^.s.:b. /;

THE

TRANSACTIONS

OF THE

EOYAL IRISH ACADEMY.

VOL. XIX.

DUBLIN:

PRINTED BY M. H. GILL,

PRINTER TO THE EOYAL IRISH ACADEMY.

SOLD BY HODGES & SMITH, DUBLIN

AND BY T. & W. BOONE, LONDON.
MDCCCXLIII.

The Academy desire it to be understood, that they are not answerable for
any opinion, representation of facts, or train of reasoning, that may appear in
the following papers. The Authors of the several Essays are alone respon-
sible for their contents.

CONTENTS.

SCIENCE.

ART. PAGE

I. Researches on the Nature and Constitution of the Compounds of Am-

monia. By Robert Kane, M.D., M.R.I.A., Superintendant of the
Laboratory, and Professor of Chemistry to the Apothecaries' Hall
of Ireland, Professor of Natural Philosophy to the Royal Dublin
Society. Read April 9, May 14 and 28, 1838 1

II. Description of the Cydippe Pomiformis Mihi (Beroe ovatus Flem.),

with Notice of an apparently undescribed Species of Bolina, also
found on the Coast of Ireland. By Robert Patterson, Esq.,
Member of the Natural History Society of Belfast. Read Decem-
ber 10, 1838 91

III. On the Longitude of the Armagh Observatory, given by fifteen
Chronometers of Arnold and Dent. By the Rev. Thomas Romney
'RoBm^o^,D.D.,M.R.I.A.,^c. Read December 10, 1838. . . .110

IV. On the Difference of Longitude between the Observatories of Ar-
magh and Dublin, determined by Rocket Signals. By the Rev.
Thomas Romney Robinson, D.D., M.R.I. A., 8^c. Read June 24,
1839 121

V. On the Direction and Mode of Propagation of the Electric Force

traversing interposed Media. By George J. Knox, Esq., A.M.,
M.R I.A. Read February 11, 1839 147

VI. On the Bolina Hibernica. By Robert Patterson, Esq., Member
of the Natural History Society of Belfast. Read November 11,
1839 154

vi CONTENTS.

VII. On the mutual Action of Permanent Magnets, considered chiefly
in reference to their best relative Position in an Observatory. By
the Rev. Humphrey Lloyd, A.M., Fellow of Trinity College, and
Professor of Natural Philosophy in the University of Dublin.
F.R.S., V.P.R.I.A., Honorary Member of the American Philo-
sophical Society. Eead February 11, 1839 159

VIII. On the Constant of Refraction, determined by Observations with
the Mural Circle of the Armagh Observatory. By the Rev. Thomas
EoMNEY Robinson, D.D., M.R.I. A., Member of other Philosophical
Societies. Eead January 11, 1841 177

IX. On the Heat developed during the Combination of Acids and Bases.
By Thomas Andrews, M.D., M.R.I.A., Professor of Chemistry in

the Royal Belfast Institution. Eead January 11, 1841 228

X. Supplement to a Paper " on the mutual Action of Permanent Mag-

nets, considered chiefly in reference to their best relative Position in
an Observatory!' By the Rev. Humphrey Lloyd, D.D., Fellow of
Trinity College, and Professor of Natural Philosophy in the Uni-
versity of Dublin. F.R.S., V.P.R.I.A., Honorary Member of the
American Philosophical Society. Eead April 26, 1841 249

XI. Supplementary Researches on the Direction and Mode of Propa-
gation of the Electric Force, and on the Source of Electric Deve-
lopment. By George J. Knox, Esq. M.R.I A. Eead May 25, 1841. 257

XII. On Fluctuating Functions. By Sir William Eowan Hamilton,
L.L.D., P.R.IA., F.R.A.S., Fellow of the American Society of Arts
and Sciences, and of the Royal Society of Northern Antiquaries at
Copenhagen ; Honorary or Corresponding Member of the Royal
Societies of Edinburgh and Dublin, of the Academies of St. Peters-
burgh, Berlin, and Turin, and of other Scientific Societies at Home
and Abroad ; Andrews' Professor of Astronomy in the University

of Dublin, and Royal Astronomer of Ireland. Eead June 22, 1840. 264

XIII. On the Minute Structure of the Brain in the Chimpanzee, and
Human Idiot, compared with that of the perfect Brain of Man;
with some Reflections on the Cerebral Functions. By James Ma-
cartney, M.D., F.R.S., F.L.S., M.R.I.A., S^c. Sfc. Eead June 27,
1842 232

CONTENTS. vii

ART. PAGE

XIV. On Equations of the Fifth Degree ; and especially on a certain
System of Expressions connected with those Equations, which
Professor Badano has lately proposed. By Sir William Rowan
Hamilton, iiy.Z)., P.R.I.A.,F.R.A.S.,' Honorary Member of the
Royal Societies of Edinburgh and Dublin ; Honorary or Corres-
ponding Member of the Royal or Imperial Academies of St. Peters-
burgh, Berlin, and Turin, of the American Society of Arts and
Sciences, and of other Scientific Societies at Home and Abroad ;
Andrews^ Professor of Astronomy in the University of Dublin, and
Royal Astronomer of Ireland. Read August 4, 1 842 329

XV. On the Compensations of Polarized Light, with the Description
of a Polarimeter for measuring Degrees of Polarization. By Sm
David Brewster, K.H., D.C.L., F.R.S, M.R.I.A., and V.P.R.S.
Edinburgh. Read November 14, 1842 377

XVI. On the Heat developed during the Formation of the Metallic
Compounds of Chlorine, Bromine, and Iodine. By Thomas
Andrews, M.D., M.R.I. A., Professor of Chemistry in the Royal
Belfast Institution. Read December 12, 1842. . , 393

■ POLITE LITERATURE.

I. A Memoir of the Medals and Medallists connected with Ireland.

By the Very Rev. Henry Richard Dawson, A.M., V. P. R.I. A.,
Dean of St. Patrick's. Read March 16, 1838, . 1

II. On the Antiquity of the Kiliee, or Boomerang. By Samuel Fer-

guson, Esq., M.R.I. A. Read January 22 and February 12, 1838. . 22

III. On the Egyptian Stele, or Tablet. By the Rev. Edward Hincks,
D.D. (Communicated by the President.) Read June 28, 1841. . 49

IV. On the true Date of the Rosetta Stone, and on the Inferences de-
duciblefrom it. By the Rev. Edward Hincks, D.D. Read May 9,
1842 72

V. An Essay upon Mr. Stewart's Explanation of certain Processes of

the Human Understanding. By the Rev. James Wills, A.M.,
M.R.I.A. Read February 14, 1842 78

viii CONTENTS.

ABT. PAGE

VI. Memoir of Researches amongst the inscribed Monuments of the
Gr (SCO- Roman Era, in certain ancient Sites of Asia Minor. By
the Rev. James Kennedy Bailie, D. D., late Fellow of Trinity
College, and Lecturer of Greek in the University of Dublin. Read
May 9 and 23, 1842 HI

ANTIQUITIES.

I. On the Irish Coins of Edward the Fourth. By Aquilla Smith,

M.D., M.R.I.A. Read November 30, 1839 1

II. On the Irish Coins of Henry the Seventh. By AQurLLA Smith,

M.D., M.R.I.A. Read June 14, 1841 50

III. On the Norse Geography of Ancient Ireland. By Geokge Downes,
Esq., M.A., M.R.I.A., Member of the Royal Society of Northern
Antiquaries of Copenhagen'^ F.H.M. M.S., Jena. Read April 26,
1841 ' 84

LIST OF PLATES.

SCIENCE.

PLATE PAOE

I ILLUSTRATIVE OF MR. PATTERSON'S PAPER ON THE STRUCTURE OF

THE CYDIPPE POMIFORMIS 109

MAP TO REV. DR. ROBINSON'S PAPER ON THE DIFFERENCE OF LONGI-
TUDE BETWEEN THE OBSERVATORIES OF ARMAGH AND DUBLIN, . V>C,

11., Ill DIAGRAMS ILLUSTRATIVE OF THE REV. DR. LLOYD'S PAPERS ON THE

MUTUAL ACTION OF PERMANENT MAGNETS, 159, 249

IV., V ILLUSTRATIVE OF DR. MACARTNEY'S PAPER ON THE STRUCTURE OF

THE BRAIN OF THE CHIMPANZEE 32S

VI ILLUSTRATIVE OF SIR D.BREWSTER'S PAPER ON THE COMPENSATIONS

OF POLARIZED LIGHT, 377

VII ILLUSTRATIVE OF DR. ANDREWS' PAPER ON THE HEAT DEVELOPED

DURING THE FORMATION OF THE METALLIC COMPOUNDS OF CHLO-
RINE, BROMINE, AND IODINE, .WS

POLITE LITEKATURE.

I., II ILLUSTRATIVE OF MR.FERGUSON'S PAPER ON THE ANTIQUITY OF THE

KILIEE, OR BOOMERANG 48

ANTIQUITIES.

I., II., III., IV. ILLUSTRATIVE OF DR. A. SMITH'S PAPER ON THE IRISH COINS OF ED-
WARD IV 40

v., VL, VII. ...ILLUSTRATIVE OF DR. A. SMITH'S PAPER ON THE IRISH COINS OF

HENRY VII 81

Direction to the Binder.
In binding the Volume, cancel the leaf in Antiquities, p. 49, of Part I.

VOL. XIX.

TEANSACTIONS

OF THE

ROYAL IRISH ACADEMY,

I. Researches on the Nature and Constitution of the Compounds of Ammonia.
By Robert Kane, M.D., M.R.I. A., Superintendent of the Laboratory
and Professor of Chemistry to the Apothecaries' Hall of Ireland ; Pro-
fessor of Natural Philosophy to the Royal Dublin Society.

Read April 9th, May 14th, and May 28th, 1838.

PART I.

ON THE SULPHATES AND NITRATES OF MERCURY, PARTICULARLY THE SUBSALTS

FORMED BY AMMONIA.

Having shown in a former memoir that by the action of ammonia on the
chlorides of mercury, there came Into operation the principle which had been
found by Dumas and Llebig to regulate the constitution of so many interesting
bodies of organic origin, — that Is to say, that by the elimination of one equivalent
of hydrogen from the ammonia, and the union of the remaining hydrogen and
nitrogen with the metal, there was generated an amide, — it became of importance
to follow out into other combinations of the metallic salts with ammonia, an
investigation which had led, in the few cases already studied, to such novel and
Interesting results. It is Intended in the present memoir to investigate the func-
tions of the ammoniacal elements of the mercurial subsalts, a department, of
which, notwithstanding the labours of many chemists, our knowledge has re-
mained imperfect, from circumstances similar to those which had led, in the same

VOL. XIX. B

2 Dr. Kane on the Compounds of Ammonia.

hands, to the conflicting opinions as to the nature of white precipitate already
noticed.

In addition to the ammoniacal subsalts of mercury, there are described in the
present paper the sub-sulphate and the sub-nitrates of the black and red oxides.
And as the necessity of a new examination of these compounds may not appear
to those who have not themselves studied the chemistry of the salts in detail, I
may state, that in order to ascertain the part which the ammonia plays in the
subsalts formed by its means, it became necessary to establish a comparison with
the ordinary subsalts most analogous in composition ; and on searching through
the analyses of the mercurial subsalts already recorded, I found the testimonies
so conflicting, and the results so imperfect, that I was obliged to commence the
subject as if it had been actually new.

In the former memoir I assumed as the atomic weight of mercury the num-
ber 202.8, which supposes the corrosive sublimate to be a bi-cliloride. This
opinion I have since found reason to alter, from evidences, partly derived from
the results contained in the present paper, and partly from other sources ; I have
therefore now adopted the Berzelian number 101.4, by which the calomel is
looked upon as a sub-chloride, and sublimate as containing an equivalent of each
ingredient. It will be found that by this arrangement the formula of these
classes of compounds become much more simple than on the plan of the larger
number, to which however they can easily be reduced.

Without occupying attention by any unnecessary prefatory matter, I shall
pass at once to the analytical results.

I. OF THE SULPHATES OF THE RED OXIDE OF MERCURY.

Before commencing the study of the action of ammonia on the sulphates of
mercury, I considered it proper to satisfy myself, by actual analyses, of the com-
position of these bodies, particularly with reference to the possible existence of
water as one of their constituents, and the more so, as from the conflicting state-
ments of chemists with regard to the nature of turpeth mineral, it was not
unlikely that a source of error not previously unveiled might exist. As, how-
ever, my results have confirmed the ordinary view of the composition of these
bodies, I will not detail any of the methods I employed, but merely state the
absolute numerical results.

Dr. Kane on the Compounds of Ammonia.

An analysis of neutral sulphate of mercury gave

! ;■. .Viltff. Vi,r,. Experiment. Theory h^o.sOj

Sulphuric acid = 26.72
Oxide of mercury = 72.98

99.70
Three analyses of turpeth mineral gave

I.
Sulphuric acid = 10.89
Oxide of mercury = 88.71

26.82

73.18

100.00

II.

III.

10.87

11.08

89.24

88.76

99.60 100.11 99.84

The theory of ngo. SO3 + 2 h^o should give

Sulphuric acid = 10.91

Oxide of mercury = 89.09

I would not have brought forward even this notice of the numbers I obtained,
were it not that from the high authority by which some of the incorrect results
had been supported, and their insertion in some of the most approved ele-
mentary books, it might have appeared objectionable to make any one of the
various formulas given the foundation of a chain of reasoning, without having
first established by experiment its superiority over the rest.

II. OF AMMONIA SUB-PEKSULPHATE OF MERCURY.

When persulphate of mercury is treated by water of ammonia, it is converted
into a white powder, which appears to be almost insoluble in water. In general,
on the first addition of the water of ammonia, there is some turpeth mineral
formed, which however gradually disappears, and the product is an uniformly
white powder. This reaction takes place more rapidly by boiling, but the nature
of the result is the same. If turpeth mineral be boiled, or treated in the cold
with water of ammonia, it is converted into the same white substance, as shall be
proved by the analyses subjoined. The existence of this white ammoniacal sub-
sulphate was noticed by Fourcroy, but he made no analysis of it, nor has it ever
been, at least to my knowledge, subjected to an accurate investigation.

This substance is heavy ; it is not decomposed by water, which, however, dis-

B 2

4 Dr. Kane on the Compounds of Ammonia.

solves some traces of it. When heated it becomes brown, exhales traces of
ammonia, much water and nitrogen, and there finally remains sulphate of the
black oxide of mercury, which by a further heat gives its usual products of de-
composition. This powder is soluble in nitric and muriatic acids. When dif-
fused through water, and treated by sulphuretted hydrogen, the mercury is all
thrown down as sulphuret, while the liquor remains perfectly neutral, and gives
by evaporation sulphate of ammonia.

I shall speak of this substance always as ammonia-turpeth, a name short, and
not involving any theory, and therefore the best calculated for use.

To analyze this compound, the following methods were pursued :

A. 5.072 grammes ammonia-turpeth were dissolved in muriatic acid, and
precipitated by muriate of barytes. The sulphate of barytes formed was washed
until the water passed quite pure ; it was then carefully dried and ignited, and
weighed, when corrected for the ashes of the filter, = 1.223 gramme, or 24.11
per cent., containing 8.28 of sulphuric acid.

The liquors filtered off the sulphate of barytes were treated by sulphuret of
hydrogen, and the sulphuret of mercury was collected on a filter, and carefully
dried until it ceased to lose weight ; when dried there was

Sulphuret and filter = 5.835 ") 4 005 „«•<?
Filter = 0.910 J ■ " *

giving H^.s = 96.9 per cent., or 83.69 mercury.

B. 10.375 grammes of sulphate of mercury were boiled with a considerable
excess of ammonia, until completely converted into ammonia-turpeth, which was
collected on a filter after the whole had been allowed to cool.

The powder was washed until the liquor ceased to give appreciable traces of
sulphuric acid ; it was then dried by a temperature of 2 1 2°, and weighed

Powder and filter = 8.590
Filter = 0.361

To the filtered liquor and washing was added an excess of muriate of barytes,
it having been first acidulated by muriatic acid. The sulphate of barytes was
collected on a filter and washed, as long as the liquors passed through containing
muriatic acid ; it was then dried and ignited. The ashes of the filter having been
allowed for, it weighed 6.112 grammes.

> 8.229 ammonia-turpeth.

Dr. Kane on the Compounds of Ammonia. 5

The liquors remaining contained a trace of mercury, which precipitated gave
0.220 of ng. s. Therefore 100 of sulphate of mercury gave

Ammonia-turpeth = 79-31

Sulphate of barytes = 58.91

•.• Sulphuric acid = 20.245

And sulphuret of mercury = 2.10 equivalent to 1.81 of mer-
cury, giving 1.96 oxide and 2.68 sulphate.

There had therefore been decomposed 100 — 2.68 of the sulphate, and 100 of
sulphate completely converted into ammonia-turpeth should give

Ammonia-turpeth = 81.48
Sulphuric acid = 20.06

The sulphuric acid in 100 of Hgo. SO3 is 26.82, of which 20.06 is almost
exactly three-fourths, for | . 26.82 = 20.115. Therefore in the ammonia-tur-
peth is contained all the mercury and one-fourth of the sulphuric acid ; its com-
position therefore comes out.

Mercury = 67.83

Sulphuric acid = 6.76
Other matters =: 6.89

83.25 j
81.48, or 8.29 [ 100.00
8.46 J

C. 7.317 grammes of ammonia-turpeth were diffused through water, and
decomposed by a current of sulphuretted hydrogen. The sulphuret of mercury
was collected on a filter, and dried carefully, until it ceased to lose weight.

Filter and sulphuret = 7.422 \ ^ ^^j^
Filter = 0.355 / ' '

Sulphuret = 96.58 per cent., containing 83.35 mercury.

The clear liquor reacted neutral ; it was evaporated in a water-bath to per-
fect dryness, and the capsule, with the residual sulphate of ammonia, carefully
weighed ; the salt then cleared out without loss, and the capsule tared ; the salt
was then again weighed on the tared slip of paper, on which it had been col-
lected, and the second not differing from the first weighing by a milligramme,
certainty of accuracy was obtained.

The sulphate of ammonia weighed 0.988 gramme, corresponding to 13.5 per
cent., and consisting of

6 Dr. Kane on the Compounds of Ammonia.

Sulphuric acid = 8.18

Ammonia = 3.48 ■ 13.50

Water =: 1.84 .

Tabulating the results of these three methods, there is obtained for ammonia-
turpeth

A.

B.

C.

Mean.

Sulphuric acid = 8.28

8.29

8.18

8.25

Mercury = 83.69

83.25

83.35

83.43

Ammonia =

3.48

3.48

Oxygen and loss :=

4.84

The positive values obtained by analysis give the proportions in ammonia-
turpeth to be :

1 atom of sulphuric acid.
1 atom of ammonia.
4 atoms of mercury.

But for the oxidation of the mercury there would be required (as, from the solu-
bility of ammonia-turpeth in muriatic acid, the whole of the mercury is proved to
be in percombination) oxygen := 6.582, a quantity which is altogether excluded
by the sum of the values of the other ingredients, which leave room for only 4.84
of oxygen. Now this number is almost exactly three-fourths of 6.582, since
§ . 6.582 = 4.937 ; and we have consequently the most complete evidence that
the fourth atom of metal is combined with some other negative radical than
oxygen. If one conceives that in this ammonia-turpeth the azote and hydrogen
exist as amidogene, the formula falls in accurately with the experimental results,
for there is

8.27 Analysis = 8.25

3.32 = 3.27

83.47 = 83.43

4.94 = 5.05

S03

=

40.16

NHj

=

16.14

4Hg-

z=

405.60

3o

=

24.00

485.90 100.00 100.00

By this formula 100 of sulphate of mercury should give 81.30 of ammonia-tur-
peth, while in experiment B there was obtained 81.48.

It will be seen that the formula h^o. SO3 + 2 ugo -\- Hg nHj is completely

Dr. Kane on the Compounds of Ammonia. . 7

analogous to that for the yellow powder formed by the action of water on white
precipitate, if we write the sulphate of mercury as h^. so^ ; then there is

Hg-. cl-\-2 ngo -{- ng nh^, and

H^. SO4 + 2 H^-O + ng NHj.

We shall have occasion, hereafter, to advert to this type of a remarkable class
of combinations.

III. ACTION OF AMMONIA ON SULPHATE OF BLACK OXIDE OF MERCURY.

When the sulphate of the black oxide of mercury is treated by cold or boiling
water no reaction occurs indicating the formation of a basic salt ; it would there-
fore appear as if there existed but one sulphate of the black oxide.

When sulphate of the black oxide of mercury is treated by water of ammonia
there is obtained a dark grey powder, which, when heated, gives water, ammonia,
sulphurous acid, oxygen, and mercury. It is thus indicated to be a basic salt,
containing ammonia ; but great difficulty was found in tracing accurately the
proportions in which complete decomposition occurred.

To determine the nature of this grey compound, the following method was
adopted : — A weighed portion of sulphate of black oxide of mercury, was treated
by an excess of water of ammonia, until the reaction appeared to be complete,
and a uniform dark grey powder was produced. It was then collected on a filter,
and the liquors, which contained but a mere trace of mercury, were mixed and
acidulated by muriatic acid, and precipitated by muriate of barytes. The sul-
phate of barytes was then collected and dried, and having been ignited, with its
filter, weighed, and the correction for ashes made.

The results of five experiments of this kind are given in the subjoined table,
the details being omitted, in consequence of my not intending to use these results
as bases for induction, and therefore it not being necessary to specify the par-
ticulars of each case :

100 of H^.O-f- SO3

A.

B.

C.

D.

E.

. Grey Powder . .
Free SO3 . . . .

Not determined.
13.83

83.08
11.73

92.3
Not determined.

90.22
8.33

88.89
9.96

8 Dr. Kane on the Compounds of Ammonia.

The sulphate of the black oxide of mercury is, when prepared by double
decomposition, anhydrous, and is composed of

Mercury = 80.80 1

Oxygen = 3.18 [ 100.0

Sulphuric acid = 16.02 J

But, from the extensive limits, within which the quantity of the sulphuric acid
removed by the ammonia, is contained, it would, be improper to assert positively
by what formula the result should be expressed. I consider that by the action
of the ammonia a certain quantity of a per-compound may have been formed,
and thus have given rise to the variable nature of the result. The results A
and B, however, tend to induce me to look upon the grey compound, when
pure, as having the composition \igo.so^-\-2ugo-\-ngtiH^, and bearing the
same relation to the ammonia-turpeth, that the powder formed by water of
ammonia on calomel, bears to white precipitate. If one might hazard a conjec-
ture, the other results would indicate a tendency to a limit in the decomposition,
when the half of the sulphuric acid had been removed, and thus there may be a
body also grey coloured h^o. SO3 + ug nh^, or rather h^ SO4 -\- Hg nh^, similar
to H^ cl -\- ug NHj, as described in the former paper.

I did not follow up any analysis of the grey powder, because it was evident,
from the variable nature of the circumstances affecting its formation, that no result
could be obtained, so closely true, as to prove either for or against the question
of the function of the ammonia, or indeed the quantity of the latter constituent
(never more than three per cent.), that might have been therein contained. It
is necessary therefore, on this point, to allow of the temporary guidance of the
analogical evidence, which we derive from the more fixed results of the analyses
of corresponding compounds.

IV. OF THE NITRATES OF THE RED OXIDE OF MERCURY.

We owe to the younger Mitscherlich an examination of the nitrates of mer-
cury, which constitutes, up to the present day, all our knowledge regarding
them. The singularity of the results to which he arrived, rendered their
repetition of importance, and the more so, as the doubts which had been thrown
upon the correctness of his analyses of the ammonia-nitrates, by Soubeiran,

Dr. Kane on the Compounds of Ammonia. 9

rendered it necessary to confirm his formula before they could be assumed as
data in an investigation like the present.

There can be obtained but one crystallized nitrate of the peroxide of mer-
cury : this salt is formed in small prisms, which deliquesce, except in a very dry
room ; when dried between folds of blotting paper, the crystals taste metallic, but
not acid. These crystals are decomposed by water, but only a portion of the
mercury is thrown down as a pale yellow powder, whilst the liquor becomes acid.
If the supernatant liquor be evaporated, the excess of acid is driven off, and there
crystallizes, on cooling, the same salt as had been previously dissolved.

To analyze this salt, the same method was pursued as had been employed by
Mitscherlich, and with exactly the same result. As the analyses were but con-
firmatory of his accuracy, I shall not enter into their details. The formula of
this crystallized pemitrate of mercury is ugo. NOj + ugo -\- 2 ho, and in num-
bers :

2 atoms of oxide of mercury = 202.80

1 of nitric acid = 54.14

2 of water = 18.00

274.94
It is well known that this salt is decomposed by water, but there still remains
some doubt as to the constitution of the subnitrate thus generated. From the
variable appearance it presents, according to the method by which it has been
obtained, it evidently is not of constant nature ; and it is generally stated by
systematic writers, that by washing it can be completely resolved into nitric acid
and oxide of mercury. Of this nitrous turpeth, as it has been generally termed,
two quantitative analyses have been recorded, of which the results follow :

Oxide of Mercury. Nitric Acid. Reference.

Braancamp = 88.0 12 An. Chim. 54

Grouvelle = 88.97 11.03 An. Ch. et Phys. 19

These results coinciding so closely, and leading immediately to the formula
NO5 4" 4 H^o, might appear to be conclusive, but several circumstances induced
me to consider a new examination necessary. Thus, all other analyses made by
Braancamp Vere inaccurate by four or five per cent., a result to be partly attri-
buted to the imperfect state of analytical chemistry at the time he wrote ; and

VOL. XIX. C

10 Dr. Kane on ike Compounds of Ammonia.

also, it appeared from the evidently inconstant nature of the subnitrates obtained
by water, that the stages of its production required to be closely studied. In
addition I had observed that nitrous turpeth, when heated, always yielded some
liquid nitric acid ; this fact should introduce water as one of its constituents,
which the results obtained by Braancamp and Grouvelle necessarily exclude.

A quantity of crystallized nitrate of mercury was treated by water, and the
undissolved portion washed by warm water until the washings no longer reacted
acid. It then appeared as a fine yellow powder, very heavy, not acted on by cold
water, but converted into a brownish red powder by boiling water, which dis-
solved out the soluble nitrate of mercury, not affecting blue cabbage paper.
When this powder is heated, it gives much red fumes and a quantity of liquid
nitric acid, and there remains red oxide of mercury, which by a stronger heat is
decomposed. As, by avoiding the use of boiling water, this powder was obtained
apparently similar in appearance and properties at different times, it was selected
for analysis.

A. 5.458 grammes of this powder were dissolved in muriatic acid, and
treated by proto-chloride of tin. There were obtained 4.170 grammes of metallic
mercury, giving 76.40 ug per cent.

B. 5.513 grammes of a portion prepared at a different time were dissolved
in muriatic acid diluted with a good deal of water, and precipitated by sulphu-
retted hydrogen ; there were obtained

Filter and sulphuret = 5.935 1 f. ^^o

Filter = 0.932 / ^

giving mercury =. 78.31 per cent.

C. A portion of the yellow powder having been treated by boiling water,
and having assumed a brownish red colour, was dissolved in muriatic acid, and
precipitated by sulphuretted hydrogen. Thus analyzed, 4.975 of this powder
gave 4.919 sulphuret of mercury, corresponding to 85.33 mercury per cent.

D. A quantity was boiled for a long time, until it had been converted into a
brick red powder, which was analyzed by solution in muriatic acid and the sepa-
ration of the mercury by proto-chloride of tin ; from 7.746 grammes were ob-
tained 6.673 mercury, or 86.17 per cent.

No matter how far the boiling might be carried, I could not reduce the
powder to thq state of pure red oxide. The residual powder dried always gave

Dr. Kane on the Compounds of Ammonia. 11

by heat red fumes, and also liquid nitric acid, but in constantly decreasing pro-
portion. I consequently considered it unnecessary to press the series of analyses
further.

The analyses A and B give the result NO5. Ho -|-3h^o pretty closely, the
theoretical numbers being

63.14 16.13

N05

=

64.14

HO

=

9.00

3h^

=

304.20

3o

:=

24.00

}
}

328.20 83.87

H^ =

77.74

0 =

6.13

NO5 =

13.83

HO =

2.30

391.34 100.00 100.00

and I am disposed to consider such as being the real composition of the yellow
sub-pernitrate prepared by water not boiling. It will be at once seen that this
formula assimilates completely the sub-nitrate of mercury with those of copper
and of bismuth, the nature of which has been lately elucidated by the experi-
ments of Graham.

With regard to the red sub-nitrate prepared by boiling water, I am inclined
to look upon it, in like manner, as having a definite composition, because, whilst
the specimen used in analysis C had been boiled but for a few minutes, and that
used in analysis D for some hours, their composition appeared to be quite the
same. When heated, this red subsalt certainly yields a trace of water, besides
nitrous acid fumes ; but this water is in such small quantity that it might be
considered as hygrometric. The quantity of mercury obtained, may serve equally
well for one or other of two formulee, thus :

NOj -f- 6 H^O NO5. HO 4- 7 H^O

Nitric acid = 7.62 6.52 ]

Oxide of mercury z= 92.38 92.39 • = 100.0

Water = 1.09 .

Although I have always found this red powder to give a trace of water, yet I
incline strongly to the first of the above formulae, to which I shall refer when
treating of some analogous ammonia compounds.

As the composition assigned by Grouvelle to the sub-pernitrate falls within
the limits of the two bodies which have been just described, it may be supposed
that he had examined a mixture of them, and not a pure substance ; this idea I
consider probably to be true.

c2

12 Dr. Kane on the Compounds of Ammonia.

By the action of water on the crystallized pernitrate it is resolved into yellow
sub-pemitrate and an acid-reacting salt, which, when evaporated, yields, as was
already mentioned, the same crystallizable nitrate, whilst the excess of acid passes
off. There takes place, therefore, a division of the mercury into two portions, one of
which passes into solution, whilst the other is left in the insoluble yellow powder.
The salt in solution does not appear to crystallize, but to give, on concentration,
nitric acid and the crystallized basic salt of Mitscherlich. The proportion of
mercury which remains in the solution approximated, in my trials, to one-third
of that precipitated, and the action of water may be explained by the following
formula :

2(N03-f 2Hg-o-i-2Ho) =: Iho.nOj-I-Sh^oJ + J H^O.NOs -f 3 Hd J
The crystalline pernitrate being considered as a double salt, which is decomposed
by water into its constituents. It may evidently be likewise considered as a
simple salt, the sum of the number of atoms of hydrogen and mercury remaining
still four, but capable of indefinite replacement within that limit.

The proportions of mercury and nitric acid in solution, after the precipitation
of the yellow basic salt by water, must be quite definite, and should, if isolated,
produce a salt h^o . nOj. ho -\- 2 ho, corresponding to the ordinary nitrates of
copper and bismuth, but which may be so easily decomposed as to be uncrystal-
lizable. Moreover, if we look to the very general tendency to the formation of
bodies containing four equivalents of mercury, it will appear not impossible but
that a type of basic nitrates Hgo.vio^.iigo-\-2ngo may really exist, and on
which Grouvelle may have happened to alight, although I could not, even after
many trials, succeed in preparing it.

Thus there should be a series of salts :

Hgo . NO5 . HO -[- 2 HO . uncrystallizable.

Hg-o. NO5 . H^o -j- 2ho . ordinary salt.

Bgo . NOj . HO -{- 2 H^o . yellow basic salt.

wgo . NO3 . H^o -\- 2h^o . Grouvelle's basic salt,
and also

Hgo . NO5. H^o 4" 4 H^o . 'red basic salt.

V. OF THE AMMONIA SUB-PERNITRATES OF MERCURY.

It has been long known, that, by adding water of ammonia to a solution of
pernitrate of mercury, there is obtained a fine white powder, which has been

Dr. Kane on the Compounds of Ammonia. 13

examined by Mltscherllch and Soubeiran, with results, however, so discrepant, as
not to allow us to draw any conclusion whatsoever from them.

Almost immediately on commencing the examination of this reaction, I
found that the nature of the precipitate obtained was liable to considerable
variation, and that very trivial alterations in the conditions, under which the
ammonia was added, changed the proportion of quicksilver by four or five in the
hundred, — limits including the values obtained by the above-mentioned chemists.
It therefore became probable that, as in the case of white precipitate, the existence
of two or more different bodies had led to the discrepancies in the statements of
those chemists ; and by paying minute attention to the circumstances which influ-
ence their formation, I was led to detect the existence of three distinct ammo-
niacal subnitrates, as prepared by mere precipitation. The circumstances which
influence the nature of the precipitate are, the concentration of the mercurial
solution, its degree of acidity, the strength of the water of ammonia, the excess
of one or other reagent, and the temperature. By slight changes of these, there
are produced modifications of composition, and frequently an imperfect change
from one to the other form takes place. In addition to these three precipitated
compounds, there are two others obtained by crystallization, of which one had
been examined by the younger Mitscherlich, and the other was met with first in
the course of these investigations.

Ammonia Sub-pernitrate, No. 1. — When a dilute, and not very acid solution
of pernitrate of mercury is treated by weak water of ammonia, (taking care not to
add an excess of the latter, and the solution being cold,) there is obtained a pure
milk-white precipitate, not granular, which remains suspended for a considerable
time. This precipitate, collected on a filter, may be exposed to a heat of boiling
water without change, and is consequently easily dried.

When this powder is heated, it becomes yellow, and gives azote, ammonia,
then red fumes, and finally oxygen and quicksilver. If boiled with water, it
becomes granular and heavier, deposits itself more easily, and has lost, in some
degree, its pure white colour. The water remains neutral, but is found to hold
some nitrate of ammonia in solution.

On analysis, this powder yielded precisely the same results as had been
obtained by the younger Mitscherlich ; on that account I shall not insert the

14 Dr. Kane on the Compounds of Ammonia.

details of the methods, which in great part resembled those already described in
the analyses of ammonia-turpeth, but shall merely note the quantities of mercury
and other constituents obtained.
In three analyses there resulted :

I. II. HI.

Mercury = 76.50 76.84 75.9

Nitric acid = 12.66

Ammonia = 4.01

These three portions had been prepared and analyzed at different periods.

The formula NO5 + nHj -\- 3 h^o gives

3 atoms mercury

=

304.20

76.17

3 „ oxygen

=

24.00

6.01

1 „ nitric acid

::=

54.14

13.54

1 „ ammonia

—

17.14

-

4.28

399.48

100.00

Mitscherlich's result was

Mercury

= 75.55

Nitric acid

= 14.33

Ammonia

=

4.68

There can, therefore, be no doubt of this being really the composition of the
substance, and if we compare it with the yellow sub-pernitrate, we shall observe a
very curious analogy. Thus the water in the common subnitrate is replaced by
ammonia, that is, by amide of hydrogen, so that the basic function which has been
so elegantly shown by Mitscherlich and Graham to belong to water, appears to
be enjoyed in a certain degree by ammonia also. This is shown, and the nature
of this white substance very elegantly proved, by an experiment well calculated
for class illustration: if some of the water subnitrate be put into a solution of
nitrate of ammonia, and boiled for a moment, the white powder is rapidly formed,
and the liquor will be found to be strongly acid. Thus,

(H0.N05 4-3Hg-0)-|-N05NH3= (NH3. NO5 + 3Hg-o) + HONO5.

Of the Ammonia Subnitrate, No. 2. — It having been found that, by boiling
the former powder with water, it altered in its appearance, and became much

Dr. Kane on the Compounds of Ammonia. 15

heavier and more granular, it was natural to expect from it a different constitu-
tion. If the solutions of nitrate of mercury and of ammonia be mixed, while hot,
or if they be boiled after mixture, the same modification is produced ; and as
Soubeiran had been led astray by the effects of boiling white precipitate, it
might be inferred that his discordant results arose from his operating with hot
solutions in this case also. The powder, thus prepared, gives the same results of
decomposition as the former ; potash, even boiling, exerts no action on either,
giving out no ammonia, and no oxide of mercury separating. The following
analyses were made :

A. 7.185 grammes were dissolved in muriatic acid, and the solution precipi-
tated by sulphuretted hydrogen. The sulphuret produced weighed Q.*l&6, or
94.17 per cent., containing 81.24 of mercury.

B. 7.353 of another portion were dissolved in muriatic acid, and the mercury
precipitated by proto-chloride of tin. There were obtained 5.978 grammes,
being 81.28 per cent.

When this powder, diffused through water, is treated by sulphuretted hydro-
gen, there is formed sulphuret of mercury, and the li(juor contains neutral nitrate
of ammonia.

From these results, and the quantity of quicksilver coinciding so closely with
that obtained by Soubeiran, there is no doubt but that the substance is the same
as that upon which he operated.

The formula given by Soubeiran is N05-lr-NH3-|-4Hg'0, which gives the
numbers

Aug = 405.60 79.71

4o = 32.00 6.29

NO5 = 54.14 10.63

NH, = 17.14 3.37

508.88 100.00

He however obtained 80.08 mercury per cent., or more than he should by
his formula; and he proved that the nitric acid and ammonia could not exist in
the powder as common nitrate of ammonia. Indeed he expressly states that the
clearing up the nature of the function played by ammonia in these combinations
should be left to a future period in science. Under these circumstances there can

16 Dr. Kane on the Compounds of Ammonia.

be no doubt but that the true formula for Soubelran's subnitrate is as follows :
H^o . NO5 + 2h^o + Hg-Ac?, which gives

4Hg- = 405.60 81.13

3o =

= 24.00

4.81

NOj =

= 54.14

10.83

NHa =

= 16.14

3.23

499.88 100.00

This compound resembles those already described containing chlorine and
sulphuric acid.

By using strong nitrate of mercury, and a considerable excess of a strong
solution of ammonia, I have on two occasions obtained a yellowish white precipi-
tate, yielding between 84 and 85 per cent, of mercury, and containing nitric
acid and ammonia in the proportions of one equivalent of each. I have not,
however, discovered the circumstances under which this third modification may
be generated at will, for in trying often to form it, sometimes by hot liquors, at
other times using the solutions cold, I have obtained the substances previously de-
scribed, or else mixtures of them. The existence, however, of a yellowish white
powder containing more mercury than either, is certain, and I consider its formula
to be probably

(h^O . NO5 -f 4 H^O + H^Arf),

I shall not, however, dwell upon it more ; the relation which it holds to the red
sub-pernitrate is quite evident.

The Crystalline Ammonia Subnitrate. — Mitscherllch had observed that if
the ammonia subnitrate of mercury be boiled with an excess of ammonia, and
nitrate of ammonia be added, a portion of the powder dissolves, and the liquor,
when it cools, yields, according as the excess of ammonia passes off, small crystal-
line plates of a pale yellow colour. I have verified this observation, but I did not
analyze those plates, because I could form but a very small quantity of them ;
and having found in all cases that Mitscherlich's analyses were remarkably
good, I considered that in the case of these crystals, which I found great diffi-
culty in preparing, I might rely upon his accuracy. He found these crystals to
be NH3.N05-t-2Hg-o. But while I believe the numbers to be true, I do not

Dr. Kane on the Compounds of Ammonia. 17

consider that to be the rational formula. These crystals are formed by the solu-
tion of Soubeiran's subnitrate in nitrate of ammonia, and the formula is

(H^NOe + 2 Hg-O -f Hgkd) + (nH^O . NOj,

which is equal to twice

(nh.,. NOj-j- 2h^o).

That such is its constitution will be clearly shown from the study of the body
next to be described.

When Soubeiran's ammonia subnitrate is boiled in a strong solution of
nitrate of ammonia it is dissolved in considerable quantity, and the liquor being
filtered while hot, deposits, on cooling, small but very brilliant needles, which
after some time lose their lustre, and become dull and opaque, an appearance
which the salt, when rapidly formed from a very strong solution, occasionally
possesses from the commencement. This salt, after it has been once dried, can-
not be again brought into contact with water without decomposition ; its consti-
tuents are reproduced, the nitrate of ammonia dissolving, and Soubeiran's sub-
nitrate being left undissolved. These circumstances rendered a few analyses
sufficient for determining its composition.

A. 6.061 grammes of this salt were diffused through water, and decomposed
by a current of sulphuretted hydrogen gas. The sulphuret of mercury was col-
lected on a filter, and having been carefullydried, weighed 4.187, corresponding
to 69-08 sulphuret and 59.60 mercury per cent. The liquor and washings, eva-
porated to dryness, in a water-bath, gave 2.173 of nitrate of ammonia, therefore
35.85 per cent.

B. 5.973 of a quantity prepared at a different time were dissolved in
muriatic acid, and treated by sulphuretted hydrogen. The sulphuret was cau-
tiously dried until it ceased to lose weight, and amounted to 4.010, giving 67.13
sulphuret, and 57.99 mercury per cent.

Hence there is

Mercury, mean value = 58.79

Nitric acid = 24.17

Ammonia = 7.65

If we divide these numbers by the atomic weights of the bodies, and reduce
them to a standard, we shall find that there are almost exactly three atoms of
nitric acid, three of ammonia, and four of mercury.

VOL. XIX. D

1 8 Dr. Kane on the Compounds of Ammonia.

The formula 3(nh40 . NO5) -\- Ango gives

4h^ = 405.60 59.78

4o = 32.00 4.72

3NH3 = 51.42 7.58

SnOj = 162.42 23.94

3ho = 27.00 3.98

678.44 100.00

I do not consider the rational formula of this compound so simple as should
appear from the above expression. It is most likely to contain the ammoniacal
subnitrate ready formed ; it being decomposed by contact with water, and yield-
ing that substance. If the mercury be as Soubeiran's subnitrate, the formula
presents a curious relation ; thus,

3 (NH4O . NOj) -\- 4 H^o =r

(NOj-Hg-O + 2Hg-0 -\- UgAd) + 2(n05. ho -|- 2hO -f HA6?).

The facility with which this salt may be formed by heating red oxide of mer-
cury with nitrate of ammonia might be used as an argument for the former view.

VI. OF THE NITRATES OF THE BLACK OXIDE OF MERCURY.

In the memoir to which I have had so frequently occasion to refer, George
Mitscherlich described two crystallized proto-nitrates of mercury, and gave
detailed analyses of them. I have had occasion to confirm his results, and I
consequently consider the composition of these two salts as well established. I
shall not describe any of my own analyses of them, but merely insert the formulae
derived from the numbers of Mitscherlich, in order that the substances, next to
be examined, may be compared with them.

The salt obtained in transparent rhombs from an acid liquor has the formula
(h^o -j- NO3) -{• 2 HO, and consists of

Black oxide of mercury = 74.54 1
Nitric acid = 19-09 ■ 100.00

Water = 6.37

When this salt is digested with more black oxide of mercury, or when an acid
solution of it is left standing on an excess of mercury, the crystals which are de-

Dr. Kane on the Cotnpounds of Ammonia. 19

posited are opaque and white, they are generally rhombic prisms. The second
(dimorphous) variety described by Mitscherlich I have not analyzed. Their
formula is 3Hgo -\-2t<io^-\-Suo, and their composition

Black oxide of mercury = 82.40 "1

Nitric, acid = 14.08 1- 100.00

Water = 3.52 J

I shall hereafter point out some reasons for considering this to be a double
salt.

It had been long since remarked that these crystallizable salts were decom-
posed by water, but great discordance had arisen among chemists as to the
nature of the subsalts thus produced. On treating the crystallized nitrates by
cold water there remains undissolved a white powder, which as long as the super-
natant liquid is acid retains its colour, but if it be washed it becomes yellow.
Further, if it be boiled, the brilliancy of the colour is injured, and by long-con-
tinued boiling it is converted into a grey powder, which, according to some
writers, must be considered as a basic salt. These various phenomena it is
necessary to study in detail.

The white powder, which is formed by the first action of water, I could never
obtain in a form justifying any inference from an analysis of it. It is evident
that, without freeing it from the liquor holding in solution a quantity of another
salt, it would be useless to examine it ; and on the other hand, by washing, the
change from white to yellow cannot be avoided ; it was thence necessary to con-
sider the yellow subsalt, as being the product to which attention should be paid.

This yellow sub-protonitrate of mercury can be easily prepared : the white
precipitate of which I spoke may be washed with cold water repeatedly, until it
is converted into a bright lemori-yellow powder ; by the use of warm water the
change may be much accelerated, and the materials may be even boiled for some
time without danger, provided that the liquors be not too often changed. The
limit is known to have been passed when the brilliant yellow is dimmed by the
supervention of a greyish shade. By a very cautious addition of a weak solution
of potash, the quantity obtainable from the soluble salt may be very much
increased, but the specimens thus prepared are seldom so completely bright and
pure as where water alone has been employed in its preparation.

D 2

20 Dr. Kane on the Compounds oj" Ammonia.

This salt, when heated, gives out red fumes and drops of liquid nitric acid,
, and leaves red oxide of mercury, which by a further application of the heat Is
decomposed. It is insoluble in water, and by boiling, is changed into a grey
powder, which by the lens is seen to consist chiefly of quicksilver in the metallic
state, and the liquor is found to contain some mercury, as nitrate of the red
oxide.

Grouvelle has published the results of an analysis of this subnitrate. It is
to be regretted that this chemist communicates no details as to his methods,
since without them the degree of confidence which should be given to his results
cannot be easily ascertained. He states this subnitrate, whether prepared by
water or by potash, to consist of

Black oxide, 2 atoms =. 88.6 \ .^^

Nitric acid, 1 atom iz: 11.4 J

These are the numbers given by theory, and it is very much to be condemned
that a chemist should publish that he established a formula by analysis, without
giving the details of a single experiment, or stating how close to the theoretic
numbers he had actually arrived. In fact I considered that the composition of
this body required to be determined, as if it had been perfectly untried.
The following analyses were made to determine its composition :

A. 6.305 grammes of a quantity prepared by hot water, without boiling,
gave, treated by proto-chlorlde of tin, 5.217 mercury, or 82.74 per cent.

B. 4,927 grammes of a quantity prepared by cold water, gave, when treated
by proto-chlorlde of tin, 4.086 mercury, or 82.93 per cent.

C. 6.513 grammes of a different portion was dissolved in muriatic acid, and
the liquid much diluted ; it was then decomposed by sulphuretted hydrogen,
and the sulphuret collected, carefully dried, and weighed with the filter. There
was obtained 6.312 sulphuret, or 96.91 per cent., containing 83.7 mercury.

It is abundantly evident that this salt contains some water as constitutional, for
when heated, it always yields, in addition to the red fumes, a dew of liquid
nitric acid. Assuming, therefore, the nitric acid to exist in the salt combined
with an equivalent of water, we obtain the formula nOj. ho -\- 2h^o, which
gives

Dr. Kane on the Compounds of Ammonia. 21

2ng

=

405.60

83.67

2o

"^

16.00

3.30

NO5

=:

54.14

11.17

HO

=

9.00

1.86

484.74 100.00

and which is abundantly confirmed by the reactions of the body and by the quan-
tity of mercury, which analysis indicated it to contain.

When a solution of proto-nitrate of mercury has been kept for a long time,
there are frequently deposited in it a fine lemon-yellow crystalline salt, of great
brilliancy. I have never seen the crystals larger than pins' heads, and they have
been always too closely aggregated to allow of an accurate determination of their
form. They react, in every respect, similarly to the powder just described, and
their composition was determined by the following analysis :

6.257 grammes were dissolved in muriatic acid, and the solution having been
considerably diluted, was treated by sulphuretted hydrogen. There was obtained
6.038 of sulphuret, being 96.5 per cent., containing 83.28 of mercury. Hence
the formation of these crystals is evidently owing to the very gradual deposition
of the basic salt from an acid liquor, and they are of the same nature as the
powder rapidly prepared.

It will be seen that in this basic salt the law of replacement of water by me-
tallic oxide holds, although the absolute number of atoms is quite different. It
was found that the first crystallized nitrate of the black oxide had for its formula

H^O.NOj-j-^HO;

and the yellow basic salt is now proved to be

HO.NOj+^H^O.

Moreover the second crystallized salt was shown to be, from Mltscherlich's
analyses, as well as my own,

2 NO5 + 3 i^o -{- 3 HO =

{h^o . NO5-I- 2ho} + {ho . NOj + 2h^o}.

Hence, as was before alluded to, there is great reason to suppose the second
crystallized proto-nitrate to be a double salt, consisting of the first and of the
yellow basic salt, united in the proportion of an equivalent of each.

22 Dr. Kane on the Compounds of Ammonia.

It would be an exceedingly Interesting point to determine whether the three
salts thus found to be generated by the replacement of successive equivalents of
water by metallic oxide, and vice versa, possess any simple crystallographic rela-
tion to one another. It would be highly important to determine, if the elements
thus replacing one another influence the crystalline form of the salt, for if the
metallic oxide which replaces water belong to the same isomorphous family,
there should exist identity of form amongst those salts, provided the sum of the
number of equivalents of water and metallic oxide remains the same.

If the yellow subnitrate be boiled with much water, in successive portions, it
becomes grey, but that alteration is always accompanied by the separation of
metallic mercury and the formation of pemitrate. Likewise, if potash be added
to the yellow subnitrate it becomes grey, but there is produced a mixture of
black oxide and unaltered salt. Thus no positive limit can be found indicating
the existence of a blackish or grey sub-protonitrate of really definite composition,
and I consider that Donovan and Grouvelle, who had asserted its existence, had
been misled by the properties of a mixture of black oxide or of mercury with the
subnitrate just described. Indeed Grouvelle, in his paper on the Basic and Acid
Nitrates, does not mention this grey subnitrate at all ; but Soubeiran, in dis-
cussing the composition of Hannehman's soluble mercury, asserts that it contains
the blackish subnitrate described by Grouvelle, of which he gives a formula
with numbers, which, by typographical errors, is rendered quite unintelligible,
and I have never been able to meet a notice of it elsewhere. It shall be shown,
moreover, in the next article, that the nature of Hannehman's mercury is quite
different, and hence that ground for supposing a grey sub-protonitrate to exist
can no longer hold.

I therefore conclude that there exists but one basic nitrate of the black oxide
of mercury, that which may be obtained as a lemon-yellow powder, or in minute
crystals of the same colour, and whose formula is ho.no5 4-2h^o.

VII. ON THE AMMONIACAL SUBNITRATE OF THE BLACK OXIDE OF MEBCUEY.

The study of the reaction of water of ammonia on the protonitrate of mer-
cury presents great difficulties, in consequence of the facility with which the
most important products of it are liable to change, and the consequent admixture

Dr. Kane on the Compounds of Ammonia. SS

of substances, which have their origin in the secondary decompositions of those
at first formed ; hence we find very irreconcileable statements put forward as to
the nature of the black powder, which is the more immediate product of this
action, by one chemist it being looked on as a mere oxide, by another as a sub-
nitrate, whilst the analyses of George Mitscherlich, to whose accuracy I have had
occasion so often to bear witness, showed that it did really contain ammonia and
nitric acid among its elements. I am inclined to believe that Soubeiran himself
now admits the incorrectness of his former statements, since in his Nouveau
Traite de Pharmacie, he adopts the results of Mitscherlich, without at all
adverting to the conclusions which he had advanced in his own paper on the
subject.

When, to a solution of protonitrate of mercury, there is added water of
ammonia, the precipitate, which at first is of a velvety black colour, gradually
changes, passing through various shades of grey, until it becomes nearly white,
and its state of aggregation varies in a similar manner : the portions first formed
are heavy, and rapidly deposit, but according as the colour becomes lighter, it
remains long suspended, at least the whitish portion, whilst a heavy grey powder
falls more quickly down.

Having satisfied myself, by treating portions of these precipitates, of various
shades of black and grey, with sulphuretted hydrogen, that the liquor contained,
after separation of the quicksilver as sulphuret, nitrate of ammonia neutral,
proving that an equal number of equivalents of nitric acid and ammonia were pre-
sent in the precipitate ; and having found, moreover, so great difficulty in decom-
posing the last portions as to render this method unavailable in obtaining a
quantitative result, I resolved to examine minutely the influence which the
variations in shade had on the quantity of mercury which the precipitate might
contain ; a result which very simple considerations will show, to lead to a com-
plete knowledge of the nature of the body under examination.

A dilute solution of pure protonitrate of mercury was taken, and there was
added to it a quantity of weak water of ammonia, about one-fourth of what
would suffice for its complete decomposition. A considerable mass of a fine
glossy black powder fell, which was collected on a filter, washed carefully, and
dried at a temperature not exceeding 100° F. To the liquor separated from this
first portion was added another quantity of water of ammonia, and thus another

24

Dr. Kane on the Compounds of Ammonia.

portion of precipitate obtained, differing but very little in shade, from the
first ; this having been likewise collected, the liquor was treated by a third quan-
tity of water of ammonia, by which a precipitate was produced of a dark grey
colour ; after this had been removed, the remaining liquor was completely de-
composed by an excess of water of ammonia, and thus a precipitate of a grey
colour was obtained.

There had been thus collected, from the one solution of protonitrate, four
portions of precipitate, which had gradually become lighter in colour according
as the quantity of ammonia added had increased ; numbering them in the order
in which they had been prepared, they were subjected to analysis :

A. 7.748 of No. 1, dissolved in muriatic acid, gave, by proto-chloride of tin,
6.374 of mercury, or 82.27 per cent.

B. 9,456 of No. 1 gave, treated in a similar manner, 7.791 mercury, or
82.39 per cent.

C. 6.403 of No. 2, dissolved in muriatic acid, and decomposed by proto-
chloride of tin, gave 5.410 mercury, or 84.49 per cent.

D. 7.093 of No. 3 gave, by proto-chloride of tin, 6.141 of mercury, or 86.7
per cent.

E. 7.943 of No. 4 gave, similarly treated, 7.067 mercury, or 88,97 per
cent.

These results, tabulated, are :

Order of Formation.

Colour.

Mercury in 100.

1

2
3

4

Fine black.
Greyish black.
Deep grey.
Grey.

82.27. 82.39
84.49
86.70
88.97

The result of Mitscherlich's analysis are shown here, in order to understand
how far his numbers are reconcileable with mine ; he obtained

98.73

Mercury

=

85.57

Ammonia

^=

2.46

Oxygen

=:

3.38

Nitric acid

— ~"

7.32

Dr. Kane on the Compounds of Ammonia. 25

Hence he deduced the formula NO5 . NH3 + 3 ugo, which should give
Mercury = 86.46

Ammonia

—

2.43

Oxygen

=

3.43

Nitric acid

==

7.68

100.00

In any ordinary case, where the error, unavoidable in manipulation, and to
which the collection of mercury in the metallic form by proto-chloride of tin, is
peculiarly liable, should necessarily tend to diminish the quantities obtained, and
consequently reduce the experimental, below the theoretical numbers, his analysis
should be considered as completely establishing the formula ; but here, there are
other circumstances which require to be taken into account, and which will lead
us to an opposite conclusion.

It is evident that in the preparation of Hannehman's soluble mercury, there
is a tendency to error from the intermixture of a greyish material, and where
the whole, or nearly the whole of the solution has been precipitated at once, this
intermixture is unavoidable ; hence it is only the first portions that can be
obtained of the fine black colour which characterizes the pure substance. Now it
has been fully proved, that according as the decomposition proceeds, the quantity
of mercury in 100 increases in proportion as the colour becomes less deep ; and
hence the error, in estimating the composition of this body, must be opposite in
direction to what generally occurs, and must tend to render the proportion of
quicksilver above the truth. Thus, the result of Mitscherlich's theory is almost
precisely that obtained in my analysis of specimen No. 3, which was not black,
but dark grey ; and Mitscherlich himself indicates the powder which he analyzed
as grey ; he says, " Nach dem Trocknen ist die Farbe des Pulvers grau und es
darf sich kein metallisches quecksilber mechanisch herausdrucken lassen ;" and
also, if the solution which I employed had been precipitated all at once, there
should have been a dark grey precipitate, and its composition should have been
the mean of the composition of the powders given by the four equal and succes-
sive additions of water of ammonia, which average would almost coincide with the
result which Mitscherlich obtained. So marked is the production of this whitish
matter, that Soubeiran collected and analyzed it, and concluded from his results
that it was an ammonia sub-protonitrate with the formula no^ . NH3 -\- 4 ugo. He

VOL. XIX. E

26 Dr. Kane on the Compounds of Ammonia.

now appears to have tacitly abandoned this opinion, and properly, for there is no
doubt but that this white powder is a compound of red oxide, and is one or other
of the bodies which have been already described in this paper. When treated with
iodide of potassium it gives a reddish yellow powder, and it dissolves gently in
muriatic acid, without the disengagement of any red fumes indicating a transition
to a higher degree of oxydation. At the same time that this white per-
compound is formed there is always some metallic mercury set free, which can
generally be recognized in the grey specimens by using a lens, but the quantity
is seldom so large as to allow of its mechanical separation by the application of
pressure only.

From all these circumstances it is evident, that the specimens of Hannehman's
soluble mercury, which are of the finest black in colour, are generated under the
circumstances most favourable to their perfect purity. And as all the chances of
error, except that of analysis, tend to increase the value of mercury, it results,
that where the error of manipulation affects all equally, the lowest estimate
should be that nearest to the truth. Hence I feel justified in assuming, with
some confidence, that the numbers 82.27 and 82.39 are those by which the true
formula may be established, and we must therefore consider Hannehman's solu-
ble mercury to be the ammonia sub-nitrate,

NHg.NOj-f 2h^o,

which should give 82.29 mercury per cent., and evidently corresponds to the
yellow subnitrate formed by water, which has been proved to be

HO.NOj-t- 2Hg-o.

Note It has been very gratifying to me to find that Ullgren, who undertook, under the direc-
tion of Berzehus, to control the analyses contained in my first memoir on the Ammonia Compounds,
has verified, even to the most minute point, all the results which I then brought forward. I did not
receive the Jahresbericht for 1837, containing Berzelius's observations, until this first part of the
present memoir had been partly printed, and hence could not earlier introduce any note of the sug-
gestions which he makes. In Germany or Sweden it will not be necessary to adopt the word
amidogene, as the word amide harmonizes better with chlor. cyan. iod. and others ; but in English
and French it is preferable that there should be a termination, as in cyanogene and oxygene, the
final ide being in these languanges restricted to binary compounds. I shall, however, for the future
adopt his terms of amidides and amidurets, as I consider them still more expressive of the nature of
the bodies, and more directly formed from amidogene than the word amides.

Dr. Kane on the Compounds of Ammonia. 27

PART II.

ON THE AMMONIACAL COMPOUNDS OF COPPER AND ZINC, AND ON THE BASIC
CHLORIDES AND SULPHATES OF THOSE METALS.

In developing the real nature of the series of quicksilver combinations which
contain ammonia or its elements, it was found, that the quantity of the metal pre-
sent, from its large equivalent number, preponderated so considerably over that
of the other constituents of the various bodies analyzed, as to render the absolute
exclusion of all theoretical views but that ultimately found correct, extremely
difficult, and it was consequently my object, from the commencement, to re-
examine in detail the ammonia compounds of certain metals with smaller atomic
weights, in order, by an accumulation of numerical facts, to lay the foundation
for a true theory of this class of combinations.

The group of metals, the compounds of which are discussed in the present
section, is one exceedingly natural, and possessed of characters, particularly in
relation to ammonia, which, when compared with those exhibited by quicksilver,
should lead the chemist to expect the most remarkable results. Whilst the pre-
cipitates given by quicksilver solutions with ammonia are insoluble in an excess
of the precipitant, those given by the metals now to be examined easily redissolve,
and the peculiar character of the zinc compounds redissolving in an excess of the
fixed alcalies, presents a point of contact, the study of which must be of the
highest interest.

It will be found that I have connected with the analyses of the ammonia
compounds, the examination of a number of basic salts, and of other substances
which do not contain ammonia. Generally speaking, I was obliged to occupy
myself with these bodies, in order to elucidate difficult passages in the history of
the ammonia compounds, and though I have often apparently wandered from
my way for the purpose of obtaining either a more elevated point of view, or a
more extensive basis for analogical deductions, yet as the discovery of such
bodies will be found, I trust, to present so many new facts in science, the proofs
of their existence and composition will be given in this memoir, whilst I shall
avoid as much as possible entering into any speculations concerning their real

E 2

^ Dr. Kane on the Compounds of Ammonia.

nature, as the views to which I have been led by these and previous investigations
will require to be developed in a distinct section.

I. OF THE AMMONIACAL SULPHATE OF COPPER.

The composition of this body has been given by Berzelius, and I have found
■ his result to be rigidly correct ; I shall therefore not bring forward any details
of my own analyses, but assume as true the formula

SO3 . CMO + 2 NH3 4" HO.

This salt crystallizes in right-rhombic prisms, which are complex macles, and
I have not been able to determine the form really belonging to it. The crystal
would appear to be produced by a number of rhomboidal plates, uniting at the
edges, and leaving very often the centre hollow, but destitute of any other definite
cleavage or direction.

When we consider the manner in which this salt is formed, we cannot look
upon the oxide of copper as being united with the sulphuric acid. On adding
water of ammonia to a solution of sulphate of copper, the action consists in the
gradual separation of more and more sulphuric acid from the copper, and when,
by an excess of alkali, the precipitate is redissolved, there is nothing in the re-
action tending to make the oxide of copper go back again, but rather the
reverse. Hence I will apply to this body the formula

(NH3 . ho) SO3 4" (nHj . cMo) ;

that is, I consider it as being sulphate of ammonia, with which is united oxide of
copper and as much more ammonia.

When this substance is exposed to the heat of an oil-bath, or of a carefully
regulated spirit-lamp, it gives out ammonia and water, and if the heat be not
carried beyond 300°, there remains a fine apple-green powder. When this
powder is further heated the result varies according to the manner in which the
heat is applied ; if rapidly, there is given out ammonia and sulphate of ammonia,
whilst sulphate, with oxide and suboxide of copper, remain behind ; but if slowly,
and that it be not carried beyond 500° F., the remainder of the ammonia can be
gotten rid of, and sulphate of copper quite pure will remain behind, there being
no water disengaged in this latter period of the process.

Dr. Kane on the Compounds of Ammonia. ^

To determine the exact nature of this decomposition, the following experi-
ments were made :

A. 1.969 grammes of crystals were reduced to fine powder, and heated, until
water ceased to be given off. It was in the state of a fine green powder, which
weighed 1.545, or 78.47 per cent.

B. 4.921 of finely powdered crystals were heated in a precisely similar man-
ner ; there remained 3.854, or 78.32 per cent.

C. 5.042 grammes treated similarly, gave 3.921, or 77.77 per cent.

D. 2.991 grammes were heated very cautiously, until all ammonia and water
were expelled ; a mere trace of sulphate of ammonia had formed, and there
remained 1.947 of sulphate of copper, or 65.1 per cent., which redissolved almost
totally in water.

The theoretical composition of the ammonia sulphate is :

SO3- = 40.16 32.58

CMC = 39.60 32.22

2NH3 = 34.28 27.89

HO = 9.00 7.31

123.04

which by heat evidently breaks up into

CMO.SO3 = 64.80 ,

NH, = 13.95

100.00

HO =

7.31

NHj =

13.94

78.75 21.25

Thus it is demonstrated by experiment, that by the first action of heat all
the water of the ammonia sulphate is expelled with half of the ammonia, and
there remains the green powder, consisting of sulphate of copper and one equiva-
lent of ammonia, which last, by a further application of the heat, may be driven
off. I endeavoured by a cautious application of heat to separate the water without
losing the ammonia, but found it impossible to effect it. In this case, therefore,
the copper does not exist as amidide, but on referring to the formula

(NH3 . ho) SO3 + (NH3 . CMO)

it is evident that the sulphuric acid is inserted between two equivalent groups.

30 Dr. Kane on the Compounds of Ammonia.

which are related to one another, through the replacement of hydrogen by copper;
the acid had been in the crystals more immediately united with that which repre-
sents oxide of ammonium, but on the application of heat, the previous affinities were
subverted, and, the acid remaining in union with the group of more permanent
constitution, the elements of the ammonia and water are set free, the formula of
the green powder being

(NH3.CM0) . SO3.

Graham had already pointed out, that when ammoniacal gas is passed over
sulphate of copper at a high temperature, but half an equivalent is absorbed, and
hence he hazarded the idea, that the resulting compound might be analogous to an
ordinary double sulphate, as

CUO . SO3 -\- (NH3 . CUO) SO3

corresponding to

CMO . SO3 -j- (NH3 . ho) . SO3.

This body can likewise be obtained when the action of the heat on the ammo-
niacal sulphate of copper is kept below 400° F. ; there are given off three-fourths
of the ammonia with the water, and there remains 2(503. cmo)-1-nh3.

It is well known that the sulphate of copper in the cold absorbs two and a
half equivalents of ammonia, and the resulting body warmed loses two, corrobo-
rating fully the view originally struck out by Graham, and to which my results
lend considerable support.

If the apple-green powder be exposed to the action of damp air it gradually
becomes blue, from the absorption of water, but the process is very slow ; if, on
the other hand, the powder be moistened with a small quantity of water, much
heat is evolved, and a full blue colour produced ; if there be any water in excess
it may be removed by cautious evaporation at a temperature below 100° F., but
a large excess produces complete decomposition. To ascertain the quantity of
water which in such case combines with the green powder, 2.820 grammes were
very slightly moistened, and the excess of water removed by a temperature of
80°. The dry blue powder remaining weighed 3.605, or the green powder had
taken 27.8 water per cent., corresponding to three equivalents, and hence the
formula NH3 . cmo -\- sOj becomes probably (nHj. ho.) SO3 -f- (cuo + 2ho).

By the results of the action of a large quantity of water on this green powder

Dr. Kane on the Compounds of Ammonia. 31

are formed sulphate of ammonia, the soluble ammoniacal sulphate of copper, and
a bluish green basic sulphate not containing ammonia. In order to understand
the reaction it was necessary to analyze this latter :

A. 3.710 grammes gave, dried, a brown powder 3.106, corresponding to
16.28 water per cent. ; this brown powder, dissolved in muriatic acid, and pre-
cipitated by chloride of barium, gave sulphate of barytes 1.766 grammes, corres-
ponding to 16.36 of sulphuric acid per cent.

These proportions approximating to those of the common basic sulphate,
another analysis was made with more complete accuracy :

B. 5.040 grammes of another specimen gave, dried, a brown powder 4.275,
which, dissolved in muriatic acid, and precipitated by chloride of barium, gave
2.678 of sulphate of barytes ; hence the composition

Theory.

Experiment.
A. B.

SO3 = 40.16

17.13

16.36 17.26

4cMO = 158.40

67.52

4 HO = 36.00

15.35

16.28 15.18

234.56 100.00

Thus the basic sulphate resulting from this reaction is the ordinary one, and
the analyses given confirm the formula SO34- 4 0^0 + 4 ho, which had been in
some degree doubtful. The decomposition can be thus explained, the water
being omitted for the sake of simplicity :

3(303. NH3) = 3nh3-|- 3SO3

S03-J-CMO-J-2NH3 = 2NH3-I- CMC-}- SO3

SO3-I-4CMO = 4CMO+ SO3

5(nh3.cmo) SO3 5nh3+5cwo-|-5so3

When this salt is heated it does not lose water until the temperature rises to
above 300°, but then it loses all, and the brown powder, if exposed to the air, re-
absorbs water slowly ; if moistened, it combines with the water rapidly, evolving
heat, and regains its original proportion, and also its proper colour.

32 Dr. Kane on the Compounds of Ammonia.

II. OF A NEW BASIC SULPHATE OF COPPER.

Having found, as In the preceding instance, that by the action of water on
the ammoniacal compounds of the metals under examination, there was gene-
rated a series of basic salts, I became desirous of re-examining some of those
already known, particularly in order to determine the function of the water
which they constantly retain. For this purpose I prepared several portions of
the sub-sulphate of copper, and I soon perceived, that, according to the quantity
of alkali employed in the precipitation, where potash had been used, there were
two distinct precipitates produced, the one of the bluish green generally de-
scribed, the other of a clear grass green, resembling that of hydrated oxide of
nickel. When ammonia was employed, the former alone was produced, and the
formation of the latter I found to occur where the whole of the copper had been
thrown down, but the liquor had not yet begun to react alkaline. It is singular
that this basic sulphate had not been observed by any of those chemists who
examined the common species. I found it in the first instance accidentally, but
I have since seldom failed in preparing it completely pure.

It was analyzed as follows :

A. 7-124 grammes were dried until all traces of watery vapour ceased ; there
remained a brown powder 5.614, or 78.8 per cent. This was dissolved in
muriatic acid, and precipitated by chloride of barium ; there was obtained
1.851 of sulphate of barytes, indicating of sulphuric acid 8.94 in 100 of green
powder.

B. 3.877 grammes were exposed to a temperature of 300° F. in an oil-bath,
until it ceased to give off water, it then weighed 3.460. The oil-bath having
been removed, the drying was completed by the spirit-lamp, at a temperature
of about 500°, after which there remained 3.042. There had been thus driven
off:

In first period = 10.76 per cent.

In second period = ] 0.52

Water in 100 of powder = 21.28
The composition resulting is :

Dr. Kane on the Compounds of Ammonia. 33

Theory.

Experiment.

, A. B

S03

= 40.16

8.83

8.94

8cMO

= 316.80

68.00

12ho

= 108.00

23.17

21.20 21.!

464.96

100.00

When the brown mass resulting from the desiccation of this salt is moistened,
it evolves much heat, and combines with a large quantity of water, forming a
green mass of a livelier colour than it originally possessed, and becoming always
of something more than its former weight. The quantity of water with which
it combines varies from 23 to 24 per cent., and hence I attribute the slight defi-
ciency in water shown by analysis, to some of the chemically combined water
having been expelled by the very moderate heat applied in drying the precipitate
for analysis.

It will be remarked that by 300° F. exactly half of the water is expelled ;
hence there must be some difference in the degrees of affinity with which the
two quantities are retained. From these considerations I am disposed to give to
the formulae for these basic sulphates the following form :

or

cuo . SO3 . cwo -\- 6 (cMO -\- 2 ho),
cuo . SO3 . CMO -j- 6cuo 4" 6ho -{- 6ho ;

the second group of equivalents of v/ater being expelled by a temperature lower
than that necessary for the separation of the remainder.

Thompson had long since pointed out the existence of a basic sulphate of
copper containing two equivalents of oxide, and this in its hydrated condition he
states to retain two equivalents of water. When this is added to those above
described, the series of basic salts follow from the neutral sulphate in the follow-
ing: order :

'&

Real neutral sulphate = cm.o + SO3

Do. with saline water = cuo . ho -f- SO3

First basic salt, dry =: cmo . cuo -j- SO3

Do. do, hydrated = cmo . cuo + SO3 -|- 2 ho.

VOL. XIX. F

34 Dr. Kane on the Compounds of Ammonia.

Second basic salt, dry = (cmo . cuo) sOg-f- 2cmo

Do. do. hydrated = (cmo . cmo) sOg-f- 2cmo-(-4ho

Third basic salt, dry = (cMo . cwo) SO3 -\- 2cuo -\- 4 CMO

Do. do. hydrated = (cmo . CMo) SO3-}- 2cmo-4-4cwo-|-6ho-j-6ho

III. OF THE AMMONIACAL CHLORIDE OF COPPER, AND OF THE COMPOUNDS

DERIVED FROM IT.

When water of ammonia is added to a solution of chloride of copper, the
precipitate which is at first formed redissolves by an excess, and a purple liquid
is produced. If this be evaporated there is deposited a bluish flocculent precipi-
tate, and the liquid loses its fine purple colour, and becomes bluish green. If in
this condition the solution be set aside to crystallize, the double chloride of cop-
per and ammonium is deposited, which Henry and Cap* have mistaken for the
ammonia-chloride, and they have consequently assigned to the latter body a con-
stitution belonging to one of a totally different nature, and which had resulted
from its decomposition.

In order to obtain the ammonia-chloride pure and crystallized, a solution of
chloride of copper must be taken, nearly saturated when hot, and a stream of
ammoniacal gas passed through it, until the precipitate which first appears has
been totally redlssolved : the mass is kept almost boiling by the heat evolved in
the condensation of the ammoniacal gas, and when set aside to cool, the ammonia
chloride is deposited in small, but well-marked, octohedrons, or square prisms
with pyramidal summits, of a deep blue colour. These crystals must be dried
with great care between folds of filtering paper, without the aid of heat, and in a
room free from any acid fumes ; even with the greatest caution it is difficult to
prevent the outer portion of the mass from acquiring a green tinge, arising from
loss of ammonia, which will affect in a corresponding degree the analytical
results.

Although the existence of this body had been generally admitted by chemists,
yet no analysis of it had appeai'ed until that by Henry and Cap ; and as it is
necessary to disprove their erroneous statement, I will detail those which I
performed.

* Journal de Pharmacie, December, 1837.

Dr. Kane on the Compounds of A^nmonia. 36

A. 5.823 grammes of crystals, slightly tarnished, were dissolved in dilute
muriatic acid, and treated by sulphuretted hydrogen, until the copper was com-
pletely thrown down. The sulphuret of copper was then separated by the filter,
and the liquid, with the washings, evaporated in a water-bath. There were
obtained 5.211 of sal ammoniac, corresponding to 89.49 per cent., containing
28.83 of ammonia.

B. 4.700 grammes of crystals, dissolved in muriatic acid, and precipitated by
caustic potash in excess, gave oxide of copper 1.692, or 36 per cent., containing
28.73 per cent, of copper.

C. 3.594 grammes of crystals were dissolved in an excess of pure nitric acid,
and precipitated by nitrate of silver ; the chloride of silver formed, collected,
well washed, dried, and fused, weighed 4.672, or 130.5 per cent., containing
32.19 chlorine.

Hence there is the formula cmc^-^- 2NH3+ ho, giving

Theory.

Experiment.

cl = 35.42

32.11

32.19

CM = 31.60

28.65

28.73

2NH3 = 34.28

31.08

28.83

HO = 9.00

8.16

and loss

10.25

110.30 100.00 100.00

There occurred here a loss of ammonia, which evidently arose from the surface
of the crystals having become a little tarnished, and likewise from that which takes
place in all evaporations of ammoniacal solutions. Nevertheless, the theoretical
and experimental results agree so closely, that there cannot be any doubt of the
truth of the formula adopted ; it resembles in every respect that of the ammonia-
sulphate, and in accordance with the principles explained in the description of
that substance, I consider the chlorine to exist in the crystals as sal ammoniac,
and the rational formula to be

NH3 . HC^-f- CMO.NHg.

When these crystals are exposed to heat, they melt, and ammonia, with watery "
vapour, is disengaged ; I could not succeed in eliminating water without losing
ammonia at the same time ; in that respect therefore it resembles the ammonia-
sulphate. By a temperature of 300° all the oxygen is separated as water,

F 2

36 Dr. Kane on the Compounds 0/ Ammonia.

together with one-half of the ammonia, and there remains a fine apple-green
powder, resembling verymuch thatfrom the sulphate, and containing the remainder
of the ammonia, with all the chlorine and the copper. Thus, 4.064 of the
crystals were heated in an oil -bath, until the disengagement of water and ammonia
had ceased; the green powder remaining weighed 3.109, or 76.5 per cent.
According to theory, the residue C/.CM.NH3 should weigh 76.3 per cent.;
0H.NH3 having been expelled. When this body c^.CMNHg is exposed to a higher
temperature it is decomposed, sal ammoniac sublimes, and sub-chloride of cop-
per remains ; there are likewise azote and ammonia given off. The ammonia is
retained by so powerful an affinity, that it cannot be expelled by any temperature,
without the substance being totally decomposed.

The existence of this body was noticed by Graham, as resulting from the
absorption of ammonia by chloride of copper at a high temperature. At ordi-
nary temperatures chloride of copper absorbs three equivalents of ammonia, of
which two are easily expelled, but the third is retained more powerfully, and con-
stitutes with the chloride the body just described. We may therefore consider
the ammonia-chlorides, formed by water, and by dry ammonia, as corresponding
compounds ; thus,

NH3CMC/-I- NH3. HO.

NH3 CMc/ 4" NH3 . NH3 ;

an equivalent of water in the one replacing an equivalent of ammonia in the
other, and both, when heated, giving the body NH3.CM.C/, by losing respectively
NH3.H0 and 2NH3.

IV. OF A NEW BASIC CHLORIDE OF COPPER.

When the body cl. CMNH3 is treated by water it is decomposed ; there is dis-
solved the ammonia-chloride of copper just described, and a quantity of sal ammo-
niac, and a bluish green powder remains, insoluble in water, and not containing
ammonia. When heated it gives off water, and becomes brown ; but exposed to
the air, it gradually regains a certain quantity of water. Its analysis was effected
as follows :

A. 1.901 grammes, dried over a spirit-lamp, gave a chocolate brown powder,
which weighed 1.522 grammes, corresponding to 80.06 per cent. This 1.522

Dr. Kane on the Compounds of Ammonia.

37

were dissolved in nitric acid, and precipitated by nitrate of silver. The chloride
of silver produced v?eighed 0.964, or 50.71 per cent, for the green powder, and
containing 12.51 of chlorine.

B. 2.678 grammes, dried over the spirit-lamp, gave, of brown powder, 2.143
or 80.02 per cent., which was boiled in a strong solution of caustic potash, and
the oxide of copper washed, until the liquors were perfectly free from traces of
free alkali; there was obtained 1.891 of oxide of copper, or 70.61 in 100 of
green powder, and containing 56.31 of metal.

Hence the formula cucl-^ AiCUo-\-6ii.o results, which gives

Theory.

c/ = 35.42

12.68

Exper
A.

12.51

iment.
B.

5cM = 158.00

56.55

56.31

4o = 32.00

11.45

Quo = 54.00

19.32

19.94

19.98

= 6.CWC/.NH3-|-4.HO.

279.42 100.00

cud -f- 4 cuo
4c/h-|-4nh3
cwc^ + 2nh3
The coincidence is quite satisfactory.

This oxychloride differs therefore from that analyzed by Berzelius, in con-
taining, to the same quantity of chloride of copper, one atom more of oxide of
copper, and two more of water. The relation between this and the ordinary
oxychloride, can be very well shown, by arranging the formulae of the two in the
following manner :

Common oxychloride =z cud. cuo + 2(cuo + 2 ho)
New oxychloride = cud. cuo + 3(cmo -j- 2 ho)

V. OF A SECOND NEW BASIC CHLORIDE OF COPPER.

Having prepared, during the course of these researches, a great number of
specimens of Brunswick green, I remarked that some, which had been produced
by a less perfect precipitation by the alkali employed, were of a much less brilliant

38 Dr. Kane on the Compounds of Ammonia.

colour, and differed markedly in their aspect from the ordinary oxychloride. I
consequently submitted these specimens to an examination, from which it results,
that there may be prepared, by the action of a base on an excess of solution of
chloride of copper, two oxychlorides ; that generally formed being the common
Brunswick green, with the formula cmc^-|-3cmo + 4ho, but that when a still
smaller quantity of base is employed a different substance is produced.

This new oxychloride resembles remarkably in its aspect that last noticed
and the sub-sulphate, but can be at once distinguished from Brunswick green by
its pale colour ; heated it gives out water, and becomes first brown, and leaves
finally a black powder. When this powder is moistened it slakes, evolving great
heat, and becoming of a very brilliant green colour, brighter than that of Brunswick
green. By heat the water reabsorbed may be again expelled, and so repeatedly,
without total decomposition taking place.

The analysis of this oxychloride was conducted in the following manner :

A. 12.390 grammes, dried over the spirit-lamp, gave a black powder, weigh-
ing 9.725, or 78.49 per cent. These 9-725 were moistened with water, and
allowed to assume throughout the rich green colour ; the excess of water, which
was very slight, was removed by a temperature of 100° F., when the green pow-
der was found to weigh 11.670, having absorbed 16.78 per cent, of water.

B. 5. 155 grammes ofthe green powder, thusformed, were keptata temperature
of 280°, until it ceased to give out watery vapour ; it had become chocolate
brown, and weighed 4.584. It had lost therefore 11.08 per cent, ofthe water
which it contained.

C. 6.185 grammes of the same green powder, dried at 500° F., gave 5.144
of black powder, or 83.17 per cent. ; hence it had lost 16.83 water.

D. The 4.584 of B was dissolved in dilute nitric acid, and precipitated by
nitrate of silver, the chloride was collected, washed, and dried, it then weighed
4.099, corresponding to 79-51 per cent., and containing 20.61 of chlorine in the
bright green condition.

E. The 5.144 of C was dissolved in dilute muriatic acid, and treated with
boiling solution of potash, the oxide of copper which separated was well washed,
and collected on a filter, and subsequently ignited. There was obtained 4.112,
corresponding to 79-93 per cent., and containing 63.78 of copper.

Dr. Kane on the Compounds of Ammonia. 39

It consequently follows, that the dry oxychloride is capable of uniting with
water in three different proportions ; thus,

In pale green powder 100 oxychloride take 27-4 water.
In bright green do. 100 do. 20.2

In brown do. 100 do. 6.9

But 6.9, 20.2, and 27.4 are nearly as 1, 3, and 4.

From C, D, and E it results, that the dry oxychloride has the composition

Theory. Experiment.

cl = 35.42 24.22 23.59

3cw = 94.80 64.84 63.78

2o = 16.00 10.94 10.77

146.22 100.00 98.14

From the proportion of water, it is evident that the dry oxychloride combines
with one, three, and four equivalents in the three different conditions in which
it exists, and that hence there are the formulas

1. CUCl-\- 2 CMC.

2. CMc/-|- 2cMo4-HO.

3. cucl-\-2cuo-\-ZvLO.

4. cmc/4"2cmo-1-4ho.

The discovery of this body leads us to some very interesting relations, in this
class of substances ; thus, this one is evidently the simplest oxychloride, being
related to the crystallized hydrated chloride, as

CMC^-|-2cMO to cmc^-j-2ho;
and the first atom of water being so strongly retained, points out the passage
through

CMd-|-HO + 2CMO

to

cud + CMO -\- 2 CMC,

the ordinary oxychloride deprived of water, but both combining with additional
quantities of water, and acquiring the brilliant green colour by which they are
respectively characterized; and the condition in which this salt retains most
water, gives to it a composition which brings to mind the crystallized hydrates of
many chlorides of the same class, as

40 Dr. Kane on the Compounds of Ammonia.

CMc/-|- 2cMO -|- 4ho.
compared with

ca.c/ -j- 2 HO -|- 4 HO.
and

Ugcl -|- 2 HO -J- 4 HO.

I will have occasion to recur to these bodies when speaking of their analogues
among the compounds of zinc.

The other new oxychloride of copper, in its dry condition, is analogous to
the chlorides which crystallize with four atoms of water, as iron and manganese.

When this oxychloride, in a dry condition, is exposed to a current of ammo-
niacal gas, an absorption takes place, with the evolution of some heat; but
although the current may be continued long after the mass shall have become
cold, yet no alteration of colour occurs, the mass remaining brown. If the
ammonia be passed over the oxychloride in its hydrated condition, it becomes
blue, water is given out, and the whole is evidently decomposed ; and if the
brown mass be wetted, there is formed a hydrated ox;j^chloride and a blue liquor,
showing total decomposition.

Dry ammonia, acting on dry oxychloride, gave the following results :

I. 4.801 of oxychloride absorbed 0.504 ammonia, or 10.4 per cent.

II. 3.970 of oxychloride absorbed 0.436 ammonia, or 11.1 per cent.

These numbers give, for the proportion absorbed, almost exactly one equiva-
lent ; and the resulting brown mass has evidently the formula

cud -j- 2cMO -j- NH3.

According to which 100 should have absorbed 11.8 of ammoniacal gas.

Now putting NH3 = ukd, the relation of this body with those last noticed
becomes very remarkable, as we must contemplate the series

cud -\- 2CM0 -j- CMO

cud -\- 2 cuo -\- HO
cud -\- 2cuo -\- nkd.

in which cm and h, o and Arf mutually replace each other.

■ Dr. Kane on the Compounds of Ammonia. 41

VI. OF THE AMMONIA-OXIDE OF COPPER.

I had examined very frequently, and under a great variety of circumstances,
the precipitates which are produced by the action of ammonia on solutions of the
sulphate, nitrate, and chloride of copper, in order to determine whether com-
pounds similar to those generated under like circumstances with solutions of the
quicksilver salts, could be produced. In all such cases, I found the precipitates
to be basic salts following certain laws of composition, and not containing
ammonia as an element. Indeed a similar result might have been anticipated
from what has been already shown in this paper ; namely, that the insoluble
ammonia-copper compounds are all decomposed by water, giving soluble ammonia
compounds and a basic salt destitute of ammonia in its composition.

However, on one occasion, on treating a solution of chloride of copper with
ammonia, I obtained a precipitate of a remarkably fine blue colour, approximating
to that of the hydrated oxide, or of the refiner's verditer. In the one operation
I obtained a sufficient quantity of it for examination, and did not since study
the exact circumstances favourable to its production, the specimen I had pro-
cured being sufficient to supply my wants, but proceeded at once to determine its
properties and composition.

This blue powder is not affected by repeated washings, to which I subjected
it, suspecting that its ammoniacal constituent might result from sal ammoniac
being attached. It may be heated to 300° F. without being changed, but above
that temperature it is rapidly decomposed with a hissing noise. It yields much
ammonia, azote, and a large quantity of water, and the residue is red coloured,
consisting of a mixture of sub-oxide of copper and of copper in the metallic state.
There is no sublimate of sal ammoniac.

Dissolved in dilute nitric acid, this powder gives no precipitate with nitrate of
silver. Its elements are therefore ammonia, water, and oxide of copper. The
following quantitative analysis was made :

A. 3.410 grammes were dissolved in muriatic acid, and the solution decom-
posed by sulphuretted hydrogen. The sulphuret of copper having been removed,
the liquor and washings were evaporated to perfect dryness in a water-bath, and
sal ammoniac, weighing 1.634, was obtained, corresponding to 15.70 per cent, of
ammonia.

VOL. XIX. O

48 Dr. Kane on the Compounds of Ammonia.

B. 3.752 grammes were dissolved In dilute muriatic acid, and decomposed by
boiling with caustic potash. The oxide of copper precipitated was collected and
burned with the filter, it weighed 2.146 or 57.19 per cent.

The difference is evidently the water, and hence the formula

3cMo-{- 2nh3-{-6ho,
which gives

Theory.

Experiment.

SCMO

= 118.80

57.37 •

57.19

2NH3

= 34.28

16.55,

15.70

6 HO

= 54.00

26.08

27.11

207.08 100.00 100.00

This result comes sufficiently close to allow of the formula being adopted, but I
will not now attempt to arrange it after any theoretical idea. The substance
evidently belongs to the same class as the fulminating oxides of silver and mer-
cury, but is still inferior in detonating power even to the latter.

