multiplier and multiplicand, are equal to the respective
inclinations of the axes of the multiplicand and multiplier to
the axis of the product of the quaternions ; and: that the
remaining spherical angle at B, which is opposite to the am-
plitude of the product, is equal to the supplement of the
inclination of the axes of the factors to each other: a form
almost the same with that under which the fundamental
connexion of quaternions with spherical trigonometry. was
stated by Sir William Hamilton, in his first letter on the
subject, to John T. Graves, Esq., which was written in Oc-
tober, 1843, and has been printed in the Supplementary number
ofthe Philosophical Magazine for December, 1844. The other
form of the same fundamental connexion, which was commu-
nicated to the Academy in November, 1843, may be deduced
from the foregoing, by the consideration of that polar or sup-
plementary triangle, of which the corners. mark the directions
of the axes of the factors and the product, and were’ then
called the representative points of the three quaternions com-
pared. Ifthe order of the factors be changed, the (positive)
axis of the product falls to the other side of the plane of the
axes of the factors, being always so situated that the rotation
round the axis of the multiplier from the axis of the multipli-
cand to that of the product is positive ; multiplication of qua-

XXXI1Y

ternions is therefore seen, in this as in other ways, to be not
in general a commutative operation, or the result depends, in
general, essentially on the order in which the factors are taken.
The same remarkable conclusion follows from the compa-

rison of the lately mentioned spherical triangle aBe with
another triangle c’Ba’, vertically opposite and equal thereto,
and such that the cgmmon corner B bisects each of the two
ares C’C, A’A, joining the two pairs of corresponding corners ;
which other triangle may represent the directions of three
lines c’, b, a’, related to the system of the three former lines
e, b, a, by the two following equations between geometrical
quotients, or quaternions,

ahh ill plains

pine? |
for then, by the definition of multiplication of such quotients
here proposed, we have the two different results,
Di goa
Dean oo

aT ee
ane c

and although these two resulting quaternion products have
equal moduli and equal amplitudes, yet they have in general
different axes, because the arcs ac and a’c’, though equally
long, are parts of different great circles, and are therefore
situated in different planes. However, in that particular but
useful and often occurring case, where the two factors have one
common axis, the order of those factors becomes indifferent ;
and if attention be paid to positive and negative signs, it may
be said that coazal quaternions may be multiplied together, in
either order, by adding their amplitudes, multiplying their
moduli, and retaining their common axis. In general, it may
be proved, from the views here given of multiplication and addi-
tion, that, although the commutative property of ordinary mul-
tiplication does not usually extend to operations on quaternions,
yet the distributive and associative properties of that operation
do always so extend ; and that the commutative and associative

XXXV

properties of addition hold good in like manner for quater-
nions: results which were indeed stated to the Academy in
November, 1843, as consequences from the algebraical defini-
tions of a quaternion, and of operations performed thereon,
‘but have now been mentioned again, as following from more
geometrical definitions also.

Comparing the view here proposed with that which was
submitted to the Academy in November 1844, a quaternion
may be said to.reduce itself to a scalar (or ordinary real num-
ber), when the two straight lines, of which it is the quotient, are
parallel; the scalar being positive when those lines are simi-
lar, but negative when they are opposite in direction. And, on
the other hand, the scalar part vanishes, and the quaternion
becomes a pure vector, when it is a quotient of two rectangu-
lar lines: and, in this last case, it may be conveniently con-
structed by a third line perpendicular to both of them, namely,
by one drawn in the direction of the positive axis of the quater-
nion, with a length which bears to an assumed unit of length
the ratio marked by the modulus. This third line, which thus
represents or constructs the quotient of two other lines per-
pendicular to it and to each other, may, by a suitable choice of
those two lines, receive any proposed length, and any pro-
posed direction; and every straight line having length and
direction in space may, in this view, be regarded as a particu-—
lar quaternion, namely, as one of the class above called vec-
tors. It is easy to prove that when lines are thus treated as
quotients, they have the same sums, differences, and quotients,
as those obtained by the processes or conceptions above de-
scribed or alluded to: and hence it would be natural to define,

_as we should be at liberty to do, that the product of two
lines is also in general a quaternion, obtained by multiplying
two vector factors together, according to the rules of multipli-
cation of quaternions. We should then be able to ‘establish,
in this new way, all the rules, already communicated to the
Academy, for the multiplication of straight lines in space ;

‘XXXVi

and especially should be conducted anew to those two rules, or
principles, which presented themselves to the author in ‘his
earliest researches on quaternions (as described in the printed
letter already referred to), and which he still regards as fun-
damental in their theory: namely, first, that the product of
two straight lines, which agree in direction, is to be considered
as a.negative number, namely, as the product of their two
lengths taken negatively ; and, secondly, that the product of
two rectangular lines is to be regarded asa third line perpen-
dicular to both, of which the length represents the product
of their lengths, and to which the rotation, from the multipli-
cand line, .rownd the multiplier line, is ‘positive. The para-
doxical, or, at'least, unusual appearance ‘of these two funda-
mental rules, combined with the variety of the applications of
which the author has found them susceptible, induce him to
hope that. he shall be pardoned for thus offering new confirma-
tions or new illustrations of them, derived from considerations
of the manner in which they present themselves from various
points of view. ;

July 14 and 21, 1845. (See pages 110 and 111.)

. The following is the substance of the communications made
to the Academy by Sir William Hamilton, on the application
of the method of Quaternions to some dynamical questions :

The author stated that, during a visit which he had lately
made to England, Sir John Herschel suggested to him that
the internal character (if it may be so called) of the method
of quaternions, or of vectors, as applied to algebraical geo-
metry,—that character by which it is independent of any
foreign and arbitrary axes of coordinates,—might make it
useful in researches respecting the attractions of a system of
bodies. A beginning of such a research had been made by
Sir William Hamilton in October, 1844, which went so far,
but only so far, as the deducing of the constancy of the plane

XXXVI

of an orbit, and the equable description of areas, under one
common formula, namely, the following :

dp dp
Pag Tae P=
from the general expression of a central force, namely, from
the equation

const,

dp d’p
Pade

which asserts merely the coawality of the vector p and the

do ‘ '
force = or the existence of one common line along which

this vector and this force are (similarly or oppositely) directed.

Since the suggestion above acknowledged was made, Sir
William Hamilton has proposed to himself to express by an
equation, on the principles of the method of vectors, the pro-
blem of any number of bodies attracting according to New-
ton’s law : and has arrived at the formula

Va _ m - Am f
aT Bae AGN sii eae
which may also be thus written,

d?a m/

df al ay tee — we, ()
and from which he has deduced anew the known laws of the
centre of gravity, of areas, and of the vis viva, under the
forms :

(<)'3.ma =-0's (c)
ie (ae) =o ©)
Ree 1a ete em _ sana

a isthe vector and m the mass of one body ; a’ and m’ of another;

XXXVIli

= sums for the system; ¢ is the time, d the characteristic of
differentiation ; A (where used) is the mark of finite diffe-
rencing.

To illustrate the' method of treating equations of such forms
as these, let us consider briefly the problem of éwo bodies, or
of one body, as it presents itself, in the method of quaternions,
with Newton’s law of attraction, coordinates being not em-
ployed. The differential equation may be thus written,

da M
df = ay(— ee)? 0)

a being the vector of the attracted body, drawn from the at-
tracting one; ¢ the time; d the mark of differentiation; and
M the attracting mass, or the sum of the two such masses.
This equation gives .

da «da
which expresses merely that the force is central; and gives by
integration a result already alluded to (as independent of that
function of the distance which enters into the law of attrac-
tion), namely,

ada daa

3d ~ dea Pi B= 9; (3)

the constant being a new vector, perpendicular in direction
to the plane of the orbit, and in magnitude representing the
double of the areal velocity, which velocity is thus seen to be
constant, as also is the plane. For we have at once, by (3),

afs + Ba = 0, (4)

implying that the variable vector a is perpendicular to the
constant vector 3; and also

{(a.da — da. a) = 26 (¢ — tb), (5)

if t, be the value of ¢ at the commencement of the integral.

XXXIX

- Make now, to distinguish between the length and direction

of the vector,
Pe ag Sy (ay PS (6)

we shall have
da = r.de + dreu, (7)

and because 7 and dr are scalar (or real) quantities,

a.da = 7ru.de —7.dr, da.a = 7°de.t—r.dr; (8)

therefore
/B.dt = 3(a.da — da.a) = 5 (ede —de.e) = 7. de, (9)

observing that the equation
? = — 1 givese.ds + di.c = 0. (10)

The fundamental equation (1) of the problem becomes, by
(6) and (9),

dda mM -dm

ude =r. wp? (1d)

(in which last member the order of the factors is not indiffe-

rent), and therefore gives, by integration, since B as well as M
is constant,

da M
— — — a A 3 12
de ht B const (12)
or, as we may also write it,
da B
i =50; 13
t dé M €5 de ( )

and finally, by (3),
az + ca + 27 = 2p, (15) pe

©

say ~ (16)

xl

the constant p being here not only a scalar but an essentially
positive quantity, because theforce is supposed to.be attractive;
or M > 0, while 3? <0. The equation (15) thus obtained,
contains the law of elliptic, parabolic, or hyperbolic motion.
For if we make (by way of comparison with known results),

Vi 2) =e lg and (a, — 2) =v, (18)
(a, — «) denoting here the angle between the directions of

a and e, we have (by the formula (a) of the abstract of last
November),

at + ca = 2ercosv; — (19)

and therefore, by (15),

eau ae oy)
which is the known equation of a conic section, referred to a
focus. The Greek letters, throughout, represent vectors: and
the Italics, scalar quantities.

Supposing that we had no previous knowledge of the pro-
perties of cosines or of conics, we might have proceeded thus to
investigate the nature of the locus represented by the equation
(15). This locus is a suxface of revolution round the line « ;
because the differential of its equation being

da.c + ¢.da + 2dr = 0 (21)

if we cut it by a series of concentric spheres round the origin
of vectors, the sections are contained in a series of planes per-
pendicular to <; since ak.
dr = 0, (22)
which is the differential equation of the first series, gives,
by (21),

daz + eda = 0, (23)
which is the differential equation of the second series. To study
more closely this surface of revolution (15), make

a= ytd, (24)

xli
y being an arbitrary constant, and a’ a variable vector ; and
since it must evidently give simpler and more symmetric
results to suppose the vector y co-axal with <, than to make
the contrary supposition, since we shall thus place the ori-

gin of the new vectors a’ upon the axis of revolution of the
surface, let

ey — ye = 0, 0ry = gs, (25)
g being an arbitrary scalar, to be disposed of according to con-
venience. Equations (24) and (25), combined with (6) and
(17), will give, for every point of space,
—a®=—(a-—yPar+97e+g(ae+ ea); (26)
and therefore, for every point of the locus (15),
—a? =r —%2r+ Ge + 2p. (27)
The second member of this last equation may be made an
exact square, by assuming

go e+ 2op' = ig? that is, g= 7 _ =e. (28)

the scalar quotient
e

ee wex

= a, or the transformation p = a(1 — e”), — (29)

being thus suggested to our attention ; and with this value of
g we shall have, by (27),

2a* = Qa ry, (30)
2a = ¥(— a?) + ¥(— a”); (31)

so that either the sum or the difference of the distances of any
point of the locus (15) from the-two foci of which the vectors
are respectively 0 and 2ae, is equal to the constant 2a. — It is.
not difficult to prove that the upper or the lower sign is to be
taken, in the formula (31), according as e? is < or >. 1. For
the case e? = 1, the recent transformation fails.

Again, to find whether the locus has a centre, we may
make :

that is,

a= y+ Sag’ + 5 (32)

xhii

gy’ being a new disposable scalar, and 8 a new variable vector ;
and, after having cleared the equation (15) of the radical 7 or
v¥(— a’), by writing it as follows,

oe ( _ ae eal =. 6, (33)

we get
O= (g'c +8)? + (p 4+ ge — a4) (34)
ed Oo a = + ca + 9"(be ai £0) eS (p + 9/e) KS ge;

if we make for abridgment

g=9 — pt ye), (35)

If y’ or g’c is to be the constant vector of the centre of the
locus, it is necessary that to every variable vector, 6, which
satisfies the equation (34), should correspond another ve ctor
— 6, equal in length but opposite in direction, and satisfying
the same equation ; therefore the terms g’(ce + 0) must dis-
appear, and we must have

ot = Nag = P aA ; (36)

the constant a being thus suggested by the search after a cen-
tre, as well as by the search after a second focus. Making
then g’ =a in (34), we find the following equanaa of the
surface, when referred to its centre,

ono 4 (ZT8) + ap; (37)
in which :
ap = a(1 — &) = a(1 + ©). (38)

And because in general, -for any two vectors 4, ¢, pe fol-
lowing relation holds good,

eee ee

xliii

we may write the equation (37) under the form

ea 2
I= +2). C8 +e) + ie 5 =) (40)

This last equation shows that
when de — <6 = 0, then? +0?= 0; (41)

that is to say, when 6 is co-axal with, or parallel to «, or, in
other words, when the vector from the centre coincides (in
either direction) with the axis of revolution of the surface, its
length is = + a, according as a is > or < 0.

The equation (37) shows that

when de + co = 0, then & + a2 (1 + &) = 0; (42)

if therefore <2 be > — 1, that is, if e? < 1, the length of every
vector drawn from the centre perpendicularly to the axis of
revolution will be

V(-S%=ayVvl-e&)=4, (43)
b being anew scalar quantity ; but ife>1,e’<—1,14+°<0,
then we shall have, by (42), the absurd result of a vector 8
appearing to have @ POSITIVE SQUARE: whereas it is a first
principle of the present method of calculation, that the square
of every vector is to be regarded as a negative number: which
symbolical contradiction indicates the GEOMETRICAL IMPOSSI-
BILITY of drawing from the centre to any point of the locus,
a straight line which shall be perpendicular to the axis of re-
volution, in the case where e >1. The locus has, in this
case, two infinite branches enclosed within the two branches
_ of the asymptotic cone which has for its equation !

Sh i == = 0; (44)

and nowhere penetrates within that inscribed spheric surface,
which has for its equation
o’+a?= 0, (45)

xliv

though it touches this last surface at the two points where it’
meets the axis of revolution. On the other hand, when
e? < 1, the locus is entirely contained within the spheric
surface (45), touching it, however, in like manner in two
points upon the axis of revolution. A finite surface of revo-
lution (the ellipsoid) might thus have been discovered, of
which each point has a constant swm of distances from two
fixed foci; and an infinite surface (the hyperboloid), with
two separate sheets, of which each point has a constant dif-
ference of distances from two such foci: and all the other
properties of these two surfaces of revolution might have
been found, and may be proved anew, by pursuing this sort
of analysis. A third distinct surface of the same class, but
infinite in one direction only (the paraboloid), might have
been suggested by the observation that the reduction to a

centre fails in the case e? = 1,22 = — 1. Its equation may
be put under the form
(ca ee ale)? ne 4p (ea! Bs ae), (46)
by making :
aa’ —Fy ae

so that a’’ is the vector from the vertex : and it lies entirely on
one side of the plane which touches it at the vertex, namely,
the plane sot Lata
ca’ tac = 0. eM (48)
In general whatever e or ¢ may be, and therefore for all the
three surfaces, the length of the focal vector perpendicular
to the axis is p; for, by (33), if we make

ca + ac = 0, (49)
we get

a + p?=0. (50)
Indeed (15) then gives r = p.
Since

atr’=0, a-datda.a+2rdr=0, (51)

xlv

the differential equation (21) of the locus (15) may be put
under the form

(re — a) da + da (re — a) = 0; (52)

thus shewing that the vector 7¢ — a is perpendicular to the
differential d of the focal vector a, or that it is parallel to the
normal to the locus, at the extremity of that focal vector.
That normal, therefore, intersects the axis of revolution in a
point, of which the focal vector is re; the position of the nor-
mal is, therefore, entirely known, and every thing that depends
upon it may be found, for the particular surfaces of revolution
which have been here considered. For example, in the ellip-
soid, the vector of the second focus, drawn from the first, has
been seen to be 2a¢; if, then, we make

2e0=—9, St"; (53)

so that 7’ denotes the length of the second focal vector, drawn
to the same pointas the first focal vector, of which the length is
7, we have — 7’¢ for the second focal vector of the intersection
of the normal with the axis; the normal, therefore, cuts (in-
ternally) the interval between the two foci, into segments
proportional to the two conterminous focal distances of the
point upon the ellipsoid, and consequently bisects the angle
between those focal distances. Again, if we divide the ex-
pression re —a by the scalar quantity 7, and multiply the
quotient by a, we find that « — « and ae — a are also ex-
pressions for vectors in the normal direction; and because
az is the focal vector of the centre, while — a is a radius of
the circumscribed sphere, opposite in direction to the focal
vector of the point upon the ellipsoid, we see that if the focal
vector of the extremity of this radius of the sphere be pro-
longed through the focus, it will cut perpendicularly the
tangent plane to the ellipsoid. Again, the expression

Toa(e+1) —a=(a—rjitaz, (54)

VOL. III. d

xlvi

is easily seen to denote here a vector perpendicular to a — re,
and therefore to the normal, because
ar + ra =r (er + Te) = 2 (ap — rr’); (55)
but 7 is also in the same plane with a and ¢, and therefore is a
vector parallel to the tangent to the elliptic section of the
locus made by a plane passing through the axis of revolution ;
a is therefore the central vector of a point upon this tangent,
because a — az is the central vector of the point of contact ;
and the central vector of the second focus being az, we have
a. — az as an expression for the second focal vector of the
same point upon the tangent; this second focal vector is
therefore parallel to the normal, because . — « is parallel
thereto, and, consequently, it is the perpendicular let fall
from the second focus on the tangent line or plane: and the
foot of this perpendicular is thus seen to be at the extremity -
of that radius of the circumscribed circle or sphere, which is
drawn in a direction similar (and not, as lately, opposite) to
the direction of the first focal vector of the point on the ellipse
or ellipsoid. We see, at the same time, that — 7 is a symbol for
the projection of the second focal vector upon the tangent line
or plane; from which we may infer, by (55), that the product
of the lengths of the two projections of the two focal vectors
on the tangent is = 77’ — ap, and therefore that it is less
than the product rr’ of the lengths of those two vectors by the
constant quantity ap, or b?, which constant must thus be equal
to the product of the lengths of the projections of the same two
vectors on the normal, so that we may write the equation |
PP’ = ap = D’, (56)
if p and v’ denote the lengths of the perpendiculars let fall from
the two foci on the tangent, while 0 is the axis minor of the
ellipse. Analogous reasoning may be applied to the hyper-
bola, or to the surface formed by its revolution round its
transverse axis. Most of the foregoing geometrical results are
well known, and probably all of them are so: but it may be

xlvii

considered worth while to have briefly indicated the manner
in which they reproduce themselves in these new processes of
calculation.