VII. OF THE AMMONIACAL NITRATE OF COPPEK.

This salt, the existence and some characters of which have been already
noticed by chemists, may be prepared very simply by the same process as that
described under the head of the Ammonia-Chloride of Copper, substituting
nitrate for the chloride. It crystallizes in a confused mass of minute octohedrons,
whose form is with difficulty ascertained. It dissolves easily in water, and on the
addition of an acid it yields the ordinary basic nitrate of copper.

When heated, this salt is decomposed in a very remarkable manner : traces
of ammonia are evolved, but no water if the salt had been completely dried ;
black points (oxide of copper) make their appearance, the salt fuses, and if the
heat be continued, suddenly explodes with a hissing noise, and the formation of a
great cloud of gaseous matter, whilst the Inside of the vessel remains lined with
oxide of copper. Several attempts were made to manage the decomposition, so
as to determine the quantity of the oxide left behind, but without avail ; even
when the powdered salt was covered in a platinum crucible, with strong nitric
or muriatic acid, and then heated, the acid boiled away, and the residual salt
underwent its explosive change, as if no such means had been applied.

Dr. Kane on the Compounds of Ammonia. 43

No quantitative analysis of this body has been recorded, and as from the
remarkable circumstances of its decomposition by heat, it is of great importance
that its composition should be accurately known, the following analysis was
made :

5.982 grammes were introduced into a globe with a strong solution of potash ;
from this globe there passed a bent tube, dipping into a tall jar containing water
with muriatic acid. The mass in the globe was boiled until all the ammonia had
been set free, and more than one-half of the liquor had distilled over. The fluid
in the jar was then carefully evaporated in a water-bath to dryness, and the sal
ammoniac obtained was found to weigh 4.717 or 78.85 per cent., containing
25.23 of ammonia.

The liquor remaining in the globe was diluted with water, and, when cold,
filtered ; the oxide of copper remaining weighed 1.856 grammes, corresponding
to 31.03 per cent.

These numbers give the formula cwo.no5-|"2nh3, by which there should
have been obtained

Experiment.
31.03

Theory.

cuo =

39.60

30.94

NOj =

54.14

42.28

2nh3 =

34.28

26.78

25.23

128.02 100.00

Since during the process for the formation of the ammonia-nitrate, the first
stage consists in the production of the ordinary subnitrate of copper, the nitric
acid in the ultimate product must unavoidably be considered as united with
ammonia, and hence the above empirical formula must, in assuming a rational
form, become

(NH3.H0) NO5 -j- CMNHj,

from which it follows, that the copper in this compound is united with amido-
gene.

It is now easy to explain the various circumstances in which this body differs
from the similarly constituted ammonia-chloride and sulphate just described. By
the application of heat, the evolution of ammonia and water cannot occur, since
the second group cmnHj is not of a nature precisely to replace it. The trace of

g2

44 Dr. Kane on the Compounds of Ammonia.

ammonia which is evolved arising probably from a partial expulsion of hnh^ by
CMNH^. The salt resists decomposition almost completely, until the nitrate of
ammonium melts, and commences to be decomposed, when the sudden burning
of the amidogene and copper, in the oxygen of the nitrous oxide formed, gives
rise to the explosive reaction which distinguishes this body.

In order to place in a still clearer point of view the peculiar nature of this
body, I shall refer briefly to some observations which I have made on the
ammonia-nitrate of silver discovered by George Mitscherlich. On analyzing it
he obtained the formula nOj-I- A^o + 2NH3, and I have verified his result,
having obtained from it 52.46 of silver, whilst his formula indicates 52.83.
This formula is evidently quite similar to that given by the ammonia-nitrate of
copper ; and here also the action of the ammonia consists in the separation of
the oxide of silver in the first stage and its solution afterwards, when the ammo-
nia has been added in excess. Giving to the formula, therefore, its true rational
construction, it becomes

and the propriety of this view is supported by a very curious reaction of this
body, which George Mitscherlich does not appear to have observed.

When heated this salt fuses very readily, and gives out a mixture of azote
and ammonia, whilst silver is separated in the metallic form, and by rolling about
the fused mass in the tube, a mirror surface is produced, as beautiful as that ob-
tained by nitrate of silver with ammonia-aldehyd. When the tube cools, the
melted mass solidifies, and is found to be nitrate of ammonia. This I consider
to be a convincing proof of the existence of an amidide of silver in this salt ; its
easy reduction, the simultaneous liberation of the elements of amidogene, and the
nitrate of ammonium being set free, unaltered, if the heat be not raised too high,
render the peculiar nature of this body too remarkable to be mistaken. Now in
the analogous copper compound, the amidide of copper is not so easily decom-
posed, its elements remain united until the nitrate of ammonium begins to yield,
and then a rapid combustion, alike of copper and amidogene, takes place in the
oxygen of the nitrous oxide formed.

Although the ammonia-copper element of the ammonia-sulphate of copper
cannot be freed from water, yet in the silver salts, the ammonia-sulphate, and its
congeners, which, in the hands of Eilard Mitscherlich, have become one of the

Dr. Kane on the Compounds of Ammonia. 45

most beautiful instances of isomorphism, crystallize without that equivalent of
water, and the emgirical formul£e

S03 + Ag-0 + 2NH3

cro3 + A^o4-2NH3
seo3 + Ag-o+2NH3

assume from the above principles the form

so,

-|- NHj.HO + Ag'NHj.

'3

cro

3

sec.

Of these I have re-examined only the sulphate, and that without observing any
fact new in its history.

When chloride of silver is dissolved in water of ammonia, rhomboidal tables
are produced, white and opaque, consisting of an ammonia-chloride ; they lose
ammonia, however, immediately on being removed from the solution, and hence
their quantitative analysis became impossible.

VIII. OF THE AMMONIA-CHLORIDE OF ZINC.

When water of ammonia is added to a solution of chloride of zinc, the white
precipitate of basic chloride which is at first produced, soon redissolves, and a
colourless liquor is obtained, from which, by evaporation at a moderate tempera-
ture, crystals may be obtained. These crystals, however, according to circum-
stances, present very different appearances, and possess quite different properties
and composition, and hence the proper methods of obtaining each variety, in a
state fit for accurate examination, must be noticed. The plan which I found
most successful was to take a strong and hot solution of chloride of zinc in water,
to pass into it a stream of gaseous ammonia, until the precipitate was completely
redissolved, and filtering very rapidly, in order to separate any traces which might
yet remain of turbidity from undissolved material, to allow the whole to cool. A
substance, in very minute, but brilliant plates, of a peculiarly soft and talcy feel,
and pearly lustre, is deposited, while the liquor cools ; but after it has cooled,
then by further evaporation a completely different salt is formed, which crystal-
lizes in stellated groups of square prisms of a brilliant vitreous lustre, and hard to

46 Dr. Kane on the Compounds of Ammonia.

the feel. These two salts I shall indicate as the tabular and the prismatic am-
monia-chlorides.

To analyze the tabular ammonia-chloride of zinc, the following method was
employed :

A. 3.374 grammes were dissolved in dilute nitric acid, and precipitated by
nitrate of silver added in excess ; the chloride of silver formed was collected,
carefully washed, and dried; it weighed 4.295 grammes, equivalent to 127-3
per cent., containing 31.40 per cent, of chlorine.

From the circumstances of the preparation of this substance, it necessarily
follows, that, as in the corresponding copper-salt, the number of atoms of metal
is equal to, and that of the ammonia double that of the chlorine ; hence the above
determination of the chlorine was fully sufficient to determine the composition of
the whole. Thus the formula zncl -{■ 2NH3-I- ho gives

Experiment.
29.10

31.89 31.40

30.90
8.11

Theory.

zn

= 32.30

cl

= 35.42

2NH3

= 34.28

HO

= 9.00

111.00 100.00

Thus the composition of this body corresponds in every particular to that of
the ammonia-chloride of copper ; and guided by similar considerations, I shall
arrange its constituents according to theory, as

NH3 . HcZ -f- NH3 . zno.

When this body is heated it gives out water and ammonia, and the result
obtained confirms fully the analytical result above described. Thus,

3.739 of this tabular ammonia-chloride, heated to 300°, until all evolution of
ammonia and of water had ceased, left a white powder, weighing 2.900, or 77.56
per cent.

In another experiment, 4.457 kept in a temperature of 300°, until the evo-
lution of water and of ammonia had ceased, left 3.426 of white matter, corres-
ponding to 76.87 per cent. But from theory there should be, supposing the
reaction similar to what has been observed in the copper series,

Dr. Kane on the Compounds of Ammonia. 4T

zncl = 60.99 ^^^ nHj = 15.45

NH3 = 15.45 HO = 8.11

76.44 • 23.56

By the loss of NH3H0 there is produced the substance NHg.zwc/, which
remains behind. When this powder is farther heated it fuses into a clear colour-
less, or very slightly yellow liquid, emitting ammonia ; by cooling, this matter
congeals into a mass like gum ; it shall be examined more minutely a little
farther on.

The form and external characters of the prismatic ammonia-chloride of zinc
have been already given ; its analysis was effected as follows :

A. 2.851 grammes were dissolved in dilute nitric acid, and precipitated by
nitrate of silver ; the chloride, collected, washed, and dried, weighed 4.550, or
160 per cent., containing 39.47 chlorine.

B. 3.540 grammes were dissolved in dilute muriatic acid, and precipitated by
carbonate of soda ; the precipitate was collected, and carefully washed, and
having been di'ied, was ignited with its filter ; the residual oxide of zinc, allow-
ing for the ashes of the filter, weighed 1.573, or 44.43, containing 35.61 of
metallic zinc.

Hence in this compound likewise, the zinc and chlorine are in the proportion
of atom to atom ; it contains likewise water and ammonia, and calculating from
the formula 2(chn) -\- 2nh3-|- ho, there is found

Theory.
2cl = 70.84

39.64

Experiment.
39.47

2zn = 64.60

36.14

35.61

2NH3 = 34.28
HO = 9.00

19.18|
5.04/

24.92

178.72 100.00 100.00

Thus this prismatic ammonia-chloride differs from the tabular salt in con-
taining, united with the same quantity of ammonia and water, double the quan-
tity of chloride of zinc, and it has evidently been produced by the dissipation
during the evaporation of the liquors, of one-half of the ammonia and combined
water which the tabular salt had contained. Hence the true nature of this salt
may be best represented as a compound of chloride of zinc with the tabular salt,
thus,

48 Dr. Kane on the Compounds of Ammonia.

Znc/-|- NH3 . HC/' -|- NHj zwo,

and recollecting the frequent replacements of water of crystallization by nHjZt
HArf, some remarkable relations present themselves, as

Zncl + NH3 . HCZ 4" HAC?HO,

zncl-\- NH3. hc/-|-2ho;
and again,

CUCl-\- NH^HCZ-I- 2hO.

Hence this prismatic salt assimilates itself very remarkably to the double
chlorides of zinc, copper, and ammonium, with water of crystallization ; a view
which is additionally strengthened by the effects of heat upon this body.

When this ammonia-chloride is heated it emits watery vapour and ammonia,
and fuses into a transparent mass, which resists a considerable temperature. This
residue, on cooling, forms a mass like pale amber, having but little or no traces of
crystalline arrangement, but fissured in every direction like starred glass. To
determine the proportion of water and ammonia lost in this reaction, the follow-
ing experiments were made.

A. 3.250 grammes of prismatic ammonia-chloride gave 2.758 of transparent
gummy-looking mass, corresponding to 84.81 per cent.

B. 12.435 grammes gave, similarly treated, 10.748, or 86.47 per cent.
From these results the nature of the substance remaining may be very simply

calculated : all the water is driven off, and as much ammonia as may be neces-
sary to account for the weight lost ; hence, there result

zncl = 75.78 ^^^ NH3 = 9.59

NH3 = 9.59 HO = 5.04

85.37 14.63

Hence it is evident that precisely the half of the ammonia is driven off with
all the water, forming the elements of oxide of ammonium, and there remains
the remainder of the ammonia, with the chloride of zinc, thus arranged :

znc/ -|- (NH3 . zw c/ ; )

wherein the body NH3. zncl, already noticed, is united with chloride of zinc, con-
stituting an anhydrous double chloride, analogous to that of zinc and of ammo-
nium or potassium.

Dr. Kane on the Compounds of Ammonia. 49

When the body NH3. zncl is heated by itself, it gradually loses ammonia, and
fuses into the same gummy-looking substance ; but the numerical results being
similar to those already noticed, it is not necessary to occupy space with them,
the more so, as the elimination of the ammonia, by itself, does not take place so
clearly as where the portion to be separated is associated with the equivalent
quantity of water.

This gummy body, when heated strongly, nearly to redness, boils, but does
not emit ammonia ; on the contrary, it volatilizes unchanged, and condenses in
amber-looking drops, possessing all its original characters. If it be heated, how-
ever, with dry lime, there is an immediate and copious evolution of ammonia ;
when treated by water it is decomposed ; there dissolves ammonia-chloride, pro-
bably in the prismatic form, and a white powder remains, which is an oxychloride
of very remarkable constitution. The same oxychloride is produced by the
action of water on the white powder NH3 . zncl, and I shall consequently treat of
the properties and composition of this oxychloride without further reference to
which of these ammonia zinc-chlorides it had been obtained from.

IX. OF THE OXYCHLORIDE OF ZINC OBTAINED BY THE ACTION OF WATER ON

NHjZnc/ or NH3 -f- 2zncl.

The substance thus obtained is a very light milk-white powder, tasteless, and
insoluble in water ; when heated it gives out water, and if Ignited, it yields some
vapours of chloride of zinc, and is completely decomposed ; water subsequently
poured upon it, extracting some of the chloride of zinc, and leaving a still more
basic combination. The quantity of water which this oxychloride retains is very
variable, as a very slight difference in the temperature used in drying it may
change, very considerably, the proportion of water with which it may be com-
bined. A quantity prepared by acting with water on nh^ . zncl, and dried at a
temperature of about 180° F., gave the following result :

A. 2.404 grammes, dried, until all escape of watery vapour had ceased, gave
2.043 of residue, which had a greyish shade. These 2.043 were dissolved in dilute
nitric acid, and precipitated by nitrate of silver ; the chloride of silver, collected
and dried, weighed 0.975, being 40.56 per cent., containing 10.01 of chlorine.

The quantity of water lost was 0.361, corresponding to 15.02 per cent.

VOL. xix. H

50 Dr. Kane on the Compounds of Ammonia.

hf But the chlorine being as chloride of zinc, and the remainder of the deficiency
being oxide of zinc, the composition of the whole may be easily calculated, and
there is found

d. 10.01 + zw 9.13 = 19.14 = zncl
o . 13.07 + zn 52.77 = 65.84 = zno

15.02 = HO

100.00

But — — - = 5.78. q.p. 6. And — = — '- — , or 6ho. Hence the empirical
9,13 ^ ^ 15 53.2' ^

formula is zncl -\- 6 zno -{■ 6 ho.

When this oxychloride is dried at the temperature of the air, it retains a
much larger quantity of water, in fact nearly double as much, since quantities of
the powder so prepared, gave, when dried, from 23.5 to 23 per cent, of water,
To establish an accurate proportion, however, the following analysis was made :

B, 2.078 of the oxychloride, prepared by the action of water on the body
NH3.ZWC?, and dried without exposure to heat, gave, when dried by the spirit-
lamp, 1.590 of a greyish residue, corresponding to 76.51 per cent. ; hence 23.49
water.

The residue was dissolved in nitric acid, and precipitated by nitrate of silver;
the chloride of silver produced was collected, washed, and dried, when it weighed
0.690, or 33.21 per cent., containing 8.29 per cent, of chlorine.

The zinc being determined in the same manner as that before described,
there results that to the same chloride and oxide of zinc, there were in this body
united ten atoms of water in place of six ; and hence the formulas of these oxy-
chlorides are :

Dried at 212°. Experiment.

cl = 35.42 9 74 10.01

Tzn = 226.10 62.20

6o = 48.00 13.20

6ho = 54.00 14.86 15.02

363.52 100.00

Dr. Kane on the Compounds of Ammonia. 51

Experiment.
8.29

Dried

1 in the open

Air.

cl

z=

35.42

8.86

7z«

=

226.10

56.59

60

=

48.00

12.01

IOhc

( :::::

90.00

22.54

23.49
399.52 100.00 ■• ■ •• "'

When this oxychlorlde, dried, but not too much heated, has been exposed to
the air, 100 parts of it gradually absorb about 15 of water, corresponding to four
equivalents, and which cannot be expelled by the temperature of boiling water.
It therefore appears to form in this proportion likewise a hydrate of definite com-
position.

When a solution of chloride of zinc is decomposed by ammonia, added in
such excess as that part of the precipitate at first formed shall be redissolved,
there is a hydrated oxychloride produced, which I have found to be in all respects
identical with that just described. It has the same amylaceous look and feel, the
same lightness, and, as shall be now shown, the same composition.

C. 4.60 grammes of this oxychloride, dried merely at ordinary temperatures,
were heated over a spirit-lamp, uijtll all evolution of watery vapour had ceased ;
there remained the greyish dry oxychloride, weighing 3.510, corresponding to
76.3 per cent., or 23.7 of water. The 3.510 residue was dissolved in dilute
muriatic acid, and precipitated by solution of carbonate of soda ; the precipitate
of carbonate of zinc was washed carefully and ignited, when it left a pure oxide
of zinc, weighing 3.237, or 70.22 per cent., containing 56.28 of metallic zinc.

D. A quantity taken from the same filter, was dried at 212° : it had the
same appearance as the former. Of this 3.165 dried, left 2.690 of residue,
giving 85,0 per cent, and 15.0 of water. The residue was dissolved in dilute
nitric acid, and precipitated by nitrate of silver ; the chloride formed, collected,
and fused, weighed 1.223, or 38.64 per cent., containing 9.53 of chlorine.
Hence this oxychloride was composed of

Dried at 60°. Dried at 2\2°.

d z= . cl = 9.53

zn = 56.28

HO = 23.70 HO = 15.00

H 2

52 Dr. Kane on the Compounds of Ammonia.

Which agree with the results of the theoretical formulae given for the oxychloride
last examined. When the ammonia employed is not sufficient to precipitate all
the zinc, the oxychloride formed is differently constituted from that just
described, and is the same with that described by Schindler, and which is analo-
gous to the ordinary oxychloride of copper. Schindler, however, appears to have
dried the specimens which he analyzed at 212°, for I have found this oxychloride
to retain four equivalents of water at 100° F. Its formula is then

zncl \- 3 zno -{- 4 ho.

As the same result, except in the estimate of the water, had been obtained by
Schindler, I will not enter into any details of my verifications of his results. I
have, however, obtained another oxychloride, which, in a less hydrated condition,
had been noticed by Schindler likewise. I prepared it by adding to a solution
of chloride of zinc, caustic potash liquor, until it began to react alkaline. The
process by which Schindler had obtained it, almost necessarily produced the
separation of the water it should contain ; thus he evaporated chloride of zinc
until it had lost a certain proportion of muriatic acid, and then diluted with much
water the remaining sirupy liquor. The formula which he obtained was

zncl -{- 9 zrao -j- 3 ho.

This oxychloride, as formed in my experiments, scarcely differs from those
already described, in its external appearance ; when heated it yields water in the
same manner. The analysis of it merely, therefore, need be given in detail.

A. 1.790 grammes, dried over the spirit-lamp, gave 1.384 of residue, or
77.32 per cent.

B. 2.131, treated in the same manner, gave 1.G46, or 77.24 per cent.

C. The 1.384 of residue, exposed to the air, gradually absorbed water, and
became 1.485; therefoi'e the quantity of water absorbed was to the original
quantity as 101 to 406, or nearly as one to four.

D. 3.030 of dried oxychloride were dissolved in dilute nitric acid, and pre-
cipitated by nitrate of silver ; the chloride produced weighed 0.938 grammes, or
30.96 per cent., equivalent to 23.93 per cent, for the hydrated oxychloride,
which contains 5.921 of chlorine.

Hence is derived the formula zncl-{-Qzno-\- 14ho, by which there should
be

Dr. Kane on the Compounds of Ammonia. 63

Theory

Experiment

c/ = 35.42

6.37

5.92

lOzre = 323.00

58.11

9o = 72.00

12.95

14ho = 126.00

22.67

22.68 25

556.42

100.00

And the dry oxychloride, zncl + 9zo, absorbs four equivalents of water,
assuming nearly the condition in which it had been examined by Schindler.
The quantity of water found by analysis Is Intermediate between three and four
atoms, but I consider that the method used was most likely to lead to an error by
deficiency of absorption than by excess, and hence I adopt four as the quantity re-
absorbed. Then there is given the formula zncl -\- 9 ino -f- 4 ho.

There are thus found to exist at least three different oxychlorides of zinc,
each of which may be obtained combined with various proportions of water.

In order to be able to trace the connexion between these oxychlorides, and
to ascertain the relation in which they stand to the hydrated neutral chlorides of
the same family, they may be arranged in the following manner :

A. 1. zncl-\-zno-\-2zno-\-2Ho 1 Hydrates of
2. zncl-\- zno-\-2zno-\- iiio I zncl -\-3zno.

B. 1. zncl-{-6zno-\-4)Ho

2. zncl-\-6zno-\-6Ho

3. zncl-\-6zno-\-10uo

C. 1. zncl-\-9zno-{-4Ho "1 Hydrates of
2. zncl-\-9zno->rl4HO J zncl-\-9zno.

The oxychloride A and its hydrates conform to the type of the Brunswick
green and of the oxychloride of mercury. Elsewhere the nature of this type
will be discussed.

The oxychloride B, in its dry form, is evidently the basic compound corres-
ponding to the chlorides, with six atoms of water of crystallization, and hence

zncl -\- Qzno
corresponds to

Hydrates of
zncl -\- Qzno.

54 Dr. Kane on the Compounds of Ammonia.

Iigcl-\- 6 HO

and other cases, of which the chloride of hydrogen is the most remarkable.

When water is saturated with muriatic acid gas, the solution being kept at
the temperature of 32° F., it acquires a specific gravity of 1.2109, and then
contains in 100 parts 42.43 of gas, by Edmund Davy's determination. If the
water be retained only at 60" the absorption does not proceed so far, the specific
gravity reaching only about 1.192, and the liquor containing only 38.38 of
chloride of hydrogen in the 100. Thompson found the strongest liquid acid to
be 1.203, and to contain 40.66 per cent, of gas. Now, if we calculate the num-
ber of equivalents of water which these results indicate as combining with one
of chloride of hydrogen, we shall find

In the acid of 1.2109 . -- = ^- and IM = 5.5

HO 49.4 9

In the acid of 1.192 . — = — '■ — and — '— = 6.5

HO 58.5 9

T ^u -J n or>o c/h 36.42 ,53.15 _ _.

In the acid of 1.203 — = ——- and = 5.91

HO 53.15 9

Scarcely any doubt can remain, therefore, that in the strongest liquid muriatic
acid, the chloride of hydrogen combines with six equivalents of water, and that it
is hence analogous to

ca.cl-\-6H0
and to zncl-\- 6zno.

This strong hydrated chloride of hydrogen cannot be heated without escape
of gas, and if it be distilled, the boiling point gradually rises until it reaches
230° F. ( 1 10° C.) when it ceases to change, and the liquid subsequently distils un-
altered. If a weaker acid be distilled, it loses water until the boiling point rises
to the same degree, when acid of the same strength distils, as in the former
instance. This acid, with a constant boiling point, has a specific gravity of 1.094,
and contains 19.19 per cent, of real acid by Davy's estimate, and 20.44 by
Thompson's ; hence the proportion is, taking the mean of their results,

E^ = 1_M2 = ?6^ and i£^ = 16.35.
HO 80.18 147.3 9

Dr. Kane on the Compounds of Ammonia. 55

Hence this acid, with constant boiling point, is composed of HcZ+ 16ho, and
its formula may properly be considered as

h.c/-4-6ho -\- IOho.
corresponding to

zncl-\-Qzno-\-\0-H.o.
the hydrated-oxychloride, which has been described.

X. OF THE AMMONIA-SULPHATES OF ZINC.

This salt was prepared by passing ammoniacal gas through a strong and hot
solution of sulphate of zinc, until the whole of the sub-sulphate precipitated had
been redissolved. The liquor, on cooling, deposited a flocculent mass, in semi-
crystalline grains resembling starch ; and if the liquor be evaporated, or kept
liot, the separation of this substance continues ; when, however, the solution is
allowed to cool, and then having been filtered, is left to spontaneous evaporation,
it remains clear ; and small, but perfectly distinct crystals are deposited, which
remain bright while moist, but effloresce, and become opaque almost immediately
on being dried and left in the open air. These two bodies contain alike, sulphuric
acid, oxide of zinc, ammonia, and water, but the quantity of the constituents is
not the same ; I shall therefore describe them separately, commencing with the
crystallized ammonia sulphate.

When this salt is heated it gives water and ammonia, and there remains sul-
phate of zinc ; if the heat be very gently applied, all ammonia may be expelled,
and the residual sulphate of zinc will be quite pure ; but if the salt be suddenly
heated, a quantity of sulphate of ammonia is produced, and the sulphate of zinc
remaining is mixed with oxide. m

As this salt, from the manner of its formation, must contain two equivalents
of ammonia to one of the sulphate of zinc, the analysis of it became very simple,
as it was to be directed specially to the examination of the quantity of water
which it might contain.

In efflorescing this salt does not lose ammonia. To determine its composition,
3.701 of clear crystals, dried between folds of blotting-paper, were heated at first
very gently, but finally to ignition. On the first application of the heat the salt
fused, and emitting water and ammonia, left a perfectly white residue of sulphate

66 Dr. Kane on the C<ympounds of Ammonia.

of zinc, weighing 2.023, corresponding to 54.66 per cent. Its composition,
therefore, is :

Sulphate of zinc = 54.66
Volatile matter = 45.34
and

54.66 80.50 = zno.soa

45li4 - 66.77 = 34.28 NH3 + 32.49

Consequently the water is — — = 3.61 equivalents, and as the salt is efflores-

cent, the true number is probably four.

When these crystals have been left in the open air for some time they lose
altogether their transparency, but retain their form, assuming the milky lustre of
the crystals of nitrate of lead. When these milky crystals are heated they melt,
and are decomposed with precisely the same phenomena as the transparent ones,
leaving a sulphate of zinc redissolving completely in water.

3.030 of these crystals, so treated, gave 1.818 of sulphate of zinc, or 60 per
cent. ; hence,

as ^ = -— and 53.66 - 34.28 = 19.38.
40 53.66

The quantity of water had evidently been reduced to one-half by efflorescence,
no ammonia having been lost, as was ascertained by experiment.

In the decomposition of this salt by heat, the ammonia and water go off
together to the end, and this is easily seen, as the material lost is exactly
2(nh3. ho).

By the first application of the heat it was mentioned that the salt fused after
it had lost a certain proportion of gas and water ; this fused mass, on cooling,
solidifies into a mass like gum, which may be again melted, and the remaining
ammonia and water expelled, as above described. In order to ascertain whether
the fusion of the mass occurred at any definite point In the process of decompo-
sition, a quantity of the effloresced salt was heated until completely fused, the
lamp was then removed, and the weight of the residual gummy-looking material
determined, — it amounted to 80.29 per cent. ; and hence it results that the
quantity of volatile matter lost had been exactly half of the entire amount, thus.

Dr. Kane on the Compounds of Ammonia. 87

Sulphate of zinc = 60.00 1 /^ • i

^ > Gummy residue.

«. Volatile matter = 20.29 J ■ •

b. Volatile matter = 19.71

Effloresced salt = 100.00

From these results follow the formulae

Transparent crystals = zwo.s03-|-2nh3-{-4ho

Effloresced crystals := ZWO.SO34-2NH3-J-2HO

Gummy mass = zno . SO3 -\- NH3 -|- ho

Which gives by heat = zrao . SO3

I shall, before proceeding further, return to the examination of the flocculent
substance which was deposited from the hot solution of the ammonia-sulphate.
It cannot be redissolved in water, which distinguishes it from the transparent
crystalline salt; when heated it fuses, and is decomposed with the escape of water
and ammonia, as is the case with the substance already described. It was ana-
lyzed as follows :

5.033 of this flaky substance was heated until all escape of water or of
ammonia had ceased ; there remained 3.821 of sulphate of zinc, corresponding
to 75.92 per cent., and

^1 = IWs' ^"^25.53-17.14 = 8.39, or nearly 9.

Hence the formula is zno . so^ -f- nh, -]- ho.

These flakes have therefore the same composition as the gummy mass
obtained by melting the crystalline salt, and this circumstance proves that the
gummy mass is really a definite chemical compound, which could not have been
so positively shown from the method by which it had been prepared.

When the crystalline salt is kept for some time at a temperature of from 80°
to 100° F. it gradually falls down into a white powder, all traces of crystalline
structure having totally disappeared ; during this decomposition, water alone
escapes, as turmeric paper left on the surface of the powder is not at any period
affected. When this powder is heated to about 212°, it gives out water and am-
monia, which continues up to a certain point, but in order to finish the expulsion
of the water, the temperature must be raised until the mass has become fused ;

VOL. XIX. I

98 Dr. Kane on the Compounds of Ammonia.

after that time, the continuance of the heat occasions the loss of more ammonia,
but no more water is disengaged. Unless the heat be very accurately managed,
sulphite of ammonia is apt to make its appearance before the last portions of the
ammonia have been expelled ; with care, however, a sulphate of zinc almost com-
pletely soluble in water may be obtained.

To determine more closely what occurs in the case just noticed, 4.238
grammes of the powder formed by the efflorescence, at 100°, of the crystals were
heated until the sulphate of zinc remained pure behind ; it weighed 2.800, or
66.07 per cent.

4.385 of the same powder were heated until it had fused, and the escape of
water had ceased, great care being taken to seize the precise time, and to avoid
the application of any unnecessary heat ; the residual mass weighed 3.470, or
79.13 per cent.

XT 66.07 80.50 J ., „. ^c^A , r.

3393 ~ 4Ym' ~ + ^' 'I" P' ^"^ + ^^*

The proportion of ammonia being a little less than two atoms.
Again, the second experiment gives

" ■ > zr 79.13 of residual fused mass;

and

Ammonia 13.06

66.07 80.50 1 80.50 z«o so,

= , or nearly — •*

13.06 15.91 17.14 NH3

The effloresced powder was therefore

zno SO3 + 2NH3 + HO,

corresponding to the crystallized ammonia-sulphate of copper, and by heat it loses
NH3 . HO, and there is formed

S03.ZnONH3,

being precisely the same as in the copper series. This effloresced powder put
into water dissolves almost without residue, provided the water be free from
carbonic acid.

The reasoning which I employed concerning the rational formulas of the

Dr. Kane on the Compounds of Ammonia. S9

ammoniacal compounds of copper, applying with equal force to those of zinc, I
will not repeat it, but arrange the results just now described, in accordance
with those views.

1. The crystalline salt = (NH3 , ho) SO3 + zno . (NH3 . ho) + 2 ho.

2. The effloresced crystals = (nHj . ho) SO3 + zwo (nHj . ho).

3. The effloresced powder = (NH3 . ho) SO3+ z«o . NH3.

4. The flakey substance = (NH3 . zno) . SO3+ ho.

5. The fused mass from 3 =: (nHj . zno) .so.

I will not enter into the consideration of any of the interesting relations
which the arrangement of this series of bodies must suggest, except to point out
in the ordinary sulphate of ammonia, the anomaly of the crystallization of which,
with an atom of water, is so curious, the analogue of the bodies 4 and 5. Thus
there is

(NH3H0.) sOg + HO and (nh3.ho)s03
as there is

(NH3 . zno) SO3 -\- ho and (NH3 zno) SO3.

When discussing the theory of these bodies in another section, I shall have
occasion to recur to these results.

XI. OF A NEW BASIC SULPHATE OF ZINC.

When the bodies (4) or (5) are treated by water they are decomposed, the
body (1) dissolves, a quantity of sulphate of ammonia is likewise formed, and the
insoluble matter is so definite and marked in its composition, that it must be
regarded as a new basic sulphate of zinc. It is white, insoluble in water, when
heated it gives water, and leaves a white powder behind. It was analyzed as follows :
2.594 grammes, dried by a spirit-lamp, gave 1.950, or 75.18 per cent., having
lost 24.82 water.

The residual sub-sulphate was boiled with solution of carbonate of soda, and
the carbonate of zinc collected on a filter, dried, and ignited ; the oxide of zinc
remaining weighed 1.635, or 64.22 per cent. Hence the composition

Sulphuric acid = 10.96

Oxide of zinc = 64.22

Water = 24.82

I 2

■60 Dr. Kane on the Compounds of Ammonia.

2.544, dried, gave 1.957? from whence

Dry sub-sulphate zz. 75.88

Water = 24.12

The dry mass, exposed to the air, absorbed water, and became 2.137? or 8.40 per

cent., having taken up almost exactly one-third of the quantity of water it had

lost.

These results point out the formula

SO3 -|- 6z^^o -j- 10 HO,
which should give

SO3 = 40.16 10.79

6zwo = 241.80 65.02

10 HO = 90.00 24.19

371.96 100.00

There are two sub-sulphates of zinc already known, of which the one
SO3-}- 4z?20 has been described by Schindler, Kuhn, and Graham. It appears to
combine with variable proportions of water, from two to ten equivalents, but
most commonly is to be found with four. The second has been examined by
Schindler alone, who gave its formula as sOj-j- 8zno -\- 2 ho. I have not had an
opportunity of verifying this result, but I consider the correctness of his analysis
as being very probable. The same chemist showed that there may be formed a
soluble compound of SO3 -j- 2 zno, which, however, is destroyed when dried.
Hence the series of basic sulphates of zinc may be thus arranged :

Real neutral sulphate = zno . so,.

Salt with saline water = (zrao.Ho) SO3.

Soluble salt of Schindler = (zwo . zwo) SO3.

Common crystals = {zno . ho) so3-|- 6 ho.

Hyperbasic salt, dry = (zno .zno)so3-\-Qzno.

Common basic salt, dry = (zwo . zwo) so3-|-2zrao.

Do. with water — Schindler = {zno . zno) . SO3 4- 2 zno -\- 2 ho.

New basic salt, dry = {zno . zno) SO3-I- 4z»o.

Do. with water = {zno . zno) SO3 -\-4:zno -{- 10 ho.

The law of replacement being precisely what was already shown in the copper
series, but still more complete from the discovery of sOj-f- 6z«o.

Dr. Kane on the Compounds of Ammonia. 61

PART III.

ON THE THEORY OF THE AMMONIACAL COMBINATIONS.

On the accession to science of any considerable body of new facts, we should
carefully examine how far they tend to modify our ideas of the nature and inti-
mate structure of the bodies to which they relate, and of the forces to the action
of which these bodies are subjected, and by remodelling our views in accordance
with the ideas thus obtained, we should endeavour after a closer approximation
to that truth, the attainment of which is the object of all scientific labour.

A body, possessing so many interesting properties as ammonia, standing as it
were, on the confines of mineral and of organic chemistry, and forming the con-
necting link between them, must even, on its own account, and still more from
the remarkable variety of classes of combinations into which it enters, occupy a
prominent place in the general theory of chemistry, and the grounds of any pro-
posed alteration in our views concerning it should be examined with the attention
due to the Importance of the subject. I shall therefore lay before chemists, for
discussion, some views of its nature and laws of combination, differing in many
important particulars from those hitherto received, which have been suggested to
me by the researches on the various classes of compounds of ammonia contained
in the present and former papers. These views are connected in a very remark-
able manner with those concerning which the opinions of chemists have been so
long divided ; it will be seen, in fact, that the principles of the theory which I
propose, embrace all that was vital in former hypotheses ; and it may be almost
considered as an argument for its sufficiency, if not actual truth, that in the de-
velopment of these views is exemplified the ordinary course of advancing know-
ledge, when the once conflicting elements of rival theories are found forced into
coalition by the grasp of some generalization of a higher order.

Before commencing the explanation of my own views, I shall briefly describe
the essential principles of the previous theories of ammonia.

A. — The oldest view :
1. That ammonia NH3 is an independant base, saturating acids and forming

salts.

62 Dr. Kane on the Compounds of Ammonia.

If, as Dulong proposed, all acids be regarded as hydrogen compounds, thus
SO3 + HO as SO4 + H, similar to c/h, the old view explains the main requisite in
all theories of ammonia, the presence of water in the salts formed by the oxygen
acids. Sulphate of ammonia becomes so^.h-j-nHj, like c/.h-j-nHj.

B. — The theory of Berzelius :

1. That the ammoniacal amalgam contains a body, nh^, which is metallic, com-
bines with oxygen, and then may replace potash in combination.

2. That when NH3 combines with hc/. the NH3 takes h, and forms NH4, with
which the chlorine combines.

3. That the water in the ammoniacal salts with the oxyacids converts NH3 into

NH^+O.

C. — The amide theory, as left by Dumas and Berzelius :

1. There was assumed a hypothetic body, nh^, which replaced chlorine and
oxygen in certain organic combinations.

2. Potassium or sodium heated in ammonia, liberated therefrom as much hydro-
gen as from water, and formed amidide of potassium or of sodium.

Ammonia is in no place called amidide of hydrogen by Berzelius or by Dumas,
nor is NH3 ever written NHj-f- h, but Dumas may have had that idea indistinctly in his
mind when he said that it was perhaps possible that as hydrogen forms hydracids
with some bodies, so it might produce hydrobases by its union with others. He
may have meant that hydrogen formed ammonia, a hydrobase, by uniting with
NH3 amidogene, but he much more probably referred to the combination of the
hydrogen at once with nitrogen ; his adherence to the common, but incorrect
ideas of the nature of the hydrogen bodies in general having completely pre-
vented him from seeing the true position of ammonia and its compounds.

The insufficiency of these views may be very briefly pointed out ; thus,

A. — The oldest view.

1. It applies only to the common ammoniacal salts, but does not attempt any
explanation of the nature of the numerous other classes of ammonia com-
pounds.

2. It states merely that nHj acts as a base, but does not explain its relation
to ordinary bases which are metallic oxides, nor the points in which the ammo-
niacal salts differ from the metallic salts of the same acid.

Dr. Kane on the Compounds of Ammonia. 63

B. — The Berzelian view.

1. It does not assign any proper function or place to ammonia itself, which
might be absolutely dropped out of the theory without loss. This view, there-
fore, leaves unexplained all combinations of ammonia with bodies which do not
contain hydrogen.

2. That NH3 -\- H.cl becomes nh^ + cl, is purely hypothetical, and highly
improbable, the ammonia not exercising any apparent affinity for hydrogen, while
that of chlorine for hydrogen is very strong. Hence the duty of proving the
change in position of the fourth atom of hydrogen rests with the Berzelian
theory, and has not been yet performed.

C. — The amide theory.

1 . Our knowledge of the amidogene combinations has been acquired almost
exclusively since the theories just noticed had been proposed, and consequently
what is now the most important principle in a complete theory, the connexion of
the ammonium and of the amidogene compounds with those containing ammonia
itself had no place therein. Hence all former theories are insufficient, from the
ground that the new facts gained by the study of the metallic amidides cannot
be explained by or included within the principles upon which they rest.

I shall now describe, in a series of propositions, the principles of the theory
which I advocate, and then taking each proposition by itself, will sum up the
evidence derived from experimental results, by which I consider its validity to be
established.

Prop. I. — That the so called hydracids are not really such ; that hydrogen, in
all its forms of combination, is analogous to certain metals of the electro-
positive class, and its compounds react like theirs under similar circum-
stances.

II- — That ammonia NH3 is amidide of hydrogen nh^ -\- h, and resembles in some
respects the oxide, in others the chloride of the same positive element.

Ill- — That NHj amidogene may combine with metals, and that the metallic
amidides have a singular tendency to combine with the chlorides or oxides of
the same metal, or of a metal of the same family, and thus form bodies
resembling the chloro-oxides, chloro-sulphurets, or oxysulphurets.

IV.— That NH3 = NHj -f- H amidide of hydrogen can perform the same functions

./r

64 Dr. Kane on the Compounds of Ammonia.

in combination as water, oxide of hydrogen, whether as basic water, or water

of crystallization, and likewise can replace the water termed saline in certain

salts by Graham.
V. — That the so called oxide of ammonium nh^o is oxy-amidide of hydrogen

NHj . H -|- HO, and that sal ammoniac is chloro-amidide of hydrogen nh^ . h -|-

ucl.
VI. — That the ordinary ammonia salts ally themselves to the salts of the copper

and zinc class, which contain two equivalents of oxide.
VII. — That if chlorine could be separated from sal ammoniac, the residual NH4

should be regarded as nH2 + 2h, sub-amidide of hydrogen, as when by

removing the chlorine from white precipitate, the sub-amidide of mercury,

NHj + ^Hg-, formed by the action of water of ammonia on calomel, should

remain.

Prop. I. — Of the general positive Nature of the Compounds of Hydrogen.

In a memoir which was published in 1831 in the Dublin Journal of Medical
and Chemical Science, I pointed out that the general bearing of the properties
of the compounds of hydrogen should induce us to assign to those bodies a totally
different position from that which the names of hydrogen-acids previously
assigned to most of them would appear to warrant. Thus that, whilst we found
hydrogen to manifest immensely superior electro-positive energies to those of
gold, platinum, or sulphur, it was quite unphilosophical to suppose, that when all
of these bodies were combined with chlorine, the hydrogen should be that least
capable of diminishing the negative power of the chlorine. I showed that from
the considerations which are suggested to us by a fair comparison of the proper-
ties of the oxides, chlorides, sulphurets, &c. of hydrogen, with those of the similar
compounds of the metals, it became quite necessary to allow, that although in some
cases, as where water united with potash or lime, the hydrogen body may per-
form the negative function, yet in the vast majority of cases the part played
by it in combination is that of positive constituent.

I shall refer to the memoir above quoted for the details of the views which I
then brought forward ; previously to that time Mitscherlich had already sug-
gested, that in the hydrated acids the water acted as a base, but this, from the indif-
ferentism of water in the generality of chemical actions, could not be considered

Dr. Kane on the Compounds 0/ Ammonia. 65

as leading to any thing like the general principle which formed the subject of my
paper. Since that period, although no writer has broadly reproduced this theory
of the hydrogen combinations, yet the progress of research has gradually lent to
it the most efficient support, by the discovery of classes of bodies identifying in
the strictest manner the chemical relations of hydrogen, and of certain of the
more positive among the metals. The beautiful investigations of Graham on
water as a constituent of salts, particularly those illustrating the conversion of the
neutral into the basic condition by the replacement of the hydrogen by a metal
of the magnesian family, has shown that in its relations to oxygen at least no line
of distinction can be drawn between hydrogen and the metals which with it
constitutes so natural a group.

Passing to the other compounds of hydrogen, there will be found in the
series of researches on the zinc and copper families, a variety of instances in
which the chloride of hydrogen is represented with remarkable closeness by the
chlorides of copper or of zinc. The examination of the various oxychlorides of
zine, in their dry and hydrated conditions, which presents to us the perfect
analogues of the chloride of hydrogen in its two stable conditions of definite
combination with water, points out an identity of action liable to little objection.
Like the chloride of hydrogen also, chloride of zinc is caustic, and when con-
centrated reddens litmus, so that the peculiarly acid character of affecting that re-
agent is to be found well developed in bodies to which, under any circumstances
of ordinary language, the name of acid could scarcely be applied.

The relation of chloride of zinc to ammoniacal gas is likewise very remarkable,
as indicating the general similarity of action between the hydrogen and zinc
compounds : the volatility of the ammonia-chloride of zinc, the permanent nature
of the ammonia-chloride of copper, indicate a closeness of union between the
metallic chloride and the ammoniacal gas, which brings those bodies into very
intimate connexion indeed with sal ammoniac.

As this proposition will receive from the evidence of several of the succeed-
ing ones a great deal of additional support, 1 will not here enter into any further
evidence in favour of it. Every fact which, in the course of these researches, be-
came the subject of examination, has tended to strengthen my confidence in the
truth of the general principle which the additions to science from the recent
investigations of other chemists have likewise uniformly tended to confirm.

VOL. XIX. K

66 Dr. Kane on the Compounds 0/ Ammonia.

Prop. TI. — That ammonia fiu-^is amidide of hydrogen, and should he written

NH2 4" H.

The re-examination of the results of Gay Lussac, Thenard, and Davy, on the
action of potassium on ammoniacal gas, gave to the interesting views of Dumas,
arising from the discovery of oxamide, a stability and importance which must be
considered as the origin of all subsequent investigations in that extensive field.
When we allow for the various sources of error to which, from the easy decom-
position of the resulting bodies, the quantitative determinations of the hydrogen
evolved from the ammonia is exposed, we shall find in the experiments of those
exact chemists a complete proof that potassium liberates from ammonia precisely
the same quantity of hydrogen as from water, and hence that the element
remaining united with the potassium is amldogene. The idea of ammonia being
itself a base differing essentially in constitution from the oxides of hydrogen or
of the metals, prevented the distinguished discoverer of oxamide from tracing in
the action of potassium on ammonia, the rational constitution of the latter, and
although he recognized completely the identity of function performed by the
metal in the one case, and the carbonic oxide in the other, yet it is evident, from
the tenor of his observations on all occasions, that he looked upon the abstraction
of the equivalent of hydrogen as subverting the constitution of the ammonia,
and that the amldogene resulting did not stand in any natural relation to the
ammoniacal gas employed.

Notwithstanding the remarkable cases discovered and examined by Henry
Rose, in which the combinations of ammonia with the various classes of salts ap-
peared to correspond so closely with the same salts containing water of crystalli-
zation, whence, taken in connexion with the existence of the amldides of potassium
and sodium, the symmetricity of nHj and oh might be inferred, and the form
NHj.H given to the former ; yet, until the discovery of the composition of white
precipitate, and of the similar bodies which I examined, and which was funda-
mental to all these researches, instances of the resolution of ammonia into amldo-
gene and hydrogen, independent of all destructive action, had not become
sufficiently positive and unexceptionable to lead any chemist to express the
opinion of its being really amidide of hydrogen, ranking with the oxide and
chloride of the same element. This view, however, results almost unavoidably

Dr. Kane on the Compounds of Ammonia. 67

from those experiments, although I myself did not finally adopt It until by the
development of the nature of the other quicksilver combinations vpith ammonia,
the complete identification of the principle of action of oxygen and amidogene,
particularly as exerted in the two classes of water and of ammonia sub-salts, left
no room in my mind for any other hypothesis.

The objection to the assumption of the existence of an hypothetic body,
amidogene, which might be supposed to weigh powerfully against the general
acceptance of this theory, is deprived of a great deal of its force when we come
to examine it with somewhat more care. In order to arrive at an idea of the
actual nature of ammonia, and of the position it is suited to occupy in the general
scheme of chemical reactions, we must investigate the laws of its affinities, and
study accurately the analogies which it presents in its combinations, with those of
other bodies of simpler constitution, and the history of which is as yet better
understood. From these data must our conclusions be drawn, and decompositions,
frequently of an accidental character, and mostly dependant on the peculiar
manner in which the affinities of the decomposing body may be exerted, should
be considered of but secondary importance, and subordinate to the study of the
general history of the substance, although still suited, under proper limitations,
to guide us usefully in our course. It is right that the exertions of chemists
should be directed to effect the isolation of amidogene, and it is to be hoped that
the same success which crowned the beautiful researches of Gay Lussac on Prus-
sic acid, will reward their efforts ; but even should this radical, like those of so
many of the most important series in organic chemistry, for a longer time elude
our grasp, it is proper and just to assume it to exist, if we, by so doing, can
obtain a more satisfactory explanation of phenomena, and link together classes of
facts previously disconnected and obscure.

Prop. III. — That amidogene may combine with metals, and that the metallic
amidides have a singular tendency to combine with the chlorides or oxides
of the same metals.

The formation of the amidides of potassium and sodium, gives sufficient proof
of the first part of this proposition, and there have been found in the researches
on the ammoniacal combinations of quicksilver, numerous instances of the truth
of the latter principle. Thus white precipitate must be looked upon as a com-

K 2

68 Dr. Kane on the Compounds oj" Ammonia,

pound of chloride and amidide of mercury, and the black substance formed by the
action of water of ammonia on calomel must be composed of sub-chloride, united
to the sub-amiduret of the same metal. More complex examples are furnished
by the yellow powder

Hgcl-\-2 Hgo -{■ Bg . NH2,
and the bodies

UgSO^ + 2 H^O + H^NH^
Hg-NOg+ 2Hg-0 + H^NHj.

In the copper family there exist some examples equally remarkable, but which
shall be referred to particularly under a distinct head.

Prop. IV. — That amidide of hydrogen can perform the same functions in
combination as oxide of hydrogen, whether as basic water, as water of crys-
tallization, or as the water termed saline by Graham.

In the most perfect cases of substitution, where the substances belong to
strictly isomorphous groups, the similarity of properties and structure existing
through the several classes of bodies formed by the mutually replacing elements,
assumes an exactness to which no parallel is found in the instances with which the
history of the ammoniacal bodies has supplied us ; yet amongst the combinations
described in the preceding sections, analogies and relations have been observed
of such closeness, as to give to the truth of the proposition now in question the
highest probability.

A vast number of bodies, such as oxygen-salts, chlorides, iodides, &c., ex-
posed to the action of ammoniacal gas, absorb a considerable quantity thereof,
and it is afterwards found that different portions of this ammonia are retained
with various degrees of force : the greater part being, generally speaking, ex-
pellable by the temperature of boiling water, whilst the remainder clings to the
substance with a much higher power, sometimes not being separable, unless the
constitution of the body be completely broken up. This fact finds a complete
parallel in the relative degree of affinity with which water is retained by ordinary
salts and acids. Thus the retention of the basic water by oxalic and common
tartaric acids, and the greater affinity of the last atom of water in the sulphates of
the magnesian class find in the compounds of ammonia their analogous combina-.

Dr. Kane on the Compounds of Ammonia. 69

tions, and one of the most embarrassing circumstances in the present investigation
arises from the fact of the relation of ammonia and water being so close, that
where the ammoniacal bodies are soluble in water, they cannot be brought into
contact with it without an exchange of position occurring to a considerable ex-
tent, and the body crystallizing in a state containing both water and ammonia.
Thus, whilst by passing dry ammonia over chloride of copper, the body
cmc^-|-3nh3 may be obtained, the result of treating a solution of chloride of
copper by ammonia is CMc/-t-2NH3-l-HO, in which the third equivalent of
ammonia has evidently given place to one of water ; and though the copper, as I
have already shown, is separated from the chlorine, however by means of heat
both bodies yield cwc/NHg; the one losing 2NH3, the other H0.NH3. Thus,
through the whole class of soluble ammonia-copper and zinc combinations, the
water replaces, in the first instance, the metallic constituent, and partly the am-
monia itself, and it is only when by the application of heat the water with some
ammonia has been expelled, that we arrive at the real combinations of the
metallic compound with amidide of hydrogen.

The basic nitrates of mercury being insoluble, furnish one of the most
striking examples to be found of the replacement of water in its basic condition
by ammonia. It was proved that the basic nitrates stood in the same relation to
the neutral salts as that which Graham had pointed out for the nitrates of the
magnesian class; and I showed, in the same section, that the ammonia sub-
nitrates were so constituted, that the nitric acid and oxide of mercury remained
the same, whilst the water of the ordinary sub-salts was replaced by the ammonia
thus : kd representing nh^. amidogene.

The yellow sub-nitrate of the red oxide is

HO.NOj-f-SH^O.

The ammonia sub-nitrate of the red oxide is

hac?.no5-}-3h^o.
The sub-nitrate of the black oxide is

HO.NO^-^- 2Hg-o.

The ammonia sub-nitrate of the black oxide is

hac?.no5-|-2h^o.

70 Dr. Kane on the Compounds of Ammonia.

These examples establish, in this case, the complete similarity of action of
hydrogen, whether combined with oxygen or amidogene.

In the second part of the present memoir will be found a remarkable instance
of the replacement of water by ammonia. There was described a new chlor-
oxide of copper, GUcl-\-'2cuo:, this unites with water, forming a brown powder,

cud -\- 2CMO + HO,

evidently analogous to dry Brunswick green,

cud -\- 2 CMo -|- cuo ;

but it also unites with dry ammonia to form a brown powder,

cud -\- 2 cuo -|- HA£? ;

under which form the replacement of ho by cuo, and of both by hac?, is evidently
showrn.

When once the principle of ammonia being considered as amidide of hydro-
gen, has been steadily brought before the mind, the nature of a vast class of
combinations, the functions of the ammonia in which had previously presented
great difficulty, is at once cleared up. Thus the combinations of ammonia with
the chlorides of tin, of antimony, of phosphorus, &c. are at once seen to resemble
those which many of the same bodies enter into with water, in equally definite
proportions ; thus snd^ + hac? is a white solid body, and snd^ -f ho is equally
white and solid. The compounds of the chlorides and oxysalts of the magnesian
class of metals present a parallelism still more close, and to which, after some
time, I shall again refer.

A class of bodies, the nature of which has frequently given occasion to dis-
cussion, is the combinations of the oxygen acids with dry ammonia. Of these,
the most remarkable and the most accurately studied is that with sulphuric acid,
and I shall consider it in these observations as the type of the whole class.

There are two opinions of the nature of this body, — first, that which vaguely
considering ammonia as a base per se, looks upon the existence of two classes of
ammoniacal salts, one merely of ammonia, the other of oxide of ammonium, as
possible, and enumerates this and other similar bodies in the former group ;
second, that which considers the sulphuric acid and ammonia as being mutually

Dr, Kane on the Compounds 0/ Ammonia. 71

decomposed, and water being formed, an amidide to be produced, with which the
water remains united. Thus there is SO3-I-NH3 or sOg-NHj-)- oh.

From the latter view, although supported by the high sanction of Dumas and
many others, I must dissent. We have no reason to suppose water to be con-
tained in the compound in this eliminated form ; and unless we find no other
legitimate method of explaining its origin and properties, an hypothesis of that
kind should not be resorted to.

Previous to discussing the first point of view, I must make some observations
as to the view of ammonia being an independent base. This phrase has had its
origin in the earliest age of organic chemistry, when the volatile ranking with
the fixed alcalies, chemists were contented with the observation that there were
salts of ammonia, as there were salts of potash and soda, without recognizing ac-
curately any difference of type of constitution amongst them. The progress of
analysis, however, pointed out the presence of water in all ordinary ammoniacal
salts of the oxygen acids, and hence the notion of the independent basic power
of ammonia became almost forgotten. Indeed, if one examines what is said by
systematic writers on the combinations of the dry acids with dry ammonia, it will
be found that no definite or distinct idea of their nature has been formed ; that
they are grouped together to separate them from the real ammoniacal salts,
which are said to contain ammonium, but that no opinion of their intimate con-
stitution has been hazarded even by Berzelius. In fact in order to understand
their nature, our opinions as to the words acid and base must be reviewed. We
can no longer look upon oxygen as being the sole negative element of basic
bodies, since sulphur identifies itself with it in all its principles of action, and the
analogy has been extended with some justice even to chlorine, iodine, and bromine.
Hence there can be no doubt but that amidogene, which relates itself to oxygen
so closely in a multiplicity of instances, may form the negative element in com-
binations of this kind, and as water, oxide of hydrogen, acts as a base, so may
ammonia as amidide of hydrogen. The difference between the vague old idea
of ammonia as an alkali, and the definite principle of the basic power of amidide
of hydrogen will be at once felt ; in fact the alkali, the body which resembles
and replaces in combination the other alkalies, potash and soda, is not ammonia,
but ammonia and water, not amidide of hydrogen, but oxide of ammonium, (of
Berzelius). Whilst the amidide of hydrogen, ammonia alone, is analogous to,

72 Dr. Kane on the Compounds of Ammonia.

and replaces oxide of hydrogen, or the oxides of the magnesian class of metals.
It is this distinctness in the point of view which will enable us to apply this
principle in a useful manner.

Now, taking the instance before described, there is

H.0-I-SO3, similar to H.Acif + sOa;

and the circumstance of the latter not precipitating barytes water, or chloride of
barium, is at once seen to result from the heterogeniety of the negative ingre-
dients in the two cases ; because, arranging the formulee according to Dulong's
view, to which the opinions of chemists now so generally incline, there is

H -j- so^ and h -\- xdso^ ;

and the formation of Ba.so^, which results naturally in the former case, becomes
complicated and difficult in the latter. In fact the body Adso^ is quite distinct
from any thing belonging to sulphuric acid, and can only give origin to it from
a complete destruction of the powerful affinities by which it was at first produced.
This view of the basic action of ammonia, and of its relation to acids, will be
found to lead to considerations of the highest interest to organic chemistry, but
which it jvould be improper to introduce here, in the detail which alone could
be of use.

Prop. V. — That the so called oxide of ammonium, nh^o, is oxyamidide of
hydrogen, and that sal ammoniac is chlor-amidide of hydrogen.

The only reason which has been advanced in support of the Berzelian ammo-
nium theory, is the beautiful symmetry with which the ammoniacal and potash
salts are by it invested, and that as the similarity and replacing power of 0H.NH3
and OK constituted one of the best authenticated facts in the doctrine of isomor-
phism, it was but reasonable to suppose the corresponding portions of those
symbols, hnHj and k to belong to the same class. The circumstance also of the
ammoniacal amalgam preserving so perfectly a metallic appearance, although its
density becomes so wonderfully diminished, lent to the idea of the existence of a
metal (ammonium) powerful support ; and there is indeed nothing in the theory
which I now bring forward to negative the leading principles of that view, by
the adoption of which so great simplicity had been conferred on the history of

Dr. Kane on the Compounds of Ammonia. 73

the ammonia salts. Thus according to my ideas, as well as in the Berzelian
view, the c/nh^ replaces c^k, and onh^ replaces ok in combination, and also nh^,
if isolated, should be considered as fulfilling the functions of k ; but in the theory
now proposed an additional step is made, by which we are conducted to a closer
and more distinct view of the inner constitution of these bodies.

When we place in contact two substances both compound, and which mu-
tually combine, in order to judge of the mode in which these elements unite, we
must examine the nature of the affinities by which a breaking up of the original
constitution might be effected, and likewise those which would tend to maintain
the two constituents in their primitive condition, and allow merely of their union
with one another. On these circumstances, and by the general mode of reaction
of the new substances formed, must the construction of its rational formula be
founded. If we contemplate the reaction of dry chloride of hydrogen and
amidide of hydrogen, when brought into contact, we shall not be able to trace
any tendency in the latter to deprive the chlorine of the hydrogen with which it
is united ; on the contrary, we find the affinity of chlorine for hydrogen so pre-
ponderating, that ammonia, by its agency, may be reduced to simple azote. It
is therefore contrary to all first principles of chemical affinity to believe, that in
the combination of the chloride with the amidide of hydrogen, all the hydrogen
can exist in one group of the formula, whilst chlorine alone constitutes the other;
since, if we had amidogene or ammonium isolated, there can be no doubt but that
chlorine could take hydrogen from both. That assumption could only become
justifiable if rendered necessary by strongly corroborating facts, and it will be
found that no facts at all sufficiently in point can be brought forward.

Regarding ammonia as amidide of hydrogen, its union with chloride of
hydrogen becomes but a particular case, although one of the most important, of
the general tendency of chlorides, oxides, and amidides of the same or of similar
radicals, to unite and form double chlor-oxides, chlor-amidides, or oxamidides.
In fact, if we look to the formation of white precipitate by corrosive sublimate
and water of ammonia, it will be seen that the decomposition and combinations
are on each side quite symmetrical ; thus, there is

2Hgcl-^ 2HAd= (Hgcl-{- BgAd) + (HcZ-f- HA(/).

The two resulting compounds, white precipitate and sal ammoniac, being strictly
bodies of the same type, one containing quicksilver and the other hydrogen.

VOL. XIX. h

74 Dr. Kane on the Compounds of Ammonia.

I sought very frequently to obtain sal ammoniac combined with water of
crystallization, in order to produce a parallel to the compound

•agcl-\-'2.yigo-\-ugKd,

but unsuccessfully. Yet if we consider the close relations of hydrogen and cop-
per, and of oxygen and amidogene, we will find in the bodies

CMc/ -|- 2 CMO + HO

cud -\- ^cuo -\- cuo

cud -\- 2 CUO 4" HA6?

similar cases, in the same way as quicksilver, gives

vigd -\- 2 Hg-o + Hg-o ;

and also the soluble ammonia chloride of copper, whether written

cud -\- 2H\d ■\- HO,
or

(hc/+ HArf) + (CMO.HArf),

presents analogies fully supplying the place of hydrated sal ammoniac.

To sal ammoniac itself the copper and zinc series affords numerous analogues.
Thus, the perfectly definite and well characterized bodies,

1. cud-\-nkd.

2. znc^-j- HArf.

3. md -\- HArf.

correspond to

n.cl -\- HAC? ;

whilst we find for the ordinary compound

cud -J- (h.c/ + -akd) + 2 ho,

the body

znd -\- (znd -\- nKd)

and also

znd -\- {znd -\- hac?) + {no.Hkd),
or else

zncl-\-iucl-\-HKd)-\-{zno.vLA.d).

Dr. Kane on the Compounds of Ammonia. *lb

These analogies are so remarkable, that any detailed comment on them is un-
necessary.

Since the oxide of ammonium of Berzelius possesses a definite constitution
only in the salts of oxygen acids with which it may unite, the superior simplicity
and distinctness of the present view becomes still more remarkable in its case than
in the former. We have seen that in combination with oxides the amidide of
hydrogen or of the metals assumes, even in the simplest cases, very complicated
formulae ; thus, the

Oxamidide of mercury is

iig\d -j- 2 H^o -j- 3 HO.

Oxamidide of copper is

2 CMAcf -j- CMC 4" 6 HO.

Oxamidide of gold is

2 Kuxdy -{■ AMO3 -f- 6 HO.

When, therefore, we come to examine the constitution of water of ammonia, a
similarly large number of molecules may be expected to be contained in its equi-
valent group, and in the fact of all the oxamidides above described, and also that
of silver, the analysis of which I was obliged to abandon, being the most dange-
rous and explosive bodies, we may trace the source of a facility of decomposition
in the oxamidides of hydrogen, which prevents us from obtaining even the degree
of definite constitution which has been found to exist in the hydrates of the
chloride of hydrogen, although the approximation in the strongest water of am-
monia to the formula nh3-|-4ho cannot be overlooked ; and therein also we
find the explanation of the want of success in obtaining, in an isolated form, the
oxide of ammonium, which has always been, and must continue, an objection to
the Berzelian theory.

The transition from the view of the constitution of sal ammoniac just de-
scribed, to the corresponding theory of the salts with oxygen acids, is very simple,
and will not require much exposition. Giving to the oil of vitriol the formula
so^-|- H, it will at once result that hydrogen combinations of that form should as
easily unite with the amidide of hydrogen as with any of the corresponding
oxides; and hence the ordinary sulphate of ammonia becomes H.SO4-I- ha6?, the
nitrate of ammonia HNOg -J- HAof. In its common form the sulphate of ammonia

L 2

76 Dr. Kane on the Compounds of Ammonia.

assumes two equivalents of water, and becomes H.SO4 + hac^.ho, with which very
many analogues will be found. Thus in the magnesian class we find the sul-
phate of copper uniting with ammonia in a similar manner to form the body
CMSO4.+ BAd. In nickel there is m.so^ + ha(/; and in the zinc combinations
there is not merely znso^ + ha^, but znso^ -j- hacJ.ho, resembling in constitution
the ordinary sulphate of ammonia. It is very much to be regretted that the cir-
cumstance of water decomposing these bodies prevents the question of their
isomorphism with the ordinary ammonia salts from being fully determined, but
it is not improbable that future research may enable some instances to be
examined.*

• In the Jahresbericht for 1837, (17th year,) page 139, Berzelius, in commenting on the inte-
resting results of Heinrich Rose on the combinations of dry sulphuric acid and the chlorides of the
alkaline metals, &c., speaks of the combination of sulphuric acid and sal ammoniac in the following
terms, which, that work being but little circulated in Ireland, I shall here translate, as the opinions of
that eminent chemical philosopher must affect considerably the judgment of chemists concerning the
views which I have proposed.

" These facts are of great theoretical interest. They appear, if not expressly to answer, at least
to give indications for the solution of a great variety of questions. That, for example, whether sal
ammoniac consists of muriatic acid and ammonia, or of the metallic body, ammonium, and chlorine.
The great analogy between chloride of potassium and sal ammoniac seems to me to speak plainly
enough in this question, but distinguished chemists appear not to approve of this evidence, and prefer
the former view as the more probable. If we consider the action of dry sulphuric acid on sal ammo-
niac as a new form of the question put in order to compel an answer, the answer given must negative
the view of hydrochlorate of ammonia. Dry sulphuric aeid, combined with ammonia, cannot be
expelled by muriatic acid, and consequently has a greater affinity for it than the latter. It is hence
clear, that if muriatic acid were present in sal ammoniac it should be expelled by the dry sulphuric
acid. On the contrary, however, the acid unites with the sal ammoniac, and forms a body, which
in all its relations corresponds to the compounds of the acid with the chlorides of potassium and
sodium, and it is only by a higher temperature being applied that decomposition sets in, and there
are formed dry sulphate of ammonia and free hydrochloric acid. My view may be rather keen-
edged, but it appears to me that these experiments of Rose's declare with positive openness the
sal ammoniac to be chloride of ammonium, and not hydro-chlorate of ammonia." — Page 141.

If wo look upon the relation between ammonia and chloride of hydrogen as being in accordance
with the old view, that of acid to base, then the criticism of Berzehus must be considered as possess-
ing very considerable accuracy and force. But it has been my great object in the present section to
show, that our views in this respect require a profound alteration. When we apply to the explana-
tion of Rose's results the lights which we receive, in addition, from the change in our point of view,
and that we consider the oxyamidide and chloro-amidide of hydrogen as related to each other, Uke

Dr. Ka^e on the Compounds of Ammonia. 77

Prop. VI. — That the ordinary/ ammonia salts ally themselves to the salts of the
copper and zinc class, which contain two equivalents oj" oxide.

The subject of this proposition is one of the most remarkable which I have
been induced to adopt in the course of these researches, and the nature of the
evidence in its favour will require a cautious and detailed examination of the
Individual instances of replacement by which it is supported.

I have pointed out already, briefly, that all those ammonia-copper, zinc, and
nickel combinations which are formed by solution in water, must be looked upon
as combinations of ordinary ammoniacal salts with metallic oxide and amidide of
hydrogen, as well as occasionally still more water, at least in their crystallized
condition. As the establishment of this principle becomes of great importance,
I shall again sum up the proofs of it, and notice one or two examples, which were
not at that time alluded to. The progress of the reaction, in which at first a
pure ammoniacal salt and a basic metallic compound is always formed, indicates
the nature of the resulting body very remarkably ; and when we consider that
the bodies generated by dry ammoniacal gas were in all cases quite different, the
evidence becomes almost complete ; likewise, where we find that in the quick-
silver compounds the formation of the ammonia-quicksilver body occurs from the
commencement, and we cannot trace any stage at which the deposition of a sub-

cbloride and oxide of potassium, it appears quite natural that sal ammoniac should combine with
acids, as chloride of potassium does in some instances, and that there should be so, -f- (hcI-\- axd)
as there is so, -|- (ho -\- H\d) equivalent to acrOj -j- kg and 2cr03 4- kc^. On this view there is no
reason for the expulsion of chloride of hydrogen as being the weaker acid, but by heat the expulsion
of HC^ can easily be understood. We cannot, by heating so, -|- Ho.HArf, expel ho, without other
effects complicating the result ; but the reaction in the case of so, -|- Hc/.HAfZ takes place with greater
ease and completeness. The compound so, -f- Hcl, formed by Aim6, though not analyzed, evidently
resembles so, -{- ho ; and by the addition of ammonia a compound of an equivalent character should
be produced. Another similar case is the brown powder, so, + (cmo -f- Hci), which, when heated,
gives so, + CMC and h.c^, as there are so, 4- cmo.ho and so, + cuo.Hxd, which give precisely
similar results. Berzelius appears to have understood from my description, that when dry c^h is
passed over dry cmo.so,, the brown mass becomes moist from free sulphuric acid; that, however, is
not the fact, water is set free only when the sulphate of copper is not dry ; the brown mass does
not fume nor grow damp ; it does not give any indication of free acid. The body so, -|- cuo.cla is
perfectly definite and well characterized.

78 Dr. Kane on the Compounds oj" Ammonia.

stance free from ammonia has occurred, some fundamental distinction must
necessarily be drawn between the resulting ammonia bodies of the mercurial
series and those containing copper, zinc, or nickel.

A remarkable example of this kind is furnished by nitrate of silver. When
dry ammonia is passed over nitrate of silver it is absorbed in quantity, but by the
application of a moderate heat it can be all again expelled. If an excess of water
of ammonia be added to nitrate of silver there is obtained the crystalline com-
pound analyzed by Mitscherlich and myself, and which, when heated, gives
common nitrate of ammonia, metallic silver, and the elements of amidogene.
Thus there are two bodies,

1. Ag-CNOj-j-^NHj.

2. HO.NO5.NH3-I- A^-,A</.

And in the latter case the formation of the common ammoniacal salt and of the
metallic amidide becomes quite manifest.

Recurring to the constitution of the ammonia sulphate of copper, there is

1. HO.sO3.HAj4~CMO.HA6?.
In the zinc series there is

2. HO.sO3.HA6J-j~zrao.HArf 4" 2 HO.

In the nickel series,

3. Ho.sOyUAd-\-mo.uAd-\-HO.

Here a property is found fully displayed, which in the ordinary aminonla salts is
either latent, or else but feebly manifested, except when in combination ; that is,
the power of combining with water of crystallization, or with a group of equiva-
lents of the same type, and capable of representing such. If we set out from the
common sulphate of potash, and one form of sulphate of ammonia, quite anhydrous,
the second gives to us in HO.so3.HArf4- ho the commencement of the series, the
completion of which, for the ordinary salts of ammonia, must be sought in the
common alums, where there is

(H0.SO3.HArf-|-6H0)4-(A403.3sO3+ 18ho),

and in which KO.SO3 is similarly circumstanced.

The complex group, partly metallic oxide and partly ammonia, which oecu-

Dr. Kane on the Compounds of Ammonia. 79

pies one portion of the formula, leads naturally to the study of still more
remarkable cases of the operation of these principles.

The bodies

1. HO.SOa.HAC?-}- HO.

2. HO.SOj.HAcf-f-ZnO.

3. CMO.SOj.HAC?.

4. zwo.sO3.HArf.
and in the quicksilver compounds,

5. Hg-O.N05.HArf-f-2H^O.

6. i{go.^OyHgh.d -\-2iigo.

7. ngo.sOyUgkd-\-2ugo.

present to our view a series passing from common sulphate of ammonia to am-
monia turbith, in which the successive stages of replacement of hydrogen by
metal are so connected, and follow so naturally, that it appears to me very
difficult to refuse consent to the proposition that the latter members are consti-
tuted on the type of the former, and consequently that we may have forms of
ammonia salts, in which the oxygen and amidogene are combined, not with
hydrogen, but with metal, and in which, therefore, the peculiarly basic character
should preponderate.

If we now for a moment contemplate the formula of a double ammonia sul-
phate of that class, whose history has been cleared up by Graham, it will be
foimd that some considerations of a most interesting nature will result from their
relations to the group last noticed. The double sulphate of copper and ammonia
is , , _

HO.SO3. HArf -\- CMO.SO3 -J- 4hO.

Graham had himself suggested the following form for the ammonia sulphate of
copper described by Rose,

CMO.SO3.HArf -|- CMOSO3 + 4 HArf,

but only as a speculation, the state of our knowledge of the ammonia compounds
then not allowing the proper demonstration of its truth. The majority of
sulphates absorb, however, a whole number of equivalents of ammonia, thus
there is

80 Dr. Kane on the Compounds of Ammonia.

1. ZWO. SO3. HAC?4"2HArf.

2. cdo . SO3 . nxd -\- 2 hac?.

3. NW . SO3, HAC?-|"2HArf.

4. coo . SO3 . nkd -\- 2 nxd.
evidently corresponding to

5. zreo.so3.HO-|-2HO, &c.

The close relation which has been thus shown to exist between the most inti-
mately united portion of the amidide of hydrogen and of the constitutional water
of the magnesian class of sulphates, may be rendered still more remarkably
evident from the following examples.

Anthon has discovered a peculiarly hydrated condition of the sulphate of
zinc, which has the formula zno . SO3 + 3|^ho. It crystallizes in rhomboids, of
which the exact form has not been determined ; this salt appears to be produced
under circumstances not yet completely known, but it would be most interesting
to ascertain exactly its crystalline admeasurement. I consider that the halving
of the equivalent of water in this salt results from precisely the same law as the
absorption of half an equivalent of ammonia by dry sulphate of copper, and that
its formula should be

1. 27ZO. S03.HO + ZWO.S03-|-6hO,

the ammonia zinc sulphate being

2. Ho.sOg.HArf-f znoso3-f-6HO.

In this salt, as I could not produce it at will, it was impossible to determine
whether the half atom of water was more powerfully retained, so as to give the
dry double salt

3. zno . SO3 . HO -\- zno . SO3,
as there is

4. cuo .sOj.uxd -{-cuoso^;

but every thing would lead us to suppose it to be in a state of combination dif-
fering from the rest.

In a family of the salts differing but very little from the ordinary alums,
there will be found some very remarkable examples of the similarity of action of

Dr. Kane on the Compounds of Ammonia. 81

two equivalents of a magnesian protoxide, with oxide of kalium, or ammonia and
water. This family was discovered by Klauer, who formed double sulphates of
alumina with the protoxides of iron and nickel, with magnesia and oxide of zinc ;
and lately one of the most remarkable examples of this class, a double sulphate
of alumina and protoxide of manganese was found forming a thick bed on the
coast of Africa, and brought to this country, where it has been analyzed by
Apjohn and by myself.

The general formula of this class, as has been accurately determined with
the manganese and zinc members, is as follows : ro =^ protoxide,

1 . (ro . SO3 . ho) -\- (A^^Og + 3 SO3) -J- 24 HO,

resembling accurately

2. (ho . SO3 . ukd) -\- {Al.p.j -{- 3 SO3) 4" 24 HO,
which it further assimilates itself to in taste and solubility.

The relation of the water of these alums to heat is very remarkable, and
indicates very accurately the nature of their constitution. Thus by a temperature
of 212°, eighteen equivalents of water are lost; by a heat of 300° there are
given out six more ; but the expulsion of the remaining equivalent requires a
temperature equal to the melting point of lead, indicating the intenseness of the
power with which it is retained ; in fact the zinc alum may be looked on as com-
posed of ordinary sulphate of zinc and ordinary sulphate of alumina,

zno . SO3. HO-]- 6ho

A4O3.3SO34- 18ho

zno . SO3 . HO -f- A/2O3. 3SO3 + 24ho.

The form mwo . SO3. ho-}- 6ho is not the ordinary condition of proto-sulphate
of manganese, but it also can be obtained with that quantity of water.

The preceding considerations showing, with considerable probability, that
two equivalents of an oxide of the magnesian class may replace in combination,
and even affect isomorphism with an equivalent of the alkaline group, it may be
proper to inquire how far evidence capable of illustrating the theory under
examination can be collected from amongst the numerous species of minerals
which are supposed to present cases of replacement of an alkali by an earth. In
such cases the substitution may take place in two ways, which renders the
demonstration of its occurrence much more difficult than it might at first be

VOL. XIX. M

82 Dr. Kane on the Compounds of Ammonia.

supposed ; in the first class, the substituting equivalents being oxides of the same,
in the second they being oxides of different bases. Thus in the former, two atoms
of lime, magnesia, or of water ; in the latter, one of lime and one of water, or
one of magnesia and one of water, likewise lime and magnesia without water,
lime and protoxide of iron, &c. The complication thus arising must render new
researches for the determination of the point not only necessary, but very diffi-
cult ; and hence, although I would look very sanguinely to a re-examination of
the harmatome and zeolitic groups for a great accession to our accurate know-
ledge of this department of science, I have not been able to deduce from analyses
at present recorded any definite results, except in one instance, which, however,
in itself may be almost looked upon as conclusive.

This example consists in the group of minerals consisting of natrolite, meso-
lite, and scolezite, which constitute one of the best instances of isomorphism
that has been as yet found, and are related to each other in constitution in a
very simple manner : the natrolite being a hydrated silicate of soda and alumina,
the scolezite being a hydrated silicate of lime and alumina, and the mesolite,
probably a product of the crystallizing of the two together, being intermediate
in constitution. Now the formula accurately given by analyses for the pure
species are, thus,

Nao . s^03 -\- A^Og . sz'Og -j- 2 ho

and

cao . s^03 + a/jOj . si'Oj -|- 3 ho, or better,

cao . HO . sioj -\- aI^o^ . siog -\- 2 ho.

Here the equivalency of cao. ho to noo is most remarkable, and certainly must
be allowed to go a great way towards confirming the views regarding the nature
of the compounds of ammonia, from which the analogy of nh.j.h to H.o, and
hence to coo or ugo, and of nh^o to cao . ho, &c. was first arrived at.*

* Since the above views were completely formed, and the memoir read, I was singularly struck
by finding in the Elemente der Crystallographie of Gustav Rose, the same view suggested of the
replacement of soda, not by lime, but by its hydrate. Intending to commence an examination of
the zeolitic group under the point of view noticed above, I began by the study of their crystallogra-
phie relations, to which I had not before applied myself, and selected his work as the system best
adapted to my purpose. In speaking of the composition of wernerite, (page 158,) the following pas-
sage occurs, which, as the work is not very common in Ireland, I shall translate. " The above

Dr. Kane on the Compounds of Ammonia. 83

During the examination of the various classes of compounds of ammonia,
which the objects of these researches rendered necessary, a variety of results were
obtained, which are calculated to throw light on the relation in which the ammo-
niacal salts stand to the ordinary basic salts of the same acid, and likewise to
illustrate the connexion between the corresponding so called neutral and basic
salts. In the cases of the nitrates of mercury, my observations have the effect of
extending to that metal the law discovered by Graham for the nitrates of the
metals of the magnesian class, but as that distinguished chemist has not deduced
any general idea of the constitution of the basic sulphates from his observations,
I shall briefly suggest such ideas as have occurred to me from my own investi-
gations.

The general principle that the transition from the neutral to the basic con-
dition in salts takes place by the replacement of water by metallic oxide, has, as
I conceive, received the fullest confirmation ; but I do not consider that the cor-
responding substitution of water for metallic oxide, which exists so markedly in
the sub-nitrates of copper and bismuth can be looked upon as forming a general
law. Thus there certainly does not appear the same perfect symmetry between

ho.no3 4"3h^o and Hg-o . N05-j-Hg-o + 2Ho

as between

cwo . NO3 -{- 3ho and ho . no^ -j- 3cmo ;

and although I do not possess absolute proof of the existence of a sub-nitrate

formula is that which Hartwell has established. According to his analyses, lime and soda replace
one another in indeterminate proportions, and are consequently placed in the formula under one
another, as isomorphous bodies, although there is not as yet known any positive example of the
isomorphism of lime and soda. The sulphate of soda or thenardite does not appear to be isomor-
phous with anhydrite, and the analyses of mesotype by Gehlen and Fuchs, show perfectly that lime
and soda may replace each other, but that in this case, the quantity of water in the compound
also changes, so that one atom of soda can be isomorphous only with an atom of lime -\- an atom of
water, which must consequently be assumed in all other zeolites where lime and soda appear to re-
place each other, as, for example, in the chabazies." It is singularly interesting to find, that starting
from an origin apparently so remote as the composition of white precipitate, I have been gradually
conducted to the development of the same principle as had already, though unknown to me, been
announced, even though but as a suggestion, by an authority so deservedly high in chemistry and
mineralogy as Gustav Rose.

M 2

84 Dr. Kane on the Compounds of Ammonia.

having the four equivalents of oxide all alike, yet I cannot consider such an
arrangement as being excluded.

Indeed an idea which was suggested to me by the mercurial nitrates is, that
the constitution of the nitrates may be better shovra by vfriting the formula of
their class as follows :

RO . NO5 . KO "1- 2 RO.

R being either water or metallic oxide. There is then

and the red basic nitrate,
and still further,

H^O . NO5 . H^O -j- 2 HO,
H^O . NO5 . HO -j- 2 H^O,

Hg-O. NO5 . H^O + 2vigO -\- 2 H^O.

H^O . NOj . HAC? -|" 2Hg'0,
HOO . NO5 . Hg'AC? + 2 UgO.

As in the copper and bismuth nitrates, no water whatsoever can be separated
without a corresponding quantity of acid being set free, it is difficult to ascertain
whether one atom of the water is more firmly attached to the acid than the other
two ; but in the case of nitrate of magnesia, Graham has found that two of the
equivalents of water may be separated much more easily than the third, and
hence its formula should be, as in the quicksilver series,

M^O . NO5 . HO 4" 2 HO.
Mg-O.NOj H0-f-2M^0.

Thus connecting still further mercury with the metals of the magnesian class.
This form of expression for the nitrates connects them much more closely with
the sulphates than the older view, and the equivalent to the right of the acid
evidently replaces the saline water of the magnesian sulphates. Thus a sulphate
of that group is generally, though not always,

RO . SO3 . no -j- 2?ZH0,
n being a whole number.

In the sulphates the most common form of basic constitution approaches still
more closely to the type of basic nitrates than in the neutral state ; thus.

Dr. Kane on the Compounds of Ammonia. ,85

1. CMO . SO3 . CMO + 2CMO.

2. zno SO3 . z?io -{- 2 zno.
which are those most easily formed, and most permanent.

A great number of circumstances conspire to render the derivation of the
basic sulphates of the magnesian class, from the neutral condition, exceedingly
complicated. Thus the neutral salts crystallize with quantities of water variable
within very extensive limits, and the proportion of metallic oxide by which it
may be replaced, is subject to fluctuations equally wide : moreover, the replace-
ment of the water by metallic oxide may be but partial, and hence the different
hydrated conditions in which the basic salts exist. From these causes may be
deduced the possible existence of a very extensive series of basic sulphates vary-
ing considerably in type, and subject only to the one restriction, that in all their
different conditions the sum of the equivalents of water and metallic oxide shall
always be equal to the sum of the same constituents in some one of the forms in
which the neutral salt may crystallize. So that the general expression of the
class becomes

RO . SO3. v o -f- 2re > o.

> indicating the sum of the mutually replacing elements. In the synopsis of
the analytical results of the basic sulphates contained in the sections on the cop-
per and zinc compounds, the instances given can be so immediately compared
with the above expression, that it is not necessary to reinsert them here.

Although the general form of the crystallized chlorides of the magnesian
group of metals, as was well shown by Graham, consists in the adhesion of pairs
of equivalents of water, yet in the construction of the basic chlorides or chlor-
oxides the form pointed out for the nitrates and some basic sulphates is adopted;
thus, the ordinary chloride of copper, cmc^-1-2ho, cannot be obtained in combi-
nation with more water, but the tendency to assume the fourth molecule is shown
in its basic forms, thus it may become

cud -j- 2 cuo,
and thence

CUCl-\-2 CUO -{- CMC

cucl-\-2cuo-\-no

cud -\- 2 CUO -\- HArf

as has been already noticed in another point of view.

86 Dr. Kane on the Compounds of Ammonia.

In quicksilver there is the oxychloride

ugcl -\- 2 ugo ■\- HgO,
and then

Hgcl 4- 2 wgo -j- Hg-At?

evidently corresponding ; but in most instances the basic chlorides follow, like
the sulphates, the form of the hydrated neutral conditions, and hence there is

zncl -\- 6 zno
cud -j- 4 cuo
cud -j- 2 cuo

as there are two, four, or six atoms of water in the crystallized conditions of
various chlorides.

Prop. VII. — That if chlorine could be separated from sal ammoniac, the resi-
dual NH^ should be regarded as nh^ -}- 2 h, sub-amidide of hydrogen, as
when by removing the chlorine from white precipitate, the sub-amidide of
mercury, nh^-J- '2,ng, formed by the action of water of ammonia on calomel,
should remain.

The discussion of this proposition leads to some considerations as to the
nature of the so called compound radicals, which of late years have played so
distinguished a part in the progress of chemical philosophy. The views which
I shall put forward I offer with considerable hesitation, as not resting directly
upon experimental evidence, but resulting from the peculiar manner in which
my researches have induced me to contemplate the nature of those hypothetic
bodies.

The fundamental idea that a compound body might so manifest its affinities
as to simulate the properties of an undecompounded substance, received its first
conception, as well as proof, from the beautiful discovery of cyanogen by Gay
Lussac, which continues even up to the present day the most glaring instance of
the truth, as well as the most excellent example of the nature of the theory of
compound radicals.

The extension of the principle involved in the very existence of cyanogen, to
explain the constitution of classes of bodies of organic origin presenting strong
analogies to the cyanides, although the compound radicals of their series could

Dr. Kane on the Compounds of Ammonia. 87

not be successfully isolated, gave to the theory of organic chemistry great clear-
ness and consistency, and was indeed philosophically just, since from the facility
of decomposition of cyanogen in a variety of ways, we must infer that many
bodies of similar nature may be so much more easily decomposed, that in our
ordinary modes of operating on them their preservation becomes impossible, pre-
cisely as the existence of cyanogen had escaped the acuteness of Proust, of Ber-
thoUet, and others, who had experimented on prussic acid at former times. I
therefore do not hesitate to place the theory of compound radicals amongst the
greatest benefits which chemistry has lately received, and hope with confident
expectation for the addition of very many new examples to the list, hitherto
restricted to cyanogen and mellon.

But what is the constitution of a compound radical ? does it consist of a
group, beyond which we cannot go without reducing it to its merely undecom-
posable constituents ? or has it, again, a symmetricity of constitution like the
whole mass from which it had been eliminated. I shall not touch upon this ques-
tion as affecting cyanogen, benzoyl, or similar bodies, limiting myself altogether
to the examination of how far our ideas of the nature of ammonium may be
affected by that point of view.

In sal ammoniac, the chlorine is certainly united with a body which replaces
potassium, and if we could discover circumstances under which the chlorine
might be transferred to another substance, leaving all the hydrogen and azote
undisturbed, then the ammonium would be isolated ; but let us examine what
this ammonium should be. The sal ammoniac is chlor-amidide of hydrogen.
If the chlorine were removed, the amidogene should remain combined evidently
with twice as much hydrogen as constitutes ammonia, and this body, sub-amidide
of hydrogen, might well be able to represent in combination, and to combine
with, metals. This partial participation in metallic properties is found in other
sub-combinations, as in the sub-oxides of copper and of mercury, and hence the
generation of the ammoniacal amalgam, its low specific gravity, the sub-amidide
of hydrogen being probably gaseous : an extension of this view might illustrate
the condition of the isomorphism of two equivalents of one oxide with one of
another, (as pointed out in the alums and certain minerals in the last proposition,)
the former, perhaps, assuming the form o (ror) : the sub-oxide represented in
the brackets relating itself as a compound radical to the oxygen outside. Hence,

88 Dr. Kane on the Compounds of Ammonia.

likewise, a consideration of the problem, whether a second oxide be a combina-
tion of metal with oxygen, or of oxygen with the first oxide, which I must
consider as decided by the circumstance of the atomic weight containing one or
two equivalents of oxygen. Thus I look upon the study of the salts of mercury
as decisive upon the red oxide of that metal being protoxide, but the examination
of the compounds of manganese assigns to the black oxide the form (ivino) -\-o.

A remarkable fact in the history of the alkaline salts suggests an extension of
the views here discussed, which is thrown out as a speculation, and to which I
do not wish to attach otherwise importance. The sulphate of ammonia may be
written on the ammonium theory, SO3+0. (nh^), or SO3-J- o(ha</h) ; and
the ammonium being a basic amidide, it results that the ammoniacal salts
are all basic salts ; hence the condition which the salts of the magnesian class
may be made artificially to assume is that naturally belonging to those of the
ammoniacal series. Now as the ammonia and potash salts assimilate so com-
pletely, the speculation may be hazarded, that research will discover in potas-
sium a structure analogous to that which I have argued to exist in the so called
ammonium, and the result may show that the reason of the alkalies not producing
basic salts, arises from the circumstance of their salts being already basic in their
common form.

SUPPLEMENTARY NOTE

ON A COMPOUND HITHERTO CONSIDERED AS WHITE PRECIPITATE.

Some time since I learned that Professor Woehler had found that the white pre-
cipitate in the possession of some Hanoverian apothecaries differed in many
important particulars from that which formed the subject of my researches, as
well as of the experiments of verification made by Ullgren. The body in ques-
tion had been prepared by precipitating a solution of sal alembroth by potash in
the cold. The precipitate which is produced, resembles externally the true white
precipitate so completely as to have been always taken for it, and hence in many
pharmacopoeias this process is given for preparing white precipitate for medicinal
purposes. It is, however, quite different in its nature, and as its analysis is of
importance as well in a practical as in a theoretical point of view, the following
brief description of its nature is subjoined :

. Dr. Kane on the Compounds of Ammonia. 89

When heated It fuses into a clear liquid, giving off at the same time azote
and ammonia, but no water, if the precipitate had been completely dried. The
fused substance sublimes ultimately in a mass partly transparent like gum, and
partly white and opaque. When the sublimed mass is treated with water, it in part
dissolves, calomel remaining undissolved, the solution is neutral, and on exami-
nation is found to contain sal ammoniac and sublimate. If this new white preci-
pitate be boiled in water there results the same yellow powder, which is produced
by boiling the genuine white precipitate ; but the sal ammoniac is formed in the
liquor in much larger quantity.

The methods of analysis pursued were precisely the same as those described
in the memoir on white precipitate, and consequently it is unnecessary to repeat
the details of them here. The results of three analyses were :

I,

n.

III.

Mercury

:zz

65.42

66.27

65.74

Chlorine

f=

22.05

22.70

22.95

Ammonia

=:;

10.65

11.01

10.94

98.12 99.98 99.63

These numbers lead directly to the formula ugd -{- sh^, which should give
sg = 101.40 65.86

d = 35.42 23.01

NH3 = 17.14 11.13

153.96 100.00

This body may therefore be looked on as consisting of an atom of sublimate
and one of ammonia. Now the result of passing ammonia over sublimate is to
generate a white substance, 2c^Hg-4-NH3, which is evidently a kind of double
chloride, iigd-\-iigAdH.cl, similar to many bodies already noticed in these
researches, as

znd -{■ znAd.nd
CMSO4 4" cuA.d.nso^

This body is likewise of interest, as standing midway between sal ammoniac
and the real white precipitate, and serving to link bodies apparently so dissimilar
still more closely to the principles of the theory of the ammonia compounds

VOL. XIX. N

^ Dr. Kane on the Compounds oj" Ammonia.

developed in the present memoir ; the chlor-amidide of hydrogen, Hcl -\- Hxd,
and the chlor-amldide of mercury, ugcl -|- ugxd, being connected by the inter-
mediate chlor-amidide of mercury and hydrogen, ugcl + ha<^,

I had remarked long since, that by the addition of sal ammoniac to the water
in which the real white precipitate is boiled, its decomposition, or at least the
formation of the yellow powder is prevented. The white precipitate remains
white, but its nature is totally altered ; it is converted altogether into the new
compound, and it will be seen that its composition would be represented, sup-
posing it to be formed by the union of the two substances which had been put in
contact, for 2 (ugcl.jiUs) = {ugcl.ugxd -f hc/.hac?).

Such a mode of representing its nature would likewise explain its various
properties, but I prefer the view first described, and look upon this body as sim-
ply expressed by ugcl -f- ha</. I would propose for it the empirical name of
Woehler's white precipitate, and if one founded on composition be deemed ne-
cessary, that of the hydrargyro-chlor-amidide of hydrogen.

A reaction which I have lately observed, and which as a remarkable property
of white precipitate, is worthy of being noticed, is, that when the chlor-amidide
of mercury is boiled with an excess of chloride of copper, it is totally converted
into sal alembroth, and there results brunswick green. The reaction appears to
be as follows :

^ cud -^ Z {ugcl -{-ngkd) -\- 6ho = 2{cucl -\- Zcuo') -\- Z{2ugcl -\- i^ufil).

In the sal alembroth thus produced the proportions of its ingredients are .diffe-
rent from those of the more common form : the sublimate containing twice as
much chlorine as the sal ammoniac. It is, however, quite definite, and can be
easily procured by dissolving together sublimate and sal ammoniac in the proper
quantities. It crystallizes in two forms, one rhomboidal, the other in long silky
needles ; in the former condition the salt is dry, in the latter it retains an equiva-
lent of water. Frequent analyses gave for their composition the formulae

Rhomboidal state = 2h^c/-{- nh^c/.
Fibrous state = lugcl •\- su^cl -\- ho.

The ordinary form being, as is well known, iigcl-\--su^cl-\- ho.

gi-

ll. Description of the Cydippe Pomiformis mihi, (Beroe Ovatus, Flem.) with
Notice of an apparent^ undescrihed Species of Bolina, also found on the
Coast of Ireland. By Robert Patterson, Esq., Member of the Natural
History Society of Belfast.

Read 10th December, 1838.

It is proposed to give in the present paper some account of the appearance,
organization, economy, and habits of a Beroe, not uncommon on our Irish coast,
in the hope that such details may prove interesting with regard to the species
described, and may be of some value as illustrative of the family to which it
belongs.

These observations were commenced in the month of May, 1835, at which
time I resided in the immediate vicinity of the small sea-port town of Larne, in
the County of Antrim. My lodging was situated on the small peninsula termed
the Corran,* and nearly midway between the two stations, whence ferry-boats
ply to the opposite peninsula of Island Magee. Through the narrow channel,
across which these boats are continually plying, the tide runs with great rapidity
into Lame Lough. Hence I had, by means of the ferry-boats, an easy mode of
taking, at all hours during the day, the small Medusce and Crustacea, which the
flow of the tide placed within reach of a small canvass towing net. As the
Beroes could thus with facility be procured, and were to me highly attractive,
my sitting-room, for between two and three weeks, was never without some of
them. They were kept in glass jars, the water in which was changed twice
each day. The particulars which I then observed, were published in the Edin-
burgh New Philosophical Journal for January, 1836, and reasons adduced for
regarding the species as distinct from the Beroe Pileus, the only tentaculated
Beroe then regarded as British.

* This word in the Irish language signifies " Reaping Hook," to which implement the little
peninsula has a striking resemblance in form.

N 2

92 Mr. Patterson on the Cydippe Pomiformis.

The ensuing summer I again visited the same locality, and had the pleasure
of taking a Beroe similar in size to the one formerly described, but exhibiting
very conspicuously an arrangement of whitish coloured vessels, v?hich had their
origin near the lower part of the stomach, and branched off to the several bands
of cilia, one vessel running out to each band, and joining it not very far from the
centre.

On the 24th of June, 1837, I was again at the Corran, and succeeded not
only in taking three Beroes, exhibiting this singular structure, but with the
assistance of a friend was enabled to have it delineated. These drawings were
unfortunately mislaid before any more finished representation could be executed.

On the 8th of the next month, in Strangford Lough, I again took an indi-
vidual of the same description, but the circumstances under w^hich I was then
placed, prevented its being subjected to any critical examination.

Its occurrence on so many different occasions excited the hope that it would
again be met with ; and when at the beginning of June, 1838, I returned to my
former lodgings at the Corran, I felt desirous of being able to observe its pecu-
liarities, and ascertain its species. This desire was augmented by a careful
perusal of Doctor Fleming's paper, read before the Wernerian Society of Edin-
burgh 18th November, 1820, in which he describes a BeroS, subsequently
designated, in his History of Bristish Animals, B. ovatus. This animal ap-
peared to be furnished with vessels similar to those I had observed, but it
differed from mine in being destitute of tentacula. The following is an extract
from Dr. Fleming's description :

" The tube which conducts from the mouth to the centre of the body, and
is prolonged in its axis to the summit, had on each side a compressed organ
adhering to its walls. These terminated in the centre, each in an ovate head,
apparently containing air. Immediately below each head, there were numerous
twisted vessels, some of which contained a reddish fluid. The tube which
descended from the summit, as it approached the centre, suddenly expanded, and
sent off a branch to a vesicle on each side, after which it appeared to unite with
the one from the mouth. Each of the lateral vesicles terminated below in a blind
cavity, which contained a glandular body, to the upper surface of which several
white threads were attached. The upper extremity of each vesicle was open,
and terminated on the surface on each side, in the space between two ribs.

Mr. Patterson on the Cydippe Pomi/ormis. 93

From each side of the vesicle, near its connexion with the central vessel, there
arose a tube, which after dividing, sent a branch to each contiguous rib. The
cavity of these tubes, at their union with the ribs, appeared to be filled with a
whitish coloured pulp. Each rib is furnished with a tube uniting with it near
the middle. In consequence of this peculiar structure, I could easily observe
the water enter the tube at the summit, pass into the lateral vesicles, and go out
at their external openings ; and in some cases the motion of the current was
reversed."

On the 10th of June, 1838, I had an opportunity, for the first time, of
examining, under a lens, one of the Beroes exhibiting the peculiar ramiform
structure already noticed. The animal was lying, like that observed by Dr.
Fleming, with the mouth downwards, and evidently in an exhausted state. To
my great satisfaction I observed the particles of fluid in motion, nearly in the manner
that author has described, and in the vessels close to the stomach could observe
there were two currents flowing In opposite directions. The same was visible in the
whitish coloured vessels, going out to the bands of cilia. It was not apparent in
the " lateral vesicles," they were filled with water, which moved at times back-
wards and forwards, but did not exhibit the active and continuous current pre-
sented by the other parts. That water issued from them was, however, obvious,
by the effect visible on the fluid adjoining the terminal aperture, and exterior to
the body of the animal. While examining one of the " glandular" bodies, I
noticed that it did not always retain the same appearance, but was capable of
expansion and contraction, and that on one occasion it was extended almost to
the surface of the animal, moving within one of the " lateral vesicles," and ap-
proaching its external orifice. I waited in hopes that both of these " glandular"
bodies would be still more fully thrown out, and would prove to be tentacula ;
but the inertness of the animal prevented at that time the fulfilment of my
expectation. Next morning another Beroe was taken, vigorous and perfectly
uninjured, and with the whitish ramiform vessels equally conspicuous as in the
previous specimen. In the course of a few minutes it unfolded to my view its
graceful and ever varying tentacula, furnished with delicate filaments, and exhi-
biting a ceaseless variety of outline.

The presence of the tentacula removes the animal from the genus Beroe of
Fleming to the Pleurobrachia of the same author. His Inaccuracy in the present

94 ' Mr. Patterson on the tydippe Pomiformis.

instance was occasioned by his description having been drawn up from an exa-
mination of a single individual, " found in the Frith of Tay, in a pool left by
the tide." The animal was then in an exhausted state, when the tentacula would
naturally be retracted within the body. Dr. Fleming referred this species doubt-
fully to the ovata of Baster, but as they form not only distinct species, but
belong to different genera, it is necessary to substitute another appellation, and
as such I propose " Pomiformis."

Lesson, in his paper " Sur les Beroides,"* conjectures that the Beroe de-
scribed by Fleming, might eventually be found, as is now the case, to belong to
those bearing tentacula. The words in which this idea is expressed are the fol-
lowing : — " Peut-etre est ce au Cydippe globuleux qu'appartient I'espece trouvee
par le Dr. Fleming (Mem. Soc. Wer. t. iii. p. 400,) dans le detroit de Tay, et
qui n'avait point de prolongemens."

Having ascertained the identity of the Irish Beroe with that of Fleming, my
next object was to have such drawings and descriptions prepared as would dis-
tinguish it from the species I had formerly described, and which in size and
external appearance it precisely resembled. For this purpose I brought up with
me in sea-water to Belfast, three of each, and hastened to a friend, to whose
pencil I had been indebted on similar occasions. On my arrival it was found
that the white radiating vessels of the C. Pomiformis, which had been so conspi-
cuous when the animal was first taken, were scarcely perceptible. I took the
earliest opportunity of procuring a further supply, but found that at the end of
a few hours these distinguishing whitish coloured vessels were no longer visible.
Knowing, however, their situation, I examined them under a lens, and though
the vessels had lost their whiteness, saw in each the circulation of the fluid going
on as usual. I then took eleven of the Beroes, in which no apparatus of the
kind was conspicuous, and on subjecting them to a similar scrutiny, had the
satisfaction of discovering that the same structure existed in all, and consequently
that Dr. Fleming's Beroe, of the capture of which we have no record, save that
of a single individual in 1820, was identical with that which I had taken so fre-
quently, during successive years, at the entrance to Lame Lough.

In bringing together, under several heads, the observations made at various

* Annales des Sciences Naturelles, tome v.

Mr. Patterson on the Cydippe Pomiformis. 95

times on this Beroe, it is necessary to make frequent reference to its congener, the
Pleurobrachia Pileus, Flem., Beroe Pileus of Lamarck, Cydippe Pileus Eschs-
choltz, Cydippe Globuleux, BlainvlUe and Lesson, that the several points of accord-
ance or of difference may be enumerated as the description proceeds. Dr. Grant's
interesting and valuable paper " On the Nervous System of Beroe Pileus, Lam.,
and on the Structure of its Cilia,"* has rendered that species well known to natu-
ralists, and furnished a standard, with which the one here recorded may with
facility be compared.

In size it is from two to nine lines in length, and about a third less in breadth.
The general form is oval, but in some it is nearly globose, and in others flattened
towards the poles, and similar in shape to an orange. The difference is to be
attributed to a contractile power possessed by the animal, and not to any perma-
nent diversity in form. The body is transparent and colourless, with the excep-
tion of the reddish coloured intestinal vessels noticed by Dr. Fleming, and which
present a different aspect in different individuals.

The eight bands to which the cilia are attached extend about three-fourths of
the distance from the mouth to the anus, but approach more nearly to the latter,
and diminish in breadth towards either extremity. In C. Pileus there are about
forty in each band ; in C. Pomiformis the number in some individuals amounted
only to fifteen, and in none which I observed did it exceed twenty-seven. Along
each band a cord or slight ridge extends, dividing it longitudinally into two
equal parts. The filaments on each band consist therefore of two parcels, which
in general move simultaneously, although each portion possesses a separate and
independent power of motion.

Dr. Grant remarks, that the cilia of C. Pileus are the largest he had yet met
with in any animal, and states that " they are not single fibres, but consist of
several short straight transparent filaments, placed parallel to each other in a
single row, and connected together by the skin of the animal, like the rays sup-
porting the fins of a fish. Viewed with the aid of a lens, the parallel fibres
appeared like transparent tubes, sometimes a little detached from each other at
their free extremities by injury done to the connecting membrane, and at these
■parts the isolated spines projected stiffly outwards. When the fins were quite

* Trans. Zool. Soc. vol. i. p. 9.

96 Mr. Patterson on the Cydippe Pomiformis.

entire, the membrane connected the tubular rays to their extremity, where the
fin presented a slightly rounded outline."

In C. Pomiformis the cilia present appearances very dissimilar to the above.
In many individuals the filaments are not connected by any membrane, but
appear numerous, flat, tapering, and slightly recurved towards the extremity.
In others they are covered by a transparent membrane, divided as usual into
two equal parts, and showing in each half but one or two divisions. They
never exhibit an entire and unbroken surface, nor a continuous and regular
margin. It was natural to suppose that a membranous covering might origi-
nally have existed in all, but had been abraded or torn, and thus caused the
apparent diversity which the cilia exhibited in the number of their sub-
divisions ; but this conjecture was shaken, by observing that specimens of less
than the average size, and which might be presumed to be young, presented the
same want of uniformity. The dissimilarity which prevails in this particular
among different Beroes, will however be better estimated by a glance at the
annexed figures, than by any detailed description.

The entire cilia, never for more than a moment remain perfectly at rest, tm-
less when the animal is in a very exhausted state, and may hence be presumed
to be organs of respiration as well as of locomotion. Sometimes, however, those
of one or two continuous bands will vibrate, while all the remainder are still ; or
be at rest, while all the others are in motion. At times a slow vibration will
commence at one extremity of a band, and pass along it, like the wave which
can be impelled along an extended piece of cloth, or like the undulations of a
fluid. Hence it is obvious that the Beroe can direct the aqueous currents which
pass along the base of the cilia into any particular band, and can regulate at
pleasure the velocity of their undulations. In the larger species, which I have
named Bolina Hibernica, these currents are very conspicuous, and may be
seen under* each band, one ascending, the other descending at the same time
with great regularity.

* The size of this ciliograde varies from little more than half an inch to nearly two inches dia-
meter ; its figure is diversiform, being nearly round, oval, or cylindrical, but most generally some-
what compressed. The lobes at each side of the mouth, at times very protuberant, giving to the
animal a rudely cordate form, like the Mnemie de Schweiger. (Vid. Blainville, pi. 8, fig. 4.) The
surface smooth.

There are eight rows of cilia, the alternate ones much shorter than the others. The cilia are

Mr. Patterson on the Cydippe Pomiformis. 97

Dr. Sharpey remarks, " in the Beroe, and others of a similar form, the
cilia* point towards the closed extremity of the body, so that the opposite or
open end is carried forward." In the two species which have fallen under my
observation, the cilia, when at rest, point not to the closed but to the open ex-
tremity of the body, and as they strike downwards towards the closed extremity,
the animal is propelled forward in the contrary direction.

The tentacula of these animals were, next to the cilia, the most attractive
parts of their organization. They were seldom displayed immediately after the

detached, flexible, tapering, pointing upwards towards the mouth. At the upper extremity of each
of the shorter bands is a circular orifice, with a ciliated margin. From each of these four apertures
issues a singular aliform or auriform appendage ; these are regarded by Merteus as tentacula covered
with skin. Their appearance is extremely beautiful, both from their transparency and from the
numerous minute delicate pointed cilia along their edges. Their aspect was ever changing. When
first viewed they were pointed, erect, and hollowed longitudinally, so as to form a miniature repre-
sentation of the ears of a horse. At other times they extended horizontally from the body of the
animal, or were seen hanging loosely down hke the ears of a lap-dog, or curved like the petals of the
Martagon lily.

Between the 6th and the 18th of June, 1838, 1 took thirty-two specimens in a canvass towing-
net, at the entrance to Lame Lough, County of Antrim. It had not fallen under my observation
during any of the three previous summers, during which I had paid occasional visits to the same loca-
lity ; nor was it met with after the date mentioned. On showing to Robert Ball, Esq. of Dublin, and
William Thompson, Esq. of Belfast, several drawings of it taken from living specimens, I had the
satisfaction of learning from these gentlemen its occurrence on other portions of the coast, it having
beeh found by them at the island of Lambay, near Dublin, on the 1st of June, 1838, (or about the
same time it was observed on the Antrim coast,) by Mr. Thompson in Strangford Lough, on the
3rd of July, (where it was in vain sought for by the writer on the 7th of August ;) and by Mr. Ball a
single specimen was taken at Youghal in June, 1837.

My object in making known, at the present time, its existence on the Irish coast, is to enable me
to refer to it for the purpose of comparison and contrast with the C. Pomiformis. At a future period
I hope to bring forward a detailed account of its structure and economy. Meantime I refer it, though
with some doubt, to the genus Bolina of Mertens, (Mem. Acad. Imp. des Sciences St. Petersbourg,
t. ii. p. 513,) established by him as a connecting link between the Callianyrae and the true Beroes ;
and as it has not been recorded as British — as it is distinct from the two species of Bolina described
by Mertens — and is not noticed by any other continental writer, to whose works I have had access,
I propose to give it provisionally the specific name Hibernica. If undescribed, this title will record
the locality where it was at first observed ; if already known, it will prove a convenient synonym,
indicative of its occurrence on the Irish coast.

• Article " Cilia" in Cyclopaedia of Anatomy and Physiology,
VOL. XIX. O

98 Mr. Patterson on the Cydippe Pomiformis.

Beroes had been taken from the net, or while the glass vessel in which they
were kept was crowded by the number it contained. When, however, not more
than five or six were placed there, the tentacula were thrown out to their fullest
extent, and were occasionally above six times the longest diameter of the body.
In two instances they even exceeded these proportions ; for a Beroe of less than
five lines in diameter, exhibited them four inches in length, and one not exceed-
ing six lines in diameter protruded them to the extent of five inches, as actually
measured by a rule applied to the side of the glass vessel, from the top of which
the tentacula extended downwards. Dr. Grant, in the paper already quoted,
remarks, — " They extend from two curved tubes, placed near the sides of the
stomach, which pass obliquely downwards and outwards, to terminate between
two of the bands, at some distance above the mouth. * * * These tubes have a
sigmoid form, and are shut and somewhat dilated at their upper extremity." In
the Irish species the tubes are not curved in the form described, and their exter-
nal orifice is at some distance, not from the mouth, but from the anus, agreeing
in this particular with Blalnville's description of their position.* Tlie tentacula
in both " consisted of two thin white filaments, round, and tapering to a very
fine extremity." " Along their whole course they present," says Dr. Grant,
" minute equidistant filaments, extending from their lower margin, which coil
themselves up in a spiral manner, and adhere close to the tentacula, when they
are about to be withdrawn into their sheaths or tubes." The filaments were in
some individuals not less than half an inch in length, and of a delicate pinl^sh
colour ; and even so many as fifty may occasionally be reckoned on a single ten-
taculum. Most accurately has Dr. Grant remarked, " The tentacula are often
thrown out from their tubes to their full extent by one impulse, and the slow
uncoiling of the slender serpentine filaments from their margin, is then very
beautiful ; when coiled up they appeared like very minute tubercles along the
side of the tentaculum." Of course, in particular points of view, they presented
a moniliform appearance ; and sometimes, while the filaments on the upper half
of the tentaculum were seen under this aspect, those in the lower half were like
delicate hairs or cilia, waving from the edge. In this respect, however, they
were incessantly varying, and the tentacula, at the same time, were continually

* Manuel d'Actinologie, p. 150.

Mr. Patterson on the Cydippe Pomiformis. 99

assuming new aspects, being retracted either separately or together, and thrown
out in the same diversified manner. It is scarcely possible to convey, by any
description, an idea of the beauty and diversity of their forms. They seem
endued with exquisite sensibility, which, however, is not always equally delicate.
At times the slightest touch will cause a tentaculum to be drawn back into its
tube, with a sudden jerk ; at other times it is apparently unfelt. The Beroes
never seemed poised, or supported in the water by their tentacula. In one
instance, however, they were extended to the bottom of the vessel, where they
seemed to act as suckers, and formed fixed points, whence the animal rose and
fell at pleasure, and appeared as if moored by these delicate and novel cables, the
mouth being retained in the usual erect position.

What are the functions of these singular organs, is a natural inquiry. My
friend, Robert Ball, Esq. of Dublin, states, that he regards them as organs of
prehension. This is the view taken by Blainville, when he speaks of them as
" servant pour attirer vers la bouche la proie qui s'y est attachee, probablement
par une matiere glutineuse."* Though unable to offer any more plausible con-
jecture, I cannot consider this opinion correct, as applied to the present species,
as during all my observations I have never seen them thus employed, and
from the comparative proximity of the orifices whence they issue to the anal
extremity, the tentacula float behind the animal, and never approach the mouth,
except at those times when the Beroe permits itself gradually to sink without
reversing its previous position in the water.

" The mouth and oesophagus," as Dr. Grant remarks, " are wide ; and the
latter continues so to the stomach, which extends to the centre of the body.
* * * There are four prominent membranous lobes placed around the mouth,
which the animal can retract at pleasure." In the present species the appear-
ance of four lobes arises from two membranous plates, which unite along their
edges at either side, and are capable of being extended, so as to inclose an almost
circular space. In general, however, they are so nearly together that they pre-
sent very different appearances in different positions. The upper edge of each
membrane is divided into two semi-circular lobes, and these are constantly vary-

• Manuel, p. 151.

o 2

100 Mr. Patterson on the Cydippe Pomiformh.

ing, both in the extent to which they are protruded and that to which tliey are
distended. It is seldom they are porrected to their full extent, but, when so,
they produce so great a change in the oval form which the animal generally pre-
sents, that they make its outline appear like a miniature representation of one of
those old fashioned bottles which we see in the pictures of the Flemish school.

The only food I have ever been able to detect in the stomach has been small
Crustacea of different kinds. The first of these was an undescribed species, since
named by my friend Robert Templeton, Esq. R. A., Anomalocera Pattersonii.*
It was one line in length, and its bright green colour, contrasted beautifully,
when in the stomach of the Beroe, with the crystalline transparency of the body,
in which it was enclosed. In some instances two of these Crustacea were visible
in the stomach of one Beroe. The second I observed was a species of Zoea, on
which Mr. Templeton also bestowed the specific appellation above mentioned.f
Besides some other Zoea, I have distinguished some of the Gammaridas. One
of this family appeared to be half the length of the Beroe, and lay across the
interior of the stomach, slightly bent, and when first observed was still living,
and occasionally shifting its position. By a note in Trans. Ent. Society, vol. ii.
p. 40, I learn that " M. Risso mentions his finding phronima sedentaria in the
interior of a Beroe."

If, however, the Beroes feed upon small Crustacea, they in turn furnish a sup-
ply of food to creatures more powerful than themselves. I have seen two of
them swallowed by the Actinia Gemmacea,J in the course of twenty minutes.
Next morning portions of the bands of cilia and more solid parts of the Beroes
were observed rolled together, and adhering, with some darkish coloured pellets,
to the filaments of the Actinia, whence after some time they were thrown off".
On another occasion I took a small Medusa of the genus Callirhoe, (of a species
undescribed by Lamarck, ) and placed in the glass vessel with it a Beroe, which
had been taken at the same time. While the latter was swimming round the
glass, with that lively and graceful movement for which it is so remarkable, it
came in contact with the filiform tentacula attached to the arms of its companion.
The arms instantly closed, and the Beroe was a prisoner. I endeavoured to
separate them, and for this purpose moved them about, by pushing them with a

* Trans. Ent. Society, vol. ii. part 1, p. 34. -f- Vol. ii. part 2, p. 114.

X Johnston's Hist. Brit. Zoophytes, p. 214.

Mr. Patterson on the C^dippe Pomiformis. 101

a carael-liair pencil, but without effect. In about half an hour afterwards, when
I again observed them, they were asunder, the Beroe swimming about, and the
cilia of its bands vibrating as briskly as usual. It had not, however, escaped un-
injured from its captor. The Callirhoe had taken from the body of the Beroe a
portion which extended transversely across three of the bands, and longitudinally
for about the one-third of its entire length. The being who had suffered this
mutilation seemed, however, quite unconscious of its misfortune, moved about in
every respect as before, and for four days, during which I afterwards kept it,
seemed to possess all its powers in unimpaired activity.

To this instance of apparent insensibility to pain may be added one illustra-
tive of the extent to which the principle of vitality, or of vital irritability, seems
diffused throughout every portion of its frame. On one occasion two Beroes
were taken after a storm, with some of the cilia abraded, and other parts of the
body shattered and even torn. Any of the cilia, however, which were attached
to these mutilated parts, retained all their former mobility unimpaired. The
most damaged of these Beroes was then cut with a pair of scissors into several
pieces, and each part exhibited in its cilia the same undiminished rapidity of
movement. One of these portions was again subdivided into parts so minute
as to possess only one or two cilia on each, yet no change in the ceaseless
motion of these extraordinary organs took place. Thirty -three hours after this
minute subdivision, several of them were vibrating as usual ; and, at the expira-
tion of forty-two hours, the two cilia belonging to one fragment showed un-
diminished activity.

If a longitudinal incision be made in the body of a Beroe when dead, and the
watery particles allowed gradually to evaporate, the bands of cilia and the tenta-
cula will appear as if painted in a confused manner on the surface whereon the
body has been placed, and when perfectly dry can be removed by a touch, as
completely as if they had never formed a portion of animated existence.

Although, from this circumstance, it is obvious that the quantity of solid
matter which enters into the composition of their bodies, must be extremely
trifling, they possess a greater degree of firmness and consistency than is gene-
rally supposed. Frequently have some of them dropped from my net into the
boat when about transferring them to the glass vessels in which they were kept ;
and, at such times, I have invariably lifted them in my fingers, and placed them

102 Mr. Patterson on the Cydippe Pomiformis.

with their companions, without their having received any apparent injury. If
the finger be pressed against one recently dead, the Beroe will not, by such a
pressure, be changed into a broken and shapeless mass. It will, on the contraiy,
by its smoothness and elasticity, slide from beneath the finger. In this respect it
formeda singular contrast to the Bolina Hibernica, which could scarcely be removed
without injury, and when taken in the hand appeared a shapeless mass of jelly.
Some of the continental writers do not appear to have noticed this difference in
the consistency of different Beroes, and have applied to the entire family, obser-
vations which are only correct when applied to particular species. Thus Lesson
describes them as " peu consistant se brisant aisement a la moindre pression ;"*
and Blainville, under the genus Cydippe, introduces the observation of Othon
Fabricius : " C'est un des plus jolis animaux qu'il soit possible de voir ; mais
aussi I'un des moins consistance, car a peine est il touche, qu'il est brise et reduit
en morceaux."f

From the inconsiderable quantity of solid material which enters into the body
of the Beroes, and the rapid circulation of water, which is apparent throughout
their frame, we would naturally suppose that any tinge which the body might
accidentally acquire would be extremely fugitive. It was found, however, to be
much less so than a priori would have been expected. My attention was drawn
to this peculiarity by the circumstance of all my glass vessels being one evening
occupied by Beroes and Crustacea, so as to compel me to place a small Medusa
in a tin vessel, which chanced to be rusted at the seams. Next morning the
colourless appearance of the animal was changed to a bright yellow, which
appeared to pervade every part, and doubtless arose from the oxide of iron dif-
fused through the sea water. This tint remained during the entire day, although
the animal was transferred to pure sea water. Wishing to try if the vessels of
the Beroe would become distinct, if filled with some coloured fluid, from which
the animal could suddenly be withdrawn, and viewed through the usual transpa-
rent medium of sea water, I placed a Beroe in a weak infusion of saffron. At
the end of twenty minutes its colour had undergone a perceptible change. I
allowed it, however, to remain immersed for about six or seven hours, when it
had assumed a bright yellow hue. It was then placed in pure sea water, but

* Annates des Sciences, tome v. p. 236. ■)■ Manuel, p. 151.

Mr. Patterson on the Cydippe Pomiformis. 103

retained its yellow colour for twenty-four hours afterwards ; and though it
gradually became fainter, it was very perceptible even at the expiration of forty-
eight hours.

Lamarck observes, " Les Beroes sont tres-phosphoriques ; ils brillent pendant
la nuit, comme autant de lumieres suspendues dans les eux ; et leur clarte est
d'autant plus vive que leurs movemens sont plus rapides."* Blainville, in his
general remarks on the family of "les Ciliogrades," describes them as "agitant
continuellement les cils dont leur corps tres contractile est pourvu, organes qui
jouissent les la faculte phosphorescente au plus haut degre ;"f thus attributing
the effect to the action of the cilia, rather than to any innate power possessed by
the animal. That at least one British Beroe was endowed with a high degree of
phosphorescence, was established by Dr. Macartney's description of B. Fulgens,
taken by him in Hearne Bay, coast of Kent.J The same species was observed
by the late John Templeton, Esq., " floating in with the waves on the shore of
Dundrum Bay," County of Down.§ The phosphorescent quality does not,
however, seem to prevail universally ; at least I have never been able to detect
its presence, though I have frequently for that purpose taken a glass con-
taining Beroes into a darkened room. My hope of observing it was renewed
by the following passage in a paper by Mr. F. D. Bennett, || " Fresh water
appears to act as a powerful and permanent stimulus on marine Noctilucae.
Those which have intervals of repose from their phosphorescence, immediately
emit their light when brought in contact with fresh water, and this fact was very
strikingly exhibited in the Pyrosomata. * * * * When also the same Molluscs
were mutilated, or so near death as to refuse to emit light upon irritation in sea
water, immersing them in fresh water produced at least a temporary revival of
their brightest gleam ; indeed I have always felt assured that the contact of fresh
water, in a darkened room, would ever elicit the luminous power of a marine
creature, were the latter of a luminous nature." Acting on the suggestion here
given, I took some Beroes into a darkened room, and transferred them to a jar

* Animaux sans Vertebres, tome ii. p. 469. •}■ Manuel, p. 143.

% Phil. Trans. 1810, p. 264.

§ Mag. Nat. Hist. vol. ix. p. 303. In the same article the following occurs : " Beroe Mull.
Pileus Gm. occasionally detected in our deep bays." We cannot from this brief record determine
whether the C. Pileus or Pomiformis is the species alluded to.

II Proceedings Zool. Soc, June 13, 1837.

104 Mr. Patterson on the Cydippe Pomiformis.

of fresh water. No luminosity ensued ; and hence if Mr. Bennett's inference
be applicable to the Beroe, I may feel warranted in concluding that the C. Pomi-
formis is not possessed of any luminous property.

But although the experiment failed, so far as the object for which it was
performed was concerned, it was not utterly fruitless, for it showed the effect
produced on the Beroes by immersion in fresh water. The moment they came
into contact with the fluid, the action of the cilia ceased, or was limited to two or
three irregular strokes, and the animal sank, apparently lifeless, to the bottom of
the jar. If instantly removed, and replaced in sea water, the cilia began again
to vibrate, but had acquired a degree of opacity they had not previously pos-
sessed, and the entire body seemed in some degree contracted, and less transpa-
rent than before. If a Beroe be plunged into boiling water or alcohol, the
instantaneous change from its ordinary diaphanous appearance is very con-
spicuous.

The ovaries in the specimen examined by Dr. Grant " consisted of two
lengthened clusters of small spherical gemmules of a lively crimson colour, ex-
tending along the sides of the intestine and stomach." In above five hundred
individuals of the present species, which I have had in different years the oppor-
tunity of observing, between May and October, these crimson gemmules were
totally wanting. In the glass jars in which they were kept, a glutinous substance
might occasionally be seen, in some cases in contact with the tentacula* of the
animal. In it were numerous small bright transparent gemmules, which I
thought might be ova. This conjecture was verified, by placing under the
powerful microscope of my friend. Dr. J. L. Drummond, portions of the body
of a Beroe, from which most of the watery particles had been evaporated. We
then distinctly saw the colourless ova, which were similar to those I had formerly
seen In the jars. On one occasion, in the glass vessels in which some specimens
of B. Hibernica were kept, I observed two glutinous strings, one about three,
and the other about five Inches in length, and both containing numerous ova,
ranged at irregular intervals, and sometimes disposed in clusters.

* When treating of the genus Eucharis of Peron, to which the present species would belong,
Lesson remarks, with a note of interrogation, " De ce retrecissement sur les cotes partent deux
prolongemens cirrhigeres, portant peut-etre les ovaires ?" — An7iales des Sciences Naturelles,
tome V. p. 252.

Mr. Patterson on the Cydippe Pomiformis. 105

Dr. Grant, in speaking of the nervous system of C. Pileus, states, that he
could perceive, at a short distance above the mouth, " a double transverse fila-
ment of a milky white colour, * * * * which formed a continuous circle round
the body. In the middle of the space, however, between each of the bands of
cilia, these cords presented a small knot or ganglion, so that there were eight
ganglia in the course of this ring." Never having been able to observe these
cords and ganglia in the C. Pomiformis, I took a number of specimens, some
living and others recently dead, and placed them under the microscope already
mentioned. But although Dr. Drummond, whose eye was well accustomed to
microscopic examination, gave his valuable assistance, we were unsuccessful in
detecting their presence.

A transparent membrane extends across a portion of the lower extremity of
the body. It is entirely superficial, and may, perhaps, be of use in giving greater
strength and stability to that part of the animal. This, however, is merely a
conjecture, which I am at present unable to confirm or to correct by the opinion
of others, as the membrane does not appear to have been noticed by any previous
observer.

The Beroe is most usually described as swimming with its mouth downwards.
Thus Blainville informs us, "II nage peu obliquement, I'anus ou I'extremite
arrondie en haut, et trainant ses deux longs cirrhes comme deux queues."*
Audouin and Milne Edwards, in like manner, state, " II existe dans I'axe des
Beroes une cavite qui va d'un pole a I'autre, et qui communique au-dehors a
I'aide d'une ouverture Inferieure, qu'on pent considerer comme I'avant bouche."f
The words of Lesson convey a very different idea i " Dans I'eau leur position est
tres oblique ou presque horizontale."J It is with the mouth downwards that the
C. Pileus is figured by Dr. Grant, and his description consequently bears refe-
rence to the animal as seen in that position. In this particular the C. Pomiformis
is the reverse of its congener, the usual position of the mouth being uppermost,
except when the animal is in a state of exhaustion, when it either rests on its
mouth, or lies languidly on its side, at the bottom of the glass. At other times,
when fresh and vigorous, its movements are lively, animated, varied, and inces-

* Manuel, p. 130.

f Quoted by Lesson, Annates des Sciences, tome v. p. 240.
% Annates des Sciences, tome v. p. 237.
VOL. XIX. J>

106 Mr. Patterson on the Cydippe Pomiformis.

sant. Sometimes it is seen rising to the surface of the water with a slow and
equable motion, like that of a balloon, then gradually descending, the mouth being
retained in its usual erect position. Next ascending with rapidity, and turning
the mouth downwards, or revolving on the transverse axis of the body ; and then
abandoning all these modes of progression, revolving on its longitudinal axis,
the body being vertical, and in this position twirling round and round the vessel.
When the movements of the body are thus varied, how great must be the variety
of motion in the cilia by which the body is propelled !

When the movements of the Beroes were thus diversified, it may be imagined
they afforded highly pleasing objects for contemplation, especially as they dis-
played in the sunshine a splendid iridescence, caused by the action of the cilia in
the water. To the various persons whom I met in the ferry-boats, plying between
the Corran and Island Magee, their existence had been previously unknown.
They seemed to be delighted no less by the novelty than by the beauty of
their appearance, and not unfrequently compared the action of the cilia to that
of the paddles of a steam-boat.

The C. Pomiformis, as now described, differs from the C. Pileus in the num-
ber and structure of its cilia, the position of the tentacula, the form of their
sheaths, the want of colour in the ova, the inconspicuous structure of the nervous
system, the existence of a transverse membrane at the anus, and the position in
which the body is held when vigorous and unexhausted. I do not include in
these distinctive characters the intestinal vessels which convey the fluid to the
several bands of cilia, as it is possible that further investigation may prove tbat a
somewhat similar arrangement prevails in both.*

When we contemplate the delicacy of structure displayed by the Beroes, we
are prompted to inquire how they escape destruction from the turbulent element
in which they live. On this subject Lesson remarks, " On doit supposer qu'ils
augmentent leur pesanteur specifique pour se precipiter a une certaine pro-
fondeur, la ou la mer est calme, et ou les lames sourdes, se font moins sentir."f

• Nov. 22, 1838. I have this day, for the first time, had access to the observations and researches
of Martens on the Acalepha of the Beroe family, (Memoires de I'Acad. Imp. des Sciences de S.
Petersbourg, tome ii. p. 479,) and am glad to find the above opinion confirmed by the authority of
that author. In his illustrative plates, drawn from living specimens, the ramiform vessels going out
to the bands of cilia are figured in several different species.

t Annales des Sciences, tome v. p. 243.

Mr, Patterson on the Cydippe Pomiformis, 107

So far as their absence from the surface during stormy weather may be regarded
as corroborative of this observation it is correct ; but the procedure appears to be
insufficient to defend them when near the coast from serious and often fatal
injury. On this subject I would refer to the diary published by me in the Edin-
burgh New Philosophical Journal for January, 1836, as to the weather of the
early part of May, 1835, considered in connexion with the number of Beroes
taken at various intervals during the same period.

That they are more abundant in some seasons than in others, may be inferred
from the fact, that in the beginning of May, 1835, I took, in crossing the ferry
from the Corran to Island Magee and returning, so many as thirty-five. In the
same locality, in the apparently more genial month of June, 1838, the greatest
number I took in any one of twelve crossings, between the 5th and the 30th of
that month, was seven. On the 10th of September, however, in the same year,
and in the same place, I took the unusual number of forty-one. All of these
were small in size, the largest not exceeding four lines in length.

Nearly a month later than this, I placed my net, &c. in the hands of my
friend Mr. W. Thompson, who, in the prosecution of his researches into our
marine productions, was going out for a day's dredging in the Belfast Lough.
In the evening he gave me the unexpected pleasure of seeing nearly eighty
Beroes, all of the present species, and rendered still more acceptable by the fol-
lowing note :

" The entire of these were taken between ten and half-past twelve o'clock
this forenoon, the day being very calm and bright for the season ; the wind
easterly. The towing net was first placed In the water opposite to Holywood ;
about three quarters of an hour afterwards, near to Cralg-a-vade, it was found to
contain twenty specimens. In five minutes more thirty-six were taken, in the
next ten minutes eight, and In another quarter of an hour fifteen."

The ensuing day, 6th October, my friend Mr. G. C. Hyndman, while en-
gaged in similar pursuits, employed my net with even greater success, and in the
same locality took nearly one hundred individuals, all of them similar to the
above.

The present species appears to be extensively diffused around the Irish coast.
It has been taken at the Giant's Causeway by Mr. Hyndman ; in the Loughs of
Lame, Belfast, and Strangford, by the author, as already mentioned ; in the Bay

p 2

108 Mr. Patterson on the Cydippe Pomiformis.

of Dublin, outside of Kingstown Harbour,* and at Lambay Island, by Mr.
Thompson and Mr. Ball, and by the latter gentleman at Youghal.

In conclusion it may be remarked, that the species now described combines
the characters in Fleming's definition of the genus Beroe : " body with vertical
ciliated ribs ; tubular vessels traverse the axis of the body with lateral and termi-
nal apertures ;" and those in his genus Pleuro-brachia, " body sub-orbicular, with
eight ciliated ribs and two ciliated arms, one on each side."

As it seems desirable to place under our view the distinctive characters of
C. Pileus and Pomiformis, as detailed in the present paper, I subjoin a brief
definition of each. They are the only British species at present referrible to the
genus Cydippe of Eschscholtz.

C. Pileus.-^Tentacula issuing near the mouth ; cilia fin-like, with slightly
rounded outline ; ovaries crimson ; nervous system, whitish cords, and ganglia.

C. Pomiformis. — Tentacula issuing near the anus; cilia divided; ovaries
colourless; nervous system inconspicuous.

• The specimens there captured were exhibited before the Natural Histor}' Section of the Bri-
tish Association in Dublin. — See 4th vol. of Reports, p. 72.

I am informed by Mr. Ball, that Mr. Bergin of Dublin has preserved some of these animals in a
solution of acetate of alumina for fifteen months. In alcohol they have generally fallen to pieces in
the course of a few weeks, or become so contracted as to be valueless as specimens.

P4

r

^'^^m^^* -Tt>

-^j

Mr. Patterson on the Cydippe Pomiformis. 109

EXPLANATION OF THE PLATE

ILLUSTRATIVE OF THE APPEARANCE AND STRUCTURE OF CYDIPPE POMIFORMIS.

Fig. 1. — Magnified representation of this Beroe in the act of revolving on the
longitudinal axis of the body.

2. — Internal structure, exhibiting the form and position of the sheaths of
the tentacula, and arrangement of the ramiform vessels communi-
cating with the several bands of cilia.

3. — The same vessels as viewed vertically ; the dotted figures mark the
outline presented in this position by the sheaths of the tentacula.

4. — Anal extremity of the body, with the transverse transparent membrane,
and part of the several bands of cilia.

5. — Membranous lobes surrounding the mouth.

6. — Cilia represented in motion.

7. — Cilia of another individual when at rest.

8.— Cilia of C. Pileus ; copied, for comparison, from the Zoological Tran-
sactions, vol. i. plate 2.

For the original drawings, which are taken from living specimens, I am
indebted to the kindness of my relative, B. J. Clarke, Esq. of La Bergerie,
Portarlington, with whom I had the pleasure of repeating many of the observa-
tions recorded in the present paper.

The Beroe is represented of about three times its natural diameter.

110

III. On the Longitude of the Armagh Observatory, given by fifteen Chronome-
ters of Arnold and Dent, Sfc. By the Rev. Dr. Robinson, M.R.I. A., &c.

Read 10th December, 1838.

IHE determination of this important element is at least as difficult as essential ;
and whatever be the care of the astronomer it often happens that after years of
observations have elapsed, the result still remains in some degree uncertain. The
various methods of determining arcs of longitude have each their peculiar causes
of error. When the methods of signals can be employed with only one inter-
mediate station, it is decidedly the best; but obviously the measurement of large
distances is in most cases impracticable, and when many stations intervene the
accumulated errors may attain a serious magnitude. The expense of this pro-
cess, and the number of assistants required, are also frequently very serious
objections.

The longitudes assigned by geodetic operations depend on an assumed figure
of the earth, whose constants are not well known, whose very existence is proble-
matical; and even if correct, it will differ from the Astronomical longitude
whenever local attractions deflect the direction of gravity to the east or west
of the theoretic vertical.

The mere observation of an occultation is the most satisfactory that can be
imagined in common cases ; but there is uncertainty enough in deducing from it
a longitude, caused by the doubtful nature of some elements that enter the calcula-
tion. It is affected by errors in the tabular place of the moon, which are not totally
corrected when the declination has been actually observed, as only one limb can
be taken, and that is affected by irradiation. It is influenced by the error of the
tabular semldlameter, and still more of the horizontal parallax, which is to a cer-
tain extent hypothetical, whether given by theory or deduced from observation.
And lastly, it depends on the assumed distance of the spectator from the earth's
centre, a quantity computed on the hypotheses of its spheroidal figure and given

The Rev. Dr. Robinson on the Longitude of the Armagh Observatory . Ill

compression, but which in strictness ought to be investigated by independent
research.

In cases when the apparent tract of the star is very oblique to the moon's
limb, its irregularities present a new source of error ; and the final result is, that
though the observations may be certain to a tenth of a second, the longitudes
deduced may differ several seconds, and the truth can only be attained by a mean
of many, taken under circumstances differing as much as possible.

The method of transits of the moon and lunar stars, though it afford an easy
and pretty accurate approximation, is affected by the influence of irradiation,
which I believe to vary not only with the telescope, but also with atmospheric
changes. The personal equation is also different in some instances, for the
planet and the stars, as I infer from the fact, that the transits observed by my late
assistant gave the longitude five seconds of time less than those observed by my-
self after his death. In this method, therefore, it is necessary not merely to have
observations of each limb, but to multiply the stations of comparison, that among
the variety of observers and telescopes a kind of mean result may be obtained.

The determination by chronometers depends on the perfection of these
machines, and in particular on their rate being unchanged by the agitation of a
long journey. This, strictly speaking, is never the case, though it is sometimes
very nearly accomplished, and its effect will disappear from the mean of the
results obtained in going and returning, if the circumstances of the two journies
are nearly similar.

Unfortunately it rarely happens that an astronomer has the power of making
these experiments on a sufficient scale ; but such an opportunity seemed to Sir
William Hamilton and myself to present itself, in consequence of Mr. Dent's
chronoraetrlc visit to Paris, and the yet more remarkable notice, read at the
Newcastle Meeting of the British Association, of the Chronometric Longitude
of Sir Thomas Brisbane's Observatory. Mr. Dent not merely promised us every
assistance, but when, having obtained the consent of the authorities of our respec-
tive observatories, we proceeded to make the necessary pecuniary arrangements,
he treated the matter as one of science, not of commerce, and not only took on
himself the expense and risk of the journey, but came in person.

The chronometers which he placed at our disposal were fifteen, of which
twelve were those that had been used in the determinations of Paris and

112 The Rev. Dr. Robinson on the Longitude of the Armagh Observatory^

Makerstown. These, latter were rated for some days at the Royal Observatory^
Greenwich, and on September 20th were delivered to Mr. Dent. The remain-
ing three were timed by the pupils of the Marine School at Greenwich, on
the same day. They were packed in two boxes, and kept steady by a stuffing
of horse hair, which to me at least appeared a very insufficient guard against the
concussions of their rapid journey, but it seems to have been effectual. Much of
this journey was performed with the marvellous rapidity of modern improvement,
yet it may be questioned whether a slower passage would not have been more
favourable ; for the jarring of the railroad is severe, and the peculiar vibration
of a steam-vessel I know to be very liable to disturb the performance of a chro-
nometer. In this instance, of the total distance travelled, 275 miles were sea,
190 in Ireland in the common cars or stage-coaches, and the rest, amounting
to 500, were performed on railways.

On the morning of September 22, the watches were compared at the Dublin
Observatory, with the transit clock, by Sir William Hamilton, his assistant Mr.
Thomson, and Mr. Dent himself; and on that of the following day, at Armagh,
by Mr. Dent and myself. As Mr. Dent's time was precious, and I attach little
or no importance to stationary rates, he started on the evening of the 24th, after
we had again each compared the watches ; and revisiting Dublin on the follow-
ing day, and again making the comparisons, he sailed in the evening for
Liverpool. The watches were finally returned to Greenwich, and compared by
Mr. Main with the transit clock on the 27th, shortly after noon.

In making these comparisons, the Dublin astronomers appear to have taken
beats of the watches, and divided the seconds of the sidereal clock. Mr. Dent
took beats of the clock, and divided those of the watch, and I waited for coinci-
dences and separation of the beats, — far the most accurate, but also far the most
tedious mode of comparison. My results were, however, almost identical with
Mr. Dent's.

Mr. Main, I believe, used the same method ; for entire and half seconds only
appear in his comparison, as must be the case when the watches beat twice in the
second.

If we denote by e the correction of a watch when leaving the eastern, w that
when arriving at the western station, i the interval of the watch's time between

The Rev. Dr. Robinson on the Longitude of the Armagh Observatory. 1 13

the two comparisons, and a its rate, (+ when losing, because it increases the
positive correction,) we obviously have

L = E— w + eXi,

and accenting the letters for the return,

l = e' — w' — r'Xi'.

If we suppose k = r', that is, either the rate unchanged on the road, or similarly
disturbed in the two journeys, then we have

^ _ (e'-w')-(e-w) ^j^

i + i'

which may be called the travelling rate, and is given by subtracting from the
watches' change between the two eastern comparisons the change between the
two western, and dividing by the difference of the intervals; and this obviously is
the rate which should be used.
We have also

2l = e'— w' + E — w-|-rX(i — 0 (2)

from which it is obvious, that if the times employed in going and returning are
equal, or nearly equal, the effect of an error in the assumed rate is insensible in
the mean of the two.

As the expression of r assumes that the longitudes obtained going and
returning are equal, it is obvious that when the travelling rate is applied, it is
useless to compute them separately.

If we suppose that e — w requires a correction e, whether caused by errors in
the comparisons, or by accidental disturbance on the journey, then we obtain a
value of R by eq. (1), which requires the correction

'' ~ I + 1'
and the correction of the mean longitude given by eq. (2)

I + I'

which in general will differ but little from that which occurs if we use stationary
rates,

VOL. XIX. Q

114 The Rev. Dr. Robinson on theLongitude of the Armagh Observatory.

rfL" = |-e + ie'

Errors caused by the journey produce opposite effects going and returning, and
as the disturbances may be expected to be nearly equal in the two cases, it is
highly probable that their effect on the mean longitude is insensible in such a
case as the present.

Having premised so much as to the principles of the process, I annex its
elements. The first column of the following table contains the number and dis-
tinguishing letter of the watch ; the second its correction at the epoch of its own
time given in the third ; the fourth and fifth are for the return.

GREENWICH OBSERVATORY.

Arnold and Dent 1034

A

+ 4".57s.36

20''.0799

4- 5"'.17^92

271.0278

»

1042

B

— 0.1.58

20.0847

4- 0,13.61

27.0218

j>

965

C

4- 3.11.15

20.0809

4- 3.24.89

27.0219

»

910

D

+ 0.19.53

20.0014

4- 0.48.81

27.0271

j>

718

E

4- 3.32.60

20.0805

+ 3.44.14

27.0278

91

1663

F

+ 0.9.33

20.0833

4- 0.30.81

27.0295

»

1155

G

— 0.0.90

20.0833

— 0.18.76

27.0322

S>

978

H

+ 6.3.82

20.0788

4- 6.23.82

27.0315

JJ .

995

I

+ 2.38.37

20.0815

4- 2.49.79

27.0321

JJ

1152

K

+ 0.56.77

20.0380

4- 0.53.09

27.0343

»>

1153

L

+ 5.25.91

20.0789

4- 6.59.05

27.0329

)>

777

M

4- 1.55.36

20.0820

4- 2.2.27

27.0369

GREENWICH NAVAL SCHOOL, REDUCED TO THE OBSERVATORY.

Arnold and Dent 820

N

4- 1.15.20

20.2083

4- 1.11.90

26.9722

1017

O

— 0.22.70

20.2083

— 0.14.40

26.9722

1045

P

+ 0.25.30

20.2083

4- 0.49.10

26.9722

The Rev. Dr. Robinson on the Longitude of the Armagh Observatory, 1 15

DUBLIN OBSERVATORY.

A

— 20»18M5

21 ".9661

— 20"'.8'.72

25'».0028

B

— 25.19.22

21.9715

— 25.12.00

25.0076

C

— 22.6.00

21.9725

— 22.0.04

25.0062

D

— 24.53.50

21.9770

— 24.39.36

25.0090

E

— 21.44.66

21.9780

— 21.39.58

25.0076

F

— 25.6.92

21.9837

— 24.56.49

25.0104

G

— 25.27.30

21.9864

— 25.34.74

25.0125

H

— 19.11.95

21.9871

— 19.3.17

25.0083

I

— 22.39.63

21.9912

— 22.33.91

25.0118

K

— 24.25.35

21.9951

— 24.26.60

25.0139

L

— 19.46.04

21.9951

— 19.31.80

25.0111

M

— 23.23.22

22.0000

— 23.20.44

25.0146

N

— 24.6.83

22.0021

— 24.7.87

25.0163

0

— 25.41.70

22.0079

— 25.38.19

25.0180

P

— 24.49.39

22.0097

— 24.39.68

25.0183

The correction of the Dublin transit clock was on the 21st = -|- 35'. 75 by
a Lyrae and a Aquarii, and its rate = + 0'- 25, using the places of the Nautical
Almanac. It is confirmed by a Aquarii, Fomalhaut and a Pegasi on the 22nd.

The correction on the 24th = -]- 36*. 53 by a Cygni, a Aquarii, a Pegasi,
and a Andromedag.

Q 2

116 The Rev. Dr. Robinson on the Longitude of the Armagh Observatory.

ARMAGH OBSERVATORY.

A

— 21">.29M0

221.9563

— 21'°.26'.95

23<'.9724

B

— 26.31.61

22.9625

— 26.29.35

23.9770

C

— 23.18.33

22.9608

— 23.16.92

23.9761

D

— 26.3.46

22.9645

— 25.58.94

23.9786

E

— 22.57.05

22.9639

— 22.55.87

23.9778

F

— 26.17.89

22.9674

— 26.14.82

23.9815

G

— 26.44.10

22.9683

— 26.46.61

23.9826

H

— 20.23.35

22.9647

— 20.20.58

23.9787

I

— 23.52.59

22.9677

— 23.50.88

23.9819

K

— 25.39.57

22.9697

— 25.40.73

23.9843

L

— 20.55.21

22.9683

— 20.51.17

23.9816

M

— 24.36.72

22.9722

— 24.35.92

23.9857

N

— 25.20.74

22.9739

— 25.21.41

23.9876

0

— 26.53.93

22.9760

— 26.53.96

23.9904

P

— 25.59.82

22.9770

— 25.58.61

23.9904

The correction of the Armagh transit clock on September 21st was = —
30'. 45 by a and /3 Lyrae ; f , 7, a and /3 Aquilae ; and a Cygni.

On Sept. 23rd, by the same stars, It = — 31'.23, and the rate = — 0'.38.

Hence I derive the following longitudes of Armagh ; each being the mean
of those coming and returning :

A .

• +

26"'.35^39

B

36.32

C .

35.46

D .

35.03

E

34.69

F

36.17

G .

35.74

H

35.56

The Rev. Dr. Robinson bw the Longitude of the Armagh Observatory, 117

I . . .

35.69

K . . .

35.12

L . . .

35.28

M . . .

35.06

N . . .

34.67

O . . .

35.12

P . . .

35.99

Me

an . . 26.35.44

The consistency of these results is very remarkable, the probable error of
their mean being less than OM, but its agreement with the longitude given by
other means is not less striking.

From solar eclipses* of 1826 and 1836, and 19 occultations, 24 in all, I

found

+ 26.35.58.

Three others were doubtful, as the star-paths were nearly tangents to the moon ;
but as the sum of the coefficients produced by the uncertainties of parallax and
declination is nearly = 0, I add their mean with the weight of two = 34M5,
and the occupation longitude is

4- 26"°. 35'. 47.

The longitudes deduced from lunar transits give

Greenwich, 7 of first L. . . 26 36.26
3 of second L. . . 32.04

Dublin, 30 of first L.
„ 9 of second L.

Cambridge, 1 1 of first L.
„ 3 of second L.

26.34.15

35.16
42.49

26.38.82

38.79

28.38

26.33.58

* The beginning in 1826 ; the beginning and end in 1836 ; and the beginning and end of the
Annulus.

118 The Rev. Dr. Robinson on the Longitude of the Armagh Observatory/ .

Konlgsberg, 8 of first L.
„ 4 of second L,

38.17
26.69

26.32.43

Paris, 2 of first L. . .

42.06

„ 3 of second L.

32.42

26.37.24

The differences are considerable, but I think the mean

26.35.64
must be very near the truth.

I have had few chronometric results previous to Mr. Dent's visit, and those
obtained with my pocket-watch. Sharp, 1760, during my visits to London, &c.
under unfayourable circumstances. They are :

Greenwich, 2 pair
Kensington, 3 do.
Edinburgh, 1 do.

26.35.44
34.54
36.04

26.35.09

But the weights of these being much less than those of the results obtained
with Mr. Dent's watches, can only be considered as depressing a little the mean
of them.

On the whole, therefore, I am not inclined to change the quantity which
some years since I gave to Mr. Stratford for insertion in the Nautical Almanac,

+ 26.35.50.

between me ana .
A .

Uubun are :

. + 1M4'.31

B

14.84

C .

. . . . 14.56

D .

14.63

E

14.30

E .

14.57

G .

14.39

H .

. . 14.30

The Rev. Dr. Robinson ow the Longitude of the Armagh Observatory. 1 19

I

14.91

K

14.18

L

14.13

M

14.46

N

13.73

0

13.95

P

Mean

14.55

+ 1.14.39

If each of these be subtracted from the corresponding longitude of Armagh,
we obtain that of Dublin, such as would be given on the system of computation
employed. But I have found by a direct comparison the longitude of Dublin :

A

a

+

25".21^08

B

21.48

C

20.90

D

20.40

E

20.39

F

21.60

G

21.35

H

21.26

I

20.78

K

20.94

L

21.15

M

20.60

N

20.94

O

21.17

P

21.44

Mean .

\- 25.21.08

It is, I think, evident, that the original longitude of the Bishop of Cloyne,
25.21.00 is the true one. That illustrious astronomer had latterly increased this
a second, probably induced by the result of lunar transits ; but though I am sure
he would not have done this without weighty reasons, yet I think the evidence
of these chronometers would have been considered by him irresistible.

120 The Rev. Dr. Robinson on the Longitude of the Armagh Observatory.

The geodetic diflFerence of longitudes is, as I have already said, altogether
unconnected with this inquiry, but in the ensuing summer I hope that we shall
be able to lay before the Academy a determination of the differences between
Dublin and Armagh, by means of Rocket signals, for which the Honourable
Board of Ordnance have afforded us most ample means, though unfortunately
too late in the autumn to be available this year. By the valuable aid of Lieute-
nant Larcom, I trust we shall be enabled to perform this interesting operation in
the most satisfactory way ; and by extending the same system to Mr. Cooper's
Observatory at Markree, we shall have an arc of longitude measured in the most
perfect manner, entirely across the island.

Armagh Observatory,
J\rov. 9, 1838.

121

IV. On the difference of Longitude between the Observatories of Armagh and
Dublin, determined by Rocket Signals. By the Rev. T. R. Robinson, D.D.,
Member of the Royal Irish Academy, and other Philosophical Societies.

Read 24th June, 1839.

In the communication respecting the Chronometric Longitudes of Armagh
and Dublin, which I had the honor of submitting to the Academy last winter, I
mentioned that it was our intention to determine the difference of our meridians
by rocket signals ; this has since been performed, and has given results which
are the subject of this paper.

The method of signals is the most obvious of all, and under favourable cir-
cumstances, the most accurate. In it, the time of one place is transported to
another, not by any machine, imperfect in its performance, and disturbed by
that very transporting ; the chronometer in it is light. If the appearance used
for a signal be instantaneous, the only known source of error is in the deter-
mination of the Observatory time, which equally affects all other longitude
methods. It appears to have been first used by the celebrated Picart, in a
journey to Denmark, for the purpose of ascertaining the true position of Tycho's
Observatory. He caused a fire to be kindled on the tower of the Observatory of
Copenhagen, which was occasionally covered by a screen, and the time of its
disappearance noted there, as well as by an observer at the ruins of Uraniburg.
The distance is not more than seventeen miles, and there must have been some
difficulty in covering the fire rapidly, as, from a passage in another of Picart's
works, it appears to have been three feet in diameter. If, instead of a fire, one
of Drummond's lights, placed in the focus of two Fresnel's lenses, directed to
the stations, were suddenly covered by a hood, we should have a signal visible
at any distance ; which, besides being perfect in its nature, might serve to
remove a doubt which has sometimes occiured to me. The impression of a

VOL. XIX. R

122 The Rev. Dr. Robinson on the Difference of Longitude

luminous object remains for one or two-tenths of a second on the eye : is this
duration the same for all persons ? Is there a corresponding delay in the per-
ception of light at its first appearance ; or, does the mind take instantaneous
cognizance of the action on the retina ? If not, is the interval of time required
the same for every observer ? The beautiful experiments of Mr. Wheatstone*
show that we can see an object whose visibility lasts only the millionth part of
a second ; but our perception of it may not be synchronous with its appearance.
All of this which concerns the astronomer might be decided by observing the
reappearance of the light, as well as its vanishing. The management of che-
mical apparatus on a mountain summit is, however, no easy matter, and Lieut.
Larcom, R. E., has suggested an application of the heliostat, which offers the
same results : directing its beam to one station, but diverting a portion to the
other by a second mirror, suitably placed, the same occultation and reappearance
may be effected with the utmost facility. The necessary apparatus was ready,
and if there had been enough of sunshine in May, I should have reported on the
performance of it ; but I hope that before these longitude operations are com-
pleted, I shall have another opportunity.

No more mention of fire signals occurs in the annals of astronomy till 1735,
when De La Condamine proposed to measure an arc of longitude by means of
the flash of cannon ; taking the idea, in all probability, from the ridiculous pro-
ject of Whiston. As the signals are generally given on mountains, where
cannon are of difficult conveyance, his proposal is scarcely less absurd ; but it
was made practicable four years after by Cassini and Lacaille, who used the
powder without the artillery. Stationed on mountains, in the south of France,
110 miles apart, these astronomers observed the flash often pounds of powder
fired at an intermediate point, and deduced, though but imperfectly, the differ-
ence of longitude. Besides the imperfection of their means of getting the time,
the quantity of powder used was excessive, and its flame must have lasted one or
two seconds. Even with so small a quantity as half a pound, this inconvenience
is felt : Professor Santini complains that the signals given with this quantity, at
Monte Baldo, in 1824, were not instantaneous, the inflammation lasting ^ of a
second. It must, however, be observed, that this is more remarkable when the
powder is unconfined, than when fired in ordnance, or in the head of a rocket.

* Philosophical Transactions, 1834, p. 591.

between the Observatories of Armagh and Dublin. 123

Nor is such a quantity as ten pounds at all necessary in respect of visibility.
Von Zach found that even so little as four ounces was seen at 150 miles, by the
reflection of its light from the air, the flash itself being below the horizon ; and
that it was visible at 140 in the twilight:* and the French observersf state,
that at twenty-seven miles one-eighth of an ounce can be seen with the naked
eye. These are important as guiding facts ; at the same time, the superior
clearness of the air in the central parts of Germany should be kept in mind.

This method was again forgotten till Von Zach revived it at the beginning
of this century. It has since been extensively used in Germany, J and by the
French and Italian astronomers in the measurement of an arc of longitude
between Marennes and Fiume.§ Where the localities of the line afford fit
stations, this method is very satisfactory ; but, where mountains of the requisite
height, and in proper places, are wanting, a sufficient elevation must be obtained
by art. I am not prepared to say how far it might be possible to obtain this by
" Captive balloons," though the fates of Pilatre de Rozier and Madame Blan-
chard are strong arguments against the union of aerostation and pyrotechny.||
The use of rockets in such cases was proposed by Robins, in 1749» and was
practised by the elder WoUaston, and some other astronomers, near London, in
1775. More lately it was used on a large scale by the French, between Brest
and Strasbourg, and by a commission of French and English, between Greenwich
and Paris. The first is briefly described in the elegant notice by Major Sabine,
given in the Quarterly Journal, vol. xxili. ; and that part which was done in
1824 is given with sufficient detail in the Memorial du Depot de la Guerre,
vol. ill., to enable us to appreciate its value. It seems to have been unsuc-
cessful, as out of 300 signals, on each branch of the arc, only six transmissions In
the first attempt occurred on one branch, and none in the other ; and on the
second trial, out of 360, only thirty-six on the first. It is possible that this may

* Correspondence Astronomique, vol. iii., p. 437.

t Nicollet Con. des Terns, 1829, p. 381.

X For details of some of these by Littrow, see Cor. Astron., vol. vii. p. 257.

§ Con. des Terns, and Plana, Arc du Parallele Moyen.

II Howitzer shells were tried by the French, but rejected, as the flash was not sufficiently bright ;
their fragments would, I think, be very dangerous to those who give the signals, and the howitzer
not easily managed on a mountain.

r2

124 The Rev. Dr. Robinson on the Difference of Longitude

have been owing to the bad quality of the rockets employed, as they are said to
be similar to those furnished for the English operation, which proved defective,
a large proportion of them bursting. They were, in fact, overloaded, the sig-
nals being given with eight ounces of powder ; and it seems that in attempting
to make them able to carry this to the requisite elevation, the limit of strength
was approached rather too closely. None of the distances are excessive. That
(La Heve, St. Clair) which in the first line barred all transmission, is but
seventy-one statute miles ; it however required an elevation of 680 yards, which
probably many of the rockets did not reach. Colonel Bonne, who reports this,
attributes the failure to the fog which rests on the Seine, as the line of sight
crossed this river seven times ; and seems to think that in all such operations,
the passing large surfaces of water should be avoided. Before adopting this
conclusion, we should remember that in 1825, when the line was changed, and
when no distance exceeded fifty-two miles, no greater success was obtained.
Perhaps sufficient attention was not paid to the selection of clear nights for the
signals ; as every astronomer is aware that sometimes small stars can be seen
almost to the horizon, while in ordinary good observing weather, this is by no
means the case. When such favourable circumstances are noticed at the
observatories, which are the extremities of the chain, a transmission of signals by
numerous intermediate posts, should run along the line as a notice to fire the
rockets, and thus success may be insured by a moderate expenditure of blue
lights and patience.

The operations on the arc between Greenwich and Paris are described by
Sir John Herschel in the Philosophical Transactions for 1826, with his usual
precision and elegance : the memoir explains the method of successive signals
with peculiar clearness, and in particular illustrates the method of using the
broken sets to the best advantage. The distances here also were moderate, the
greatest (La Canche, Lignleres) being only fifty-six miles ; yet the success was
not very great, ten complete transmissions being obtained only on four nights out
of twelve, by 120 signals at each of the three stations. It Is however evident,
that Colonel Bonne's opinion of the difficulty of passing water does not hold
with respect to sea ; for, while 109 of the Wrotham signals were seen at 26
miles, ninety-two of those at La Canche, at fifty-two miles, were visible.

These operations were not followed up in Great Britain for several years.

between the Observatories of Armagh and Dublin. 125

but in 1834 the British Association expressed a wish that the longitudes of
Cambridge, Oxford, Edinburgh, Dublin and Armagh should be determined by
the method of signals, and by chronometers. For this object it appointed a
committee from its astronomical members, and gave them authority to apply to
Government for any assistance that might be necessary. Of this Sir William
Hamilton and myself are members ; and I am happy to say that its work has
commenced in Ireland. As far as the chronometric part is concerned, there is,
perhaps nothing to be desired, except the personal equation of the Greenwich
observers, which will be determined when an opportunity offers ; and though
the signal-measure, which is the subject of the present communication, relates to
the smallest of the arcs, it is important, both on its own account, and as a means
of training us for more extensive lines.

The Observatories of Armagh and Dublin are situated very unfavourably
for the signal-method, there being no point visible from both. About four miles
south of the first, a range of hills rises from 600 to 1000 feet above its level ; but
these are shut out from the view of Dublin, by a ridge about twelve miles to the
north of it, 500 feet high. Even with powerful rockets it was not easy to clear
these barriers ; but our difficulties were removed by the aid, and, I may add,
encouragement which we received from our friend Lieutenant Larcom. He
not only gave us whatever information we required, but added a personal atten-
tion to the details of our work, without which it would, perhaps, have failed.
Among other matters for which we have to thank him, was a diagram, in which
he laid down the observatories, and all the mountains which could possibly serve
as signal stations. To each was annexed its height, distance, azimuth at each
observatory, altitude affected by the average terrestrial refraction ; and when the
line of sight was thrown up by an intervening ridge, the height there, and the
elevation at which it passed the summit of the station, and which, of course, it was
necessary that the rocket should clear, after allowing for refraction.* This

* It is really wonderful how completely every undulation of the ground has been registered in
the Survey. The altitudes sent to me, which must have been computed from the general sections,
agree with observation in the most extraordinary way. A fact of another kind will show such
members as may not be acquainted with these things the precision of the Ordnance Survey. I set
a telescope to the azimuth given for Slieve Gullion, and ascended the intervening hill with a
theodolite, which I moved till, by signal from the Observatory, it was in the Una ; then I took, with

126 The Rev. Dr. Robinson on the Di^erence of Longitude

showed at once that our choice lay between two — Loughanleagh, in the county
of Cavan, and Slieve GuUion, at the southern extremity of Armagh. The
first would divide the distance better, but as its line passes through the smoke
of the town of Armagh, the other was adopted.

Its summit, 1893 feet above the sea, is occasionally visible at Dublin, but is
800 feet below my view, the distances being 50.9 and 18.2 miles, as shewn in
the annexed map, for which I am obliged to Lieutenant Larcom ; the section
beneath shows the character of the intervening land. From this, the necessary
size of rockets can be inferred; the pound rocket (1'". 7 diameter) rises 1400
feet, on an average, but cannot carry four ounces of powder, while it is evident
from Sir J. Herschel's paper, that the two-pounder (2'". 1 diameter) is quite
sufficient. These projectiles, when of such a size, require extreme care in the
details of manufacture ; and, if ill made, are not merely uncertain, but actually
dangerous ; and the case seeming of sufficient importance to authorize an appli-
cation to Government, I made an application to the Board of Ordnance, stating
the nature of my work, and requesting a supply of rockets. My reliance on
that liberality which I have always found in the Government, when the import-
ance of any scientific object is duly laid before them, was not disappointed, and
I have much pleasure in acknowledging the kindness with which the Master-
General, Sir Hussey Vivian, and the other members of the Board attended to
me ; not merely giving the rockets, but tents for the firing party, and other
matters which were necessary, but which I had in the first instance overlooked.*
I may add, that as a measure of precaution against the interference of curious
visitors, two of the police were placed at my disposal ; it was, however, un-
necessary, as, though great crowds of the peasantry were attracted by an
exhibition so new to them, they shewed every disposition to oblige and assist.
Having made all requisite preparations, I proceeded, on the 13th of May, to

the theodolite, the angle between the telescope and the pile on the mountain top, where our rockets
were to be fired ; it proved 180°. 0'. 0"., or the three points were in one right line.

* The rockets were remarkably good ; not one burst, which certainly is a singular contrast to the
French rockets in Sir J. Herschel's and Colonel Bonne's operations. Their average rise, on the
only evening that I measured it, was 800 yards ; they had, however, only four ounces of powder,
but the part of the case which contained it weighed six ounces more, so that they actually carried a
greater weight than the French.

Seals 20 kHa » One. fii.-/,

Veriiad, Scaii m^rrated W t.

W.kW AN© SECTDOKS

SHEWING THE RELATIVE POSITIONS OF THE OBSERVATORIES OF

BUBUJ^. AEMASH iJ^JU BJAJS-KEEE.
1840

between the Observatories of Armagh and Dublin. 127

establish my party at the mountain. This month was found by the officers of
the Survey favourable for their w^ork, and I knew it to be equally so for
astronomical observations. On arriving, I found all difficulty removed by the
kindness of Dr. Campbell, the rector of Forkhill, who had, with the hospitality
for which he is remarkable, even in Ireland, provided such assistance that we
were able to have the tents pitched, and the stores arranged within a couple of
hours ; nor was his attention bounded with this, but continued during the
whole of our operations.*

The wind blew furiously from the N.W., and next day the snow fell several
inches deep on the mountain. I had not reckoned on such weather, but the sky
was clear at intervals ; and I knew that even a gale will not affect the ascent of
a well proportioned rocket. I therefore left my eldest son, Mr. T. A. Robin-
son, in command of the party, with directions to commence firing at ten,
and give a signal every five minutes, as far as twenty, unless the night was
decidedly cloudy. It would have been better to have arranged signals with
him, but in my uncertainty of the quality of the rockets, I was desirous to
economize them as much as possible.

Sir W. Hamilton (H) and myself (R) had arranged a list of stars to be
observed daily, and, as I have stated. Lieutenant Larcom had given us the means
of directing our instruments to the mountain with astronomical precision. The
signals were, in fact, visible at Dublin, when the weather was fine, by the naked
eye, but this could not be trusted to in moonlight or cloud, and they were observed
there with Sharp's equatorial, whose telescope, by Cauchoix, has an object glass of
flint-glass and quartz, 5'". 2 aperture, with a power of 54. The time was
noted by Arnold's clock. At Armagh the locality permitted the use of more
instruments. My assistant, Mr. Edmondson (E), observed, by the transit clock,
with a 3<} feet achromatic, by TuUey, of 3'". 2 aperture, power 30, placed at the

* The tents were pitched at the cairn, which is the trigonometrical point of the Survey. It is
of great size, and contains a sepulchral chamber, in the form of a cross. The peasantry open it with
great reluctance, and close it as soon as possible, believing it the dwelling of a sorceress, one of
whose feats is given in Miss Brooke's Relics of Irish Poetry. Afterwards, when the weather
became still more tempestuous, they were moved about 600 yards northward, near the lake which
is found on this lofty summit. This new position is about 100 feet lower, but the rockets were
much too powerful to make this of any consequence ; they might in fact have been fired in the
valley of Forkhill, had I been aware of their excellence.

128

The Rev. Dr. Robinson on the Difference of Longitude

southern window of the transit room. I had intended to use my great reflector,
with a power of 70, but the rapid motion of the rockets across the field* of view,
and the oblique movements of the equatorial, 2". 1 5". from the meridian embar-
rassed me, and after losing a few, I betook myself to its finder, 2|'° aperture,
power 18, with a field of 1|^ degrees, which proved quite satisfactory. The
clock is by Sharp, with a mercurial pendulum. Mr. Robert Finlay (F) was to
observe with Troughton's equatorial, 2|'" aperture, power 75, but as the field
of view is narrow, and from not being accustomed to such instruments, he was
even more embarrassed than I ; he also was driven to the finder, which is a com-
mon affair, with an aperture of an inch. The clock has a gridiron pendulum.

The equatorial clocks were compared with the transit clock by chronometers,
before and after the observations of each night ; and as the simple reduction of
these indications to sidereal time is not likely to involve any mistake, the obser-
vations are given in sidereal time, as it seems needless to occupy valuable space
by setting down the actual clock times noted. They are as follow :

May 14, 1839, cloudy, high wind, fourteen rockets fired.

ARMAGH. DUBLIN.

_, |-Seen, but not observed. , . . .

No. 2. R
E

}

Seen.

No. 3. R Seen.

E 13*. SG". 24'. 68

H 13\ 37". 39'. 10

E observed with the naked eye.
No. 4. R1
E

No. 5. R
E

}Seen.
iDitto.

H . 42"". 32'. 10
H . 48 25 10

* They rose, on an average, a degree of declination above the boundary of view, while the field
is but 38 minutes.

between the Observatories of Armagh and Dublin. 120

ARMAGH.

No. fi.

R i;i\
E

.51"

. 5V.

.|

No. 7.

R .
E

56

46

"}

No. 8.

R 14
E

1

51

"}

No. 9.

R .
E

6

28

^1

No. 10.

R .
E

11

28

24)

E
Doubtful at Dublin

DUBLIN.

H

13\

bT. 5'.

30

H

•

58 0

10

H

14

3 6

10

H

•

7 44

00

H

•

12 43

10

H

17 33

10

No. 11. R . 16 18 43)

E . . 18 67j

Marked doubtful at Dublin.

No. 12. R . 21 34 23) ^ _ H . 22 49 10

E . . 34 67i

No. 13. R

>Lost in cloud, ..... H

28 51 10

No. 14. R 14 31 56 23| ^ H 14 33 10 60

E . . 56 my

The flash, at lighting the rockets, was seen at Dublin ; the train, as well as
the explosion, (which was Instantaneous,) was visible by the naked eye at
Armagh.

On May l6th, thirteen rockets were fired, but the evening became rainy,
and many were missed. .

VOL. XIX. s

130

The Rev. Dr. Robinson on the Difference of Longitude

No. 1.

No. 2.

No. 3.

ARMAGH.

R 13\

SS""

3r.

80

E .

,

31

67

F

R .

40

48

30-

E .

,

47

67

F .

•

47

33

R .

45

41

79

E .

.

46

67

F

}
}
}

DUBLIN.

H 13*. 36". 46'. 62

H

H

42 2 12

R noted the disappearance of the train in the cloud, which was sudden. E
suspected the explosion. H saw train but not explosion, and did not note the
time of disappearance, which, however, may sometimes give a good result.

No. 4. R . SO". 40^ 89a

E . . 40 67i . . . . H . . . ,
F . . 42 23J

The rocket turned before exploding, and was not seen in Dublin.

No. 5.

R
E
F

55"". 57'. 79
. 57 67
. 57 43

}

H

Faint, not seen in Dublin.

No. 6.

No. 7.

No. 8.

R 14\

E .

F .

R .

E .

F .

R

E .
F

r. l4^ 08a

. 13 m\

. 13 39J

5 45 78a

. 45 65 V

. 45 99J

10 48 56 >

between the Observatories of Armagh and Dublin. 131

ARMAGH. ' DUBLIN.

No. 9. R Lost in cloud.

3 > .
No. 10. Lost in heavy rain, though it was clear at the mountain.

;}

Observed at Dublin by Mr. Thompson, Sir Wra. Hamilton's assistant.

No. 12. R . 30". 39^ 75>v

E . . 39 36j> . . . . T . Sr. 54'. 12
i)

E . 15". 44'. m
F

No. 11. R . 25". 55^ 75-

E .. 55 66 V . . . . T . 27°. 10'. 12
F . . 55 48,

F . . 39 28-

No. 13. R . 35 23 94a

E . . 23 55 V . . . . H . 36 38 12
F . . 23 22J

The rocket-stand was moved, as the fury of the gale made it impossible to
remain at the cairn, and all work was impracticable till the 20th, when it was
fine on the mountain, but there was much haze below, strongly illuminated by
the moon ; and some annoyance from flying clouds. Twenty rockets were fired.

No. 1. R 13\52". 38'. 79^

E . . 38 63 V . . . . T 13\ 53". 53'. 70
F . . 39 IsJ

Faint at Armagh.

No. 2. R . 57". 43'. 79-

E . . 43 63 5> . . . . T . 58 58 32

F . . 44 18>

'}

No. 4. R and T saw train but not explosion.

No. 3. R 14\ 2-". 14'. 92-

E . . 15 16^ . . . . T 14 3 29 82
F

and T saw train but not explosion.

s2

13'2 The Rev. Dr. Robinson on the Difference of Longitude

AKMAGH. DUBLIN.

No. 5. Train seen, but not flash, , . '. T . IS". 37'. 70
No. G. R . \T. 3ff. 96-v

E V • . . . T Train, but not flash.

F . . .37 22J

No. 7. R . 22 24 13

}

E . . 23 77 > . . . , - T Not seen.

F . .24 22-

No. 8. R . 27 19 53-

E . . 19 27 5- T Train, but not flash.

19 271- .
19 22)

F . .19 22.
No. 9. Train seen, but not flash, . . . T . 33". 29'. 70

No. 10. R . 30"". 5.5'. 73-

E . . 55 77 ^ • • • • T . 38 10 10

}

F . . 55 71
No. 11. R . 42 1 93^

E . . 6 78l . . . . T . 43 17 70

F

■

R noted the disappearance in the cloud. T appears to have taken the same.
E was a suspicion. R used the large reflector for the next three.

No. 12. R . 47"". 9'. 13>.

9 08 1 . . . T . 48"". 23'. 70

9 20J

No. 13. R . 52 9 03-^

E . . 9 48i . . . . T . 53 23 70
F . . 9 20J

Barking of dogs troublesome at Armagh.

No. 14. R . 57"". 25'. \3>.

E . . 24 78[> . . . . T . .58 39 70
F . .25 20J

between the Observatories of Armagh and Dublin.

133

ARMAGH.

No.

1.5.

R

15".

2"

.17'.

93

E

.

17

78

F

•

18

19

No.

16.

R
E
F

7

24
24
24

43

68
69

No.

17.

R

12

22

63

E

.

22

78

F

•

22

99

No.

18.

R
E
F

17

41
41
41

91

28
69.

DUBLIN.

}
}
}

T 15". 3". 31'. 70

8 38 70

13 36 70

18 55 70

This did not rise into the field of R's telescope, but was noted as above by
another person at the same clock, with the naked eye.

No. 19. R . 22". IT. 84'
E . . 17 68
F . . 18 07-

No. 20. R 15 27 16 93'

K 15 27 It) \y6\
E . . 16 79!>
F . . 17 17-^

T

23"". 31'. 70

15 28 31 20

On the 21st, twenty rockets were fired.

No. 1. Not seen

No. 2. R 14". P. 35^ 87^

No. 3.

E .

. 35

73

F .

. 35

62

R .

6 15

87>

E .

. 16

23

F .

. 16

02.

}
}

T 13", 57". 35\ 38

T 14 2 50 38

7 30 38

134 The Rev. Dr. Robinson on the Difference of Longitude

ARMAGH. DUBLIN.

No. 4. R . ir. 25'. 36-v

E . . 25 73 V . . . . T . 12"'. 39^ 38
F . . 25 6lJ

No. 5. Not seen. . . . . . . T . 17 59 88

No. 6. Not seen H . 22 37 38

H notes that it seemed to last from 36'. to 38' . ; it was probably the train
seen through an opening in the cloud.

No. 7. Not seen T . 27". 54'. 38

No. 8. R . 31'°. 39'. 82-^

E > . . . . T Saw train but no flash.

F J

No. 9. R . 36 33 83>v

E . . 34 23 i . . . . H . 37'". 48'. 38
F . . 34 7lJ

No. 10. R . 41 41 03-^

E . . 41 isl . . . . H . 42 55 38
F . .40 7lJ

No. II. R . 47 0 33^

E . . 0 I4I . . . . H . 48 14 38
F . . 0 77J

R noted this as low. F lost it for a time, but saw the flash.

No. 12. R . 51>". 45'. 23-.

E . . 45 44J. . . . . H . 52 59 88
F . . 45 67J

No. 13. R . 56 41 02-.

E . . 41 04 V . . . . H . 57 55 38
F . . 40 76^

No. 14. Exploded before it rose to its full height and was not visible at
Armagh.

between the Observatories of Armagh and Dublin. 135

ARMAGH. DUBLIN.

No. 15. R 15\ 6". 51'. 02-v

E . . 51 24 V . . . . T 15\ 8™. 5'. 38
F . . 51 76)

This also exploded at less than the usual elevation.

No. 16. R . 11". 52\ 72-^

E . . 52 75 t . . . . H . 13 7 38
F . . 52 76)'

No. 17. R . 17 21 6l-\

E . . 22 25 > . . . . T • . 18 35 88
F . . 22 24^

At Armagh the rocket disappeared in cloud, but passed through it, and the
train and explosion were well seen.

No. 18. R . 21"". 53'. 81-

:

E . . 53 65;. H . . 8 38

T . 23™. 7'. 38

F . . 53 74 ■
H observed with a night-glass, held in the hand, but is unquestionably

riffht.

9. R . 26™. 43'. 29>i

H . 27"". 58'. 38

No. 19.

R .

26™. 43'.

29-

E .

. 43

25

F .

. 43

73

No. 20.

R .

31 44

49

E .

; 44

45

F .