The vector drawn from the focus first considered to any
arbitrary point upon the normal, may be represented by the
expression

v= (l—n)a+ nrz, (57)
in which v is an arbitrary scalar; and if this normal intersect
another normal infinitely near it, then we may write, as the
expression of this relation,

0 =dv = (1— 72) da + nedr + (re— a) dn: (58)
comparing which differential equation with the forms (52) and
(21) of the differential equation of the surface of revolution
(15), we can eliminate the scalar differential dz, and deduce
for n itself the expression

da®

One way of satisfying these conditions is to suppose

n=l, dn 10; Poza TLE 5 (60)
which comes to considering the intersection of the given nor-
mal with the axis, and therefore with the other normals from
points of the same generating circle of the surface of revolu-
tion : and this intersection is accordingly one centre of curva-
ture of that surface. The only other way of obtaining an
intersection of two normals infinitely near, is to suppose, by
(58), the element da coplanar with a and «, or to pass to con-
secutive normals contained in the same plane drawn through
the axis; that is to say, the other centre of curvature of the
surface is the centre of curvature of its meridian. The length
of the element of this meridian, that is the length of da, is
denoted by the radical ¥ (— da’), because the differential da
is a vector; and the length of the projection of this element
on the focal vector is += dr = y (+ dr°), because dr is a sea-

xl viii

lar differential ; therefore the length of the projection of the
same element on a line perpendicular to the focal vector, and
drawn in the plane through the axis, is denoted by this other
radical, 4/ (— da? — dr?) ; but the length of this last projec-
tion is evidently to the length of the element itself, as the
length p of the perpendicular let fall from the focus on the
tangent is to the length 7 of the focal vector of the point of
contact ; such, therefore, is, by (59), the ratio of n—# to 1, if
the scalar-n, in the equation of the normal (57), receive the
value which corresponds to the centre of curvature of the me-
ridian ; therefore we have

N fre—a p? pp’ pa’ (61)

w denoting the length of the portion of the normal which is
comprised between the meridian and the axis, and r denoting
the length of the radius of curvature of the meridian. The
projection of this radius on the focal vector is evidently the
focal half chord of curvature, of which half chord the length
may be here denoted by c; we see then that if we again
project this half chord on the normal, the result is the normal
itself, that is the portion n, because this double process of
projection multiplies x twice successively by n—*; and if, once
more, the normal be projected on the focal vector, the third
projection so obtained is equal in length to the semiparameter
p, because, by (15) and (16),

ure — a) + (re — a) e = 2p; (62)

hence

rr’ Qrr’
RN) =c=up=—=
v (RN) Lariat

(63)

that is, for any conic section, the geometrical mean between
‘the radius of curvature and the normal is equal to the harmo-
nic mean between the two focal distances; of which distances
the second, namely 7’, is to be regarded as negative for the

xlix

hyperbola, and infinite for the parabola, and the harmonic
mean determined accordingly. We have also, for every conic
section (if r’a— be suitably interpreted),

‘che tai ao |

Np pal’ ee

so that the semiparameter, the normal, the focal half chord of
curvature, and the radius of curvature, are in continued geo-
metrical progression: and the analysis may be verified, by
calculating directly, on the same principles, the length of the
normal, as follows:

N= ¥ §-(re—a) §=v SETI) +27(p—r)} =v(P).65)

a

The general relation ofa conic section to a directria is

an immediate geometrical consequence of the equation (15),
which has been here (in part) discussed, and may be regarded
as its simplest interpretation. Some of the foregoing sym-
bolical results respecting such a section admit of dynamical
interpretations also; and, in particular, the.expression a — ae,
whieh has been seen to represent, both in length and in direc-
tion, the perpendicular let fall from the second focus on the
tangent, may suggest, by its composition, what is, however,
a more immediate consequence of the equation (12), that in
the undisturbed motion of a planet or comet about the sun,
the whole varying tangential velocity may be decomposed into
two partial velocities, of which both are constant in magni-
tude, while one of them is constant in direction also. ‘The
component velocity, which is constant in magnitude, but not
in direction, is always in the plane of the orbit, and is
_ perpendicular to the heliocentric radius vector of the body;
the other component, which is constant in both magnitude
and direction is parallel to the velocity at perihelion ; and the
magnitude of this fixed component is to the magnitude of the
revolving one in the ratio of the excentricity e to unity. The
author supposes that this theorem respecting a decomposition

l

of the velocity in an excentric orbit is known, though he does
not remember having met with it ; but conceived that it might
properly be mentioned here, as being a very easy and imme-
diate consequence of the present analysis: respecting the
general principles of which analysis, the reader is requested
to consult the Abstract, already referred to, of the communi-
cation of November, 1844, printed at the commencement of
the present volume of the Proceedings of the Academy.
There is no difficulty in deducing, on the same principles,
from formule of the present paper, the known differential

equation,
dr\2\¢ Bie (go ;
qa -*— 2) oe

which connects the radial component of velocity with the
heliocentric distance and the time, and may be integrated by
the usual processes.

No. V.

December 8, 1845. (See page 150).
Tue following is the communication made by Sir William R.
Hamilton on some additional applications of his theory of
algebraic quaternions.

It had been shown to the Academy, at one of their meet-
ings* in the last summer, that the differential equations of
motion of a system of bodies attracting each other according
to Newton’s law, might be expressed by the formula:

da m -- Am (1)
dt? ~~ — Aa ¥( — Aa’)
in which a is the vector of any one such body, or of any ele-
mentary portion of a body, regarded as a material point, and
referred to an arbitrary origin ; m the constant called its mass ;
a + Aa, and m + Am, the vector and the mass of another
point or body of the system; = the sign of summation, rela-
tively to all such other bodies, or attracting elements of the
system; and d the characteristic of differentiation, performed
with respect to ¢ the time. :
If we confine ourselves for a moment to the consideration
of two bodies, m and m’, and suppose 7 to be the positive num-
ber denoting the variable distance between them, so that 7 is
the length of the vector a’ — a, and, therefore, by the princi-
ples of this calculus,

r= Vf @ —4)"}5 (2)
we shall have, by the formula (1), the two equations,

d2a mir da’ mr

dé? a de. Mean a

5

* See Appendix No. IIT., page xxxvii.

VOL, III. e

hii

which may also be thus written,

d2

m -- = mm'r- (a’ — a),
dq’ :

m! = = mm’r~ (a — a’),

and which ae
0= m(8a5 aia 43) + m’ (30S pis + soos Sa’) + ae
de ar dé@ ' dé

Sa, da’ being any arbitrary infinitesimal variations of the vec-
tors a, a’, and ér being the corresponding variation of pe
because

Sa(a’ — a) + (a’ — a) da + da'(a — ’) + (a — @’) da’
= — (6a' — 8a) (a’ = a) — (a — a) (60 — 0a)
=—3d8.(@—af=68.r = 2rér = — 2738 cr}.
And by extending this reasoning to any system of bodies,

we deduce from the equation (1) this other formula, by which
it may be replaced :

13..m (805 ie s+ aa) + == 0. (3)

Although it is believed that this result (3), if regarded
inerely as a symbolic form, is new, as well as the method by
which it has been here obtained ; yet if we transform it by the
introduction of rectangular coordinates, x, y, 2, making for
this purpose

a= ia + jy hz, a’ = ie’ + jy’ + he’,.. (4)
and eliminating the squares and products of the three imagi-
nary units, 2,7, &, by the nine fundamental relations which were
communicated to the Academy in 1843, namely,

P=f SE => = ls 7
ij = hjk =i, hi =; L (5)
ji=-h Y= i,k =~7; 3

we are conducted, from the equation (3), to a well-known

liti

equation of Lagrange, which may be written thus:

mm!

Som (Saoe + Gey + Gee) sos :

:
where 7, by (2), (4), (5), is equal to the known expression,
r= V{@— a! + — y+ — 2%-

If the law of the attraction were supposed different from
that of the inverse square, a different function of 7, instead of
7—, should be multiplied by the product of two masses.

But further, it is not difficult so to operate on the formula
(3), as to deduce from it another equation which shall be equi-
valent to the forms that were proposed by the present author,
in his papers ‘* On a General Method in Dynamics” (pub-
lished in the Philosophical Transactions*), as being, at least
theoretically, forms for the integrals of the differential equa-
tions of motion of any system of attracting bodies. For if we
observe, that by the principles of the calculus of variations,
combined with those of the method of vectors, we have the
identity,

da a + dada = d(dada + da da) — (da?) ;

and if we write ,
Vinh... @

denoting by v the magnitude or degree (but not the direction)
of the velocity of the body of which the vector is a; we may
transform the equation (3) into the foNowing :

as. Maitedta) s2(%F4 2%) <0:

t
which, when operated upon by the characteristic ) dé, that
‘ ,

is, when integrated once with respect to the time from 0 to ¢,
becomes
d
2.4 (30 ape

d
ar ae ay bay a 8a) + or-—.0, (8)

* 1834, Part II. 1835, Part I.
e 2

liv
if we make for abridgment

u mv min!
= procul sacri C
r=\au(s 2 ae r ) )

and denote by day and ie the values which the variation of a,

and the differential coefficient of that vector taken with respect
to ¢, are supposed to have at the origin of the time. The defi-
nite integral denoted here by the letter F is the same which
was denoted by the letter s in the Essays already referred to,
and which was called, in one of those Essays, the Principal
Function of the motion of a system of bodies; and if we now
regard it as a function of the time ¢, and of all the final and
initial vectors, a, a’,+- dy; a’o,-- of the various bodies of the
system, and suppose (as we may) that its variation, taken
with respect to all those veetors, is determined by an equation
of the form,

0 = 28F + X(cda — ada, + Sa. — day. a9); (10)

in which o, o, are vectors, we are conducted, by comparison
of the coefficients of the arbitrary variations of vectors, in the
equations (8) and (10), to the two following systems of for-
mule :

da’
m= = 4, m! = yo (11)
d da’
m 0 = of m! 2 = alos» +5 (12)

of which the former may be regarded as intermediate, and the
latter as final integrals of the differential equations of motion.
The determination of the (vector) coefficient o, from the varia
tion of the (scalar) function F, is an operation of the same
kind as the known operation of taking a partial differential co-
efficient, and may, in these new calculations, be called by the
same name; but in order to be fully understood, it requires
some new considerations, of which the account must be post-
poned to another occasion.

lv

Consider a system of ¢hree attracting masses, m, m’, m’,
with their corresponding vectors, a, a’, a”; and make for
abridgment a’ — a = (3, and a” — a= y; we shall have,
by (1), for the differential equations of motion of these three

masses, referred to an arbitrary origin of vectors, the following :
4

a _ m’ m : 7
ee eye ay 1 |
(a+ PB) _ m mm
~~ BVCB)* Gn Vvi-G- wy
(a + d(a+y) _ m m’

dy V(= 7) * G=BV{-G=BT
which give, for the internal or relative motions of m’ and m”
about m, the equations :
dpm +m’ a! (B= yy" vie 1
dé > BY (=) W{-B=M VAS
dy _ m + mi" ea {or i a
a? ~ yV(—¥) Ne Oe G—B)} VB)

If we suppress the terms multiplied by m” in the first of
these equations (14), or the terms multiplied by m’ in the
second of those equations, we get the differential equation of
motion of a binary system, under a form, from which it was
shown to the Academy last summer, that the laws of Kepler

(14)

can ‘be deduced. If we take account of the terms thus sup-
pressed, we have, at least in theory, the means of obtaining the
perturbations.

Let m be the earth, m’ the moon, m’” the sun; then B
andy will be the geocentric vectors of the moon aad sun ; and
the laws of the disturbed motion of our satellite will be con-
tained in the two equations (14), but especially in the first of
these equations. By the principles of the present calculus we
have the developments,

i) oa a eve hy By By! 23 (15)

and

pay Gooy - 2 ={1- Byte +e Paar PAP
v{-G-BY} 7 Y

+ hese)

lvi

if then we reject the terms of the same order as m’ 3” y—*,
that is, terms depending on the inverse fourth power of the
distance of the sun from the earth, the disturbing part of the
expression for the second differential coefficient, taken with
respect to the time, of the moon’s geocentric vector, will
reduce itself in this notation to the following :
Er Mt oe —!I igi 2 3 ,
yy aa gh ta =3m!'(— 7) (B + 3y~'By). (17)
This symbolic result admits of a simple geometrical in-
terpretation. The symbol y— Py denotes a vector in the
plane of the two vectors 3 and y, which has the same length
as (3, and is inclined at the same angle to y, but at the other
side of that line; so that y bisects the angle between 3 and
y Py. If then we conceive a fictitious moon among the
stars, so situated that either the sun, or a point opposite to the
sun, as seen from the earth, bisects the are of a great circle on
the celestial sphere, between the fictitious and the actual moon
(the bodies being here treated as points); and if we decom-
pose the sun’s disturbing force on the moon into two others,
directed respectively towards the extremities of that celestial

are which is in this manner bisected : one component force,
resulting from this decomposition, will be constantly ablati-
tious, tending directly to increase the distance of the moon
from the earth, and bearing to the attractive force in the
moon’s undisturbed relative orbit, a ratio compounded of the
direct ratio of half the mass of the sun to the sum of the masses
of the earth and moon, and of the inverse ratio of the cubes
of the distances of the sun and moon from the earth; and the
other component force, directed towards the fictitious moon,
will be exactly triple of the ablatitious force thus determined ;
provided that we still neglect all terms depending on the
inverse fourth power of the sun’s distance, as we have done in
deducing the equation (17), of which the theorem here enun-
ciated is an interpretation. A similar result, of course, holds
good, for every satellite disturbed by the central body of

lvii

asystem. The theorem admits of being proved by conside-
rations more elementary, but was suggested to the author
by the analysis above described ; which may be extended, by
continuing the developments (15), (16), to the case of one
planet disturbed by another, and to a more accurate theory of
a satellite.

Without entering into any farther account at present of
the attempts which he has made to apply the processes and
notation of his caleulus of quaternions, or method of vectors,
to questions of physical astronomy, the author wished to state
that he had found those processes, and that notation, adapt
themselves with remarkable facility to questions and results
respecting Poinsot’s Theory of Mechanical Couples. A single
force, of the ordinary kind, is naturally represented by a vec-
tor, because it is constructed or represented, in mathematical
reasoning, by a straight line having direction; but also a
couple, of the kind considered by Poinsot, is found, in Sir
William Hamilton’s analysis, to admit of being regarded as
the vector part of the product of two vectors, namely, of those
which represent respectively one of the two forces of the cou-
_ ple, and the straight line drawn to any point of its line of

direction from any point of the line of direction of the other
force. Composition of couples corresponds to addition of such
vector parts; and the laws of equilibrium of several forces,
applied to various points of a solid body, are thus included in
the two equations,

6 0; ~=(ap'— Ba) = 0; (18)
the vector of the point of application being a, and the vector
_ representing the force applied at that point being 6. ‘The
condition of the existence of a single resultant is expressed by
the formula,

3B. =(a4B — Ba) + T(aB — Ba). ze = 0. (19)
Instead of the two equations of equilibrium (18), we may

employ the single formula
S.aG = —c, (20)

lyiii
c here denoting a scalar (or real) quantity, which is indepen-
dent of the origin of vectors, and seems to have some title to
be called the total tension of the system.