. 44

73

}
}

H . 31 59 08

In consequence of the miscarriage of a letter, there was no firing on the
22nd, the only perfectly fine night of the whole period ; and though nine were
fired on the 23rd, of which six were seen here, none were visible at Dublin.
The moon was now so nearly full, and so low, that it became difficult to see the
rockets at Armagh : and the results already obtained proved so satisfactory, that
it was thought needless to repeat the signals from this station. Indeed, bad
as the weather was, it was as favourable as that which has succeeded it.

136 The Rev. Dr. Robinson on the Difference of Longitude

As the most important part of longitude measures is the determination of
the Observatory time, I annex the transit observations, and the clock corrections
deduced from them.

The instrument at Armagh is 5:^ feet focal length, and 3.8 inches aperture,
power 1 60 ; its axis was examined by the level daily, and its meridional position
constantly verified by two marks, which being exactly adjusted to the meridian,
would also detect any error of coUlmatlon, if it existed. This was insensible, as
also is shown by six reversions made on May 25th, for the purpose of verifying
the equality of the pivots, the difference of which is given by them = 0'. 0004,
in fact, evanescent. At the same time their figure was tried by examining the
inclination at every twenty degrees from the northern to the southern horizon ;
but though tenths of seconds of space can be estimated on the level, no error
could be found. The transits were, except in two instances, taken by Mr.
Edmondson.

At Dublin, they were taken by Mr. Thompson : the instrument has six feet
focal length, and four inches aperture, power = 100. The inclination of its
axis was found by the level, on the 8th, 17th, 22nd, and 23rd, = -}-2'. 18; its
meridional position by nine observations of Polaris, from April 30 to May 22,
and its error of coUimation by four of the same star, on May 20th, reversing
between the wires, from which it appears that the observed transits require tlie
correction,

— o'. 5371 + o'. 6134 tang 8 — o'. 1059 secant 8.

The clock corrections are deduced from the places of Encke's Jahrbuch,
which for 7 Ursa?, and some other stars, agree better with our observations than
those of the Nautical Almanac.

between the Observatories of Armagh and Dublin.

137

DUBLIN.

ARMAGH

CO

CO

-J

m

a

DATE.

STAB.

OBSERVED TKANSIT.

S

o o

STAR.

OBSERVED TRANSIT.

?

21

o

o
o

c

O

May 12.
O

Sirius,

6'>. 38". 5»

26

9

— 2n9

Procyon R,

7 30 54

72

9

—2 02

Pollux R,

7 35 30

14

9

—2 21

a Hydrae,

9 19 43

40

9

—2 03

t

Regulus,
^ Leonis,
y Ursae,
Polaris, S.P.
Spica,

Level

9 59 50
11 40 54
11 45 24
13 1 5
13 16 47
4- 1" 45

81
36
91
48
13

9
9
8
3
9

-1 99
-1 89
-1 79
— 1 25
-1 80

„ 13.

0 Leonis,

11"

40m

.57^

34

5

— 4^.32

g Leonis,

11 40 54

06

9

— 1 65

)

Polaris, s.p.

13

1

27

00

1

—5 68

y Ursae,

11 45 24

52

9

— 1 50

Spica,

13

16

50

32

5

-4 19

Polaris, s.p.

13 1 6

90

3

-0 96

7, Ursae,

13

41

18

91

5

-4 20

Spica,

13 16 46

61

9

-1 31

Level

-f- 1" 45 lowered a

xis.

„ 14.

y Ursae,

11

45

27

10

5

—3 99

Procyon,

7 30 53

97

9

-1 23

i

Pollux,
Regulus,
Level

7 35 29
9 59 50
+ 0" 50

33
26

9
9

— 1 36
-1 40

„ 13.

Rigel,

5

6

53

15

3

-4 38

Capella,

5 4 49

60

7

-1 63

5

a Hydrae,

9

19

46

60

5

—4 50

Rigel,

5 6 49

68

3

-1 58

Regulus,

9

59

53

94

5

—4 58

Sirius,
Pollux,

Level

6 38 4

7 35 29

+ 0" 85

63
56

6
3

—I 58
— 1 63

„ 16.

|3 Leonis,

11

40

57

76

5

-4 77

Procyon,

7 30 54

02

9

-1 29

n

y Ursae,

11

45

27

72

5

-4 62

Pollux,
Regulus,
^ l,eonis,
y Ursae,
Level

7 35 29

9 59 60

11 40 53

11 45 24

4- 0" 22

39
28
94
54

3

2
9

8

— 1 43
-1 43
— 1 44
-1 34

„ 17.

Polaris, s.p.

13

1

27

00

1

-3 15

?

Spica,

13

16

50

86

5

—4 76

„ 19.

Regulus,

9 59 49

73

9

-0 90

©

iS Leonis,
y Ursae,
Spica,

Level

11 40 53
11 45 23
13 16 46
- 0" 12

32
83
22

7
6
9

— 0 84
-0 65
— 0 87

VOL. XIX.

138

The Rev. Dr. Robinson on the Difference of Longitude

DUBLIN.

ARMAGH.

J

Eli

a

at

u2

tf

a s

a

" M

DATE.

STAR.

OBSERVED TEANSITS. 1

^

STAR.

OBSERVED TRANSIT. 1

S

° S

6

2

o

e

O

May 20.

Capella,

5".

4"-. 53^

39

5

-5«.17

Capella,

S". 4'°.48».

50

9

-O'-SS

5

Rigel,

5

6 53

93

4

—5 16

Sirius,

6 38 3

62

9

-0 49

Procyon,

7

30 58

52

5

-5 24

Procyon,

7 30 53

01

9

-0 31

Pollux,

7

35 33

61

4

—6 35

Regulus,

9 59 49

16

8

-0 36

P Leonis,

11

40 68

24

5

—5 29

0 Leonis,

11 40 52

74

4

-0 28

y Ursae,

11

45 28

02

4

—6 05

y Ursae,

11 45 23

33

8

-0 21

Polaris, s.P.
reversed,

13

1 29
. 37

60
33

2
2

-4 08
—5 08

I Spica,

13 16 45

59

9

-0 24

• Serpentis,

15

36 28

86

5

-6 19

Level

+ 0" 15

-0 14

„ 21.

Sirius,

6 38 3

15

3

S

a Coronae,

15

28 0

46

5

—5 09

Spica,

13 16 45

15

9

+0 19

a Serpentis

15

36 28

84

6

—5 16

V Ursa;,
Level

13 41 14
+ 0" 42

40

9

-f 0 26

„ 22.

Capella,

5

4 63

17

6

—4 94

Capella,

5 4 47

72

6

+0 46

s

Rigel,

5

6 53

80

2

—5 03

Rigel,

5 6 47

52

3

+0 62

0 Tauri,

5

16 12

63

2

-5 Jl

^ Tauri,

5 16 6

80

9

+0 35

Sirius,

6

38 8

98

5

-3 12

Sirius,

6 38 2

67

9

+0 27

Procyon,

7

30 58

06

5

-4 79

Regulus,

9 59 48

26

9

4-0 53

Pollux,

7

35 33

36

6

—5 12

0 Leonis,

11 40 51

76

3

4-0 70

Regulus,

9

69 64

28

5

—4 99

y Ursae,

11 45 22

42

8

40 69

Polaris, s.P

13

1 33

10

3

-6 57

Spica,
1) Ursae,
Leve

13 16 44
13 41 13

I + 0" 44

67
83

8
8

40 68
4-0 87

Hence I deduce the clock corrections :

May 14, Dublin, = — 4'. 25 at 11\ 56'"

Armagh, = — 1 34 „ 15 0

„ 16, Dublin, = — 4

Armagh, = — 1

„ 20, Dublin, = — 5

Armagh, = — 0

„ 21, Dublin, = — 5

Armagh, = -|- 0

65

j>

12

47

35

»>

15

0

22

>>

13

22

20

j>

15

50

13

»

13

38

26

»

15

50

between the Observatories of Armagh and Dublin.

139

It will be observed that both clocks were accelerated at the 15""; this was
chiefly caused by a fall of the barometer of three-fourths of an inch (Memoirs
Ast. Soc, vol. V. p. 125). The mercurial pendulum of my clock is accelerated
0'. 37 by a fall of one inch ; the coefficient for the gridiron pendulum which
belongs to the Dublin clock is probably greater, but as the effisct is only dif-
ferential, it seemed unnecessary to allow for it.

The differences of longitude given by the signals are as follows :

DATE.

NO.

R.

£.

F.

MEAN.

May 14.

3 .

1

m.l4s

42

Mean of R (8) 1"

.14'.

45

6 1

■".135

85

.

E(4) .

14

80

7

13

35

8

14

36

9

15

26

10

14

86

'

11

14

67

14

43

12

14

87

14

43

14

14

37

13

94

,, 16.

1 1

2
11
12

14
13
14
14

82 1
82
37
37

14
14
14
14

95

45 1

46

76

■°.14».
14
14

79
64

84

Mean of R (5) 1
E(5) .
F(4) .

14
14
14

31
64
79

13

14

18

14

57

14

90

„ 20.

1

2

3

10

14
14

14
14

91
53
90
37

15
14
14
14

07
69
66
33

14
14

14

52
14

39

Mean of R (1 4) I 14 45

or omitting the two doubtful

R'(12) 1 14 40

Mean of E (13) .14 40

-

11
12

15
14

77?
57

14

62

14

.1
50

Mean ofF(12) .

14

12

13

14

67

. 14

22

14

50

14

. 14

57

14

92

14

50

15

. 13

77

13

92

13

51

16

. 14

27

. 14

02

14

01

17

14

07

. 13

92

13

71

18

. 13

79?

. 14

42

14

01

19

. 13

86

14

02

13

63

20

. 14

27

. 14

41

14

03

„ 21.

2
3
4
9

. 14
. 14
. 14
. 14

61
51
02
55

. 14

. 14

. 13

14

65
15
65
15

14
14
13
13

76
36

77
67

Mean of R (14) 1
Meanof E( 14) .
Mean of F (14) .

14
14
14

47
41
24

10

. 14

35

. 14

25

14

67

t2

140

The Rev. Dr. Robinson on the Difference of Longitude

DATE.

NO.

R.

E.

F.

MEAN.

May 21.

11

1". 14'. 03

V^.UK 24 1

■".13*. 61

^

12

14 65

. 14 44

14 21

13

. 14 36

. 14 34

14 62

15

. 14 36

. 14 14

13 62

16

. 14 66

. 14 63

14 62

17

. 14 27

. 13 63

13 64

18

. 14 57

. 14 73

14 64

19

. 15 09

. 15 13

14 65

20

. 14 59

. 14 63

14 35

Were we to suppose the results of each night of equal weight, and take the
arithmetical mean, we should find,

K = 1". 14'. 44
E = . 14 44
F = . 14 38

but this condition cannot be assumed ; for a greater number of signals are
observed on some nights, and the clock correction is concluded with unequal pro-
bability. The probable error of the difference of observed times is, denoting by
e that of the transit of a single star supposed the same at each observatory (as it
is at Armagh and Dublin in fact), and by s the number of stars,

If the number of rockets be r, and the probable error of the observation of
one at both observatories be ± em, that of the mean of the night is ± -7=,
and therefore that of the night's result

(e) = ±eX>/i+i,-|-^^

By examining these results, I find e = ± 0'. 065 and em = dz 0'. 23 for
E and E, F being greater, and hence the probable weight of each night

between the Observatories of Armagh and Dublin. 141

1

w = *

1+1 + 12

s s r

To apply this, the Dublin correction on the 14th Is derived from one star,
and the mean of three on the preceding, and two on the following day. I assume
* z= 3.

At Armagh s' = 3.

On the 16th, two stars, and the mean of three preceding and one following
give * = 3 ; *' = 5.

On the 20th, s = s' = 7.

On the 21st, two and the mean of seven and seven give s := 9 ; at Armagh,
four and the mean of seven and nine give s' = 11.

Hence, calling the decimals of the second of a result l, we have

May 14, w z= 0.46154 . . . wl = 0.20769 r
0.27273 0.08182 e

May 16, . . 0.34091 0.10568 r

Same 0.21818 e

0.22059 0.17426 F

May 20, . . 0.875 ^ 0.39375\ r

0.77778/ 0.31040J r'

0.82727 0.33091 E

0.61765 0.07412 F

* This expression of w shows, that with us the flash can be observed with about the same pre-
cision as the appulse of a star to a wire ; but a more important deduction may be made respecting

the method by successive signals. As each of these adds to the denominator of w a term _

r
their number diminishes it rapidly. Thus on the 20th, if, as in the Paris and Greenwich arc, we had

employed two intermediate stations, it would have been but 0.37 of its actual value, even supposing

the transmission perfect. I am therefore decidedly of opinion, that stations of transmission should

be made absolute stations, when it is possible, by furnishing them with transit instruments : this

guards against failure, and scarcely lessens the value of the result. Thus in the case supposed, w is

0.33, but it will be obvious that in Sir J. Herschel's operation, had this been done, instead of the

ten complete results which he obtained, he would have got at least ninety.

142 The Rev. Dr. Robinson on the Difference of Longitude

May 21, . . 0.94414 0.44375 k

Same, 0.38710 e

0.74356 0.17845 f

The final means are, therefore,

R = 1". 14'. + ^'•^^^^'^ = Im. 14'. 439
^ 2.62159

k' = 1 14 + 1:9^^ = 1 14 423
^ 2.52437

E = 1 14 + 2:21^ =1 14 427
^ 2.38505

F=l 14 +-5i^ = l 14 270
^ 1.58180

The result F has obviously far less weight than the other two, which must
be attributed not merely to Mr. Finlay's total want of practice in such obser-
vations, but also to the small optical power of his telescope. Though it differs
but little from the others, I think it best to omit it, and consider the mean of r'
and E as the definitive result

l™. 14'. 425.

But had I used it and retained the two omitted on May 20th, this would be
only 0'. 03 less, and identical with the result given by Mr. Dent's chronometers.

These, however, require a correction for what is called the Personal Equation
of the transit observers. It may appear strange that two practised observers
should not observe the passage of a star over a spider's line at the same instant,
but the fact is undoubted, and the difference is not of a decimal or two, but in
the case of perhaps the first of European astronomers, it exceeds a second. The
cause is unknown, but as from its being almost invariably independent of the
declination, it appears not to originate in the eye, the probability is, that it is
caused by some exercise of thought in associating the indications of the ear to
those of the eye. In most cases it is constant for many years in the same indi-
vidual ; in some, probably by carelessness, it goes on increasing.

The usual method of determining its amount is thus : the observer, e, ob-

between the Observatories of Armagh and Dublin. 143

serves the transit of a star at the first wires, and t at the remainder. Each wire
is then reduced to the centre ; this is repeated for many stars. If they agree,
there is no personal equation ; otherwise, it is their difference. Or they may
observe entire transits alternately on one night, and again inversely on a sub-
sequent one, each taking the stars which the other had previously examined.
The clock rates deduced from these will be ultimately too great, and too little, by
the personal equation, which, therefore, is half their difference. Or, lastly, by a
method shown to me many years since by Sir James South, which I prefer, as
enabling the astronomer to decide several questions connected with the subject.*
This requires an equatorial, whose micrometer wires are to be separated any
quantity, i% and set parallel to the meridian. Let p, the personal equation, be
the correction to be added to e, the time observed by one, to reduce it to t, that
by the other ; then

t' — e' — p' = i' X secant 8 ;

then move the equatorial, by its horary movement, into another position, and
repeat the process till a sufficient number be obtained ; then let the order of ob-
serving be inverted, and we have

e" -f- p' — t" = i' X secant 8 ;

and hence we find

2p' = s (t' — e') — s (e" - t'O-

If the equatorial were very much out of adjustment, and the hour angle
considerable, this process might require a correction, which, however, presents
no difficulty. Far from the meridian a correction for refraction might also be
required, but such circumstances will always be avoided.

I sent Mr. Edmondson to Dublin for the purpose of making such a com-
parison, which, after much delay by rainy weather, he effected on August 18th.
Sharp's equatorial was used for the observations.

* In particular as to the moon. In many cases, I believe, the personal equation for this planet is
different from that for stars ; and that even for the first and second limbs it is not always equal.
The bearing of this on the longitude method, by moon culminating stars, is evident, as also the
mode of ascertaining its influence and amount.

144 The Rev. Dr. Robinson on the Difference of Longitude

With 71 Aqullae, 8 = _ 1° 40' by 16 pairs,

E' - Ts = 24s 2871 „ _ , 0' 147
t' - e' =24 581/^ - +0.147

25 Aquarii, 8 = -|" 1° 31 by 17 pairs, with another opening of the wires,

E — T = 20' 0881 , „ ,^^

T' - E' = 20 412) ^ = + 0-162

Another set of 14 pairs,

E — T = 20» 053\ „ ^n^KA
T'-E'=20 37l|'^ = + °-^^*

63 Aquarii, 8 = — 5° 6', 16 pairs,

E— T = 20»100\„ im^o
T'-E' = 20 444) ^ = + 0-1^2

Again 15 pairs,

E — T = 20' 207) , n ono

T'-E'= 20 613} ^ = + 0-203

The mean of the seventy-eight pairs is -\- 0'.167, or Mr. Thompson observes
so much later than Mr. Edmondson. I regret that the moon was not observable.
They tried the sun's second limb, and found by 14 pairs p = + 0.225.

Hence, our true difference of longitude is by

Rocket signals . 1". 14'. 258
Chronometers . . 14 220

I stated that it appeared unnecessary to continue the signals at Slieve
Gullion ; and this, I hope, will be admitted in reference to the object proposed,
the determination of the arc of longitude between Dublin and Armagh.

As, however, calculating on the number of failures in the French rockets, I
had got more than proved to be required, it is my intention to employ the re-
mainder in a way, which, while it verifies the present work, will determine the

between the Observatories of Armagh and Dublin. 145

position of another point, likely to become of great importance, the Observatory
of E. J. Cooper, Esq., at Markree ; which, not merely from the magnificence of
its instruments, but the intention of its possessor to make it a permanent estab-
lishment, merits this distinction. It will be seen, on referring to the map, that
the high mountain Cultiagh, in Leitrim, has been selected with this view : it is
visible from Markree, barely hid from Armagh by Cairnmore ; and, though
eighty-two miles from Dublin, yet, as 1700 feet above its summit will reach the
view at that place, this, also, is completely within the scope of these rockets.
If there be any fine weather in autumn, I hope to perform this then ; and,
afterwards it will be our object to connect the Irish observatories with those of
Scotland and England. Several points in Antrim are visible from Armagh,
and also from the west coast of Scotland : and if the method of successive signals
were employed, there is no difficulty in reaching Edinburgh. But for reasons
already given, I would use this only as a last resource, and then make the inter-
mediate stations absolute, which, if they are chosen at primary points of the tri-
angulation, is likely to give very useful geodetic information.

But in the present instance I conceive it quite possible, by using large
rockets, to effect the junction with one signal station. The mountain Goatfell,
in the Island of Arran, has been chosen as the station. Its height is 2865 feet,
and if the rockets can add to this 3300, they will be in view both here and at
Edinburgh, the distances being 105 and 86 miles.

That this can be accomplished is certain, for a few which I made recently, no
heavier than those which have been described, rose, with four ounces of powder,
4.500 feet ; and if the Board of Ordnance continue their powerful aid to us, I am
confident of success.*

Similar rockets will, I think, also connect immediately Oxford with Dublin.
If fired on Plinlimmon, 1500 feet will bring them within view of the latter, and
also of the other, probably, unless the circumstances of the ground in its vicinity
forbid it. But as to this I have not yet consulted my geodetic Mentor. If,
however, it be necessary to observe them from one of the neighbouring hills,

* Since this was written, the Board have granted my application for a supply of rockets capable
of ascending to the required height.

VOL. XIX. U

146 The Rev. Dr. Robinson on the Difference of Longitude, Sfc.

that is scarcely an objection, if it be so near the observatory that time can be
transmitted certainly by powder signals, as they can be multiplied to any
, extent.

The junction of Oxford with Greenwich is a matter of no difficulty.

T. R. ROBINSON.
Armagh Obsebvatoby.

147

V. On the Direction and Mode of Propagation of the electric Force traversing
interposed Media. By George J. Knox, Esq., A. M., M.R.I.A.

Read February 11, 1839.

Whatever theory be adopted to explain the passage of the electric force
traversing an intervening fluid or solid substance not undergoing electrolyzation,
— whether we suppose it to originate in an inductive influence affecting the
circumambient ether of each particle of the substance in the line of direction of
the force, in whose alternate states of induction and equilibrium consists the pas-
sage of the electric current, (the rapidity of such changes constituting its inten-
sity,) while the vibratory motion produced in the particles of the ether on each
successive return to a state of equilibrium causes the phenomena of the light
and heat developed ; or whether we adopt the gross conception of the passage of
a fluid ; still it is important to determine if the electric force passes along the
surface of the interposed substance, or through the interior of its mass.

Dr. Faraday* has shown that water will convey a feeble current of electricity,
without undergoing electrolyzation. To determine whether, under such circum-
stances, it will convey an electrical current along its surface or through its
substance, a glass tube, ten feet long, and half an inch internal diameter, bent in
the centre twice at right angles, was filled with distilled water. Two copper
wires, twenty feet long, having platina wires soldered to their extremities, were
inserted in barometer tubes of six feet in length, the platina wires being sealed
in the tubes within half an inch of their extremities. The other ends of the cop-
per wires were connected with a delicate galvanometer, and a constant battery
of successively one, two, four, &c. pair of elements.

On immersing the platina wires in the liquid, their relative distances from
each other should decrease if the current passes through the water, but should

• Series VIII. (970.)

U 2

148 Mr. Knox on the Direction and Mode of

increase if it passes along the surface, the deflexion of the galvanometer indicating
the path. With one pair of elements there was no deflexion of the galvanometer^
with two pair of elements there was a slight deflexion visible through a lens,
which increased slightly on immersing the platina wires in the liquid. With
four pair of elements, a deflexion of two degrees took place when the platina
wires were on the surface of the water ; a deflexion of four degrees when they
were immersed to the bottom of the tubes. As the number of alternations in
the battery increased, so did proportionably the comparative deflexions of the
galvanometer : the experiments proving that water, whether undergoing elec-
trolization or not, conveys an electric current through its substance, and not
along its surface, and that the decomposition of the water is an effect produced
by the passage of the electricity when of sufficient intensity, and not the neces-
sary consequence of its passage.

A similar experiment having been tried with phosphorus melted under spirits
of wine, (being a non-conductor,) it was found to Obey the same law with water ;
that is, to convey the current through its substance.*

To determine whether the metals followed the same law, I suspended from
the top of the new patent shot tower at Waterloo-bridge a leaden pipe, 170 feet
long, and three-fourths of an inch Internal diameter, through which was drawn an
insulated copper wire, 180 feet long, one extremity of which being soldered to
the inside of the end of the pipe, this end was sealed with fused metal, and to its
external surface was soldered a copper wire of the same length as the former ;
round the tube, at its orifice, was twisted a copper wire ten feet long. The insu-
lated wire being connected with a constant battery of one pair of elements in
contact with one pole of an exceedingly delicate galvanometer, (constructed by
Mr. E. M. Clarke of the Lowther Arcade, ) the other pole of the galvanometer
was brought successively in contact with the extremities of the uninsulated wires.
The deflexion was greater when the current passed along the wire connected
with the orifice of the tube, (although here the contact was not so good,) than
when it passed along that soldered to the sealed extremity.

Again, the uninsulated wires being connected with separate galvanometers,

• It was unnecessary to try similar experiments with the analogous bodies, sulphur, selenium,
and iodine.

Propagation of the Electric Force. 149

so as to allow the current of electricity to pass along either of the uninsulated
wires alone, or to be distributed between both, it was found (as well as could be
determined by transposing the galvanometers,) to have divided itself into two
equal currents flowing along both wires.

From the first experiment we may infer that a current of electricity passes
with greater facility along the surface of a metal than through the interior of its
mass, although we cannot hereby infer that it could not pass through the inte-
rior of the metal, when this is the only road open for its transit.*

To the experiments with phosphorus it might be objected that its capability
for conducting an electric current is due to the presence of water, of which some
have supposed that it could not be entirely deprived, although the experiments
of Sir H. Davy, wherein he obtained hydrogen and oxygen from sulphur and
phosphorus by heating them in contact with potassium and sodium, and by sub-
mitting them to the electrolytic action of a powerful galvanic battery, did not
prove that they were united with the basis of these substances in such proportions
as to form water, nor indeed does he appear to have entertained such an opinion
himself. His opinion of the nature of sulphur was, that it was "a compound of
small quantities of oxygen and hydrogen, with a large quantity of a basis, that
produces the acids of sulphur In combustion, and which, on account of its strong
attraction for other bodies, will probably be difficult to obtain In Its pure form."f
To put the question beyond any further doubt, I will mention some experiments
which I tried In the Laboratory of the Royal Dublin Society in the year 1837,
having had, through the kindness of Professor Davy, a galvanic battery of sixty
pair of plates, five Inches square, put at my disposal.

When fused phosphorus, sulphur, selenium and Iodine, were submitted sepa-
rately to the action of this battery charged with a strong acid solution, they
conveyed the electrical current freely during the whole time, giving a spark
whenever contact was broken ; yet at the end of two hours they showed not the

* The high conducting power of mercury for electricity renders it almost impossible to deter-
mine, by this method, whether metals in i\ie fluid state obey the same laws of conduction as when
in the solid state. If they do not, it is highly probable there is a general law, that all solids condixct
along their surface, and all fluids through their substance. The investigation of such general law
I propose to continue in another paper.

I Bakerian Lecture, 1809.

1 50 Mr. Knox on the Direction and Mode of

slightest trace of decomposition, no gas being evolved at either pole, which would
have been the case had there been any water present.

Having by these experiments shown the direction of propagation of the
electric force, I will now consider the source from which it originates in the
voltaic pile, the mode of its transfer, and its sustaining principle.

Sir H. Davy's* opinion that the contact of the metals was \}a.Q 'pr'imum mobile
of voltaic excitement, having been proved by Dr. Faradayt to be erroneous,
chemists are now pretty generally agreed that the electrical force developed in
the voltaic pile is due altogether to chemical action, concerning which there are
different opinions ; of these, I will mention two, which are the most applicable
to the present argument — Dr. Faraday'st and Mr. Becquerers.§ The former
supposes that the development of electricity is due to decomposition alone, and in
no case to the chemical union of bodies, while the latter contends that it is due
to both, and in proof of his opinion shows that when an alkali unites with an acid,
with a neutral salt, and in fact with any solution whose natural state is with re-
gard to it electrically negative, a current of electricity will flow from the alkali
to that solution. Sir H. Davy|| has taken a different view of these experiments
from Mr. Becquerel, supposing that the electric current is produced by the ac-
tion of the acid or alkali upon the platinum plates ; but the latter has shown that
the electrical current is produced equally when no such action could take place,
the platinum poles being placed in separate cups filled with water.lj

The accuracy then of Mr. Becquerel's experiments having been fully esta-
blished, the question arises, how are we to reconcile them with other well known
contradictory facts ? such as for instance those of Sir H. Davy,** — solid potash
and sulphuric acid combining in an isolated platinum crucible, and causing no
electrical development. Again, a plate of copper and of sulphur, when heated,
have their electrical states increased until chemical action begins, when they
cease.

* Phil. Trans., Bakerian Lecture, 1826. t Eighth Series, (880).

X Eighth Series, (927) (928). § Tom. ii. from page 77 to 81.

II Phil. Trans., Bakerian Lecture, 1826.

T He might have added another experiment, free from all objections — namely, the increased
intensity consequent upon an increased number of alternations of acid and alkali.
•* Phil. Trans., Bakerian Lecture, 1807.

Propagation of the Electric Force. 151

The simplest and clearest course, and that most reconcileable with the laws of
statical electricity, seems to me to be : — to consider that no electrical development
is caused by the union of an alkali with an acid, (the electricity being thereby dis-
guised,) but that, at the instant before the union takes place, the particles of the
alkali and of the acid, being in opposite electrical states, affect their surrounding
particles by induction, causing thereby a feeble current of electricity to circulate
from the acid through the galvanometer to the alkali, which supposition is borne
out by the fact that a dry acid and alkali, when in contact, show opposite electrical
states.

The same arguments apply equally well with regard to thermo-electricity.
The contact of two metals produces in them opposite electrical states. Their
chemical union in an Isolated vessel gives no electrical development ; thus a
" solid amalgam of bismuth and lead become liquid when mixed together, with-
out producing any electrical effect." * Again, " a thin plate of zinc placed
upon a surface of mercury, and separated by an insulating body, is found to be
positive, the mercury negative ; but when kept together a sufficiently long time to
amalgamate, the compound gives no signs of electricity."*

These experiments explain why the contact of the two extremities of metallic
wires, constituting a closed circuit, should, as the potash and nitric acid just
mentioned, produce an induced electric current. That the electric states of dif-
ferent metals in contact, when excited by heat, do not follow the law of their
natural electrical states, and change on increase of temperature, is no argument
against the explanation I have given, for upon what this change in the electrical
excitation produced by heat depends, whether upon a peculiar arrangement of
the crystalline parts of the metal, or of their compound elementary particles,
we are as yet perfectly ignorant.

That the same general law of the contact of metals and of fluids applies
equally (although in an inferior degree, owing to their want of conducting
power) to the contact of the gases, may be shown by the experiment of Dr.
Faraday (Sixth Series) of the union of hydrogen and oxygen by a plate of pla-
tinum ; the electrical force, which circulates by the Interposed platinum plate,
facilitating the union of the two gases.f

* Phil. Trans., Bakerian Lecture, 1807.

■\ Aqueous solutions of different gases, when brought into contact, have been found to produce
electrical currents.

152 Mr. Knox on the Direction and Mode of

To return to the source of the voltaic force in the battery. Zinc, when
placed in contact with a dry acid, has been found to become positively electrified.
When the zinc plate h>!as been immersed in the acid solution, being positive, it
attracts oxygen, by union with which its electrical state is disguised, while the
hydrogen, set free in a highly positive electrical state, reacts upon the oxide of
zinc, rendering it negative by induction. The platinum wire connecting the posi-
tive solution with the negative zinc plate, reduces all for the moment to a state
of equilibrium, so that the electricity becomes disguised, not transfen-ed bodily
from the platinum to the zinc ; which state of equilibrium is no sooner restored
than it is destroyed, the zinc regaining its positive state, and the oxide being
removed by the acid.

If we consider then what takes place, we shall perceive that the zinc plate un-
dergoes alternate states of induction and equilibrium, as do likewise the particles
of the solution between the zinc and platinum plates, and, in fine, the platinum
plate itself, and that as the number of alternations of zinc and platinum increases,
the electrical energy of the zinc plate increases, as does also the rapidity of its
oxidation and deoxidation, and as a consequence the rapidity of change of
induction and equilibrium upon which the intensity of the current depends.

The decomposition of the electrolyte may be considered to be the effect
produced by two forces acting upon its particles ; the attraction of the poles*
of the battery (whether they be metal, water, or air) originating, while the
electrical states induced upon the particles give the direction to the electrolytic
action.

From what has been said above, we may, I think, presume that an electric
current originates in a natural electro-inductive power of bodies when brought
into contact, and is continued by alternate states of induction and equilibrium,
the rapidity of change of state constituting its intensity. And inasmuch as the
accumulation of the electric ether on the surface of the particles by the inductive

* In place of poles, I should more properly have said electrodes, their bounding surfaces. It
follows, as a consequence of the theory, that the particles of oxygen in contact with the electrodes
should be attracted by, and set free from, those electrodes upon each alteniation of the states of
induction and equilibrium ; and that, when the induced state has not sufficient energy to overcome
the affinities already engaged, the current of electricity passes without producing electrolyzation.
For a different explanation, vid. Dr. Faraday's Series of Researches, 493, 494, 495, 534, 535, 536,
337, 807.

Propagation of the Electric Force. 153

force, and its recession on each return to a state of equilibrium produces what
may be called an oscillation in the ether, the theory may be otherwise stated
thus : — the mass of oscillating ether which surrounds the particles constitutes the
quantity, while the rapidity of the oscillations constitutes the intensity of an
electric current.

The late experiments of Dr. Faraday upon induction (Eleventh Series) shew-
ing that an insulated body (the particles of bodies may be presumed to be such)
cannot receive an absolute charge of electricity, but only an inductive charge,
afford a strong argument in favour of my views.

The theory proposed in this paper, and deduced from the experiments of
Sir H. Davy, given in his Bakerian Lectures, is an extension of the views
therein developed, reconciles the contact with the chemical theory, and re-
duces to the laws of statical electricity all the phenomena of electricity in
motion. I will now endeavour to show how the law of the definite nature of
electro-chemical decomposition, so beautifully developed by Dr. Faraday, follows
as a consequence from this theory. Were the particles of all bodies endued with
the same quantity of electricity, and of the same density, it is evident from the
laws of statical electricity, that no one body could have an attraction or repulsion
for another ; consequently, it is an evident fact, that the quantity and density of
the electric ether varies in different bodies ; and as, from the theory above stated,
electricity never leaves the particles, but merely (to use the words of statical
electricity) accumulates upon the surface, and returns, it follows that the electri-
cal states of the particles of bodies are constant and unalterable, and therefore
it is obvious that the law discovered by Dr. Faraday follows as a consequence
from this hypothesis, which is at once clear and simple, which includes all the
phenomena, and is but a reference of the laws of statical electricity to the par-
ticles of bodies in place of their masses.

VOL. XIX.

154

Mr. Patterson on the Bolina Hibernica.

VI. On the Bolina Hibernica. By Robert Patterson, Esq., Member of
the Natural History Society of Belfast.

Read November 11, 1839.

In a paper on the Cydippe pomiformls, read before the Royal Irish Academy
in December, 1838, and published in the present volume,* the occurrence on our
coast of another species of ciliograde was mentioned, its figure described, and
some particulars respecting its economy brought forward. The present is
intended as a sequel to the former communication respecting this animal,
the Bolina Hibernica.

The specimens from an examination of which I am enabled to give the
particulars here recorded, were obtained the 11th of July, 1839, when I was

Explanation of the Figures.

F^, 1. Front view.
2. Lateral view.

3. Anterior portion viewed from above.

4. Posterior portion seen from beneath.

Ante, page 91.

Mr, Patterson on the Bolina Hibernica. 155

lodging at Bangor, county of Down ; and such was their abundance on that day,
that in the course of twenty-five minutes, one hundred and twenty-six individuals
were taken in the bay by means of two small canvass towing nets. On several
occasions, both before and after that date, my efforts to obtain specimens were
totally unsuccessful.

The general movement of the animal appears more deliberate, or less
vivacious than that of the Cydippe pomiformis, though always graceful and
varied. The spiral motion on an axis, mentioned by Mertens as the mode of
locomotion, may occasionally be seen, but is not habitual. Like Cydippe pomi-
formis, it generally swims in an erect position, with the mouth upwards. Its
increase of power does not seem proportionate to its increase of size, for a small
medusa of the genus Geryonia of Cuvier, which chanced to be thrown into the
glass, attached its peduncle to a Bolina from twelve to sixteen times its own
bulk, and with great apparent ease towed it round the vessel, reminding the
spectator of a pigmy steam tug towing a stately merchantman.

This species of beroe is extremely susceptible of injury, and hence, when any
number are taken, some are sure to be found in a shattered state, perhaps, with
so much as one-half of the body torn away. Any of the cilia detached from
the body, along with a small piece of skin, will continue to vibrate for many
hours ; this is particularly apparent in the four tentacula, and in the four
ciliated rings or orifices, from which these organs are protruded. In both, we
do not merely behold marginal cilia in rapid and continuous motion, but their
number and variety of position is such, that the mutilated part to which they
belong, is moved about with the briskness and activity which we are apt to
regard as characteristic of a perfect and vigorous animal. Under each of the
bands of cilia, two aqueous currents are easily discernible, one ascending, and
one descending with great regularity.*

The tentacula were formerly mentioned as " extremely beautiful in appear-
ance, both from their transparency, and from the numerous minute, delicate,
pointed cilia along their edges." Their great attraction, however, is their
versatility of form. They may be seen pointed, erect, and hollowed longltudi-

* In a communication on C. Pileus, made by Mr. Garner, at the late meeting of the British
Association, it was stated that such currents are occasioned by the action of minute internal cilia,
placed on the parietes of the vessels.

x2

156 Mr. PATTERSOisr on the Bolina Hibernica.

nally like the ears of a horse, or somewhat funnel shaped, and occasionally either
flattened or concave, with the extremity rounded. At times their position is
horizontal, at others they hang " loosely down like the ears of a lap-dog, or are
curved like the petals of the martagon lily."

A whitish cord-like body extends round the orifice of the mouth ; another
round each of the four apertures, whence the tentacula issue. From each
of the longer bands of cilia, a similar cord of a whitish milky colour, extends
over the lobes at the mouth, touches the one first mentioned, and is con-
tinued to the four orifices already noticed, one going to each.* These orifices
are connected in a similar manner with each, those on the same side of the body
by a sti'aight cord, those on opposite sides by an arched one, which adapts itself
to the expansions or contractions of the body. The cords from all the bands
converge near the anal extremity.

The two prominent lobes adjoining the mouth, and which sometimes consti-
tute one-fifth of the entire length of the animal, are not permanent in their form,
but vary not only in the regularity of their outline, but also in the extent to
which they are distended, and at times, especially when the animal is in an
exhausted state, become so reduced in size as to be scarcely perceptible.

During the time the drawings were in progress, specimens of the animal
were kept in glass vessels of various dimensions, for the convenience of reference
and examination, and one of these containing several individuals, was placed on
the mantle piece, adjoining to some glasses filled with garden flowers. On
looking at these through the transparent body of the Bolina, the flowers were
seen so distinctly, that the several kinds were at once recognised, and the parts
of fructification in some campanulate corollas, were with ease distinguished.

On taking a glass containing one of these heroes into a dark room, no
luminosity was apparent, but on its being shaken, transient gleams of light were
emitted. The animal was then taken and plunged in a glass of fresh water,
which appeared instantaneously filled with innumerable small bright globules

* The following passage in Jones's" Outline of the Animal Kingdom," occurs in treating of the
Beroeform species of Ciliograde Acalephse. " From both extremities of the digestive cavity, arise
vascular vessels, one surrounding the oral, and the other the anal portions of the body: from
these two rings eight double vessels arise, which run longitudinally from one pole to the other
of the creature, beneath each of the cartilaginous ribs, upon which the cilia are placed." — p. 73.

Mr. Patterson on the Bolina Hihernica. 157

of fire, all in motion and rapidly disappearing ; and on a light being brought,
the Bolina was found lying lifeless at the bottom. In glasses containing a few
individuals, flashes of light were given out, sufficient to render the figures on
the dial plate of a watch visible for a moment, but too transient to allow the
hour to be observed. Two large opaque vessels, each containing twenty or
thirty individuals, were next subjected to examination in the dark cellar in
which they had been placed. On agitating the first of these, light of a pale
green tinge seemed instantly to diffuse itself through the water. On doing the
same with the second, the whole contents of the vessel became lighted up so
completely, as to render all the adjacent objects visible for a moment. On stir-
ring it round, the animals were seen like lamps suspended in the water, to which
their own radiancy imparted* a milder and fainter effulgence. On touching
them with the hand, light was invariably given out with increased brilliancy,
the bands, and every portion of the cilia being distinctly exhibited, with a
splendid greenish lustre as beautiful as it was evanescent. It was impossible to
behold these bodies of innocuous fire, floating amid the brightness which they
themselves diffused, and not feel, that to convey an adequate idea of their
beauty, would be a task more fitted for the imagery of the poet, than the
language of the naturalist.

Being obliged to leave Bangor early next morning, the sea water in one of
the larger vessels was not changed during the day, and in consequence of this
neglect, I found, on my return at night, that all its occupants had died. The
water, owing to their decomposition, then presented a discoloured milky appear-
ance, and emitted a peculiar and disagreeable odour. On being agitated in the
dark, no light was given out, thus proving that the luminosity of the previous
evening was peculiar to the living animal, and was not extended to the putres-
cence of its decaying parts. This species, and the Beroe fulgens of Macartney,
taken by J. Templeton, Esq., on the Down coast, are the only Irish cilio-
grades in which the luminous power has hitherto been observed.

Being desirous of ascertaining if the present species had been recognized
in any other localities, I exhibited the accompanying figures at the late meeting

* " lis brillent pendant la nuit, comme autant de lumieres suspendues, dans les eux." —
Lamarcli.

158 Mr. Patterson on the Bolina Hihernica.

of the British Association in Birmingham, and solicited information on the
subject. It was unknown to any of the naturalists then present ; and my friend
Edward Forbes, Esq., who communicated a valuable paper " on the Ciliogrades
of the British Seas," pronounced it to be distinct from any of the eight species
enumerated by him.

As it does not appear to have been previously recorded, either by British
or Continental writers, the specific name Hibernica, before applied provisionally,
may now be regarded as permanent. It would be premature to say the same
of its generic title ; for although it agrees with the Bolina of Mertens more
nearly than with any other at present defined or figured, we recognise in the
diminished size of the lobes, and in the more extended portion of the longer
bands occupied by cilia, a still nearer approach to the true heroes ; so that it is
possible when we attain a more extended knowledge of the various species of
ciliogrades, the present may be referred to an intermediate genus, yet to be
established, or ranked with some of those now existing, under one common and
comprehensive appellation.

The localities in which it has hitherto been observed are, Larne Lough, county
of Antrim, (R.Patterson); Bangor, Bay, (R.Patterson); Strangford Lbugh,
county of Down, (W. Thompson) ; Lambay Island, county of Dublin, (R. Ball,
and W, Thompson) ; and Youghal Harbour, county of Cork, (R. Ball).

The present species is not likely to be confounded with either of its two
congeners, — B. elegans, of a pink colour, found in the South Sea, or B. sep-
trionalis, clear bluish, taken in Beering's Straits. The following brief specific
description may suffice to distinguish it from other British ciliogrades.

Bolina Hibernica. Form variable, generally ovate, rounded, and compressed.
Hyaline, lobes contractile, and not more than one-ififth of the entire length of
the animal. Longer bands, ciliated nearly to their apex.

For the accurate figures by which the present paper is illustrated, I am
indebted to the skill and kindness of Miss Masson of Bangor. A much greater
number would, however, be requisite to convey an adequate idea of the diversi-
form aspect of the animal, especially with regard to the inflated appearance occa-
sionally presented by the upper portion of the body.

TnoK -g./.A.^TOL.'XK/t./^g.'

3CIEKCE PLATE N» 2.

'SOS

ivr

159

VII. On the mutual Action of Permanent Magnets, considered chiefly in
reference to their best relative Position in an Observatory. By the Rev.
Humphrey Lloyd, A.M., Fellow of Trinity College, and Professor of
Natural Philosophy in the University of Dublin, F.R. S., V.P.R.I. A.,
Honorary Member of the American Philosophical Society.

Read February 11, 1839.

It is a problem of much Importance, in connexion with the arrangement of a
Magnetical Observatory, to determine the relative position of the magnets in
such a manner, that their mutual action may be either absolutely null, or, at
the least, readily calculable.

As a preliminary step to the solution of this problem, it is necessary that we
should know the direction and intensity of the resultant force exerted by a
magnet upon an element of free magnetism placed in any manner with respect
to it. This question has been already solved by Biot, on the supposition
that the action of a magnet is equivalent to that oi two forces of equal intensity,
one attractive, and the other repulsive, emanating from two definite points or
poles. There is no difficulty in generalizing the problem, and in obtaining a
solution independent of this particular hypothesis.

The middle point o, of the magnet ns, (Fig. 1) being taken as the origin
of coordinates, and the line connecting it with the magnetic element m as the
axis of abscissae, the distance, mq, of that element from any point (x, y) of the
axis of the magnet-bar is

V{a-xf-^y\

the distance om being denoted by a. Hence, if m denote the quantity of free
magnetism in the magnetic element M, q the corresponding quantity in a given
elementary portion of the magnet at q, the force exerted by the latter on the
former is

160 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

the law of the force being similar to that of gravity, 1. e. directly as the pro-
duct of the magnetic masses, and Inversely as the square of their distance.
Let this force be resolved In the direction of the axes of coordinates. The
portion parallel to the axis of x Is

mq{a — x)

and that parallel to the axis of ^ Is .

mqy

and the sums of these portions, taken throughout the entire length of the
magnet, are the components of the total action.

Let the distance oq = r, and the angle moq = 0,

0^ = r cos 0, y = /■ sin 0 ;
and substituting, the components of the force exerted by q on m are

mq (a — /•cos0) mqr sin <f)

(a* — 2 ar cos 0 + r^)i ' (a^ — 2 ar cos 0 + ^i '

Hence If ^ and F denote the components of the total force exerted by the magnet
Ns on M, we have

+1 -+/
v-^C (a - r cos (f>)qdr y_^ smtf^grdr

^-™ (o^_2arcos0+Ol' (a^ — 2 ar cos 0 + r^)! ' ^^

I being half the length of the magnet. The quantity q being an unknown function
of r, it is manifest that the integration of these formulae cannot be effected
in finite terms.

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 161
If we develop the trinomial factor

(a' - 2 or cos 0 + A' ^ = o-^ ( 1 — 2 ^ cos (^ + -^,)7

it is manifest that the quantity within the brackets will be expressed by a series
ascending by the powers of - ; and that accordingly the preceding integrals may

Cv

be developed in serial of the form

m C ^^ . U, . U„ . U-t

-|f^„+E + ^^ + ^^ + &e.),
a^\ a a^ a^ }

in which the coefficient of the general term is

U„=V

\ qr'" dr.

V being a function of the constant angle 0. Now, if the distribution of free
magnetism be symmetric on either side of the centre, the alternate coefficients,
U^, U^, U^,kc. vanish, the values of q being equal, with opposite signs, at the cor-
responding distances r = ± s. We have therefore, in this case,

„ m fA. , Aj , A. , . \
a' \ a * a^ ^ a^ ^ J

(2)

the two series descending according to the odd powers of a.

When the length of the magnet is small, in comparison with the distance a,
these series converge rapidly, and, for most purposes, the first term affiards a
sufficient approximation to the actual value. We have then, approximately,

X = ^, Y=^; (3)

a^ a^ ^ ^

VOL. XIX. Y

162 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

and denoting the total force by R, and the angle which it makes with the axis
of abscissae by w,

tan«. = -jl, i?= -^ \ (4)

Now, stopping at the first dimension of - m the development of the trino-
mial factor,

(l -2%os0 + -^) ^ = l+3^cos0, q.p.

and substituting, we find

^, =;= 2 COS 0 \ qrdr = 2 Mcos 0, B^ = sin 0 V qrdr = Msin <f> ;

putting, for abbreviation,

\ qrdr = M.

Finally, substituting these values in (3) and (4)

^ iMm , ^ Mm . , ...

X = ^— cos 0, Y = — ,- sm 0 ; (5)

a^ a'' ^ '

j\f iffi

tan 10 = -|- tan 0, R = — j v 1 -{- 3 cos^ 0. (6)

The theorems expressed by the formulae (6) were taken by Biot as the basis of
his well-known theory of terrestrial magnetism.

If we desire to push the approximation further, we must include (in the

r^
development of the trinomial factor) the terms involving -y. We thus find

Aj = 2Mj cos 0 (5 cos^0 — 3), B^ — ^M^ sin 0 (5 cos' 0 - 1) ;

in which we have made, for abridgment,

V qr'drzziM.^.

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 163
Hence the components of the force are

X= ?|- cos 0 {m, + ^X5 cos^ 0 - 3)1

[ (7)
F=^sIn0|il/,+ |-^X5cos^0-l)};

the integral Involving the first dimension of r being denoted, for distinction
hy M,.

When 0 n 0, these values become

2m r,^ . 21/,

r=o, X=^^(^.+^-^.);

and the resultant force is, consequently, directed in the connecting line.
When 0 = 90", we find

and the force is altogether perpendicular to the joining line. ,

Returning to the approximate formulae (5), it is easy to deduce the directive
force, or the moment of the action exerted by one magnet on another, the length
of each being supposed small in comparison with the distance between them.
In this, and other similar applications of the formulae, we may consider the
distance a, and the angle 0, as the same for all the elements of the magnet acted
upon ; the variations of these quantities being of the order of those which we have
already neglected in this approximation.

Let us assume that the two magnets ns and n's' (Fig. 2) are in the same
horizontal plane, and that the magnet acted on, n's', is capable of motion in
that plane round an axis passing through its centre of gravity. Let J^ and Y
denote, as before, the components of the force exerted by the former upon any
element of free magnetism, q', situated at the point q' of the latter. These forces
being directed in the line oq', and in the line perpendicular to oq', respectively,
their moment to turn the magnet n's' round its centre of motion o', is

o'a' (Xsin n'q'o — Fcog n'q'o).

y2

164 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

Now the angle q'oo' being very small, we may (in the same order of approxima-
tion as before) put oo for oq, noo' for noq', and n'o'o for n'q o ; and accord-
ingly, denoting the distances oo' and o'q' by a and r', and the angles noo' and
n'o'o by (f) and (f>', we have (5)

^ 2Mq' ^ ^ Mq' . ^

X =■ — 3-^ cos 0, y = — ^ sm 0 ;

ilf being the moment of free magnetism of the acting magnet, as already defined.
Hence the moment of these forces to turn the magnet n's' is

— ^-12 cos 0sln0' — sin 0cos0'i=: ^3 j sin (0 4" 0') — 3sin (0— 0')> ;
and multiplying by dr', and integrating, the total moment is

^'{sin (0 + 0') - 3 sin (0 - 0')}, (8)

in which M' denotes the moment of free magnetism of the second magnet, or the
value of the integral \q'r'dr., taken throughout its entire length.

Let us apply this result to the case of the mutual action of two horizontal
magnets, the axis of one which, ns, lies in the magnetic meridian, while that of
the other, n's', is perpendicular to it (Fig. 3). Such is the position of the magnets
in the instruments used in determining the declination, and the horizontal com-
ponent of the intensity of the earth's magnetic force.

The moment of the force exerted by the second magnet on the first is in

this case (8)

MM' ,. „ „ ,.
-2^j-(l — 3cos2 0);

since 0 -j- 0' = 90". Hence, that this moment may be nothing, we must have

cos20 = i. (9)

Accordingly the mean direction of the first magnet will be undisturbed by the
second, when the line connecting their centres is inclined to the magnetic me-

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 165

ridian at the angle 0 = 35° 16'. Mr. Weber has already arrived at this result
by other methods.

With respect to the deviations of the magnet from its mean position, (or the
apparent variations of the declination,) it is manifest that they will be increased
or diminished in a given ratio, the action of the second magnet on the first
being in the same direction as that of the earth, and therefore altering the
directive force in a given ratio. The true variations will therefore be obtained
from the apparent, simply by multiplying by a constant coefficient.

The reciprocal action of the first magnet on the second, however, is not
directed either in the magnetic meridian, or in the line perpendicular to it, and
the second magnet is therefore disturbed by the first. With two magnets, ac-
cordingly, it is impossible to neutralize the effects of mutual action.

Now let a third magnet be introduced ; and let us suppose, in the first
instance, that this magnet h fixed, being destined only for the purposes of cor-
rection. We have, in this case, only to consider the forces exerted upon the
first and second magnets.

Let A, B, c, (Fig. 4) be the three magnets — of which a is the declination
bar, having its axis in the magnetic meridian ; b the horizontal intensity bar,
whose axis is perpendicular to the magnetic meridian ; and c the third, or cor-
recting bar, the azimuth of whose axis is arbitrary. Lines being supposed
drawn joining the centres of these magnets, let the sides of the triangle opposite
to the points a, b, c, be denoted by a, b, c, respectively, and the angles which
these lines form with the magnetic meridian by a, |3, 7 ; let the angle which
the axis of the third magnet c makes with the same meridian be denoted by f ;
and finally, let the magnetic moments of the three magnets be A, B, C.

The forces exerted by the magnet b, upon any element m of the magnet a,

in the direction ab, and in the direction perpendicular to ab, respectively,

are (5)

, 2Bm . Bm

+ —^ sm 7, - —3- COS7 ;

the magnetism of m being supposed to be northern, and the positive and ne-
gative signs being employed in the usual conventional manner. Let these forces

1 66 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

be resolved each into two, in the magnetic meridian, and perpendicular to the
magnetic meridian. The former components are

, 2-Bm . , Bm .
-j- — ;^sin7C0S7, -1 -3- sm 7 cos 7;

and the latter

, 2 5m . „ Bm „

+ —5- sm' 7» — — ,- cos''7.

c

Again, the forces exerted by c upon the element m of a, in the direction ac,
and in the direction perpendicular to ac, are

. 2 Cm , ^, Cm . , ^.

+ -^cosa-^), --^sm(f-^);

and the resolved portions of these forces in the magnetic meridian are

+ ?^cosa-i3)cos^, +^sin(f-^)sin^;

while the components perpendicular to the magnetic meridian are

+ ^^ cos (^ - p) sin p, - ^? sin (f - /3) cos /3.

Accordingly, the conditions of the complete equilibrium of the forces exerted
by B and c on a, are

-T5 1 2 cos ((3 — ^) cos /3 — sin (]3 — f ) sin j3 1 + 3 -^ sin 7 cos 7 = 0.

-^3 12 cos (i3 - f ) sin i3 + sin (jS— f ) cos iSJ + — (2 sin^ 7 - cos' 7) = 0 .

In like manner, the forces exerted by the magnet a upon any element m of
the magnet b, in the direction ab, and in the direction perpendicular to ab,
respectively, are

, 2 Am , Am .

+ --r— C0S7, +--j-sm7.

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 167

And the forces exerted by c upon the same element, in the direction bc, and in
the direction perpendicular to bc, are

2 Cm , . Cm.,
^^*^n«-U' - -^-sinCa-f).

Resolving these forces, as before, in the direction of the magnetic meridian,
and in the direction perpendicular to it, and making the sum of the resolved
parts in each direction equal to nothing, the equations of equilibrium are found
to be

c c . "> J.

— 5 -< 2 cos (a — f ) cos a — sin (a — f ) sin a V -| (2 cos^ 7 — sin* 7) = 0,

— 5 -j 2 cos (a — f ) sin a -\- sin (a — f) COS a I -j- 3 —j sin 7 COS 7 = 0.

If we resolve the trigonometric products, and make, for abridgment,

A B a h

^=P, -^=Q, -=p, - = g,

the four equations of equilibrium become

3cos(2/3 — f) + cos^ -1-3 Qq^sm2y = 0, (10)

3sin (2j3 — f) + sinf + ^^'(1 — 3cos27) = 0, (11)

3cos(2a — f) + cosf +P/(14-3cos2 7) =0, (12)

3sin(2a — f) + sin f-1- 3 Pp' sin 2 7 = 0; (13)

of which (10) and (12) relate to the forces in the magnetic meridian, and (11)
and (13) to those perpendicular to it. The ratios p and q are functions of the
angles a, j3, 7, f, expressed by the formulae :

sin (^-7) _ sin (g - 7)

^~sin(a-j3)' ^~sin(a-|3)' ^^

The complete solution of the problem is contained in the preceding equa-
tions ; and it follows, in general, that they may be satisfied by means of the four
arbitrary angles, a, /3, 7, f, — and consequently the desired equilibrium produced

168 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

by suitably determining the positions of the three magnetic bars, whatever
(within certain limits) be their relative intensities.

In the case which we have at present in view, — that is, when the third
magnet is merely used as a counteracting power, — its intensity may be taken at
pleasure ; and accordingly one of the ratios, P or Q, is disposable, as well as
the four angles. It follows from this, as there are but four conditions to be
fulfilled, that one of the five quantities abovementioned remains arbitrary ; and
the nature of the problem obviously suggests that this should be the angle 7,
which determines the position of the line connecting the two principal magnets,
and that the conditions of equilibrium should be fulfilled by means of the other
variables, which determine the position and force of the subsidiary magnet.

Let us suppose, for example, that it has been chosen to take the line con-
necting the magnets a and b coincident with the magnetic meridian ; or that

7 = 0.
The equations (10, 11, 12, 13) thus become

3 cos (2 j3 — f ) + cos f = 0,

3sin(2^-f) + sin^ = 2gy^

3 cos (2 a - f ) + cos f = — 4 Pp\

3sin(2a — f)+sinf = 0.

From the first and fourth we have, at once,

i + cos 2 i3 ^ ^ sin 2 a

^-X ^=:— tanC=-i ?r--

sm 2 /3 ^ ^ — cos 2 a

Another relation between the angles a and § may be inferred from the second
and third of the foregoing equations, from which we obtain, by division and sub-
stitution,

^ — cos2a_ T^ Q q^ ^ B sin' a

^r2|3 ■" ^ Yf ~ ^'A' sin'jS '

From this and the preceding equation, the values of a and j8 may be obtained
by elimination. These angles being known, f is given by means of either of the
expressions for tan ^ above written ; and one of the ratios, Q or P, by the second
or third equation, the other remaining arbitrary.

The Rev. H. Lloyd on the mutual Action 0/ permanent Magnets. 169

We have hitherto considered the third magnet as fixed, and serving only to
complete the equilibrium of the forces arising from the mutual action of the
other two. This magnet may, however, be a moveable one, and its movements
serve to exhibit the changes of one of the magnetic elements. In fact, three
independent variables are required, in order to determine completely the ter-
restrial magnetic force, (or its changes,) in direction and intensity ; and, ac-
cordingly, whatever elements be taken as the basis of this determination, three
separate instruments will be, in general, requisite for their observation. In this
case, then, it becomes necessary to consider the action of the first and second
magnet on the third.

The third magnet employed in the Dublin Magnetical Observatory, is in-
tended for the determination of the variations of the vertical component of the
earth's magnetic intensity. It is a horizontal magnet, supported on knife edges,
and capable of motion in a vertical plane. The plane passing through the
centres of the three magnets being horizontal, the axes of the magnets neces-
sarily lie in the same plane ; and, consequently, the action of the first and
second on the third is directed in that plane. Let this force be resolved into
two, one in the direction of the axis of the magnet, and the other perpen-
dicular to it. It is obvious that the latter component can have no effect on the
position of the magnet, being at right angles to the plane in which it is con-
strained to move ; we may, therefore, confine our attention to the former, —
that is, to the resolved part of the force in the direction of the magnet.

Using the same notation as before, the forces exerted by the magnet a,
upon any element m of the magnet e, in the direction ac, and in the di-
rection perpendicular to ac, respectively, are (5)

,2Am „ , Am .

+ — ^cos^, 4.__sm/3;

and the resolved parts of these forces in the direction of the axis of the magnet

c are

,2Am „ ,„ ^. , Am . ^ . ,

+ — ^cospcos(f-^), +-^sm^sm(f-/3).

In like rtianner, the forces exerted by p upon the same element m of c, in the
direction bc, and in the direction perpendicular to bc, are

VOL. XIX. z

170 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

, 2Bm . , Bm

sin a, -j 3— cos a ;

a^ ' ' a^

and the resolved parts in the direction of the axis of c are

2Bm . . Bm

-I -5-sinacos(a — ^), + —5- cos asm (a — f).

Making the sums of these resolved parts equal to nothing, and performing the
same reductions as before, the condition of equilibrium of the forces exerted
upon the magnet c, in the direction of its axis, is expressed by

P/ {3cos (2^ - f) + cos f} + Qq' {3 sin (2a -^ + sinf} = 0. (15)

For the conditions of equilibrium of the disturbing forces exerted upon the
three magnets, a, b, c, by their mutual action, we must combine equation (15)
with the four equations (10, 11, 12, 13) already given; and, as there are but four
arbitrary angles, it follows that complete equilibrium is not attainable, except
for determinate values of the relative forces of the magnets.

It fortunately happens that, for the special purposes which we have here in
view, we may, without inconvenience, dispense with one of the conditions of equili-
brium,— that, namely, of the forces exerted upon the magnet b resolved in the
direction of the magnetic meridian. This condition, (which is expressed by
equation (12)) being left unfulfilled, it follows from (13) that the resultant
force exerted upon the magnet b by the other two, will be directed in the mag-
netic meridian itself, and will therefore conspire with, or directly oppose, the
force exerted by the earth on the same magnet. Consequently the changes of
position of the magnet bar, (which, in this instrument, are proportional to the
changes of force divided by the total force,) are thereby only diminished or in-
creased in a constant ratio, — namely, the ratio of the force of the earth to the
sum or difference of that force and the resultant force of the two magnets.
The changes sought are therefore obtained simply by multiplying by a constant
coefficient. Accordingly, the four equations (10, 11, 13, 15) being fulfilled,
the disturbing action exerted upon the magnets a and c will be completely
balanced ; and, with respect to that exerted upon the magnet b, its effect may
be at once eliminated from the results, by altering in a suitable manner the
constant in the formula of reduction.

The Rev. H. Lloyd on the mutual 'Action of permanent Magnets. 171

It follows at once from the equations (10, 13, and 15) that

sJn27 = 0; (16)

and therefore that 7 = 0, or 7 = 90°. The line connecting the magnets a and
B must therefore be parallel or perpendicular to the magnetic meridian. Sub-
stituting the former of these values, equations (10, 11, 13) become

3cos(2j8 — f) + cosf = 0, (17)

3sin(2,3 — f)'-|-sinf = 2(?9', (18)

. 3sin(2a — f)-|-sinf = 0; (19)

in which a = -r—-, r. Equation (15) is rendered identical. When we make

^ sm(a — /3) ^ ^

7 = 90°, the only difference is, that the second member of (18) becomes

40cos^a . , J f. 2Qsin^a • 1 ^ 1. u

, mstead 01 . 3- -r. It is easy to see m what manner we should

sin'(a— i8)' sin^(a — /3)

proceed for the purpose of eliminating among these equations ; the final equa-
tion, however, will be one of much complexity.

In the application of the original formula it will often occur that we are not at
liberty to consider the four angles, a, )3, 7, f, as all arbitrary, some circumstance
connected with the locality determining one or more of these quantities, or
establishing one or more relations among them.

Let us suppose, in the first place, that there are but three arbitrary quan-
tities, so that we can satisfy but three of the equations of condition. We shall
select for that purpose the equations (10, 11, 13), leaving (15) unfulfilled, as
well as (12). This being done, the disturbing action exerted upon the magnet
c remains unbalanced ; but, as the effective part of this action is directed in the
axis of the magnet itself in its mean position, it does not alter that position,
but merely diminishes or increases the deviations from it in a given ratio. In the
case of this magnet therefore, as in that of the magnet b, the effect of the dis-
turbing action may be allowed for, by a suitable alteration in the coefficient by
which the changes of angle are multiplied.

In order to illustrate this, and at the same time to apply the formulae in a
very important case, let it be required that the centres of the three magnets

z2

1 72 The Rev. H. Llovd on the mutual Action of permanent Magnets.

shall be situated in the same right line. This condition is expressed by the
relations

the two equations being equivalent to a single condition, inasmuch as one of
them is a consequence of the other. Substituting in the formulae (10, 11, 13),
and expanding, they become

(^ + cos 2a) cos f + sin 2a sin f + Q ?' sin 2a = 0, (20)

(^-cos2a)sinf+sin2acosf + ^ y'(^ - cos2a) = 0, (21)

(^ — cos 2a) sin f + sin 2a cos f + P/ sin 2a = 0. (22)

Dividing (20) by (21), we find, on reduction,

cos f = 0, and therefore f = 90°. (23)

Accordingly the plane in which the magnet c is constrained to move must be
perpendicular to the magnetic meridian.

Now, making f = 90° in the three equations (20, 21, 22), the two former
are found, of course, to be identical ; and we have

l-|-gj3_0j ^— cos2a-|- Pp'sin2a = 0.

From the first of these we obtain

which determines the place of the centre of the intermediate magnet c. Again,
in virtue of the relation p -\-q =i 1, there is

Wherefore putting, for abbreviation,

the second equation becomes (|^ — cos 2a) -f- A;sin 2a = 0 ; and we find

The Rev. H. Lloyd on the mniual Action of permanent Magnets. 1 73

tana=-f^±V^T^^* + ^; (26)

which determines the azimuth of the line connecting the three magnets. This
arrangement of the magnets is represented in Fig. 5.

This is, in many respects, a very advantageous disposition. The disturbing
forces exerted upon the magnet a are in complete equilibrium, so that this
magnet (which is that employed in absolute determinations of declination and
intensity) may be used as if it were insulated ; and, with respect to the magnets
B and c, the effect of the disturbing forces is corrected by a simple change of a
coefficient. As to the Observatory itself, one long and narrow room, about
forty-eight feet in length, and sixteen feet in breadth, will suffice ; the hearing
of the axis of the room, along which the three magnets are to be disposed,
being determined by (25, 26). The magnet a should be so far from one end
as to allow a space of eight or nine feet in a direction perpendicular to the mag-
netic meridian, on either side, for experiments of deflection ; the magnet b may
be close to the other end. The place of the intermediate magnet will be de-
termined by (24).*

Having considered the case in which three only, of the four variables, are
arbitrary, it remains to examine that in which there are but two disposable
quantities ; the other two being either absolutely determined, or else connected
with the rest by given relations.

We can satisfy, in this case, but two of the equations of equilibrium ; and
we shall select for that purpose (\\) and (13), which express the conditions of
equilibrium of the forces exerted upon the magnets a and b in the direction
perpendicular to the magnetic meridian. These being fulfilled, the resultant
action on each of these magnets is directed in the magnetic meridian itself,
and therefore conspires with, or directly opposes, the force of the earth. Hence
the mean position of the magnet a is unaltered ; and the changes of position of

* These dimensions have reference to magnets whose directive power is about the same as in
those employed in the Dublin Magnetical Observatory. The magnet bars, a and b, are here of
the same size — each 15 inches in length, f of an inch in breadth, and -J- of an inch in thickness ;
they are of course magnetized, as nearly as possible, to saturation. The magnet c is 12 inches
in length, but much smaller than a and B in its other dimensions.

174 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

both magnets are merely diminished or increased in a constant ratio, — namely,
in the ratio of the force of the earth to the sum or difference of that force and
the resultant force of the magnets. Lastly, it appears from what has been
already said, that the mean position of the magnet c is likewise unchanged by
the disturbing action, and that its variations of position are only altered is a con-
stant ratio. The effect of the disturbing forces, therefore, is in every case
readily allowed for.

As an example of this case of the general problem, let it be required that
the three magnets shall be in the same right line, that line being no longer ar-
bitrary, as before, but determined. The two equations (11) and (13) are in
this case reduced to (2 1 ) and (22). Dividing the former by the latter, we have

PP' _i-C0s2a p_^ Q/^-cos2ax

This equation, in which the second member is known, determines the place of
the centre of the intermediate magnet. Denoting the second member, for
abridgment, by r, we have p = qr, p -\- q ■= 1; whence

It is manifest from (27) that we cannot have cos 2a = ^, or sin 2a z: 0, and
accordingly that the angle a cannot have any of the values 0°, 90°, or 35° 16',
otherwise the intermediate magnet would be infinitely near one of the ex-
tremes.*

To determine the azimuth, f, of the plane of the intermediate magnet, we
divide either of the original equations (21) or (22) by sin 2 a, and substitute for

* In order that the intermediate magnet should be equally distant from the other two, the angle
must have one of the values determined by the equation

i— cos2« PA S A / 9 A^ 1

- =: — ^: — , or tan a :

sin2« ~ Q~ B' ~4B— \6 B' ^ 2'

When A^B, or the forces of the extreme magnets equal, this becomes

tan . = ^-^^^ (r= 1.781, or = - 0.28l);
and the corresponding values of a are -}- 60° 41', and — 15o 41'.

The Rev. H. Lloyd on the mutual Action of pormanent Magnets. 175

4 — cos 2a . , Pp^ ' , •

' -o^ Its value ;^3 above deduced. We thus obtain

Whence

COS^ I s'"^ f I 1 _

, ^ — mn ± V'm^ -\- n^ — I ,^ ,

tanf = -,_r . (39)

in which we have put, for abridgment,

— _J_ _ ^ _ _J_ _ Cc'

This solution becomes impossible when m* -f- ra* < 1, or

(30)

The formulae (11) (13) suggest of themselves many other cases of easy
solution. Thus, if it be assumed that 7 = 0, a = 90, or the line connecting
A and B coincident with the magnetic meridian, and the line connecting b and c
perpendicular to it, equation (13) gives ^ = 0. Substituting in (11), it be-
comes 3 sin 2/3 = 2 Qo', or, since in this case g — ,

^ cos j3

sin /3 cos* /3 = ^ Q ;

from which the angle /3 is determined. This disposition of the magnets is
represented in Fig. 6.

The equilibrium is fulfilled in this case independently of the value of P, or
of the relative forces of the magnets a and c : the reason of this is evident.
On the other hand, the solution requires that Q shall not exceed a small limit ;
for the first member of the preceding equation is a maximum, when tan /3 = ^,
and substituting, the greatest possible value of Q is *^ = 0.859 •

Again, if we have cos 27 = ^, /3 = 0, (11) gives f = 0 , as before ; and

(13) becomes 3 sin 2a 4- 2 ^^^Pf = 0. But /> = - -^^ = -^. — ,

sm a v'3 sm a

176 The Rev. H. Lloyd on the mvtucU Action of permanent Magnets.

and substituting,

sin* a cos a = ^^ P ;

from which the angle a is determined. This arrangement is represented in
Fig. 7.

The conditions of equilibrium are here satisfied independently of Q. As
to P, it cannot exceed the limit determined by making the first member of
the preceding equation a maximum. This gives tan a ■=. 2; and, for the
greatest value of P, ^^^^ = 3.155.

177

VIII. On the Constant of Refraction determined hy Observations with the Mural
Circle of the Armagh Observatory. By the Rev. T. R. Robinson, D. D.,
Member of the Royal Irish Academy , and other Philosophical Societies.

Read 11th January, 1841.

IT may, perhaps, appear presumptuous in me to approach a subject which has
already occupied so many of the greatest masters of mathematical science, and
in the opinion of many is exhausted. But if we look without prejudice at the
labours of Laplace, Bessel, Ivory, and Plana, besides many others of less renown,
and carry our examination a little beyond the mere analytical work, we shall
find that the problem of astronomical refraction has not been rigorously solved
by theory, and I am even inclined to think never can be. All it appears to me
that theory can be expected to perform, is the supplying astronomers with ready
means of approximating to tables of refraction, which shall satisfy their observa-
tions ; and on the other hand they are bound to remember, that such tables,
however carefully verified for one observatory, may be defective when tried at
another.

For in fact it is universally assumed in these investigations, that the atmos-
phere is arranged, with the surfaces of equal density spherical and concentric to
the earth ; this gives the differential of refraction in function of the density and
distance from the centre. Now, firstly, this fundamental hypothesis is not even
approximately true. Near the earth, the surfaces of equal temperature (and
therefore of equal density) must depend on the figure of the ground ; the air
over a hill must be very differently circumstanced in respect of heat, from that
at the same height over a deep valley. Forests, large bodies of water, and the
vicinity of cities must exert a similar disturbing influence, and that to an extent
which cannot be neglected. In a set of hourly observations, made some years
since on the altitude of my meridian mark, I found an increase of refraction,

VOL. XIX. 2 A

178 The Rev. Dr. Robinson on the Constant of Refraction.

amounting sometimes to 13", when the intervening valley was overshadowed by
clouds, though the meteorological indications at the observatory remained
the same. But how much greater would the disturbance of a star have been
whose light must have passed through many miles subject to these anomalies ?
For we have no reason to suppose that they are confined to the immediate
vicinity of the earth's surface ; they must extend as far as the clouds, (whose
existence shews an irregular distribution of heat,) or at least six miles high ;
more than three times the height of Quito, at which Bouguer found the
refraction only two-thirds of what it is at the level of the sea. Some remarkable
facts respecting the variation of terrestrial refraction, when the ground is
covered with snow, and immediately after sunset, are given by Struve, in his
Gradmessung, but one still more in point is mentioned by the Rev. G. Fisher,*
in the Appendix to Parry's Second Voyage, page 175. He found, while ob-
serving at Igloolik, that at temperatures of from 20° to 30° below Zero, and at an
altitude of 3° 8', the refractions of Sirius were about a minute less when observed
over open sea to the south-east, than over land covered with snow or ice, to the
south-west. The existence of these local anomalies can only be ascertained by
low refractions ; and therefore theory is in such cases unavailing.

But secondly, even were the hypothesis on which the differential equation
of refraction is based strictly true, yet that equation cannot be integrated without
assuming a relation between its variables, their real relation being unknown.
Philosophers have been guided in this, either by supposed conformity to the
law of nature, or by facilities of integration ; but in both cases their results cannot
be supposed to have any value except as far as they are confirmed by observation,
and therefore all must be pronounced alike empirical. But at low altitudes
observations are both difficult and uncertain, and therefore it is by no means easy
to pronounce on the results of a given hypothesis ; so that besides that lately
published by Biot (but which I believe has not yet been applied to construct
refraction tables) there are at least four of high authority ; that of Newton, as
modified by Bessel, supposing the temperature uniform, but changing the modulus
of atmospheric elasticity by an experimental co-efficient; that of Simpson,

* To whom I am indebted for much valuable information respecting the important observations
published there, and indeed for ray acquaintance with the book itself.

The Rev. Dr. Robinson on the Constant of Refraction. 179

assuming the density to decrease uniformly as the height increases; that of
Laplace, expressing the density by a product of two factors, representing the

preceding hypotheses, and that of Ivory, supposing it asf 1 — —y- J .* Now these

are obviously mere arbitrary assumptions, and the verifications which some of
them are supposed to receive by exhibiting the decrease of temperature at a
small elevation, and the barometric formula for heights, are worth little ; the
first being unknown at any given place,f and the second being a consequence of
any law which will make the temperature decrease nearly uniformly within a few
thousand feet. The slightest attention to meteorological facts will show that
there cannot be any general formula expressing the density in terms oHhe height
alone, and that even could it be found for one place by experiment, it would be
entirely inapplicable to any other. It is certain, that between the tropics there
is an ascending current of heated air, replaced by a stream of cooler from the
north, while it flows towards the poles, descending in its turn and giving out its
heat ; and it is therefore equally certain that the law of atmospheric temperature
must depend on the latitude. It is not impossible, that in the arctic regions we
may find a uniform temperature, or even an increase on ascending. Such must
indeed be the case, if there be any truth in the conclusions of Fourier, or Poisson,
respecting the temperature at the termination of our atmosphere ; for if with the
former we suppose it = — 58° of Fahrenheit, or with the latter, much more
elevated, approaching 32°, yet cold below either has been observed by northern
travellers. At a given place we might, perhaps, by aeronautic investigations,
ascertain the law of decreasing density and temperature, for a certain epoch ; but
it is highly probable, that this would not obtain when the sun had a different
declination, or the weather was different ;| it is unquestionable, that it would be

* The last appears the best, but it is to be regretted that Mr. Ivory has assumed the use of the
internal thermometer, and not given separate reductions for the temperature of the barometer.
This last also applies to the very convenient tables of Bessel's Refractions, given by Mr. Airy.

f Because the decrease in free air cannot be the same as that observed on the side of a mountain,
and in contact with a mass of matter influenced both by the air and the earth's internal heat.

{ In the celebrated ascent of Gay Lussac, the temperature at Paris was 87o Fahrenheit, so that
the air cannot have been in a normal condition : the meteorological instruments below should have
been noted every few minutes, and the times of observation above given. In the published

2 a2

180 The Rev. Dk. Robinson on the Constant of Refraction.

disturbed by wind, or variations in the hygrometric state of the air. And it
must be remembered, that at least three-fourths of the entire refraction are pro-
duced in the region which is thus affected ; and that in observation we find
differences of 15 or 20 seconds in the same star, when the thermometer, barome-
ter, and hygrometer of the observatory shew no change.

It appears to me, therefore, vain to expect an a priori solution of the problem
of astronomical refraction, and that it will always be necessary to reform by
observation whatever tables may be proposed to us. The tables of Bessel or
Ivory — (if the refractive and thermometrical constants of the latter were cor-
rected, I should prefer them) — are sufficiently exact for this purpose in the
observatories of Europe.* Down to 74° zenith distance, it is known, that the
law of density has no sensible effect on the refraction ; and in ordinary cases
this is sufficient for the astronomer, who seldom observes so near the horizon,
because there the fluctuations of a star are so great, that a great number of
observations are necessary to give even moderate precision. But he must occa-
sionally observe, under such circumstances, comets and planets ; and, besides, it is
necessary for an accurate determination of the principal constant, that he should
go as far from the zenith as is possible, without risking the certainty of his
correction. In my latitude, at 74° zen. distance, an error in the constant is
only doubled ; and the average discordance of observation will be near a second ;
so that were we limited to the use of stars above this altitude, it would be almost

account it is stated, that the thermometer was steady at 30-75 cent. As light clouds existed far
above the balloon there must have been an evolution of heat from their formation. Still it is to be
wished that the experiment were repeated.

* In the Arctic regions all the tables fail completely. I give a couple of instances from the
Appendix to Parry, already noticed, p. 209. They are Nos. 25 and 29. The first gives from 108

observations, the refraction = 665".9 at zen. dist. 84°.13', 82, Bar. 29.79, A. T. -|- 45, Ext. T

35°.9. After correcting for latitude, Bessel's refraction is 18" .72 in defect. Ivory's 13" .27, and
mine 20''.7I. Again, 32 observations give refraction =r 342" .5 at 79°40'. 61, bar. 29.86, A. T.
+ 45°, E. T. - 260.7. Here Bessel's is 40".31 in excess, Ivory 31".66, and mine 22".78. It seems to
follow from these and similar instances, that in such extreme cases the arrangement of the atmos-
phere must be regulated by very different laws from those that prevail in more temperate latitudes ;
and it seems equally obvious, that its influence on refraction commences much nearer the zenith.
It is my intention to recur to these Arctic observations in a subsequent communication on the lower
refractions.

The Rev. Dr. Robinson on the Constant of Refraction. 181

impossible to determine it to the tenth of a second. But it is practicable to go
about 10° lower, by a principle, first, I believe, remarked by Laplace ; namely,
that the refraction computed on the hypothesis of uniform temperature is greater
than the truth, and on the hypothesis of uniformly decreasing density less, and
that the mean of the two is nearly exact. For instance, Laplace gives for the
horizontal refraction, (t = 32° ; barometer, 29.92,)

U. Temp. . . . 2394". 6 i
Observed . . . 2106 .o'
Uniform decrease of dens. 1 824 . 1 \

The arithmetical mean = 2109.3; the geometrical =: 2090. Ivory finds
(t = 50, bar. = 30.00,)

French tables . . . 2031.5 <

U. D. D.* ... 1722.7 \ ^^^-^

In this case the second deviates the most, arith. mean = 1988.6 ; geometri-
cal = 1970.7.

At zen. dist. 85" 16'.70, t = 54.2, bar. 30.24, I find with Ivory's constant,

U. T 624.3 > 3 Y

Ivory's first tables . . 620.6 \
U. D. D 615.8^4.8

Henderson found the refraction (by 29 Cape observations of 7 Draconis) =
614.10, which, when increased for the difference between Ivory's constant, and
Bessel's reduced to the Cape, would become 617.86.

The arithmetical mean =: 620*05, the geometrical = 620.03.
Ivory has given a table constructed on the hypothesis of u t for t = 70
and B = 28.85, from which I take, at zen. dist. 86°,

U. T 653.1 > g 5

Ivory .... 646.6^

U. D. D. . . . . 642.5S^-1
Arithmetical mean = 647.80, geometrical 647.77.

* As corrected by Plana (Observations, Int. Ixxxvi.) The series for u T is slowly convergent,
and the computation would be very troublesome, were it not for the tables of the integral which
Bessel gives in the Fundamenta.

182 The Rev. Dr. Robinson on the Constant of Refraction.

U. T 802.5 > j2 4

Again, zen. dist. 87°,

U. T.

Ivory .... 790.1 J

U. D. D. . . . . 776.1 \ ^^-^

Arithmetical = 789.30 ; geometrical = 789-19.

Lastly, Brinkley gives the comparison of 42 observations of a Lyrae s p
with these hypotheses, zenith distance = 87°.42', t = 35°, B. 29-50,

U. T. . . . . 1067". 0> 20.5

Observed . . . 1046 .bl

U. D. D. . . . 1011 .OS^^-^

Arithmetical = 1039" ; geometrical = 1038-6. But it must be remarked,
that the temperature is by the internal thermometer, the external being 31.3 ;
the barometer also is 0'.078 too little ; in respect of the first of which the observed
refraction should be lessened 9"-2, and for the second 2".90.

It is evident that these means are not in error one-twentieth of the difference
between the two hypotheses ; and, therefore, as far as 85° from the zenith may
be depended on as certainly as any table extant.

Laplace used this principle not only in constructing the French tables, but
also to show that the refractions above 74° are independent of the law of density.
Brinkley, however, showed that the same method could assign them as far as
80°.45 ; the most important of the terms omitted by Laplace in the development
of R in tang. 6 has at that zen. distance in the two hypotheses the values 2".60
and 1".73 ; the arithmetical mean of these cannot be 0".43 wrong, and its error
is probably less than 0".04. The opinion expressed by this great astronomer in
his second memoir on refraction. Transactions Royal Irish Academy, vol. xiii.
p. 169, that, by the method given there, a table of refractions could be more
certainly derived from observation " than from any hypothesis respecting the
actual variation of density," probably hindered him from pursuing the pre-
sent method to its full extent, which, however, may be done with extreme facility.
In his notation. Transactions Royal Irish Academy, vol. xii. p. 83, the
equation of refraction is,

_ — rfp X oft sin 0 / 1 + V

CLd. —

2r(l + 6p)y l + V-^(l+¥)sin^e

The Rev. Dr. Robinson on the Constant of Refraction. 183

when p is the density at the distance r from the centre, p and a, the same quan-
tities at the earth's surface ;* hp the refractive force of air at the density p, and
6 the apparent zenith distance.
If v?e assume,

A = ■/!+ V sin e

V\-\.bp — {l-\-bp')im'e
Q = refraction if the earth vpere plane,

r — a

s = r,

r

Brinkley has shown, page 85, that,

, — ^ bAdp
'' = ^+b^ •

/ 1 + (2* - s') X A^
and by developing a we find,

omitting higher powers of b. Developing • (^r we have,

* These quantifies more strictly relate to the osculating circle, and the constant of a table must
be modified accordingly. The quantity — is one of these ; if we assume the mean radius of curva-
ture as the standard, and the earth's compression ^^^, then for another latitude,

I I

-7 = - X 1 + 0.0004991 X cos 2l.

Laplace has remarked that this should make the refraction to the north and south unequal. In fact,
if we suppose the last rays of twilight to be once reflected, and that refraction ceases with reflection,
(in which case I find, taking into account the curvature of the ray, which Delambre has neglected,
that the height of the reflecting point is 41.536 miles,) andthe rayis acted on in the case of horizontal
refraction, through 8" 43' of latitude. The change of the radius of curvature, and the place of its
centre, must make a sensible difference in the two refractions, but the effect of the difference of tem-
perature in the two trajectories is perhaps still greater.

The value of I is also inversely as local gravity, and that of b (or of the density corresponding to
a given barometric column) directly as it ; they must therefore be divided and multipUed respectively
by 1 — 0.002695 X cos 2l.

These corrections may seem minute, but are very sensible in low refractions.

184 The Rev. Dr. Robinson on the Constant of Refraction.

dR = dQ

X — f*X3A' + 10A'+7A«)

+ 1 s%a' + 15a' + 35a« + 21a")
&c.

l+bp

From the height of the atmosphere given in the preceding note = 7-53 X I,
it appears that ¥s is nearly = s\ and, therefore, we need not develope beyond
terms of this order, and the equation becomes

dRzzdQ
.X^.e[l + ^&(p'-p)(l + 3tang^0)]

-^*'X 3^- ^ tl+^^('''-/'H3 + 5tang^0)]

+ ^s' X ^.0 . [l+5tmg\e-^ih(p'-p) (3+30tang'+35tang*)]

COS

- f s*X ^^.0[3+7tang^0+^J(/)'-)t))(15+7Otang^04-63tang*e)]

OOo

+ t«'X tS • ^ [1 + 14 tang* + 21 tang* 6 + ^b (/- p) (5 +
105 tang* e + 315 tang* + 231 tang^)].

-\-ibdpX

cos"

These terms are of the form s'dp, and s'p dp.

The hypothesis of uniform temperature is expressed by the equation,

1

as

p = e ',

giving the density unity at the surface, and evanescent at an infinite height.
Between these limits we have,

■^\''dp=--^X{n.n-l 2.1)

C« „ , l-'fn.n — l n

The hypothesis of uniformly decreasing density gives.

The Rev. Dr. Robinson on the Constant of Refraction. 185

P = l-^

as

21

}/P'^P=-a"^(n + l)in+2r

The term ^sdp, is the same on either hypothesis, being a result of the atmo-
sphere's equilibrium ; the coefficients of the higher terms differ, those on the hy-
pothesis u T Increasing much more rapidly, ifrdp is that which Brinkley added to

5 P
Laplace's expression, using the arithmetical mean, which gives - X —5. I have pre-

o a

ferred the geometric mean of the separate terms, as giving less weight to u t,

which is especially necessary near the limit of convergence.* If we develope q,

pass from sines to arcs, and put u for . , ,. — , we shall have,

^ ^ sin 1

r" = ^ X tang e

V? sin 1" u'sin^ \"

+ ^^-f^ X tang' e + t^^ X tang^ 6 (q'. q")

— -X^, X - . ^ e [1 .00000 + 6 X tangle (1.06698)1 (a. a ')
sm 2 a cos'' "- ' o \ /^ \ j

+ shr2^ ><^^-^^t2.44949 +6 X tangle (5.04119)] (/3. /3')

- si;^ ^ S • S" ^ ^8.65117 + h X tang^ e (26.92202)] (7. y')
+ ^ ^ ^* ^ • ^ [38.43867 + h X tang^ 6 (160.08103)] (8 . I')

A xi^,.^. 0 [199.22000 &c.].

sm 2 a* cos''

* The original intention was to have assumed the terms zz ^01 X a'l' ; a and a' being arbitrary
factors determined by observation ; but as the simple -v/i X i' was found to satisfy my observations,
VOL. XIX. 2 B

186 The Rev. Dr. Robinson on the Constant of Refraction.

41
The terms /3, 7, and 8 have nearly the ratio — X tang* 6, and therefore the

Or

convergence ceases when the fraction =: 1 ; or below 85°. Near that limit several
of the higher terms are equal with opposite signs, and therefore (Lacroix, III.
p. 160) I retain half the two last, which I find give at 85° the same results as a

much more extended development, including all affected with ¥ and — ~- 6.

This expression may be put into the form given by Brinkley, certainly the
most convenient with which I am acquainted,

B, = fiX tang 6 — c ;

the last of which quantities can be tabulated with the argument zenith distance,
and is, in most cases, independent of the barometer and thermometer.