In mentioning finally some applications of his algebraic
method to central surfaces of the second order, the author
could not but feel that he spoke in the presence of persons,
of whom several were much better acquainted with the gene-
ral geometrical properties of those surfaces than he could pre-
tend to be. But, while deeply conscious that he had much to
learn in this department from his brethren of the Dublin
School, as well as from mathematicians elsewhere, he ventured
to hope that the novelty and simplicity of the symbolic forms
which he was about to submit to their notice might induce
some of them to regard the future development of the princi-
ples of his method as a task not unworthy of their co-operation.
He finds, then, that if a and 3 denote two arbitrary but constant
vectors, and if @ be a variable vector, the equation of an ellip-
soid with. three arbitrary, and, in general, unequal axes, re-
ferred to the centre as the origin of vectors, may be put under
the following form

(ap + pa)” — (Bo — eB)? = 1. (21)
One of its circumscribing cylinders of revolution is denoted
by the equation
— (Be — eB) = 1; (22)
the plane of the ellipse of contact by
ap + pa = O; _ (23)

and the system of the two tangent planes parallel hereto, by
(ao + pa) = 1. (24)

A hyperboloid of one sheet, touching the same cylinder in
the same ellipse, is denoted by the equation

(ap + pa) + (Be — 0B)’ = — 15 =)
its asymptotic cone by

(ap + ga)” + (Bo — of) = 0; (26)

lix

and a hyperboloid of two sheets, with the.same asymptotic
cone (26), and with the tangent planes (24), is represented
by the formula

(ap + pa)’ + (Be — eB) = 1. (27)
By changing p to 9 — y, in which y is a third arbitrary
but constant vector, we introduce an arbitrary origin of vec-
tors, or an arbitrary position of the centre of the surface as
referred to such an origin; and the general problem of deter-
mining that individual surface of the second order (supposed
to have a centre, until the calculation shall show in any parti-
cular question that it has none), which shall pass through nine
given points, may thus be regarded as equivalent to the pro-
blem of finding three constant vectors, a, (3, y, which shall,
for nine given values of the variable vector o, satisfy one
equation of the form

talo—y)+o—y)a}? = {Bo-y)-(-7)BP= = 15 28)
with suitable selections of the two ambiguous signs, depending
on, and in their turn determining, the particular nature of the
surface. It is not difficult to transform the equation (28), or
those which it includes, so as to put in evidence some of the
chief properties of surfaces of the second order, with respect
to their circular sections.

The recent expressions may be abridged, if we agree to
employ the letters s and v as characteristics of the operations
of taking separately the scalar and vector parts of any quater-
nion to which they are prefixed ; for then we shall have

ap + pa = 28. ap, Bo — pB = 2v. Bo; (29)
‘so that, by making for abridgment 2a = a’, 26 = 3’, the
equation (21) of the ellipsoid (for example) will take the
shorter form,

(s. ao)? — (v. Blo)? = 1. (30)

Another modification of the notation, which, from its geo.
metrical character, will often be found useful, or at least illus-

lx

trative, may be obtained by agreeing to denote by the geome-
trical symbol Ba the vector 3 — a, which is the difference of
two other vectors a and 3 drawn to the two points a and B,
from any common origin ; so that Ba is the vector ¢o B from a.
Denoting also by the symbol cBa the quaternion cB Xx Ba,
which is the product of the two vectors cB and Ba; by peBa
the continued product pc X cB X Ba, and so on: the fore-
going equations of central surfaces may be transformed, and a
great number of geometrical processes and results expressed
under concise and not inelegant forms. For example, the

symbols

V.ABC

. S. ABCD
mie (31), and

V.ABC”

(32)

will denote, in length and in direction, the perpendiculars let
fall, respectively, from the summit B on the base ac of a tri-
angle, and from the summit D on the base azc of a tetrahe-
dron: the sextuple area of this tetrahedron azcp being
expressed in the same notation by the symbol s. asco.

The developments (15) and (16), with a great number of
others, may be included in a formula which corresponds to
Taylor’s theorem, namely, the following :

flatda)=(1454 04...) fa; (33)

the only new circumstance being, that in interpreting or
transforming the separate terms, for example, the term 3d?/a,
of the resulting development of the function f(a + da), if a
and its differential da denote vectors, we must in general em-
ploy new rules of differentiation, having indeed a very close
affinity to the known rules, but modified by the non-commu-
tative character of the operation of multiplication in this cal-
culus of vectors or of quaternions. It is thus that, instead of
writing d.a’ = 2ada, 8.a” = 2ada, we have been obliged to
write

d.at =a-da+da.a; (34) 6.a2 =a.da + da.a. (35).

No. VI.

METEOROLOGICAL JOURNAL,
COMMENCING
Ist JANUARY, 1845, anp ENDING 31stT DECEMBER, 1845,
BY

GEORGE YEATES.

THE instruments employed, and the general circumstances
of the mode of observing, have been described in the prelimi-
nary observations to the Tables of the year 1843, in the 2nd
volume of the Proceedings of the Academy, Appendix V.

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“PULA ‘uley | ‘Woieg |*WowseYy Ty, ‘pul ‘urey | “Woreg |*Wousety, “pul ‘uley | ‘woirg |*wourery,

‘WAANTOT | “MGAWHAON ‘IAIO.LOO

[etn a Nn SS SS

January ......... ‘oye owe
GOIN GG oan Ome oo

September = jee = Svar ey Pee
Cie Tae SSeS ee erases

Mean of last three years . .

xvi

MEAN TEMPERATURE

OF LAST 3 YEARS.

1843. | 1844.
40.9 | 41.8
37.8 | 38.6
40.8 | 43.0
49.8 | 51.4
53.5 | 55:3
58.9 |.59-0
62.0 | 60.0
63.2 | 57.9
59.6 | 57.0
48.0 | 49.9
43.7 | 48.7
47.6 | 41.1
50.6 | 50.1

1845.
42.6
40.8

48.3

- RAIN LAST 3 YEARS.

2.589
1.635
1.643
2.645
4.644
2.277
1.773
1.541

637
3.302
2.425
0.138

25.249

23.711

1845.

3.495

-762
1.412
-909

. 1.680

3.131
3.170
2.523

-705
2.677
2.810
1.539

26.628

No. VIL.

Tue following is an abstract of the paper read by Profes-
sor Harrison on the 26th of January, 1846. (See page 184),

It is generally known that Baron Cuvier, in the ‘“* Regne
Animale,” mentions two distinct species of Cassowary, one,
the Galeated, or the Struthio Casouarius, found in several of
the islands of the Indian Archipelago ; the other, the Casoua-
rius (or Dromaius) Nove Hollandiz.

The first, or galeated cassowary, has the bill compressed
laterally, the head surmounted with a bony prominence, co-
vered with a corneous substance; the skin of the head and
top of the neck naked, tinted with a sky-blue and flame colour,
with pendant caruncles, like those of the turkey ; the wings
have stiff feathers, without barbs, and serve as weapons in
fighting ; the claw of the internal toe is much the strongest.
Next to the ostrich, this is the largest bird in nature, from
which, however, it differs in internal organization, the intes-
tines being short, and the ceca and cloaca small, and no in-
termediate stomach between the crop and gizzard; it lives on
fruit and eggs, but not on grain. Its eggs are ofa green
colour. The second, or New Holland cassowary, has the
bill depressed, no helmet on the head, naked round the ear
only; the plumage is brown, thicker, and more bearded; no
caruncles or alar spines, and the claws are nearly equal. On
its internal organization the Baron makes no remark, neither
does he allude to the peculiar condition of the trachea, which
forms a striking discriminating character between it and the
galeated bird. Dr. Knox, the distinguished anatomist and
lecturer in Edinburgh, in an extremely interesting paper,

VOL, III. f

Ixviii

read before the Wernerian Natural History Society, and pub-
lished in the Edinburgh Philosophical Journal, in April, 1823,
has entered more fully into a comparison of the internal orga-
nization of these two species, and has given the first account
I have met with, of the remarkable tracheal sac in the emu.
His anatomical description, however, of this curious appendix,
is brief and imperfect, which may be accounted for by the
‘specimen he examined being greatly mutilated before it fell
into his possession. His account of it is as follows :—* At
the fifty-second ring, counting from the glottis, there is found
a large muscular bag, about the size of a man’s head, into
which the windpipe opens by a large orifice, occasioned by a
deficiency of part of the circumference, in about thirteen tra-
cheal rings; or rather the rings, instead of closing round to
form the tube of the trachea, expand outwards, and are at-
tached to the sides of the bag; it has no communication with
any of the air cells’ —p. 36. ‘ This muscular bag is as large
as the human head, is closely attached to the sides of the
trachea and expanded rings, is situated in the neck, immedi-
ately above the bone called the merrythought; it was seen
by me in the female, though it is probable the male also pos-
sesses it. It is quite peculiar to this bird, no such appendage
having been ever seen attached to the trachea of any of the
feathered creation, nor do I know of anything analogous to
it in any other animal, excepting in the chameleon, to the
upper portion of whose trachea there is appended a compara-
tively large membranous bag.’—p. 138. ‘It has not the
most distant resemblance to the tracheal appendages found in
other birds. In thus differing so singularly and mysteriously
from the analogous structure of birds of the old and new con-
tinents, it fully confirms the opinions of some naturalists, that
the living productions of Australia will, when properly exa-
mined, be found to present peculiarities altogether wonderful,
and, perhaps, yet, for a long period, quite inexplicable.”—
p. 139.

ixix

Meckel, in the tenth volume of his Comparative Anatomy ,
alluded to the discovery of this air sac by Fremery, in the
year 1819, but states that he has noticed it in a vague and
imperfect manner. I have not had an opportunity of consult-
ing this work of Fremery. Meckel does not describe this air
sac with that clearness and precision so characteristic of this
writer. His account rather consists of quotations from Knox,
and of the varying statements of other writers, than of any
observations of his own. Carus, in his System of Compara-
tive Anatomy, makes no mention of it. It does not appear
to have been known to Cuvier, as there is no. notice of it
either in his Anatomie Comparée, or in his Regne Animale,
neither is it alluded to in-the new edition of that invaluable
work, now in course of publication. In the elaborate and
excellent article ‘* Aves,” in the Encyclopedia of Anatomy
and Physiology, edited by Dr. Todd, of London, and which
article is from the pen of Mr. Owen, who is justly regarded
as the first comparative anatomist and zoologist of the present
day, this peculiar appendage is alluded to; but, strange to
say, the brief and imperfect account which is there given of it
is wholly incorrect, a circumstance I can only attribute to
some accidental inadvertence. Mr. Owen says, “that the
trachea of the emu is remarkable for a sudden dilatation;
but, in this instance, the cartilaginous rings do not preserve
their integrity at the dilated part, but are wanting posteriorly,
where the tube is completed by membranes only.” I have
made some researches into the writings of other authors also,
but have not met with any accurate description of this appa-
ratus.

As I have lately had an opportunity of examining this
appendix in the living bird, as well as in one recently dead,
I shall state such facts as I have observed in the former con-
dition, as well as the appearances I have remarked in the
latter. I may first observe, that this exists both in the male

and female; for some time since I dissected a male emu, and
ine

lxx

found the opening in the trachea, but the soft parts were too
much injured by decomposition to admit of an accurate exa-
mination of the sac itself. The specimen from which the
following account is taken is an adult, or probably, an old
female.

The cervical air-bag (fig. 1) occupies a broad and deep
depression on the forepart of the neck, immediately above
the sternum and furculum bone, which latter in this bird is
small and imperfect. The sac is not observable either in the
living or the dead bird, unless distended, when it slowly bulges
forwards and laterally, and fills the depression above-mentioned ;
it is not, however, even then so prominent as to cause any
remarkable deformity. On examining this region during life,
the sac being undistended, I found the skin very moveable; it
gave to the hand the sensation of great warmth, when con-
trasted with the surrounding parts. The entire of the trachea
was very moveable to either side; but on fixing it steadily, and
carrying the fingers along its forepart down to the sternum,

the tube was felt a little above the latter to be flattened or
depressed, but no slit or opening could be distinguished ; the
sac was perfectly flaccid and compressed, and the communica-
tion with the trachea was closed. ‘This examination did not
appear to cause any peculiar uneasiness in the part, or to
excite any general irritation in the respiratory system. ‘This
bird, however, is very restless and timid, and very impatient
under any restraint; it is also possessed of great muscular
power, three or four men being required to secure it, and the
attempt to do so is by no means free from danger, either to
itself or to those around, as it struggles with great violence,
and strikes with its powerful claws in every direction. I suc-
ceeded twice, however, to my satisfaction, in feeling this
region; and I think I am warranted in concluding that the
tracheal opening is usually closed, and that it may be opened
at the pleasure of the animal. - The plumage in this situation
is thin and scanty ; the feathers are chiefly of the double spe-

xxi

cies, that is, two barbs proceeding from one quill; the barrel
of the latter is small, and filled with pith, and the feathers are
fine and hair-like. This, indeed, is the general character of
the plumage of the struthiones.

A few days after the death of one of these birds (a female), I
carefully examined the sac, larynx, and trachea, and the follow-
ing is an accurate account of the several appearances. ‘The
integuments covering the air-bag differ in no respect from the
general investment of the neck; beneath the skin is a strong
and red muscular lamina, expanded over its sides and fore-
part; the fibres are chiefly longitudinal, but several strong
fasciculi run in different directions; the subjacent areolar
tissue contains numerous nerves and vessels, especially veins.
On opening the bag, the tracheal orifice (fig. 2) is seen dis-
tinct and well-defined, of the form of a long parallelogram ;
the mucous membrane of the tube is continued around its free
margin, is reflected over, and adheres to the anterior and
lateral parts of the tube considerably beyond the edges
of the opening, and then expands in all directions to line
this capacious reservoir, which is sufficiently large to con-
tain at least a quart or three pints of fluid. This mem-
brane is soft and vascular; numerous capillaries and large
veins, with long tortuous nerves, are seen distinctly through
it. The tracheal opening (fig. 4) is situated about three
inches above the furculum, and in the middle line of the
tube; it is two inches and a half long, and scarcely half an
inch wide, but it can be easily extended to three inches
in the vertical and to three-quarters of an inch in the transverse
‘direction; it is produced by a deficiency in the anterior part
of six rings (in the two specimens I have examined the num-
ber was the same); the cartilage above and that below the
opening is broad and well defined; the extremities of the six
lateral cartilages are sharp, thin, and very moveable; there is
no dilatation, at least to any appreciable degree, in this part of
the tube, and the rings are not all extended or continued into

lxxil

the parietes of the sac, but, on the contrary, are bent towards
each other of opposite sides, and can, by a little lateral pres-
sure, be brought into contact. On the interior of the back
part of the trachea, exactly opposite the opening in the me-
dian line, a remarkable prominence, or vertical keel-like pro-
jection is observed standing forward into the tube, and pre-
senting a ridge of rounded bifid points or tubercles ; when the
sides of the opening are approximated, the anterior extremi-
ties of the six rings come into contact with and are supported
by this posterior ridge, so that the trachea is there divided into
two channels, one at either side of this middle line; and thus,
when the opening into the sac is closed, the respiratory pas-
sage is maintained free and uninterrupted, while at the same
‘time its anterior wall is well supported against any collapse
into the cavity, and is also enabled to resist the weight or pres-
sure of the external atmosphere, under the suction influence
of the inspiratory efforts: this posterior keel-like projection
extends for some distance on the back part of the trachea, both
above and below the opening. When the trachea is relaxed
in the longitudinal direction, the rings are all approximated,

and those bounding the opening are a little overlapped by that —

above and that below it, and the apposition of the several seg-
ments is still further secured by the pressure of the superin-
cumbent soft parts. This cervical air-bag bears no analogy
to the air-cells disseminated through different parts of the
bodies of birds; such are formed of cellular tissue, but this
is an extension of the mucous surface, and has no communi-
cation with the air-cells, excepting through the trachea and
lungs.

The toneue (fig. 1) is small, flat, thin, and triangular ;
its surface presents but few papillz, but is studded with innu-
merable small points, orifices of mucous follicles; its margins are
neatly fringed with five or six loose, denticulated folds on either
side, some of which are a quarter of an inch in length. From
the base of the tongue proceeds backwards a thick semilunar

a

xxiii

fold of membrane, of the same colour and texture ; from its
centre is a short, conical projection, analogous in its position,
in front of the glottis, to an epiglottis, and capable of acting
as such to a slight extent ; it is devoid of cartilage, but when
the tongue is retracted, this process can cover the anterior
half of the glottis. The Hyorp sons, or rather cartilage,
supports the tongue by a broad basis, from the centre of
which a short, strong style passes forwards in the median
line; a similar process descends in front of the thyroid carti-
lage, and is attached to it, and to the forepart of the trachea,
by elastic ligament; the cornua are pliant and elastic, and
curved backwards in a tortuous form; they support the pha-
rynx and fauces, and admit of considerable expansion. ‘The
glottis, or superior larynx is well developed, and bears some
resemblance to the rima in mammalia ; its aspect is obliquely
upwards and backwards, and is placed, as usual in birds, on
the posterior plane of the trachea, though not to the same
extent; but it is devoid of all spines, tubercles, and papillz,
nor has it the chink-like form so common in that class. ‘The
thyroid cartilage bounds the larynx in front, the cricoid be-
hind: on the upper edge of the latter are two thin broad plates,
passing forwards, from the inner side of the centre of each
there is a prominent and firm fibro-mucous body, projecting
inwards; these bodies bear some analogy to arytenoid carti-
lages; they nearly touch, and can easily be made to do so,
whereby the opening is divided into two parts; the anterior,
small and triangular, can be covered by the epiglottis when
the tongue is retracted; the posterior is round or oval, and
_ean only be closed by the action of the surrounding muscles
pressing its sides into contact during the act of deglutition.
These two portions bear a close resemblance in form to the
human rima glottidis, when subdivided into two by the approxi-
mation of the long, anterior, basilar processes of the arytenoid
cartilages (fig. 1) ;
The trachea is of considerable length, the rings are all

Ixxiv

cartilaginous, compressible, and elastic; they are 104 in num-
ber in the female, (I did not count them in the male speci-
men) ; sixty-four are above the tracheal opening, six corres-
pond to the open portion of the tube, and there are thirty-four
between this and the division into the right and left brenchi ;
in each of the latter are six semicircular cartilages, and three
rudimental fragments; beyond these, the air-tubes abruptly
become membranous and muscular, and no cartilages are con-
tinued into the lungs. The form of the tracheal tube is
somewhat transversely elliptical, but is indented posteriorly
through its whole extent ; that is, each ring is curved poste-
riorly, so as to be convex towards the canal, and concave to-
wards the spine; this general indentation is increased by the
slightest pressure; the cesophagus is closely connected to it,
and when distended, during the deglutition of any large sub-
stance, would appear to derive some accommodation from
this structure. This posterior indentation is much increased in
depth opposite the tracheal opening, and thus accounts for
the corresponding vertical prominence internally already de-
scribed ; in this particular situation, the cartilages are also
somewhat differently modified, as we shall notice presently.
A yellowish elastic structure extends the whole length of this
posterior depression on the trachea (fig. 5); this increases
in strength inferiorly, and terminates at the division into the
two bronchi; beneath this elastic ligament, opposite the tra-
cheal opening, and a little above and below it, short, but
strong, transverse muscular bands pass across the groove, and
are inserted into the cartilages at either side (fig. 5); these
fibres, by approximating this attachment, will tend to pre-
serve, and even protrude the keel-like projection within, and
thus enable it the better to support the approximated ends of
the lateral cartilages in front; the longitudinal elastic liga-
mentary tissue admits of the extension of the trachea, and can
restore it to its state of rest, on the subsidence of the extend-
ing force.

Ixxv

The tracheal cartilages present some difference in size and
form in different portions of the tube; their diameter gradu-
ally, but. slightly, increases from above downwards, and a
very trifling swell is observable in the region of the opening.
The upper and middle rings present flattened surfaces, and their
edges, above and below, are connected by elastic membrane;
those below the opening, though forming larger circles, are
small, round, and weak, and have an oblique direction down-
wards and forwards; this portion of the tube is very elastic;
the four or five last cartilages are deficient posteriorly, in a
narrow, angular interstice, which is closed by lining mem-
brane, weak muscular fibres, and elastic tissue; from the last
ring no internal ridge or bar proceeds, but from the angle be-
tween the bronchi the mucous membrane rises mesially in a
prominent falx-like fold, which is increased or diminished in
depth and tension in proportion as the trachea and bronchial
tubes are shortened and contracted, or elongated and distended ;
the bronchial cartilages are little more than semicircles, their
extremities being somewhat thick and expanded; the two su-
perior present, externally and posteriorly, small projecting
processes, into which some fibres from the long cervical mus-
cles are inserted; the posterior wall of each bronchus is mus-
culo-membranous; although there is no inferior larynx, yet
each bronchial opening,—which is of an oval form, the long
axis from before backwards, or, during life, from above down-
wards,—is capable of great alteration in size, figure, and ten-
sion of its lateral boundaries; these changes can be effected
by the varying degrees of inspiration and expiration, by exten-
- sion and flexion of the neck, and also by the action of the,
tracheal muscles.

The six cartilages which are concerned in. the tracheal
opening, deserve particular notice; they are peculiarly elastic,
and appear composed, each, of two symmetrical portions, one
on either side; each lateral portion is crescentic (fig. 6) ;
the anterior cornu, flat, thin, and very moveable, is enveloped

Ixxvi

in mucous membrane, and engaged in the edge of the tracheal
opening ; the posterior cornu meets the corresponding cornu
from the other side, in the posterior indentation, and both
project forwards from the posterior wall of the trachea, and
present the appearance internally already noticed. These pos-
terior cornua, from the right and left crescentic cartilages,
are, in some, connected together by a narrow and thin carti-
laginous structure ; in others, by a narrow line of dense cellu-
lar tissue; so that we may regard this portion of the trachea
as composed not of six cartilaginous rings, open in front, but
of twelve crescentic cartilages, six on each side; their ante-
rior cornua either bounding the sides of the opening when
this is open, or in contact, when it is closed; their posterior
cornua bent forwards, so as to form the keel-like prominence
internally, which will come into contact with and support the
anterior cornua when these are approximated and the orifice
closed, and the tracheal canal thereby divided into two lateral
tubes.

From an examination of the several parts concerned in
this curious apparatus, and from observing the animal during
life, I am led to infer that it possesses the voluntary power of
not only expanding this air-bag, but also of retaining it in
that state for an indefinite time, without any continued mus-
cular exertion, and that it can either rapidly or slowly con-
tract, or empty it, and perfectly close its communication with
the trachea. It has been remarked that on some days it is
not dilated; on others it is frequently expanded, and as fre-
quently contracted, in a few moments, or retained in a dis-
_ tended state for a considerable time; and on some occasions
mt remains in that condition when the bird is at rest, or appa-
rently asleep. When about to fill it, he raises and slightly
extends the neck, and darts it a little forward; little or no
muscular exertion is apparent, and the bag swells out, most
probably by an expiratory effort, the glottis being previously
closed, and the muscular wall of the sac being relaxed, so as

Ixxvil

to admit of more easy dilatation ; perhaps, also, the posterior
transverse muscular fibres of the trachea may, by increased
contraction, tend to divaricate the anterior cornua of the car-
tilages, whilst the extension of the neck and elongation of
the trachea have separated the cartilages above and below the
opening; once the bag has been filled by this expiratory
effort, the glottis being closed, it may be retained in that
state, even should this opening become relaxed, provided the
walls of the sac do not contract, and respiration may continue
without the reservoir being affected, further than that the in-
cluded air may be more or less changed by the admixture of
fresh air from each inspiratory current: the closure of the
glottis, and an expiratory effort, then appear to be the simple
agencies whereby the distension of the sac is effected.

The sac can be emptied by the contraction of its muscular
covering, the distending force having ceased, and the air may
be expelled by expiration, or it may be drawn into the lungs
by inspiration; the elasticity of the cartilages, and the com-
pression of the surrounding parts, will then approximate the
edges of the opening, which will be supported by the internal
vertical projection on the back part of the tube, and thus the
orifice will become so perfectly closed, that inspiration can
have no effect in drawing within it the superincumbent soft
parts.

When, from surveying this curious and elaborate struc-
ture, we turn our attention to its use, and endeavour to explain
the design of this anomalous arrangement, we are at once met
by the fact, that although this bird is in all respects so simi-
Jar to the ostrich, and to the Indian cassowary, yet in it alone
is this bag developed. Were a similar structure found in all
the struthiones, we should have had little hesitation in con-
necting it—though, no doubt, erroneously—with some of the
peculiar habits and endowments of this class generally ; but
such not being the case, we naturally ask, is there any pecu-
liarity of climate, or any other circumstance in the locality in

Ixxvili

which this species is found, that will explain the necessity of
it, or account for its presence, or is there any peculiar power
or faculty possessed by this bird of which those allied to it
are deprived? or are we to regard it as one of those examples
of creative omnipotence which often displays itself in the va-
riety of its works, without any other obvious result but the
mere manifestation of that power ?—a remark which appears
strongly verified by many of the peculiarities of the living
productions of Australia.

Dr. Knox considers that the emu has been furnished with
this peculiar provision to preserve it amidst those dangers
from sudden floods to which New Holland is particularly
exposed. ‘* The sandy plains of this country,” he says, “are,
during a great part of the year, inundated, and become then
boundless marshes ; and the plains generally are exposed to sud-
den inundations. The rivers, moreover, running westward from
the great chain of mountains, terminate in vast muddy inland
marshes ; the emu, forced to seek his food amidst these fens,
may, when obliged to have recourse to swimming (which
must often be the case), fill the muscular bag of the trachea
with air, and thus convert it intoa swimming bladder. It may
also assist the bird in escaping from his pursuers; but on this
I do not mean to insist, as this organ is wanting in the galea-
ted cassowary and in the ostrich, both equally remarkable for
speed of foot.” Dr. Knox further remarks, that when the
bag has been distended by an expiratory effort, and the glottis
retained in a closed state, the air may be alternately circu-
lated between the lungs, air-cells, and tracheal bag, without
the bird being necessitated to allow it to escape, in order
again to perform the act of inspiration, and thus give it an
additional advantage in running. This. explanation appears
extremely probable, and, no doubt, if the inspiratory efforts
are thereby rendered less frequent, this creature may be ena-
bled to sustain its running flight (which, in speed, is said to
surpass the race-horse or the grey-hound) for a longer time,

Ixxix

and with less fatigue, than the quadruped or man, who are in-
capable of keeping up long-continued rapid progression, not
so much from debility in the muscular system generally, as
from a failure in the inspiratory muscles, which, under such
exciting and exhausting circumstances, are called on to exert
additional force, in order to maintain the due quality of the
blood, as well as to regulate the current of the circulation,
and which exertions, when too long continued, are speedily
followed by that overwhelming and well-known, though al-
most indescribable, sensation denominated fatigue. It appears
to me, also, that this organization, may still further minister
to the respiratory function, by extending the surface of the
mucous membrane on which the chemico-vital changes in the
blood are effected. The lining membrane of this reservoir
presents not only a very extensive surface, but it is also as
highly organized as that lining the trachea and bronchial
tubes, with which it is continuous ; numerous capillaries and
tortuous nerves branch throughout its texture, and several
large veins course irregularly along its wall; it is, therefore,
highly probable that the same changes which are effected in
the blood through the parietes of the minute pulmonary ca-
pillaries, and through the thin coats of the large veins which
traverse the air-cells in the bodies of birds generally, may all
take place on the lining membrane of this cervical air-bag ;
and that this additional respiratory agency will be supplied at
that very time when the function of respiration is required in
the highest degree to maintain the muscular exertion and the
nervous energy which the animal evinces during its rapid ex-
cursions. This adjunct to the respiratory apparatus may
even be the more necessary to this animal as a compensation
for the imperfectly-developed, or almost rudimental wings,
which are not only of little or no avail in locomotion, but
which, from the absence of those large air-cells and blood-
vessels which exist in the wings of other birds, can here in
no way contribute to the respiratory function.

Ixxx

That this peculiar organization is connected with the vo-
cal powers of this bird, I conceive there can be very little
question ; it is with surprise I have read the remark of Meckel,
that this bird has no voice. Those who have frequently
visited these birds in the Zoological Gardens, must have no-
ticed the different sounds they emit; in fact, they have two
_ distinct voices, just as they possess distinct organs; the most
ordinary isa harsh, disagreeable, hissing voice, not unlike that
of the common goose; this is frequently heard, as the bird
follows visitors round the enclosure in expectation of food ;
this voice I attribute to the structure, or organization of the
. superior glottis. The other, and more peculiar sound, is only
occasionally emitted, probably because, while in a state of
captivity, the ordinary excitements are not so frequently pre-
sent; this resembles a low, hollow sound, not unlike that
caused by gently striking a large drum, or moving an empty
barrel; sometimes it is sharp, short, and sudden; at other
times it is long and muffled, like the rolling of thunder, or of
a smoothly-running distant carriage; sometimes it is soft,
continued, and rather melodious; but at others it is disagre-
ably interrupted by harsh and rough grunting sounds. The
animal only occasionally emits this voice; on visiting the
Gardens, in hope of hearing it, I have been frequently disap-
pointed ; on other occasions, the birds have repeated it several |
times. The care-taker informs me that in his morning visits
to open the aviary and feed the birds, they frequently make
this extraordinary noise, and which he compares to the sound
of thunder. The ear detects this sound as proceeding from
the upper part of the sternum, that is, from the position of the
sac, and, while making it, the animal extends and alters the
curve of the neck, and fills this tracheal bag ; there can be no
doubt, therefore, that this voice is connected, in part, with
the inferior glottis, or the two narrow bronchial openings, and,
in part, if not essentially, with this peculiar appendix; there
is nothing in the superior larynx, or in the inferior, alone, that

Ixxxi

can account for it, whereas the great capacity of this reservoir,
‘its free communication with the trachea, immediately above
the narrow bronchial aperture, its sudden distension, and as
sudden contraction, or the alternate partial action and relaxa-
tion of the distending and compressing agencies, together with
the free and elastic vibrating borders of the tracheal opening,
the resisting wall behind, and the long and softly resonant
tube, leading upwards, may, I think, satisfactorily account for
these peculiar vocal phenomena. What may have been the
design of imparting to this being this peculiar endowment, it
would be as vain to speculate upon as to attempt to account
for the infinite variety of voice that prevails throughout the
animal world; that it is voluntary I have no doubt, and may
be exercised either for sexual attraction or social union, or as
indicative of nervous emotion, the result of anger, terror, or
alarm.

This remarkable air-bag is not only peculiar to this ani-
mal, but there is nothing exactly analogous to it in any other
member of the class Aves. In the trachea of several water
birds there have been long observed peculiar swellings, or
dilatations of the tube, in the structure of which the entire
of a certain number of rings are engaged, but there is no dis-
tinet sac'or bag. The laryngeal or tracheal sac in the cha-
meleon, bears,as Dr. Knox has remarked, some remote analogy
to it; the laryngeal sacs in certain of the quadrumana, and
even the ventricles in the human larynx, and the sacculi la-
ryngis, which lead from each upwards and forwards, may be
regarded as rudimental conditions of the same structure.

EXPLANATION OF THE PLATE.
Fig. 1.—Superior glottis, tongue fimbriated.
Fig. 2.—Front view of the tracheal sac; a few feathers re-
main.
Fig. 3.—Sac laid open, and drawn over to the right side:
a, opening in the trachea: }, sharp, thin extremities of the six

Ixxxil

rings: c, prominence on the back of the trachea: d, section of
the cutaneous covering; e, of the muscular; f; the lining
muvous membrane, extending over the front and outside of the
rings, and then continued round the edges of the opening
into the trachea,
Fig. 4.—Section of the trachea: a, 5, c, as in last figure.
Fig: 5.—Posterior view of the sac: a, indentation on the
trachea corresponding to the internal ridge in figs. 3 and 4;
-b, longitudinal elastic ligament, dissected off, and drawn to
one side ; c, transverse muscular fasciculi, attached to the con-
vexities of the cartilages on either side, raised on a small twig.
Fig. 6.—Horizontal view of three tracheal cartilages: a,
from the upper portion; c, from the lower; b, corresponds to
the opening, shews two semicircular cartilages, their posterior
cornua projecting forwards into the tube, and ending in round
and slightly bifid points; d d, mucous membrane of the trachea
-and sac.

No. VIII.

ACCOUNT

OF THE

ROYAL IRISH ACADEMY,

FROM Isr APRIL, 1845, TO 31st MARCH, 1846;

ee

THE CHARGE.

To balance in favour of the Public on 3lst | £

March, 1845, .
Parliamentary ‘Grant for 1845 (paid 1s ist Au-
gust, 1845),
Quarterly Warrants from Treasury,
Total from Treasury,

INTEREST oN Stock:
Half year’s on £1643 19 6, 34 per Cents.

Ditto, ;; 1117 +1 10, 3° 35 ‘
Ditto, 39 1643 19 é 3} ”
Ditto, , 867 1.10; 3 »

Less Commission for receiving

Dividends, s « 5 4
Stamp for Power of ‘Attorney for
receiving Dividends, . « 0 0

—

Total Interest on Stock,

AMOUNT OF STOCK SOLD:
To £250 3 per Cent. Consols, sold at 983,
_ 33 days’ Interest, wre

Power of Attorney for sale of
Stock, . .

0
Commission for ale ae ditdot 3

1 0
0 6

“Total Amount of Stock sold, . . .-

Rent or State, due lst November, 1845,

Ss.

300 0 0
146 17 8

246 5 O
13 6

246 18 6

446 17 8

8118 3

245 12 3
21 0 0
91419 4

0

lxxxiv

Brought forward,

PUBLICATIONS SOLD:

Transactions and Proceedings sold here,
Ditto, sold in London by Messrs. Boone,
Ditto, sold in Dublin by Messrs. pnees
and Smith,
Total Amount of Books sold,

OUTSTANDING SUBSCRIPTIONS FOR THE PuR-
CHASE OF Messrs. HopGes AnD SMITH’s

MSS., coLLECTED DURING THE YEAR:

Ly LORS EGG" So ER

D. H. Kelly, Esq., a SA

J. T. Banks, M. D., saps

John E. V. Vernon, Esq., «

Durham Dunlop, Esq., .