Their influence is, when necessary, easily allowed for : if a unit of air at 50°

become l-\- e(t — 50) at f, the quantity - must be multiplied by this factor,

Or

and that of fi or b divided by it, from which we deduce the change of c for
temperature,

D = e (^ - 50°) X[a' + p- 2q' - 3q" - 7],
which is always small from the absence of a, the largest of the terms.

this was unnecessary. Assuming Bessel's jj. to be 67" .524, and Ivory's 58".496, my table, when
changed for these values, gives at their normal circumstances,

1. dist.

R — B.

B — I.

770 .. . — 0".ll . . . — 0".02

78

— 0 .10

— 0 .05

79

^0 .11

— 0 .07

80

— 0 .12

— 0 .10

81

— 0 .06

— 0 .12

82

— 0 .08

— 0 .19

83

<

— 0 .10

— 0 .25

84

— 0 .13

— 0 .30

85

— 0 .28

— 0 .42

The diflference obviously depending on some slight difference between the values of jj. and those
used in computing the tables. It is equally evident, that to the zenith distance of 85 the results of
the three formulae are identical for all practical purposes.

The Rev. Dr. Robinson on the Constant 0/ Refraction. 187

If the barometer become h -j- A, Instead of h, the normal pressure, the terms

H 4- A
a, /3, 7, &c., are to be multiplied by ; q', a , /3', &c., by its square, and

H

q" by its cube ; we find the barometric change of c,

E = - X [c + q' + 2q" - a' + ^ &c.].

If h be one inch, the value of e at 85° = — 2".34, so that these corrections can
be worked by mental computation.*

* This form of the refraction has the advantage of being easily applicable to the equatorial. In
a memoir on this instrument, (Trans. R. L A. vol. xv.,) I have shewn that most of its corrections
depend on an arc of the hour circle passing through the star intercepted between the pole and a
perpendicular from the zenith. It is also equal to the intercept between the horizon and equator,
whence I call it the horizontal declination. Denoting it by the symbol ?, the polar distance by d ;
and being satisfied with the approximation, Refr. in P. Dist.z= Refr. in Zen. Dist. X cosine of angle
of position, we have,

(H) = ,Xtang(x>-0-cX^-^^^g^.
c may be put in the form,

^.9 Iq' sin«a —a + b tang* 9 — c tang^fl &c.],

cos'
and its resultant in declination.

(c) =
tang /■ ..x cos* ^

|- [q' sin' (D — ?) — a + 6 tang' (d — ?) - c tang* (d — ?)]

The first of these three terms is obviously the value of c taken with the argument (d — ?) instead

cos' ^
of 0, and multiplied by . ^ , of which latter a table for each hour is sufficient. The second is
Sin 13,L

never =r 0".01 ; and the third, which is insensible above 80°, is computed by the formula

^^ ,. _ ,)^ X (^- i)[iog-' (6.28162) - iog-'^!:!^<i^t!))}

cos* sin'lat ^sm'lat / \- ° ^ ' ° cos'(d — ?) '-"

which at 85° zenith distance and 6 hours from the meridian, is only 1"58, and (if it be thought

2b 2

188 The Rev, Dr. Robinson on the Constant of Refraction.

To construct a table of refractions from this formula, we require the nume-
rical values of -, of fi at some given temperature and pressure, and of e the

expansion of air for one degree of Fahrenheit. The last of these has almost
universally been taken from Gay Lussac, who found that a unit of any gas or
vapour at the freezing point of water, became 1.375 at the boiling point. But
the experiments of Rudberg have shown that this number is too great, and that
the true increase is 1.365. I have, therefore, used this coefficient, notwith-
standing the opinion of some whose authority is of much weight, that even Gay
Lussac's number should be increased on account of the moisture of the atmos-
phere. But the expansion of vapour is the same as of dry air : if water be
present, it does indeed seem greater, because heat increases the quantity as well
as the bulk of the vapour, and a correction to this effect is necessary to the
barometric measurement of heights. In respect of refraction the case is other-
wise ; aqueous vapour and dry air refract alike under equal pressure and tem-
perature ; when, therefore, more vapour is added to the atmosphere, the effect
is the same as if so much dry air were added as is equivalent to its tension.
Observation leads to the same conclusion ; for the illustrious astronomer of
Kbnigsberg found that the coefficient which satisfies the variations of refraction
is 1.00364. — Tab. Reg. p. Ix. The only way in which the hygrometric state
of the atmosphere can affect refraction is by changing the value of I, or by
varying the arrangement of the strata. The latter of these cannot be taken into
account, and the former is, in this climate, insensible within the limits of this
inquiry.

The value of / used is that given by Arago and Blot in their experiments on
the refractive power of air. They give It for 0 centesimal ; but as their experi-
ments were made at the mean temperature 10° cent, or 50° Fahrenheit, the
normal temperature of most refraction tables, their result is not affected by the
error of Gay Lussac's expansion.

There remains only the refractive power of air, which may be investigated

necessary to employ it) can be computed by the sliding rule. A table of ? for every minute of the

first 6 hours is almost essential to the use of the equatorial, and if my first table and the second

cos^IT
X . ., were added to it, the refraction can be as easily computed as on the meridian,
sm't •'

The Rev. Dr, Robinson on the Constant of Refraction. 189

either by direct experiment, as was done by Arago and Blot,* or by astronomical
observations. Notwithstanding the well known accuracy of these distinguished
philosophers, it seems desirable that their conclusions should be verified by the
more refined means of examination, which Arago himself has since indicated.
At present, the result appears in excess, giving for fi at 50° and 29'.60 the value
57". 82. That which is most generally received is De Lambre's, employed in
the French tables, as well as in those of Brinkley and Ivory. It is at the same
temperature and pressure 57". 72, and was deduced from observations made with
the repeating circles of Le Noir, so that it would not have much weight now
were it not for the confirmation which it seemed to derive from the comparison
of simultaneous observations by Brinkley and Brisbane, at Dublin and Paramatta.
The sum of the Dublin north polar, and Paramatta south polar distances gives
very nearly 180 degrees, and the resulting value of /x is 57-77 ; but it must be
remarked, that the temperature used in computation is that by the internal
thermometer, which, however necessary at Dublin, may not be so at the other
observatory. It is also important to notice, that the Dublin barometer is by no
means perfect. I have been enabled to determine its error by comparison with
that of the Magnetic Observatory of Trinity College, (by Newman, and differing
from mine and the standard of the Royal Society merely in having the cistern of
glass.) Observations made during thirteen successive days at 22 " give

A. T.

41.60
37.70

The difference of height of these stations is, according to Captain Larcom, 258.8
feet, and I compute that the actual pressure at the upper station was 29.702 ; so
that the reading there requires the correction -|- 0.077. Subsequently this has
been confirmed by the kindness of Dr. Coulter, who compared two portable
barometers, by Cary, with that of the magnetic observatory, very carefully. They
were then carried out to the astronomical observatory, compared there, and on
their return compared again with the magnetic. From the result of the two
sets I deduce the corrections -\- 0.0770, and + 0.0800, the mean -|- 0.0785
I consider preferable to the other, and this would reduce the constant 57.72 to

* Memoires des Scavans Etrangers, T. vii.

BAR.

E. T.

Magnetic Observ.

30.001

41.60

Astronom. Observ. .

29.625

35.53

190 The Rev. Dr. Robinson on the Constant of Refraction.

.57.567> a remarkable approximation to that of Bessel. This is, however, for the
temperature of the barometer 37° ; but it vs^ill probably avail for 50° also ; as if,
on the other hand, the Dublin barometer has a wooden mounting, on the other
there is probably a little air in the upper part of the tube which will compensate
for its inferior expansion of scale.

Bessel has given for a or r^T-r* 57-538 at 48°.75, but the barometer at 50°.

He, however, found afterwards, that the refractions of his table require to be

multiplied by 1.00l779> which would make it at the normal temperature and

pressure 57.4993, hence ^ = 57.524. This appears to satisfy the Greenwich

observations, as well as* those at the Cape of Good Hope ; and its unexpected

agreement with Brinkley shows how safely it may be depended on. At the same

time, the very circumstances of that agreement give additional weight to the

opinion which I have already expressed, that every fixed observatory should

verify the refractions which it employs, and employ meteorological instruments

of the best quality that can be made.

The observed refraction of a star below the pole is obviously (omitting

degrees)

R = o — 8,

o being the observed polar distance, 8 the assumed declination of the star.
Calling do and dh the corrections which these require, the true refraction is

o — 1-\- do — dZ.

If we put /i X V for the tabular refraction, we have,

V (/x -|- dfi) ■=. vi -\- do — dl.

Now, the polar point having been determined with an erroneous refraction, all
the polar distances require the correction rf/x X p ; and if we determine the
declination by observations above the pole, we have,

rfo = (^/i X P ; dh-=. — dti.[y'-\-v)\
and hence,

R — v/t = rfB = c?/i [v — v' — 2p] = c?/x X k.

* When the necessary corrections for the latitude and the change of the length of the pendu-
lum are applied.

The Rev. Dr. Robinson on the Constant of Refraction. 191

The constants v and v' must be computed for the mean refraction of each
set of observations ; p from the annual mean temperature and pressure, as the
observations for index correction and latitude extend through the year.

If we observe a star of southern declination, and assume it to have been well
determined at some place where it passes near the zenith, we obtain d/i with a
much larger coefficient, for we find in the same way,

^E = d/j, (y -\- f) = d/j, X y^-

It may be doubted, however, whether anything is gained by the superior mag-
nitude of K ; for it is unsafe to argue, as if the results of one set of instruments
were identical with those which another would give in the same locality. The
refraction used at the southern observatory must also have been carefully verified,
as p' the polar constant is in those existing very considerable.

The process must, of course, be applied to as many stars as possible, both for
the sake of accuracy in the final result, and also because the identity of the values
of dfi, obtained at different zenith distances, is an evidence of the correctness of
the formula used to compute the refraction. Among the various modes of com-
bining the partial results, I prefer that which makes the sum of the squares of
errors of observation a minimum ; not taking into account those irregular fluc-
tuations to which low stars are liable, caused by momentary changes in dfi, or in
the law of density, and, therefore, scarcely coming within this application of the
theory of probabilities.* This gives the formula,

_ K X s (dR)-\-K' X s jdR')

^ ~ K^ X w + k'- xn'

The Armagh circle has been described by me in the Memoirs of the Royal
Ast. Soc. vol. ix. After using it pretty extensively, during the last six years, I
have found no reason to change the favourable opinion of it which is expressed
there ; and, in particular, find no trace of the evil which Mr. Airy considers pro-
bable in circles divided on the face, namely, great and irregular fluctuations of
run in the microscopes, (Mem. R. Ast. Soc. vol. x. p. 266.) So far from this,
it is remarkably steady in that respect. A change of 30° alters the mean run of
the four microscopes from 0".25 to 0".47 ; the utmost force that can be applied

* See on this subject, Bessel Ast. Nachrichten, No. 358.

192 The Rev. Dr. Robinson on the Constant of Refraction.

drawing the instrument from the pier, and pushing it toward it, makes only a
change of 0".02 ; of 30 sets taken round the circle at different times, the
greatest I have found is 0".75, and the least 0".00 ; and during the last three
years that at 360° (which equals the mean of the 30 sets) has been within the
limits of 0".25 and 0".54. In respect of its division, after a careful examination
of 288 diameters in four positions, I have stated, that I considered It good ; trifling,
however, as the resulting error may be. It is obviously always necessary to correct
for It when it is known. I have not, however, obtained my con-ections in the pre-
sent Instance by the method described in that memoir. The errors which I found
were absolutely casual, so that it was Irapessible to Interpolate between them ;
the Individual research of each would have demanded an impracticable sacrifice
of time ; and even could this have been afforded, the value of the result appears
to me at least doubtful. All such modes of examination assume, that the divisions
keep the same relative position while the circle is turned through any arc ; but
it is found in actual experience, both with this and other circles, that occasionally
the correction of a diameter varies with its situation to a whole second or even
more. I have, therefore, applied twelve equidistant microscopes to the circle ;
and presuming (as is also shown by the table of errors which I had constructed
by my first method of correction) that their mean is free from sensible error, I
use It to correct that of the four reading microscopes. In a way as simple as I
believe it to be effective. Let m^ m^ be the means of the reading microscopes,
and of the twelve when any number x is at the index. Then, on this supposi-
tion, we have,

m, — 'm„ = u, — u„-\-e{x) — e (o).

We may assume the reading of the four at o to be a zero to which all others are
referred, and therefore,

e {x) = (m, — m„) — (m, — M„),

which only implies the permanence of the microscopes while the readings are
taken. Out of more than 100 of these -corrections most are negative, which
arises from the zero reading m„ requiring, according to my former mode of
examination, a correction of-|-0".93; about one-fourth of the number differ
from this more than ± 0.49, and in some I have found reason to suspect a
minute change depending on the temperature. As, however, it can be deter-

The Rev. Dr. Robinson on the Constant of Refraction.

193

mined In a few minutes at the very time of observation, this is of no conse-
quence.

The index correction of this instrument is deduced from observations of
Polaris. The star is observed five times near the meridian, and reduced to it by
a table computed from the formula,

rfo =: A 4- A* X tang 8 X sin 1",
where,

sin X cos . 8

sinl'

X versme p.

These, compared with the mean places of Bessel brought up by the constants of
Baily's catalogue (for the time) and corrected for the term 2 3) , give the approxi-
mate correction. When conjugate observations (above and below the pole) can
be obtained, the mean is independent of any error of the assumed declinations ;
but at other times the difference between Bessel's place and my own is applied as
a correction.* As long as the difference of individual results is manifestly mere
error of observation, it is assumed that the mean is the index correction during
that period. Its changes are slow, having an annual period, and a given extent
of variation during the eight years that the instrument has been used. The
most probable cause of this appears to be some influence of temperature on the
hill, for the transit instrument, and a telescopic meridian mark about fifty feet
south, suffer analogous variations. As the fact is curious, I annex a table of the
index corrections during 1839, which will also show that no error can arise from
its occurrence.f

• Equal to -I- 0".21 by 700 conjugate observations,
t 1838, Dec. 18, , _ ^ ^
1839, Feb. 24, \ /^^
April 7,
,, 24,
May 16, , _ 3 g^
Junes, |_i63

OK >

' ] — 4.75
] — 5.20
t — 4.19

e '''}-0.14

Sept. 11, -J ggg

0'='-i8'|_a49

1840, Feb. 28,

VOL. XIX.

80 obs.

40

50

55
115

10

75

45
105

25

2c

194 The Rev. Dr. Robinson on the Constant of Refraction.

The declinations of those refraction stars which are in the Nautical Almanac
were compared with its places, as long as they were given to the second place of
decimals. Afterwards, they were reduced by the constants of Baily's catalogue,
and compared with its mean places for the year, corrected when necessary for
proper motion. The others were taken from that catalogue, and reduced by its
precession, corrected for Bessel's last value of n, and for secular variation (com-
puted from its value compared with the precessions given in the Fundamenta).
When any of them have been observed at Greenwich, by Airy, the proper
motion has been deduced from his results by the formula,

_ A — cat 4- f (p — b) — 1".053 X cos a

'^ - '- WVt '

where p — b Is the number found in the last column of the Fundamenta, t the
time in years from 1830, and 1.053 the correction for the error in the constant
of precession used in that work. When Airy had not observed the star, I use
my own declination changed for Bessel's refraction.

The low stars are often neat spectra (that of aLyrae, I have found 22" long);
sometimes the blue and violet disappear for several seconds, and sometimes,
though less frequently, the red, the rest remaining unabsorbed. When the
colours are distinctly separated, I take the yellow where it borders on green, which
I think a tolerable average for the mean of the spectrum. The star should be
carefully watched during its whole transit, for the undulations that produce
irregular refraction are often of long duration ; and sometimes a star, which is
apparently well bisected for several seconds, will leave the wire altogether.

The temperature is observed by a thermometer of Troughton which I found
here. I have verified its freezing and boiling points to assure myself that it had
not undergone the change said to have occurred in some thermometers. I have
also compared it at several points with a standard instrument made for me by
Troughton and Simms, in 1834<, and think it of equal excellence. It is established
at a north window of the eastern tower, about four feet above the centre of the
circle, and twelve distant in a horizontal direction. In a semicylinder of polished
copper, and an interior one of tin, arranged so as to permit a free circulation of
air, but excluding all external radiation. In summer, when the rays of the sun
reach the northern side of the tower, a second thermometer Is used at a southern

The Rev. Dr. Robinson on the Constant of Refraction. 195

window of the same tower, till both agree, which generally is the case an hour
after sunset. The internal temperature is also in most cases recorded, from a
third standard thermometer attached to the telescope near its centre ; but in this
observatory it is not to be used in computing refraction. If any error were
produced by preferring the external, its amount should be greatest when the
difference is greatest, which I do not find to be the case. For instance, among
39 refractions of a Cygni, I find,

9 with I — E from 0° to 3°, mean 2°.37, give diff. from mean — 0".22.
10 from 3° to 4° difF., mean 3°.39, give - 0".17
10 from 4° to 5° diff., mean 4°.45, give + 0".58
10 from 5° to 7°, mean 6°.01, give — 0".21

In this star, 1° would change the refraction 0".72.
Among southern stars, 23 of \ Sagittarii.

8 from 0° to 3° mean 2°.l6 give — 0".22
8 from 3° to 5° mean 3°.78 give — 0".ll
7 from 5° to 7° mean 5°.66 give + 0".33

Here 1" gives a change of 0".65. In these the discordances obviously have no
connexion with the state of the internal thermometer ; and the case is the same
with other stars.

The barometer used was, till December 4, 1835, a portable one, by Ramsden.
It was then replaced by a standard one of Newman, similar to that described by
Mr. Baily in the Philosophical Transactions for 1837, p. 431. Mr. Newman
states, that the specific gravity of its mercury is 13.545 at 60°, and that the
diameter of its tube is 0'.570. In such a tube the correction for capillary action
is nearly insensible ; but it happens to be unnecessary here, for a reason given
by Laplace, Conn, des Tems, 1829, but not, that I am aware, noticed in any
English work. In barometers like this, the scale is terminated at its lower
extremity with a point which is brought into contact with the mercury of the
cistern ; but the surface of the latter is also curved, so that the contact, if near
the edge, is made at a surface lower than the real zero. K the distance from
the edge be properly assumed, this may be made to counteract the depression
above : it is rather too great here, giving only 0'.003, but the rest is neutralized
by the fact, that the contact (if estimated, as I do it, by the meeting of the point

2 c2

196

The Rev. Dr. Robinson on the Constant of Refraction.

and its reflected image) does not take place without a minute depression of the
mercury, which is between 0.001 and 0.002.

The refractions have been computed with ji — 57.7682 (Brinkley's reduced
to my latitude), and the colatitude 35° 38' 47". 3. In this climate and this
exposed situation, it is not very easy to observe by reflection, and I have not yet
definitively settled this element.

With the first division of the circle, 41 pair give 47". 22
With the second „ 58 „ 47". 48

With the third „ 132 „ 47". 37

mean . 47". 37
The first and third are corrected for error of division. In the second, three
divisions were read at each microscope. It is obvious that these give no reason
for changing 47".3, which had previously been determined with Troughton's
equatorial by upwards of 200 pair of observations ; and equally so that whatever
uncertainty there be, can have no effect.

The following are the results that I have obtained :

45 up' Cygni.

Twelve observations (1838. 772) with Brinkley's Constant of Refraction
give the Declination for 1830,

8= + 48° 23' 1". 51.

Precession = + 11". 844 ; sec var. = -f 0". ^12 ; proper motion = + 0".033.

DATE.

E. T.

I. T.

A. T.

BABOK.

ZEN. DIST.*

OBS. SEFBACT.

da.

1836,

Feb. 14.

42.2

43.5

44.2

30.122

77°

10'. 53

256.67

+ 0.01

» 17.

36.2

38.3

39.1

30.241

77

10 55

256.51

— 4.47

„ 26.

29.7

34.5

35

28.979

77

10 65

252.63

— 0.77

1838,

Feb. 7.

37.0

39.5

40.1

29.804

77

10 27

253.50

— 3.07

„ 8.

37.5

39.9

41.4

30.173

77

10 27

255.00

— 4.58

„ 15.

38.8

44.1

45

29.768

77

10 36

250.60

— 4.70

)>

„ 17.

33.5

39.3

40.6

29.367

77

10 35

251.06

— 2.62

>f

„ 23.

31.2

35.6

37.1

29.474

77

10 28

256.20

— 0.76

»

„ 29.

43.8

46.8

48.3

■ 30.409

77

10 29

236.63

— 1.44

* The figures after the minutes of zenith distance are decimals.

The Rev. Dr. Robinson on the Constant of Refraction.

197

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DI8T.

OBS. BEFBACT.

dti.

1839, Feb. 9.

37.1

43.1

30.084

770

9'. 89

257.20

— 1.64

„ 12.

36.7

a ,

40.9

30.046

77

9 90

257.59

— 1.19

» 14.

35.8

. .

40.5

29.733

77

9 93

256.58

— 0.33

„ 17.

34.2

• .

39.5

29.915

77

9 95

261.75

+ 2.73

„ 18.

31

34.2

29.380

77

9 96

255.97

— 0.17

,, 24.

33.1

. ,

37.4

29.462

77

10 02

253.11

— 2.59

„ April 5.

•40.9

, ,

43.7

29.733

77

10 12

253.17

— 0.72

» 7.

38.1

40.9

42.2

30.091

77

10 07

236.50

— 1.94

1

l1Xdvi = — 28".25
K = 2.8861

dB.= — V'.m
dfi=— 0.576

31. o Cygni.
Twelve observations (1838. 533) give
8 = + 46° 13' 45". 59.
Precession = + 10". 648 ; sec var. = -f 0". 228 ; proper motion = + 0". 039.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

dB.

1837,

March 1.

29.2

34

35

30.193

79°

18'.

92

314.06

— 2.27

>5

„ 14.

34.1

37.3

39.3

30.287

79

18

91

314.91

+ 0.98

J)

„ 23.

32.2

34.3

33.8

29.665

79

19

03

307.47

— 1.38

)>

„ 24.

29

33.3

36.8

29.725

79

19

03

307.50

— 4.04

>»

„ 30.

36.1

38

42.1

29.758

79

19

03

309.29

+ 2.16

»

April 3.

35

37.8

39

29.429

79

19

03

308.90

+ 4.41

•>■>

» 4.

35

38

40.3

29.683

79

19

11

304.79

— 2.36

)»

„ 7.

38.9

41.7

43.2

30.297

79

19

03

309.08

— 1.77

1838,

Feb. 20.

31

34.4

35

29.496

79

18

51

305.76

— 1.88

3>

„ 21.

31.8

35.5

36.6

29.577

79

18

78

307.62

— 0.41

IJ

March 6.

38.8

39.7

40.2

29.456

79

18

93

301.81

— 0.42

9f

„ 7.

36.5

38.8

40.3

29.790

79

18

86

305.76

— 1.42

»

„ 8.

37.9

39.9

41.7

30.176

79

18

79

310.09

— 0.10

>»

„ 17.

35.8

39.1

40.9

29.368

79

18

95

301.48

— 1.78

>)

„ 23.

31.3

35.7

37.3

29.480

79

18

88

309.24

+ 1.86

**

„ 29.

44.2

47

48.5

30.410

79

18

83

309.43

+ 1.04

16 X </r = — 7".38
K = 3.7450

6?B

d}x :

■0".46
0.160

198

The Rev, Dr. Robinson on the Constant of Refraction.

Capella.
Eighteen observations (1837. 65) give,
*8 = +45°48'54".12.
Precession = + 4.840 ; sec var. = — 0".627 ; proper motion = — 0".472.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DI3T.

OBS. BEFBACT.

dB.

1837,

June 22.

58.3

63.6

64.8

30.114

79°

44'.

17

307.47

— 0.54

)f

„ 23.

50

56.9

59

30.076

79

44

10

311.98

— 0.43

»>

July 7.

55.8

60.3

62

30.100

79

44

15

309.64

+ 0.23

»

„ 8.

58.8

62.9

65

30.019

79

44

18

308.36

+ 1.57

>»

» 9.

55.3

62

64

29.899

79

44

16

309.66

+ 1.91

)>

„ 13.

56.4

61

64.5

29.472

79

44

28

302.94

+ 0.19

Jl

„ 14.

58.3

65.4

64.2

29.544

79

44

11

302.49

+ 0.34

»

„ 16.

58.8

60.6

62.3

29.917

79

44

22

306.27

— 1.46

»

„ 26.

60.1

62.1

64.1

29.762

79

44

32

301.23

— 2.22

l>

„ 27.

55.4

59

62

29.571

79

44

30

301.86

— 2.56

)>

August 5.

48.9

53

55.9

30.150

79

44

11

313.34

— 1.24

J>

„ 6.

52.8

56.9

59

30.239

79

44

17

311.43

— 1.55

>»

„ 7.

53.5

57.8

60.3

30.264

79

44

15

311.58

— 1.28

»

„ 8.

56.1

59.5

61.8

30.193

79

44

18

309.35

— 1.02

)»

„ 14.

58.2

61.3

64

30.069

79

44

21

307.58

— 0.09

»

„ 15.

60.9

62.5

64.5

30.079

79

44

25

306.22

+ 0.03

1838,

July 25.

52.1

• •

59

29.897

79

44

11

307.74

— 2.08

>>

„ 26.

52.4

57.1

58.5

29.678

79

44

20

303.13

— 4.27

»

August 4.

56.7

• •

62

29.203

79

44

24

299.29

— 0.56

»

54

58

60

29.008

79

44

27

298.63

— 0.83

20 X e^E = — 15".86
K = 3.7318

<^R = — 0".79
dn = — 0. 212

• Brinkley's* .

. = 54".70

Airy (Cambridge,) .

54".78

Bessel's, .

53 .61

Argelander,

53 .50

Airy (Greenwich,)

53 .40

Mine, .

54 .31

The Rev. Dr. Robinson on the Constant of Refraction.

199

P.XXI. 157 Cygni.

Fifteen observations (1838. 800) give,

*8 for 1838. Jan. 1, = + 45° 42' 55". 74.

Precession = + 15".586.

DATE.

E. T.

I. T.

A. T.

BAROH.

ZEN. DIST.

OBS. BEFBACT.

dR.

1837, March 13.

29.2

33.6

34.8

30.211

79° 50'. 72

329.51

— 2.93

„ 14.

33

36.8

38

30.277

79 50 69

331.53

+ 1.14

,, 24.

28.2

33

35.1

29.726

79 50 81

325.78

— 1.96

„ 29.

32.1

35

38

29.535

79 50 84

324.26

+ 1.31

„ 30.

34.7

36.5

42.1

29.760

79 50 82

326.20

+ 2.68

„ April 1.

33.8

35

39

29.810

79 50 85

324.39

+ 0.29

» 3.

33

37

38

29.438

79 50 92

320.41

— 0.91

1838, „ 11.

40.5

45

46

29.849

79 50 64

321.39

+ 0.99

8 X <^R = + 0".62
K = 4 .0544

Jr = 4- 0".077
dfi = -\-0 .019

22. Andromedce.

Eleven observations (1838. 337) give,

8 = + 45° 7' 33". 65.

Precession = + 20". 056 ; sec var. = — 0". 009 ; proper motion = + 0."005.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

dB.

1837, May,

3.

44.7

46.2

50

29.722

80° 23'. 54

331.12

— 2.21

1838, „

4.

44.2

48.8

60.1

30.008

80 23 12

334.64

— 3.13

)J ?)

6.

48.7

62

63.5

30.200

80 23 12

334.72

— 0.89

>» S>

6.

52.1

54

55.8

30.163

80 23 16

332.73

— 0.11

» J>

8.

56.5

60

61.8

30.176

80 23 19

329.47

+ 0.56

5J >J

10.

47.1

53.2

56

30.260

80 23 06

338.20

+ 0.90

» )>

11.

49.1

53.5

55.2

30.132

80 23 15

332.81

— 1.72

1839, April,

17.

37.8

40.8

43.4

29.101

80 22 82

328.10

— 2.83

* This star has not been reduced to 1830, as I am doubtful of Piazzi's place ; the right ascension
which he gives is also erroneous.

It is rather too faint for subpolar observation here.

200

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. BIST.

OBS. BEFBACT.

ds..

1839,

April,

18.

36.9

43.3

44.2

29.212

80° 22'. 77

331.71

— 1.05

19.

40

42.7

43.9

29.766

80 22 70

336.39

— 0.38

23.

46.8

60.5

51.3

29.916

80 22 79

331.63

— 2.02

24.

44.4

47.4

49.2

29.912

80 22 73

335.20

— 0.05

30.

60.6

53

54

29.818

80 22 87

327.36

— 2.54

May

2.

46.1

48.1

53

29.890

80 22 77

332.96

— 0.78

7.

49.8

51

53.1

29.875

80 22 86

327.98

— 3.12

10.

43.2

47.4

49.2

30.124

80 22 76

334.07

— 1.90

)>

12.

44.9

47.9

50.8

30.002

80 22 81

331.43

— 3.30

17 X <^R = — 24".57
K = 4.1560

dvL = ■
dfi = •

. 1". 44

• 0". 348

/3 AurigcB.
Nine observations (1837. 675) give
* 8 = + 44° 55' 12". 66.
Precession = + 1". 132 ; sec var. = — 0". 642 ; proper motion = — 0."019.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DI8T.

OBS. BEFBACT.

dB.

1833,

July 23.

49.9

66.6

29.718

80° 37'

. 97

.339.66

4- 2.07

August 1.

56.3

62.2

, ,

30.348

80 38

00

339.51

— 0.64

,, 2.

55.9

61

, ,

30.268

80 38

05

336.49

— 2.98

1835,

July 29.

66.1

, ,

, ,

30.076

80 37

99

331.64

— 6.36

*>

„ 31.

57.7

62

.,

29.993

80 37

93

335.03

+ 0.71

)»

Aug. 2.

58.2

62

..

29.871

80 37

98

331.46

— 1.66

91

„ 6.

53.8

61.6

, ,

29.796

80 37

91

336.55

+ 0.96

>J

„ 30.

57.2

60.6

..

29.868

80 37

97

333.56

— 0.47

1837,

July 8.

67.7

63

64.2

30.025

80 37

79

334.92

+ 0.52

yy

„ 9.

54.1

61

63.0

29.896

80 37

73

338.34

+ 1.98

99

„ 10.

66.3

62.3

65

29.846

80 37

80

334.37

+ 0.22

99

„ 13.

66

59.8

63.1

29.454

80 37

89

329.11

— 1.10

»

„ 14.

57.7

65

64

29.644

80 37

85

331.49

+ 0.55

Airy (Greenwich, 36 and 37) . . 11". 40 Argelander

„ (Cambridge) . . . 12 . 35 Mine .

11". 00
12 ,76

The Rev. Dr. Robinson on the Constant of Refraction.

201

DATE.

E. T.

I. T.

A. T.

BAROH.

ZEN. DIST.

OBS. BEFBACT.

da.

1837,

July 16.

55

60

61.8

29.908

80» 37'.

75

337.77

+ 1.72

»»

» 20.

55 5

61

63

29.934

80 37

86

331.43

— 4.50

»»

» 27.

55.8

68.2

61.6

29.671

80 37

88

330.75

— 0.80

»

August 3.

47.8

52

549

30.152

80 37

67

339.71

— 4.35

>»

„ 6.

51.5

54.9

57.2

30.239

80 37

75

339.43

— 2.82

l>

„ 7.

51.2

55.7

59

30.264

80 37

74

339.63

— 3.14

»l

„ 8.

55

58.9

61

30.193

80 37

79

336.78

— 2.43

>»

» 14.

57.1

61

63

30.069

80 37

82

335.27

— 1.07

>»

,, 15.

68.8

61.9

63.1

30.081

80 37

81

333.83

— 1.49

9t

„ 16.

60.9

63

65

29.971

80 37

89

331.26

— 1.41

n

„ 26.

50.9

55.8

59

29.930

80 37

71

339.54

+ 0.45

»>

„ 29.

48.2

64.9

57.3

29.429

80 37

86

333.88

— 1.49

„ 31.

50.1

56

67

29.266

80 37

97

330.74

— 1.54

1838,

July 25.

50.8

, ,

68

29.883

80 37

71

338.42

— 0.21

>»

„ 26.

51.2

. •

57

29.680

80 37

75

.336.39

+ 0.30

ti

August 4.

55.7

, ,

61.5

29.205

80 37

86

330.06

+ 2.41

>»

„ 6.

53.1

• •

59.1

29.013

80 37

98

323.32

— 4.03

30 X 6?R = — S0".59 dvi= — 1".02

K = 4.2046 dfx=— 0.242

a Cygni.

Twenty- four observations (1838. 105) give,

*8 = _j_44°40'35".50.

Precession = -j- 12". .597 ; sec var. = -\- 0".226 ; proper motion Insensible.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

dB.

1836, Feb. 17.

36.2

38.2

38

30.241

80°

31'. 08

339.84

— 2.16

„ 26.

29.7

346

35.5

28.983

80

31 40

348.59

— 3.39

„ March 7.

34

39.8

40.2

29.166

80

51 49

349.11

— 1.78

1837, March 12.

28.4

33.1

35

29.617

80

51 07

359.68

— 0.80

» 13.

29.2

34

35

30.193

80

31 02

362.03

— 4.85

» 17.

38.1

40.4

41.3

30.206

80

31 09

358.74

— 1.30

„ 24.

28.6

34.9

36.8

29.722

80

31 12

357.98

— 3.63

i> )i *9.

32

37.4

38.2

29.330

80

31 20

353.88

— 2.77

• Brinkley's*

. — 36.25

Airy, Greenwich, (36),

. = 34.76

Bessel,

34.21

Challis (1837,)

35.95

Argelander,

33.50

Mine, ....

35.70

Airy, Cambridge,

35.14

VOL. XIX.

2d

'

202

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

£. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OB8. BEFBACT.

dR.

1837,

April

1.

34.6

38

40

29.816

80o

51' 20

353.68

— 4.48

»

99

3.

34

37.5

38

29.438

80

51 27

350.08

— 4.00

))

99

4.

34.4

37.8

40.3

29.683

80

51 18

354.39

— 3.08

)>

99

7.

37.6

40.6

42

30.308

80

51 15

357.57

— 4.79

»

9)

9.

39

42.1

43.2

30.245

80

51 10

359.99

— 0.77

99

99

16.

35

40.2

41

29.558

80

51 23

352.35

— 2.29

)9

*>

17.

42

43.2

44.5

29.764

80

51 23

352.02

+ 0.18

1838,

March

7.

37

39.5

40.1

29.804

80

50 96

352.08

— 3.93

»

jj

8.

37.3

39.6

41.4

30.173

80

50 86

358.00

— 2.10

99

99

17.

35.2

39.6

40.3

29.366

80

51 00

351.13

— 0.77

9}

jj

23.

31

35.5

36.9

29.468

80

50 93

356.10

— 0.45

99

*»

29.

43.8

46.8

48.3

30.409

80

50 93

357.18

— 0.67

99

April

11.

41.3

45.4

47

29.830

80

50 97

356.23

+ 3.14

»9

99

12.

43

46.1

47.6

30.188

80

50 94

357.43

+ 1.56

1839,

Feb.

9.

37.1

■ •

43.1

30.084

80

50 48

360.18

+ 0.28

)f

99

12.

36.7

• •

40.9

30.046

80

50 50

369.80

+ 0.97

)»

>9

17.

24.2

• •

28.2

29.244

80

50 58

356.36

— 0.74

99

>9

18.

31.7

..

34.2

29.374

80

50 62

364.75

— 0.03

99

99

20.

28.9

• •

33.5

30.066

80

50 44

366.35

+ 0.10

99

>9

24.

33.1

r •

37.3

29.462

80

50 65

353.85

— 0.86

99

March

2.

37

• •

44

29.856

80

60 66

364.79

— 1.53

)j

99

3.

40.2

• •

43.6

29.820

80

50 71

362.37

— 1.18

9}

59

17.

34.2

39.5

29.915

80

50 67

367.23

— 2.06

99

99

25.

36.6

, ,

42.9

29.424

80

50 83

348.45

— 3.13

99

9>

27.

41

, ,

45.4

29.082

80

50 93

341.86

— 2.40

99

April

5.

40.9

45

43.7

29.735

80

50 85

347.89

— 4.28

99

99

6.

38.1

42.8

44.8

30.122

80

50 66

359.67

+ 0.93

yj

99

7.

38.1

40.9

42.2

30.091

80

50 69

357.61

— 0.78

9)

99

11.

39.9

43

46

30.442

80

50 62

361.86

+ 0.79

J)

99

12.

44.2

46.5

47.1

30.270

80

50 72

356.80

— 0.02

99

99

19.

44.8

47

47.6

29.708

80

50 86

347.01

— 1.92

39 X rfR = - 58". 99 d& = — 1".51

K = 4.5685 dfi z=z— 0.331

46 Andromedcs.

Thirteen observations (1838. 083) give,

8 = + 44° 38' 7". 08.

Precession := -j- 19".065 ; sec var. = — 0".l6l ; proper motion = — 0".0l7.

BATE.

E. T.

I. T.

A. T.

BABOU.

ZE!». DIST.

OBS. BEPBACT.

dR.

1837, May 18.

1838, May 5.
» 11 6.

45.1
47.2
49.9

49.9
50.7
52.8

50

52.2

54.1

30.193
30.200
30.165

80° 52'. 63
80 52 30
80 52 34

355.18
352.96
350.11

— 0.18

— 0.65

— 1.09

The Rev. Dr. Robinson on the Constant of Refraction.

203

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DI3T.

OB8. BEFBACT.

da.

1838,

May 8.

53.7

57.9

60.1

30.172

80°

52'

36

349.05

+ 0.59

))

» 10.

46.0

52.1

53.4

30.261

80

52

22

357.59

+ 2.47

»

» 11.

47.1

52

54.5

30.128

80

52

32

351.68

— 1.09

»

„ 15.

39.4

45.2

47.7

29.688

80

52

31

352.44

— 0.97

)»

„ 23.

48.2

56.7

54.5

29.780

80

52

45

344.70

— 3.26

»)

» 24.

49.2

53

54.7

29.864

80

52

36

350.03

+ 1.84

1839,

April 23.

45.8

48

50.2

29.912

80

52

02

349.51

— 1.63

>»

May 2.

44.3

49

50

29.884

80

51

98

351.59

— 0.27

>y

„ 6.

45

51

52.5

29.989

80

51

97

352.78

+ 0.30

)»

» 7.

46

49.9

51.3

29.864

80

52

05

347.81

— 2.63

9>

„ 10.

41

45.8

48

30.136

80

51

88

358.50

+ 1.21

»

„ 12.

43

46.1

49

29.984

80

51

89

357.08

+ 3.10

»>

„ 21.

44.8

50.2

52

30.050

80

52

00

351.48

— 1.94

W

» 22.

42.7

46.2

49.2

30.176

80

51

92

356.59

+ 0.31

»

„ 25.

48

53.8

55.2

30.028

80

52

04

349.25

— 1.51

>)

„ 26.

48.2

52

54.7

29.987

80

52

05

348.53

— 1.63

J 9 X (^R = — 7".65 rfR = — 0".40

K = 4.4839 dfi — - 0.090

64 ^ Cygni.

Twelve observations (1838. 767) give,

8 = + 43° 15' 11".98.

Precession = + 14". 104 ; sec var. = + 0".219 ; proper motion = + 0".033.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

<;b.

1838, March 8.

36.8

39.4

41.1

30.170

82°

15'

02

417.67

— 3.05

,, 17.

34.6

39.6

40.3

29.377

82

15

18

409.25

— 2.41

„ 23.

30.4

35.0

36.6

29.549

82

15

13

413.15

— 8.52

>> )» -*"•

43.5

46.6

48.1

30.408

82

15

10

416.00

— 1.84

„ April 8.

42.3

45.1

46

29.460

82

15

32

403.74

— 2.09

1839, Feb. 20.

28.5

33.1

30.060

82

14

52

427.84

+ 1.34

» » •^4.

33.1

• •

37.2

29.467

82

14

75

415.18

+ 1.16

„ March 3.

39.3

• •

43.5

29.820

82

14

81

41.3.24

— 0.09

» 17.

34.9

• •

39.5

29.917

82

14

79

417.30

-1.41

„ 27.

40.8

• •

45

29.070

82

15

10

398.47

— 3.27

„ April 6.

37.4

42.1

44.2

80.125

82

14

79

418.96

— 0.24

7

37.9

40.7

42

30.089

82

14

86

414.90

— 3.51

„ 11.

39.3

43

45.2

30.440

82

14

72

423.71

+ 1.89

„ 12.

43.3

45.8

46.9

30.270

82

14

92

411.74

— 4.26

14 X (^R = — 21".30.
K = 5.6710.

dK = — I". 52.

dn= — 0.268.
2d2

204

The Rev. Dr. Robinson on the Constant of Refraction.

17 AndromedcB.

Fifteen observations (1838. 801) give,

S = +42° 19' 39". 41.

Precession = -\- 19". 883 ; sec var. = -\- 0.051 ; proper motion = -\- 0.042.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN

DIBT.

OBS. BEFBACT.

<;b.

1837,

April

16.

31.3

35

35.9

29.578

83"

9'.

22

468.26

+ 1.25

17.

36.8

40.7

42.1

29.875

83

9

23

466.92

+ 2.45

yt

*)

22.

40

42.8

43

29640

83

9

33

459.87

+ 0.81

1)

May

3.

45.2

49.7

50

29.673

83

9

46

452.95

— 1.35

1838,

May

5.

49.8

53

54

30.190

83

9

05

455.77

— 1.44

6.

52.8

54.3

55.9

30.156

83

9

09

453.39

— 0.36

>>

j>

8.

58.2

60

62.9

30.180

83

9

13

450.20

+ 1.43

1839,

April

17.

37.9

42.8

43.4

29.101

83

8

78

448.57

— 3.56

18.

38.1

42.8

44.5

29.209

83

8

74

451.33

— 2.23

19.

40.2

42

43.8

29.764

83

8

62

458.92

— 1.13

9f

)»

24.

44.9

47.3

49.7

29.916

83

8

59

460.91

+ 2.43

9f

May

2.

47

50.2

53.1

29.894

83

8

73

453.09

— 2.04

5.

47

49.7

51.1

29.786

83

8

75

451.66

— 1.91

l>

9»

7.

50.8

52.2

54.2

29.873

83

8

78

450.22

— 0.94

14 X </r = — 6".59 dii = — 0".47

K = 6.2444 dfx=— 0.075

10 UrscB Majoris.

Twelve observations (1837. 932) give,

*8 = + 42° 26' 58". 89.

Precession = — 13". 522 ; sec var. = — 0". 418 ; proper motion = — 0". 294.

DATa.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

<2b.

1835, Aug. 30.

„ Sept. 6.

»> II 8.

» 12.

53.9
53.9
46.9
49

58.5
56.7
54.7
53.8

29.870
29.827
29.509
29.277

83° 5'. 56
83 5 53
83 5 48
83 5 78

444.58
447.82
451.05
435.41

— 0.35
+ 2 47
+ 5.00

— 5.45

Argelander's *= 57". 80 ; proper motion =: - 0". 286.

The Rev. Dr. Robinson on the Constant of Refraction.

205

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN

DIST.

OBS. BEFRACT.

<2b.

1835,

Sept.

15.

48.3

52.5

29.427

83°

5'.

65

441.67

— 1.92

Oct.

3.

46.1

50.2

, ,

29.227

83

5

64

445.37

+ 1.51

1837,

Aug.

30.

47.2

51.8

54.7

29.252

83

6

06

442.15

— 0.31

• 1838,

Sept.

9.

44.3

48.8

52.5

30.127

83

5

96

458.33

— 0.28

20.

44.5

53.9

29.606

83

6

27

446 88

— 3.86

23.

49.9

, ,

55.5

29.560

83

6

36

442.07

— 2.77

24.

46.8

56.9

29.721

83

6

21

451.16

+ 1.14

25.

45.5

54

29.860

83

6

17

453.78

— 0.78

Oct.

4.

45.1

55

30.286

83

6

09

460.06

— 0.24

1839,

Sept.

5.

52.9

57

57.9

29.474

83

6

69

434.36

— 5.60

Jf

10.

51.3

54.1

56.2

29.888

83

6

54

444.38

— 4.27

11.

48.4

52 2

55.1

29.714

83

6

56

443.35

— 5.44

21.

46.6

51.7

53.5

29.390

83

6

59

444.18

— 1.08

Oct.

2.

43.1

49.7

52

29.620

83

6

49

452.28

— 0.28

4.

42.1

45.1

47

29.888

83

6

36

460.33

+ 2.64

^t

12.

46.8

48

50.1

29.664

83

6

57

448.62

— 1.17

99

9)

16.

44.2

47.3

47.9

29.582

83

6

59

448 01

— 3.14

17.

41.2

49

49.9

29.956

83

6

51

445,46

— 4.19

18.

43.1

46.8

48.8

29.788

83

6

50

453.58

— 1.68

»f

»

20.

45.9

48.8

49.4

29.778

83

6

57

450.11

— 2.32

24 X c?R = — 32".38
K= 6.1247

dR= — I". 35
rf/i= — 0".220

Precession =

/i Urscs Majoris.
Ten observations (1838. 235) give,
8=+42°21'4". 05.
— 17".877 ; sec var. = — 0".236 ; proper motion = — 0".015.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEW. DIST.

OBS. REFRACT.

«fB.

1835,

Sept. 22.

49.9

52.9

28.907

83° 11'. 96

439.21

— 1.13

)»

„ 23.

47.3

52.4

, ,

29.285

83 11 90

443.02

— 5.51

»>

„ 24.

45

49.6

, ,

29.727

83 11 66

457.80

+ 0.16

»»

Nov. 22.

39.3

45.6

, ,

29.411

83 11 86

460.16

+ 1.66

1838,

Sept. 23.

49.8

. ,

54.8

29.571

83 12 77

446.78

— 4.61

1839,

Sept. 30.

44

50.3

52.3

29.828

83 12 97

458.09

— 3.23

»»

Oct. 2.

42.5

47.1

49.8

29.625

83 12 98

458.14

— 3.86

>»

» 4.

42.9

45.8

47

29.919

83 12 88

464.49

+ 0.59

206

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

B. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

dR.

1839, Oct. 5.

41.3

47

50.2

30.148

83° 12'. 84

465.82

— 3.09

» 12.

45.5

47.5

49.2

29.703

83 12 97

461.13

+ 3.15

„ 15.

43.2

48.9

49.1

29.570

83 13 04

457.58

— 0.66

„ 16.

44.2

47.8

47.8

29.610

83 13 08

455.33

— 2.65

» 17.

39.9

46.1

47.5

29.947

83 12 91

465.57

— 1.75

„ 20.

44.2

46.8

48.5

29.786

83 13 09

455.46

— 5.23

,, 27.

41

46.1

47.3

30.298

83 12 86

470.96

— 0.75

„ Nov. 11.

43.3

45.5

48.1

29.000

83 13 28

448.78

— 0.75

,. 12.

41.9

45

47

29.320

83 13 24

452.70

— 3.19

„ 13.

38.2

42.2

45.5

29.679

83 13 12

459.66

— 5.50

l8Xt^R = — 36".35 6?R=— 2".02

K=: 6.2821 «?/*=— 0.321

V Persei.

Twelve observations (1838. 416) give,

8 = -f 42° 2' 2". 57.

Precession = -\- 11.954 ; sec var. = — 0.471 ; proper motion = — 0.004.

DATE.

E. T.

I. T.

A. T.

BAKOH.

ZEN. DIST.

OBS. BEPKACT.

dB.

1837, June 3.

45.2

54.6

29.891

83° 27'. 37

475.51

— 0.42

j> » 5.

50

56.9

57.3

30.005

83 27 35

476.63

+ 3.92

}> » 1".

52

55.1

57.1

29.500

83 27 66

458.63

— 4.40

» » 14.

52.1

57.1

59

29.735

83 27 57

464.67

— 1.85

» » 23.

62.4

63.8

65.3

30.122

83 27 68

457.66

— 4.70

1838, June 12.

52

54.9

59

29.632

83 27 32

460.78

— 3.94

1839, June 16.

52.9

57.9

58.8

30.144

83 27 05

468.37

— 3.25

7 X «?K = — 14".64
K = 6.5578

dR — — 2".09
dfi=— 0.326

The Rev. Dr. Robinson on the Constant of Refraction.

207

Precession = —

58 AurigcB.
Twelve observations (1837. 561) give,
8 = + 41° 58' 16". 86.
3".376 ; sec var. = — 0". 613; proper motion = — 0". 138.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OB8. BEFEACT.

dK.

1833,

Aug. 14.

47.7

53.3

29.708

83°

32'

89

473.59

— 2.77

1835,

July 29.

53.2

58

, ,

30.066

83

32

84

475,56

— 0.72

7J

» 31.

56.5

62

, ^

29,990

83

32

87

473.71

+ 1.98

1»

Aug. 30.

55.2

59.5

, ,

29.868

83

32

86

467.04

— 4.14

1837,

July 16.

512

59,1

61.2

29.897

83

32

96

470.52

— 2.03

n

„ 20.

53,7

59

60.9

29.944

83

32

92

473.26

— 0.11

>'

Aug. 5.

46,3

51

53.9

30.152

83

32

72

486.84

+ 2.05

»

„ 6.

51

53.9

55

30.245

83

32

86

478.50

— 3.03

»

» 7.

49.4

54.8

58

30.260

83

32

77

483.46

+ 0.27

9>

„ 15.

57.9

61

63

30.084

83

32

99

470.93

— 0.87

»

„ 26.

49

54.7

56.5

29.939

83

32

94

475.06

— 3.63

n

,, 29.

46.5

52

54.6

29.429

83

32

99

471.83

— 1.31

1838,

Aug. 4.

54.8

, ,

60

29.204

83

33

18

461.39

+ 0.21

>»

» 11.

56.9

, ,

62.2

29.764

83

33

09

467.64

— 0.22

5>

„ 12.

56.3

, ,

61.8

29.840

83

33

07

477.92

— 0.99

>»

„ 13.

51.8

, .

58.5

30,060

83

32

92

467.64

+ 0.08

1839,

July 15.

50.1

52.8

57.3

29.853

83

33

00

474.37

— 1.85

»»

» 19.

51.4

54.4

59.2

29.071

83

33

20

462,91

+ 0.45

»

» 24.

52.9

58

59.3

29,578

83

33

15

466.32

— 2.82

?>

„ 27.

52.2

60

61.5

29,636

83

33

07

471.34

+ 0.84

»

» 31.

47.8

52

55.2

29,624

83

33

05

472.63

— 2.37

»

Aug. 2.

56.1

57.1

59.8

29.762

83

33

15

467.52

— 1.25

»»

,, 4.

52.3

57.4

59.9

30.184

83

32

98

477.59

— 1.68

j>

» 12.

49.1

56

58

30.124

83

32

94

480.66

— 0.84

24 X rfR = - 24".75
K = 6.5578

dr)i = — 1".03
dfi=— 0.157

208

The Rev. Dr. Robinson on the Constant of Refraction.

y AndromedcB.
Twelve observations (1837. 531) give,
*2 = + 41° 30' 34". 54.
Precession = + 17".647 ; sec var. = — 0". 260 ; proper motion = — 0".057.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEM. DIST.

OBS. BEFBACT.

dn.

1836,

May

28.

54.2

59.4

61

30.281

83°

58'.

12

506.19

— 1.47

1837,

i»

12.

46.7

51.6

52.1

29.617

83

87

88

499.84

— 2.78

>»

»

14.

44 5

51.8

62.8

30.013

83

57

66

513.25

— 0.08

»

»»

18.

44.8

48.4

60

30.193

83

57

61

616.38

+ 0.24

99

)»

2(i.

43.5

51.1

61

29.588

83

57

72

510.12

+ 2.89

9t

»»

27.

50

54.2

64.1

29.800

83

57

84

503.23

— 0.62

l>

>»

30.

46.9

52.5

53.2

29.837

83

57

74

508.82

+ 1.15

)>

June

3.

48.7

54.6

66.8

29.896

83

57

77

506.96

+ 0.40

1838,

May

15.

38.2

44

46.9

29.684

83

67

33

612.64

— 1.91

»

f>

17.

39

45.9

47.1

29.716

83

67

32

51395

— 0.20

»

»i

23.

47.4

51.3

53.3

29.786

83

57

54

500.86

— 4.08

9f

19

24.

48.3

62.1

63.9

29.870

83

67

42

608.03

+ 0.84

*»

»»

25.

50.4

54

65.5

29.906

83

67

47

505.28

+ 0.70

99

>»

26.

52

54.S

56.9

29.931

83

67

45

506.31

+ 3.17

1839,

May

25.

46.7

51

53.7

30.208

83

67

05

510.21

— 3.21

99

)>

26.

46.2

60

53.1

29.988

83

67

13

505.87

— 4.06

»>

>»

28.

56.2

57.1

58

30.064

83

57

24

499.33

— 3.75

9>

yy

29.

53 8

56.2

60

30.077

83

57

16

503.79

+ 0.56

>»

it

30.

56.1

68

61.2

30.044

83

67

22

500.26

+ 0.02

>»

fy

31.

67

58.8

62.1

29.916

83

67

27

497.68

— 0.67

tt

June

1.

52.8

55.5

59.2

29.786

83

57

21

600.65

+ 1.18

99

)»

2.

52.1

56

69.8

29.624

83

57

26

498.09

+ 0.58

1)

>»

3.

46.9

50.4

52.5

29.500

83

57

20

501.67

+ 0.41

23 X <^B = — 10".59
K = 7.1337

dvL =
dfi, zz

- 0".46
— 0".065

* Argelander's » . . . = 35". 20
Airy, Greenwich, (1836 and 1837,) 34 11

Mine, .

, 34". 74

The Rev. Dr. Robinson on the Constant 0/ Refraction. 209

58 Persei.
Eight observations (1837. 198) give,
8 = 4- 40° 54' 24". 32.
Precession = + 8".07l ; sec var. = — 0".329 ; proper motion = — 0".035.

DATE.

E. T.

I. T.

A. T.

BAROH.

ZEN. DIST.

OBS. KEFHACT.

da.

1837, June

11.

60.7

58

58.7

29.506

84° 34'. 35

540.79

— 3.89

a »

13,

51.7

65.5

57

29.602

84 34 27

546.15

4-2.77

14.

61.2

56.1

67.2

29.735

84 34 26

647.53

— 0.78

1839,

16,

51.6

66.8

58.8

30.144

84 33 87

551.15

— 3.66

28.

47.1

60

53.8

29.881

84 33 89

550.96

— 4.89

>» I>

29.

45.9

50.1

54.9

30.102

84 33 72

560.81

— 0.28

6xdR = — 10".73
K = 7.8566

d&= — l".79
dn—— 0.228

58 Cygni.

Twelve observations (1838. 024) give,

8= + 40° 30' 58". 86.

Precession = + 13". 603 ; sec var. = + 0". 233 ; proper motion = + 0". 018.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

da.

1837, March 24.

28.5

33.9

36.1

29.722

84°

66'.

49

604.06

— 9.41

,» » 29.

32.2

36.1

38.2

29.630

84

66

58

599.77

— 4.47

„ April 1.

33.9

37.0

39

29.812

84

66

40

610.71

+ 2.96

1838, March 8.

36.8

39.4

41

30.170

84

66

20

604.29

— 5.79

„ 17.

34.6

39.6

40.3

29.377

84

56

38

596.87

— 1.39

„ „ 23.

30.4

35

36.6

29.469

84

56

32

600.31

— 4.61

» » ^"'

43.5

46.6

48.1

30.408

84

66

35

599.37

— 6.09

1839, April 6.

37.8

42.2

44.2

30.126

84

55

98

606.53

— 0.66

1840, Feb. 26.

31.8

35.8

37

30.357

84

56

43

619.21

— 0.74

,, 27,

28.6

34

36.3

30.258

84

65

41

620.33

— 2.47

,, ,, jy.

32

35.7

36.5

30.264

84

55

48

616.43

— 2.48

„ March 1.

30.8

33.6

34.9

30.330

84

55

43

618.21

— 2.80

)) >i ■^•

34.5

35.7

36.2

30.382

84

55

59

609.34

— 7.60

VOL. XIX.

2e

210

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

ODS. BEFRACT.

dB.

1840, March

3.

34.2

35.8

37.2

30.415

84° 55'. 40

621.50

+ 3.82

4.

35.5

37.2

38.2

30.247

84 55 45

618.75

+ 6.38

5.

38.2

38.2

40.2

30.108

84 55 71

603.40

— 2.67

6.

44.2

43.1

43.1

30.249

84 55 84

595.56

— 5.10

9.

40.3

42.8

43.5

30.481

84 55 69

605.34

— 5.13

18.

38.2

42.8

44.5

30.150

84 55 79

600.66

— 3.91

20.

35.6

40.1

43.2

30.380

84 55 75

603.22

— 9.06

23.

86

37.9

40.2

30.261

84 55 71

606.31

— 6.98

21 X rfR = — 67".20
K = 8.8831

</b = _3".20
dfi = — 0.360

The discordances in the separate values of d/x have obviously no relation to
the zenith distance, or the time of year, and may therefore be regarded as
casual.

If we combine them according to the method already assigned, we obtain,

NAME.

HO. OB8.

nclR X K

nXK'.

d/i.

45 Cygni.
31 „
Capella.
Pxxi. 157.

22 Andromedae.
3 Aurigae.
a Cygni.

46 Andromedae.
64 Cygni.

10 Ursse Majoris.
17 Andromedae.
H Ursae Majoris.
> Persei.
58 Aurigae.
y Andromedae.
58 Persei.
58 Cygni.

17
16
20

8
17
30
39
19
14
24
14
18

7
24
23

6
21

— 81.5223

— 31.2112

— 59.1490
4- 2.4732

— 102.0713

— 128.6188

— 269.4501

— 34.3018

— 120.7923

— 198.2566

— 41.1506

— 228.3543

— 93.8717

— 162.3056

— 75.5459

— 84.3546

— 596.9444

445.642
224.400
278.526
131.505
293.630
530.360
813.976
382.002
450.243
900,287
545.895
710.366
287.796
1032.114
1170.462
370.351
1657.992

— 0".576

— 0 160

— 0 212
+ 0 019

— 0 348

— 0 242

— 0 331

— 0 090

— 0 268

— 0 220

— 0 075

— 0 321

— 0 326

— 0 157

— 0 065

— 0 228

— 0 360

Sum . .

317

— 2305.4273

10225.547

Hence

dfx =

2305.4273
10225.547

= — 0.2255.

The Rev. Dr. Robinson on the Constant of Refraction. 211

The value of ft used in computing the refractions is,

/x = 57.7682 ;
<//! = — 0.2255 ;

sum = 57.5427.

This may perhaps require a correction for the run of the microscopes, which

though very small is sensible. From the erection of the circle to July 8, 1837»

0" 18 ">( a'
its effect on the mean of four microscopes was = — — '~r77r — ^* *^^^ *^™^

it was changed by the rough operations necessary in attaching another pair of

a'
microscopes, and has been since considered permanent at -f- 0". 41 X —;• This

is, however, a mean value, being deduced from readings of the four, in 30
equidistant positions of the circle. Hence 1 found as above

_38^2909^
^ ^10225.547 ^
and

M = 57".5464

a value whose near approximation to Bessel's 57".524, will prove very remark-
able, if when I have means of determining the length of the seconds' pendulum
here, it should be found little different from that of Konigsberg. That obser-
vatory is a little north of me, but it is only 90 feet above the Baltic ; while this
is 211 feet above the sea, and the substratum, dense limestone, so that the local
gravity must be nearly alike in both cases.

As to the southern stars, I have used the declinations of the St. Helena
catalogue, reduced to Bessel's refractions, by the table given page 22, and
those of Professor Henderson. (Mem. R. Ast. Soc. X. 80.) The two are not
strictly comparable in respect of refraction, for the St. Helena Observatory,
being 700 feet above the sea, and resting on dense volcanic rocks, may be
expected to have an excess of gravity above the Cape, and therefore larger
refraction. At the latter place I find, by comparing the length of the pen-
dulum with that of Greenwich, that Bessel's refractions should be multiplied by
0.9984 ; and, in fact, Henderson's observations on refraction shew, that even a
greater diminution is required. I have not, however, changed them further than

2 E 2

212 The Rev. Dr. Robinson on the Constant of Refraction.

by reducing them to 1830, with the precession, &c., annexed to each star. When
possible, the proper motions are deduced by comparison with Airy's Greenwich
places.

24. o* Canis Majoris.

8 = — 23° 35' 23". 83. J. (Johnson).

Precesslon = — 4". 846; sec var. = — 0".352; proper motion = -f"0 " -Oil-

DATE.

E. T.

I. T.

A. T.

BAEOH.

ZEN. DIST.

OBS. BEFBACT.

dB.

1837,

Feb.

18.

34.3

41

41

29.274

77°

52'.

73

269.48

+ 2.37

March 12.

29.8

35.6

36.8

29.575

77

52

85

274.78

+ 1.19

>}

$1

13.

30.7

34.8

86

30.174

77

52

66

276.29

— 2.10

17.

38.6

41.8

43

30.211

77

52

74

271.47

— 2.76

21.

38.8

40.1

41.1

29.712

77

52

79

268.76

— 0.88

9)

))

23.

32.2

36

37.6

29 663

77

52

76

270.51

— 3.10

24.

32

36.5

38.1

29.727

77

62

77

270.15

— 3.51

1838,

Feb.

8.

38.7

39.8

40.2

28.524

77

53

02

254.86

— 4.14

jy

13.

27

30

31.2

29.479

77

62

86

270.93

— 3.51

20.

31.8

34.7

35.7

29.483

77

52

76

273.16

+ 1.59

21.

32.9

36.1

38

29.583

77

52

82

269.90

— 2.06

March

15.

39.2

44.8

47.2

29.798

77

52

88

267.99

— 2.08

)>

)>

17.

36.2

39,8

41.2

29.344

77

52

93

265.12

— 2.64

13xrfR = — 21".63
K = 5.2240

rfR = — 1".16
C?;U = — 0.318

15 Argus.
*8 = — 23°49'8". 58.(J. H.)
Precession = — 10". 051 ; sec var. = — 0". 317 ; proper motion = + 0".075.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

dR.

1837, March 13.

„ 14.

» » 23.

29.2
34.1
32.2

34.1
37.3
34.5

35

38.4

35.8

30.185
30.287
29.657

78° 6'. 92
78 6 96
78 7 03

282.69

280.78
277.17

— 2.28

— 1.17

* Johnson's *...=: 7" .80 Henderson's i

Had the first been used, the refractions would be 0".78 less ; <//*:= — ,0".306.

= 9".36

The Rev. Dr. Robinson on the Constant of Refraction.

213

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN

. DIST.

OBS. BEFBACT.

da.

1837,

Aprilj

3.

35

37.8

39

29.429

78°

7'.

11

272.91

— 1.63

)>

»»

4.

35.7

38.7

40.3

29.683

78

7

00

279.65

+ 3.22

1838,

Feb.

20.

31.2

34.4

35

29.496

78

7

08

279.34

+ 2.90

)J

)»

21.

31.8

35

36.9

29.577

78

7

13

276.93

— 0.96

IJ

March

17.

35.8

39.1

40.9

29.368

78

7

22

274.61

+ 1.11

1839,

Feb.

20.

29.6

• •

34.1

30.066

78

7

20

283.91

+ 0.06

]>

»

24.

33.8

, ,

38

29.461

78

7

13

274.69

— 0.86

)}

March

17.

35

• •

40

29.907

78

7

12

279.87

+ 0.89

»

»»

25.

37.9

• •

43.9

29.424

78

7

59

269.77

— 3.14

>>

April

5.

40.4

, ,

44

29.722

78

7

47

272.52

— 1.69

fJ

)>

6.

39

44

45.8

.S0.118

78

7

39

273.57

— 1.05

ft

)>

7.

38.5

40.2

43.2

30.094

78

7

45

276.75

— 2.00

3J

>»

11.

41.8

45.2

47

30.442

78

7

42

274.51

— 5.48

l6xrfR = — 14".62
K = 5.5356

<;r = — 0".9l
dfi=— 0.165

16. o' Canis Major is.

8 = — 23' 58' 35".82. J.

Precession = — 4". 092 ; sec var. = — 0". 353 ; proper motion = — 0".059.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

da.

1837,

Feb,

18.

34.3

41

41

29.274

78°

15'

70

279.53

+ 3.05

))

March

12.

29.8

35.6

36.8

29.575

78

15

68

283.13

+ 1.06

>f

■ »»

13.

30.7

34.8

36

30.174

78

15

71

281.70

— 5.65

tt

»

17.

38.6

41.8

43

30.211

78

15

76

278.48

— 3.56

)>

»»

23.

32.2

36

37.6

29.663

78

15

76

279.06

— 2.43

»)

>»

24.

32

36.5

38.1

29.727

78

15

73

280.69

— 1.62

1838,

Feb.

8.

38.7

39.8

40.2

28.524

78

15

97

265.28

— 1.72

»»

>>

13.

27

30

31.2

29.479

78

15

72

281.30

— 1.67

)»

»

20.

31.8

34.7

35.7

29.483

78

15

72

282.64

+ 2.59

))

21.

32.9

36.1

38

29.583

78

15

79

278.13

— 1.89

it

March

15.

39.2

44.8

47.2

29.798

78

15

87

275.23

— 3.36

tt

)>

17.

36.2

39.8

41.2

29.344

78

15

91

273.32

— 4.36

»>

>>

23.

33.5

35.2

39.7

29.500

78

15

87

275.28

— 3.91

lSXdR=— 23".47
K = 5.5514

dR :
dfi :

: — 1".81
— 0.325

214

The Rev. Dr. Robinson on the Constant of Refraction.

Precession
0".012. (A.)

^ Argus.

♦8 =—24° 26' 17".90. (J.)
8".647 ; sec. var. = — 0".329 ; proper motion

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEK. DIST.

OB3. REFBACT.

da.

1837,

March

12.

28.5

33.4

35

29.604

78°

43'

68

296.33

+ 1.38

))

»)

13.

29.2

34.1

35

30.182

78

43

62

300.13

- 0.04

14.

34.2

37.6

39

30.287

78

43

68

296.36

— 1.64

29.

32.2

38.6

40

29.521

78

43

59

290.11

— 1.47

9>

»

30.

36.1

38.2

42

29.757

78

43

61

288.93

— 2.57

1838,

Feb.

20.

31.4

34

35.2

29.496

78

43

81

293.98

+ 1.93

21.

31.9

35.2

36.9

29.577

78

43

87

290.84

— 1.68

IJ

March

29.

45.1

47.1

48.5

30.410

78

43

95

289.59

— 2.93

1839,

Feb.

20.

29.6

• •

.34.1

30.066

78

43

86

297.64

— 1.18

March

17.

35.1

• •

40.1

29.912

78

44

02

291.56

— 2.24

jy

„

23.

38.9

• •

44.1

29.424

78

44

15

283.90

— 2.83

)t

April

5.

40.3

• •

44

29.717

78

44

16

284.37

— 4.48

»

»

7.

38.9

40.4

43.2

30.094

78

44

07

289.26

— 4.12

13 X <^R = — 21".87
K = 5.7931

ds. = — V'M
diMz=— 0.290

22 \ Sagittarii.
f 8 = — 25° 30' 23". 90. (J.)

Precession = + l".528 ; sec. var. = -|-0".537; proper motion = —0".291. (J.)

DATE.

E. T.

I. T.

A. T.

BAROH.

ZEN. DIST.

DBS. BEPBACT.

da.

1837, July 20.

,, 27.

„ August 5.

54.7

55

46.9

57.3

57

51

61

61.6

53.9

29.940
29.571
30.152

790 46'. 40
79 46 48
79 46 36

308.74

306.47
313.99

— 1.29
+ 0.43
+ 0.53

• Airy (15 observations, 1836-7) . 18".93
f The declinations of this star are discordant :
Airy (16 in 1837) .... 25".79
Johnson , . . . 23 .90

Maclear

24".45

The Rev. Dr. Robinson on the Constant of Refraction.

215

DATE.

E. T.

I. T.

A. T.

BAROH.

ZEN. DI3T.

OBa. KEFBACT.

dR.

1837,

Aug.

6.

61.2

54

56.2

30.240

79° 46'. 32

316.17

+ 0.76

>»

19

7.

50.3

54

68

30.261

79 46 20

313.75

— 2.54

l>

)»

14.

56.8

60

62

30.070

79 46 43

309.84

+ 0.05

)>

Jl

15.

58

61

63

30.082

79 46 45

308.51

— 0.84

J>

9>

16.

60.6

62.1

64

29.968

79 46 54

306.71

— 0.95

»»

»

29.

47.6

52.2

56

29.430

79 46 41

311.51

+ 2.19

>*

»

31.

48.7

63

56.1

29.275

79 46 49

306.92

— 0.16

1839,

July

15.

60.2

62.8

57.3

29.853

79 46 29

815.08

+ 3.41

»>

If

19.

51.8

54.6

59.2

29.071

79 46 51

301.84

— 0.68

>>

>J

24.

53.7

69.2

61

29.578

79 46 42

307.17

+ 0.62

»»

»>

28.

62.4

57.2

61.8

29.778

79 46 13

311.02

+ 2.96

»

»»

31.

48.1

63.8

56.1

29.622

79 46 32

313.22

+ 2.62

»»

Aug.

2.

66.9

57.9

60.1

29.764

79 46 46

306.70

— 0.84

»

)>

4.

62.9

58.1

60.2

30.186

79 46 30

314.58

+ 0.44

)»

»

19.

47.1

54.2

56.2

29.960

79 46 29

316.52

+ 0.72

»»

s»

20.

50.8

56

67.8

30.084

79 46 33

313.05

— 0,66

))

J)

21.

63.2

56.2

68.9

29.932

79 46 36

311.48

+ 0.90

n

)»

26.

61.2

65.5

59.1

29.620

79 46 39

310.31

+ 1.73

»>

Sept.

5.

55.9

58

61.7

29.428

79 46 50

303.39

— 0.28

))

»

11.

51.2

67.2

60

29.736

79 46 42

308.58

— 1.20

23 X ofR = + 7".92
K= 6.1035

c?K = + 0".34
dfx=z-{- 0.056

Antares.

* 8 = — 26° 2' 47". 69. (J. and H.)

Precession = — 8".556 ; sec var. = -\- 0".487 ; proper motion = — 0".031.

DATE.

E. T.

I. T.

A. T.

BAROM.

ZEN. DIST.

OBS. BEPBACT.

dB.

1837, June 14.

51.2

55.1

57.2

29.735

80° 19'. 80

325.90

— 0.49

„ 15.

50.9

57.1

61.1

30.090

80 19 72

331.25

+ 0.43

July 7.

56.2

59

62.2

30.106

80 19 83

325.18

— 2.27

»i » "•

56.9

63.7

65.4

29.905

80 19 89

321.55

— 3.16

,, 10.

60.1

64.2

66.5

29.846

80 19 93

319.50

— 2.47

» 16.

56.6

61

63.1

29.923

80 19 85

322.83

— 2.37

,, 18.

57

60.2

63.5

29.612

80 19 81

320.07

— 1.40

♦ Airy, »(18 obs. in 36 and 37) . 48".ll Argelander

Henderson . . . . 48 .68 Mine

Johnson, . . . . 46 .71

46".50
47 .44

216

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DI3T.

OBS. BEFBACT.

rfB.

1837,

July 20.

57.0

60

63

29.934

80°

19'.

82

325.53

+ 0.55

August 5.

51.2

53.8

57.1

30.147

80

19

76

329.79

— 1.56

1»

„ 13.

63

63

66

30.075

80

19

97

320.11

— 2.53

1838,

July 1.

53.2

57.3

58.7

29.806

80

19

99

325.10

— 1.23

„ 25.

53.2

57.5

60

29.904

80

20

00

325.21

— 2.15

»

„ 31.

57.3

, ,

62

29.812

80

20

01

324.79

+ 1.32

1»

August 4.

58.8

, ,

63

29.192

80

20

14

313.62

— 2.35

1839,

June 14.

48.1

53.8

56.2

29.892

80

20

03

331.01

+ 0.21

»t

„ 16.

51.6

56.8

58.8

30.144

80

20

06

329.49

— 1.70

»»

„ 28.

47.1

50

53.8

29.881

80

20

03

331.33

+ 0.66

„ 29.

45.9

50.1

54.9

30.102

80

19

94

337.18

+ 2.54

July 9.

52

54.8

58.8

29.370

80

20

26

318.29

— 4.17

it

» 10.

53.9

56.6

60.2

29.517

80

20

22

320.71

— 2.00

)>

„ 20.

55.3

57.2

60

29.360

80

20

23

320.04

— 0.07

?>

„ 22.

55.4

59

60.9

29.750

80

20

15

324.57

— 0.78

22 X rfB = — 24".99
K = 6.3200

1".14
0.180

19 2 Sagittarii.
8 = - 29° 53' 25". 75 (J).
Precession = -\- 0".884 ; sec var. = + O"- ^59 ; proper motion = — 0". 014.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN

. DIST.

OBS. BEFBACT.

dB.

1837,

July

20.

54.8

57.3

62

29.938

84°

6'.

24

507.06

+ 0.36

M

)>

27.

65

57

61.5

29.671

84

6

37

499.91

— 4.38

}I

Aug.

6.

51.2

54

56.2

30.240

84

6

10

516.16

— 3.91

7.

50.3

64

68

30.261

84

5

95

524.71

4- 3.45

9f

)>

14.

56.8

60

63

30.069

84

6

34

608.72

— 8.85

>>

))

15.

58.6

61

63

80.082

84

6

30

604.49

— 6.74

16.

60.6

62.1

64.5

29.970

84

6

33

502.80

— 2.47

29.

47.6

52.2

56

29.430

84

6

16

613..58

+ 3.08

31.

48.7

63

56.1

29.275

84

6

27

506.99

4-0.78

1838,

Aug.

4.

65.1

• •

60.5

29.200

84

6

45

494.66

— 2.04

14.

52.1

• •

60

30.040

84

6

18

611.22

— 4.24

1839,

July

15.

50.3

52.8

57.3

29.853

84

6

13

511.52

— 2.81

)»

?}

24.

53.7

69.2

61

29.678

84

6

17

509.15

4:0.98

31.

48.1

53.8

66.1

29.622

84

6

17

509.50

— 2.34

Aug.

11.

50.9

50

58.9

30.162

84

6

07

516.65

— 2.19

)>

!j

19.

47.1

.54.2

56.2

29.960

84

6

08

516.41

— 3.34

))

Sept.

5.

55.9

58

61.7

29.428

84

6

32

501.96

4.1.11

S>

)»

11.

51.2

37.2

60

29.736

84

6

29

504.57

— 7.76

18 X «?R = -
K = 9.5710

41".41

dK—— 2".30
dn=- 0.241

The Rev. Dr. Robinson on the Constant of Refraction.

217

34 a Sagittarii.

*h= - 26° 29' 55".31. (J.)

Precession = -|- 3".889 ; sec var. = + 0".532 ; proper motion = — 0".093.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

dB.

1838,

Aug.

4.

54.8

60

29.204

80°

45'.

20

330.87

— 1.19

»>

>»

13.

51.8

, ,

68.5

30.060

80

45

09

309.30

— 4.91

5>

)>

14.

52.9

• •

58.2

30.0.33

80

45

06

340.34

— 2.80

1839,

July

19.

51.4

54

67.3

29.072

80

46

09

333.01

+ 0.37

»)

},

24.

53.7

59.2

61

29.578

80

45

07

334.58

— 5.18

})

j»

28.

51.5

55.7

60

29.776

80

44

97

840.62

— 0.43

»

))

31.

47.4

51.2

66

29.627

80

44

93

342.88

4-0.46

)J

Aug.

2.

56.1

57.1

59.8

29.762

80

45

06

335.22

— 2.56

)>

jj

3.

52.7

56.8

59.2

30.026

80

44

95

341.96

— 1.11

J»

»

4.

62.3

57.4

59.2

30.184

80

44

90

345.06

— 0.12

»)

jj

11.

51

56.2

58.2

30.169

80

44

89

345.50

— 0.45

»

j»

12.

49.1

56

58

30.124

80

44

82

860.24

4- 3.50

J>

)j

19.

47.7

51.7

56.2

29.960

80

44

92

344.39

— 1.56

>J

»»

21.

53.1

56.4

58.1

29.930

80

46

01

339.40

— 2.41

)>

»

24.

54.8

57.7

60

29.746

80

45

00

339.45

+ 1.02

>»

>»

26.

51

54

59.1

29.620

80

44

98

841.03

4- 1.40

>)

Sept.

5.

54.9

57

60.8

29.442

80

45

10

334.20

— 0.73

17 X ^R = - 16".70
K = 6.7651

dfji

0".98
0.145

* This star is doubtful.

i by Airy (3 observations), . . . . .
Henderson (Edinburgh, 5 obs.), Bessel's Refraction,

„ Cape,

Maclear, Direct,

„ Reflected, ......

Johnson, ........

67".52

54 .66
58 .11
58 .17
57 .23

55 .31

VOL. XIX.

2f

218

The Rev. Dr. Robinson on the Constant of Refraction.

c Canis.

*8 = — 28° 44' 45". 35 (J. and H.)

Precession = — 4". 507 ; sec var. = — 0". 333 ; proper motion = — 0". Oil.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DI8T.

OBS. HEFKACT.

dB.

1837,

Feb.

18.

34.8

39.6

40.2

29.295

82°

59'.

03

452.35

+ 3.28

))

March

12.

29.3

33.5

36.8

29.575

82

58

95

460.15

+ 1.31

13.

30.4

34.7

36

30.177

82

58

89

463.88

— 3.05

17,

38.2

41.4

43.1

30.211

82

59

01

453.46

— 6.04

it

23.

32.1

35.2

37.6

29.663

82

59

00

457.54

+ 0.28

J>

J)

24.

32

36.5

38.1

29.727

82

59

02

456.63

— 1.73

1838,

Feb.

8.

38.7

39.5

40.2

28.524

82

59

43

430.66

— 3.38

13.

27

30

31.2

29.478

82

59

02

456.53

— 3.29

$)

>J

21.

32.9

36.1

88

29.583

82

59

14

450.18

— 5.18

1839,

Feb.

12.

36.2

41.2

30.034

82

59

05

459.29

+ 0.50

14.

36.1

• •

40.9

29.734

82

59

13

454.90

4-0.50

17.

22.7

, ,

29.8

29.210

82

59

08

458.68

— 1.38

f}

),

18.

29.7

34.1

29.400

82

59

15

454.22

— 1.67

20.

29.8

• •

34.9

30.054

82

58

95

466.47

4- 0.75

March

3.

40.2

, ,

45.5

29.820

82

59

22

452.36

+ 0.74

ft

»

17.

35.2

••

40.5

29.912

82

59

15

457.61

— 0.49

I6xdn = — 18".85. rfa = — 1".18.

K = 8.6376. dfi=- 0.136.

SI r] Cants Majoris.

n = — 28° 58' 35". 79 (J.)

Precession = — 6". 642 ; sec var. = — 0". 323 ; proper motion = — 0".011.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

da.

1837,

Feb.

18.

34.8

39.6

40.2

29.295

83°

12'.

90

465.05

+ 2.24

March

14.

34.7

38.6

40.8

30.287

83

12

74

477.79

— 0.62

))

17.

38.2

41.4

43.1

30.211

83

12

89

469.29

— 4.19

)»

>»

23.

32.1

35.2

37.6

29.663

83

12

85

471.85

+ 0.67

* * by Airy (26 obs.) . . 46".38 Henderson, Cape, . . . 46".36

■\ Henderson's declination is a second greater, but rests on a much less number of obser-
vations.

The Rev. Dr. Robinson on the Constant of Refraction.

219

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFRACT.

dK.

24.

32

36.5

38.1

29.727

83

12

83

473.37

+ 1.12

30.

37

40.1

42.1

29.756

83

13

00

463.15

— 4.39

1838,

Feb.

8.

38.5

39.3

40.2

28.524

83

13

30

444.99

— 1.94

21.

32.4

35.5

38

29.583

83

12

98

473.32

+ 3.62

1839,

Feb.

9.

39

43.7

30.064

83

13

04

468.45

— 1.86

12.

36.2

41

30.040

83

13

04

468.91

— 4.10

14.

35.9

40.8

29.733

83

13

11

465.39

— 3.16

17.

22.3

29.8

29.220

83

12

93

477.02

+ 2.32

18.

30.7

34.1

29.394

83

13

09

467.04

— 1.65

20.

29.9

34.3

30.058

83

12

92

477.85

— 2.20

March

17.

35.4

, .

40.1

29.908

83

13

10

470.39

— 1.47

J)

>>

25.

40.1

••

44.1

29.416

83

13

33

456.61

— 2.76

16 X rfR = — 18".37
K = 8.8592

d^= — 1".15
<f/i = — 0".I30

8 Canis Majoris.

8 = -26°7'42". 18.(J.)

Precession = — 5". 316 ; sec var. = — 0". 340 ; proper motion = -f- 0". 021.

DATE.

E. T.

I. T.

A. T.

BABOM.

ZEN. DIST.

OBS. BEFBACT.

dK.

1837,

Feb.

18.

34.8

39.6

40.2

29.295

80°

24'

02

335.17

— 0.90

)»

March

12.

29.3

33.5

36.8

29.575

80

23

93

343.39

+ 0.18

J5

13.

30.4

34.7

36

30.177

80

23

88

346.83

— 2.54

>?

14.

34.7

38.6

40.8

30.287

80

23

95

343.81

— 3.55

)>

?j

17.

38.2

41.4

43.1

30.211

80

23

99

340.16

— 3.81

JJ

))

23.

32.1

35.2

37.6

29.663

80

23

94

343.68

+ 1.53

»>

9J

24.

32

36.5

38.1

29.727

80

24

02

338.56

— 4.42

1838,

Feb.

8.

38.5

39.3

40.2

28.524

80

24

28

321.45

— 3.17

»

9)

13.

27

30

31.2

29.479

80

24

00

339.75

— 4.16

»>

?»

20.

31.8

34.7

35.7

29.483

80

24

17

338.76

— 1.70

21.

32.9

36.1

38

29.583

80

24

03

339.11

— 1.57

J?

March

15.

39.2

44.8

47.2

29.798

80

24

13

335.69

— 2.74

?>

J)

17.

36.2

39.8

41.2

29.344

80

24

19

338.60

— 1.80

>J

?9

23.

33.5

35.2

39.7

29.500

80

24

09

338.62

— 0.68

14 X fifR = — 29".33
K = 6.5921

dvL = — 2".09
<^/i=— 0.318

2f 2

220

The Rev. Dr. Robinson on the Constant of Refraction.

f Canis Majoris.

8 = - 29° 59' 34". 62 (J. H.)

Precession = — 1".205 ; sec var. = — 0". 335 ; proper motion = — 0".022,

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DI3T.

OBS. BEFBACT.

(2b.

1837, Feb.

18.

34.7

41.6

41.4

29.264

84°

12'.

13

533.37

+ 3.77

„ March

12.

30

36.4

37

29.562

84

12

09

537.47

— 3.17

1838, Feb.

8.

39

39.8

40.6

28.530

84

12

48

510.98

— 0.89

)) 99

13.

27.6

30.3

31.8

29.474

84

12

15

539.80

— 2.61

1839, Feb.

10.

42

, ,

44

30.116

84

12

23

527.50

— 9.27

12.

36.2

, ,

41.4

30.034

84

12

02

540.77

— 1.01

)J >)

14.

36.3

41.5

29.735

84

12

13

534.72

— 2.63

1840, Feb.

13.

34.8

37

40.2

29.625

84

12

15

534.57

— 2.30

)) )»

26.

33.8

36.7

40.1

30.370

84

12

14

542.88

— 8.82

28.

32.7

35

37.2

30.234

84

11

96

548.47

— 2.02

„ March

2.

33.5

35

38.5

30.386

84

11

89

553.44

+ 1.33

?> »

3.

34.8

36.4

38.4

30.416

84

11

87

554.56

+ 3.43

j> ??

4.

35.8

38

40

30.254

84

12

09

541.50

— 5.59

5.

38.2

39.7

41.5

30.128

84

12

13

539.00

— 2.90

9.

44.9

44.8

45

30.477

84

12

11

540.30

+ 0.55

9? ?J

17.

42.2

46

49.1

30.214

84

12

16

537.84

— 0.45

J> »

18.

41

45.3

49

30.146

84

12

17

537.55

— 0.95

17 X (^a = — 33".53
K = 10.0672

dvi=- 1".97
rf/i= — 0".196

38. f Sagittarii.
*g = — 30°6'49". 15. (J.)
Precession = + 4".487 ; sec var. = + 0",543 ; proper motion (J.) = — 0".013.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFBACT.

dK.

1837, Aug.
>» »
)j »>

6.
6.
7.

46.1
48.8
49.2

51
53.2

54.8

53.7

55

56.2

30.155

30.248
30.259

84° 18' 64
84 18 48
84 18 63

538.27
546.92
538.23

— 2.57
+ 6.15

— 0.39

* The proper motion is deduced from J., as Airy's places for 1836 and 1837 differ 2".68.

The Rev. Dr. Robinson on the Constant of Refraction.

221

23 X <^R = - 2,2". M
K = 9.8637

dfi :

: - 1".41

— 0'M42

DATE.

E. T.

I. T.

A. T.

BABOH.

Z£N. DIST.

OBS. REFBACT.

dB.

1837,

Aug.

15.

57.9

60.4

62.8

30.090

840

18'.

97

518.33

— 8.92

Jt

)>

16.

69.2

62

64

29.965

84

18

98

518.13

— 4.12

»)

26.

49

64.7

56.6

29.939

84

18

77

531.06

— 3.10

29.

46.5

52

64.6

29.429

84

18

86

526.97

— 1.99

1838,

Aug.

4.

54.8

• •

60

29.204

84

18

94

515.17

4- 1.34

13.

51.8

• •

68.6

30.060

84

18

75

527.16

— 5.21

14.

53

, ^

68.2

30.033

84

18

70

530.00

— 0.42

1839,

July

24.

52.5

57.4

59.2

29.578

84

18

65

526.57

4- 3.79

27.

52.2

60

61.5

29.636

84

18

68

624.82

— 0.46

28

51.5

55.7

60

29.776

84

18

63

628.18

— 0.27

1)

31.

47.4

61.2

56

29.627

84

18

63

528.60

— 1.22

Aug.

2.

56.1

57.1

59.8

29.762

84

18

72

523.14

+ 1.12

3.

52.1

56

59.2

30.026

84

18

57

532.28

-1- 0.99

»*

J>

4.