M. O. R. Dease, Esq.,

Sir P. Crampton, Bart.,

Sir P. N. Nugent, Bart.,

Rev. Dean Lyons,

Halliday Bruce, Esq., . -
Total Amount of Manuscript ‘Fund,

Lire Compositions:

Daniel Connolly, LL. D.,
John Ball, Esq.,
Robert Forster, Esq.,
Walter Sweetman, Esq.,
James C. Sherrard, Esq.,
E. King Tennison, Esq.,
* Total Life Compositions,

ENTRANCE FEEs:

_ W. Hogan, Esq., . -

J. A. Galbraith, Esq.,
J. F. Waller, Esq.,
James Jameson, Esq.,
N. P. O’Gorman, Esq.
Lord Farnham, ;
Lord Wallscourt, .
W. Le Fanu, Esq.,
William Henn, Esq, . .
Digby Pilot Starkey, Esq.,
Charles Bournes, Esq., .
W. C. Dobbs, Esq.,
P. J. Blake, Esq,, .

£8 dd. |
39 16 8
50 18 2
9°76
| saad ie
i Ailied Lge)
1 1 0
5 0 O
1 1 0
1 0 0
2 0 0
2 0 0
1 0 0
100
21 0 0
18 18 0O
21 0 0
21 0 O
21 0 O
21 0 0

Or Ov Or Or Or Ou Or Oe Cr Cr OH GO.
ROA AN ON Or CH OTN Gr

68 5

)

oooooooocoeooccocoe

100 2

16 4

123 18

1155 3

4

8

Ixxxv

Brought forward,
Wyndham Goold, Esq., . :
C. C. King, Esq., .

Daniel Connolly, LL. ‘De

J.S. Close, Esq., .

David Moore, Esq.,

James Claridge, Esq.,

Right Hon. D. R. Pigot,

J- Talbot, Esq., a
Adolphus Cooke, Esq., .
James S. Hiffe, Esq., .
William Lloyd, Esq.,
Benjamin Wilme, Esq., .

T. Jolliffe Tuffnell, Esq.,
Charles W. Williams, Esq.,

E. K. Tenison, Esq,., .

Mathew Baker, Esq.,

Rev. Classon Porter,
Conyngham Ellis, Esq.,

Very Rev. Henry Cotton, Dean of Lismore,

Rickard Deasy, Esq.,

Arthur R. Nugent, ea :

Rey. J. Connell,

Robert Francks, Esq.,

Pierce Morton, Esq.,

Richard Cane, Esq., -

J. T. Evans, Esq. - e

Robert C. Williams, Esq. ae

H. W. Massy, Esq.

R. R. Madden, Esq,., .

Earl of Enniskillen, .

Thomas Butler, Esq.,

C. W. Levinge, Esq., .-

Stephen O’Meagher, Esq., . :
Total Entrance Fees, .

ANNUAL SUBSCRIPTIONS AND ARREARS:

W. Hogan, Esq., . .
Charles Hanlon, Esq.,
Rev. R. Butler, i
Charles Vignoles, Esq,, .
John Mollan, Esq.,
Henry Close, Esq.,

F. Churchill, M. D.,
Rev. Francis Crawford, .
Rey. Dr. West,

iti)
i)

845,

at

Oe OO UU UUM TO UT OOD

RA MAMAN AMMAN ANNAN AMANAAARMA AAA MAAAAAAMAN Er”

|

WONMNNNNNN,WY
NNNNNNNNW
ooocooceoo

18 18 Q

Bech a!
[Gyss Bye
241 10 0}

1396 13 8

Ixxxvi

Brought forward, mee,
John Hamilton, Esq, . . . . - 1845,
Waltham Murray; Hsq.,.. sores. <<.) 55
Wes. O'Brien, HsqiyM.P.. ras nee ey,
Bdward Hutton; Hsq.,, . -. ©...» 65 “sy
Cope Webber, Wsgj)0 F004,
efeide Coopers Esq. Gio ease fb. sb hed gp
Alexander Ferrier, Esq., .-... + ,,
William Longfield, Esq., . . . .1844,
Ditto; MR. Oe) RSs sap ie) sepa D
Jacob Owen, Esq, . . . aa
W. B. Wallace, Esq, sh. seg aed nbs
Henry Watson, hes eg rt. oe Oe to OAD
Ditto, : . . fs 0 as + 1843,
DDIGGO NO. Set a va ne wo RBA
Ditto, . . . as te ts re LOAD:
M. O. R. Dease, Esq, cat ech re alo
J. G. Abelishauser, Esq... -. ..-. -,,-
William Mac Dougal, SIS, Alsi tee wey a
Dre OGrady, gt 6. eA Tp ig
Hon. J. King, . airtel
Durham Dunlop, Esq., « :
William Edington, Esq.,
T. F. Kelly, Esq.,
William Hill, Esq., .
Sir William Betham,
Thomas Cather, Esq.,
J. Anster, LL.D.,
W. R. Wilde, Esq.,
J. Huband Smith, Esq, . . . ;
ee. Gayery LED.) oes ep ys
WrsOsborney (es ge ia
W. Barker, M.D.,
G. D. Latouche, Esq,
Robert Tighe, Esq., .
Dr. Montgomery, .
W. T. Mulvany, -
Rev. James Wills, .
Goddard Richard, Esq., .
W. E. Hudson, Esq,
J. H. Jellet, Esq.,
W. T. Lloyd, Esq.,
A. Smith,M.D. . . .
W. T. Mac Cullagh, Esq., ‘
R. C. Walker, Esq., . 3
James Apjohn, M. D.,

a tr
e
.
~

2
: mt
NWNNMONMNMNNPNMNYPNNNNPNNNNNNNNNNNNNNNNNNMNNNNNNNNNNNNNNND®
- —
PNY NYNNNNNHNNNNNNNNNNNYNYNNYNYNNYNNYNNNNNYNNNNNNNNNNNNOD”

—
—_
ie)
@

EO. St vals
1396 13 8

Sze=oocooecoocoocoooocoooooosooooooooooooooocoooocoooosoocoococooo=

0 |1396 13 8

lxxxvli

Bees | £ s d.
Brought forward, . . .| 11 1396.13 8
George Wilkinson, Esq, . . . . 1845,
Sir Thomas Staples, Bart, . . + 4,
Edward Bewley, M.D... . . + 5;
eR enna BEG.e . si yt wt ogg
Lord Farnham, . . Prise s
Most Rev. Archbishop of Dublin, ee
Lord Wallscourt,. . . Ses
Baws Burtony Msg. Wo OR 8! ag
Robert Law, Esq, © - . » « © 49
ober Dall; Wsqhy Sh oo. ah 0h 5S 5a
William Drennan, Esg., . . .. ,,

Gerald Fitzgibbon, ie gf st 2 hols
J. Magee, Esq, . . Rhee Cha tae
Reb Ogilby, Esq: FT a Gs

as

3 8 0

2 Zee

2 2°40

2 2 0

2 2 .0

220

2 2 0

2.72" 0

22 0

2 20

2 2 0

2.20

2 2 0

2 2 0

2 2 0

Thomas Grubb, Esq, . . . . ~ 455 2 2.0

C. W. Hamilton, a: oP [ieee bates tess 2 2 0

Dr. Toleken, aby 8k 2°2 0

* William Monsell, Bq Bis | a eA, 2 2 .0

Rev. W. Lee, . . Le. ele SOAS 2 2 0

Seba-Ball MeQaen Sk kak 5 2 2 0

E. E. H. Orpen, Esq., ; Ae: 2 2 0

Sir John Kingston James, Bart., . 1845, ya ta 0)

Thomas Oldham, Esq, . Oe aS eel 2 2.0

C. G. Otway, Esq, - . - « . 1843, PDO

Pate bey S BSS he ao :sTSe |. SOR Le

Ditto; ws Shyer e Sa lBEo: 2 2 0

H. F.C. Logan, D. D., a Oe Tee eee a 2.5250

Hon. F. Ponsonby, 9.6 oe eg 2 2 0

Rev. dames Reidss oo. Ne oe gs 2 2 0

William Blacker, Esq... . . . - 55 2, 20

Philip Reade, HisG, S - .l os gy 21250)

Dean of Ossory, aren So Pape pe) aK 0)
Sir Lucius O’Brien, Bart, ADT 32 Wg ag 22 0 -

A. B. Kane, Esq., . A ae ee er 2 2. 0

Right Hon. Chief Baron, te ee Biv wn of

Hon. Justice Crampton, . -.. 4 2 2 0

Edmund Davy, Esq, . . + » » 4 Qe2aO

‘Sir P. Crampton, Bart., Bae Ry 2.520

ae) Alton, (Hegq.%) Ge...) pe eo!,- L844, 2 2 0

Mr Beauchamp, & . » 42). ..1845, Dh 25 20

KE. Cane, Esq... .« EAN she acai catia 2 2 0

W. Grimshaw, M. D., spe ner airs ne 2 2 0

gohn Finlay, LL.D.,5 - (+ ae e- es oy 2.2 0

Rk. A. Wallace, Esq., BD cla Oe ee ach Dree2 0

A.C. Stipkgey Esq, - 0. eek + 45 2 2-.'0

207 18 0 11396 13 8

Brought ie ward,

T. E. Beatty, Esq.
H. H. Joy, Esq., .
M. M‘Master, Esq.,
C. Bolton, Esq., :
Sir Robert Kane, M. D.
G. J. Allman, M. D.,
F. W. Conway, Esq.,
M. Longfield, Esq., :
Sir Edward Borough, Bart.,
W. Andrews, Esq., .
Acheson Lyle, Esq., .
Ditto, Site
R. Cully, Esq.,
Sir Richard Morrison,
Ditto, .
Ditto, . :
James Patten, M. oe
Ditto, .
John Davidson, Jun., “Esq, ,
Samson Carter, Esq.,

Henry L. Lyndsay, ‘sq,

William Roberts, Esq., .
G. A. Fraser, Esq.,. .
Rev. R. Chato,

Gaearn, Hsin. os. 7h.

Dean of Kildare, .

J. §S. Hiffe, Esq., .

W. Gregory, Esq.,
Ditto; 2 Ges

E. J. Cooper, Esq ,
Ditto, . 4

_ M. Mac Master, Esq-,

A. Jacob, M. D.

O. Sproule, Esq. ;

J. Hart, M.D., :
Ditto, oa 5

Thomas Stack, Esq.,

G. A. Kennedy, Esq.,

Abraham Abell, Esq.,
Ditto, . }

B. J. Chapman, Esq,,

Wrskeid, -. \.

Wyndham Goold, Esq:, 5

Charles Vignoles, Esq., .

R. Graves, M.D, . .

Ixxxvill

t»
—

NNO NYNYNNNNNNTNNNNNNNYNNNYNYNNNYNNNYYNNNNNNNNYNYNNNYNNNNYY-
SSeSoSoOoOSCOSoO OSC O OOOO OCC COO OSC OS OOo OSCOSoOSoOOOSOSoOSoOSOSoSOSOF

302 8 0

bet,
wo
Ot
oy)
— oH
(Se)
aos

1396 13 8

Praeget Sy ward,

F. Churchill, M. D.,
D. Moore, Esq.,-. .
R. A. Wallace, Esq.,
W. B. Wallace, Esq.,
P. D. Hardy, Esq.,

G. A. Hamilton, Esq., M.P.,

R. W. Smith, Esq., .

Sir Matthew Barrington, Bait,

Very Rev. Dean ae
Ditto, .
Ditto, -

James Pim, Jun., Esq, Behe

William Stokes, M. Ds
George Cash, Esq., :
E. J. Clarke, Esq.,
J. Burrowes, Esq.,
Captain H. James, :
Sir M. Chapman, Bart.,
Sir Robert Kane, M. D.,
C. T. Webber, Esq,
Rev. R. Butler, :
James O’Grady, M. D.,
Ditto, tits ‘i
William Hill, Esq., .
J. Nelson, Esq. 4“

Ixxxix

. 1844,

. 1845,

. 1846,
. 1845,

Total Amount of A Annual Subser iptions,

Tue ToTaL CHARGE,

tt

NDNNNMNNNNMNNNYNNNNNNNNNNNNNNNW WH

nH

NWNNMONMNNNNNNNNYNNNNYNNNNNNYMNNNNO’

£ S70 d:
1396 13 8

354 18 0

1751 11 8

XC

THE DISCHARGE.

ANTIQUITIES PURCHASED.

Browne, small bronze sword, 3rd Jan. 1846,
Campbell, D., for a crystal ball, 2nd Apr.
1845,. .
Glennon, Richard, porpyhry | hammer, 21st
January, 1846, . : :
Kearney, Patrick, for gold bracelet,
Kerrigan, William, for silver pin and bracelet,
19th March, 1845,
M‘Cullagh, James, plated antique ornament,
16th December, 1844, . .
Ditto, brass kettle and spear head, 13th Feb.,
1846,. .
yer ocd, J ames, old Beal’ 6th May, 1844,
Wallace, prenney bronze me 21st Jan.,
1845,... .-
Wynne, H., antique aes ring! 18th Ne Ov.,
1845,. .
Total cae of Antiquities,

Booxs, PRINTING, AND STATIONERY.

Barthes and Co., duty and carriage on books,
19th J anuary, 1846,
Bennett, Francis, cleaning eopperplates, vi th
February, 1845,
Camden Society, ‘subscription for ithe year
1843_44, :
Curry, Eugene, deciphering “anita pies,
Ist July, 1845, 5
‘D’ Alton, John, on ‘Amal of Boyle pron Figs:
tory of Ireland, 24th May, 1845,. . .
Gall, ML H., printing, 23rd Decephen, 1844,
Hanlon, G. A., wood engtaving?, gitn Jan.
1845, -
Hodges and Smith, Pomagciene. “ik XX.
Petrie’s Round Towers, 6th August, 1845,
Jones, J. F., Books, &c., 4th August, 1845, .
Ditto, for Memoirs of Dr. O’Connor,
llth March, 1846, . .. .

3 10
0 10

0 15

fey)
oS
So (=) oo i=) f=) oo j=) i=)

2 16

—
fo)
i=) Len} So wo i) i) j=) oO

68 19 0

68 19 0

Xl

Brought forward,

- M‘Dowell, William, cleaning pied gaa to
January 26th, 1846, .

Marshall, A., Post Office Divestory, 13th
December, 1845, é

Mullen, George, bookbinding 13th Octobe,
to 7th February, 1845,

Perry, J. H., and Co., aaa 4

O'Shaughnessy, J.d., flanged prints, 7th Aug.
1845, . ;

Plunkett, James, Dee Qist. ened 1845,
to 10th January, 1846,

Ponsonby, E., ink, &c., 29th Geidbar. 1845,

Sharpe, Charles, Transactions, 31st January,
1846,. .-

Tallon, J pine ie un., Stationery 19th May,
1845,. . =

bncieryood, J. H, Eaieon’s History Le Kil-
mainham, 12th "December, 1845, .

Wiseheart, red ink and paper, 3rd May, 1845,

Webb, Thomas, cartridge paper, 26th May,
1845,

Trish MANUSCRIPTS PURCHASED.

Baggot, B. W., Irish MS., 6th Dec. 1845,
Total of Trish MS., :

Coats, CANDLES, &c.

Allen, William, oil, &c., 20th March, 1846,

Alliance Gas Co., gas to 31st Dec. 1845,

Ditto, far coke and ete Oct.
13th, 1845,

Edmundson, ae and Gos oil, 13th June, 1846,

Hoey, C., 2 tons coal, and ee 31st Jan.
1846, .°

Kiernan, James, Sond Dogwood, 22nd Nar
1845, -- (:

Piele, Thomas, 1 bon Conk ane carriage, 3rd
July, 1845, «. + F

Wilson, T. P., 15 tons cou aad ee

Total Amount Coals, &e., . :

£
711

17

34

Qe tis}

Total Baek Berne pad Stationery, aso

6

0

13

—

18

12

=
Oo
oo i=) So Om Ore

—
om

|

112 Vins

38 17 10

"886 14-5

XCll

Brought forward, . .«

CONTINGENCIES.

Carriage of parcels from Athlone, 3rd May,
RS othe REMAN bow, aan cece eee

Ditto, from Liverpool, 16th May,
1845, .

Ww. Hamilton, carriage of parcels 29th. April
1845,. .

Steam Bhe aeh ak a a 30th May, 1845,

Freight of books from London, 8th mat:
1845, .

Fannin and Co. freight of a parcel “4th Die!
1845, .- .

Freight of pereels from London, 12th Mar ch,
1845, : wate

Clifford and Co., som Ape 4th, 1845,

Ditto, varnish, ditto,

Clibborn, E., carriage of antiquities,

Boyle and Co., ins Boone’s draft in
London, . c Bonen

Maguire for ae 9th May, . :

Rooke, C., for 98 3d. stamps,

Postage and postage stamps, -

Maguire for twine, . .

Clibborn, E., sundries for Shrine eae ane
16th January, 1846,. it pt

Total Contingencies,

Repairs oF Houses, &c.

Barrington, F., repairing stove, 3rd February,
1846, . ,

Brown, John, cleaning de, 28th cine
1846,. .

Ditto, painting ditto, 2st J uly, 1845,

Ditto, glazing ditto, 4th December, 1845,

Ditto, varnishing the hall-door, 12th Dec.,
1845, .

Ditto, painting taitenn: on ‘roof of librar y
24th December, 1845, . .

Ditto, sundry painting, 18th Feb., 1845,

Ditto, cleaning windows, 21st Jan., 1846,

Murphy, J., sweeping chimneys, 4th March,
MEAG) 6 ah es. fk 5 EI Re

ne oe. a ae

—
j=)

CONF OS ooOoF

— —
SOW bw nr nr bo bb ay —_

—
eT Re

(=)

—
o>. ©

SOS CORSwW BAN © HM CO

@

nr [op) oon i=) woo

£5" 182) dd.
886 14 5
Life bene asad

904 17 6

X¢cll

BSA ae
Brought forward, . 2112 5
Murphy, J., sweeping chimneys, 18th Oct.

1845,.. . by de -6
Malone, J ohn, cleaning ashpit, ‘27th Jan. 1846, 0 4 0
Rounds, Brother s, painting museum, &c., 13 15 6
Walsh, J., for Academy’s ss cial of cost

ofpump in yard, . . 010 0

Total Repairs of House, &e.,
Furniture Repairs, &c.
Boylan, P., satin paper, May 22nd, 1845, 0 4 0
Casey, P., ae et &e., Novem. 15th,
1845, . ae : 2a 6
les: “d.
Duffy, John, glass case, . . . - 14 0 0
Cash advanced for materials, as in
Peeudite i) st tty oe 6 OO
ate sae Aeensy OpFG
Edmundson and Co., fitting up gas, 14th ari

1845, . 8 8 3
Ditto, fndicviicke ey ie Bhs 3.5 8
Malone, P., shaking carpets, 22nd Oct. 1845, 0 3 6
Perry, James and Co., coal scuttle, 14th June,

1845,. . 312 0
Pim, Brovhers: ian Cs eres foe "8th Nov.

| Y'5) See ae 1 18 11
Porter, D, earthenware, 12th April, 1845, 0 2 0
Ditto, ditto, 13th April, 1845, Ont 9
Sibthorpe and Son, glazing oe &e., 4th

August, 1845, . . Le ong
Sparks, R. W., ‘table cover, bei, "14th April

1845, : i Ray

Total Furniture Repairs, &e. .
Rent, TAXES, AND INSURANCE.
Symes, A., half year’s rent of house, sine

Ist August, 1845, ; OA) ek
Ditto, ditto, Te Feb. 1846, 52 4 6
Taxes, ministers’ Poe one year, 15th Oct.

1845, . 215 5
Ditto, pipe water, one year, ending 24th J une,

1845, Shad ; 110 0
Ditto, for watering streets, one year, 09 2

Fe Cee ae

£18k de
904 17 6

ay Da

118 10 11

1060 17 10

xclV

Brought forward, . .
Boyle, Low, Pim, and Co., proportion of poor
rate on stable for 1843, 1844, 1845,.
Globe office, one year’s mies 2 tie 26th
December, 1845, . . .
National office, one year’s insurance, ending
26th December, 1845, wid
Ditto, ditto, pada nonele eee cette!
Total Amount of Rent, Taxes, and Insurance,

SaLaRies, SERVANTS’ WAGES, &e.

Clibborn, Edward, half be & s palery, due 16th
June, 1845,. .

Ditto, ditto, ‘due 16th
December, 1845, Be yay:

Ditto, quarter oa dino, due
16th March, 1846, :

Ball, Robert, Esq., Treasurer, one year, due

16th March, 1846,

ES
109

Kane, Sir Robert, Secretary to Council, due |

16th March, 1846,

Mac Cullagh, James, LL.D., Secretary to ‘the
Academy, due 16th March, 1846, -

Drummond, Rev. W. H., D.D., Librarian, due
16th March, 1846, .

Curry, A. , attending meetings, &e., 23rd J une,
1845,. .

Ditto, coe 14th J uly, 1944, to 16th

- March, 1845,

Halahan, G., medicine for porter, 2 22nd Dect
1845,

enailton, William porter, wages, 16th March
to 16th June, 13 weeks,

Ditto, 16th a une ao
27th December, 28 weeks, .

Ditto, allowance to hime
self and wife at Christmas, .

Ditto, wages, fram 27th
Dec. to 16th March, 1846, 11 weeks, .
‘Kenny, Thomas, pike nding as hall porter,
during the porter’s sickness, two weeks,
Kane, B., and daughter, attending meetings,
Magill, John, gical 20. a 14 2 days,

@l56, . <3

315

Se

3

iu eee

d. Be she od:
7 {1060 17 10

1186 4 0 |

XCV

Brought forward, . . 315 2 7 j|1186 4 0
Sloane, H. C., attending fone 7th April
to 26th May, We45a ey: 1D ae 6
Plunkett, J., cleaning and arranging museum, 2 12 Of]
Smith, J ohn, delivering notes, &e., 19th April
to 4th August, 1845, . 0 13.76

Todhunter, Isaac, making up eee eo
22nd March, 1845, to 16th March, 1846,
51 weeks @ 20s. . ae 51 0 O .

-Total Salaries, Servants? Wages, ces ————| StU a

Toran DiscHakGR, . . . . «|. =: « - £1556 14 7
Balance in favour of the Babich sain ee serene 194 17 I
1751 11 8

STATE OF THE BALANCE.

pay ere 2

In Bank of Ireland, .. . athe cope eo he Dee 1
In Treasurer’s hands, as per Account, TE es NS:
BS A a Ge |

The Treasurer reports, that there is to the credit of the Academy in
the Bank of Ireland, £867 ls. 10d. in Three per Cent. Consols, and
£1643 19s.-6d. in Three and a quarter per Cent. Government Stock, the
latter known as the Cunningham Fund.

(Signed, ) Rosert Bat,
Treasurer:
3lst March, 1846:

No. IX.

METEOROLOGICAL JOURNAL,
Ist JANUARY, 1846, anp enpDING 31st DECEMBER, 1846,

GEORGE YEATES.

THE instruments employed, and the general circumstances
of the mode of observing, have been described in the prelimi-
nary observations to the Tables of the year 1843, in the 2nd
volume of the Proceedings of the Academy, Appendix V.

VOL. III. h

XCVUL

‘gs Aq a | 080° | 01°66 1g “mM 'S 800° | 092°6¢ | 6F | 98 | Te
a *S G00" | 066°6G 0g “MS 200° |.029°66 | ap | LS | 08
“HN 020° | 0¢0°08 62 “nm AqdsM | 002° | 066°6c | OF | OS | 66
"MN Z00° | 049°6z 86 ‘MS ¥S0° | OFS°Gs | AF | £9 | 82 “MS O91" | OST°6s | IF | IS | 8Z

“A OOL’ | 084°66 LG ‘s OF0" | OGP'6S | OF | 49 | LZ “M'S 0g0° | 00S"Gs | SF | GS | 46

“wm Aq *N | OST’ | 06°66 96 ‘a's G10" | O8F'6@ | GF | FS | 92 ‘M'S 020° | 068'8c | 4h | $8 | 92
“MS 001" | 061°63 c@ || “SAq°M | SHO" | 0Gb'6z | Lh | 9S | Sz "mM ‘Ss 08%" | 066°8¢ | SP | &S | SZ

*s Aq “M |} O10" | 061°6Z ¥G ‘aS 00Z° | O€1°6S | SF | 6S | FZ “M OO" | OOF'GS | 1% | 49 | FG

*s Aq -M | 800° | 086°8@ GS "MS 800° | 049°6% | GF | 9S | gz ‘a's 080° | 000°6G | 1F | IS | 8%

“gs Aq *M | GhS" | 086°8Z GS “MS 090° | O2r'6a | Lh | 8S | Go “M 00g" | 002°8a | gh | IS | 62
“"M'S COI" | 060°62 1 "mM 'S “* * | 098°6G | SF | S¢ | Iz a cio" | OFl'Gs | se | 4h | 16
“a ON “+ | 089°6S 06 “a “++ | 066°6G | 68 | LF | 06 "M 00s° | 060°6G | 6g | IS | 02

Ss 020° | OLS°Sz 61 *M "+ | 016°6 | OF | 9F | 6I ac OFs’ | 082°8a | 98 | 4V | GI
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January....

Kebruanyn 2)-0.

September. . .
October...
November. . .

December...

ee ee | ee

3

No. X.

ABSTRACT

OF

THE ACCOUNTS OF THE ACADEMY,

FOR

THE YEAR ENDING 3lst or MARCH, 1847.

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‘AWIGVOYV HSIY] TVAOY GHL 1O SLNQNOOOW AHL 40 LOVaLsay

ACCOUNT

OF THE

ROYAL IRISH ACADEMY,

FROM 1st APRIL, 1846, TO 31st MARCH, 1847.

THE CHARGE.

To balance in favour of the Public on 3lst |
March, 1846, . .
Parliamentary Grant Se 1846, (poid 18th |
August, 1846), ‘
Quarterly Warrants from Treasury,
Total from Treasury,

INTEREST ON STOCK :

Half year’s on £1643 19 6, 34 per Cents. |

DOREO; 2s 867 1 10, 3° ee
Ditto, 4; 1643 19-63) -;,
Ditto, i 867 1 10,3 oA

Total Interest on Stock,

TRANSACTIONS AND PROCEEDINGS SOLD:
Transactions, Proceedings, and a s
Memoirs, sold here, . . .
Transactions and Proceedings sold i in Lon-
don, by Messrs. Boone, £14 12s. less
Commission, £1 9s.,
Total amount ee Books sold, -

Rent oF STABLE, to Ist November, 1846,
£21, less Poor-rate, 10s. 11d.

Lire Compositions:
William Lloyd, M. D., .
Charles Haliday, Esq., .
Rey. William Reeves,

Forward,
VOL. Ill. ; 1

|

£3: at0s
300 0 0!
14617 8
26.14 3
13.01 th
26 14 3
13-051
12 18 0
130 Sh
Dest Oe 0
21.0% 0
21 0.0
63 0 0°

446 17

79 8

.26 1

20 9

evi

Brought forward,
Rey. Henry Tibbs (non-resident),
J. O. Curran, M. B.,

Total Life Compositions,

ENTRANCE FEES:
J. C. Deane, Esq.,
John Alcorn, Esq., .
P. Bevan, M.D.,. .
M. H. Stapleton, M. B.,
J. B. Kennedy, Esq.,
J. O. Curran, M.B., .
Abraham W. Baker, Esq.,
George Lefroy, Esq.,
John Aldridge, M. D.,
T. P. Boyd, Esq.,
Rev. R. M‘Ghee, .
J. T. Beasly, Esq.,
John Tyrrell, Esq., .
Charles Haliday, Esq.,. .
Charles P. M‘Donnell, Esq.,
F. J. Sidney, Esq., :
W. N. Hancock, Esq.,
William Brooke, Esq., .
Rev. W. Reeves, . :
D. J. Corrigan, M. D.,
J. K. Ingram, Esq... .-
Leonard Dobbin, Esq., .
Right Hon. Justice Perrin,
Rey. H. Tibbs, .
Hon. and Rev. W. Wingfield, .
M. P. Darcy, Esq.,

Total Berane Fees, 7

ANNUAL SUBSCRIPTIONS:
Charles Hanlon, Esq., -
W. M. O’Grady, M. D.,
R. Adams, Esq., .

A. Cane, Esq.,

C. W. Hamilton, Esq., -
Rev. Dr. West, :
William Hogan, A. M.,
Algernon Preston, Esq.,
John Hamilton, Esq.,

J. S. Cooper, Esq.,

F. W. Barton, Esq.,

Forward,

Or Gr Or Gr Ov Or Oe Oa Oe Ou OH St OH GU UO UT OH OT OH.

NONNMNYNNHNNNN WW

1)
5°)

Oe Oe OOO OU TU OUT OU

NNNMNNNNN Nb Yo

iw)

136 10 O

1003 18 6

G. Fitzgibbon, Esq., .
Rev. J. G. Abeltshauser,
William Edington, Esq.,
F. W. Conway, Esq.,

evil

Brought forward,

Most Rev. Archbishop of D Dublin,

Sir Lucius O’Brien, Bart.,
Thomas Cather, Esq.,

Alexander Ferrier, Jun., Esq.,

William M‘Dougall, Esq.,
Aquilla Smith, M. =
John Mollan, M. D.,

Rev. J. Wills, . :

J. Huband Smith, Esq.,
Sir John K. James, Bart.,
C. C. King, Esq.,
Thomas Beatty, M. D.,
Henry Clare, Esq.,

R. Tighe, Esq., .
Hon. F. Ponsonby,
William Murray, Esq.,
William Longfield, Esq.,
G. D. La Touche, Esq.,
James M‘Donnell, Esq.,
Charles Bournes, Esq., .
E. J. Cooper, Esq.,_.
Alexander Taylor, Esq.,
J. F. Waller, Esq.,

G. J. Allman, M. D.,
Philip Reade, Esq., .
Edward Hutton, Esq., .
G. Yates, Esq., . .
Rev. H. F. Logan, D. De

W. S. O’Brien, Esq., M-P.,

Edward Bewley, M. D.,
Rev. W. Lee, . ;
Right Hon. Chief Baten,
J. Davidson, Jun., Esq.,
- Rev. C. Porter,

_ Sir M. Barrington, Bart,
J. Magee, Esq., :
M. O. R. Deane, Esq, - :
N. P. O’Gorman, Esq., -.
H. C, Beauchamp, M. D.,
James Pim, Jun., Esq.,
William Stokes, M.D.,

Forward,

12

"1846,

bo
WLIW MN NNNYU NUN NUNN NNN NY NNNNNNUNUNNHNNNYNYNNUNNUNNMNINNe

i

—
—
~J
_
bo

WONWNNNYNNNNNNNNPNNNNPNNNNNNNNNNNNNNNNNNNNNNNNNNHNNYNYGD

ocoocoocoocok

o| CcCococooCooCoCoCCCeoSoOSoCSCOSeoSSOSCSCSCSCSCSOSOSSOSCOSCSCSCSCSCSOSSSoSo

£ my “ak
1003 18 6

1003 18 6

Brought forward,

James Talbot, Esq., .
William Blacker, Esq.,
George Carr, Esq.,

D. P. Starkey, Esq.,
G. A. Frazer, Esq., .

R. W. Townsend, Esq.,

Rev. F. Crawford,
Hon. James King,

R. Cully, Esq.,

Rev. J. Galbraith,
H. G. Hughes, Esq.,
W. E. Hudson, Esq.,

Francis L’Estrange, Esq., .

Rev. George Longfield,

William Roberts, Esq., .

W. T. Kent, Esq.,
Ditto ae

M. Longfield, LL. D.,

J. Osborne, M. D.,

J. Hart, M. D.,

M. R. Sausse, Esq., .

Samson Carter, Esq.,

T. F. Kelly, Esq.,

Hon. Judge Crampton,

W. T. Mulvany, Esq.,

T. N. Redington, Esq., .

Lord Farnham,

Benjamin Wilme, Esq., :

W. C. Dobbs, Esq., .
James Claridge, Esq.,
James Jameson, Esq.,
J. S. Eiffe, Esq., .
James Apjohn, M. D.,
Robert Mallett, Esq..
Capt. Sterling,

Rev. Samuel Haughton,
William Lefanu, Esq., .