52.1

67.8

59.2

30.184

84

18

62

629.28

— 4.75

11.

51

56.2

58.2

30.169

84

18

61

530.05

— 6.02

12.

49.1

56

58

30.124

84

18

49

537.07

+ 0.74

24.

54.8

57.7

60

29.746

84

18

81

618.55

— 4.74

26.

51

54

69.1

29.620

84

18

68

526.98

+ 1.70

Sept.

5.

54.9

57

60.8

29.442

84

18

86

517.96

4- 0.16

>>

)j

11.

50.8

53.7

68

29.736

84

18

76

522.60

— 5.14

Fomalhaut.

* 8 = -30° 31'. 15".26. (H. J.)

Precession = + 19".073 ; sec var. = + 0".13.5 ; proper motion = — 0".180.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. REFBACT.

dR.

1839,

Oct.

12.

44.8

46.8

48.9

29.710

84°

■39'.

95

566.45

+ 2.07

17.

39.1

44.9

46.5

29.944

84

39

82

576.00

— 1.11

>9

ii

27.

41.1

45

47

30.293

84

39

70

683.29

+ 3.22

S»

»>

28.

43.1

46.2

48.5

30.412

84

39

94

569.18

— 10.86

» Airy, (Greenwich, 22 obs.)

16".00

Johnson,

14".75

„ (Cambridge, 21) .

13 .38

Mine,

14 .36

Henderson, (Cape,)

15 .78

Bessel, (Tab. Reg.)

20 .24

222

The Rev. Dr. Robinson on the Constant of Refraction.

DATE.

E. T.

I. T.

A. T.

BABOH.

ZEN. DIST.

OBS. BEFEACT.

dB.

1839,

Nov.

11.

42.9

44

47.3

28.998

84°

40'.

18

556.57

+ 2.57

»

»)

12.

40.9

43

46.1

29.332

84

40

17

557.07

— 4.92

j»

26.

32

35.8

40

29.173

84

39

83

578.74

+ 8.02

Dec.

2.

38.2

40.8

42.4

29.758

84

40

00

568.91

— 5.24

»

28.

29.8

34.2

37.2

29.762

84

39

82

579.90

— 5.53

1840,

Sept.

28.

47.1

50

51.1

29.016

84

39

83

650.25

4- 2.36

)J

»)

29.

45.1

47.8

49.1

29.582

84

39

54

568.21

+ 2.97

Oct.

2.

42

45

46.1

30.148

84

39

46

574.50

— 1.28

3.

39.5

47

49.8

30.160

84

39

45

674.35

— 4.67

J>

4.

40.8

46

46.8

30.119

84

39

47

672.97

— 3.79

9)

10.

41.8

43.8

45.5

30.210

84

39

42

677.23

+ 0.09

11.

42.8

45.2

46

30.295

84

39

42

577.20

— 0.26

;»

}»

12.

45.9

47.5

49

30.405

84

39

52

571.35

— 4.20

yj

»

14.

41.2

43.2

45.5

30.208

84

39

31

584.18

+ 6.84

)»

Nov.

21.

43.9

42.8

43.8

29.470

84

39

84

656.80

— 4.16

»

»>

27.

41.4

42.8

43

30.130

84

39

70

565.66

— 11.08

20 X rfR = — 28".96
k = 10.6207

rfR = — 1".45
(^/x = _ 0.136

Combining, we obtain,

NAME.

NO. OBS.

ndBXK

nK«.

df.

o' Canis.
15 Argiis.
o' Canis.
1 Argus.
^ Sagittarii.
Antares.
J Canis Maj.
a- Sagittarii.
I Canis Maj.
n Canis Maj.
i Sagittarii.
t, Canis.
f Sagittarii.
Foraalhaut.

13

16
13
13
23
22
14
17
16
16
18
17
23
20

— 112.9950

— 80.9305

— 130.2914

— 126.6960
+ 48.3397

— 157.9369

— 193.3463

— 112.9772

— 162.8188

— 162.7435

— 396.3260

— 337.5632

— 318.9921

— 307.6758

3-54.772

490.286

400.634

436.280

856.812

878.733

608.381

778.032

1193.730

1255.767

1648.873

1722.926

2237.730

2255.988

— 0".318

— 0 165

— 0 325

— 0 290
+ 0 056

— 0 180

— 0 318

— 0 145

— 0 136

— 0 130

— 0 241

— 0 196

— 0 142

— 0 136

Sum . .

241

— 2552.8420

15118.944

The Rev. Dr. Robinson on the Constant of Refraction. 223

, , —2552.842 ^,^„o

and du. = = — 0.1688

^ 15118.944

The correction for run for these stars give,

and we have,

fi = 57.7682

— 0.1688

— 0.0063

57.5931

which agrees so nearly with the determination from sub-polar stars (their dif-
ference being only 0".5 at Fomalhaut) that there is obviously no necessity for
supposing any discrepancy between the northern and southern refractions at
this observatory, especially as it would vanish entirely were the Cape declinations

not used. If now we take u := 57.546 ; the value of — reduced to my latitude

a

is 0.00129263, and (using the well-known notation of Mr. Babbage to save
space) the equation of refraction becomes for t = 50, barometer 29-60,

R = tang . e X log-' (1.7600151)
-f tang^ . e X log-' (7.9045751) {1 +tang^ . 6 X log. -' (6.44559)}

— ^^ . 6 X log-' (8.8715498) {1 -f tang* . 6 X log. "' (6.77484)}

+ ^^ . 0 X log-' (6.3720995) {1 +tang* . 6 x log"' (7-06014)]

— ^^ . 6 X log-' (4.0315728) {1 + tang* . 6 X log-' (7-23971)}
t»us

+ ^^ . 0 X log -' (1.7907405) {1 -f tang* . 6 X log"' (7-34007)]

cos'

224 The Rev. Dr. Robinson on the Constant of Refraction.

From this the following tables have been computed. In the first, the column

X • .1 1 -1 pM(1 + 6(t— 50)) , , l-fe'(T — 50)

A contams the logarithm of -^ — - ,-,, „^ -^, and b that of -—{ — 777 -— ;,

29.0O \-\-e (T — 50)

e' the expansion of the brass scale being taken = 0.0000 1 0479 ; and e" that of
mercury = 0.0001.

The second table contains c, the sum of all the terms except the first, for the
argument zen. distance ; d =: the change of c for one degree increase gt tem-
perature ; and e its change for one inch rise of the barometer. This last serves
also to change c for a slight variation in /x, the constant, for

fin

-r = E X 0.5144

and A must be changed by log /x' — log fi.
The refraction is given by

log k' = A 4" B 4" log tang apparent zen. dist. -f- log. bar.
R = u' — c — D X (t — 50°) — EX (bar. — 29.60.)

Argument of A, external thermometer = t
Argument of b, attached thermometer = t
Argument of c, d, and e, apparent zenith distance.

The Rev. Dr. Robinson on the Constant of Refraction.

225

Table I.

Ther. = 50' ; bar. = 29-60 Inches.

T.

A.

B.

T.

31

A.

B.

T.

A.

n.

0

0.33343g,

0.30517,8

+ 74

1 62

0.27864,3

- 46

1

0.332499,

32

0.30429,,

+ 70

63

0.27781,3

- 60

2

0.33 165g,

33

0.30341,,

+ 66

1 64

0.27698,,

- 54

3

0.3306 Ig,

34

0.30253,8

+ 62

65

0.276168,

- 58

4

0.32968g,

35

0.30165,7

+ 68

66

0.27534,3

62

5

0.32874^3

36

0.300788,

+ 54

67

0.27451,,

- 66

6

0.3278 Igj

37

0.29991,,

+ 50

i 68

0-27369,,

- 70

7

0.32688^3

38

0.29904,,

+ 46

! 69

0.27287,,

- 74

8

0.32595;,,

39

0.29817,,

+ 42

70

0.27205,,

- 78

9

0.32503g,

40

0.29730,,

+ 39

71

0.27123,,

- 81

10

0.324 lip.

41

0.29643,6

+ .':i6

72

0.27042,.

- 85

11

0.323 1 9g,

42

0.29557,6

+ 31

73

0.26961,,

- 69

12

0.32227g,

43

0.29471,6

+ 27

74

0.268808,

- 93

13

0.32 136g.

44

0.29385,,

+ 23

75

0.267998,

- 97-

14

0.32044„,

45

0.29298,6

+ 19

76

0.26718e,

- 101

15

0.319539,

46

0.29212,6

+ 15

I 77

0.2663790

- 105

16

0.318629,

47

0.29126,,

+ 11

78

0.26557,,

- 109

17

O.3177I9,

48

0.29041,,

+ 7

1 79

0.26476,0

- 113

18

O.3I68O9,

49

0.28956,,

+ 3

i 80

0.2639690

- 117

19

0.315899„

50

0.28872,,

0

81

0.26316,0

- 121

20

0.314999„

+ 117

51

0.287878,

- 3

i 82

0.262368,

- 125

21

0.3l409g„

+ 113

52

0.28703,,

- 7

! 83

0.2615690

- 129

22

0.31319,9

+ 109

63

0.286188,

- U

j 84

0.2607690

- 1.32

23

0.312309„

+ 105

64

0.28534,

- 15

i 85

0.25996,0

- 136

24

0.31140,9

+ 101

55

0.28449,,

- 19

86

0.26916,9

- 140

25

0.3 1051 90

+ 97

66

0.28365,,

- 23

87

0.25837,9

- 144

26

0.3096189

+ 93

57

0.28281,,

- 27

88

0.26758,9

- 148

27

0.3087289

+ 89

58

0.28197,,

- 31

89

0.25679,9

- 152

28

0.3078389

+ 85

59

0.28113,3

- 35

90

0.25600,9

- 156

29

0.3069488

+ 81

60

0.28030,3

- 39

91

0.25521.9

- 160

30

0.3060689

+ 78

61

0.2794783

- 42

i 92

1

0.25442

- 163

VOL. XIX.

2g

226

The Rev. Dr. Robinson on the Constant of Refraction.

Table IL

Z. D.

c.

D.

E.

Z. D.

c.

D.

E.

Z. D.

c.

D.

£.

40

0.01

76° 20'

4.693,

0.002

0.14

81=55'

20.82„

0.006

0.63,

10

0.01,

40

5.0*3,

0.002

0.16

82 0

21.42,3

0.006

0.64,

15

0.02,

77 0

5.42,,

0.002

0.16

5

22.06,,

0.006

0.66,

20

0.03,

20

5.84„

0.002

0.18

10

22.70,,

0.006

0.68,

25

0.04,

40

6.31,,

0.002

0.19

15

23.38,„

0.006

O.7O3

30

0.05,

78 0

6.83,3

0.002

0.21

20

24.08„

0.006

0.73,

35

0.073

10

7-n3„

0.002

0.21

26

24.81,,

0.006

0.75,

40

0.10,

20

7.4I3,

0.002

0.22

30

25.57,,

0.006

0.77,

45

0.15,

30

7.7233

0.002

0.23

36

26.35,3

0.006

0.79,

46

0.16,

40

8.063,

0.003

0.24

40

27.18,,

0.007

0.82,

47

0.17,

50

8.4O3,

0.003

0.26

45

28.03,,

0.007

0.85,

48

0.18,

79 0

8.763,

0.003

0.26

60

28.92,3

0.007

0.87,

49

0.19,

10

9.15,,

0.003

0.28

55

29.85„

0.007

O.9O3

50

0.20,

0.01

20

9.57,,

0.003

0.29

83 0

30.82,.„„

0.008

0.93,

61

0.21,

0.01

30

10.01,,

0.003

0.30

5

31.82,.„,

0.008

0.96,

62

0.233

0.01

40

10.47,,

0.003

0.31

10

32.88,.,„

0.008

0.994

53

0.25,

0.01

50

10.96,3

0.003

0.33

15

33.98,.,,

0.009

1.03,

54

0.27,

0.01

80 0

11.49,,

0.003

0.35

20

35.13,.,,

0.009

1.06,

55

0.29,

0.01

5

11.77,,

0.003

0.35

26

36.32,.,,

0.010

I.IO4

66

0.323

0.01

10

12.05,,

0.003

0.36

30

37.66,.3,

0.010

1.14,

57

0.35,

0.01

15

12.343„

0.004

0.37

35

38.87,. 3,

0.011

I.I84

58

0.39,

0.01

20

12.643,

0.004

0.38

40

40.24..,,

0.012

1.22,

59

0.43,

0.01

25

12.9533

0.004

0.39

45

41.66,.,„

0.013

1.27,

60

0.47,

0.01

30

13.283^

0.004

0.40

50

43.16,.,,

0.013

1.31,

61

0.52,

0.02

35

13-61,3

0.004

0.41

65

44.73,.,,

0.014

1.36,

62

0.58.

0.02

40

13.963,

0.004

0.42

84 0

46.37,.,,

0.015

1.41,

63

0.65^

0.02

45

I4.3I3,

0.004

0.43

5

48.09,.,„

0.016

1.47,

64

0.72,

0.02

50

14.67,,

0.004

0.44

10

49.89,.,,

0.018

1.53,

65

0.80,,

0.03

55

13.05,0

0.004

0.46

15

51.78,.„

0.019

1.69,

66

0.91,,

0.03

81 0

16.45,,

0.004

0.46,

20

S3.77,.„,

0.022

1.65,

67

1.03,,

0.03

5

15.86,,

0.004

0.48,

26

55.86,.,„

0.023,

1.72^

68

1.17,,

0.04

10

16.28,,

0.004

0.49,

30

58.06,.3,

0.0263

1.79,

69

1.34,;

0.000

0.04

15

16.72,,

0.004

0.60,

36

60.37,.,,

0.0283

1.87,

70

1.53„

0.001

0.05

20

17.17„

0.004

0.52,

40

62.82,.,,

0.031,

1.96,

71

1.80,,

0.001

0.06

25

17.64,,

0.005

0.53,

45

66.40, .,

0.035,

2.04,

72

2.093,

0.001

0.06

30

18.12,„

0.005

0.54,

50

68.11,.,,

0.039,

2.13,0

73

2.48,,

0.00]

0.08

35

18.62,,

0.005

0.56,

66

71.003.„,

0.044,

2.23,,

74

2.97,,

0.001

0.09

40

19.14,,

0.005

0.58,

85 0

74.06

0.050

2.34

75

3.59,,

0.001

0.11

45

19.68,,

0.005

0.59,

76

4.373,

0.001

0.13

50

20.24,,

0.005

O.6O3

The Rev. De. Robinson on the Constant of Refraction. 227

Example.
Fomalhaut, zen. dist. 84° 39'. 46 ; e. t. 42° ; bar.' 30\148 ; a. t. 46M.

tang z. D. . 1.02913 c — 62.56

A. . 0.29557 (d) + 0.25 = _ 8' X — 0.031

B. 4- 15 (e) — 1.01 = 4- 0.548 X — 1 -95
30.148 1.47926 —63.38

2.80411 636.96 = r'

573.58 = R.

The Reader is requested to make the following Correction :-
Page 223, last line, /or 1 + read 1 — .

2g2

228

IX. On the Heat developed during the Combination of Acids and Bases. By
Thomas Andrews, M. D., M. R. I. A., Professor of Chemistry in the Royal
Belfast Institution.

Read 11th January, 1841.

1. IT has been long known that chemical actions are in general accompanied
by the evolution or abstraction of caloric. In most cases the change of tempera-
ture depends upon the result of the action of different causes, some of which
tend to increase, and others to diminish the initial temperature of the reacting
bodies. Thus, in the decomposition of a solution of carbonate of soda by con-
centrated sulphuric acid, the combination of the sulphuric acid with water and
with the alcali are two distinct sources of heat, while the separation of the
carbonic acid from the soda, and its evolution in the gaseous form, are equally
distinct causes of a diminution of temperature. To estimate the influence of
each of these circumstances in any particular instance is a problem of great
difficulty ; and we can only expect to accomplish its complete solution, by
confining our investigations, in the first place, to these simpler cases, where the
variations of temperature are produced by the operation of one single cause.
For this reason, I have confined myself, in this preliminary inquiry, to the
examination of the calorific phenomena which occur during the combination of
acids and bases with each other, under the most favourable circumstances, for
obtaining results free from complication.

2. The experiments to be hereafter described were all performed with very
dilute solutions, by which means no correction was required for the heat evolved,
when strong solutions of certain acids and alcalies are diluted. The method of
operating is easily described. In separate glass vessels solutions of determinate
weights were prepared, one containing the quantity of alcali whose power of
generating heat was sought, and the other, a little more than the equivalent of

Dr. Andrews on the Heat developed, Sfc. 229

acid required to neutralize the alcali. After the liquids had acquired the same
temperature, they were mixed together in the jar containing the alcali, and the
increase of heat carefully observed by a delicate thermometer. This process
was adopted from the facility of its execution and the uniformity of its results.
It is, however, obvious, that a large portion of heat would be absorbed by the
glass vessel ; and it was, therefore, necessary to establish, by a series of inde-
pendent experiments, the corrections to be applied to the temperatures thus
obtained.

3. As a basis to this whole investigation, the heat developed in the combina-
tion of nitric acid and potash was carefully determined. But before describing
the method employed, I must anticipate an observation which will be afterwards
proved, viz., that the same amount of heat is developed when a given quantity
of an alcali is united to an acid, whether the acid added be just sufficient to
neutralize the alcali, or be considerably in excess.* The addition of a slight
excess of acid does not, therefore, in any way interfere with the results, except
in so far as it renders them more uniform and certain, by producing a rapid and
complete neutralization of the alcali.

4. A cylindrical vessel of very thin brass was procured, capable of containing
rather more than the quantity of liquid employed. Into this vessel was introduced
the solution of caustic potash, the weight of which solution was about nine times
greater than that of the dilute nitric acid destined to neutralize it. This vessel
was so thin that we may assume, without any sensible error, its temperature to
have been identical with that of its liquid contents. It weighed 6.63 grammes,
which, assuming the specific heat of brass to be .094, is equivalent to 0.623 gr.
water.

5. As the weights of the glass and mercury in the bulb and immersed
portion of the tube of the thermometer were both unknown, I was obliged to
have recourse to a direct experiment, in order to ascertain their equivalent of
water. For this purpose, 30 grammes of water (the quantity of liquid usually
employed) were introduced into the brass vessel, and the increase of its tempera-
ture carefully observed, when the thermometer, previously heated through a

• These observations, as well as others of a similar kind in subsequent parts of this paper, refer
always to dilute solutions, such as are employed in these experiments.

230 Dr. Andrews on the Heat developed

certain number of degrees, was suddenly cooled by Immersion in it. Denoting
by t the loss of heat sustained by the thermometer, and by If the temperature
gained by the liquid, I obtained in different trials the following numbers :

12 3

t = 59°.00, t = 69°.00, t = 72°.00.

t'= o°.9o, tf = r.oo, if= 1M5.

Hence, we deduce for the value of the thermometer in grammes of water,

12 3 Mean.

0.47, 0.45, 0.49, 0.47.

6. From the last two results we may therefore conclude, that the brass vessel
and thermometer, taken together, are equivalent to 1.09 gr. water.

7. A very important source of error in this and other similar investigations,
where the variation of temperature of a liquid requires to be observed with the
utmost precision, arises from the cooling influence of the surrounding air during
the time occupied by the observation, which, in the experiments I am about to
describe, amounted to nearly 1'. Where the increase of temperature does not
exceed 2° or 3° Fah., the common method of cooling the liquid before the
experiment begins, as many degrees below the temperature of the air as it will
afterwards rise above it, may be employed with success ; but for greater incre-
ments of heat, this process is liable to a serious error, which it is necessary to
avoid. In fact, on mixing the liquids together, the thermometer attains, in
a very few seconds, almost its ultimate point of elevation, and it occupies at
least four-fifths of the entire time in rising through the last half degree. As,
therefore, the mixture continues much longer in the upper than in the lower
half of its range of temperature, the method just described will necessarily yield
results sensibly below the truth.* In practice, this error may be effectually
obviated, by reducing the initial temperature of the liquid so far below the
temperature of the air, that its final maximum may never reach higher than
2° F. above the same point.

• A similar observation has been made by M. Regnault in his recent and valuable memoir on
the " Specific Heats of Simple and Compound Bodies" (Ann. de Chin. t. 63, p. 23) ; but the error
thus induced he corrects by means of an interpolating formula.

during the Combination of Acids and Bases. 231

8. The strongest nitric acid employed in these experiments contained 13.3
per cent, of real acid, and when one part of such an acid is diluted with nine
parts of water, no sensible production of heat can be discovered by the most
delicate thermometer. The corresponding solution of caustic potash, containing
only 1.3 per cent, of alcali, was of course far beyond the limit of such sources
of heat. That simple dilution exercised no influence on the result was further
proved, by increasing the weight of the acid liquid, and diminishing that of the
alcaline, while, at the same time, the quantities of acid and alcali in each, as also
the total weight of both liquids, remained the same ; yet such variations in the
form of the experiment produced no change whatever in the elevation of tem-
perature observed on mixing them.

9. Having discussed the corrections arising from the form of apparatus, I
now proceed to give the details of the fundamental experiment, on the absolute
amount of heat evolved in the union of nitric acid and potash. The general
accuracy of these results was tested and confirmed by repeating the experiments
in the form of a series, in which (the weight of the whole liquid remaining
constant) the quantities of the combining substances were taken successively, in
the proportions expressed by the numbers 1, 2, 4 ; and it will be seen that
the corresponding increments of temperature bear a similar ratio to each
other.

10. Into the brass vessel before described, a solution of caustic potash, con-
taining .0882 gr. of alcali was introduced. It weighed 27.3 gr., which, added
to 1.09 gr., the equivalent in water of the vessel and thermometer (6), makes
the whole equal to 28.39 gr. water. The acid solution, in a small glass tube,
weighed 2.83 gr., and contained .106 anhydrous nitric acid. Thermometer in
air stood at 38° F.

Temp, of acid, ....

J, alcaline solution,

Mean temp, before mixture,
Temp, after mixture.

Increase in temp. (31.22 water) . r.64

11. The last experiment repeated. Ther. in air 39°.

38°

.20

37°

.00

37°

.11

38°.75

232 Dr. Andrews .o« the Heat developed

Temp, of acid, , . . 39°.00
,j alcallne solution , 37°.50

Mean temp, before mixture 37°.64
Temp, after mixture, . . 39°.25

Increase (31.22 gr. water) . V.Ql

12. Alcaline solution weighed 27.2 gr., and contained .1765 gr. of pure
potash, or double that in the last experiments. Acid solution weighed 2.85, gr.
containing .212 anhydrous nitric acid. Ther. in air 39°.5.

Temp, of acid, . . . 39°.00
„ alcfline solution, . 37°.00

Mean temp, before mixture, 37°. 18
Temp, after mixture, . . 40°.40
Increase (31.14 water), . . 3°.22

13. Alcaline solution 26.85 gr., containing .353 potash ; acid liquid 3.25 gr.,
containing .424 anhydrous nitric acid. Ther. in air 39.3°.

Temp, of acid . . . 39°.70
„ alcaline solutions . 34°.30

Mean. Temp, before mixture, 34°.86
Temp, after mixture, . . 4r.45
Increase (31.19 water) . . 6°.59

14. Reducing these results to the quantity of alcali (.353 gr.) used in last
experiment, and to 30 gr. of water, we obtain the following numbers :

12 3 4 Mean.

^°.83, 6°.70, 6°.68, 6°.85, 6°.76.

15. This may be otherwise expressed, by stating that 1 gr. of potash, in
combining with nitric acid, is capable of heating 85 gr. of water through 6°.76
of Fahrenheit's scale, or, which is the same thing, of heating 574.6 gr. of water
through 1°. It must, however, be carefully observed, that in this experiment it

during the Combination of Acids and Bases. 233

is not pure water, but a weak solution of nitrate of potash, which is actually
heated ; and the above numbers would therefore require a further correction, in
consequence of the difference between the specific heats of these liquids. This
correction, however, must be extremely small, from the very dilute solutions
obtained : it would probably be within the limit of the errors of observation.

16. Many of the subsequent experiments would have been performed with
difficulty in a metallic vessel. I therefore substituted a pretty thick glass jar for
the brass vessel, and both solutions were brought as nearly as possible to the tem-
perature of the surrounding air, at the commencement of each observation. In
this way, numerous experiments were easily performed, which yielded results
comparable with each other, although all below the truth. It was, therefore,
necessary to ascertain the absolute loss of heat when the experiment was per-
formed in this way, and whether it was proportional to the elevation of tem-
perature. For this purpose, solutions were prepared containing the same quan-
tity of potash and nitric acid as in the experiments with the brass cylinder.

17. Alcaline solution 27 gr., containing .0882 gr. potash ; acid solution 3 gr.,
containing 1.06 nitric acid.

Temp, rose on mixture, 1°.45.
Another experiment gave 1°.45.

18. Alculine solution 27 gr., containing .1765 potash ; acid solution 3 gr.,
containing .212 nitric acid.

Temp, rose on mixture 2°.90.
Another experiment gave 2°.95.

19. Alcaline solution 27 gr., containing .353 potash ; acid solution 3 gr.,
containing .424 nitric acid.

Temp, rose on mixture 5°.8.
Another experiment gave 5°.8.

20. Alcaline solution 24 gr., containing .353 potash ; acid liquid 6 gr.,
containing .424 nitric acid.

Temp, on mixture rose to 5°.9.

21. Collecting these results, we obtain for the elevation of temperature of
VOL. xix. 2 H

234 Dr. Andrews on the Heat developed

30 gr. of water, in a glass vessel, by the combination of .353 gr. potash with
nitric acid :

1

2

3

4

5

6

Mean.

5^8,

5°.8,

5".8,

5°.9,

5°.8,

5°.9,

5°.83.

This number differs by 0.93° from the absolute quantity of heat before found,
which is the loss of heat by this method of performing the experiment. It also
appears from the coincidence of the results obtained with different proportions of
alcali, that the loss of heat is proportional to the rise of temperature, and
hence the necessary correction for this error is, in all cases, easily made.

22. When the base is insoluble in water, and slowly soluble in the acid, a
new element enters into the observation, and requires to be estimated, viz., the
cooling of the liquid during the prolonged duration of the experiment. In the
observations last described, the thermometer attained its maximum in about 45"
from the time the liquids were mixed, but in the solution of such substances, as
magnesia or the oxide of zinc, not less than 2', or 2|-' will elapse before the
liquid becomes transparent, and the thermometer stationary. Even to complete
the solution within this period, the liquid requires to be constantly stirred with a
glass rod. This circumstance renders these results less precise than those in
which the combination occurs instantaneously ; but the amount of error thus
produced may be estimated, by repeating the same experiment in precisely the
same manner, with a solution of caustic potash, containing exactly the quan-
tity of alcali (as deduced by calculation from the foregoing experiments) which
should produce the same elevation of temperature as had been obtained with the
slowly soluble base. The difference between the increase of heat actually found,
and that deduced from calculation, will be equal to the loss of caloric occasioned
by the stirring, and length of the experiment ; and consequently the required
correction for the number obtained by observation. The precise value of this
correction will be given hereafter.

23. The general conclusions which I shall endeavour to establish in the
subsequent part of this communication, may be enunciated in the form of the
three following laws :

Law 1. — Tlie heat developed during the union of acids and bases is de-
termined hxj the base and not hy the acid; the same base producing, when

during the Combination of Acids and Bases. 235

combined with an equivalent of different acids, nearly the same quantity of
heat ; but different bases a different quantity.

Law 2. — When a neutral is converted into an acid salt., by combining
with one or more atoms of acid, no change of temperature occurs.

Law 3. — When a neutral is converted into a basic salt, by combining with
an additional proportion of base, the combination is accompanied with the
evolution of heat.

24. To the first of these laws important exceptions are presented by the
peroxide of mercury among the bases, and by the hydrocyanic, and probably the
carbonic acid, among the acids ; and it is not improbable that more extended
investigations will lead to the discovery of other exceptions. The second law
has been established by numerous experiments, and can scarcely be said to be
liable to any well-marked exception ; but I feel much less confidence in enun-
ciating the third, as a general principle, from the very limited number of cases of
soluble subsalts in which it was possible to verify its accuracy.

25. In order to obtain results of as much uniformity as possible, the standard
alcaline solution was always mixed with rather a greater quantity of acid than
was necessary to neutralize it.* The combination was thus effected more rapidly
and certainly, than if an attempt had been made to form an exactly neutral
compound. That this excess of acid did not produce any sensible difference in
the result, will be rendered evident, when the experiments are examined, which
will be hereafter cited, in illustration of law second ; and, indeed, if no basic
compound existed, the numbers obtained were identical, whether an equivalent
of base was neutralized by an excess of acid, or a like equivalent of acid neutralized
by an excess of base. I have arranged, in distinct tables, the increments of
temperature obtained by combining an equivalent of each base with the acids.
The equivalents taken were .353 grammes potash, .234 gr. soda, .129 gr.
ammonia, .572 gr. barytes, .213 gr. lime, .154 gr. magnesia, .301 gr. oxide of
zinc, .834 gr. oxide of lead, .870 gr. oxide of silver, and .810 gr. peroxide of

* In the cases of the phosphoric and arsenic acids, the quantity of acid was just sufficient to con-
vert the alcali into the common phosphate and arseniate ; that is, half an equivalent of acid for an
equivalent of base. The reason of this will appear again (35). The number for chromic acid is
only deduced from an indirect experiment upon the bichromate of potash.

2h2

236

Dr. Andrews on the Heat developed

mercury. The entire weight of the solution, after the mixture was made,
amounted in every Instance to 30 grammes. In the first four tables, the first
column of numbers contains the elevation of the thermometer actually observed ;
and the second, the result corrected for the loss of heat, occasioned by the mode
of performing the experiment (21).

26. Table 1. — Potash.

ACID.

FOUND.

CORRECTED.

DIFFERENCE FROM
MEAN.

Sulphuric,

Nitric,

Phosphoric,

Arsenic,

Hydrochloric,

Hydriodic,

Boracic,

Chromic,

Oxalic,

Acetic,

Formic,

Tartaric,

Citric

Succinic,

Mean, ....

6°.30
5.83
5.70
5.70
5.65
5.80
5.60
5.55
5.70
5.50
5.50
5.25
5.25
5.25

7°.32

6.76
6.61
6.61
6.56
6.74
6.50
6.46
6.62
6.39
6.39
6.10
6.10
6.10

+ 0°.80

+ 0.24
+ 0.09
+ 0.09
+ 0.04
+ 0.22

- 0.02

- 0.06
+ 0.10

- 0.13

- 0.13

- 0.42

- 0.42

- 0.42

6.52

during the Combination of Acids and Bases.

237

27. Table II.— Soda.

ACID.

FOUND.

CORRECTED.

DIFFERENCE FROM
MEAN.

Sulphuric,

Nitric,

Phosphoric,

Arsenic,

Hydrochloric,

Hydriodic,

Boracic,

Oxalic,

Acetic,

Tartaric,

Citric,

Succinic,

Mean

6°.40
5.55
5.55
5.60
5.80
5.70
5.80
5.75
5.45
5.10
5.10
5.10

7°.44
6.45
6.45
6.50
6.74
6.62
6.74
6.68
6.34
5.93
5.93
5.93

+ 0°.96

- 0.03

- 0.03
+ 0.02
+ 0.26
+ 0.14
+ 0.26
+ 0.20

- 0.14

- 0.55

- 0.55

- 0.55

6.48

28. Table III. — Barytes.

ACID.

FOUND.

CORRECTED.

DIFFERENCE FROM
MEAN.

Nitric,

Hydrochloric,

Hydriodic, ......

Acetic, .......

IV^ean • . •

5°.90

5.85
6.00
5.50

6°.85
6.79
6.97
6.39

+ 0°.10
+ 0.04
+ 0.22
- 0.36

6.75

238

Dr. Andrews on the Heat developed

29. Table IV. — Ammonia.

ACID.

FOUND.

CORRECTED.

DIFFERENCE FROM
MEAN.

Sulphuric,

Nitric,

Arsenic,

Hydrochloric,

Hydriodic,

Oxalic,

Acetic,

Tartaric,

Citric,

Succinic,

IVIean

5°.45
4.80
4.90
4.80
4.80
4.90
4.70
4.40
4.35
4.40

6°.34

5.58
5.69
5.58
5.58
5.69
5.47
5.11
6.05
5.11

+ 0°.82
+ 0.06
+ 0.17
+ 0.06
+ 0.06
+ 0.17

- 0.05

- 0.41

- 0.47

- 0.41

6.52

30. The remainder of the bases examined, being either insoluble or very
slightly soluble in water, were added in the solid state to the acid solution, whose
weight was always so adjusted as, together with that of the base, to be equal to
30 grammes. The bases were all taken in the anhydrous state, except lime,
which dissolves with extreme difficulty even in the dilute acids, unless previously
converted into a hydrate. The experiments performed with these bases occupied
from 80" to 100" longer than those with the soluble alcalis. This renders the
application of a new correction necessary. The method of determining the
amount of this correction has been already explained (23). In the remaining
tables, the first column contains the result as found by experiment ; the second,
the duration of the observation ; the third, the correction applied for the heat
lost thereby ; the fourth, the corrected result ; and the fifth, the difference
from the mean.

during the Combination of Acids and Bases.

2.39

31. Table V. — Magnesia.

ACID.

FOUND.

TIME.

COB. TIME.

CORRECTED.

DIFFERENCE
FROM MEAN.

Sulphuric, . .
Nitric, . . .
Hydrochloric,

Mean,

7°.00
6.70
6.60

2'
2

2

0°.30
0.30
0.30

8''.48
8.13
8.11

+ 0°.24

+ 0.11
— 0.13

8.24

32. Table Yl.—Lime.

ACID.

FOUND.

TIME.

COR. TIME.

CORRECTED.

DIFFERENCE
FROM MEAN.

Nitric, . . .
Hydrochloric,
Acetic, . .

Mean, . .

5°.95

5.85
5.80

0''.25
0.25
0.25

7°.20

7.08
7.03

+ 0°,10

— 0.02

— 0.07

7.10

33. Table VII. — Oxide of Zinc.

ACID.

FOUND.

TIME.

COR. TIME.

CORRECTED.

DIFFERENCE
FROM MEAN.

Sulphuric, . .
Nitric, . . .
Hydrochloric,
Hydriodic,

Mean, . .

4°.45
3.90
4.00
3.50

2'

2
2

4

0°.20

0.20
0.20
0.45

5°.40

4.76
4.88
4.59

+ 0°.49

— 0.15

— 0.03

— 0.32

4.91

240

Dr. Andrews on the Heat developed

34. Table VIII. — Oxide of Lead.

ACID.

FOUND.

TIME.

COR. TIME.

CORRECTED.

DIFFERENCE
FROM MEAN.

Nitric, . . .
Acetic, . . .

Mean, .

3°.45
2.95

2'

3

0M5

0.30

4°. 18
3.78

+ 0°.20
— 0.20

3.98

35. The oxide of silver gave, with nitric acid, an increase of temperature of
2°.7 corresponding, when corrected, to an actual elevation of 3°.23.

36. To render the numbers in each table strictly comparable with one
another, would require a minute investigation of the influence of every possible
source of a variation of temperature in the experiments ; such are, differences in
the specific heats of the solutions formed, alterations in the density of the liquids
after mixture, &c. However, from very dilute solutions being employed, and
also, from the results being identical when the strength of the solutions was
greatly varied (9), it is probable that the errors arising from such causes could
not amount, in most cases, to more than a few hundreths of a degree. Taking,
therefore, the results as they appear in the tables, it will be found on exami-
nation, that they are in accordance withLaw 1, (24). If we refer to the first,
second, and fourth tables, as being the most extensive, from the large number of
soluble compounds formed by potash, soda, and ammonia, it will be observed,
that the sulphuric acid developes from 0°.8 to nearly 1° more than the megn heat
given by the other acids, while the tartaric, citric, and succinic acids fall from 0°.4
to 0°.55 short of the same. A minute investigation of the influence of the disturb-
ing sources of heat will, no doubt, discover the cause of these discrepancies ; the
high numbers for sulphuric acid are probably connected with that acid's well-
known property of developing much heat when combined with successive atoms,
of water. All the other acids develope very nearly the same amount of heat in
combining with the same base ; the greatest divergences from the mean quan-
tity being in the case of potash, -\- 0°.24, and — 0°.13 ; in that of soda, -j- 0°.26,

during the Combination of Acids and Bases.

241

— 0°.14 ; and in that of ammonia + 0°.17 and — 0°.05. These differences are
almost within the limits of the errors of experiment. In the other tables a
similar agreement will be found to exist. Indeed the sulphuric acid does not
exhibit in them so wide a discordance from the other acids as before. I must,
however, remark that the numbers for the insoluble bases are scarcely so exact
as those which are contained in the first four tables.

37. Whether the base be soluble or insoluble in water, the increments of
temperature obtained, by combining the same base with different acids, may be
compared with each other ; but if we wish to discover the relations subsisting
between the temperatures developed by different bases, it becomes necessary to
take into consideration the heat absorbed by the insoluble bases, in passing from
the solid to the fluid state. I am not at present acquainted with any method
whereby the heat thus abstracted can be estimated. But the numbers for the
insoluble bases, from this cause, will be all too low. We may, therefore, arrange
the bases in the following order, in respect to their power of developing heat
when combining with the acids ; but this arrangement is liable to be disturbed
when the value of the unknown quantities shall be determined. It must also be
recollected that the potash, soda, barytes and lime were in the state of hydrates
before mixture, while the magnesia, oxide of zinc, oxide of lead, and oxide of
silver were anhydrous.

Magnesia, .... 8°.24 + a:

. 7.10 + a;'

. 6.75

. 6.52

. 6.48

. 5.52

. 4.91 +y'

. 3.98 + a;'"
. 3.23 + x""

Lime,
Barytes,
Potash,
Soda, .
Ammonia,
Oxide of Zinc,
Oxide of Lead,
Oxide of Silver,

38. The peroxide of mercury has given results altogether at variance with
the preceding. It developes with the nitric and acetic acids nearly the same
quantity of heat, but with the hydracids the most singular anomalies occur, as
will appear in the next table.

VOL. XIX. 2 1

242

Dr. Andrews on the Heat developed
39. Table IX. — Peroxide of Mercury.

ACID,

FOUND.

Nitric, . .
Acetic, , ,
Hydrochloric,
Hydrocyanic,
Hydriodic, ,

1°,20
1,20
3,80
5.85
9,20

2'
2
2
2
3

CORR. TIME.

0°,05
0,05
0.20
0,25
0,60

CORRECTED,

r.27

1,27

4.65

7,10

11.40

40, To the last number some objection may be made, as a large excess of
hydriodic acid was used to prevent the formation of the Insoluble perlodlde of
mercury ; but even if we omit it altogether, the other parts of the table exhibit
singular discrepancies. It is probable that a more extended investigation will
discover other metallic oxides, resembling the peroxide of mercury, in yielding
different quantities of heat, when they combine with the hydraclds,

4 1 , The hydrocyanic acid stands not less apart from the other acids than the
oxide of mercury from the rest of the bases, in its development of heat when
forming compounds ; and it is remarkable that no analogous property appears
with the hydrochloric and hydriodic acids. The hydrocyanic acid used in these
experiments was perfectly pure : it was employed immediately after being
rectified over chalk, and had no action on vegetable colours, I have collected
together the elevations of temperature produced by it, and contrasted them with
the mean quantities of heat given by the other acids with each base.

BASE.

HYDROCYANIC
ACID.

MEAN OF OTHER
ACIDS.

DIFFERENCE.

Potash,

Soda,

Barytes,

Ammonia,

Peroxide of Mercury, , .

1°,45

1,45
1,68
0.51
7,10

6°,52
6.48
6,75
5,52

5°,07
5,03
5,07
5,01

during the Comhination of Acids and Bases. 243

42. Thus the hydrocyanic acid developes with potash, soda, barytes, and
ammonia, 5° less than the other acids. On the other hand, it yields no less than
7°.l in combining with the peroxide of mercury, while the oxyacids produce
with the same base, only r.27.

43. I now proceed to cite a few experiments in illustration of Law 2 ; viz.,
that during the conversion of a neutral into an acid salt, no evolution of heat
occurs.

44. 23 gr. of a solution of caustic potash, containing .353 gr. of alcali, were
mixed with 7 gr. of a solution of oxalic acid, containing .271 gr. (or 1 equiv.) of
acid.

Temp, after mixture rose 5°.7.

45. 31 gr. of a solution of neutral oxalate of potash, containing .624 gr. of
the salt, were mixed with 9 gr. of a solution of oxalic acid, containing .271 gr.
(1 equiv.) acid.

Temp, after mixture rose 0°.0.

46. The solution of binoxolate of potash, obtained in last experiment, was
mixed with 18 gr. of the solution of oxalic acid (2 equiv.)

Temp, rose after mixture 0°.15.

After some time, crystals of quadroxalate of potash began to form, which
accounted for the slight elevation of temperature.

47. On adding to a solution of sulphate of potash a second atom of sulphuric
acid, the temperature of the mixture rose only 0°.l, although the combination of
the first atom had produced 6°.3 of heat.

48. Similar results were obtained with the oxalate, tartrate, and acetate of
soda, when converted into the corresponding supersalts ; and by neutralizing
these acid salts with the base, the same heat was invariably produced as if the
excess of acid had existed in a free state. I may cite particularly the case of the
bichromate of potash, which gave, when converted into the neutral chromate, a
quantity of heat corresponding with that developed by the acids in general with
potash, viz., 6°.45. In verifying this principle, care must be taken to select
examples where all the compounds are soluble salts ; otherwise, the latent heat
extricated by the solid precipitate would interfere with, and complicate the

2i 2

244 Dr. Andrews on the Heat developed

result. It is for this reason that the formation of the bitartrate of potash is
accompanied by heat, although none is evolved when the neutral tartrate of
soda combines with a second atom of acid.

49. As a farther illustration of the same principle, I am unwilling to omit
the description of an interesting experiment, although its complete explanation
involves the consideration of a class of phenomena which I have carefully ex-
cluded from the present communication. Three solutions were prepared, each
containing 25 gr. of liquid ; the first, holding in solution .353 gr. of pure
potash ; the second, .520 gr. of carbonate of potash ; and the third, .683 gr. of
bicarbonate of potash ; consequently the amount of real alcali the same in all.
They were then separately neutralized by 5 gr. of a solution of nitric acid,
containing a considerable excess of acid, and the two latter solutions were well
stirred, to expel, as far as possible, the carbonic acid gas before the final tempe-
rature was observed. The elevations of temperature were, for

DIF.

Pure Potash,

. 5°.8

Carbonate of Potash,

. 1.7-

4.1

Bicarbonate of Potash, .

. 0.4

1.3

50. Thus we see that the effect of separating the first atom of carbonic acid,
in the gaseous state, from its combinations with the alcali, was to cause the
disappearance of 4°.l of heat ; while the separation of the second atom, and its
complete expulsion in the gaseous state, produced a further diminution of
temperature of only 1°.3. In these observations, two distinct sources of an
absorption of caloric exists ; one, the separation of the chemical compound into
its constituents ; the other, the change of one of those constituents from the
liquid to the gaseous state. Had both causes acted equally on the second as on
the first atom of carbonic acid, we should have obtained with the bicarbonate, as
great a diminution of temperature as had occurred with the carbonate, or the
thermometer would have sunk 2°.4 instead of rising .4°. But the conversion of
the second atom of carbonic acid into the gaseous state is completely effected,
while a considerable portion of the first atom remains dissolved in the liquid ;
and consequently, the striking difference in the result can only be accounted for,
on the principle stated in the second law, that the combination, or separation of

during the Combination of Acids and Bases. 245

the second atom of carbonic acid is attended with no evolution or abstraction of
heat.

51. The tribasic, phosphoric, and arsenic acids, in their combinations with
the fixed alcalis, present a slight divergence from this law, and at the same time,
give results closely coincident with each other. In the following table, the
increments of temperature are exhibited which were observed, when solutions,
containing the compounds denoted by the first and second members of the ex-
pression, were mixed together. The symbol NaO corresponds, as before, to
.234 gr. soda, and the entire weight of the solution was 30 grammes.

POUND.

COBRECTKD,

(NaO + ^PA) + ^PA •

, 0°.40 .

. 0°.46

(NaO + fPA)+iPA •

. 0°.30 .

. 0°.35

52. In other words, the combination of the common phosphate of soda with
half as much acid as it already contains produces an increment of temperature of
0°.46 ; and its complete conversion into the biphosphate, a farther increase of
0°.35. Similar numbers were obtained with the arsenic acid.

(NaO+^-AsA) + iAsA •
(NaO + 1 As,0,) + iAs,0, .

54. The same acid gave with potash,

55. From these experiments it follows, that during the conversion of the
common alcaline phosphates and arseniates into supersalts, a quantity of heat is
evolved, which is about one-seventh part of that produced during the formation
of those salts themselves. As, however, the alcaline phosphates and arseniates
are not strictly neutral in composition, and their solutions have an alcaline re-
action, it is, perhaps, scarcely correct to adduce them as exceptions to Law 2.
The pyrophosphoric acid, in similar circumstances, scarcely produces any beat ;

FOUND.

COKRECTED.

0°.40 .

. 0°.46

0^35 .

. 0°.40

FOUND.

CORRECTED,

0°.80 .

. 0°.93

FOUND.

CORRECTED.

0°.15 .

. 0M7

0°.00 .

. o°.oo

246 Dr. Andrews on the Heat developed

resembling, in this and its other thermal properties, the ordinary acids. Denoting
the pyrophosphoric acid by Pyr. we have,

(NaO + ^PyrA)+iPyrA
(NaO+|PyrA) + iPyr.A

55. The formation of the alcaline subphosphates and subarseniates, by the
direct union of the common phosphates and arseniates, with an additional
equivalent of base, is accompanied with a definite evolution of heat. On adding
to solutions of these salts, containing the equivalents of alcali before referred to
(NaO, .234 gr. KO, .353 gr.), alcaline solutions having half as much base as was
already in the salts themselves, I obtained very uniform results.

FOUND.

CORRECTED.

(NaO + ^-PA) + ^NaO .

. . r.7 .

. r.97

(NaO + ^AsA)+^NaO .

. r.7 .

. r.97

(KO + ^AsA) + ^KO . .

. r.7 .

. r.97

(NaO + iPyrA) + iNaO .

. OM .

. 0°.12

56. That the heat produced was connected with the formation of the sub-
salt, appears distinctly from the circumstance, that a further addition of alcali
was not attended with any increase of temperature. The absence of any heat in
the case of the pyrophosphate of soda is easily explained on the same principle,
as Graham has shown that no subpyrophosphate of soda exists.

57. The formation of these subsalts exercises a remarkable influence on the
quantities of heat developed, when the base is neutralized by successive portions
of acid. In ordinary cases, the heat evolved in this way is proportional to the
quantity of acid added. Thus, on mixing a solution of pure potash with one-
fourth, one-half, &c., an equivalent of nitric acid, the elevations of temperature
will be one-half, one-fourth, &c. of what is observed when the alcali is completely
neutralized. And the same principle I find to hold good, when successive por-
tions of the phosphoric (tribasic) and arsenic acids are added to solutions of the
pure alcalis, till the subsalts are formed ; but, after that point, a very different
law is followed, as will be seen in the next tables :

FOUND.

CORRECTED.

4°.65

5''.40

0.90

1 .04

4°. 75

5°. 5 1

.85

.99

4.80

5°.57

.90

1 .04

during the Combination of Acids and Bases. 247

I. NaO + iP,0„ . . .
(NaO + ^PA+F^OJ .

II. NaO + ^AsA. •

(NaO + ^AsA) + MsA. •

III. KO + ^AsA

(KO + ^AsA)+iAsA .

58. Had the evolutions of heat corresponded with the additions of acid the
second numbers would have been one-half of the first in each set of experiments.
Hence, the increments of temperature for equal portions of acid are nearly as
2.5 : 1, before and after the formation of the subsalt. The pyrophosphoric acid,
on the contrary, presents no similar irregularity, developing equal increments of
heat, for equal additions of acid, till the pyrophosphate of soda (NaO -{- i|PyrA)
is formed.

59. It may, perhaps, be prematnre, from such imperfect and limited data, to
offer any general observations on the preceding experiments ; but I shall, never-
theless, venture to show the accordance of laws second and third, with those
general views of the constitution of the salts which have been so ably illustrated
by Graham. The conversion of a neutral into an acid salt being in reality the
formation of a double salt, is not accompanied by any disengagement of heat ;
because such combinations as the latter do not evolve heat. No caloric is
extricated when the tartrates of potash and soda unite ; and, consequently, none
ought to be given off, when the tartrate of soda is combined with the tartrate of
water. But, on the other hand, heat is disengaged when the base in the tartrate
of water is replaced by soda; because soda, in its combinations with the acids,
evolves much more heat than water. How far the heat evolved in the formation
of the different hydrated acids may be the same, is an interesting question not
yet determined ; but there can be little doubt that water holds a very low rank
among the bases, in reference to its power of generating heat when combining
with the acids. On the same principles, and again referring to the observations
of Graham, we can understand the cause of the evolution of heat during the

248 Dr. Andrews on the Heat developed, Sfc.

conversion of the neutral phosphates and arsenlates Into basic salts. In reality,
an equivalent of water is here again replaced by an equivalent of alcali, just as
occurs in the direct combinations of the acids and alcalis.*

* When the experiments detailed in the foregoing paper were almost completed, I received
the 6th No. oiPoggendorff's Annalen, for 1840, containing the first part of a valuable Memoir, by
M. Hess, entitled " Thermo-chemical Researches." The experiments detailed by M. Hess refer
principally to the heat developed when sulphuric acid and water combine together — a subject not
touched upon in the present paper. He has, however, extended his inquiry to the heat evolved
during the combination of sulphuric acid with potash, soda, ammonia, and lime ; and also of hydro-
chloric acid with potash, soda, and ammonia. But the results obtained by M. Hess cannot be im-
mediately compared with those given in this communication, as his experiments were performed
with stronger acids, which disengaged heat when diluted with water. The quantity of heat thus
extricated, M. Hess has shown to be the same, whether the acid and water be mixed together in
presence of a base or alone ; and he has likewise furnished accurate data, by means of which the
heat derived from this source, in his experiments, may be estimated. Now, assuming with him,
as a term of comparison, the number of grammes of water which would be heated through 1° cen-
tigrade, by saturating with each alcali 1 gramme of sulphuric acid, or the corresponding equivalent
(0.908 gr.) of hydrochloric acid — all taken in the state of very dilute solutions — we deduce from the
foregoing tables the numerical results in the first of the following columns ; while those in the second
are derived from the memoir of M. Hess :

TABLES. HESS

rPotash, 407 . . .406

Sulphuric Acid with . . -s Soda,

■

Ammonia,

C Potash,
Hydrochloric Acid with < Soda,

V. Ammonia,

413 . . . 411

352 . . . 403

364 .. . 362

373 . . . 368

310 . . . 318

It is very satisfactory to observe how closely these numbers agree with each other, with the
single exception of that which expresses the heat evolved when sulphuric acid and ammonia com-
bine. The cause of this discrepancy I have endeavoured in vain to discover ; but it probably depends
upon some condition in the experiment of M. Hess, which may have escaped my observation.

■?;«nj A^.'TOL.XE>. EOS

SCEITCE PIATE .m .

9 O

Hb

fi'l o

-H'

JJf>*.,.iJi!

249

X. Supplement to a Paper " On the mutual Action of permanent Magnets,
considered chiefly in Reference to their best relative Position in an
Observatory." By the Rev. Humphrey Lloyd, D.D., Fellow of Trinity
College, and Professor of Natural Philosophy in the University of Dublin,
F.R.S., V.P.R.I.A., Honorary Member of the American Philosophical
Society.

Read April 26, 1841.

In a former paper I have investigated the conditions of equilibrium of the
forces exerted upon one another by three magnets, such as those employed in
the Dublin Magnetical Observatory, and in the Observatories since established
by the British government, in observing the three elements* of the Earth's
Magnetic Force. The axes of these magnets being supposed to lie in the same
horizontal plane, the forces which they exert upon one another are necessarily
directed in that plane ; and the conditions of equilibrium of these forces are
expressed hy five equations, the forces exerted upon one of the magnets, in the
direction perpendicular to its axis, being destroyed by the reaction of its sup-
ports. To fulfil these conditions, there are only four arbitrary quantities, —
namely, the angles v^rhich the lines connecting the centres of the three magnets
make with the magnetic meridian, and the azimuth of the axis of one of the
magnets. Hence it followed, that complete equilibrium was not attainable,
except for determinate values of the relative forces of the magnets. I was,
therefore, compelled to select among the conditions of equilibrium, all of which

* These elements are the declination, and the horizontal and vertical components of the force.
The magnets employed in observing the first and second of these elements are capable of motion in
the horizontal plane, the axis of the first being in the magnetic meridian, and that of the second
perpendicular to it ; the third magnet, being supported on knife-edges, is capable of motion only in
a vertical plane, and its azimuth is arbitrary.

VOL. XIX. 2 K

250 The Rev. H.Lloyd on the mutual Action of permanent Magnets.

are not of equal practical value ; and I was thus led to consider some less
complete solutions of the problem, in which three, or even two only, of these
conditions are satisfied.

But all these solutions are exposed to the objection, that the positions
of the magnets which fulfil the conditions are dependent upon their relative
forces, and are, therefore, subject to vary along with them : — in other
words, that upon any change of these forces, the equilibrium already effected
will be destroyed, and a new arrangement of the magnets be required to
restore it.

To obviate the inconvenience arising from such a displacement of the
magnets employed in the observations, it has been suggested to fulfil the con-
ditions of equilibrium by means of additional magnets, whose positions could be
readily altered as the forces varied. To this, however, there are serious objec-
tions. In the first place, by thus increasing the number of balancing actions,
the chances of error in the positions of the centres of force, as well as the
liability to alteration in their intensities, are multiplied ; and, secondly, on
account of this liability to change, no absolute measurement could be safely
made, without a re-examination of the relative forces of the magnets, and a
readjustment of their positions ; so that nothing appears to be gained.

Under all these circumstances, the best course appears to be, to satisfy so
many of the conditions of equilibrium, as are capable of being fulfilled independ-
ently of the relative forces of the magnets, and to apply corrections for the
actions which remain unbalanced. In this manner, the changes which the forces
of the magnets may undergo, in process of time, will not disturb the equilibrium
which has been effected ; and the unbalanced actions, being in definite directions,
will admit of being determined by an easy experiment, and allowed for by a
simple correction.

In order that any one of the equations of equilibrium* may subsist inde-
pendently of the ratios of the forces of the magnets, the part which contains one
of these ratios, and that which is independent of it, must separately vanish, and
the five equations are resolved into the following :

* Equations (10, 11, 12, 13, 15), pp. 167, 170.

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 251

3 cos (2)3 — f ) + cos f = 0, sin 27 = 0 ; (1)

3 sin (2/3 — f ) + sin f = 0, 1 — 3 cos 27 = 0 ; (2)

3 cos (2a — f ) + cos f = 0, 1 + 3 cos 27 = 0 ; (3)

3 sin (2a — f ) + sin f = 0, sin 27 = 0 ; (4)

3 cos (2^ — ^) + cos ^ =z 0, 3sin(2a-^) + sinf = 0. (5)

Now it will be seen, on a little consideration, that of these five pairs of
equations, the equations (2) and (3) exclude, each, the other four ; so
that if we fulfil the condition expressed by (2), or that expressed by (3), in
this way, we cannot at the same time satisfy any other. On the other hand,
each pair of the remaining conditions, expressed by the equations (1, 4, 5),
has one equation in common ; so that for the fulfilment of these three con-
ditions, three equations only are to be satisfied ; and these three equations
are not only not inconsistent, but even leave one of the angles still un-
determined.

These equations are

sin 27 = 0, (6)

3cos(2/3 — 0 + cosf = 0, (7)

3 sin (2a — f ) -f sin f =: 0. (8)

The first of them determines the angle 7 ; and as the other two contain three
arbitrary angles, they maybe fulfilled in an infinite variety of ways. Accordingly
we must have

7 = 0, or 7 = 90°; (9)

that is, the line connecting the magnets a and b must be parallel or perpen-
dicular to the magnetic meridian. And the angles, a, /3, f, which determine
the place and azimuth of the third magnet, are connected by the relations,

^ + cos2^_ sin2a ,

sin2i3 - ^'^^^-i- cos 2a' ^^"^

so that when one of these angles is assumed or given, the other two are deter-
mined.

2 k2

252 The Rev. H. Lloyd on the mutual Action of ■permanent Magnets..

The natural course is to assume the azimuth of the magnet c, and thence
determine the place of its centre. Let us suppose, then, that the plane of the
magnet c is parallel to the magnetic meridian, or that

The equations (J, 8) then give,

cos 2j3 = — ^, sin 2a = 0 ;

and these two equations, together with (6), solve the problem. As we cannot
have 7 = 0, a = 0, simultaneously, there are two solutions, namely :

7=0, a = 90°, 1

S = 54° 44'.
7 = 90°, a = 0, J ^

The corresponding arrangements of the magnets are represented in Figs. 1
and 2.

Again, if the plane in which the magnet c is constrained to move be perpen-
dicular to the magnetic meridian, or

f = 90°,

the equations (^, 8) are then reduced to

sin 2^ = 0, cos 2a = ^ ;

which, in conjunction with (6), furnish the two solutions :

7 = 0, /3 = 90°,"

, a = 35° 16'.
7 = 90°, 13 = 0,

These arrangements are represented in Figs. 3 and 4.

In estimating the comparative merits of these four arrangements, we should
observe that the magnet c is usually much less massive, and therefore less
powerful than either of the other two ; and, accordingly, that the arrange-
ments represented in Figs. 1 and 4, in which the distance, ab, of the stronger
magnets is the shortest side of the triangle abc, are, on that account, in-

The Rev. H. Lloyd on the mutual Action 0/ permanent Magnets. • , 253

ferior to those represented in Figs. 2 and 3. Of the latter, the arrange-
ment (Fig. 3) is to be preferred, where our object is to diminish as much as
possible the residual action upon the declination magnet, A ; and, on the other
hand, the arrangement (Fig. 2) should be chosen, if we prefer to diminish the
action upon the magnet b.

There is still another particular disposition which deserves to be considered :
that, namely, in which the magnet c is equally distant from the other two. This
condition is expressed by the relation,

a + p^lSO";

and eliminating, by means of it, the angle /3 in (10), we have

cos 2a -|- ^ sin 2a

sin 2a cos 2a — ^ '

whence cos'' 2a — sin* 2a zz ^, sin 2a ^ ± ^, and

a = ± 20° 54'.
Again, substituting this value in (10), we have

tan f = -i-^- = d= 1.6180, f = 58° 17', or = 180° - 58° 17'.
^/5 — 1

Accordingly, the arrangement of the magnets is that represented in Fig. 5,
or the reverse arrangement, in which the magnet c is in the corresponding
position on the opposite side of the line ab.

Let us now consider, briefly, the corrections required for the residual actions,
and the manner in which they are to be experimentally determined.

In virtue of the equations (6) and (7), the action exerted by the magnets b
and c upon a, in the magnetic meridian, is null ; the disturbing action is, there-
fore, perpendicular to the meridian, and operates only as a deflecting force.
The amount of the deflection produced by this resultant force is easily deter-
mined ; for we have only to reverse the magnets b and c simultaneously, and it
is obvious that the difference of the readings of the magnet a, in these two
positions of the deflecting magnets, is double the deflection sought. In order to

254 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

eliminate the actual changes of declination which may occur in the interval of
the two parts of the observation, simultaneous observations should be made with
an auxiliary apparatus in another apartment ; or, should such an apparatus be
not at hand, the effect of the changes may be got rid of by making a series of
readings of the magnet a, with the deflecting magnets alternately in the two
positions. The amount of the deflection, thus determined, is to be applied
as a correction in measurements of the absolute declination : being a constant
quantity, or nearly so, its effect upon the declination changes may be disregarded.
Lastly, there being no disturbing force upon the magnet a, in the magnetic
meridian itself, the absolute horizontal intensity, determined by experiments of
vibration and deflection, according to the method of Gauss, will need no cor-
rection.*

On the other hand, the disturbing force exerted upon the magnet b, by the
other two, is directed in the magnetic meridian itself, and therefore con-
spires with, or opposes, the force of the earth. The correction required for
its action is determined with the same facility as in the former case. We have
only to reverse the magnets a and c simultaneously, and to note the change of
position of the magnet b thereby produced. Half the change, converted into
parts of the whole force by multiplying it by a coefficient already known, is the

ratio, -, of the disturbing force to the total force ; and, in order to correct for this

f
force, we have only to multiply the observed results by the coefficient 1 ::p -, usmg

F

the upper sign when the disturbing action conspires with that of the earth, and
the lower when it is opposed to it.

Finally, with respect to the magnet c, the disturbing action, being perpen-
dicular to the plane in which the magnet is constrained to move, is destroyed by
the reaction of its supports, and no correction is needed.

* The remdtani of the force of the earth, and of the disturbing action, will of course differ,
theoretically, from the former ; but, in genera), by an inappreciable amount. If x denote the
earth's horizontal force, and J the deflection produced by the disturbing action, the resultant force
will be X secant i. Now, supposing J to be two minutes (which is greater than any amount it can
have with magnets of the size of those employed in the Dublin Observatory, and at the distances
recommended below) the resultant force will exceed x by the quantity .0000002x.

The Rev. H. Lloyd on the mutual Action of permanent Magnets. 255

It may be useful to suggest, in a few words, the form of building adapted to
these arrangements.

For the arrangement represented in Fig. 3, the ground-plan of the building
may be a square, whose sides (24 feet in length) are parallel and perpendicular
to the magnetic meridian, (Fig. 6). This area may be conveniently divided into
four parts, viz. : a principal room, 24 feet in length and 16 feet in width ; two
subordinate rooms, and a vestibule. The principal room should contain the
magnets a and b, which may be placed at an interval of 18 feet,* the joining
line being the axis of the room. Two pedestals, a' and b', (at an interval of
4^ feet), will serve to support the reading telescopes ; and the observer's chair
may be placed between them. The magnet c should be placed in one of the
small rooms, its distance from the magnet a being ac = ab X tang 35° 16' =
18 X 0.707 = 12.73 feet. In order to diminish, as far as possible, the de-
flecting force exerted by the magnets b and c upon a, these magnets should
have their poles similarly placed (i. e. the same pole in each turned to the east) ;
for, in this case, the resulting action is the difference of the forces exerted by
the separate magnets.

It will be convenient to fix another pedestal, D, for the support of an incli-
nation instrument, in the second of the small rooms, and at the point corres-
ponding to c in the first ; — the line bd being perpendicular to . the magnetic
meridian, and the distance bd = ac. It is manifest that, in this position, the
action of the magnets b and c upon a magnetic particle at d will be perpen-
dicular to the magnetic meridian ; and will, therefore, have no effect upon the
position of the inclination needle, being destroyed by the reaction of its supports.
And, in order that the action of the magnet a may be in the same direction, it is
only necessary to turn it round, so that its axis may lie in the line ax, which
makes with the magnetic meridian an angle bax = bad. For tan d = v'2 ;

and tan dax = 5 z: 2 v''2 ; so that tan d = ^ tan dax, and db is the

* At this distance, the deflection produced by the magnet b upon A, (the deflecting magnet
being of the size and power of those employed in the Dublin Magnetical Observatory), is only
about 1^ minutes ; and the greater part of this small disturbance will be annulled by the opposing
action of the magnet c .

256 The Rev. H. Lloyd on the mutual Action of permanent Magnets.

direction of the force exerted by the magnet a (in that position) upon the point
D. This temporary adjustment of the magnet a may be at once effected by
means of a line drawn on the supporting pedestal ; and it is obvious that it
may be accomplished v^'ithout removing the magnet from its stirrup, or inter-
fering in any vpay with its permanent adjustments.

The building required to receive the magnets, in the arrangement repre-
sented in Fig. 5, may be still simpler ; consisting only of a single room, 26 feet
in length, and 16 feet in width, and having a portico with a second door, to
prevent draughts of air, (Fig. 7).

To find a suitable place for the inclination instrument, we have only to
determine the point on the line ab, at which the action of the magnet c is per-
pendicular to ab. Then, the action of the magnet b being perpendicular to
AB at every point of this line, the forces exerted by b and c will be perpendicular
to the meridian, and will therefore be destroyed by the reaction of the sup-
ports ; and, in order that the same thing should hold also for the magnet a,
we have only to turn that magnet, temporarily, into a position perpendicular to
the meridian.

Let D (Fig. 5) be the point sought, and do a line perpendicular to ab ;
then the condition requires that tan cdo :=. ^- tan ocd ; or, denoting the angle
CDA by x, cotan x = 7]- tan {x — 58° 17')- Whence, developing and substituting
the value of tan (58° 17')» we have the following quadratic for the determi-
nation of tan X,

tan -X — 4.854 tan a; — 2 = 0.

Accordingly, tan 3; = 5.236, or =: — 0.382 ; and :r = 79° 1 1', or r= — 20°
54', Of these solutions the former is that adapted to the present purpose ; the
latter giving the point a itself.

The pedestal erected at the point d will likewise serve to support the reading
telescope of the magnet b, which may be inserted in a groove cut in the top, so
as not to interfere with the other instrument. The supporting pedestal of the
telescope of the magnet a should be on the line da, its centre being four or five
feet from the point d, so as to admit the observer's chair between the two
pedestals.

257

XI. Supplementary Researches on the Direction and Mode of Propagation
of the electric Force, and on the Source of electrical Development. By
George J. Knox, Esq., A. M., M. R. I. A.

Read May 25th, 1840,

XI AVING in my former paper* described some experiments which proved that
water and phosphorus convey a current of electricity through their substances,
while metals convey the current along their surface, and feeling anxious to
discover some general law regarding the direction of propagation in liquid and
solid bodies, I have continued the investigation to fluids ; not only those which
convey the feeble current of the voltaic pile, but to others which require the
high intensity of the electrical machine ; and although the experiments be few,
yet I think that they may be considered to be sufficient to establish the law
regarding fluids, that they convey through their substance in all directions alike ;
an opinion which one would be inclined to adopt previous to experiment, from
considering the difference between the nature of liquid and solid bodies, the one
having their particles chained down by powerful affinities, which no ordinary
electrical force can overcome, while the other, from the perfect mobility of their
particles, allow the electric state to be induced upon them with equal facility in
one direction as well as another.

That there exists no regular law with regard to solids, appears from the
Researches of Dr. Faraday (XI. and XIV. Series), in which he shows, that the
lines of induction do not pass through metallic bodies (1221), (affording a corro-
borative proof to mine that they do not convey through their substance), while
several solid bodies, such as shell-lac, sulphur, &c. (1228, 1308, 1309, 1310),
allow the inductive force to pass through them with greater facility even than
air.

• Tran. R. I. A., vol xix. p. 147 ; Phil. Mag. vol. xvi. p. 185.
VOL. XIX. 2 L

258 Mr. Knox on the Direction and Mode of

EXPEKIMENTS.

The bent glass tube which I employed In my former experiments having been
filled alternately with muriatic acid, hydriodic acid, sulphate of copper, and mu-
riate of ammonia, and the circuit being completed by a current from a sustaining
battery of one pair of elements, the same law was found to subsist as when water and
phosphorus were employed, i. e. that the current passed through their substance
and not along their surface. The same likewise took place when the tube was
filled with fused chloride of tin, which conducts by electrolysis, and fused periodide
of mercury, which conducts by conduction.

To determine whether this law with regard to liquids which convey a gal-
vanic current subsists when non-conducting fluids are employed, I filled the
tube alternately with alcohol, naphtha, oil, fused lard, bees' wax, and resin, and
having connected one of the insulated wires with the ground, I connected the
other with an insulated brass ball, fixed at the distance of four-tenths of an inch
from the prime conductor, of a nine inch electrical machine.

ALCOHOL OR NAPHTHA.

When the platinum wires were immersed in the legs of the bent tube until
their extremities were placed at the distance of five inches, ten sparks passed in
one revolution of the plate ; when at two feet distance, eight sparks ; when at four
feet distance, six sparks.

OIL.

At the distance of five inches, seven sparks passed in one revolution of the
plate; at the distance of two feet, four sparks passed ; and at the distance of four
feet, two sparks passed in one revolution.

FUSED LARD.

At the distance of five inches, two sparks passed in one revolution of the
plate ; at the distance of two feet, one spark in one revolution ; at the distance of
four feet, one spark in three revolutions.

bees' wax.
At the distance of five inches, one spark passed in one revolution of the
plate ; at the distance of two feet, one spark in one revolution and a half; at the
distance of four feet, one spark in two revolutions.

Propagation of the Electric Force. 259

RESIN.

At the distance of five inches, one spark passed in one revolution of the
plate ; at the distance of two feet, one spark in two revolutions ; at the distance
of four feet, one spark in two and three-fourth revolutions.

These latter substances begin to conduct when in the viscid state, and the
conducting power Increases up to the boiling point.

SOURCE OF ELECTRICAL DEVELOPMENT.

Before reconsidering the source of electrical development, I shall briefly
mention the arguments which may be brought forward against the emission, and
in favour of the vibratory theory, the former supposing a transference of elec-
tricity from particle to particle, the latter assuming that the atoms of matter
are encircled with ethereal atmospheres, the atoms of which can oscillate within
certain distances. The arguments in favour of this latter theory, independent
of such as the mathematician may bring forward, rest upon the hypothesis
proposed by Sir H. Davy,* " which, after a lapse of twenty years, continued,
as it was in the beginning, to be the guide and foundation of all his re-
searches;" a theory now almost universally received as established — that chemical
affinity is an electrical phenomenon, and that the entire subject of chemistry
is an illustration of that primary law of electricity, the attraction of oppositely
electrical bodies. If the electric forces which cause the attraction of bodies be
definite, as they are, being their atomic numbers, how can this be consistent with
a theory which supposes that the electricity leaves the particles, allowing them at
one moment to contain more electricity than at another, and, consequently, a
higher affinity, and a different atomic number ?

When two atoms are brought into contact, their electrical ethers, being
disturbed, cause a disturbance to take place in the electrical ethers of adjacent
atoms, which disturbance should increase until it arrives at a maximum, when
combination takes place. The same may be said of the compound atoms or
molecules, of the compound molecules or particles, and of the compound par-
ticles or bodies en masse ; and that such a development of electricity by contact
of the latter does take place, the original experiments of Volta, together with

• Bakerian Lecture, 1807-1826.

2 l2

260 Mr. Knox on the Direction and Mode of

the late experiments of Fechner and Peclet, have fully established. Fechner*
has proved (having shown that the same experiment was incorrectly tried by
Delarive), that when potassium, or sodium, are brought into contact with pla-
tinum, electrical development takes place without chemical action. Pecletf has
proved that electrical excitation is caused by the contact of platinum and gold,
wherk chemical action could not take place. In support of the opposite opinion
is the experiment of Delarive,| who found, that when chlorine gas is passed
through an insulated copper tube, the condenser exhibits electrical develop-
ment, which, he remarks, decreases when chlorine, unmixed with atmospheric air,
is employed, and also when the chemical action between the chlorine and copper is
violent ; circumstances which admit of a simple explanation by the contact theory,
according to which the air receives an electrical charge from the chlorine while in
contact with the copper, which charge so much of the gas as combines with the
copper loses. The same explanation may be given to the experiments of Peclet,§
who has satisfactorily shown that the presence of moisture is necessary in order
that the oxidation of the amalgam on the rubber of an electrical machine should
develope electricity, the aqueous vapour in this case receiving the charge.
Experiments, then, having proved, that contact and not chemical action causes
the development of electricity, the question arises, how are we to explain the
phenomena ? When two atoms unite, it is difficult to avoid the conclusion, that
the compound atom (molecule) must have oppositely electrical surfaces. Two
such polarized molecules approaching cause a disturbance to take place in the
electrical ether, which disturbance is propagated by induction to a distance; but
when the molecules approach sufficiently near to combine, the two oppositely
electrical surfaces of one molecule coming in contact with the two oppositely
electrified surfaces of the other, no development of electricity can take place,
the electrical states becoming completely disguised ; and such a supposition is
borne out by every fact in crystallography, which shows that the molecules have
poles. The particles being compound molecules should have poles likewise ; and
when they unite, or chemical combination takes place, there should be no de-
velopment of electricity ; and, consequently, when oxygen unites with zinc (as in

* Phil. Mag. vol. xiii. 1838. f Annales de Chimie, fom. Ixxi. p. 80.

X Bib. Univer. N. S. torn. iii. kj Annales de Chimie, torn. Ixxi. p. 83.

Propagation of the Electric Force. 261

the galvanic battery) no development of electricity should take place from
their union ; but the hydrogen, whose positive pole had been previously united
with the negative pole of the oxygen, should induce negative electricity upon
the oxide, while the negative pole should induce positive electricity upon the
next particle, and so on to the platinum plate.

The greater the number of particles of hydrogen inducing electricity upon
the platinum plate, the greater, of course, the quantity of electricity induced upon
that plate ; the number of particles of hydrogen being the measure of the quan-
tity, whether it was oxygen, chlorine, iodine, or bromine, with which the
hydrogen may have been previously in combination ; and that such is the case is
proved by experiment. That alternate recombinations and decompositions take
place has been shown by Grothhus and Faraday.

How beautiful is the analogy which subsists between statical and voltaic
electricity when the contact theory is adopted ! By friction (lateral contact)
between silk and glass opposite electrical states are induced upon each. By the
contact of zinc with a dry acid, or alkali, opposite states are induced upon each.
When the plate of the electrical machine is put in motion, the prime conductor
receives a charge whose intensity is directly as the non-conducting or insulating
nature of the glass, and as the distance between the collecting forks and the
rubber when the axis is made of glass. When the zinc is placed in contact with
the acid, or alkali in solution, the charge is allowed to pass from the zinc to the
platinum, being in this case a charge by induction, as in the former case it was
one by convection ; and the intensity varies as the insulating state of the solution,
and as the distance between the platinum and zinc, as is proved by the experi-
ments of Delarive,* which show that the water battery charges to a higher
intensity than the acid battery, although it takes a longer time than the latter to
charge to a given amount. Again, when a small electrical machine is rotated
rapidly, while a larger one is rotated slowly, the former will charge to a given
intensity in a shorter time than the latter, although it never can rise to an equal
intensity. So in the acid and water batteries, the former, owing to the rapidity
of alternations of induction and equilibrium, charges to a given intensity In a
shorter time than the latter, yet still it never can rise to an equal intensity.
Similarly may be explained why, when two metals in a solution form a closed

* Bib. Univer. torn. iv. p. 360.

262 Mr. Knox on the Direction and Mode of

circuit, whatever increases the chemical action upon one more than upon the
other, increasing the rapidity of alternate states of induction, produces a charge
in a shorter time ; and this takes place not only when two different metals are
employed, but also, when plates of the same metal being used, a difference of
polish or a difference of heat applied alters the chemical action upon one plate
more than upon the other. A further analogy is faintly borne out by the
following experiments, which may lead to an explanation of some curious facts
regarding the alternate increase and decrease of intensity in the voltaic pile,
dependent upon the number of alternations, as observed by Delarive* and others.
Having connected, by means of insulated copper wires, the insulated conductors
of an electrical machine, with two insulated brass balls, the spark that passed
between the two balls measured one-fourth of an inch. When the insulated
negative conductor of this machine was connected with the insulated prime
conductor of another similar one, and its insulated negative conductor with one
of the brass balls, and the two machines rotated simultaneously, the length of
the discharging spark was increased to one-half; with three electrical machines
similarly arranged, the length of the spark which passed was one-third ; with
four, it returned to one-half; beyond this number no regularity in the length
of the discharging sparks was observable. The quantity in the electrical ma-
chine increases with the number of collecting forks, when the rubbers and forks
are disposed in such a manner, that the latter can receive the greatest quantity
of electricity from the excited glass ; so in the voltaic pile, the quantity is as the
number of particles of hydrogen set free against the surface of the platinum.

The effect which a current of electricity, considered to be a row of particles
whose oppositely electrified surfaces are ranged in the same direction, undergoing
alternate states of induction and equilibrium, produces upon contiguous particles,
should be to induce in them oppositely electrified surfaces, which, in undergoing
alternate states of induction and equilibrium, should obviously give rise to a cur-
rent of electricity in an opposite direction, — and this is agreeable to fact.

To afford an explanation of magnetism, considered as an electrical phenomenon,
no theory as yet proposed is adequate. That of Ampere (although exceedingly
beautiful) is yet all but physically impossible, for how can we suppose that when
the electrical current which magnetizes a steel bar ceases, the electricity in the

* Bib. Univer. Tom. iv. p. 360.

Propagation oftlie Electric Force. 2()3

bar continues to revolve round the particles of the steel ? Does not the marked
difference between iron and other metals, and between steel and soft iron in the
same metal, show that magnetism (if electrical) must be a case of statical electri-
city ? What arrangement of electrified bodies may produce such a state of
statical power may possibly be within the reach of experiment ; but to deter-
mine the condition of the electrical ether in a bar of steel, is a question which, as
it regards the mutual actions of systems of attracting and repelling points, being
far beyond the reach of experiment, requires for its solution a higher, more
elegant, and more comprehensive instrument of research, mathematical analysis.

264

XII.— Ow Fluctuating Functions. By Sir William Rowan Hamilton,
LL. D., P. R. I. A., F. R, A. S., Fellow of the American Society of Arts
and Sciences, and of the Royal Northern Society of Antiquaries at Copen-
hagen ; Honorary or Corresponding Member of the Royal Societies of
Edinburgh and Dublin, of the Academies of St. Petersburgh, Berlin, and
Turin, and of other Scientific Societies at hom^, and abroad ; Andrews'
Professor of Astronomy in the University of Dublin, and Royal Astronomer
of Ireland.

Eead June 22nd, 1840.

The paper now submitted to the Royal Irish Academy is designed chiefly to
invite attention to some consequences of a very fertile principle, of which indica-
tions may be found in Fourier's Theory of Heat, but which appears to have
hitherto attracted little notice, and in particular seems to have been overlooked
by PoissoN. This principle, which may be called the Principle of Fluctuation,
asserts (when put under its simplest form) the evanescence of the integral, taken
between any finite limits, of the product formed by multiplying together any two
finite functions, of which one, like the sine or cosine of an infinite multiple of an
arc, changes sign infinitely often within a finite extent of the variable on which it
depends, and has for its mean value zero ; from which it follows, that if the other
function, instead of being always finite, becomes infinite for some particular values
of its variable, the integral of the product is to be found by attending only to the
immediate neighbourhood of those particular values. The writer is of opinion
that it is only requisite to develope the foregoing principle, in order to give a
new clearness, and even a new extension, to the existing theory of the transfor-
mations of arbitrary functions through functions of determined forms. Such is,
at least, the object aimed at in the following pages ; to which will be found
appended a few general observations on this interesting part of our knowledge.

SiE William Rowan Hamilton on Fluctuating Functions. 265

[1.] The theorem, discovered by Fourier, that between any finite limits,
a and b, of any real variable x, any arbitrary but finite and determinate function
of that variable, of which the value varies gradually, may be represented thus,

1 (** C®
fx zz -\ da\ d^cos (/3a — Px)/a, (a)

with many other analogous theorems, is included in the following form :

/x = \ da\ dp(f)(x,a,^)fa; (b)

the function 0 being, in each case, suitably chosen. We propose to consider
some of the conditions under which a transformation of the kind (b) is valid.
[2.] If we make, for abridgment,

^|r{x,a,p) = \ c?p0(ar,a,/3), (o)

the equation (b) may be thus written :

Jx =:\ dayjf (x, a, <x)fa. (d)

This equation, if true, will hold good, after the change of/a, in the second
member, to/a -\- va ; provided that, for the particular value a = a?, the additional
function Fa vanishes ; being also, for other values of a, between the limits a and
h, determined and finite, and gradually varying in value. Let then this func-
tion F vanish, from a = a to a = \, and from a=:/xto a^6; \ and jjl being
included, either between a and x, or between x and h ; so that x is not included
between \ and fi, though it is included between a and b. We shall have, under
these conditions,

0=\ (/a 1^ (x, a, go) Fa; (e)

the function f, and the limits \ and fi, being arbitrary, except so far as has
been above defined. Consequently, unless the function of a, denoted here by
■^ (or, a, 00 ), be itself = 0, it must change sign at least once between the limits
azz\ a=: n, however close those limits may be ; and therefore must change
sign indefinitely often, between the limits a and x, or x and b. A function

VOL, XIX. 2 m

266 Sir William Rowan Hamilton on Fluctuating Functions.

which thus changes sign indefinitely often, within a finite range of a variable on
which it depends, may be called a fluctuating function. We shall consider now
a class of cases, in which such a function may present itself.

[3.] Let N„ be a real function of a, continuous or discontinuous in value,
but always comprised between some finite limits, so as never to be numerically
greater than ± c, in which c is a finite constant ; let

M„= ^ rfaN^; (f)

and let the equation

M« = a, (g)

in which a is some finite constant, have infinitely many real roots, extending
from — CO to -j- oc, and such that the interval a„^, — a„, between any one root
a„ and the next succeeding a„4.,, is never greater than some finite constant, b.
Then,

and consequently the function n must change sign at least once between the
limits a-=. a^ and a = a„^j ; and therefore at least m times between the limits
az=an and az=.a,^j^my this latter limit being supposed, according to the analogy
of this notation, to be the m"' root of the equation (g), after the root a„. Hence
the function n^„, formed from n„ by multiplying a by /3, changes sign at least m
times between the limits a = \, a =. n, if *

\ > P~^a„, /i < ^~' a„^„ ;
the interval /x — \ between these limits being less than |3~' (m -\- 2) b, if

\ > ^~'a„_„ /x < p~'a„^™^,;
so that, under these conditions, (j3 being >0,) we have

m > — 2 + |3b~'(/x — A).
However small, therefore, the interval /x — A may be, provided that it be greater

* These notations >• and -< are designed to signify the contradictories of > and < ; so that
" a > V is equivalent to " a not > b," and " a < b" is equivalent to " a not < b."

Sir William Rowan Hamilton on Fluctuating Functions. 267

than 0, the number of changes of sign of the function n^„, within this range of
the variable a, will increase indefinitely with /3. Passing then to the extreme or
limiting supposition, /3 = oo , we may say that the function n„„ changes sign
infinitely ofien within a finite range of the variable a on which it depends ; and
consequently that it is, in the sense of the last article, a fluctuating function.
We shall next consider the integral of the product formed by multiplying toge-
ther two functions of a, of which one is N^„, and the other is arbitrary, but finite,
and shall see that this integral vanishes.

[4.] It has been seen that the function n„ changes sign at least once between
the limits a:=an, a=:anj^y Let it then change sign k times between those limits,
and let the k corresponding values of a be denoted by a„ ,, a„ j, ... o^, 4. Since
the function n,. may be discontinuous in value, it will not necessarily vanish for
these k values of a ; but at least it will have one constant sign, being throughout
not < 0, or else throughout not > 0, in the interval from a = a„ to a = a„ , ; it
will be, on the contrary, throughout not > 0, or throughout not < 0, from a„^
to a„,2 ; again, not < 0, or not > 0, from a„ ^^ to a„ 3 ; and so on. Let then n„
be never < 0 throughout the whole of the interval from a„ ; to a„i^, ; and let
it be > 0 for at least some finite part of that interval ; i being some integer
number between the limits 0 and k, or even one of those limits themselves, pro-
vided that the symbols a„o, a„i^jare understood to denote the same quantities
as a„, Onj^y Let F„ be a finite function of a, which receives no sudden change of
value, at least for that extent of the variable a, for which this function is to be
employed ; and let us consider the integral

c?a N„F„. (1)

Let f' be the algebraically least, and f^^ the algebraically greatest value of the
function f„, between the limits of integration ; so that, for every value of a
between these limits, we shall have

F„ — f' <: 0, f'' — F„ < 0 ;

these values f^ and f^', of the function f„, corresponding to some values d„i and
a\i of the variable a, which are not outside the limits a^i and 0^,1 + 1- Then,
since, between these latter limits, we have also

2m2

268 Sir William Rowan Hamilton on Fluctuating Functions.

N„ <: 0,

we shall have

\ ' ^'rfaN„(F„ — F^) < 0;
\ rfaN„(F^^ — F„) <0;

(k)

s.

the integral (i) will therefore be not < *„ j f\ and not > *„,( f'\ if we put, for
abridgment,

and consequently this integral (i) may be represented by *„ , f', in which

f' < v\ f' D> f",
because, with the suppositions already made, s„_i > 0. We may even write

f' > f\ f' < f\

unless it happen that the function f„ has a constant value through the whole
extent of the integration ; or else that it is equal to one of its extreme values,
f' or f'\ throughout a finite part of that extent, while, for the remaining part of
the same extent, that is, for all other values of a between the same limits, the
factor N„ vanishes. In all these cases, f' may be considered as a value of the
function f„, corresponding to a value a'„i of the variable a which is included
between the limits of integration ; so that we may express the integral (i) as
follows :

in which

In like manner, the expression (m), with the inequalities (n), may be proved to
hold good, if N„ be never > 0, and sometimes < 0, within the extent of the
integration, the integral «„_j being in this case < 0 ; we have, therefore, rigo-
rously.

r«""4-i

\ rfa N. F, = *„,„ F,; -f5„,,F^ +... + *„,tF,i .