J. Neilson, Esq.,

W. Monsell, Esq,.,
John Phillips, Esq., .
F. M. Jennings, Esq.,
T. Oldham, Esq.,
Lord Wallscourt,

Durham Dunlop, Esq.,

John Finlay, Esq.,
Forward,

evil

“1846,

117 12

WNW HNNDNNNNNNNYNYNNNNNNNNNNNNNYNNNHNNNYNHNNNNNNYNNWNYNNNNY
WWW NNNYNMUNNNNNNNYNNYNNNNWNNNNNNNNNNNNNYNNNYNNYNNNNNNYNW

|

212 2 0

Be Gn
1003 18 6

1003 18 6

cix

Brought ie ward,

Forward,

bo

Rev. N. J. Halpin, ©. . . 1846,
Walliant Tienns Bsqs <= <el.. .. <,,
Walliam’ Andrews, Esq... 2... -. -. %s
James 8. Close, Esq, . 1. 2. - 155
Revere wellekin Bae. ae! ots 555
Sir R. Morrison, . nD MAME ais, tcthcgss
Charles Doyne, Esq, . . . . . 1845,
Ditto, . . Spel i412 S46,
Sir Edward Borough, Bane 9 Be 4
Hon. and Very Rev. H. Pakenhann
Dean of St. Patrick’s, .°. . . 1845,
Ditton Aes. bet 846,
We sloydyaq., Be Fo) Pees,
Pero. tis lake; MSG GE! at) a th) obs
Robert Law, Esq., 5 Be Soest tea otc
John M‘Mullen, mee eee aeBSHS,
Ditto 2 eh ed eae URA GL
Reeomon, Hsq:, eS) a TF ae ot,
DaOMriscolly Msg, V2 cil .2 =,
Abraham Palmer, Esq., . . . .. 1845,
Ditto,. . Sieh. lis4o%
Sir Thomas Staples, Bart. 4 ar eater
RG. Walker; Hsg.,. ©. 202s + oy
Sir William Betham, . .. .. 5
EE doy, Psd. S.—- .j IE. +. ge
ReepomreirpetBISG.s 0c) sae ee re Hb
Arthur Jacob; M.D, . J. .f) 263;
W. Grimshaw, Esq, -- 2000 5,
O. Sproule, Esq., SWRI ior Unt anae Aa
See Nelican.) MEDS.) oj snnarh- she
JohmeAnster WIAD. «| 2) 46 payer So
E. 8. Clarke, M. D., ; phe eet ee
Rev. Edward Marke D. De 5 Mapas ieee
Week. Wildeslisg., 10.) We et
Wavy, sti, etait =) ee te ts ay
ie Smiiubee snes: al Ns A,
GAs Kenedy, MW oe ee ne ay
- Rev. James Reid, i ee a a
Robert werd. Men) See WG a OS
VohmTolekent ava De 9) so) 1 3
Francis Barker, M.D., . . . . .1845,
DBL, ke 00-8 21846;
Jee vans s> he aioe oP OS,
ihomas Grubbs (sq. 9s 69 3. 9 G5
Edward Getty, Esq, . - . - + »

EGS SA Os eres s. ad.
12 2 0/1003 18 6
2° N28

Naa)

RE DEAD

Qive2 AO

De AD. tO

2) a2 OM)

2°20

2402-70

ZF E20

WNNNNMNNNNNNNNNWNNNNNNNMNNNNNNNNHNNYNW LH
WNONNNNNNNNNNNYNNNYNNNNNYNNNNNMNYMNNNYNNNWNW
SCecooceocooooocoocoooooosoooocooooooooeooeeco®

2
2
2 |

304 10 0 1003 18 6

cx

Se |G. a| come Sanacr
Brought forward, . . | 304 10 0 |1003 18 6

Samuel Ferguson, Esq., - . . 1845, 2 2 0

Ditto Ae S50 . 1846, 2:2 30
William Barker, M.B., deat 2 2 0
AEE. DPArey,) Bagh. 6. 3) Re BA 2 2 0
James Patten, M.D, . . . . .1846, 22 0
RR. Madden, M.D, 2. 2 on 184%, 2 2 0
Rod. Graves, MOD. . Shel 1846) 22 30
George Yates, Esq.) . Mw! . 21847, Di 2 Oa
Very Rev. James Gregory, Dean of

Kaldare, “ge. of 3 aa 2 2 0
George Cash, Esq. oH ach ames hea 22 0
John Burrowes, Hsq.; . 2... 1847, 22 0
Charles Vignoles, Esq., I 2212560 :
Charles Hanlon, Esq, . . . . a 2, 2NaL0
Aquila Sunidhi Ds ie ae, 2 2 0
Very Rev. Henry Cotton, Dean of
Cashel, Bat SEEN sc Wines Aaa 2 2.0

Wyndham Goold, Esq., are 2 -2 0
George Wilkinson, Esq., . 1846, 2 2-0

Ditto ay We aA uh 21947 a ane
Rey. Thomas Stack, . . . . .1846, 2 2 0

Ditto, Se ee tls Repel SAT 2 2
Henry L. Lindsey, Esq., . . . .1846, 2 2 0
P. D. Hardy, Esq., Rae came 2 2 0

Ditto, . a . 1847, 2° 220
James Pim, Jun., Esq, - . . . 4, 2 2 0
William Smith O’Brien, Esq., M.P., ,, 2° 2 0

Total amount of Annual Subscriptions, |-—-———_ 357 0 0

List or SuBscRIPTIONS FOR THE PURCHASE
OF THE “DomnacH AirGiID” IrisH Ma-
NUSCRIPT :

C. P. Croker, M.D. .
J. Mac Cullagh, LL. D.,
Thomas J ennings, Esq.,
F. M. Jennings, Esq.,

G. W. Hemans, Esq.,
Rev. H. Lloyd, D. D.,
John Burrowes, Esq.,
William Hill, Esq., . . .
Arthur R. Nugent, Esq.,
Hon. Judge Crampton,
Rev. Chas. Strong,

Hon. G. S. Gough,

bo
—

bo
bet ed et ee

—
ecooocoocooco

Pommard, 2) See O 0 T3600 1RiE

cXi

Brought forward,
Thomas Fortescue, Esq., :
Lord Wallscourt,

Alexander Ferrier, Esq. = i un.

J. R. Corballis, Esq., .
Alexander Parker, Esq.,

Aquilla Smith, M. D., -

His Grace the Duke of Leinster,
Marquis of Kildare, .

Right Hon. H. Tenorchere: M. P.,
Robert Forster, Esq., :
Miss Edgeworth, .

C.K. Tenison, Esq.,

Very Rev. Henry Cotton, Dean of Cashel, :

Rev. James Wilson, D. D.,
Rev. S. Butcher,

Bindon Blood, Esq.,

T. N. Redington, Esq... «
Rev. W. H. Drummond, D. Dp.
R. Franks, Esq., .

Rey. T. R. Robinson, D. ay,
A. B. Hope, Esq., M: P.,
Karl of Leitrim,

James Talbot, Esq., .
William Lloyd, Esq.,
William Stokes, M. D.,

J. Davidson, Jun., Esq.,

G. J. Allein, M. De baie.
Captain T. A. Larcom, R.E.,
Bishop of Chichester,
Bishop of St. David’s,
Robert Tighe, Esq.,

W. Sweetman, Esq.,
Charles Bournes, Esq., .
Henry Courtney, Esq., .
John Wynne, Esq., .

J. O’Ferrall, M.D., .

N. P. O’Gorman, Esq., .

_ W. R. Wilde, Esq., .
Wyndham Goold, Esq.,

M. M. O’Grady, M. D.,
Charles Vignoles, Esq.,

M. P. D’Arcy, Esq.,

Jacob Owen, Esq.,

Charles Hanlon, Esq., . .
Col. Harry D. Jones, R. E.,

Forward,

t

Or
(2

Ne ee eS, eS) MO. OS ee Ot a SC em Bo) Ol te)

———

—

—

—
Sooocooc oOo Oooocoooocomooeocoonmnoooocooco°oceo 6s 3] oe HSH" S o

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SOE Sey ne SOS SASS ayaa evo) =) (SSeS) S) SS SSP SSS) SSNS SS) SSN 5

(=)

BS a Ys
1360 18 6

exil

Brought s bitalg

G. A. Grierson, Esq.,
E. J. Cooper, Esq.,
Haliday Bruce, Esq. .
Conyngham Ellis, Esq.,
A. B. Cane, Esq., ..
Sir W. R. Hamilton, le. D.
Rey. Charles Mayne,
W. E. Hudson, Esq.,
Thomas Cather, Esq., Pel abe hal)
Wallianr Ioefamu, Esq... 3 |
A. Whyte Baker, Esq., aie
Rev. Charles Graves, A.M., .
J. R. Da by B, Clibborn, Esq.
Rey. J. H. Todd, D. D.,
Sir John M‘Neill, :
Sir Thomas Benoa, Bart., M. P.,

Total Amount of Subscriptions,

bee
—_ nn
-onn?

—

—
NNO NO Oa
eaooocoorococeoqooooo?

212 10 O

1573 8 6

Re | scooscccosooccccec®

Tue ToTaL CHARGE,

CX1il

THE DISCHARGE.

ANTIQUITIES PURCHASED, ETC. |; £ 8 d@| £ soa.
Brown, Robert, sePaaTINS, copper ee
26th May, 1846, 0 4 0;
Chambers, H., copper coins, , 20th June, 1846, Oct 0
Donegan, John, a ornament, 11th ae |
1847, carte : 2% Oy; 0 |
Ditto, gold caecis 29th. January, 1847, cate 2 0 0
Baniskillen, Earl a erozier, . . 1 5 6
Gore, Francis, old glass bottle, 1st May, 1846, 0 2 6
Griffith, Wm., antique Be ornament, 29th
January, 1847, . . 215 0O
Kennan, Wm., for repairing antiquities, 26th |
June, 1846, : : Ste 0 4 2
Keegan, enecles, antique glass ale Ist
February, 1847, . . O. i OH
Leary, Nicholas, coin and pike-head, 2nd No- | |
vember, 1846, cee Re 0 5 0
M‘Donagh, B., Cork, for repairing antiques,
27th June, 1846, : 0 2 6)
Rice, Paul, antique bronze ‘sword, 19th Feb., : |
OE <i} hm kOe Os
Scanlan, John, ancient spear-head, 20th June, |
1846, lige 010 0|
Strickland, Thos. gold bracelet, 8th Feb.. 1847, Qe gi
Underwood, ames two iron poopie 6th
April, 1846, . : Len Over 8
Wright, Antony, encaustic tiles, Aug. 9, 1846, 115 0|
Total amount of Antiquities, ——/ 92:10 8
|
Books, PRINTING, AND STATIONERY, Ec. |
Bellew, G., Stationery, 3rd December, 1846, 0 2 2
Brown, J., initial wafers, 29th July, 1846, OPO!
Camden mone subscription to Ist wa |
-1845, es, ae (eae GI
Du Noyer, G. wa drawings, 19th
August, 1846, . . ney be eon ONO
Ditto, do. 8th
December, 1846, . .... 111 6
Ditto, do. 9th
February, V8470 . 8.2. V4. Loo
ee plese

LOT UCOT ON gg ck et et os HPL E 4. 8b) 22 10> 8

CX1V

Brought forward,
Edwards, Geo., manuscript copy
of forfeited estates, 2 ee is econ. nec)
Ditto, for collating the
above and index, . - 310 0
Ditto, Tedwich’s Uae
quities, . . : rain! Gl)

Ferrier and Co., ink, 15th June, |
USA, ne, sielh ei Re i wer es, eet ee A ea
Ditto, do, 4th July, 1846,.. 0 1° 9)

Geological Society, for wood-cuts, 10th fee

1846, . . :
Gill, M. H., petty printing, to

20th March, 1846, teal eon Aueag
Ditto, on account of print-

ing Transactions and Proceed-

ings, 23rd December, 1846, . 200 0 0
Hanlon, G., wood-cuts, 15th Dec., 1846,
Hodges and Smith, books, to 31st

December, 1845, . . . . .£43 6 6
Ditto, do, . 31st
December, 1846, . . . . . 35 5 2

Jones, blank account books, 26th ay ae
1846, . . .
M‘Dowell, George, copper rplate en-
graving, 11th August, 1846, . £15 19 6
Ditto, do., 22nd February, 1847, 8 8 0

Marshall, A., Directory, 4th Januar y, 1847,
Millard, Thomas, wood-cuts, 7th August,
1846, .. 5 i
Mullen, George, aookbindine) to
29nd May, 1845, 4 es peb18 (6 19
Ditto, do., to 31st Deeemcen 1846, 32 4 9
Ditto, do, to 4th March, 1847, . 27 12 0
O'Shaughnessy, J. J., copperplate a)
printing, 24th August, 1846, .£24 5 0)
Ditto, for Be paper, 22nd May, |
1846, Ogle 4)
Ditto, pearl 27th J nae 1846, 0 2 6

Forward,

Rear)
i 2

29 11

78: Ul

78 3

22 10 8

CXV

Brought forward,
Oriental Translation Fund for

MONS oy sis Ss ee OP LO™, 65
Ditto, for 1846, 1010 0}
Ditto, for 1847, 1010 0
O’Neill and Duggan, wafers, 30th

July, 1846, . . £0 3 0)
Ditto, Bleak iasoka,

19th February, 1847, . . oe
O’Reilly, John, books, 21st De-

cember, 1846, . . £0 16 0
Ditto, ditto, 27th Fe-

bruary, 1847, . . . . OL15).:0),
Plunket, J., drawings, 25th April,

1846, CaP 3 gre * ies, b Pen sunnier 0 NE
Ditto, do., 17th May, 1846, 1 0
Ditto, dog Ist AGe., do. ..; 3 10
Ditto, do., 13th Nov., do. . 3 1
Ditto, do., 17th Oct., do. . 4 8
Ditto, do., 13th Feb., 1847, 17 0

Porter, Jos., books, 26th February, 1847,
Rathborne, J. and H., wafers, &c., 8th Decem-
ber, 1846, eats Pit at
Ray Society, subscription for 1845, :
Robertson, John, book, 6th August, 1846.
Sharpe, for books, lst October, 1846,
Taylor, R. and J. E., Scientific Memoirs. j
Talon, J., envelopes, &c., 21st Dec., 1846, .

Wiseheart, J., red ne &c., 14th poe

Osis mers
Total Books, Printing, &e.,
Coats, Gas, &c.

Alliance Gas Company, gas to 3lst Decem-
ber, 1846, Z

eadndsen, J. and Co., a (on 10th January, |

1846,

Hoey, Charles, for 31 ae cone! fengh carriage,

to 5th March, 1847, :
Total amount Woals; one

Forward, .

31 10 O

AGTHaSCoD oo

i=)
bo
bo

591 14 11

cxvi

Brought forward,

Repairs OF HOUSE.

Brown, John, glass, 24th July,

1846, . . . putne £0 4 6
Ditto, cleaning yn oT
to 2nd June, 1846, . ... 3 0 0

Casey, Paul, Hanne’ grates, &e., 17th Octo-
ber, 1846, . .

Malone, P., cleaning carpets, 30th | @etobed!
1846, :

Muapy J., sweeping "chimneys, 12th March,
1847, . .

Roberton, J., sweeping chimneys, 31st March;
1846, . .

Sibthorpe, H., acl Son, glazing, 11th Nowedt!
ber, 1846, ;

Surman, George, Guepenten® work, 12th Feb.,
1846, ; :

Total Repairs of House,

FURNITURE AND REPAIRS.

Brown, John, painting, 27th January, 1846, si

aemmndenn! J.,and Gas gas-fittings, ditto,
Nannetti, G., ornamental er ae 31st Octo-
ber, 1845, :
Surman, George, repairs of ‘sundries, 15th
April, 1844, : :
Total Furniture and Repairs,

Rent, TAxeEs, AND INSURANCE.

National Insurance Company, insurance, to

25th December, 1847, . . a

Globe Insurance aoa do., to 25th De-
cember, 1847,

39

9
5

Rent of house, one year, fo ist Reh: "1847, | 104

Ministers’ Money, to 29th September, 1846,

Pipe Water Tax, to 24th June, 1846, 4
Total Rent, Taxes, and Macnee

Forward,

SCA Ss

NASM: SO

Eis. a.
666 4 4

50 3 10:

13 4 4
124 13 1

CXVIi

Brought forward,

SaLARiEs, Wacgss, &c.

Ball, Robert, Treasurer, one year, to 16th |

March, 1847,

@libborn, E., one year, A 16th Mawel, 1847, |

Curry, A. sundry attendances, to 26th “March,
1847,

pieamaad. 2 Rev. WwW. He D. Ds, ee

16th March, 1847,

Graves, Rev. Charles, A. M., Secretary ae

Council, 18th March, 1847,
Hamilton, William, Hall Porter,

to 13th March, 1847, .....£34 4 8
Ditto, Christmas allowance, do. . 2 2 O

Lockhart, J., suit of livery for Hall Porter,
26th March, 1846, -

Magill, John, M Messenger, to 12th Sep, 1846, |
O’Brien, Thomas, do., to 27th March, 1847, ..|

Todd, Rev. J. H., D. D., Secretary of Aca- |

demy, 16th March, 1847,

Singleton, John, hat for Hall Porters 26th |

March, 1847,

Todhunter, Tease, Mecountnt, Ge 27th Marck |

1847,
Woodhouse, John, for dees buttons 26th
March, 1847, : ;
Total Salaries, Wises, Gee ;

CONTINGENCIES.

Bannin, William, rings for es 6th Feb.,
1847, -

Barthes ead Lowell, duty. ame as arges on Rooks
9th July, 1846, ;

Boone, T. and W., duty and. charses) on Sores,

Box, W. R. , gutta percha, 9th July, 1847,

Boyle, ene Pim, and Co., commission for re-
ceiving dividends on Stock, .

Clibborn, Edward, allowance for
cleaning house, ue oe J uly,
1846, Bute £5

Ditto, do. , to 16th J anuary, "1847, 5

Ditto, in, to 16th J. anes 1846,

pried 1 in last account, 5

Forward,

!

EOC. Le Sa
Li Rae Saag
DeriOe0
150 0 0
5 5.0
Syi00 10
AsicOHcO
36 6 8
Ay yk
18 15 0
life wow
221 0 0}
015 O
48 0 0
116 6
eet BP B6G) 7. 2
0 5 8
013 0
2 8 6
0 8 6
0 5 2
iL
1 O00

19 0 10 1220 12 9

eCXVili

Brought forward, :
Clifford and Co., gum, &e., 9th July, 1846,
Curry, E., carriage of parcel from Sligo,
Daniel, P., brass eles &c., 27th Oct., 1847,
Donnelly, M., cleaning ash. pit, :
Gerty, E., conch hire of eae and Sep-
tember, RSAG | ahve
Hodges eal Sans, for nals 6th Marah 1847,
Johnson, T., gum, ce. " 3lst January, 1846,
Kennan, William, eee of keg of bog but-
_ ter, 31st July, 1846, 3
Leg, William, repairing cask, 5th August,
1846, .
Maguire, oe to “31st 7 aneey, 1846, A
Pamplin, for duty and charges on books, 12th
May, 1846, . .
Rigby, W. and J., ih: punches 2nd J anuary,
MOA ek =
Sharp, Re repairing elock, a 31st January,
1847, . .
Salmon and 4, one {stone plister ‘ee Paris,
17th October, 1846,
Stamp receipt for Treasury warrant,
Yates, George, for tin cases, &e., 27th June,
1846, - :
Freight and carriage of sundry packages fr from
Liverpool and London, &c., . :
Postages, and Post Office orders, .
Total Amount of Contingencies,

S Irish MANUSCRIPT.

Paid on account of the purchase of the “‘ Dom-’

nach Airgid,” .

Total Discharge, .
Balance in favour of ane Pablict

Total amount of Charge, .

£0 8 od eed.

19 0 10 /1220 12 9

0 810

0 2 0

0 5 9

0 3 0

318 0|

On. 53

02-7

0 2 6|

02 4}

016 3

1 2 6

0 5 0

28 6

0 1.0

0 5 0

1a Sg

a) Ging

13.18 5
eee 05) ee af
200 0 0
.£1470 16 4
. | 102 12 2
£1573 8 6

cCxix

STATE OF THE BALANCE.

ES el

Thay TBs, oc 2d G0 Ge ee age rs 6117 1
In Treasurer's hands, as per Account, 40 15 1
£102 12 2

The Treasurer reports that there is to the credit of the Academy in
the Bank of Ireland, £867 1s. 10d., in Three per Cent. Consols, and

£1643 19s. 6d., in Three and a quarter per Cent. Government Stock,
the latter known as the Conyngham Fund.

(Signed, ) RoBeRT Batt,
Treasurer.
3lst March, 1847.

CO

aaa ftatia
Kes aflster 4 ffm srectuad 3 ger pitirntes altetfameur Kaa
aymegas Mad copuad Proadimyy fag Ges Gey Cm ILL: LZ lory
bx ¢ Lubes hase bee apse ted, 3 bts hang ese Higher b> Seam
We hearths pilta3¢3 Liles LAM ohabux Une 1steP UH actis bing
Yager. pertnerthe a a ((lem y Mua ehonty, & altese, gat off-
pera 4 Tes ackhberrime 8 pebutpdstmne tovieey puemte Db biiny
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No. IV.

SYNOPSIS OF THE ACCOUNTS OF THE ROYAL

FROM MARCH 17, 1816, TO MARCI 31, 1846;
PREPARED FROM THE RETURNS AS CERTIFIED BY THE GOVERNMENT AUDITORS.

Printed by Order of Council, \Gth Irebruary, 1846,

TRISH ACADEMY,

Ponte scone

Sa ee Se ee “epage | atctere | MAGEE | RR iang, | atin. | EE Jenne |"Romie | em | Moat | Wiese | ePatt | MamE | em. | Aan | Gomis meine | nine [antes
es Es Tete oa|] oaks a. | Retiol | His Come- | Barer ||, Ancua [pee 88, tom Treaty Panlanent ‘Ault —— ae ae tock meolistiog | ae ances

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[ e00) “OW OM A oe sore | ss 34 | 7117 113) 11 19 13) 34 2 6] 32917 G} 28 8 9) 5SG17 G/-.... 16013 0} 350 0 o|/...... -.-| 79014 8] 184011 Of] 12 4 Gf 139210 9]......]-+--- OEE ERIE) CECE OTE se EO ANG CEO G0) ||.cecalloanecellauecer uO) ll AGaese 1016 11 94) 823 19 24

|| 20 9 6 vata | 226 s10 | 925 0 3.0 0/17 1 3] 4510 0] 3916 1] 3813 G 166 15 0} 325 0 0 | 6 823 19 23| 1541 18 04]/ 4 4 6] 9711 5}) 21 5 23).--.--| 21 19 10 ee 75 0! 214 G/ 213 6 Gk 19816 0] 41019 s|...... aes Ciascous SWNT: §3|/cebeee 1030 8 4/51 9 5

}3000 0 oO} ..... las 1 9 | 96 5 0) sis ofi7 1 3 assi6 G| 4510 0| osu o]...... | io 13 0) 325 0 o}..... Beene fi Sver C805) ER Tse Te) SE ts ei Soop EONIK) Li RIES ocean PE ah RIE LOE Ce UIE Zip .ocooc|looeves|lencuas 2015 1/42 5 ol! 5317 1(\lse612 4

ieocotone a -. | 39915 3 111 5 0] 3 0 Of] 17 1 3] 182 0 O} 2215 O} G314 O|-....-.]/ 16613 0} .. : 96 5 566 12 4') 1133 0 7 || 58 511] 3119 24) 2012 O}.+..--)20 O11 | 3911 2})...... 6 1 4)203 1610)))g01 13, 8} 267 17 IDNs. | 10 0 Ol... .-4 138 5 5 873.16 4||\ 259 4 3

}sis0 0 of ...... Jaisa2 0 Jin 0 0 TWO | WA ssooallocases 7A 0 Of}... 83 6 6/325 0 O||..... ollb ace oo 259 4 3] 983 2 9]] 5010 2] 78 1 9] 718 G|---..- 2512 4/18 0 7}]..--.. CSC G3 NY CBE loo coadiloveoasllaveon -| 814 0 : 770 3 33) 912 19 54

ss00 0 0} ...... |iss2 3 9 | 12917 G|1cs 4 9|17 1 3| 159 5 o| 17 1 3| o314 0|-.....]) 24919 G} 325 0 O|]......]...... 212 19 53] 1340 2 Sy 27 1 5)) 114 4 9H 50 411 ]-----. 135 BO | 3415 Sy COREE COTES VNC OED |. oceoo|| TO Ullsggucull $0 Ollcascac W735 74\| 166 17 1

416210 0] ...... |} 312 9 0 |} 43 2 G| 3 5 0/17 1 3] 4510 0} G21 3) 4019 O/-.-... | 16613 0/650 0 O}...... sae+-+ | 16617 1) 129519 1} 851211) 10611 4] 21f 2).,.,.. S11 4 2419 Sy ye. -- COUR OIE OF OO || soccaall fi 0 Ollonanoa (2) O)\lounses 1131 1 24) 164 17 10g

‘ |asc2 10 0 ~ | 358 7 0 | 58 0 0] a3 s of i7 1 3] 68 5 0] 28 8 9] 77 7 Ole +--+] 1951211) 325 0 OF ....--)-. ae oi a7 sy] 298 7] 347 1 1H 8 2 |... 3416 4 |25 5 of) 221410] 2713 3] 16918 G| oi o o sis. 2 oka 9 ERE 4 sone +) 88414 8 | 290 3 15
4100 0 0 isa 1) op) 1s2 9 Gj] 0 7 6|..--. #2 0 0] di 10 0] 3514 0 146 17 8 | 300 0 0 (230 314 S01 7 ogi 9512 9 /osic 9] 4 ool). ..... (267 1p) 28 2114) 22. EES NE YE Gl Ge enco||oocu00 713 0% ...--.1 5 9 ate... =|] 639 2 113) 262 4 0p

4100 0 0} ....., |ss2 1 0 15117 6] 1214 G| 3110 0) 21 0 0} 6s 5 0} SOTA O}-.... - | 14617 8) 300 0 O}}/.,,...]...... UAC ERLE | EHO Oh) SCE Oe crs crs LEG SP GEIS 1) CN EAS RISES TEESE CE MESEITENIE: <il| co ocoalaosasallagan oc 7 5 114}...-..]} 708 10 43]] 312 13 2
598412 0} ...... | 456 610 | 149 3 0) 20 1010/1515 0) 84 0 0/105 0 0} 8118 O}..-... | 14017 8 | 300 0 of|...... Giomis 14517 8] 5014 1] 4216 G| 24 G O}..,... AIG BEG EE) | oom CTC TEESE. SGP ESD es 3 S000 |) 000 170 0 0 + +++] 15 10 10 ++. |] 697 14 7 |) 548 3 1

398412 0} ...... | 470 9 3 | 149 3 0) 1015 3/1515 0/115 10 0} 5210 0/12616 O}.~..... 182 16 8 | 299 1010 |2727 G 1])...... 4228 5 11}/ 71 911) 305 611) 11 5 0 --|29 0 9 | 801110 |..... Goll 8} 15t 0 Of 195 8 oOboT4s 12 5 | 104 8 7] 7411 9 Bei) wae Clone 384616 8 |l3s1 9 3
|1500 0 0| aso 0 0 || 46613 8 | 14115 0| 33 3 6/21 0 0/100 1 0| os 0 0| of 4 2]- - 14613 7] 999 3 o|/...... noonce 1294 0 3]/ 14610 4]... 10 8 G| 2 2 2/297 210 |27 4 3 }.. - | 18 7 0) M41 it 5\}\202,19 6il139 7 10) a8 1G 7||......)...-.- 13°79 ' 79718 0 || 496 2 3

1500 0 0} 3150 0 o wr 5 0 | ur 0 0 414 0/21 0 0|14118 0] 5715 0| 10118 0|-.....|} 148 9 G|s00 0 o||...... noo M4116 9}/ 8810 7) 53313 8] 51 7 8} 517 2/33 3 0 | 14 210 }.... 3919 0] 156 2 9/204 0 o ..] 14213 s| 20 0 o|...... 1s 4 calle cM isoa1e s\lasr 2 4

1500 0 0/3150 0 0 sia 8 6 | 22010 0 19 6 6/21 0 0] 6 1 0} 7515 0) 1516 O}......} 192 6 3) ao0 0 o}.. acqaoc 148 17 1])/ 3017 G6) 11 3 3) 4216 0} 1116 7|17 7 © | 29 8 O 5 0 0} 2019 5/283 5 11} 32519 2 Rte. ff. O Ollanaws< 12/16 Gille+-2-«l|(rersiu 4llisse) 4m

1500 0 0} 3150 0 065511 6 | 147 0 0| 93 9 G|21 0 0/231 0 o|1isa0 0] 11712 0|......]} 45317 0] 975 0 ol]... 152013 5 || 17917 2] 82 5 0] 8 G 8} 6 83 9/25 4 4 |26 7 4 ].... $2713 1| 145 16 6) 204 0 o|..... ol) 247 GOTO OOllhesgoe 23 4 of1 5 0] 1387 710}) 13315 7

1500 0 0) 2000 0 0 || go2 2 9 | 132 0 0| 93 1 9/21 0 0| 20615 0| 105 0 0] 11 G o|...... 158 17 0 | 300 0 olism co o|...... 139.15 7 | 223315 10}/219 1 7) 5 10] 10 7 4] G18 G|3519 1 |5119 3 |.....- 96113 2) 15511 0) 21610 0)...... 165 0 0) 44 0 o]...... 21 1 o}....../] 1893 111]} 30 311

1500 0 0} 2000 0 0} G67 14 0 || 9710 0) 26 G oO] 21 0 0) 231 0 0) 147 0 0} 14418 O}--.... || 153 17 0} 300 0 0|) 402 9 8]...... 340 311] 1924 4 7]) 656 1 6) 255 4 1) 235 5 8 616 0/32 3 1 |2016 8 | 8816 4 90 7 1/158 1G 2/243 1 2]... ced binel baat ||dernee atl 20 FUG |lsksce 1763 10 7 || 160 14 0

1500 0 0) 1500 0 0) G14 5 7 | 9710 0) 1114 7) 21 © 0} 22212 0) 12015 0} 14014 0 oe « | 15317 0/300 0 O Cab Aono 160 14 0} 122816 7]) 21311 G/14919 5} 51 5 O 818 3/42 9 1 )21 40 /]-. . 1918 1/160 1 6) 243 G 8}. 8715 0 ey etoper sil licrerekerere 24 4 0/41 0 0} 102612 G/} 202 4 1

1500 0 0 1500 0 0 | cat 5 0 | 9710 0) 5 2 0)21 0 0} 195 6 0| 12015 0| 20112 0 ) 148.12 6| 500 0 o}/......]...... 202 4 1/1902 1 7/1 15210 7] o517 1| 82 5 Oo] 615 7) 4818 8 | 9715 8 eee 8518 8|/162 1 7] 24416 5]...... fa G ilece 7510 0) ss\tv 7 |\n--- << 106413 4 |] 997 8 3
1500..0.D},1500..0..0.)).734.0..)) 9710 0) 26 9 3)21 0 0\ 15618 0) 16215 0\ 029 8 o}.....-| 14017 @| 300 0 o||......|.....- 207 8 3) Mos G 4}/ ico 4 1/997 14 G} co1d 0} 98 4 3|/ 5519 9 | 30 Sto |-..... 1977 8 (15918 5) 205 4 1\_..,..\ 40 0 0| 3910 0).....- 29 9 O)...... 19714 7 |) 130 Oo

1500 0 0 | 1344 10 | 706 1 0 9515 4) 20 3 8/21 0 0} 20718 O0| 84 0 0} 277 4 O|...-...|} 14617 8] 300 0 0} 142 4 O Rebatement | 190 11 0) 425 14 5 }) 115 12 4 | 39014 4) 151 8 10 6 G6 G/4517 G6 |} 36 6 7 |...-- 135 3 9) 140 1011) 25013 G)......) 18 8 0} 1919 4 400 7 135110 8 |} 74 3 9

1500 0 0) 1367 5 8) 59213 1 946 7) 214 6/21 0 0) 16518 0} sf 0 0} 2% 14 O|....-. Jus a7 8 300 0 O}/...... Dae 74°39) 10416 2} 5119 0/285 1 8] 49 0 G| 8 6 9} 47 G1 | 17M sae LEO GSE CRON See GIO. Alle srocolGoede call woooas ~~ || 1055 1410) so 1 4

1581 4 1 | 128611 3 73612 8 97 0 8| 3719 0/21 0 0} 170 2 0} 16215 0| 247 16 0 14617 8| 300 0 0}/ 53012 o|..... 59 1 4/173 3 8}| 9017 D0] 55811 1) 8414 4] 51310) 9417 5 | 35 O 8 |....-.1] 7210 10} 147 1110) 177 8 10396316 2|.._... Rich WSL GCG} ......}.-.-.. |] 1574 14 3h) 198 9 4h

| 1643 19 6 | 117 110) 6 6 8 88 7 4) 817 4/21 0 0} 9915 0/110 5 0\ 206 2 o|...... 146.17 8/300 0 O}/,..,..]..... 198 9 44) 123913 8}/ 1010 0) 1310 G| ...... 1 2 0/3818 2 |21 5 8 Wit G} 16 3 G} 159 17 11) 343918 8) 358 8 4] 9619 O}......| 20 8 S| ......].-.--.|] 1058 19 11] 910 13 9}

| 1643 19) 6) 1117 1 10) A62 Bos 6 4) 14 G3] 21 0 0} 1545 0] 89 5 0 | 29016 01|.....- 146 17 8) 300 0 0} s34 2 3)...... | 21018 Of Mid 2 SH) 7813 7) 51617 8] 10612 2] 2 0 G| 9 2 5 |54 9 7 | 18 8 S| 7 8 6/198 9 1) 26212 2) 4918 7) 93 2 o| 191510] so11 o| ... ++] 1243.16 9 |) 210 5 Gy

|) 245 19 6) danza! 10)9 (aso 1s ons <0] m2... 2100/2110 0210 0 olss115 068 5 6 017 8 900 0 o}.. +++++-| 210 5 6} 976 2 BH) 81 0 3} 9 8 G| 5214 G] 419 oO] or 5 7 |45 1 7 | GS 1 5] 198 S11) 134 O 43 265 4 1)......I135811 o|....-.|393 0 9| ...... +++ |] 2676 IL 83) 11911 0

ae 19 6) 867 110) 993 6 9 8118 5) 100 2 4/21 0 0/ 12318 0| 24110 0| 35418 0| 16 4 0 146.17 8/300 0 0} 24512 3]... 119 11 0} 15111 8]/ G41 0 4f] 9319 8] 3419 8 3 0 G| 381710 | 18 3 1 |] 118 1011) 37 9 5) 125 G 2) 37010 7]... L. GW |jseocec 6819 0 . -+-.-./] 155617 2) 19 4 6

* The accounts for these dates bave not yet been certified by the Audit Commissioners

+ Thia Sum contains the Life Compositions and Entrance Fecr, which are nolspecified in the audited Account for this Year,

t OF this sum, £1

Ils. was paid Mr. Petrie, that being the balance due him on account of the Essay on the Round Towers.

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