(0)

Sir William Rowan Hamilton on Fluctuating Functions. 269
But also, we have, by (h)

0 — Sn,o + Sn,y-\- •■•-{■ Sn,k; (p)

the integral in (o) may therefore be thus expressed, without any loss of rigour :

k

in which

n'hi + i

\ rfaN<.F„ = S„.„ A„,„ + ...4-*n.iA„,*, (q)

»JCL.

so that A„,i is a finite difference of the function f„, corresponding to the finite
diflference a'„i — a„ of the variable a, which latter difference is less than a„+i —
a„, and therefore less than the finite constant b of the last article. The theorem
(q) conducts immediately to the following,

\^_, c?aN^„F„ = /3 '(s„,„8„,„ + ... + ;?^a8„,*), (s)

in which

8„,i = F^-,„.^_. — F^-,„„; (t)

so that, if /3 be large, ?„_; is small, being the difference of the function f„ corres-
ponding to a difference of the variable a, which latter difference is less than
/3~'b. Let±8„be the greatest of the/c-l-l differences 2„,oj-'^n,*> or let it
be equal to one of those differences and not exceeded by any other, abstraction
being made of sign ; then, since the k-\-l factors 5„,o> •'■ \k are alternately posi-
tive and negative, or negative and positive, the numerical value of the integral
(s) cannot exceed that of the expression

But, by the definition (1) of 5„_i, and by the Umits ±c of value of the finite func-
tion N„, we have

±«n,i > (a«,i + l — «n,Oc; (v)

therefore

± (*»,o — «n,, + •■• + (— 1)* *n,*) > («« + , — a„) c ; (w)

and the following rigorous expression for the integral (s) results :

270 Sir William Rowan Hamilton on Fluctuating Functions.

i

"M + l

6„ being a factor which cannot exceed the limits ±1. Hence, if we change
successively n io n-\-\,n-\-2, ..n-\-ni ~\, and add together all the results,
we obtain this other rigorous expression, for the integral of the product n^„ f<j
extended from a =z j3~' a„ to a = |3~* a„^m :

\_ (^aN^„F„=0^-'(a„^,„-«,)c8; (y)

'^ n

in which 8 is the greatest of the m quantities 6„, 8„^j, ..., or is equal to one of
those quantities, and is not exceeded by any other ; and 6 cannot exceed ±: 1 .
By taking j3 sufficiently large, and suitably choosing the indices n and n-\-m,
we may make the limits of integration in the formula (y) approach as nearly as
we please to any given finite values, a and b ; while, in the second member of
that formula, the factor ^~' (a„ + „ — «„) will tend to become the finite quantity
h — a, and 6c cannot exceed the finite limits ±c ; but the remaining factor 8
will tend indefinitely to 0, as j8 increases without limit, because it is the difference
between two values of the function f,., corresponding to two values of the varia-
ble a of which the difference diminishes indefinitely. Passing then to the limit
^ zr GO, we have, with the same rigour as before :

■J)
da N,„ F„ = 0 ; (z)

which is the theorem that was announced at the end of the preceding article.
And although it has been here supposed that the function f„ receives no sudden
change of value, between the limits of integration ; yet we see that if this func-
tion receive any finite number of such sudden changes between those limits, but
vary gradually in value between any two such changes, the foregoing demonstra-
tion may be applied to each interval of gradual variation of value separately ;
and the theorem (z) will still hold good.

[5.] This theorem (z) may be thus written :

^

lim r* , ^ , ,\

= 00 3/«N^«F« = 0; (a)

Sm William Rowan Hamilton on Fluctuating Functions. 271
and we may easily deduce from it the following :

jSzToo J/aN^(a-x,F<. = 0; (V)

the function f, being here also finite, within the extent of the integration, and :v
being independent of a. and j3. For the reasonings of the last article may easily
be adapted to this case ; or we may see, from the definitions in article [3.], that
if the function n„ have the properties there supposed, then N„_a; will also have
those properties. In fact, if n„ be always comprised between given finite limits,
then N„_x will be so too ; and we shall have, by (f ),

^ rfaN„_^=\ c;aN<. = M„_^— M_,; (c')

in which M_a; is finite, because the suppositions of the third article oblige m„ to
be always comprised between the limits a ± be ; so that the equation

c?aN„_^ = a — M_^, (d')

which is of the form (g), has infinitely many real roots, of the form

a = a;-\-a„ (e')

and therefore of the kind assumed in the two last articles. Let us now examine
what happens, when, in the first member of the formula (b'), we substitute,
instead of the finite factor f„, an expression such as (a — ^)~ Va? which becomes
infinite between the limits of integration, the value of x being supposed to be
comprised between those limits, and the function y^ being finite between them.
That is, let us inquire whether the integral

i'

(in which ^ > a, < b), tends to any and to what finite and determined limit, as j8
tends to become infinite.

In this inquiry, the theorem (b') shows that we need only attend to those
values of a. which are extremely near to x, and are for example comprised be-
tween the limits orqie, the quantity e being small. To simplify the question, we
shall suppose that for such values of «, the function/^ varies gradually in value ;

272 Sir William Rowan Hamilton on Fluctuating Functions.

we shall also suppose that No = 0, and that n„ a"' tends to a finite limit as a. tends
to 0, whether this be by decreasing or by increasing ; although the limit thus
obtained, for the case of infinitely small and positive values of «, may possibly
differ from that which corresponds to the case of infinitely small and negative
values of that variable, on account of the discontinuity which the function n„ may
have. We are then to investigate, with the help of these suppositions, the value
of the double limit :

lim . lim . (•' + ' . ^_, ^ , ,.

6 = 0 /3 = 00 \ f" ^pu-x^ (« - ^) /a ; (g )

this notation being designed to suggest, that we are first to assume a small but
not evanescent value of e, and a large but not infinite value of /3, and to effect
the integration, or conceive it effected, with these assumptions ; then, retaining
the same value of e, make /3 larger and larger without limit ; and then at last
suppose 6 to tend to 0, unless the result corresponding to an infinite value of j8
shall be found to be independent of e. Or, introducing two new quantities y
and »7, determined by the definitions

yzz^{a~x), »7 = /3e, (h')

and eliminating a and ^ by means of these, we are led to seek the value of the
double limit following :

lim . lira . c " , _, .

in which rj tends to oo, before e tends to 0. It is natural to conclude that since
the sought limit (g') can be expressed under the form (1'), it must be equivalent
to the product

/,X^ dyTfyy-'; ^ (k')

and in fact it will be found that this equivalence holds good ; but before finally
adopting this conclusion, it is proper to consider in detail some difficulties which
may present themselves.

[6.] Decomposing the function yV+t^-'s i^^to two parts, of which one is inde-
dent of y, and is =^x» while the other part varies with y, although slowly, and

Sir William Rowan Hamilton on Fluctuating Functions. 273

vanishes with that variable ; it is clear that the formula (i') will be decomposed
into two corresponding parts, of which the first conducts immediately to the
expression (k') ; and we are now to inquire whether the integral in this expres-
sion has a finite and determinate value. Admitting the suppositions made in
the last article, the integral

^ ^^N,^ '

•^-i

will have a finite and determinate value, if f be finite and determinate ; we are
therefore conducted to inquire whether the integrals

are also finite and determinate. The reasonings which we shall employ for the
second of these integrals, will also apply to the first ; and, to generalize a little
the question to which we are thus conducted, we shall consider the integral

0«N„F„J (!')

F„ being here supposed to denote any function of a which remains always positive
and finite, but decreases continually and gradually in value, and tends indefinitely
towards 0, while a increases indefinitely from some given finite value which is
not greater than a. Applying to this integral (1') the principles of the fourth
article, and observing that we have now Fa„i<f<.„j «'7.,i being > a,„ and a„ being
assumed <; a ; and also that

we find

± 5J'"rfaN„ FX^bc (F„^ - F„„^_) ; (n')

and consequently

p^n + tn
-3a„ «^«N„F„<^bc(F<,„-F„^^,^). (O')

This latter integral is therefore finite and numerically less than g- be f„ , however
great the upper limit a„^„maybe; it tends also to a determined value as m

VOL. XIX. 2 N

274 Sir William Rowan Hamilton on Fluctuating Functions.

increases indefinitely, because the part which corresponds to values of a between
any given value of the form o^^.^ and any other of the form a„4.„+p is included
between the limits ± ^ be f„ , which limits approach indefinitely to each other
and to 0, as m increases indefinitely. And in the integral (1'), if we suppose the
lower limit a to lie between a„_, and a„, while the upper limit, instead of being
infinite, is at first assumed to be a large but finite quantity b, lying between a„^„
and a„_^™_^„ we shall only thereby add to the integral (o') two parts, an initial and
a final, of which the first is evidently finite and determinate, while the second is
easily proved to tend indefinitely to 0 as m increases without limit. The integral
(1') is therefore itself finite and determined, under the conditions above supposed,
which are satisfied, for example, by the function f„ = ar\ if a be > 0. And
since the suppositions of the last article render also the integral

\ rfaN^o"*

determined and finite, if the value of a be such, we see that with these supposi-
tions we may write

w = C C?aN„a~S (p')

w being itself a finite and determined quantity. By reasonings almost the same
we are led to the analogous formula

w-=C " day^a-'; (q')

and finally to the result

,^ = 70-^ + TU-" = C rfaN<.a-i; (r')

in which w' and zs- are also finite and determined. The product (k') is there-
fore itself determinate and finite, and may be represented by zs/^.

[7.] We are next to introduce, in (i'), the variable part of th^ function y^
namely,

which varies from/*a;_„ tofx+^i while y varies from — ^ to + 17, and in which
€ may be any quantity > 0. And since it is clear, that under the conditions

Sir William Rowan Hamilton on Fluctuating Functions. 275

assumed in the fifth article,

e ™0 \ =00 ' i_fi ^yy~' (/-+--' y — /x) = 0, (s')

if f be any finite and determined quantity, however large, we are conducted to
examine whether this double limit vanishes when the integration is made to
extend from y=^ioy=.'q. It is permitted to suppose that f^ continually
increases, or continually decreases, from a ■=. x to az=L x -{- e ; let us therefore

consider the integral

SI
C?aN„F„G<., (f)

in which the function f„ decreases, while g„ increases, but both are positive and
finite, within the extent of the integration.

By reasonings similar to those of the fourth article, we find under these con-
ditions,

and therefore

\ p^n + m •

+ (^«n+, - ^-n^-a) «<•« + .+ (^»« + 3 - ^°. + .) «"« + 4 + ^'^- -

This inequality will still subsist, if we increase the second member by changing,
in the positive products on the second and third lines, the factors g to their
greatest value g„ ; and, after adding the results, suppress the three negative

terms which remain in the three lines of the expression, and change the functions
F, in the first and third lines, to their greatest value F„ . Hence,

±\ rfaN„F„G„<3bcF g ; (w')

this integral will therefore ultimately vanish, if the product of the greatest values
of the functions f and g tend to the limit 0. Thus, if .we make

2n 2

276 Sir William Rowan Hamilton on Fluctuating Functions.

the upper sign being taken wheny^ increases from az=a:toa=:3;-\-e; and if
we suppose that f and rj are of the forms a„ and On+m ; we see that the integral
(t') is numerically less than 3 be a„~' (/"«+. — f^), and therefore that it vanishes
at the limit 6 = 0. It is easy to see that the same conclusion holds good, when
we suppose that rj does not coincide with any quantity of the form a„^„„ and
when the limits of the integration are changed to — tj and — f . We have
therefore, rigorously,

lim . lim .(*»», _,. ..
6 = 0 ^=00 3_/^N*3/ '(/x+«,-»— /x) = 0, (x')

nowithstanding the great and ultimately infinite extent over which the integration
is conducted. The variable part of the functiony may therefore be suppressed
in the double limit (i'), without any loss of accuracy ; and that limit is found to
be exactly equal to the expression (k') ; that is, by the last article, to the deter-
mined product -sr/j;. Such, therefore, is the value of the limit (g'), from which
(i) was derived by the transformation (h') ; and such finally is the limit of the
integral (f), proposed for investigation in the fifth article. We have, then,
proved that under the conditions of that article,

B zToo " W« N^ (a-x) (« - ^r'/a = ■=[/■- ; (y')

and consequently that the arbitrary but finite and gradually varying functiony"j.>
between the limits x ^a, x=: b, may be transformed as follows :

f. = ^~' ^ rf«N.(„_^) (a — .r)-'/„ ; (z')

which is a result of the kind denoted by (d) in the second article, and includes
the theorem (a) of Fourier. For all the suppositions made in the foregoing arti-
cles, respecting the form of the function n, are satisfied by assuming this function
to be the sine of the variable on which it depends ; and then the constant sy,
determined by the formula (r'), becomes coincident with tt, that is, with the
ratio of the circumference to the diameter of a circle, or with the least positive
root of the equation

Sir William Rowan Hamilton on Fluctuating Functions. 277

sin j:

X

0.

[8.] The known theorem just alluded to, namely, that the definite integral
(r') becomes = tt, when n,, := sin a, may be demonstrated in the following man-
ner. Let

c" , sin So
A = V da i— ;

C" , cos /3a
B = Wa T-r^ ;
J« 1 + a^

+ '
then these two definite integrals are connected with each other by the relation

^=(S/^-i)«'

because

C^ 1^ C 1 sin /3a
V rf/3B = \ da l" ,

d c" 1 a sin /3a

and all these integrals, by the principles of the foregoing articles, receive deter-
mined and finite (that is, not infinite) values, whatever finite or infinite value
may be assigned to /3. But for all values of /3 > 0, the value of a is constant ;
therefore, for all such values of /3, the relation between a and b gives, by inte-
gration,

e-^ 1(5 <;/3 + l) B — a1 = const. ;

and this constant must be = 0, because the factor of e~^ does not tend to become
infinite with ^. That factor is therefore itself = 0, so that we have

A = (^''rf^+l)B, if^>0.

Comparing the two expressions for a, we find

B + ^B = 0, if^>0;

278 Sir William Rowan Hamilton on Fltcctuafing Functions.

and therefore, for all such values of ^,

B e^ = const.

The constant in this last result is easily proved to be equal to the quantity a,

by either of the two expressions already established for that quantity ; we have

therefore

B =: a e~^,

however little the value of /3 may exceed 0 ; and because b tends to the limit -
as ^ tends to 0, we find finally, for all values of /3 greater than 0,

These values, and the result

\

J sm a

da ^: -n.

to which they immediately conduct, have long been known ; and the first relation,
above mentioned, between the integrals a and b, has been employed byLEGENDRE
to deduce the former integral from the latter ; but it seemed worth while to
indicate a process by which that relation may be made to conduct to the values
of both those integrals, without the necessity of expressly considering the second
differential coefficient of b relative to /3, which coefficient presents itself at first
under an indeterminate form.

[9.] The connexion of the formula (z') with Fourier's theorem (a), will be
more distinctly seen, if we introduce a new function p„ defined by the condition

N„ = J"rfaP„, (a")

which is consistent with the suppositions already made respecting the function n„.
According to those suppositions the new function p„ is not necessarily continuous,
nor even always finite, since its integral n„ may be discontinuous ; but p„ is sup-
posed to be finite for small values of a, in order that n„ may vary gradually for
such values, and may bear a finite ratio to a. The value of the first integral of
p. is supposed to be always comprised between given finite limits, so as never to
be numerically greater than ± c ; and the second integral.

Sir William Rowan Hamilton on Fluctuating Functions. 279

M„ = (rrfa)^P„, (b")

becomes infinitely often equal to a given constant, a, for values of a which extend
from negative to positive infinity, and are such that the interval between any one
and the next following is never greater than a given finite constant, b. With
these suppositions respecting the otherwise arbitrary function p„, the theorems
(z) and (z') may be expressed as follows :

and

b ""

fx = -=f~' \ do.\ d^ P^(a_x)/a ; (or > a, < 6) (b)

■u being determined by the equation

CO 1^

^=\ da\d^V,^. (c")

Now, by making

p„ = cos a,

(a supposition which satisfies all the conditions above assumed), we find, as
before,

and the theorem (b) reduces itself to the less general formula (a), so that it
includes the theorem of Fourier.

[10.] If we suppose that x coincides with one of the limits, a or h, instead
of being included between them, we find easily, by the foregoing analysis,

/„ = ^^-'f*</afc//3p,,_„/„; (d")

f,-^-'ida\d^v,,^_,,f^; ■ (e")

in which

^^ = '^da ^ rf/3 P,„ ; (f")

•a

280 Sir William Rowan Hamilton on Fluctuating Functions.

^^^=:J^°rfaj'rf/3p,,; (g")

so that, as before,

\ 1 w

TSr — TIT -y- w .

Finally, when x is outside the limits a and b, the double integral in (b) vanishes ;
so that

b *"

0 = f dai fl?/3p^(„_x)/„, if ^ < a, or > 6. (h")

And the foregoing theorems will still hold good, if the function y^ receive any
number of sudden changes of value, between the limits of integration, provided
that it remain finite between them ; except that for those very values d of the
variable a, for which the finite function y^ receives any such sudden variation, so
as to become =y^ for values of a infinitely little greater than a, after having
been =y^^ for values infinitely little less than a, we shall have, instead of (b),
the formula

-T + -r = C da f rf/3 P,(„_„,/„. (i")

[11.] Ifp<.be not only finite for small values of a, but also vary gradually
for such values, then, whether a be positive or negative, we shall have

lim

and if the equation

_ .N„a- = P„; . (k")

a = 0

N._. = 0 (1")

have no real root a, except the root a = a:, between the limits a and b, nor any

which coincides with either of those limits, then we may change/^ to ^^ -f^,

in the formula (z'), and we shall have the expression :

/x = '=r~'Po\ c^aN«(„_x,N„_!^/„. (m")

Instead of the infinite factor in the index, we may substitute any large number,
for example, an uneven integer, and take the limit with respect to it ; we may,
therefore, write

Let
then

Sir William Rowan Hamilton on Fluctuating Functions. 281

(2n-l-l)(a— »)

f -1^ ^'™ C*^ So day,

" So dav^

\ dav,— Q„,„\ dav,; (o")

*'(2B — l)a *'o

l+Qaa + Q».2 + ... + Q.» = ^-^ ^^' (P")

So^« Pa

and the formula (n") becomes

/. = ^-' P„ (^* rfa/„ + 2(„)1 5* rfa Q_ .,„/„) ; (c)

in which development, the terms corresponding to large values of n are small.
For example, when p,. = cos a, then

w = TT, Po = 1, Q„,„ = 2 cos Ina,

and the theorem (c) reduces itself to the following known result :

/, = ^-' (J* flfa/„ + 2 2,„r.£ ^« COS (2«a - 2w^)/„) ; (q")

in which it is supposed that x ^ a, x < b, and that h — o !J> x, in order that
a — X may be comprised between the limits ± tt, for the whole extent of the
integration ; and the function y^ is supposed to remain finite within the same
extent, and to vary gradually in value, at least for values of the variable a which
are extremely near to x. The result (q") may also be thus written :

/. = -n-' 2(„;_:C ^«cos {2na - 2nx)f^ ; (r")

'J a

and if we write

it becomes

0v = ^ 2cn,- : J d^ COS (n(8 - ny) 0^ (s")

the interval between the limits of integration relatively to /3 being now not

VOL. XIX. 2 o

282 Sir William Rowan Hamilton on Fluctuating Functions.

greater than 27r, and the value oi y being included between those limits. For
example, we may assume

2a =: — TT, 26 = it,

and then we shall have, by writing a, or, and/, instead of /3, y, and 0,

1 f» "

f' — -^ 2(„) _ » J rfa COS (na — nx)f^, (t")

in which a; > — w, or < tt. It is permitted to assume the function/ such as to
vanish when a < 0, > — tt ; and then the formula (t") resolves itself into the
two following, which (with a slightly different notation) occur often in the
writings of PoissoN, as does also the formula (t") :

2" \ daf^ + 2(„r, \ da cos {na — nx)f, = -nf^ ; (u")

h ^ «?«/a + 2(„r. J' da cos {na + nx)f^ =z 0 ; (v")

2

'0

^ being here supposed > 0, but < tt ; and the function/ being arbitrary, but

finite, and varying gradually, from a = 0 to a = tt, or at least not receiving any

sudden change of value for any value x of the variable a, to which the formula

(u") is to be applied. It is evident that the limits of integration in (t") may be

made to become z^il, I being any finite quantity, by merely multiplying na — nx

■n . 11.

under the sign cos., by y, and changing the external factor k~ to ^r^- ; and it is

under this latter form that the theorem (t") is usually presented by Poisson :
who has also remarked, that the difference of the two series (u") and (v") con-
ducts to the expression first assigned by Lagrange, for developing an arbitrary
function between finite limits, in a series of sines of multiples of the variable on
which it depends.

[12.] In general, in the formula (m"), from which the theorem (c) was
derived, in order that x may be susceptible of receiving all values > a and < b
(or at least all for which the function /^^ receives no sudden change of value), it
is necessary, by the remark made at the beginning of the last article, that the
equation

Sib William Rowan Hamilton on Fluctuating Functions. 283

rc?ap„=0, (w")

should have no real root a different from 0, between the limits qr (& — a). But
it is permitted to suppose, consistently with this restriction, that a is < 0, and
that 5 is > 0, while both are finite and determined ; and then the formula (m"),
or (c) which is a consequence of it, may be transformed so as to receive new
limits of integration, which shall approach as nearly as may be desired to negative
and positive infinity. In fact, by changing a to \a, j; to Xx, and^^; to y^;, the
formula (c) becomes

/, = \^-' p„ (J^-,^ <^«/a + 2(„ri J;^-!^ da Q,._,,,„/„) ; (x")

in which \~'a will be large and negative, while X~^b will be large and positive,
if \ be small and positive, because we have supposed that a is negative, and b
positive ; and the new variable x is only obliged to be > \~*a, and < X''^, if
the new function y*t be finite and vary gradually between these new and enlarged
limits. At the same time, the definition (o") shows that PaQx„_x,,„ will tend
indefinitely to become equal to 2P2„^(„_,) 5 in such a manner that

lim . PflQxa— Xj.n ■■ /„"^

\ = 0 2"7 ; ~ ' ^^ ^

at least if the function p be finite and vary gradually. Admitting then that we
may adopt the following ultimate transformation of a sum into an integral, at least

under the sign \ rfo,

*^ CO

X^i^'o ■ ^ ^ (^ ^» + ^^'•" ^-M»-.)) = j^ d^ P.(a-.). (Z")

we shall have, as the limit of (x"), this formula :

fx — ^~^\ G?« W^P;9(a_x)/a; (d)

which holds good for all real values of the variable x^ at least under the conditions
lately supposed, and may be regarded as an extension of the theorem (b), from
finite to infinite limits. For example, by making p a cosine, the theorem (d)

2o2

284 Sir William Rowan Hamilton on Tluctuating Functions.

becomes

/, = TT-' C da\d^ COS (/3a — /3a;)/„ (a'")

which is a more usual form than (a) for the theorem of Fourier. In general,
the deduction in the present article, of the theorem (d) from (c), may be regarded
as a verification of the analysis employed in this paper, because (d) may also be
obtained from (b), by making the limits of integration infinite ; but the demon-
stration of the theorem (b) Itself, in former articles, was perhaps more completely
satisfactory, besides that it involved fewer suppositions ; and it seems proper to
regard the formula (d) as only a limiting form of (b).

[13.] This formula (d) may also be considered as a limit in another way, by
introducing, under the sign of integration relatively to /3, a factor f^^ such that

F„=l, F^=0, (b'")

in which k is supposed positive but small, and the limit taken with respect to It,
as follows :

/- = A; = 0 ' '^~' \ ^" (^ ^^ P^f— ) ^*^)/"- (^)

It is permitted to suppose that the function f decreases continually and gradually,
at a finite and decreasing rate, from 1 to 0, while the variable on which it
depends increases from 0 to oo ; the first differential coefficient f' being thus
constantly finite and negative, but constantly tending to 0, while the variable is
positive and tends to cc. Then, by the suppositions already made respecting the
function p, if a — or and k be each different from 0, we shall have

\ c?^P^(a_x)F*^ = Ft^N^(„_^, (a — or) '
— k{a—x) 'V flf/3N^(„_,)F'i^;

(C'")

and therefore, because f^ = 0, while n is always finite, the integral relative to j8
in the formula (e) may be thus expressed :

m

\ «?^P^(„_x)Fi^ = (a — ar)-'i|ri_,(„_^„ (d'")

the function ^ being assigned by the equation

Sir "William Rowan Hamilton on Fluctuating Functions. 285

For any given value of A, the value of this function ^ is finite and determinate,
by the principles of the sixth article ; and as \ tends to oo, the function i^ tends
to 0, on account of the fluctuation of n, and because f' tends to 0, while 7 tends
to GO ; the integral (d'") therefore tends to vanish with k, if a be different from
X ; so that

lim

k

™0-J (//3p„„_,f., = 0, ifa>ar. (f")

On the other hand, if a = or, that integral tends to become infinite, because we
have, by (b'"),

Thus, while the formula (d'") shows that the integral relative to /3 in (e) is a
homogeneous function of a — x and k, of which the dimension is negative unity,
we see also, by (f") and (g"')> that this function is such as to vanish or become
infinite at the limit A; = 0, according as a — :r is different from or equal to zero.
When the difference between a and x, whether positive or negative, is very small
and of the same order as k, the value of the last mentioned integral (relative to
/3) varies very rapidly with a ; and in this way of considering the subject, the
proof of the formula (e) is made to depend on the verification of the equation

00

z^-'C dX^^\-'=\. (h'")

But this last verification is easily effected ; for when we substitute the expression
(e'") for ^„ ai^d integrate first relatively to X, we find, by (r'),

oo

C rf\N,,\-' = ^; (i'")

it remains then to show that

- f rf7 f; = 1 ; (k"')

and this follows immediately from the conditions (b'"). For example, when p

286 Sir William Rowan Hamilton on Fluctuating Functions.

is a cosine, and f a negative neperian exponential, so that

p„ = cos a, F„ = e~%
then, making \ = A;"' (a — x), we have

C rfjS e-'^ cos (|3a — /ar) = (a - t)-' -^^ ;

0

» -

V-x = Wy e"^ sin X7 = — — - ;
and

It is nearly thus that Poisson has, in some of his writings, demonstrated the theo-
rem of Fourier, after putting it under a form which differs only slightly from the
following :

lim f* (*

/. = 7r-^^^^^^rfaJ^rf^e-*^COs(|3a-j3ir)/; (1'")

namely, by substituting for the integral relative to /3 its value

k
1^ -\- {a — xf '

and then observing that, if k be very small, this value is itself very small, unless
a be extremely near to x, so that f^ may be changed tof^ ; while, making
a=z x-\- k\, and integrating relatively to \ between limits indefinitely great, the
factor by which this function y^, is multiplied in the second member of (1'"), is
found to reduce itself to unity.

[14.] Again, the function f„ retaining the same properties as in the last
article for positive values of a, and being further supposed to satisfy the condition

F_. = F„, (m'")

while k is still supposed to be positive and small, the formula (d) may be pre-
sented in this other way, as the limit of the result of two integrations, of which
the first is to be effected with respect to the variable a :

Sir William Rowan Hamilton on Fluctuating Functions. 287

Now it often happens that if the function y^ be obliged to satisfy conditions which
determine all its values by means of the arbitrary values which it may have for a
given finite range, from a :=a to a = b, the integral relative to a in the formula
(f) can be shown to vanish at the limit Ar = 0, for all real and positive values of
/3, except those which are roots of a certain equation

Qp = 0 ; (g)

while the same integral is, on the contrary, infinite, for these particular values of
j8 ; and then the integration relatively to /3 will in general change itself into a
summation relatively to the real and positive roots p of the equation (g), which is
to be combined with an integration relatively to a between the given limits a and
b ; the resulting expression being of the form

/x = 2,(<^a0.,„,X (h)

For example, in the case where p is a cosine, and f a negative exponential, if
the conditions relative to the function y be supposed such as to conduct to expres-
sions of the forms

in which h is any real or imaginary quantity, independent of a, and having its
real part positive ; it will follow that

1

S

dae-''^' (cos /3a — v/ — I sin /3a)/.

_Vr(/3v/-l+^) ^(/3v/-l-A;)

(P'")

0(^/-l+A;) cpip^-l-k)

in which v^a* is = a or = — a, according as a is > or < 0, and the quantities
^ and k are real, and k is positive. The integral in (p'"), and consequently
also that relative to a in (f), in which, now.

p„ = cos a, F„ = e **^'•^

288 Sir William Rowan Hamilton on Fluctuating Functions.

will therefore, under these conditions, tend to vanish with k, unless ^ be a root p

of the equation

</>(pv/-l)=0, (O

which here corresponds to (g) ; but the same integral will on the contrary tend
to become infinite, as k tends to 0, if /3 be a root of the equation (q'")- Making
therefore |3 = p -J~ ^^' ^"<^ supposing k\ to be small, while p is a real and posi-
tive root of (q'"), the integral (p'") becomes

k-'

1+V
in which A^ and b^ are real, namely.

,(A,-v/-lBj. (r'")

' ^'{p^-l)^<t>'(-pv'-iy

(n

(f) being the differential coefficient of the function 0. Multiplying the expres-
sion (r'") by 7r~' d^ (cos ^x -^ \/ — 1 sin ^x), which may be changed to
Tr~^ kd\ {cos px -\- \/ — 1 sin pa:) ; integrating relatively to X between indefi-
nitely great limits, negative and and positive ; taking the real part of the result,
and summing it relatively to p ; there results,

/x=2p(ApCospar-HBpSinp^); (t'")

a development which has been deduced nearly as above, by Poisson and Liou-
viLLE, from the suppositions (n'"), (o'"), and from the theorem of Fourier
presented under a form equivalent to the following ;

/x = ^^™Q • '^"^ J ^^ S "^^ «'* "^"^cos i^a - ^x)f^ ; (u'")

and in which it is to be remembered that if 0 be a root of the equation (q'")) the
corresponding terms in the development ofy^; must in general be modified by
the circumstance, that in calculating these terms, the integration relatively to A
extends only from 0 to oo.

For example, when the function y is obliged to satisfy the conditions

Sir William Rowan Hamilton on Fluctuating Functions. 289

the suppositions (n'") (o'") are satisfied ; the functions 0 and ^ being here such
that

^ (A) = C rfa («*('-") — e*(»-'))/„ ;

therefore the equation (q'") becomes in this case

cos pi = 0, (w'")

and the expressions (s'") for the coefficients of the development (t'") reduce
themselves to the following :

2 c'
^(, = Y^ da cos /Ja/„ ; B„ rz 0 ; (x'")

so that the method conducts to the following expression for the function y^ which
satisfies the conditions (v'"),

/. = ^2,.-cose^^;i::^(.«cos e^il^/.; if)

in which y^ is arbitrary from a = 0 to a = /, except that fi must vanish. The
same method has been applied, by the authors already cited, to other and more
difficult questions ; but it will harmonize better with the principles of the present
paper to treat the subject in another way, to which we shall now proceed.

[15.] Instead of introducing, as in (e) and (f), a factor which has unity for
its limit, we may often remove the apparent indeterminateness of the formula (d)
in another way, by the principles of fluctuating functions. For if we integrate
first relatively to a between indefinitely great limits, negative and positive, then,
under the conditions which conduct to developments of the form (ii), we shall
find that the resulting function of j3 is usually a fluctuating one, of which the
integral vanishes, except in the immediate neighbourhood of certain particular
values determined by an equation such as (g) ; and then, by integrating only in
such immediate neighbourhood, and afterwards summing the results, the develop-
ment (h) is obtained. For example, when p is a cosine, and when the conditions
(v'") are satisfied by the function yj it is not difficult to prove that

VOL. XIX. 2 p

290 Sir William Rowan Hamilton on Fluctuating Functions.

\ da cos ipa-px)f^= — LT/ ^-COS^x\ daCOS^af^; (z'")

m being here an Integer number, which is to be supposed large, and ultimately
infinite. The equation (g) becomes therefore, in the present question and by
the present method, as well as by that of the last article,

cos plzzO ;

and if we make p zz p-^-y, p being a root of this equation, we may neglect y in
the second member of (z"'), except in the denominator

cos §1:=. — sin pi sin 7/,

and in the fluctuating factor of the numerator

cos (2toj3/ -\-?l-{- ^'^) = — sin pi sin (2myl -\- yl) ;

consequently, multiplying by tT^ dy, integrating relatively to 7 between any two
small limits of the forms ipe, and observing that

lim .2^' sin(2TO/7 + /7)^2^
m = 00 7r J_, sin ly I '

the development

2

yi = r 2p cos /9^ \ da COS pa/^,

which coincides with (y'")» ^^^ is of the form (h), is obtained.

[16.] A more important application of the method of the last article is sug-
gested by the expression which Fourier has given for the arbitrary initial tem-
perature of a solid sphere, on the supposition that this temperature is the same for
all points at the same distance from the centre. Denoting the radius of the
sphere by I, and that of any layer or shell of it by a, while the Initial temperature
of the same layer is denoted by a~^J'„, we have the equations

/o=0,/,+ ./. = 0, (a-)

which permit us to suppose

V being here a constant quantity not less than — /"', and/"' being the first diffe-
rential coefficient of the function y^ which function remains arbitrary for all values

Sir William Rowan Hamilton on Fluctuating Functions. 291
of a greater tlwn 0, but not greater than /. The equations (b^*") give

(]8cosj8/+»/sin/30\ fl?asinj3a/„= . (c^'')

(P sin §l—v cos /3/) \ da cos ^a/, - cos ^a (/„ ^ , +/„_,) ;
SO that

{p sin pZ — 1/ cos /)/) \ da cos /)o/„ = cos pa(f,+, +/„_i), (d'O

if p be a root of the equation -

p cos pl-\-v sin pi = 0. (e^O

This latter equation is that which here corresponds to (g) ; and when we change
^ to p-\-y, 7 being very small, we may write, in the first member of (c^''),

j3cos/3/-l- *'sinpZ = 7 [(1 -\- vl) cospl — pl^m pi}, (f-"')

and change j3 to /j in all the terms of the second member, except in the fluctua-
ting factor cos §a, in which a is to be made extremely large. Also, after making
cos /3a := cos pa. cos 701 — sin pocsin 7a, we may suppress cos yac in the second mem-
ber of (c^*^), before integrating with respect to 7, because by (d^^) the terms
involving cos7« tend to vanish with 7, and because 7"' cos yx changes sign with

7. On the other hand, the integral of is to be replaced by tt, though

it be taken only for very small values, negative and positive, of 7, because « is
here indefinitely large and positive. Thus in the present question, the formula

/, = ! . 1™ • C c/psin^.r(''°(/asinpa/„ (g^O

TT a = CO Jo ♦^i-a

(which is obtained from (a'") by suppressing the terms which involve cos /3jr, on
account of the first condition (b^''),) may be replaced by a sum relative to the real
and positive roots of the equation (e^'') ; the term corresponding to any one such
root being

{1 -\- vl) cos pi — plsmpl* ^ ^

if we suppose p > 0, and make for abridgment

2 p 2

292 Sir William Rowan Hamilton on Fluctuating Functions.

,»+'

(i-)

Rp = (1/ COS pi — p sin pi) \ da sin paf^

+ sin /»«(/„+, -{-/_,).

The equations (b^^) show that the quantity r^ does not vary witli a, and there-
fore that it may be rigorously thus expressed :

Rp = 2 (1/ cos pi — p sin pl)\ da sin paf^ ; (t^' )

we have also, by (e^''), p being > 0,

2(1/ COS/)/ — pmipl) 2/> ■ .jy

cos pl-\-l [v COS /)/ — /9 sin pi) pi — sin pi cos pi'

And if we set aside the particular case where

the term corresponding to the root

P=0, (n-)

of the equation (e^''), vanishes in the development ofy^^ ; because this term is,

by {gn,

''-^d^{p^^'^da^m^af}j, ' (0^0

a being very large, and j3 small, but both being positive ; and unless the condi-
tion (m^'') be satisfied, the equation (c^^) shows that the quantity to be integrated
in (0^''), with respect to p, is a finite and fluctuating function of that variable, so
that its integral vanishes, at the limit a =1 00 . Setting aside then the case (m'^'^^),
which corresponds physically to the absence of exterior radiation, we see that the
function y^, which represents the initial temperature of any layer of the sphere
multiplied by the distance x of that layer from the centre, and which is arbitrary
between the limits a: = 0, a: =^ l, that is, between the centre and the surface,
(though it is obliged to satisfy at those limits the conditions (a^^) ), may be deve-
loped in the following series, which was discovered by Fourier, and is of the
form (h) :

2p sin px \ da sin paj"^
'' pi — sin/)/ cos/)/ '

Sir William Rowan Hamilton on Fluctuating Functions. 293

the sum extending only to those roots of the equation (e^'') which are greater
than 0. In the particular case (m^''), in which the root (n^^) of the equation
(e^'') must be employed, the term (o^'') becomes, by {c'^) and (d^^),

.||{^°^Wa«c-/(/„^.+/„_Oac]-, (q-)

in which, at the limit here considered,

but also, by the equations (b^''), (m^*^),

the sought term ofy^ becomes, therefore, in the present case,

and the corresponding term in the expression of the temperature x'^fx is equal
to the mean initial temperature of the sphere ; a result which has been otherwise
obtained by Poisson, for the case of no exterior radiation, and which might have
been anticipated from physical considerations. The supposition

»'^+l<0, ' (u^'')

which is inconsistent with the physical conditions of the question, and in which
Fourier's development (p^O may fail, is excluded in the foregoing analysis.

[17.] When a converging series of the form (h) is arrived at, in which the
coefficients 0 of the arbitrary function f, under the sign of integration, do not
tend to vanish as they correspond to larger and larger roots p of the equation (g) ;
then those coefficients 0^„,p must in general tend to become fluctuating functions
of a, as /9 becomes larger and larger. And the sum of those coefficients, which
may be thus denoted,

2p0x.a,p=^^.a,p> (l)

and which is here supposed to be extended to all real and positive roots of the
equation (g), as far as some given root p, must tend to become a fluctuating func-

294 Sir William Rowan Hamilton on Fluctuating Functions.

tlon of a, and to have its mean value equal to zero, as p tends to become infinite,
for all values of « and a; which are different from each other, and are both com-
prised between the limits of the integration relative to a ; in such a manner as to
satisfy the equation

J^^«^.„.»/„ = 0, (k)

which is of the form (e), referred to in the second article ; provided that the
arbitrary functionyis finite, and that the quantities \, /i, x, a, are all comprised
between the limits a and b, which enter into the formula (h) ; while « is, but x
is not, comprised also between the new limits A and jjl. But when a.-=^ x, the
sum (i) tends to become infinite with p, so that we have

■fx,,.« = co, (l)

and

\ d<^i;.a.^fa=A., (m)

e being here a quantity indefinitely small. For example, in the particular ques-
tion which conducts to the development (y'"), we have

2

0;,,^p = J- cos px cos pa, (\"')

and

(2ra — l)7r
P = 2? ' ("^^

therefore, summing relatively to p, or to n, from w = 1 to any given positive
value of the integer number n, we have, by (i),

. mr (a — x) . mr(a4-x)

sm ^ sm — ^-j-^ — -

and it is evident that this sum tends to become a fluctuating function of a, and to
satisfy the equation (k), as p, or n, tends to become infinite, while a, and x are
different from each other, and are both comprised between the limits 0 and l.
On the other hand, when a becomes equal to x, the first part of the expression

Sir William Rowan Hamilton on Fluctuating Functions. 295

n

(x^'') becomes = j, and therefore tends to become infinite with n, so that the

equation (l) is true. And the equation (m) is verified by observing, that if
or > 0, < /, we may omit the second part of the sum (x^^), as disappearing in
the integral througli fluctuation, while the first part gives, at the limit,

mr (a — s)

sm-

2/sm-4^

If X be equal to 0, the integral is to be taken only from 0 to e, and the result is
only half as great, namely,

. mra.
sin— J-

but, in this case, the other part of the sum (x^^) contributes an equal term, and
the whole result is^g. If x =.1, the integral is to be taken from / — e to /, and
the two parts of the expression (x^'') contribute the two terms ^y^ and — ^y),
which neutralize each other. We may therefore in this way prove, d posteriori,
by the consideration of fluctuating functions, the truth of the development (y'")
for any arbitrary but finite function y^j and for all values of the real variable x
from X ^0 to s=: I, the function being supposed to vanish at the latter limit ;
observing only that if this function/*^ undergo any sudden change of value, for
any value x'^ of the variable between the limits 0 and /, and if x be made equal
to ar" in the development (y'")> the process shows that this development then
represents the semisum of the two values which the function y receives, imme-
diately before and after it undergoes this sudden change.

[18.] The same mode of a posteriori proof, through the consideration of fluc-
tuating functions, may be applied to a great variety of other analogous develop-
ments, as has indeed been indicated by Fourier, in a passage of his Theory of
Heat. The spirit of Poisson's method, when applied to the establishment, a
posteriori, of developments of the form (h), would lead us to multiply, before the
summation, each coefficient 0^„_p by a factor Fk,^ which tends to unity as k tends

296 Sir William Rowan Hamilton on Fluctuating Functions.

to 0, but tends to vanish as p tends to co ; and then instead of a generally/ fluc-
tuating sum (i), there results a generally evanescent sum (k being evanescent),
namely,

2pFA,,0^_„_, = Xx,a,*:,p» (n)

which conducts to equations analogous to (k) (l) (m), namely,

;-^™o5'rf-Xx.a...-/» = 0; (o)

^!!"nX..x,...=ao; (p)

k = 0

lim -'+•

k

%^^_dax.,.,.,.f.=f.. (q)

It would be interesting to inquire what form the generally evanescent function
X would take immediately before its vanishing, when

F*.. = «'*"

and

2p sm px sin pa

''' pi — sin pi cos pV

p being a root of the equation

pi cotan pi = const. ,

and the constant in the second member being supposed not greater than unity.

[19.] The development (c), which, like (h), expresses an arbitrary function,
at least between given limits, by a combination of summation and integration, was
deduced from the expression (m") of the eleventh article, which conducts also to
many other analogous developments, according to the various ways in which the
factor with the infinite index, n«(„_x)) May be replaced by an infinite sum, or
other equivalent form. Thus, if, instead of (0"), we establish the following equa-
tion,

\ rfap„=: R„„V rfap„, (a'')

♦^(2n_2)o •^0

we shall have, instead of (c), the development :

Sir William Rowan Hamilton on Fluctuating Functions. 297

/x=^ 'Po2(„)"\ daR^_^^„f^; (r)
which, when p is a cosine, reduces itself to the form,

/r = - ^,Z C ^« cos (2^r^ . "^^^j/^, (b ")

X being > a, < ft, and h — a being not > tt ; and easily conducts to the known

expression

f 1^:. »C' ^ (2w— l)7r(a — ^)
/x = ^ 2^„) , "^^da cos ^ '—f^ /„, (cO

which holds good for all values of x between — I and -j- 1- By supposing 7^ ■=■
y"_a> we are conducted to the expression (y'") ; and by supposingy^ = — y_„,
we are conducted to this other known expression,

„ 2 ,„ . (2n— l)7r^c' . (2w— l)7ra
/x = ^2(„)iSin^ __^^^c^asm-5^ ^f^—fah (dO

which holds good even at the limit x -=1, by the principles of the seventeenth
article, and therefore offers the following transformation for the arbitrary func-
tion/"< :

f 2_ 00^ ,xnC' J • (2/i— l)7ra

/,= --2(„)i(-l)"J^^asin^ ^[-^—fa- (eO

For example, by making^ = a*, and supposing ^ to be an uneven integer num-
ber ; effecting the integration indicated in (e ^), and dividing both members by f,
we find the following relation between the sums of the reciprocals of even powers
of odd whole numbers :

in which

[^•]*z=^(^•-l)(^•-2). . .(e_A;+l); (g")

and

-.*=2Q V>(2^-ir*; (hO

thus

1 = w, = 3w., — 3. 2. 1. 01, =z 5«.2 — 5. 4. Bw^ + 5. 4. 3. 2. 1 Wg, (i'')

VOL. XIX. 2 Q

298 Sm William Rowan Hamilton on Fluctuating Functions.
so that

«2 = 1> <«4 = i. ^e = !%-• (kO

Again, by making j^ zz a*, but supposing i = an uneven number 2k, we get the
following additional term in the second member of the equation (f ^)}

(-i)*[2;cr«,.^„ (F)

in which

thus

1 = w, = 2a.2 - 2. 1 tt.3 =4m2 — 4. 3. 2«., + 4. 3. 2. 1 m^, (n'')

so that

Wj = 1, W3 = ^, Wj = ^. (o'')

Accordingly, if we multiply the values (k '') by — , --, t— -, we get the known

values for the sums of the reciprocals of the squares, fourth powers, and sixth

It 1^
powers of the odd whole numbers ; and if we multiply the values (0'') by -, -t^j

^, we get the known values for the sums of the reciprocals of the first, third, and

fifth powers of the same odd numbers, taken however with alternately positive and
negative signs. Again, if we make^^ = sin a, in (e''), and divide both members
of the resulting equation by cos I, we get this known expression for a tangent,

which shows that, with the notation (h''),

tan^ = «»j^' + w4P+We^* + ...; W)

so that the coefficients of the ascending powers of the arc in the development of
its tangent are connected with each other by the relations (f^), which may be
briefly represented thus :

V^^\ = (14- V"^ D„)^*- tan 0 ; (r ^

the second member of this symbolic equation being supposed to be developed, and

Sir William Rowan Hamilton on Fluctuating Functions. 299

Dj* tan 0 being understood to denote the value which the i'" differential coefficient
of the tangent of a, taken with respect to a, acquires when o := 0 ; thus,

1 = Dj tan 0 = 3Dj tan 0 — d/ tan 0 ]
= 5DotanO — 10D„HanO + D„*tanO. J

Finally, if we make y^ = cos a, and attend to the expression (p''), we obtain, for
the secant of an arc /, the known expression :

7_v - 2(-l)"+'
sec I - 2.(„,_„ ^2^ _ !■) ^ _ 2/ '■>

(f)

which shows that, with the notation (niQ,

iecl=.<i)J°-\- (i)^P-{- wj^ -{- ...y (u'')

and therefore, by the relations of the form (n^).

/ - 1 (1 - (^- 1 D„)^*secO) = (1 + /- 1 D„)=*tanO ; (v^

thus

1 = secO = 2D„tanO — Do^secO 1

r y" }

= 4d„ tan 0 — 4d/ tan 0 + Do* sec 0. J

Though several of the results above deduced are known, the writer does not
remember to have elsewhere seen the symbolic equations (r*'), (v''), as expressions
for the laws of the coefficients of the developments of the tangent and secant,
according to ascending powers of the arc.

[20.] In the last article, the symbol r was such, that

and in article [11.], we had

1 + 2(„)'; Q„,» = N2„„+„ N,-'. (y 0

Assume, now, more generally,

V^s^^ = N^„Nr*; (zO

and let the operation v^ admit of being effected after, Instead of before, the
integration relatively to a ; the expression (m") will then acquire this very gene-
ral form :

2q2

300 Sir William Rowan Hamilton on Fluctuating Functions.

fx = •a--' Po V ^ \ da. s„_^,^/„ ; (s)

which includes the transformations (c) and (r), and in which the notation V„ is
designed to indicate that after performing the operation V/3 we are to make the
variable /3 infinite, according to some given law of increase, connected with the
form of the operation denoted by v •

[21.] In order to deduce the theorems (c), (r), (s), we have hitherto sup-
posed (as was stated in the twelfth article), that the equation n„ = 0 has no real
root different from 0 between the limits :+:(& — a), in which a and h are the
limits of the integration relative to a, between which latter limits it is also sup-
posed that the variable x is comprised. If these conditions be not satisfied, the
factor N„"l'j, in the formula (m"), may become infinite within the proposed extent
of integration, for values of a and x which are not equal to each other ; and it
will then be necessary to change the first member of each of the equations (m"),
(c), (r), (s), to a function different fromy^, but to be determined by similar
principles. To simplify the question, let it be supposed that the function n„ re-
ceives no sudden change of value, and that the equation ,

N„ = 0, (a'-O

which coincides with (w"), has all its real roots unequal. These roots must here
coincide with the quantities a„^j, of the fourth and other articles, for which the
function n„ changes sign ; but as the double index is now unnecessary, while the
notation a„ has been appropriated to the roots of the equation (g), we shall denote
the roots of the equation (a''^), in their order, by the symbols

and choosing v^ for that root of (a^^) which has already been supposed to vanish,
we shall have

v, = (\ (c'O

while the other roots will be > or < 0, according as their indices are positive or
negative. If the differential coefficient p„ be also supposed to remain always finite,
and to receive no sudden change of value in the immediate neighbourhood of any
root V of (a''^), we shall have, for values of a in that neighbourhood, the limiting
equation :

Sir William Rowan Hamilton on Fluctuating Functions. 301

a zz. V

and p„ will be different from 0, because the real roots of the equation (a''0 have
been supposed unequal. Conceive also that the integral

QO

tends to some finite and determined limit, which may perhaps be different for
different roots v, and therefore may be thus denoted,

as j3 tends to oo , after the given law referred to at the end of the last article.
Then, by writing

and supposing j3 to be very large, we easily see, by reasoning as in former articles,
that the part of the integral

which corresponds to values of a — .r in the neighbourhood of the root v, is very
nearly expressed by

and that this expression is accurate at the limit. Instead of the equation (s), we
have therefore now this other equation :

2. W, PT'/x + v = V . \ da S„_:r,;s/„ ; (t)

the sum in the first member being extended to all those roots v of the equation
(a^^), which satisfy the conditions

x-\-v>a,<b. (k^O

If one of the roots v should happen to satisfy the condition

x-\-v = a, {V)

the corresponding term in the first member of (t) would be, by the same princi-
ples,

302 Sir William Rowan Hamilton on Fluctuating Functions.
in which

And if a root v of (a''^) should satisfy the condition

the corresponding term in the first member of (t) would then be
in which

Finally, if a value of ^ + j/ satisfy the conditions (k''^), and if the function y
undergo a sudden change of value for this particular value of the variable on
which that function depends, so thatyzr^^^ immediately before, andy=y^ imme-
diately after the change, then the corresponding part of the first member of the
formula (t) is

And in the formulas for w,, ts,, w\, it is permitted to write

N„ + p,a-> = C dt Pta + fi,' (s''0

[22.] One of the simplest ways of rendering the integral (e^") determinate at
its limit, is to suppose that the function p„ is of the periodical form which satisfies
the two following equations,

p being some given positive constant. Multiplying these equations by da, and
integrating from a = 0, we find, by (a"),

N_a + N„ = 0, N„+j, + N„ = N,; (u''0

therefore

Np = Np + N_p = 0, (v''0

and

N„ + p = — No, N„ + jp = N„, &C. (w''0

Sir William Rowan Hamilton on Fluctuating Functions. 303

Consequently, if the equations (t^^) be satisfied, the multiples (by whole num-
bers) of p will all be roots of the equation (a^^) ; and reciprocally that equation
will have no other real roots, if we suppose that the function p.., which vanishes

when a is any odd multiple of ^, preserves one constant sign between any one

P
such multiple and the next following, or simply between a = 0 and « = ^- We

may then, under these conditions, write

Vi = ip, (x''')

i being any integer number, positive or negative, and vi denoting generally, as
in (b''^), any root of the equation (a''^). And we shall have

^"</aN. + ,pa-' = (-l)*^, if)

k being any integer number, and w still retaining the same meaning as in the
former articles. Also, for any integer value of k,

P^ = (-1)*P.. (z"')

These things being laid down, let us resume the integral (e''^, and let us sup-
pose that the law by which j3 increases to co is that of coinciding successively with
the several uneven integer numbers 1, 3, 5, &c., as was supposed in deducing the
formula (c). Then §v in (e ^^) will be an odd or even multiple ofj), according
as V is the one or the other, so that we shall have by (x''^), (y^^, the following
determined expression for the sought limit (f '^^) :

^, = (-l)V; (a-0

but also, by {x"'), (z^O.

P.,. = (-1)'P,; (b"")

therefore

^.pr' = ^Po-', (c'-^O

the value of this expression being thus the same for all the roots of (a^^). At
the same time, in (i''^),

the equation (t) becomes therefore now

304 Sir William Rowan Hamilton on Fluctuating FuJictions.

^ifr + ip = •=^~' Po V ^ ) da S„_^,^/„, (u)

/3 tending to infinity by passing through the successive positive odd numbers, and
i receiving all integer values which allow x-\-ip to be comprised between the
limits a and b. If any integer value of i render x -\-ip equal to either of these
limits, the corresponding term of the sum in the first member of (u) is to be \fa,
or ^/"j ; and if the function y receive any sudden change of value between the
same limits of integration, corresponding to a value of the variable which is of the
form X -\- ip, the term introduced thereby will be of the form ^/^ -j- ^J'^\
For example, when

P„ = cos a, sr =. TT, p — -n, i^'^")

we obtain the following known formula, instead of (r"),

^i/.+i. = T-> 2(„) .:( da COS (2na - <2nx)f^ ; {{"")

which may be transformed in various ways, by changing the limits of integration,
and in which halves of functions are to be introduced in extreme cases, as above.
On the other hand, if the law of increase of j8 be, as in (r), that of coinciding
successively with larger and larger even numbers, then

and the equation (t) becomes

2i(-l)'/x+.v = ^''Po V,J c?«s<._,,^/„. (v)

For example, in the case {e^^'), we obtain this extension of the formula (b''),

2i(-iy/x + ,v = 7r-'2w_:^'rfacos(2^m.^T:::i:)/„. (h''^^)

We may verify the equations ({^") (h^") by remarking that both members of
the former equation remain unchanged, and that both members of the latter are
changed in sign, when x is increased by tt. A similar verification of the equa-
tions (u) and (v) requires that in general the expression

Sir William Rowan Hamilton on Fluctuating Functions.

305

should either receive no change, or simply change its sign, when x is increased
by p, according as j3 tends to co by coinciding with large and odd or with large
and even numbers.

[23.] In all the examples hitherto given to illustrate the genei'al formulas of
this paper, it has been supposed for the sake of simplicity, that the function p is
a cosine ; and this supposition has been sufficient to deduce, as we have seen, a
great variety of known results. But it is evident that this function p may receive
many other forms, consistently with the suppositions made in deducing those
general formulas ; and many new results may thus be obtained by the method of
the foregoing articles.

For instance, it is permitted to suppose

p„=l, ifa^<l; (k''")

p, = 0; {V")

* n l_0 — ■

and then the equations (t^^) of the last article, with all that were deduced from
them, will still hold good. We shall now have ^^

and the definite integral denoted by zr, and defined by the equation (r'), may
now be computed as follows. Because the function n„ changes sign with «, we
have

T3- = 2C rfaN„a-'; (o''^^)

but

and
Hence

N„ = a, from

a 1= 0 to a = 1

...2-a,

... 1 ... 3

...a-4.

...3 ... 4

N„ + 4

= N„.

\ rfa N„ a ' = 6 log 3 — 4 log 4,

(P^")

(q''")

(r-O

the logarithms being Napierian ; and generally, if m be any positive integer num-
ber, or zero,

VOL. XIX. 2 R

306 SiE William Rowan Hamilton on Fluctuating Functions.

P4III + 4 „4

^ fi?aN„a"">=\ c?aN„(a-f-4m)'''

= Am log (4m) — (8m -|- 2) log (4m -|- 1 )
+ (8m + 6) log (4m + 3) - (4m + 4) log (4m + 4)

But, by(h''),

if A; be any integer number > 0 ; therefore

1 0~2t ,„^ 2*

^ = 2,

^""^(^ + i)

/■7r\

ft»2;t being by (q'') the coefficient of ^-* ' in the development of tan x. From
this last property, we have

^m -0^^ = t (S^ d^) t^" ^ = 1 S] ^^ log «ec a: ; (v^O

therefore, substituting successively the values ^ = ^ and ^ = t, and subtracting
the result of the latter substitution from that of the former, we find, by (u'^^^),

Q - -

^ = - f Y^ — y j dr log sec s
= -y dx log tan s

4

8 r*-

- y rf*- log cotan z. ( w ''")

TT .
0

Such, in the present question, is an expression for the constant w ; its numerical
value may be approximately calculated by multiplying the Napierian logarithm
of ten by the double of the average of the ordinary logarithms of the cotangents
of the middles of any large number of equal parts into which the first octant may
be divided ; thus, if we take the ninetieth part of the sum of the logarithms of

Sir William Rowan Hamilton on Fluctuating Functions. 307

1* 3" 5" 177" 179"
the cotangents of the ninety angles j-j j-> ^' • • • "X"' ^P' ^^ S'^^n by the or-
dinary tables, we obtain nearly, as the average of these ninety logarithms, the
number 0,5048 ; of which the double, being multiplied by the Napierian logarithm
of ten, gives, nearly, the number 2,325, as an approximate value of the constant
■57. But a much more accurate value may be obtained with little more trouble,
by computing separately the doubles of the part (r''^^), and of the sum of (s"^)
taken from m= I to m = (x^; for thus we obtain the expression

#

■a- = 12 log 3 — 8 log 4

in which each sum relative to in can be obtained from known results, and the
sum relative to k converges tolerably fast ; so that the second line of the expres-
sion (x''") is thus found to be nearly = 0,239495, while the first line is nearly
:= 2,092992 ; and the whole value of the expression (x''") is nearly

w = 2,332487. (y''")

There is even an advantage in summing the double of the expression (s*^-^^ only
from m =: 2 to m := CO , because the series relative to k converges then more

OS

rapidly ; and having thus found 2 \ dati^ar\ it is only necessary to add thereto
the expression

2C (/aN, a-' =12 log 3 -20 log 5 + 28 log 7 — 16 log 8. (z'")

The form of the function p and the value of the constant sr being determined as
in the present article, it is permitted to substitute them in the general equations
of this paper ; and thus to deduce new transformations for portions of arbitrary
functions, which might have been employed instead of those given by Fourier
and PoissoN, if the discontinuous function p, which receives alternately the
values 1, 0, and — 1, had been considered simpler in its properties than the tri-
gonometrical function cosine.

[24.] Indeed, when the conditions (t''^) are satisfied, the function p^ can be

2r2

308 Sir William Rowan Hamilton on Fluctuating Functions.

developed according to cosines of the odd multiples of — , by means of the for-

mula (y'"), which here becomes, by changing I to^, andy to p,

Px = 2(„j, A,„_, cos ^ -^ , (a''"')

in which

4r'| (2w — l)7ra /uy/z/N

0

the function n^: at the same time admitting a development according to sines of
the same odd multiples, namely,

and the constant ts being equal to the following series,

Thus, In the case of the last article, where jp = 2, and p„ = 1 from a =: 0 to
a = 1, we have

^"-'"tt 2«-1 ' ^^ >

Px = -(^cos — — 3 'cos— -4-5 'cos— ...j; (f^"^)

y. = -, (^sin Y - ^ ' sm — + 5 ^ sm -^ - ...j ; (g"-"')

^ = -(1-^-3-^+5-^ — 7-'+"-); (h''''0

so that, from the comparison of (w^^^) and (h^^^^), the following relation results :

0

But most of the suppositions made in former articles may be satisfied, without
assuming for the function p the periodical form assigned by the conditions (t^^).

Sir Wjlliam Rowan Hamilton on Fluctuating Functions. 309

For example, we might assume

p„ = - r do sin 0-^ cos (2a sin B) ; (k''^")

which would give, by (a"), and (b"),

N„ = ^ r do sin e sin (2a sin 6) ; {V"')

M^zz-Tc/i' vers (2a sine); (m^^^^)

and finally, by (r'),

z;r = 2r(;0sin0 = 4. {n''"')

This expression (k^^^^) for p„ satisfies all the conditions of the ninth article; for

4
it is clear that it gives a value to n„ which is always numerically less than - ; and

7r
the equation

which is of the form (g), is satisfied by all the infinitely many real and unequal
roots of the equation

C f^0cos(2asin(?) = O, (p^^^^)

which extend from a= — cotoa=GO, and of which the interval between any
one and the next following is never greater than w, nor even so great ; because
(as it is not difficult to prove) these several roots are contained in alternate or even
octants, in such a manner that we may write

mr TT nit
"">-2-4'<T- (1 >

We may, therefore substitute the expression (k''^") for p, in the formulae (a),
(b), (c), &c. ; and we find, by (b), if jp > a, < 6,

/, = TT-' \ da^ d^ r de sin 0^ cos {2^ (a - x) sin 0}/, ; {v''"')

^a •^o •^o

that is,

{t''"')

310 Sir William Rowan Hamilton on Fluctuating Functions.

/, = i- ^ 1™ f de sin e'\ da sin (2^ (a - ^) sin 6} (a - x)-'f ; (s''^^^

a theorem which may be easily proved a posteriori, by the principles of fluctua-
ting functions, because those principles show, that (if x be comprised between the
limits of integration) the limit relative to /3 of the integral relative to a, in (s^^"),
is equal to Ttf^. In like manner, the theorem (c), when applied to the present
form of the function p, gives the following other expression for the arbitrary
function/", :

^ rj> ^ do sin 6 sin (2 (a — x) sin 6^ cos (An (a — x) sin 6^ ;

+ (n)^)^ «/a 5; de sin e sin (2 (a — x) sin o)

X being between a and b, and b — a being not greater than the least positive root
V of the equation

- C rfe sin 0 sin (2 V sin e) = 0. - (u """ )

And if we wish to prove, a posteriori, this theorem of transformation (t'^"), by
the same principles of fluctuating functions, we have only to observe that

1+22," cos 2ny = !!^^±i^), (v-)

and therefore that the second member of (t*^^^^) may be put under the form

iirv, p' ^"f/Csin 6sin ('(4re + 2) (a — ^)sin0^

1™ i daf— ^— ■ — — — _— _Z . (vf'^'")

n=ccJa •^" 2 5^ rfe sine sin (2 (a — a:) sine) ' ^ ^

in which the presence of the fluctuating factor

am (^{An -\- 2) (a — a;) sine),

combined with the condition that a — a; is numerically less than the least root of
the equation (u^^"), shows that we need only attend to values of a indefinitely
near to x, and may therefore write in the denominator,

C de sin e sin (2 (a — x) sin e') = tt (a — x) ; (x''"')

Sir William Rowan Hamilton on Fluctuating Functions. 311

for thus, by inverting the order of the two remaining integrations, that is by
writing

^ da^ de... = ^ d6\ da.., {f")

we find first

lim P^ sin ((4^ + 2) (g-^) sine) _ '

for every value of 6 between 0 and tt, and of x between a and b ; and finally.

[25.] The results of the foregoing articles may be extended by introducing,
under the functional signs n, p, a product such as §r^, instead of j3«, 7 being an
arbitrary function of a. ; and by considering the integral

in which f is any function which remains finite between the limits of integration.
Since 7 is a function of a, it may be denoted by 7^, and a will be reciprocally a
function of 7, which may be denoted thus :

While a increases from a to b, we shall suppose, at first, that the function 7^ in-
creases constantly and continuously from 7„ to 74, in such a manner as to give
always, within this extent of variation, a finite and determined and positive value
to the differential coefficient of the function 0, namely,

We shall also express, for abridgment, the product of this coefficient and of the
function f by another function of 7, as follows,

0'.Fa = ^ (d«)

Then the integral (a"^) becomes

312 Sir William Rowan Hamilton on Fluctuating Functions.

and a rigorous expression for it may be obtained by the process of the fourth
article, namely

4" 0^' (a„^ „ — a„) cl ;

in which, as before, a„, a„^„ are suitably chosen roots of the equation (g) ; c is
a finite constant; 6 is included between the limits ±1 ; and I is the difference
between two values of the function ^^, corresponding to two values of the varia-
ble 7 of which the difference is less than ^~'b, b being another finite constant.
The integral (a^^) therefore diminishes indefinitely when ^ increases indefinitely ;
and thus, or simply by the theorem (z) combined with the expression (e"), we
have, rigorously, at the limit, without supposing here that n^ vanishes.

i

rfaN,^F„ = 0. (w)

The same conclusion is easily obtained, by reasonings almost the same, for the
case where 7 continually decreases from 7„ to 74, in such a manner as to give,
within this extent of variation, a finite and determined and negative value to the
differential coefficient (c^'''). And with respect to the case where the function 7
is for a moment stationary in value, so that its differential coefficient vanishes
between the limits of integration, it is sufficient to observe that although ^ in
(e") becomes then infinite, yet f in (a^'^) remains finite, and the integral of the
finite product das^^F^, taken between infinitely near limits, is zero. Thus,
generally, the theorem (w), which is an extension of the theorem (z), holds good
between any finite limits a and b, if the function f be finite between those limits,
and if, between the same limits of integration, the function 7 never remain un-
changed throughout the whole extent of any finite change of a,

[26.] It may be noticed here, that if j3 be only very large, instead of being
infinite, an approximate expression for the integral (a^^) may be obtained, on the
same principles, by attending only to values of a which differ very little from
those which render the coefficient (c^^) infinite. For example, if we wish to find
an approximate expression for a large root of the equation (p ''^^^ ), or to express
approximately the function

Sir William Rowan Hamilton on Fluctuating Functions. 313

If"

7^ = -\ da cos (2/3 sin a), (g")

when /3 Is a large positive quantity, we need only attend to values of a which

differ little from - ; making then

sin a =: 1 — J/*, da

__^dy

(h«)

v/2— y'

and neglecting y^ in the denominator of this last expression, the integral (g^^)
becomes

y^ = A^cos2^+B^sin2^, (i^*)

in which, nearly,

*^ = — i /^cos(2^^/^) = -_=;

v/2 7r/3
B, = ^L.^sin(2^y) = ^;

^

(k")

so that the large values of ^ which make the function (g") vanish are nearly of
the form -

n-n TT
2"~8'

(1-)

n being an integer number ; and such is therefore the approximate form of the
large roots a„ of the equation (p'^^^O • results which agree with the relations
(q''^^^), and to which Poisson has been conducted, in connexion with another sub-
ject, and by an entirely different analysis.

The theory of fluctuating functions may also be employed to obtain a more
close approximation ; for instance, it may be shown, by reasonings of the kind •
lately employed, that the definite integral (g^^) admits of being expressed (more
accurately as j8 is greater) by the following semiconvergent series, of which the
first terms have been assigned by Poisson :

/,= ;^2,,UO]-n[-^]0W)-^cos(2i3_^-j); (m-)

and in which, according to a known notation of factorials.

vol. XIX.

2s

314 Sir William Rowan Hamilton on Fluctuating Functions.

[0]-' = 1-1. 2-'. 3-'.

1 .

[-i-r = -7

1—3—5 1— 2^■

(n«)

2 ' 2 2 ' 2 ■ .
For the value ^ = 20, the 3 first terms of the series (m^^) give

9 \ cos 86°49'52" , 1 sin 86°49'52'

•^^—\} 204800 J

(o«)

204800; ■/20^ ' 320 x/^Q^

= 0,0069736 + 0,0003936 = + 0,0073672.

For the same value of j3, the sum of the first sixty terms of the ultimately con-
vergent series

/.=Vo([or)*(-/3')' (p")

gives

/,o = + 7 447 387 396 709 949,9657957 t

- 7 447 387 396 709 949,9584289

J

(q^^)

= + 0,0073668

The two expressions (m^^) (p^^) therefore agree, and we may conclude that the
following numerical value is very nearly correct :

-'{do, cos (40 sin a) = -\- 0,007367- (r")

[27.] Resuming the rigorous equation (w), and observing that

we easily see that in calculating the definite integral

in which the function f is finite, it is sufiicient to attend to those values of a.
which are not only between the limits a and h, but are also very nearly equal to
real roots or of the equation

7x = 0. (U-)

The part of the integral (t"), corresponding to values of a in the neighbour-
hood of any one such root x, between the above-mentioned limits, is equal to the
product

j'rfa5"#P^/„ = .2.-^, (X-)

Sir William Rowan Hamilton on Fliictuating Functions. 315

7« J_„ «— a;' ^ '

in which /3 is indefinitely large and positive, and the differential coefficient 7'^ of
the function 7 is supposed to be finite, and different from 0. A little considera-
tion shows that the integral in this last expression is = it w, -cr being the same
constant as in former articles, and the upper or lower sign being taken according
as 7'x is positive or negative. Denoting then by 1/7' x^ the positive quantity,
which is = + 7'a; or = — 7'^, according as 7'^ is > 0 or < 0, the part (v^^)
of the integral (t^^) is

-5^5 (w")

and we have the expression

^ J^

the sum being extended to all those roots x of the equation (u^^) which are > a
but < b. If any root of that equation should coincide with either of these
limits a or h, the value of a in" its neighbourhood would introduce, into the se-
cond member of the expression (x^^), one or other of the terms

7a 7a 7» 7»

the first to be taken when 7^ = 0, 7'a > 0 ; the second when y^ = 0, y'a < 0 ;
the third when 7^ =0, 7'^ > 0 ; and the fourth when 74 = 0, 7'j < 0. If,
then, we suppose for simplicity, that neither 7„ nor 74 vanishes, the expression
(x^'^) conducts to the theorem

2./x = ^-' ( rfa C dp P,y„ /7J ; (X)

•^a »^o

and the sign of summation may be omitted, if the equation 7* = 0 have only one
real root between the limits a and b. For example, that one root itself may then
be expressed as follows :

X=zr-'^ da^ dp P^ a VT?. (z«)

The theorem (x) includes some analogous results which have been obtained by
Cauchy, for the case when p is a cosine.

2 s 2

316 Sir William Rowan Hamilton on Fltictuating Functions.

[28]. It is also possible to extend the foregoing theorem in other ways ; and
especially by applying similar reasonings to functions of several variables. Thus,
if 7, 7^'> ... be each a function of several real variables a, a^", . . . ; if p and n be
still respectively functions of the kinds supposed in former articles, while p<'\
n'", ... are other functions of the same kinds ; then the theorem (w) may be ex-
tended as follows :

\ c^aV da('>...N.^N'<./i)...F„,„(i),.,. =0, (y)

the function f being finite for all values of the variables a, a^", ..., within the ex-
tent of the integrations; and the theorem (x) may be thus extended :

Ja Ja('> 0 •■^0 *■ (Z)

•••/a,a('\..VI7; J

in which, according to the analogy of the foregoing notation,

— 00 0

and L is the coefficient which enters into the expression, supplied by the princi-
ples of the transformation of multiple Integrals,

while the summation in the first member is to be extended to all those values of
or, d?''^, . . . which, being respectively between the respective limits of integration
relatively to the variables a, a^", ... are values of those variables satisfying the
system of equations

7., x(», . . . = 0, yllln), ...=0,.... (c*)

And thus may other remarkable results of Cauchy be presented under a gene-
ralized form. But the theory of such extensions appears likely to suggest itself
easily enough to any one who may have considered with attention the remarks
already made ; and it is time to conclude the present paper by submitting a few
general observations on the nature and the history of this Important branch of
analysis.

Sia William Rowan Hamilton on Fluctuating Functions. 317

Lagrange appears to have been the first who was led (in connexion with the
celebrated problem of vibrating cords) to assign, as the result of a species of in-
terpolation, an expression for an arbitrary function, continuous or discontinuous
in form, between any finite limits, by a series of sines of multiples, in which the
coefficients are definite integrals. Analogous expressions, for a particular class of
rational and integral functions, were derived by Daniel Bernouilli, through
successive integrations, from the results of certain trigonometric summations,
which he had characterized in a former memoir as being incongruously true. No
farther step of importance towai'ds the improvement of this theory seems to have
been made, till Fourier, in his researches on Heat, was led to the discovery of
his well known theorem, by which any arbitrary function of any real variable is
expressed, between finite or infinite limits, by a double definite integral. Poisson
and Cauchy have treated the same subject since, and enriched it with new views
and applications ; and through the labours of these and, perhaps, of other writers,
the theory of the development or transformation of arbitrary functions, through
functions of determined forms, has become one of the most important and inte-
resting departments of modern algebra.

It must, however, be owned that some obscurity seems still to hang over the
subject, and that a farther examination of its principles may not be useless or un-
necessary. The very existence of such transformations as in this theory are
sought for and obtained, appears at first sight paradoxical ; it is difficult at first
to conceive the possibility of expressing a perfectly arbitrary function through any
series of sines or cosines ; the variable being thus made the subject of known and
determined operations, whereas it had offered itself originally as the subject of
operations unknown and undetermined. And even after this first feeling of pa-
radox is removed, or relieved, by the consideration that the number of the opera-
tions of known form is infinite, and that the operation of arbitrary form reappears
in another part of the expression, as performed on an auxiliary variable ; it still
requires attentive consideration to see clearly how it is possible that none of the
values of this new variable should have any influence on the final result, except
those which are extremely nearly equal to the variable originally proposed. This
latter difficulty has not, perhaps, been removed to the complete satisfaction of those
who desire to examine the question with all the diligence its importance deserves,
by any of the published works upon the subject. A conviction, doubtless, may

318 Sir William Rowan Hamilton on Fluctuating Functions.

be attained, that the results are true, but something Is, perhaps, felt to be still
wanting for the full rigour of mathematical demonstration. Such has, at least,
been the impression left on the mind of the present writer, after an attentive
study of the reasonings usually employed, respecting the tranformations of arbi-
trary functions.

PoissoN, for example, in treating this subject, sets out, most commonly, with
a series of cosines of multiple arcs ; and because the sum is generally indetermi-
nate, when continued to infinity, he alters the series by multiplying each term by
the corresponding power of an auxiliary quantity which he assumes to be less
than unity, in order that Its powers may diminish, and at last vanish ; but, in
order that the new series may tend Indefinitely to coincide with the old one, he
conceives, after effecting Its summation, that the auxiliary quantity tends to be-
come unity. The limit thus obtained is generally zero, but becomes on the con-
trary Infinite when the arc and Its multiples vanish ; from which It Is Inferred by
PoissoN, that if this arc be the difference of two variables, an original and an
auxiliary, and if the series be multiplied by any arbitrary function of the latter
variable, and integrated with respect thereto, the effect of all the values of that
variable will disappear from the result, except the effect of those which are ex-
tremely nearly equal to the variable originally proposed.

PoissoN has made, with consummate skill, a great number of applications of
this method ; yet It appears to present, on close consideration, some difficulties
of the kind above alluded to. In fact, the introduction of the system of factors,
which tend to vanish before the Integration, as their Indices increase, but tend to
unity, after the integration, for all finite values of those indices, seems somewhat
to change the nature of the question, by the Introduction of a foreign element.
Nor is it perhaps manifest that the original series, of which the sum is indeter-
minate, may be replaced by the convergent series with determined sum, which
results from multiplying Its terms by the powers of a factor Infinitely little less
than unity ; while it is held that to multiply by the powers of a factor Infinitely
little greater than unity would give an useless or even false result. Besides there is
something unsatisfactory In employing an apparently arbitrary contrivance for
annulling the effect of those terms of the proposed series which are situated at a
great distance from the origin, but which do not themselves originally tend to
vanish as they become more distant therefrom. Nor is this difficulty entirely

Sir William Rowan Hamilton on Fluctuating Functions. 319

removed, when Integration by parts is had recourse to, in order to show that the
effect of these distant terms is insensible in the ultimate result ; because it then
becomes necessary to differentiate the arbitrary function ; but to treat its diffe-
rential coefficient as always finite, is to diminish the generality of the inquiry.

Many other processes and proofs are subject to similar or different difficulties;
but there is one method of demonstration employed by Fourier, in his separate
Treatise on Heat, which has, in the opinion of the present writer, received less
notice than it deserves, and of which it is proper here to speak. The principle
of the method here alluded to may be called the Principle of Fluctuation, and
is the same which was enunciated under that title in the remarks prefixed to this
paper. In virtue of this principle (which may thus be considered as having
been indicated by Fourier, although not expressly stated by him), if any func-
tion, such as the sine or cosine of an infinite multiple of an arc, changes sign in-
finitely often within a finite extent of the variable on which it depends, and has
for its mean value zero ; and if this, which may be called a fluctuating function,
be multiplied by any arbitrary but finite function of the same variable, and after-
wards Integrated between any finite limits ; the integral of the product will be
zero, on account of the mutual destruction or neutralization of all its elements.

It follows immediately from this principle, that if the factor by which the
fluctuating function is multiplied, instead of remaining always finite, becomes
infinite between the limits of integration, for one or more particular values of the
variable on which it depends ; it is then only necessary to attend to values in the
immediate neighbourhood of these, in order to obtain the value of the integral.
And in this way Fourier has given what seems to be the most satisfactory pub-
lished proof, and (so to speak) the most natural explanation of the theorem called
by his name ; since it exhibits the actual process, one might almost say the in-
terior mechanism, which, in the expression assigned by him, destroys the effect of
all those values of the auxiliary variable which are not required for the result.
So clear, indeed, is this conception, that it admits of being easily translated into
geometrical constructions, which have accordingly been used by Fourier for that
purpose.

There are, however, some remaining difficulties connected with this mode of
demonstration, which may perhaps account for the circumstance that it seems
never to be mentioned, nor alluded to, in any of the historical notices which

320 SiK William Rowan Hamilton on Fluctuating Functions.

PoissoN has given on the subject of these transformations. For example,
although Fourier, in the proof just referred to, of the theorem called by his
name, shows clearly that in integrating the product of an arbitrary but finite
function, and the sine or cosine of an infinite multiple, each successive positive
portion of the integral is destroyed by the negative portion which follows it, if
infinitely small quantities be neglected, yet he omits to show that the infinitely
small outstanding difference of values of these positive and negative portions,
corresponding to the single period of the trigonometric function introduced, is
of the second order; and, therefore, a doubt may arise whether the infinite
number of such infinitely small periods, contained in any finite interval, may not
produce, by their accumulation, a finite result. It is also desirable to be able to
state the argument in the language of limits, rather than in that of infinitesimals ;
and to exhibit, by appropriate definitions and notations, what was evidently fore-
seen by Fourier, that the result depends rather on the fluctuating than on the
trigonometric character of the auxiliary function employed.

The same view of the question had occurred to the present writer, before he
was aware that indications of it were to be found among the published works of
Fourier ; and he still conceives that the details of the demonstration to which
he was thus led may be not devoid of interest and utility, as tending to give
greater rigour and clearness to the proof and the conception of a widely applicable
and highly remarkable theorem.

Yet, if he did not suppose that the present paper contains something more
than a mere expansion or improvement of a known proof of a known result, the
Author would scarcely have ventured to offer it to the Transactions* of the
Royal Irish Academy. It aims not merely to give a more perfectly satisfactory
demonstration of Fourier's celebrated theorem than any which the writer has
elsewhere seen, but also to present that theorem, and many others analogous
thereto, under a greatly generalized form, deduced from the principle of fluctu-

* The Author is desirous to acknowledge, that since the time of his first communicating the pre-
sent paper to the Royal Irish Academy, in June, 1840, he has had an opportunity of entirely re-
writing it, and that the last sheet is only now passing through the press, in June, 1842. Yet it may
be proper to mention also that the theorems (A) (B) (C), which sufficiently express the character of
the communication, were printed (with some slight differences of notation) in the year 1840, as part
of the Proceedings of the Academy for the date prefixed to this paper.

Sir William Rowan Hamilton on Fluctuating Functions. 321

atlon. Functions more general than sines or cosines, yet having some correspon-
dent properties, are introduced throughout ; and constants, distinct from the ratio
of the circumference to the diameter of a circle, present themselves in connexion
therewith. And thus, if the intention of the writer have been in any degree ac-
complished, it will have been shown, according to the opinion expressed in the
remarks prefixed to this paper, that the development of the important principle
above referred to gives not only a new clearness, but also (in some respects) a
new extension, to this department of science.

VOL. xrx. 2 T

322

XIII. — On the Minute Structure of the Brain in the Chipanzee, and of the
human Idiot, compared with that of the perfect Brain of Man ; with some
Reflections on the Cerebral Functions. By James Macartney, M. D.,
F. R. S., F. L. S., M. R. I. A., &c. &c.

Read June 27, 1842.

JVIANY years ago I discovered, with only a common pocket lens, a reticulation
of fine white fibres, immediately under the surface of the cerebrum, in birds.
This first led me to believe that the medullary fibres, as they are called, extended
farther, and were more subdivided than had been hitherto supposed. I have since
been able to demonstrate to medical students, and to several teachers of anatomy,
the existence of those filaments in every part of the brain, by simply moistening
the substance of the organ, during the dissection, with a solution of alum in
water, which has the effect of slightly coagulating, and rendering the finer fila-
ments visible, which, in their natural condition, are transparent. By this means,
I have shown that the filaments (which I prefer to call sentient, instead of white
or medullary) everywhere assumed a plexiform arrangement, and that the most
delicate and intricate plexusus were to be found inclosed in the grey or coloured
substances of the brain. This fact proves the analogy between the coloured sub-
stances of the brain, and the ganglia of the nervous system, in which there is a
close reticulation of nervous fibres. I have long been in the habit of consider-
ing the magnitude and form of the entire brain, and of its several parts, as being
merely subservient to the number, extent, and connexions of the various plexuses,
in which, and especially in those occupying the coloured substances, I believe the
sensorial powers of the brain to reside.

A Chimpanzee (the pigmy of Tyson) having some months ago died in Dub-
lin, and the dissection of it having been entrusted to Mr. Wilde, I proposed to
him that I should undertake the examination of the animal's brain, in my own

Dr. Macartney on the Structure of the Brain in the Chimpanzee, ^c. 323

manner. Tyson and others had described the bulk, shape, and external appear-
ance of the different parts of this creature's brain, but the intimate structure had
never been examined by any anatomist.

I shall now lay before the Academy an account of what I observed in the
brain of the Chimpanzee, and likewise in those of two idiots ; by which it will
appear that the brain in the latter possesses a still lower degree of organization,
than in the former animal.

DISSECTION OF THE BRAIN IN THE CHIMPANZEE (siMIA TROGLODYTES. LIN.)

The external for^n bore so great a resemblance to the human brain, that,
excepting the difference in size, the one might be mistaken for the other. The
convolutions were as decidedly marked, and the proportions of the cerebellum to
the cerebrum were exactly as in man. On the under surface of the brain I ob-
served that the two white pea-shaped bodies, called corpora candicantia, were
very indistinct ; and they did not appear to be, as in man, the continuation of the
anterior crura of \he fornix. The pons, which unites the lateral lobes of the
cerebellum, was, perhaps, rather flatter than in the human subject, and the fifth
pair of nerves entered it, and passed for a little way distinctly, which is so re-
markable in the sheep. The pyramids did not decussate to any extent ; only
two superficial bundles of fibres crossed. The corpora olivaria did not project
distinctly, and the band which surrounds them was not observed. The structure
internally of these bodies consisted of white filaments included in grey substance.
The branches of the arbor vitce were, perhaps, not so deep, but quite as numerous
as in us. The white filaments composing the trunk were not so fine, nor so
strictly interwoven, as in man, and therefore they were more easily distinguished.
The corpus Jimbriatutn was a long shape, and appeared to be composed chiefly
of grey substance, and wanted the denticulated edge. The part called locus
niger, in the crura of the cerebrum, was a small, greenish-grey mass, of an irre-
gular figure, and less than a pea, instead of the crescentic form, as in man ; and
it did not mingle with the white fibres of the crus. The pineal gland was large.
It was removed in making a cast of the ventricles, and lost ; it was not, therefore,
ascertained whether it had any calcareous matter in it or not. The parts in the
lateral ventricles corresponded very nearly with the same in man. The soji com-

2t2

324 Dr. Macartney on the Structure of the Brain in the Chimpanzee and

missure was particularly strong, and held distinct white filaments. The linea
semilunaris was faintly marked. The two anterior of the tubercula quadrigemina,
called nates, were the smaller. The fourth ventricle was much prolonged into
the lateral lobes of the cerebellum. The grey substance on the floor of the ven-
tricle was not raised into the appearance of two ganglia, and there were no white
stria. The sentient or white filaments formed looser or less complicated plexuses,
wherever they were examined, than in man, and I could not discover any of the
delicate arborescent filaments in the base of the corpora striata.

DISSECTION OF A FEMALE IDIOT, WITH EXTRAORDINARY BRAIN.

The whole mass of the brain was small, but the front part did not recede. The
convolutions were rather small, but sufficiently deep for the size of the brain.
The lobes of the cerebellum were not the one-third of the usual size. The gyri
were scarcely distinguishable, and the divisions were few and shallow. The arbor
vitce had but two principal branches, and the sub-divisions of these were few.
The anterior part of the lobes was supplied by two clusters of membranous cells,
filled with red jelly or albuminous fluid, such as we find substituted for the
brain in acephalous foetuses. The corpus fimbriatum was indistinct, wanted the
denticulated margin, and the proper structure interiorly, and was not half the
proper size. The pons was exceedingly small, and its internal structure obscure.
The pyramids were parallel cylindric forms, and did not appear to decussate. The
corpora olivaria had little prominence, and the coloured substance was deficient.
The locus niger was imperfectly formed, and not of a dark colour. The corpora
striata were very small, as also the white filaments contained in them. The pineal
gland was rather of a large size, and contained a cluster of round soft bodies, in
place of the calcareous granules. In fine, the character of the whole brain was
imperfection of intimate structure. The plexuses were not intricate, and the
grey substances pale, and not in sufficient quantity. This person had been a
patient in the Whitworth Hospital. The account I received of the state of her
intellect from the house pupil was, that she was foolish, and that he could never
get a rational answer from her. She was extremely ugly, with projecting jaws
and teeth, and an idiotic countenance. She was an unmarried woman, but not a
virgin, notwithstanding the great deficiency in her organ of amativeness.

Human Idiot, compared with that of the perfect Brain of Man. 325

DISSECTION OF THE BRAIN OF A MALE IDIOT.

The cerebrum was small, and the anterior lobes especially so. The cerebellum
projected beyond the posterior lobes of the hemispheres. The convolutions of the
cerebrum were small, particularly those of the anterior lobes on the left side, —
they were so imperfectly developed, and so closely connected to each other, that
they had more the appearance of a tuberculated than of a convoluted surface.
The olfactory nerves were small, and very deficient in grey substance, indeed all
the coloured parts of the brain were rather pale. The pyramids could scarcely be
distinguished, being extremely small, and confounded in the projection of the
corpora olivaria ; they did not appear to decussate ; the one on the left side was
particularly small. The left hemisphere of the brain was smaller than the one
on the right side. The tubercula quadrigemina were of an equal size, and a grey
colour on their surface. The pineal gland was large, semi-transparent, and con-
tained very little of the gritty matter. On the surface of the left crus of the
cerebrum there was a green tinge observed, which, on being cut into, proved to
be the locus niger in a disorganized and nearly dissolved state. There were no
white strice in the fourth ventricle. The plexus of white filaments at the roots of
the olfactory nerves was very plain on the right side, but very imperfect on the
left. The brain was tolerably firm. The spinal marrow was hard, and the cere-
bellum was soft. The structure, as well as form of the parts in this brain, was
imperfect throughout, but most remarkably so on the left side ; the want of agree-
ment between the two sides would necessarily impair the functions of the brain.

The first deviations from the perfect brain of man appear to be with respect
to the following parts : — The locus niger, the corpus fimbriatum, the white strice
in the floor of the fourth ventricle, the decussation of the pyramids, the distinc-
tion of the anterior crura of the fornix, the corpora olivaria, the degree of inter-
mixture of the sentient or white filaments in the arbor vitce, the corpora candi-
cantia, and the existence of calcareous granules in the pineal gland.

It is remarkable, that many of these parts are not found in the first stages
of foetal life, and some of them not until after birth. The pineal gland, accord-
ing to Meckel, is not perfect until the seventh year of infancy. The same parts,
also, first decline, and ultimately disappear in animals, according to their scale of
organization ; and further, it is chiefly with respect to these parts, that varieties

326 Dr. Macartney on the Structure of the Brain in the Chimpanzee and

of structure are observed in the brains of different rational human beinffs. I
have found many deviations from the ordinary structure in subjects, without being
able to ascertain what peculiarities of character belonged to them when alive ;
but in one instance, of a deaf and dumb person, the white strice of the fourth
ventricle (with which the auditory nerves communicate) were imperfectly formed,
were not subdivided, and did not unite with each other. If, therefore, we can
ever arive at correct notions of the functions of the brain, it must be by careful
dissections of the interior parts of the cerebral organ, and by ascertaining the
correspondence between the minute structure, and the endowments and disposi-
tions of the different individuals ; taking into account, at the same time, the influ-
ence of the various organs of the body, instead of ascribing to certain parts on
the surface of the brain, distinct and often opposing faculties, as Gall and Spurz-
heim have done.

It seems to be particularly absurd to suppose that the cerebellum, a part evi-
dently as highly organized, and of as much importance as the cerebrum itself,
should be designed to produce merely the sexual instinct. In animals that have
the lateral lobes of the cerebellum very small, or who want them altogether, this
instinct is stronger than in man. In those instances which are known of the absence
of a part, or one lobe, or the whole cerebellum, no want of the venereal appetite
existed ; and a case is related of a person in whom the sexual desire was so ungo-
vernable, that mechanic restraint became necessary ; and it was found, after death,
that both lobes of the cerebellum were wanting in this person. In animals that
propagate only at particular seasons of the year, the testicles and ovaries are sin-
gularly developed at those periods, and afterwards decline, while at the same time
no change takes place in the cerebellum. The abolition of the sexual instinct,
by the extirpation of the testes, or of the ovaries, puts it beyond all doubt that this
impulse does not originate in any part of the brain.

It would appear that all instincts depend upon the condition and state of feel-
ing in those organs with the functions of which they are immediately connected ;
thus, the maternal instinct (at least in mammiferous animals) is in a great mea-
sure the result of the tension of the mammary glands. As soon as this is removed,
by the absorbents carrying off the milk, quadrupeds lose all care and anxiety about
their young. The cerebral organ would, perhaps, of all others, be the most unfit
for the generation of instincts. The brain is destined to direct or control instinc-

Human Idiot, compared with that of the perfect Brain of Man. 327

tlve feelings, and therefore it cannot create them. If a person attempt to command
any instinctive impulse to be felt, he will find it as impossible to do, as to rise
from his chair, merely by willing it, without the aid of the muscles.

I have ascertained and demonstrated, by repeated dissections, that all the
plexuses of the brain are continuous with each other ; that no part of the nervous
system is isolated ; and, consequently, the different parts must exercise a mutual
influence on each other. I have proved that the spinal nerves, as well as those
of the brain, are not inserted in the same way as the roots of plants penetrate
the earth, which has been heretofore believed, but that they are united with the
parts from which they are supposed to arise, and that the spinal nerves form a
chain of communication with each other, after they enter the spinal marrow. It
is in consequence of the integrity of the whole nervous system, that the various
sympathies, both natural and morbid, exist between the different organs of the
body. If the continuity of the sentient or nervous filaments were to be inter-
cepted at any one place, their functions would be arrested at that point, in the
same manner as the division of a nerve, destroys sensation and voluntary motion
in the parts to which the nerve is sent.

Some anatomists, it is true, have supposed that the various reticulations of the
nerves, and the intermixture of the filaments of the brain, were merely to bring
them into contact, and that there was no incorporation of the sentient substances.
This opinion is consequent upon another, as ill supported by facts ; namely, that
there is a subtile or nervous fluid, which carries impressions made on the nerves
to the brain, and thus causes sensation ; and that the same fluid, proceeding from
the brain to the muscles, produces voluntary motions. It has never been, however,
attempted to explain how this imaginary fluid could become the instrument of
sensation or volition, more than the sentient substance itself. For ray part, I am
satisfied with the knowledge of the undoubted fact, that the peculiar matter which
exists in the nerves, and the white filaments of the brain, is endowed with the
power oi feeling — a power perfectly distinct from every other in nature ; and I
think it is equally obvious that the various modifications of sensorial function we
observe are the result, and require for their 'production, the multitude of sub-
divisions and re-unions that take place in the sentient filaments of the brain and
nerves. Voluntary motion appears to me to be the natural consequence of the
connexion between the central part of the nervous system, and the muscles which
move in obedience to the will or desire of the individual.

328 Dr. Macartney on the Structure of the Brain in the Chimpanzee, S^c.

EXPLANATION OF THE PLATES.

Plate I. — Fig. 1. Was drawn from an accurate plaster cast of the upper sur-
face of the brain of the Chimpanzee.
Fig. 2. Was taken from the cast of the lower surface of the same
brain. Both these figures are of the natural size.

Plate II. Exhibits the different parts as they were found on the inferior sur-
face of the brain of an idiot.
a a. The two lateral lobes of the cerebellum, exceedingly small,

and imperfectly formed.
h h. The membranous cells, which held a reddish fluid.
c. The pons or commissure of the cerebellum, also small and im-
perfect.
d d. The pyramidal bodies.

e e. The olive-shaped bodies, making scarcely any projection.
ff. The olfactory nerves.
gg. The optic nerves.
, h h. The third pair of nerves.
The other nerves were not preserved.

..^pgg'^'^^^ft^jpiw-" r^^^.

Fi^j'?

'■^sas^sis*' •

[r*;W?»r^'"^-;'

PLATE 2.

J^nufru, cot- JJ^m* dv (?Jhf Ncfytf

^imiZMo }6 7Hm9f^

329

XIV. — On Equations of the Fifth Degree : and especially on a certain System
of Expressions connected with those Equations, which Professor Badano*
has lately proposed. By Sir William Rowan Hamilton, LL.D., P.R.I.A.,
F.R.A.S., Honorary I/ember of the Royal Societies of Edinburgh and
Dublin ; Honorary or Corresponding Member of the Royal or Imperial
Academies of St. Petersburgh, Berlin, and Turin, of the American Society
of Arts and Sciences, and of other Scientific Societies at home and abroad ;
Andrews' Professor of Astronomy in the University of Dublin, and Royal
Astronomer of Ireland.

Eead 4th August, 1842.

1. JLAGRANGE has shown that if a be a given root of the equation

a"-' -I- a"-* + . . . + a* -f a+ 1 ^ 0,
n being a prime factor of m, and if n denote for abridgment the quotient

1.2.3. ..m
(1.2.3...-)

then the function

t = x' -{- ax" -{- a^x'" + . . . + a^-'ar'""

has only jj. different values, corresponding to all possible changes of arrangement
of the m quantities a/, x", ... jr'"", which may be considered as the roots of a
given equation of the m"* degree,

^■» _ Aar^-' + Bar*"-*— c^"-^ -j- . . . = 0 ;

• Nuove Ricerche sulla Risoluzione Generale delle Equazioni Algebriche del P. Gebolamo
Badano, Carmelitano scalzo, Professore di Matematica nella R. Universita di Geneva. Geneva,
Tipografia Ponthenier, 1840.

VOL. XIX. 2 U

330 Sir William Rowan Hamilton on Equations of the Fifth Degree.

and that if the development of the n'* power of this function t be reduced, by

the help of the equation

a":=l,

(and not by the equation a"~' -f- &c. = 0,) to the form

r = ^'°' + a^ + a'l" + . . . + a"-' ^"-",

then this power f itself has only - different values, and the term ^°' has only

— T-^ — rr such values, or is a root of an equation of the degree
n{n — \) ^ *'

1.2.3....m

m\"'

^(7^_l)(l.2.3...-J

of which equation the coefficients are rational functions of the given coefficients
A, B, c, &c. ; while ^', ^", . . . ^'"~" are the roots of an equation of the degree
n — 1, of which the coefficients can be expressed rationally in terms of ^''" and
of the same original coefficients A, ... of the given equation in x.

2. For example, if there be given an equation of the sixth degree,

x^ — KX^ 4" B.r'' — cj;^ -j- Yix"^ — eo: + f := 0,

of which the roots are denoted by x', x", x'", x'^, x^, x"^, and if we form the

function

t-x'^ax"\ a^x'" + a^x'''-\- a' x" -{- a? x"",

in which a = — 1 ; we shall then have

ni = 6, 7^=2, /x = ^ = 20, ^ = 10, , ^ ,, = 10;
3b n n{n — \)

and the function t will have twenty different values, but its square will have only
ten. And if, by using only the equation a^ ■=. 1, and not the equation o = — 1,
we reduce the development of this square to the form

f = ^o' + ar,

the term ^°* will itself be a ten-valued function of the six quantities x' , . . . x'';
and ^ will be a rational function of ^'"^ and a, namely,

r = A^ - 1^°).

Sir William Rowan Hamilton on Equations of the Fifth Degree. 331

3. Again, if with the same meanings of ^', . .. x^', we form t by the same
expression as before, but suppose a to be a root of the equation

a^ + a 4- 1 = 0,
then

m = 6, n = 3, /i = -^ = 90, ^ = 30, , ^ ^. = 15;
8 n n{n—\)

so that the function t will now have 90 different values, but its cube will have
only 30 ; and if that cube be reduced, by the equation v^ z=. 1, to the form

^rr^^o' + ar + a^r,

then 1'°' will be a root of an equation of the fifteenth degree, while ^ and ^" will
be the roots of a quadratic equation, the coefficients of this last equation being
rational functions of ^'°', and of the given coefficients a, &c.

4. And if, in like manner, we consider the case

m = 5,n = 5,fji = 120, ^ = 24, - , ^ ,, = 6,

n n{n — \)

so that o(f , . . x^ are the roots of a given equation of the fifth degree

X' — KX^ -|- -Qx'^ — cr^ ■\-ttX — E = 0,
and

t=x' -^ ax" + c? x"' + a^x"'-i- a'x'',

in which a is a root of the equation

a* -1- a' 4- a^ -j- a + 1 = 0,

then the function t has itself 120 different values, but its fifth power has only
24 ; and if this fifth power be put under the form

f = ^o' + ar 4- a" r' + aP ^" + a' ^'\

by the help of the equation a* = 1, then ^"^ is a root of an equation of the sixth
degree, of which the coefficients are rational functions of a, b, c, d, e, while
^, ^", ^'", ^""^ are the roots of an equation of the fourth degree, of which the co-
efficients are rational functions of the same given coefficients A, &c., and of 1'°'.

5. Lagrange has shown that these principles explain the success of the
known methods for resolving quadratic, cubic, and biquadratic equations ; but

2 u 2

332 Sir William Rowan Hamilton on Equations of the Fifth Degree.

that they tend to discourage the hope of resolving any general equation above
the fourth degree, by any similar method. And in fact it has since* been shown
to be impossible to express any root of any general equation, of the fifth or any
higher degree, as a function of the coefficients of that equation, by any finite
combination of radicals and rational functions. Yet it appears to be desirable to
examine into the validity and import of an elegant system of radical expressions
which have lately been proposed by Professor Badano of Genoa, for the twenty-
four values of Lagrange's function f referred to in the last article; and to in-
quire whether these new expressions are adapted to assist in the solution of equa-
tions of the fifth degree, or why they fail to do so.

6. In order to understand more easily and more clearly the expressions which
are thus to be examined, it will be advantageous to begin by applying the method
by which they are obtained to equations of lower degrees. And first it is evident
that the general quadratic equation,

A-* — A^ -f- B = 0,

has its roots expressed as follows :

x' = a-\-^, x" =ia — ^',

a not here denoting any root of unity, but a rational function of the coefficients
of the given equation (namely t}a), and /3^ being another rational function of
those coefficients (namely j^A^ — b) ; because by the general principles of article

1., when m = 2 and n := 2, we have - = 1, so that the function (x' — x"y is

n

symmetric, as Indeed it is well known to be.

7. Proceeding to the cubic equation

X^ — AX'^ -\- BX — C = 0,

and seeking the values of the function

f = (or' + ex" -f e' x"'y,

in which 6 is such that

e^ + 0 + 1 = 0,

* See a paper by the present writer, " On the Argument of Abel," &c., in the Second Part of
the Eighteenth Volume of the Transactions of this Academy.

Sir William Rowan Hamilton on Equations of the Fifth Degree. 333
we know first, by the same general principles, that the number of these values is

two, because - =: 2, when m = 3, ra := 3. And because these values will not
n

be altered by adding any common term to the three roots a/, x", x'", it is per-
mitted to treat the sum of these three roots as vanishing, or to assume that

x' + x" + x'" = 0 ;

that is, to reduce the cubic equation to the form

x'^ -|- px' -{■ q-=zO.

In other words, the function

e={x, + ex,-^6'x,y,

in which x^, x^ x^ are the three roots of the equation with coefficients a, b, c,
will depend on those coefficients, only by depending on p and q, if these two
quantities be chosen such that we shall have identically »

ar* — A^'^ -\-'&x — c — {x — \ kf ■\- f {x — :j a) -1" §-.

8. This being perceived, and x" and x'" being seen to be the two roots of
the quadratic equation

y^+yy + y^ + p = o,

which is obtained by dividing the cubic

. x"^-\-px" — x'^ -px' = Q,

by the linear factor xf' — x' \ we may, by the theory of quadratics, assume the
expressions

x" = a-{-p, x"' = a—p,

provided that we make

a=-l-x', ^ = -^x"-p,

that is, provided that we establish the identity

(x" - af — ^ = x"' + X' X" + x'^ + p.

And, substituting for x', x", x'", their values as functions of a and /3, and reduc-
ing by the equation 0^ + 0 -f- 1 = 0, we find

334 Sir William Rowan Hamilton on Equations of the Fifth Degree.

in which

a' = - 27 a (a^ - ,3=), /3'^ = _ 27 ^^ (9a^ - ^f.

But a and /3' are rational functions of x' and p ; and substituting their expres-
sions as such, we find corresponding expressions for a! and ^^ namely,

a' = ^-x' {x'- +;,), ^"^ = ^ (Sy^ + 4p) (3a;- + pf.

9. Finally, or' is such that

x'^-\-px' = — q;

and it is found on trial to be possible by this condition to eliminate x' from the
expressions for a' and j3'^, obtained at the end of the last article, and so to arrive
at these other expressions, which are rational functions of p and q :

a'^-Y*?. r = ^(27?^ + 4/).

In this manner then It might have been discovered, what has long been other-
wise known, that the function ^ is a root of the auxiliary quadratic equation

(t'y-{-2lq (f)-27p'=0.

And because the same method gives

(y + ex" + e'x'") (x' + e' x" + ex'") = ga^ + 3^ = — Sp,

we should obtain the known expressions for the three roots of the cubic equation

x" -\- px' -\- q - 0,
under the forms :

•^-3 ?'^"-3~r-^-3 T'

which are immediately verified by observing that

't\3

'^ = >. ©-(?)=-'■

The foregoing method therefore succeeds completely for equations of the third
degree.

10. In the case of the biquadratic equation, deprived for simplicity of its
second term, namely.

Sir William Rowan Hamilton on Equations of the Fifth Degree. 335

x'*-\-px'^-\-qx' -{-r-O,
so that the sum of the four roots vanishes,

we may consider x", x'", x"', as roots of the cubic equation

x"^ + x' x'" + {x'^ -\-p) x" + x'^ ^px'-\-q = 0;

and this may be put under the form

(^x" — ay — 3rj (x" — a) - 2e = 0,

of which the roots (by the theory of cubic equations) may be expressed as fol-
lows :

x"=a-\-p-\-y, .r'" = a + e/3 + eV x"" = a -{■ e'p-\- By,

/3, 7, and 6, being such as to satisfy the conditions

^3 _j_ ^3 _ 2e, j8y = »;, 02 4- e -I- 1 = 0.

Comparing the two forms of the cubic equation in x", we find the relations

x'= — 3a, x'^ -\- p = 3 (a-" — 7]), x" -\- px' -\- q = — a' -\- 3ari — 2e;

which give

a=-^x', ri = - ^ (2x'' -^ 3p), e =-^(20x" + I8px' + 27q).

Thus, any rational function of the four roots of the given biquadratic can be ex-
pressed rationally in terms of a, j3, 7 ; while a, ^, and /3' -\- 7^ are rational func-
tions of x', p, q ; and the function x'* -\- px"^ -\- qx' may be changed, wherever it
occurs, to the given quantity — r.

1 1 . With these preparations it is easy to express, as follows, the function

{x' - x" + xf" - x'y,

which the general theorems of Lagrange, already mentioned, lead us to con-
sider. Denoting it by 4^, we have

z = (— 2a+ ep + 6^7)2 = a' + els' + ey ;
in which

a' = 4a? -\- 2/^7, /3' = 7^ - 4a]3, 7 = ^* — 4a7 :

and the three values of z are the three roots of the cubic equation

336 Sir William Rowan Hamilton on Equations of the Fifth Degree.

(^ _ a!f — 3»/ {z — a!) — 2e' = 0 ;
in which

a' z= 4a^ + 2rj,

vi = j3'y = V- + iGa'-*/ — Sae,

e' = 1 (^'3 + y'3) — 2e2 - t;3 — 12aej7 + 48a^ 17^ - 64a^e.
Substituting for a, 7], e, their values, as functions of x', p, q, we find

V = i (— I2x'* — 12j9a;'^ - 12^0;' +/) ;
€' = 315: (72jo:c'* + 72pV* + 72iJ(?a/ + 27?^ + 2p^) ;
and eliminating x', by the condition

«''' -|- px'^ -\- qx' := — r,

we obtain

V=i(12r + ;>^);

e' = 3^(-72p/- + 27?^ + 2/).

The auxiliary cubic in z becomes therefore

(^ + ^Py - i (12r +/) (2r + §;>)+ 2V (72;>r - 27?^ - 2f) = 0 ;

that is

;23 + 2j9 0^ + (/ — 4r) 5? — 9-^ = 0 ;

and if its three roots be denoted by z', z", z"\ in an order such that we may
write

z' = \{:d^x" -x'" -x'^y-d-^^^i,

Z" = l {x' - x" + x'" - x'y = a' + e^ + e'y',

s'"= 1 (x' - x" - x'" + x'^f =: a' + 0^-p'+ ey,

we may express the four roots of the biquadratic equation under known forms,
by means of the square roots of z', z", z'", as follows :

x' =+^/^ + iV^" + ^V^",
y = + |V^' - 1/^" - iV^",
a/" = - ^/^' + \^z" - \V2f",

x'^=-i^z'-^v'z"-\-iv^z"'.

Sir William Rowan Hamilton on Equations of the Fifth Degree. 337

It may be noticed. also that the present method gives for the product of these
three square roots, the expression :

y/z'. ^Z".^Z"' = ^ (X' + X" - X'" — X'") {X' - X" + X'" - x'")

(^a;'_a:"-x"'^x"')

= (_ 2a 4- /3 + 7) (— 2a + ej3 + O'y) ( —2a + 6'p -\- Oy)

= — 8a^ + 6ar] 4" 2e = — q ;

a result which may be verified by observing that, by the expressions given above
for a, t]', e', in terms of a, 7], e, we have the relation

z'z"z"' = a'' — 3a r,' + 2e' = (— 8a^ + Barj + 2e)^

12. In this manner, then, it might have been discovered that the four roots
:i'„ X2, Xp x^, of the general biquadratic equation

X* — Ax^ -\- Bx'' — ex -\- T> =^0,

are the four values of an expression of the form a -|- 13 + 7 -{- 8, in which, a, /3- -|-
7- -j- 8', /378, and )3^7^ -j- y'i- + c-^'; are rational functions of the coefficients
A, B, c, D, and may be determined as such by comparison with the identical
equation

(a + ^ + 7+S_a)^-2(p^ + 7^ + 8^)(a + ^ + 7+5-a)^

+ (/3' + r + ^7 = 8i37K« + ^ + 7 + S - a) + 4 (^y + 7^8^ + 8-'/30,

of which each member is an expression for the square of 2 (^y + 78 + ^P)- It
might have been perceived also that any three quantities, such as here /S'-, y\ 8',
which are the three roots of a given cubic equation, may be considered as the
three values of an expression of the form a -}- ^ -\- y', in which, a', ^'y, and
^^ -f 7'^ are rational functions of the coefficients of that given equation, and may
have their forms determined by comparison witli the identity,

(*' + ^ + 7 - «■')' - 3py' {a! + ^' 4- 7' _ a') - ^" - 7'' = 0.

And finally that any two quantities which, as here /3'^ and 7', arc the two roots
of a given quadratic equation, are also the two values of an expression of the form
a" -f /3 ', in which a" and ^'^ may be determined by comparing the given equa-
tion with the following identical form,

(a" + p" _ cc"f - ^"-^ = 0.
VOL. XIX. 2 X

so that
and

338 Sir William Rowan Hamilton on Equations of the Fifth Degree.

Let us now endeavour to apply similar methods of expression to a system of five
arbitrary quantities, or to an equation of the fifth degree.

13. Let, therefore, x^, x.-^, x^, x^, x^, be the five roots of the equation

X^ — AX* + BX^ — CX'^ -}- T>X — E = 0, (1)

and let .r', x", x"', x^^, x^, be the five roots of the same equation when deprived
of its second term, or put under the form

x" + px'^ + ya-'2 + rx' + * = 0, (2)

a/ + or" + 3f" + x'"" + a;'' = 0, (3)

^ x,zzx' + ^^, x^ = x"+^h, &c. (4)

Dividing the equation of the fifth degree

x"' -af^^p {x"^ - x") + q {af" - x'^) + r {x" -3f)zzO, (5)

by the linear factor x" — a;', we obtain the biquadratic

x"* + x'x"^+ {xf^ + p) 3f^+ {a/^ + px' + q)x"-\-x"-irp3/''-\-q3^ + r = 0, (6)

of which the four roots are x", x'", x^^, x ^. Hence, by the theory of biqua-
dratic equations, we may employ the expressions :

provided that a, j3, 7, 8 are such as to satisfy, independently of x", the condi-
tion :

{oo"~«.y-2{^^f+l-^){x"-c.f-S^l{x"-c.) + ^+y*^i*

-2(^Y-f 7^8^ + g'^p^)
= ar"" + x'x"' + {x"" + p) x'"" + {of' + px' + q) x" -f x'* + px'^

-\-qx' -\-r;
which decomposes Itself into the four following :
— 4a = a;' ;

+ 6«^-2(^^.f 7^ + 8^) = x'^-j-j9;

-4«'+4«(/3^ + 7^+8^)-8/378 = a/'+j9a;' + y; [ (9)

+«^-2a^(|3^+ 7'^+g^).f 8a^7g-f (^* + 7^ + 8^)'^-4(py+7'8^+ 8^/3^)

(8)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 339

and, therefore, conducts to expressions for a, /3' + 7' + ^^ /^T^? and ^V -|- 7^8'^ +
8^j3^, as rational functions of a/, jo, y, r. Again, by the theory of cubic equations,
we may write :

^- = e-\- K-\-\ 7' = e + 0a: + (f\ 8^ = e + 0^ + OX, (10)

in which 0 is a root of the equation

02 + 0 -1_ 1 ::: 0, (11)

while e, *-A, and k^ -|- X^ are symmetric functions of /3^ 7'^ 8^. Making, for
abridgment,

^78 rz 17, Af\ rr <,

we have, by (10) and (11),

/r'^ + \3 = ^^ — £3 4- Set,

and

/S^ + 7^ + 8^ = 3e, PY + 7^8^ -I- 8'^j3^ = 3 (e' - t) ;

and, therefore, by (9),

— 4a = y ; Qi^c^ — e) -zz a/"^ -\- p ;

— 4tt='+12ae — 8i; = y^+p,r'4-y; '
a* - Qa\ + 8a»7 — Se^ + 12^ = x" + J9x'^ + ya/ + r ;

conditions which give

a = ~i^ ;

e = -^i^(5y^ + 8p);

t = +^:f(10y*4-ll;>y^+9?^' + p^+12r). J

Thus, a, e, 7/, and «, on the one hand, are rational functions of x', p, q, r; and,
on the other hand, x\ x", a/", a'^^, x^ may be considered as functions, although
not entirely rational, of a, e, rj, i. In fact, if these four last quantities (denoted
to help the memory by four Greek vowels) be supposed to be given, and if, by
extraction of a square root and a cube root, a value of k be found, which satis-
fies the auxiliary equation

/ _ (^2 _ ^3 ^ 3,^) ^3 _(. ^3 _ 0, (17)

2x2

(12)

(13)
(14)

(15)

(16)

340 Sir William Rowan Hamilton on Equations of the Fifth Degree.

and then a corresponding value of X by the condition kX = i, we shall have ± )3
by extraction of another square root, since j3' = e -|- a- -f- X ; and may afterwards,
by the extraction of a third square root, either find ± y from the expression
y^ =z e-{- 6k -\- 6-\, and deduce 8 from the product ^yh =. t), or else find
— (7 "f" ^) from the expression

{y + if=2e-K-X + ^; (18)

and may then treat oc", x'", .x'*', x^, as the four values of « -}- /3 + 7 + 8, while
x" ^ — 4«. Hence any function whatever of the five roots of the general equa-
tion (1 ) of the fifth degree may be considered as a function of the five quantities
A, a, e, t;, t ; and if, in the expression of that function, the values (16) be substi-
tuted for a, 6, t], I, so as to introduce in their stead the quantities x', p, g, r. It Is
permitted to make any simplifications of the result which can be obtained from
the relation (2), by changing a/* -\- pi^'^ + (l^^-\- ''•^'j wherever it occui-s, to the
known quantity — s.

14. Consider then the twentyfour-valued function, referred to In a former
article, and suggested (as Lagrange has shown) by the analogy of equations of
lower degrees ; namely, t% in which

t zz x^-\- wx^ + MV3 -|- to^x^ + f^^^.v (19)

and

«* + «.' -f ft)^ -f « -f 1 = 0 ; (20)

a) here (and not a) denoting an imaginary fifth root of unity, so that

«*=1. (21)

Observing, that by (4) and (20), x^, &c. may be changed in (19) to x', &c. ; and
distinguishing among themselves the 1 20 values of the function t by employing
the notation

4»erf, = «,V' -f w^x^'^ -f «.V=> + a.V"' -j- u,'x^'\ (22)

which gives, for example,

^■2345 = ^ + « V + «V" + wV + wx ''; (23)

we shall have, on substituting for x' Its value — 4a, and for x", x'", x'^, x"
their values (7), the system of the twenty-four expressions following

'&

Sir William Rowan Hamilton on Equations of the Fifth Degree. 341

^12345 = — 5a + B/3 + C7 + dS ;
<i3J64 = — 5a + B/3 — C7 — d8 ;
'i4S23 = — 5a — B/3 + C7 — d8;
^.5432 = — 5a — B^ — C7 + d8 ;

(24)

'^53 = — 5a + B7 + c8 + Dp;
<i423s = — 5a + B7 — c8 — D/3;

*15321

—

+

—

^13542

—

—

+

^12534 ^^

So + B?

5 + <

:P + D7;

*1S243 --

+

—

—

■ *13425 —^

—

+

—

*143S2

—

—

+

^12354 — ^

5a + Bj3 + (

:8 + D7 ;

*l 324.1 —•

+

—

—

*15423 •—

—

+

—

^14532 ^=

—

—

+

*12543 -—

5a4-B8

+ C7 + DP;

*I5234 •—

+

—

—

^14325 ^^

—

+

—

*13452 •—

—

—

+

^12435 -^

5a -}- B7 -(-

Cp + D8;

^14253 = —

+

—

—

*13524 -^

—

+

—

*15342 -^

—

—

+

in which we have made, for abridgment,

(25)

(26)

(27)

(28)

(29)

342 Sir William Rowan Hamilton on Equations of the Fifth Degree.

-&z=. w^ -\- u? — w' — tt),

c — io" — u? -\- u? ~ w, V (30)

D n w'' — iii^ — ai^ + w.

But also, by (22) and (21),

ticdea — ^taicdef * bcdea — t abode ) (, " /

making then

^1 abed —— T^abcd) (."^/

the twenty-four values of the function t^ will be those of the function t which
arise from arranging in all possible ways the four indices 2, 3, 4, 5 ; that is, they
are the fifth powers of the twenty-four expressions (24) . . . (29). It is required,
therefore, to develope these fifth powers, and to examine into their composition.
15. For this purpose it is convenient first to consider those parts of any one
such power, which are common to the three other powers, of the same group,
(24) or (25), &c., and, therefore, to introduce the consideration of six new func-
tions, determined by the following definition :

VaJc ^^ 5 (T^iabc ~\~ "^aieb "T '^bcia "T '^cbai) » (*^«^)

which gives, for example,

V3,, = (- 5a)^ -f 60 (- 5a)^ BCD/378

+ 10 {(— 5ay + 2bcdj378} (b^/3^ -f cV + d'?') ■ (34)

+ 5 (- 5a) (b^^ + cy + X)V + 6B^c'i8V + 6c^DVg^+ 6D^B^g^^) ; J

this being (as is evident on inspection) the part common to the four functions
^23455 T3254, T^523' ^5433, Or to tho fifth powcrs of the four expressions in the group
(24). By changing /3, 7, 2, first to 7, 8, ^, and afterwards to 8, /3, 7, the ex-
pression (34) for V345 will be changed successively to those for v^^g and v^3j,
which, therefore, it is unnecessary to write ; and \^^„ v^y, v^3^, may be formed,
respectively, from v.^^, V453, V53^ by interchanging 7 and 8. Or, after substitut-
ing in (34) for /3", 7-, 8^, their values (10), and writing 17 for j&y8, it will only
be necessary to multiply a: by 6, and X by 6% wherever they occur, in order to
change V345 to v^^.,; and to repeat this process, in order to change v^53 to \^:
while V345, V453, V534, will be changed, respectively, to V354, Vj„, v^g^, by inter-
changing 6 and 0', or k and X.

Sir William Rowan Hamilton on Equations of the Fifth Degree. 343
16. In this manner It is not difficult to perceive that we may write

V345 = g + ^^ + h

v,,3 = ^ + 0A + 0\-, I (35)

y^ = g + evi + ei,

and

y,,,=g' + h' + i',

y,,, = g' + eh' + eH',
y.^^gf + G'h' + ei',

(36)

m

which,

gzizg' ={— 5ay + 60 (— 5a)- j;liCD

+ 10{(— 5a)^ + 27/BCD}e(B^+C^+D^)

+ 5 ( - 5a) e« (b^ + C* + D^ + 6c V + 6d^b^ + 6b^c^)

+ 10 (- 5a) t (b* + c* + d* — 3cV - 3dV - 3bV) ;

h=kK-\-l\\ i = k'X -{- 1' k"" ;
h' =k\-\- Ik\ i' = k'K + I'X^ ;

yfc = 10 {( - 5a)^ + 2i;bcd} (b^ + ee + 0V)

+ 10 (- 5a) e (b^ + 0c* + e^D* — 3c-D^ — 3eD^B^ — S^^b^c') ;

/ = 5 ( - 5a) (b* + ec' + eV + 6c^D* + eCDV + 60-b'c') ;

(37)

(38)

(39)

and k', I' are formed from k, I, by interchanging 6 and <?^ Hence also, by the
same properties of e, t}, i, which were employed in deducing these equations, we
have :

hh' = kh + l\^ + kl {'rf - e^ 4- Set) ;

1

h'-\-h'^ = 2{?>k''-th)U-\-{k-^?,lh)k{'>f—e^-\-^ei) J^PI^tf-e^2,eif;\

(40)

and «', P -{■ i'^ have corresponding expressions, obtained by accenting k and /.
17. If then we make

^ = Hi + ^/H« ^' = H, — \/h2 ;
h^ -\- h'^ = 2H3, h^ — h" = 2\/h, ;

t'' + i^ = 2H„

V'3.

i' = 2\/H,;

(41)
(42)
(43)

344 Sir William Rowan Hamilton on Equations of the Fifth Degree.

we see that the six functions v may be expressed by the help of square-roots
and cube-roots, in terms of these six quantities h, by means of the following for-
mulae :

V345= Hi+ V^H^ + \/h3 + \/h, -f \/h.

'v/h.;

V453 = H, + \/Hj + 0A/H3-f \/h,+ 0Vh,

Vh^;

Vm4 = Hi + V'h^ + 0VH3 4-\/H4-f eVn^

Vh^;

(a)

and

'354

= H, — \/H2-f V'Hj — \/h, + V'Hj + V'He;

, = H, - Vh, + 6 Vn^ - Vh, + e"- Vh, + Vhb ;

H, — Vh^-^-OWh^ — Vh^+ 0 Va^-\- Vhq-.

(b)

which have accordingly, with some slight differences of notation, been assigned
by Professor Badano, as among the results of his method of treating equations
of the fifth degree. We see, too, that the six quantities h,, . . . h„, (of which in-
deed the second, namely, u^, vanishes), are rational functions of a, e, rj, t; and
therefore, by article 13., of .r', p, q, r. But it is necessary to examine whether
it be true, as Professor Badano appears to think (guided in part, as he himself
states, by the analogy of equations of lower degrees), that these quantities h are
all rational functions of the coefficients jo, y, r, s, of the equation (2) of the fifth
degree ; or, in other words, to examine whether it be possible to eliminate from
the expressions of those six quantities h, the unknown root .r' of that equation, by
its means, in the same way as it was found possible, in articles 11. and 9- of the
present paper, to eliminate from the correspondent expressions, the roots of the
biquadratic and cubic equations which it was there proposed to resolve. For, if
it shall be found that any one of the six quantities h,, . . . h^, which enter into the
foriTiulae (a) and (b), depends essentially, and not merely in appearance, on the
unknown root jc'; so as to change its value when that root is changed to another,
such as x", which satisfies the same equation (2) : it will then be seen that these
formulze, although true, give no assistance towards the general solution of the
equation of the fifth degree.

18. The auxiliary quantities w, b, c, d, being such that, by their definitions
(20) and (30),

(44)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 345

— 1-1-b4-c + d = Au)\

— 1+B — c— DZI 4w',

— 1 — B-|-C — D = Ad?,

— 1— B — C + D = Aw,

while w, tt>^ w', w* are the four imaginary fifth roots of unity, we shall have, by
the theory of biquadratics already explained, the following identical equation :

{{x-\- \f - (b^+ c^ + d*)}* - 8bcd («+ 1) — 4 (bV+ c^*+ dV)

= {(a; + l)^+5r + 40(:c+l) + 180, (45)

the second member being equivalent to

«* + 4ar' + 4 V + 4'a; + 4^

we find,' therefore, that

b2 4-c*-|-d2 = — 5; BCD = -5; bV+ cV + dV = — 45; (46)

and, consequently,

B*+C* + D*= 115. (47)

Hence, by (37), the common value oi g and g-', considered as a function of a,
e, J/, £, is :

g- = ^ = 125 (— 25a* + 50a?e — GOa'f} + 31 ae* - lOOai + 4>eri) ; (48)

and if in this we substitute, for the quantities a, e, i], i, their values (16), or
otherwise eliminate those quantities by the relations (15), and attend to the de-
finitions (41) of the quantities Hj and H2, we find : .

H, = ^ (25a;'* + 25^^=' + 25^0;'^ + 25rar' + pg) ; (49)

and, as was said already,

H, = 0. (50)

It is therefore true, of these two quantities h, that they are independent of the
root a/ of the proposed equation of the fifth degree, or remain unchanged when
that root is changed to another, such as a:", which satisfies the same equation :
since it is possible to eliminate a/ from the expression (49) by means of the pro-

VOL. XIX. 2 Y

346 Sir William Rowan Hamilton on Equations of the Fifth Degree.

posed equation (2), and so to obtain Hj as a rational function of the coefficients
of that equation, namely,

125

H. = -Y2-(i'?-25«). (51)

Indeed, it was evident a priori that h, must be found to be equal to some ra-
tional function of those four coefficients, p, q, r, s, or some symmetric function
of the five roots of the equation (2) ; because it is, by its definition, the sixth
part of the sum of the six functions v, and, therefore, the twenty-fourth part of
the sum of the twenty-four different values of the function t ; or finally the mean
of all the different values which the function f' can receive, by all possible changes
of arrangement of the five roots y, . . ^^, or jr,, . . x^, among themselves. The
evanescence of h^ shows farther, that, in the arrangement assigned above, the sum
of the three first of the six functions v, or the sum of the twelve first of the
twenty-four functions t, is equal to the sum of the other three, or of the other
twelve of these functions. But we shall find that it would be erroneous to con-
clude, from the analogy of these results, even when combined with the corres-
ponding results for equations of Inferior degrees, that the other four quantities
H, which enter into the formulas (a) and (b), can likewise be expressed as ra-
tional functions of the coefficients of the equation of the fifth degree.

19. The auxiliary quantities b^ c% d% being seen, by (46), to be the three
roots »„ z^, z^ of the cubic equation

z'+5z^— 45« — 25 = 0, (52)

which decomposes itself into one of the first and another of the second degree,

namely,

z — 5 = 0, z^-^10z-\-5 = 0; (53)

we see that one of the three quantities b, c, d, must be real, and =z ± V5,
while the other two must be imaginary. And on referring to the definitions
(30), and remembering that w is an imaginary fifth root of unity, so that w* and
w' are the reciprocals of w and w\ we easily perceive that the real one of the
three is d, and that the following expressions hold good :

B^zz— 5— 2d; c'= — 5-f-2D; d* = 5; (54)

with which we may combine, whenever it may be necessary or useful, the rela-
tion

Sir William Rowan Hamilton on Equations of the Fifth Degree. 347

BC li: — D. (55)

If then we make, for abridgment,

f - (0 - 0') D = (0 - 6') («' - «,' - 0,^ + «), (56)

9 being still the same imaginary cubic root of unity as before, so that

r = -15; (57)

we shall have, in (39),

r,^ + es' + e'c' = 10 - 2^,
D* + 0B* + 0«c* = — 20 + 20f ,
B^c" + 0c'd^ + e^D^B" = 30 + lOf ;

and, consequently (because bcd =. — 5),

0A;=-lOO(5-f)(25a' + 2^) + 5OO(ll+f)«e; , ^^^^

(58)

el= — 2000 (2 + f ) a ;

while &^k' and GH' are formed from Ok and 61, by changing the signs of f . It is
easy, therefore, to see, by the remarks already made, and by the definitions (42)
and (43), that the quantities H3, h^, H5, Hg, when expressed as rational functions
of a, €, 7], I, or of x', p, q, r, will not involve either of the imaginary roots of
unity, 6 and w, except so far as they may involve the combination f of those
roots, or the radical -s/ — 1 5 ; and that Hj will be formed from H3, and Hg from
H4, by changing the sign of this radical. We shall now proceed to study, in par-
ticular, the composition of the quantity h^ ; because, although this quantity,
when expressed by means of a/, p, g, r, is of the thirtieth dimension relatively to
y, (p, q, and r being considered as of the second, third, and fourth dimensions,
respectively), while H3 rises no higher than the fifteenth dimension; yet we shall
find it possible to decompose h^ into two factors, of which one is of the twelfth
dimension, and has a very simple meaning, being the product of the squares of
the differences of the four roots x", x"', x^^, x^ ; while the other factor of h^ is
an exact square, of a function of the ninth dimension. We shall even see it to be
possible to decompose this last function into three factors, which are each as low
as the third dimension, and are rational functions of the five roots of the original
equation of the fifth degree ; whereas it does not appear that H3, when regarded

2 Y 2

348 Sir William Rowan Hamilton on Equations of the Fifth Degree.

as a function of the same five roots, can be decomposed into more than three ra-
tional factors, nor that any of these can be depressed below the fifth dimension.

20. Confining ourselves then for the present to the consideration of h^, we
have, by (42) and (38), the following expression for the square-root of that
quantity :

/h, = \{>^- X') {^' - ^kPKk — P (/.' + X') } ; (60)

and, therefore, by (59), and by the same relations between *-, \, and e, rj, i, which
were used in deducing the formula of the sixteenth article, we obtain the follow-
ing expression for the quantity h^ itself, considered as a function of a, e, rj, i:

H, = 2'»5'« { {rf - e^ + Secf - 4i'} l' ; (6l )

in which we have made, for abridgment,

L = /t' - Sifiu-" + (ri" -e' + del) i^, (62)

and

;x = (-5+f)(5a^ + f^)+(ll + ^)ae,. = 4(2+f)«. (63)

Now, without yet entering on the actual process of substituting, in the expression
(61), the values (16) for a, e, rj, t; or of otherwise eliminating those four quan-
tities by means of the equations (15), in order to express h^ as a function of or',
p, q, r, from which j/ is afterwards to be eliminated, as far as possible, by the
equation of the fifth degree ; we see that, in agreement with the remarks made
in the last article, this expression (61) contains (besides its numerical coefficient)
one factor, namely,

(^2_e3_l-3et)2_4t^= (;r3_V)^ (64)

which is of the twelfth dimension ; and another, namely, l*, which is indeed it-
self of the eighteenth, but is the square of a function (62), which is only of the
ninth dimension : because a, e, i], i, are to be considered as being respectively of
the first, second, third, and fourth dimensions ; and, therefore, fi is to be re-
garded as being of the third, and v of the first dimension.

21. Again, on examining the factor (64), we see that it is the square of
another function, namely, a-' — X^ which is itself of the sixth dimension, and
is rational with respect to y, x'", x'^, x'^, though not with respect to a, e, t], i,
nor with respect to x\ p, q, r. This function k^ — X^ may even be decomposed
into six linear factors ; for first, we have, by ( 11 ),

Sir William Rowan Hamilton on Equations of the Fifth Degree. 349
k^-\^ = {k — X) (v — ex) {k — e'\) ;
and, secondly, by (10),

3ic = ^ -\- ey -\- eh'', 3\ = 0" ^ ey^ -\- e^i\

expressions which give

^-\ =^(e-e^)(i^-y^),
,-ex = i(i-e)(^-z'),

.-e^X = ^(e^-l)(y^-^');

but also, by (7),

h^-y' = l {x" - a/") (x" - x'""),

|3^ - 8^ = I {x" - x''') {x'" - x"),

y--^ = :^{x"-x''){x''' -x'");

(65)
{QQ)

(67)

(68)

and

therefore,

{e - ff) (1 — 0) (0^ - 1) = (1 - 0)^ = — 3 (0 — 0^) ;

(69)

r' _ \3 = _ 2-«

3-^(e-e^){x"-j/"){af'-x^'^){x"-x'') 1

(y- _ o;^'') (a;'" - a: 0 (or^'' - or 0-

J

Thus, then, the square of the product of these six linear factors (70), and of the
numerical coefficients annexed, is equal to the function (64), of the twelfth di-
mension, which itself entered as a factor into the expression (61) for h^; and we
see that this square is free from the imaginary radical 0, because, by (11),

(0 — 0^)^ = _ 3 ;

(71)

and that it is a symmetric function of the four roots x" , x'", x'^, x^, being pro-
portional to the product of the squares of their differences, as was stated in article
19. : so that this square (though not its root) may be expressed, in virtue of the
biquadratic equation (6), as a rational function of af, p, q, r; which followed
also from its being expressible rationally, by (64), in terms of e, v], i.

22. Introducing now, in the expression (64), here referred to, the values
(16), or the relations (15), we find, after reductions :

350 Sir William Rowan Hamilton on Equations of the Fifth Degree.

— 2-« ^-^{25x'^ + 75;?^* + (48/+ 45r) x'^-\- 27pqx' \ (72)

— 2p^ + 72pr — 27q''};

(K'+\J=(rf—e'+3eiy=2-''3-^{625x"'+3l50p3f''+(8025p'+2250r)s"
+ ISbOpqx" -\- (7100/ + 10350pr — 1350y') x" + 4050pV"
+ (2004/ + 15120pV — 4050j9y' + 2025r') x'*

+ (2592/y + 2430p^r) a:'' ^(73)

+ (— 192/ + 6732/r — 1863pY + 6480pr" — 2430jV) x'^
+ (— 108pV + 3888py — U58pq') x'
+ 4/ — 288/r + 108/^' + 5184/r^ — 3888^yV + 729*7*1 ;

4v='V = 4t' = 2-'" 3-« { lOOOy" + 330qpa;'«' + 2700^0/"

+ (3930p'+ 3600r) j;'«+ 5940pya;"+ ( 1991;)'+ 7920pr + 2430^') x'^

+ (3807/?+ 6480?r) or' ^+ (393j9*+ 5076pV+ 2673^5* + 4320r') x"

+ (594p'5 + 7I28i??r + 729?0:r'' !-(74)

+ (33/ + 792/r + 243/9^ + 4752pr' + 29I69V) x"

+ (27pV + 648pV + 3888?r') x'

+ / + 36/r + 432pV' + I728r'} ;

and, finally,

(/.' - \=')'^ = (^^ - e' + 3et)^ _ A? =

— 2-"^ 3-' { 125x'" + 350py "• + 400yy» + (285/ + 450r) x'^
. + SSOp^-a^" + (32p» + 790pr + 410y') y" + (4 1 4/y + 9609r) ^

+ (— 1 6/ + 192/r + 546py' + 565r'') or'*

+ (— 8/9 + 966pyr + 108«7^) ^" ^ ^^^^

+ (12/— 132/r + 105py + 464pr" + 522yV) x""

+ (S/gr — 48pV + 54p?^ + 576yr') x'

+ l6pV — 4py _ 128/r=' + 144pyV + 256/^— 27y'}.

23. This last result may be verified, or rather proved anew, and at the same
time put under another form, which we shall find to be useful, by a process such

Sir William Rowan Hamilton on Equations of the Fifth Degree. 351

as the following. The biquadratic equation (6), of which the roots are x", x'",
x''', x^, shows that, whatever x may be,

{x — x"){x — x"'){x — x"'){x — x'')= 1

X* + x'x' + ocfx^ + x'^x + x'* \ (76)

+ JO (a;'' _|_ x'x + «'*) + «7 (^ + y ) + r ; j

and, therefore, that

(^ _ x") (y - y") (or' _ x'") {x' — x'') = 5x'* + 3px" + 2qx' + r. (77)

If then we multiply the expression (75) by the square of this last function (77),
we ought to obtain a symmetric function of all the five roots of the equation of
the fifth degree, namely, the product of the ten squares of their differences, mul-
tiplied indeed by a numerical coefficient, namely, — 2~'^3~^, as appears from
(70) and (71) : and consequently an expression for this product itself, that is for

{x" — x'''f{x^'-x''y{af" — x"y {x"' — x''f{x'''-x'')\ J

must be obtained by multiplying the factor 125^* + &c. which is within the
brackets in (75), by the square of 5^* + Zpaf^ + 2qx' + r, and then reducing

by the condition that x'^ + px"^ + qxf^ + /-^ = s. Accordingly this process

gives :

p = 3125s^ _ 2,'7bOpqg'
+ (108/ — gOOpV + 825j!jY + ^OOOpr" + 2250yV) s"
— {I2p*qr — ] 6pY — 56qpV + 630p^V + leOO^r' — lOSy*) s
+ iGpV^ — Ap^'qV — 128pV* + 144j)^V=' + 256r^ — 27?^ ;

an expression for the product of the squares of the differences of the five roots of
an equation of the fifth degree, which agrees with known results. And we see
that with this meaning of p, we may write :

{k^ - \')^ = _ 2-'=' 3-^ p {5x'* + 2>px'^ + Iqx' + r)-\ (80)

The expression (61) for h^ becomes, therefore :

J, _ g-2 3-3 5,B r (f'"- 3'/^'-' + (^' - ^' + 3») Al .81)

H4_-2 6 5 P(, 5x^' + ?,px'' + 2qaf+r j' ^^^^

/x and V having the meanings defined by (63).

(79)

352 Sir William Rowan Hamilton on Equations of the Fifth Degree.

24. With respect now to the factor l, which enters by its square into the
expression (61), and is the numerator of the fraction which is squared in the
form (81), we have, by (62), (63), and (57),

L = I (15625a9 + 24375a'e + 3750a«»;

— l6l25aV + 1500a*t + SgOOa^ef] + 7605aV

_ 8820a^e« — 6260aV — 1290a^€'»; + I20u'r]i. + I56aerf + 8ri')

+ l| ^ ( 15625 (a"— a'e) + 3750a«»;— 125aV + 15500a^ — 2500a^€»7

+ 1125aV— 4500a='«_100aV— 10aV^+1240aV— 100a6?;'' + 8i7^) ;

(82)

and when we substitute for a, e, »;, t, their values (16), we find, after reductions,
a result which may be thus written :

2«5'l = 5l' — f l" ; (83)

if we make, for abridgment,

l' zr 25X' + 275^y' + ( 135p^ — 350r) j/' + 2l0pqj;'*

+ (141/— 500pr+ SS5q^)3f' + {9Sp'q-20qr)x"'-^20pq'a/—4q

l" = 1750^^ + 2825py^ + 2100q.v"' + (1120/ + 1825r) x" \ (84)

+ I6l5j9yy*4. (39/ + 1060pr + 500q^) x"
+ (109p*^ + 620qr) a;'^ + 68pq^j/ + 12q\

With these meanings of l' and l", the quantity H4, considered as a rational func
tion of a/, p, q, r, may therefore be thus expressed :

5L'-fL'

H4 = — 2-"3-^5

.p(.

bx"' + Spx"" + 2qs'

+ J'

(85)

p being still the quantity (79). and f being still = v' — 15.

25. Depressing, next, as far as possible, the degrees of the powers of or',
by means of the equation (2) of the fifth degree which 3/ must satisfy, we
find :

(86)

in which the coefficients are thus composed :

Sir William Rowan Hamilton on Equations of the Fifth Degree. 353

and

l'„ = - 110/5 - 4^' + 350rjf,

l', = — llOjoV + ^Qpq" — 275qs + 350r^

l'j =z — 17/5' — 2-5p* + 55qr,

L'3 = + 31/ - I75pr + llOy^

l/,= -90pq;

l"„ = — 45/* + 12^^ - 75?-* ;

l", = — 45pV + 68^5^ — 350^* — 75r" ;

l"j = + 64/y - 107 5ps + 195yr ;

l"3 = — 6p^ — 90pr + 150^^ ;

l", = + igOpq — 1750*.

} (87)

I (88)

But because, after the completion of all these transformations and reductions, it
is seen that the five quantities

5l'

•^"0.

5L',-fL"„ 5L',-fL"„ 5l'3-^l"3, 5L',-fL"4, (89)

which become the coefficients of y, x'\ y, ,r'^ af\ in the numerator 5l' — ^l"
of the fraction to be squared in the formula (85), are not proportional to the five
other quantities

r, 2q, 3p, 0, 5, (90)

which are the coefficients of the same five powers of a/ in the denominator of the
same fraction, it may be considered as already evident, at this stage of the inves-
tigation, that the root .7/ enters, not only apparently, but also really, into the
composition of the quantity h^.

26. The foregoing calculations have been laborious, but they have been made
and verified with care, and it is believed that the results may be relied on. Yet
an additional light will be thrown upon the question, by carrying somewhat far-
ther the analysis of the quantity or function H4, and especially of the factor l ;
which, though itself of the ninth dimension relatively to the roots of the equation
of the fifth degree, is yet, according to a remark made in the nineteenth article,
susceptible of being decomposed into three less complicated factors ; each of these
last being rational with respect to the same five roots, and being only of the third
dimension. In fact, we have, by (62), and by (11), (12), (13),

2z

vol. XIX.

354 Sir William Rowan Hamilton on Equations of the Fifth Degree.

L = (/i + «•!/ + \v) (n + Okv + e^Xv) (fi 4- eVv + exv) ;

that is, by (10),

L = (/i — ev-\- ^\) (fji — ev + r/u) (fi — ev + h\) ;

in which, by the same equations, and by (63) and (57),

M-ev = (-5 + f)(5a'+|/3y8)+(l-^)a(/3^ + y + 8^);

V

(91)
(92)

(93)

(94)
(95)

= (8 + 4^)a; f = x/-15.
Thus, L is seen to be composed of three factors,

L = MjMjMa,
Ml := /x — ev + ^v, Mj = /i — ev -\- 7^1/, M3 = /it — 61/ + g'l/,

of which each is a rational, integral, and homogeneous function, of the third di-
mension, of the four quantities a, /3, 7, 8, and, therefore, by (7), of the four
roots xf' ■, x'", x^^, x^, of the biquadratic equation (6); or finally, by (4), of the
five roots a:,, x^, x^, x^, x^, of the original equation (1) of the fifth degree : be-
cause we have

Xf' = OTa — ^ (or, + X2 + Xj + Xi+ OTj), &c. ; (96)

or because

20a = x^ + X3 + x^+ X, — 4x^,

4/3 = jCj + iBg — or^ — x^,

4:y = x^—X3 + x^ — x^

TcO ^^ iJTrt ^^ "^s """" ^4 "T" 5*

(97)

And the first of these three factors of L may be expressed by the following equa-
tion:

100m, = 5m', - f m", ; (98)

in which,

M', = 4.x,' - 3a:.* (or, + x, + x, + x,) - 2x, {x^^ + x^ -f x^ + x^) n

— 1x, {x^3 -f x^x^ -\- 6a;, {x^ + 0^3) (or, + x^ > {m)

+ 2{-«^2^3(^2+^3)+^4-«^5(^4+^6)} " 3 { J^2^3(-«^4+^5) + ^A(^2 + ^3)} ; J

and

Sir William Rowan Hamilton on Equations of the Fifth Degree. 355

+ \Ax, {x^x^ + x^x,) — Qx, (x^ + 0:3) (x^ + X,)

-{j;^'-^x,'+x,'-\-x,'-2(x^^+x,^)(x,+x,)-2(x^^+x,') (x^+x,)] ; .

while the second factor, m^, can be formed from Mj by merely interchanging ^3
and x^ ; and the third factor M3 from m^, by interchanging x^ and Xy

27. If, now, we substitute the expression (94) for the numerator of the frac-
tion which is to be squared in the formula (81), and transform also in like man-
ner the denominator of the same fraction, by introducing the five original roots
Xj, . . . x^, through the equations (77) and (4), we find :

H4 =

(•*"l -^2) (-^l ^3) {^1 •^4) {^1 ^5)
and we see that this quantity cannot be a symmetric function of those five roots,
unless the product of the three factors Mj, m^, M3 be divisible by the product of
the four differences a:, — x^ . . . x^ — Xy But this would require that at least
some one of those three factors m should be divisible by one of these four dif-
ferences, for example by or, — x^; which is not found to be true. Indeed, if
any one of these factors, for example, Mj, were supposed to be divisible by any
one difference, such as x^ — x.^, it is easy to see, from its form, that it ought to
be divisible also by each of the three other differences; because, in m,, we may in-
terchange x^ and Xj, or x^ and x^ or may interchange x^ and x^, or x^ and x^, if
we also interchange x^ and x^, or x^ and x^ : but a rational and integral function
of the third dimension cannot have four different linear divisors, without being
identically equal to zero, which does not happen here. The same sort of reason-
ing may be applied to the expressions (95), combined with (93), for the three
factors M„ M2, M3, considered as functions, of the third dimension, of a, j8, 7, 8 ;
because if any one of these functions could be divisible by any one of the four
following linear divisors,

or, — a:^ = — 5a— (/3 + 7 + 8),

x^ — x^= — 5a—(^ — y — h),

Xi — x^= — 5a—(—p-\-y—d),

Xi — x^^ — 5a

(_p_7 + 8), J

(102)

2z2

356 Sir William Rowan Hamilton on Equations of the Fifth Degree.

(103)

it ought from its form to be divisible by all of them, which is immediately seen
to be impossible. The conclusion of the twenty-fifth article is, therefore, con-
firmed anew ; and we see, at the same time, by the theory of biquadratic equa-
tions, and by the meanings of e, tj, i, that the denominator of the fraction which
is to be squared, in the form (81) for H4, may be expressed as follows :

5.r'* + 3px" + 2qx' -\-r = {a;, — x.,) (or, — x^) (^, — x,) (x^ — x,)
=z (5ay - 6e (5a)* + 8r] (5a) — 3 (e^ - 4^ ;

a result which may be otherwise proved by means of the relations (15).

28. The investigations in the preceding articles, respecting equations of the
fifth degree, have been based upon analogous investigations made previously with
respect to biquadratic equations ; because it was the theory of the equations last-
mentioned which suggested to Professor Badano the formulas marked (a) and
(b) in the seventeenth article of this paper. But if those formulae had been sug-
gested in any other way, or if they should be assumed as true by definition, and
employed as such to fix the meanings of the quantities h which they involve ;
then, we might seek the values and composition of those quantities, h„ . . . h^, by
means of the following converse formulas, which (with a slightly less abridged
notation) have been given by the same author :

H3 + Vh, = 2V (V345 + ^'^453 + o^^mT ;
H, - v^He = 2V (V345 + ^^53 + ^^34)' ;

and

H, - ^/H, = ^ (v3,4 + v^3 + V43J ;

(c)

H5 + \/He = 2V (^3*4 + ^v,« + e'\,^y

(d)

Let us, therefore, employ this other method to investigate the composition of h^,
by means of the equation

54 ^/H4 = (V34, + 0^4,3 + ey,^y - (v3,4 -f 6%,, + ev,,,y ; (104)

determining still the six functions v by the definition (33), so that each shall still
be the mean of four of the twenty-four functions t ; and assigning still to these
last functions the significations (32), or treating them as the fifth powers of

Sir William Rowan Hamilton on Equations of the Fifth Degree. 357

twenty-four different values of Lagrange's function t, which has itself 120
values : but expressing now these values of t by the notation

taicde = ">^^a + w"^* + "'''^c + "'"j^rf + WX„ (105)

which differs from the notation (22) only by having lower instead of upper in-
dices of x; and is designed to signify that we now employ (for the sake of a
greater directness and a more evident generality) the five arbitrary roots x„ &c.,
of the original equation ( 1 ), between which roots no relation is supposed to sub-
sist, instead of the roots x', &c., of the equation (2), which equation was sup-
posed to have been so prepared that the sum of its roots should be zero.

29. Resuming, then, the calculations on this plan, and making for abridg-
ment

A = Xa + Xi -{- Xe -{- a;a-\- x„ (106)

so that — a is still the coefficient of the fourth power of x in the equation of the
fifth degree ; making also

Vfaicde = iCa* X^ + 2Xa^ x/ -j- 4Xa^ X, X, + GXa" Xi^ X,-\-\ Ix^ Xj X^ X^, (10?)

and

Xjcde = 5 (Vf abode + ^bcdea + ^cdeai + ^fdeatc + ^eabcd) j ( 1 08)

we find (because w* = 1), for the fifth power of the combination (105) of the
five roots x, the expression :

^aicde = A^ -f ( w" — 1 ) Xicde +(«»'— 1 ) Xceid ] / ^09)

+ (w — 1) Xedcft -f (ur^ — 1) Xdiec ; J

and, therefore, for the six functions v, with the same meanings of those functions
as before, the formula :

"Vcde^^ ■^{i^Kcde ~\~ i tcied-\- t^ldeie-\- ''ledci) I OlO)

= A*-f-(«)-f «."- 2)Yed,-l-(a.'-+ ".'-2)y,„; J

in which,

4 Ycde ^^ ^icde + ^c2ed "T" ^deic "T ^edc2- \^^^)

If then we make

y^, = ^\ + y'\, y,3,= <,-y",, 1

v,,,= y'3+v"3, Y,,, = y',-Y"„ , (112)

Y,34 = y'4 + y'\, Y354 = Y'4 — y'\ ;

358 Sir William Rowan Hamilton on Equations of the Fifth Degree.

we shall have, by (20) and (30), the following system of expressions for the
functions v :

'345

= a*-5y', + dy",;

V4.M = A* - 5¥'3 + dy'

'534

= a*-5y'4 + dy"4;

and

(113)

V354 = A^ - 5y'4

-dA;

V543 = A* — 5y'3

-DY^'a;

V435 = a' - 5y',

-DY",;

(114)

(115)

D being still = w* — w' — w^ + «, so that d^ is still = 5. We have also the
equation :

^2345 "T ^3254 "T ^4523 "l ^^5432
"r ^2453 T" ^4235 T" ^5324 T" ^3542
"T ^2534 "I" ^5243 "l" ^3425 "T ^4352

^2354 I ^^3245 "T" •'^5423 T ^4532

"T ^2543 + X5234 + X4325 + X3452

T" ^2435 "T ^4253 T ^3524 l" ^5342 »

because the first member may be converted into the second by interchanging any
two of the four roots x^, x,, x^, x^, on which (and on ^,) the functions x depend,
and therefore the difference of these two members must be equal to zero ; since,
being at highest of the fifth dimension, it cannot otherwise be divisible by the
function

^=(x^- a?3) (x., — X,) (x^ - X,) (^3 — x^) (x^ — X,) (x, — X,), (116)

which is the product of the six differences of the four roots just mentioned, and
is itself of the sixth dimension. We may therefore combine with the expres-
sions (113) and (114) the relations :

^345 ~r Y453 + ¥534 =^ Y354 -f- Y543 -f- Y435 ; K^^t )

and

y"3+y"4 + y",iz0. (118)

30. With these preparations for the study of the functions v, or of any com-
bination of those functions, let us consider in particular the first of the three
following factors of the expression (104) for 54 x/h^ :

Sir William Rowan Hamilton on Equations of the Fifth Degree. 359?

V346 - V543 + ^' (V453 - V435) + ^ (V534 - V354) ;
V345 - V435 + ^ (V453 — V354) + ^ (V534 - V543) ;

6 being still an Imaginary cube-root of unity. We find :

V345 - V354 = 5 (y', - y'O - dy"3 ; 1
V534 - V435 = — 5 (y', - y',) - dy"3 ;
V453-V5,3 = 2dy"3;

(119)

(120)

expressions which show immediately that

V345 + V453 + V534 = V354 + V543 + V43y (121)

and, therefore, by (c) and (d), that

H2 = 0,
as was otherwise found before. Also,

20» _ 0 _ 1 = (0 _ 1) (20 4- 1) = - (1 - e) (e - e') ; (122)

and, consequently, by (120), the first of the three factors (119) is equivalent to
the product of the two following :

1-e, 5(Y,-y\)-^Y'\; (123)

in which, as before,

f = (0 — 0^) D = a/^=T57

But, by (112) and (117),

2 (Y'4 - y's) = Y53, — Y435 - (y^, — y,^) = 2 (y^ - Y^) + Y,,3 - Ym3, (124)

and

(125)

(126)

•^^3 — ^453 ^543 »

so that the first factor (119) may be put under the form :

^ (1 - 0) {10 (y,3, - Y,3,) -4- (5 - f ) (y«3 - v^3)}.
Besides, by (111), the three differences

Ycde ~~ Ycedj Ycde ~~ Yedct Ycde ~~ ^dcet \^"' )

360 Sir William Rowan Hamilton on Equations of the Fifth Degree.

are divisible, respectively, by the three products

{x^ — x^) (Xa — x^), {x.^ — Xi) (Xe — Xa), (x^ — x^) (x^ — Xj) ; (128)

and, therefore, the factor (126) is divisible by the product

(x^ — x,)(x^ — x,), (129)

the quotient of this division being a rational and integral and homogeneous func-
tion of the five roots x, v?hich is no higher than the third dimension, and which
it is not difficult to calculate.

31. In this manner we are led to establish an equation of the form :

V345- V354 + ^'(V453- V543) +^(V534- V435) = (1 " ^) K" ^3) i^^-^^) ^l' (130)

in which if we make

2N, = 10N', + (5-f)N% (131)

we have

(^2-*3)(^4-«5) (^2 - -^3) (^4 - ^5)

Effecting the calculations indicated by these last formulae, we find

n', = |(m".-m',), N".= -fM"„ (133)

m', and m", being determined by the equations (99) and (100) ; and, therefore,
with the meaning (98) of m„ we find the relation :

n,= -125m,. (134)

Thus, the first of the three factors (119) may be put under the form :

— 125(1 -e)(x,-x,) {x,-x,)m,; (135)

■:.■:■ - )
in deducing which, it is to be observed, that the first term, Xa* x^, of the formula

(107) for Waicdc gives, by (108), the five following terms of Xjcd«:

5Xa* Xi + SiCj' Xa + 5Xe' Xa + 5x/ X^ + 5Xe* Xa l ( 1 36)

and these five terms of x give, respectively, by (111), the five following parts
of Y<afa:

^iR William Rowan Hamilton on Equations of the Fifth Degree. 361

5 "^l \J^2 'T" '^0 "V "^d I "^eji
% (^2 "^0 r ^c '^2 1 "^d ^e "T" -^e "^dji
^ y^c '^d I •'^2 "^s ~T~ "^e "^2 ~r '^'' "^c-V'
^ (^JT^ .Tj -{- Xg Xi -j- JTj J^c "T~ Xq X.^Ji

|(rr/ + ^/ + a^/ + a:2*)a;,;

(137)

which are to be combined with the other parts of y, derived, in like manner,
through X, from the other terms of w, and to be submitted to the processes in-
dicated by the foi'mulae (132), in order to deduce the values (133) of n', and
n"„ and thence, by (131) and (98), the relation (134) between n, and Mj, which
conducts, by (130), to the expression (135). For example, the first and last of
the five parts (137) of y, contribute nothing to either of the two quotients
(132), because those parts are symmetric relatively to x^ x^, Xe', but the second
part (137) contributes

— I (^i + ^i ^d + ^2 a;/ + a-/ -f xj" + J-/ Xc 4- X, Xc^ + x,'),
to the quotient

* crfe ^ edc

(•^2 — "^d) (-^e — •*"c)

and

+ I (-^2' + -^2' ■^■e + .^2 ^e" + ^e' + ^c' + ^c" X'i + X^ X^ + ^/),

to the quotient

Ycde ^dci

(138)

(139)
(140)

(141)

\«*2 ^e) \X(. XfiJ

this second part (137) of y contributes therefore, by (132),

— I (•^2' + ^i ^3 + -^2 ^i + ^f + ^' + ■^4' ^5 + ^* ^t + -^a'), (142)

to the quotient n'j, and the same quantity with its sign changed to the quotient
n", : and the other parts of the same two quotients are determined in a similar
manner.

32. The two other factors (119) may respectively be expressed as follows :

^ 125 (1 - e^) {x., - X,) {x^ - X,) M2, (143)

and

- 125 (0 - 0") {x^ - X,) {x, - X,) u, ;

(144}

VOL. XIX,

3 A

362 Sir William Rowan Hamilton on Equations of the Fifth Degree.

in wliich, Mj and Mg are formed from M„ as in the twenty-sixth article ; be-
cause the second factor (119) may be formed from the first, by interchanging x.,
and x^, and multiplying by — 6"-; and the third factor may be formed from the
second, by interchanging x^ and x-^, and multiplying again by — 0'. If then we
multiply the three expressions (135) (143) (144) for the three factors (119)
together, and divide by three, we find :

18\/h, = — 5^(0 — e^)7^M,M3M3; (145)

-sr denoting here the product (116) of the six differences of the four roots x^ . . .
x^. The expression (101) for H4 itself is therefore reproduced under the form :

H,= - 2-^3-'5'«w^m,^m/m3^; (146)

and the conclusions of former articles are thus confirmed anew, by a method
which is entirely different, in its conception and in its processes of calculation,
from those which were employed before.

33. It may not, however, be useless to calculate, for some particular equa-
tion of the fifth degree, the numerical values of some of the most important
quantities above considered, and so to illustrate and exemplify some of the chief
formulae already established. Consider therefore the equation :

x'' - Hx'' -\- Ax = Q ; (147)

of which the roots may be arranged in the order :

X, = 2, or, = 1, X3 = 0, x,=z — 1, x^ = —2; (148)

and may (because their sum is zero) be also written thus :

x' = 2, x" = 1, x'" = 0, x'" =-h x" =-2. (149)

Employing the notation (32), in combination with (22) or with (105), we have
now :

T,^, = (2 + «,*-ft,^-2«,)''; 1

T3,,,=r(2 + «.3-2«,*-«.>^; ^ ^j5Q^

T,,,3 = (2-«.''-2«.^ + «,7';
T3,3, - (2 - 2«.^ -u?^ u>)\
But ftt* 1= 1 ; therefore.

Sir William Rowan Hamiuton on Equations of the Fifth Degree. 363

T,,,, = (- 2 - «.' + ^-^ + 2u>f, (151)

and

T,3,, + Tj,,,, = 0. (152)

Again,

T3^ = (1 _ a^-^r (2 - «)^ T,,^ = (1 - u,-f (2 - 0,^ ; (153)

and if we make

(2 — «.)^ = E-o, (2 +«,)*= E + o, (154)

we shall have

Ezi 32 + 80w^+10wS o = 80w + 40«)^ -f o;^ ; (155)

also,

(1 — uPf = - 5«)^(1 - w^) (1 - w- + w*) ; (156)

we find, therefore, by easy calculations,

(1 — wy E = 300 4- 430« - llOw^ — 540«.' — SOw\ ]
(1 — w^)^ 0 = 600 +190« — 405«.^ — 395«)^ + 10«)''; j

and by subtracting the latter of these two products from the former, and after-
wards changing w to its reciprocal, we obtain :

T3254 = - 300 + 240co + 295«»^ - 1 45«»-' — 90u,\ ] ^'^^

T^= — 300 + 2400."+ 295w^ — 145tt.-^ — 90«. j

We have, therefore, by (20),

T32M + T«.3==-750; (159)

and, consequently, by (33) and (152),

v,.= -^5. (160)

34. In like manner, to compute, in this example, the second of the six func- '
tions V, we have

adding then the two products (157) together, and afterwards changing w to w^
and w^ successively, we find, by (154) :

3 a2

364 Sir'William Rowan Hamilton on Equations of the Fifth Degree.

T532, = 900 + 620«.^ — 515«»^ — 935«» — 70«.^ J

but, by (20), (30), and (54),

2 (a. + «.") = — 1 + D, 2 («)^ + «.^) = — 1 — D, D^ = 5 ; (163)

therefore,

T2453 + T3M2 = 0, t,,3,+ t,3^ = 2250-1000d; (164)

and

v,„ = ^(1125-500d). (165)

35. To compute the third of the functions v, we have, in the present ques-
tion, the relations :

'^2534 ''3254' ''"5-243 '^4235' ''"3425 '^5324' ''"4352 '''4523 ' (. ^'^"j

and, therefore, by (159) and (164),

y,3, = — 375 + 250D. (167)

For the fourth function v, we have, by processes entirely similar to the forego-
ing :

T«a4=-(l--o^(2 + «'0^ T,,3, = _(l_«,^)*(2 + ..)^ 1

T2354 + T4532 = - 2250 - IOOOd ; j ^ ^

'3245

T3245-fT,«3=+750; ] ^ "^^

V3^=z— 375 — 250d. (170)

For the fifth function v, we have the relations :

'''2543 ''"2354 5 ''"5234 -~ ''"4325 5 ^3452 ^^ T4532 5 \^' '■J

and, therefore, by (168),

v^3=i(1125 + 500d). (172)

Finally, for the sixth function v, we have

''"2435 — - ''"5423> ''"4253 ''"3524' ''5342 -— ''"3245 5 ( W <J '

and, therefore, by (I69),

Sir William Rowan Hamilton on Equations of the Fifth Degree.

375

v.,. = — ■

365

(174)

The three first values of v may therefore be thus collected :

TfTV345=-3; tI7V453=9-4d; ^|^v334 = - 6 + 4d ; (175)

and the three last values, in an inverted order, may in like manner be expressed
by the equations :

^V435 = -3; ^|^v^3=:9 + 4d; ^^y^=-Q-\j,. (176)

36. It Is evident that these six values of v are of the forms (113) and (114),
and that they verify, in the present case, the general relation (121). They shov?
also, by (c) and (d) of article 28., that not only h^, but h„ vanishes in this ex-
ample ; the common value of the two sums (121), of the three first and three
last values of v, being zero. Accordingly, if we compare the particular equa-
tion (147) with the general forms (1) and (2), we find the following values of
the coefficients (b, c, d, e, not having here their recent meanings) :

A = 0, B = _ 5, c = 0, D =: 4, E = 0, (177)

and

p = — 5, y = 0, r = 4, 5 = 0; (178)

and therefore the formula (51) gives here

H, = 0. (179)

We find also, with the same meanings of Q and f as in former articles :

tIt (V345 + 0^v,,3 + 0v,3,) = 3 (40^ - 0) + 4f ;

29«
126

(V354 + e'va43 -f 0v,3,) = 3 (40 _ e^) -f 4f ;

and, therefore, by (c) and (d),

2^ 2? 5-' (H3 + x/hJ = {3 (W -6) + 4^r,
2' 3^ 5-« (H3 - ^/HJ = {3 (46 - 6'-) + 4^Y ;

equations which give, by (11) and (57) :

/H,= 2-=5'»(0-0^)(23-f3f);

and

H, = -2-^3' 5^»( 197 + 69d-

(180)

(181)

(182)
(183)

366 Sir William Rowan Hamilton on Equations of the Fifth Degree.

Let us now compare these last numerical results with the general formulae found
by other methods in earlier articles of this paper.

37. The method of the thirteenth article gives, in the present example,

arr_-|-, )3 = 1, 7 = }, 8 = 0, e = ^^, ,j = 0,

—[T^' ^ — 12 ' I — KA — y^,

(184)

^3+X3_^^^ l(,.3_X3)__2-5 3-.(e_^,).

and, therefore, by (59),

|g = 5(l_a S=12(2 + a I ^185)

k' — SkP^X — P (k^ + \3) = _ 2^ 3' 5"" (23 + 3^) ; J

and, accordingly, if we multiply the last expression (184) by the last expression
(185), we are led, by the general formula (60), to the same result for Vu^, and
therefore for H4, as was obtained in the last article by an entirely different me-
thod. The general formula (60) may also, in virtue of the equations (13), (59),
(62), (63), (70), (116), and (4), be written thus :

18v/h, = — 5'»(0 — 0^)TirL; (186)

which agrees, by (94), with the general result (145), and in which we have now

Ti7 = 1 .2.3.1.2.1 = 12; (187)

while L may be calculated by the definitions (62) and (63), which give, at pre-
sent, by the values (184) for a, e, 1/, i,

M = f(l-rX "==-2(2+^), (188)

and

L=-^(23 + 3^): (189)

and thus we arrive again at the same value of 's/h4 as before. The same value
of L may be obtained in other ways, by other formulae of this paper ; for example,
by those of the 24th and 25th articles, which give, in the present question,

l' = — 2^ 3' 5^ 23 ; l"=z + 2' 3^ 5\ ( 19Q)

We may also decompose l into three factors m, which are here :

Sir William Rowan Hamilton on Equations of the Fifth Degree. 367

M.= -^-(3 + 4^); M, = A.(3_^); M3=f; (191)

and which conduct still to the same result.

38. An equation of the fifth degree, which, like that here assumed as an ex-
ample, has all its roots unequal, may have those roots arranged in 120 different
ways ; and any one of these arrangements may be taken as the basis of a verifica-
tion such as that contained in the last five articles. But we have seen that no
such change of arrangement will affect the value of either H, or Hj ; and with
respect to H4, which has been more particularly under our consideration in this
paper, it is not difficult to perceive that an interchange of any two of the four
last roots (.r^, x^, x^, x^, or x", x'", x^^, x^), of the proposed equation of the
fifth degree, will merely change the sign of the square-root, a/h^, in the fore-
going formulte, without making any change in the value of H4 itself, which has
been shown to depend on the first root (^, or x') alone. It will, however, be
instructive to exemplify this last-mentioned dependence, by applying the fore-
going general processes to the case of the equation of the fifth degree (147), the
two first roots being made to change places with each other, in such a manner
that the order shall now be chosen as follows :

X, = 1, s, - 2, x^ = 0, x^ =z-l, x, = - 2, (192)

or (since the sum of all five vanishes),

x' = l, x" = 2, x"'=zO, x"'=-l, x''= — 2. (193)

We find, for this new case, by calculations of the same sort as in recent articles
of this paper, the following new system of equations for the values of the six
functions v :

Ti7V34, = 12 + 4D; ^|.^v,,3 = -9-4d; ^|^v,3, = _3; j

tItV435 = 12 — 4d ; TfTV543 = — 9 + 4d ; t|-3-^'354 = — 3 ; J

in which, d has again the meaning assigned by (30) : and, consequently,

S (V345 + eV,,3 + ew,,0 = 3 (50^ _ 26) - 4f ; 1

rh (V3M + eV,„ + ev«5) = 3 (56 -26') -4^; J

2' 3' 5-'' Vh, = {3 (50-^ _ 26) — 4f }^ — {3 {56 — 26') _ 4^Y ; ]

VH,= 2-'5m6-6'){55-60', 1

and

(194)

(195)
(196)

368 Sir William Rowan Hamilton on Equations of the Fifth Degree.

H, = _2-«3'5'«7'(497 — 132^): (197)

results which differ from those obtained with the former arrangement of the five
roots of the proposed equation (147), but of which the agreement with the ge-
neral formulae of the present paper may be evinced by processes similar to those
of the last article.

39. As a last example, if the arrangement of the same five roots be

X, = 0, a,\ =1, Xj = 2, x^ = — 1, JTs = _ 2, (198)

we then find easily that all the six quantities v vanish, and, therefore, that we
have, with this arrangement,

\/h4 = 0, H4 = 0. (199)

All these results respecting the numerical values of H4, for different arrange-
ments of the roots of the proposed equation (147), are Included in the common
expression :

H,__2 3 5 (^ 5x''-l5x'-'+l J' (^"^>

which results from the formula (85), combined with (79) and (86) (87) (88) :
and thus we have a new confirmation of the correctness of the foregoing calcula-
tions.

40. It is then proved, in several different ways, that the quantity h^, in the
formulae which have been marked in this paper (a), (b), (c), (d), and which have
been proposed by Professor Badano for the solution of the general equation of
the fifth degree, is not a symmetric function of the five roots of that equation.
And since it has been shown that the expression of this quantity h^, contains in
general the imaginary radical ^ or \/ — 15, which changes sign in passing to the
expression of the analogous quantity Hg, we see that these two quantities, h^ and
^g, are not generally equal to each other, as Professor Badano, in a supplement
to his essay, appears to think that they must be. They are, on the contrary,
found to be in general the two unequal roots of a quadratic equation, namely,

h/ + QH, + K* = 0, (201)

in which

Q = - (h, + hJ = 2-" 3-^ 5'*w^ (5l'^ - 3l"*), (202)

and

B = Vuy Va, = — 2-'" 3-' 5'' ^"^ (5l'* + 3l"^), (203)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 369

Tsr, l', and l", having the significations already assigned ; and the values of the
coefficients q and r depend essentially, in general, on the choice of the root x',
although they can always be expressed as rational functions of that root.

41. It does not appear to be necessary to write here the analogous calcula-
tions, which show that the two remaining quantities Hj and Hj, which enter into
the same formula (a), (b), (c), (d), are not, in general, symmetric functions of
the five roots of the proposed equation of the fifth degree, nor equal to each
other, but roots of a quadratic equation, of the same kind with that considered
in the last article. But it may be remarked, in illustration of this general result,
that for the particular equation of the fifth degree which has been marked (147)
we find, with the arrangement (148) of the five roots, the values:

H3 = 2-^3-^5»(1809 — 914^), H, = 2-^ 3-^5" (1809 + 914^); (204)
with the arrangement (192),

H3= 2-^ 3-* 5^(1269+ 781^), H5 = 2-^ 3-2 5^ (1269 — 781^); (205)
and, with the arrangement (198),

H3 = 0, H, = 0. (206)

The general decomposition of these quantities H3 and Hj, into factors of the fifth
dimension, referred to in a former article, results easily from the equations of
definition (42) and (43), which give :

<2n,= {h + h'){h + eh'){h + e^h'); 1

2h, = {i + i') (i + ei') (i + eH'). J

And the same equations, when combined with (40) and (38), show that the
combinations

H3^ — H, = A^ h", h/ — u^ = P i\ (208)

are exact cubes of rational functions of the five roots of the equation of the fifth
degree, which functions are each of the tenth dimension relatively to those five
roots, and are symmetric relatively to four of them ; while each of these func-
tions, hh' and ii', decomposes itself into two factors, which are also rational func-
tions of the five roots, and are no higher than the fifth dimension.

42. In the foregoing articles, we have considered only those six quantities h

VOL. XIX. 3 B

(209)

(210)

370 Sir William Rowan Hamilton on Equations of the Fifth Degree.

which were connected with the composition of the six functions v, determined
by the definition (33). But if we establish the expressions,

Tc2ed ^^ Vcde "T" —

T<fc2c = Vcde — + —

Tedca — ' cde — "r"

which include the definition (33), and give,

■y cde ^ ^ \'^2cde "7" T^cied — Tde2c — T^dcj),
V cde ^ ^ (Tacde — "T — ))

v"'c<ie=i(T2cie — — + ),

we are conducted to expressions for the squares of the three functions v', v",
v'", which are entirely analogous to those marked (a) and (b), and have ac-
cordingly been assigned under such forms by Professor Badano, involving
eighteen new quantities, H-, . . Hj^ ; which quantities, however, are not found to
be symmetric functions of the five roots of the equation of the fifth degree,
though they are symmetric relatively to four of them.

43. In making the investigations which conduct to this result, it is convenient
to establish the following definitions, analogous to, and in combination with, that
marked (111) :

4Y cde ^ Xjcde ~}~ ^csed — ^ddc ^edcif |

4y cde ^ Xacde — "T — »

4Y cde ^ Xjcde — — "T '

for thus we obtain,

Xacte :^ Ycde -J- '^ cde'V '^ cde "V ^ cdej
■ Xc3ed ^ ^cde "t~ '

^de2c '—■ ^cde "T~ 5

Xe(te2 ^^ '^cde — — "l" '

V'ei. = (w* — w) Y'cde + («"' — «') y" dec,
y"cde = (w* - w) Y"cdc - («' - "•') y'dc,,
y"'cde =(«." + «- 2) y'"c.. _ (a,-' + 0.^ -

(211)

(212)

2)y''

dee*

(213)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 371
Introducing also the following notations, analogous to (112),

y' — Y'' 4- y'" y" — y" — Y^"

* 345 *• 5 ~ ^ 55 ''435 * 5 ^ 5>

y' — y" 4- y'" y"

» 453 "31" 3' "^54

^\ - ^"\,

y' — Y^' 4- y'" y" — V^' V^" •

'534 ^4"* 4' '354 ''4 ' 4»

''345 '' 5r'' 5»'^435 ^ 5 '' 5»

y" Y^" 4- Y^"" y' V^^ v""

'443 "si'' 3 J "^ 513 "3 " 3'

y" Y^^' 4- Y^"' y' — Y^"" V^^" •

*534 * 4T'' 4> "354 '^ 4 ■' 4»

and

345

.\\V „\^^"

Y^''^ -4- Y^^"' y'" v'

^ air '^ 5'* 435 '^

'■ 453 *■ 3 T^ » 3» " 543 '' 3 »■ 3»

■' 534 " 4T^'' 4> * 354 ^ 4 '' 4'

we find, by (30), results analogous to (113) and (114), namely.

V —

* 345

v' —

' I'll — ■

» All "™'

v" —

BY^', + CY^"„ V',33 = BY-, - CV-"„
By^+CY-'3, V',3 = BY-'3 - CY-"3,
BY^ + CY% V'3^ = BY^-CY^^"4;

435 ^ ^ 5

+ BY-",, v",3, :

= CY^

CY-'3 + BY-"3, V",,3

= cy\

and

CY^

■ BY-',,

■BY-'3,

BY-'4;

v"' —

345

v"' —

453

v'"

DY-, - 5y-"'„ y'",3, = DY-', + 5y-"„
DY-^ - 5y-"3, v'",,3 = DY-'3 + 5y"-'3,
DY--4 - 5y-"'4, v'"354 = DV^"4 + 5y--'4.

(214)

(215)

(216)

(217)

(218)

. (219)

And squaring the eighteen expressions (217) (218) (219), we obtain others, for
the eighteen functions v'^ v"*, v'"*, which depend indeed on eighteen others of
the forms y, determined by the definitions (211) (214) (215) (216), but which
are free, by (54) and (55), from the imaginary fifth root of unity, w, except so
far as that root enters by means of the combination d, of which the square is = 5.
44. If, now, we write like Professor Badano (who uses, Indeed, as has been
stated already, a notation slightly different),

3 B 2

372 Sir William Rowan Hamilton on Equations of the Fifth Degree. H

'^''V = Hi9 + '/H20 + a/h,, 4- \/h,, + Vh

bM
III 2

•19
^19

Vh„

24'

= H,9 + \/h2o + 0Vh„ + 1/H22 + 0\/h,3 — /h24 :

(a'")

and

• R45 ^^ ^*1<

* 435 "19

H„

\/h2o + VH^TyXa + Vh23 + Vh24 ;
/h^o + e^^^i — /h,2 + 0'Vhj3 + v'h24;
\/h2„ + eVHo, — 7h^+ <?\/h,3+ a/h^^;

(b'")

together with twelve other expressions similar to these, and to those already
marked (a) and (b), but involving the functions v' and v" ; we shall have, as the
same author has remarked, a system of converse formulas, analogous to (c) and
(d), for the determination of the values of the eighteen quantities h,, ... H24.
Among these, we shall content ourselves with here examining one of the most
simple, namely the following :

H,« = i (v"'3./ + y"'J + v'".34^ + y'\.J + V"J + v"',3/) ; (220)

for the purpose of showing, by an example, that this quantity is not Independent
of the arrangement of the five roots of the original equation of the fifth degree.
45. Resuming with this view the equation (147), and the arrangement of
the roots (148), we find the following system of the twenty-four values of the
function Xjcie :

-- 500; X3,,, = - 90; x,,,3 = 240; x^,, = 500 ;

^4235 •

^2453= 1165;

^2634 9" 5 ^5243 V^^ J

— — 935 ; X5324 — — 515 ; x^^^ — — 1 165 ;

'■3425

= 515;

'•4352

= -620; X3^,= -295; x^^=145;

*4532 '

= — 240 ;
70;

Xj543 — b20 ; X5234 — — 720 ; X4325 — 720 ; X3452 — — 70 ;

= — 145; X4253 = 375;

= -375; x^, = 295;

which give, by (211),

4y"'34,= -150; 4y"',,3=1450;

4y'

534

4y"',3,=:150;
and, therefore, by (216),

4y'"^3 = 550;

4y'" —
^* 354 —

= — 1600 ;
400;

(221)

(222)

(223)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 373

8y^^^ = 0 ; 8y^% = 2000 ; 8y^^^', = - 2000 ; 1

8y"^'j=— 300; 8y"'"3 = 900; 8y"^", = — 1200 ; J

whence, by (219),

■^v"'^ = Z; ^f^v-,3=-9+4D; Tf7V-3,= 12-4D; |
^^y-,, = _3;Tf7v"',3=9 + 4D; ^-f^v'^,, = - 12-4d; J

and the squares of these six second members are

9, l6lq:72D, 224q:96D, (226)

so that we have, by (220), with this arrangement of the five roots of the equa-
tion (147),

H,9=2-'3-'5n97. (227)

But with the arrangement (192), we find, by similar calculations,

^v-3,3 = 6 + 4d ; Tf7v'"4S3 = - 9 - 4d ; yf^ v'"^ = - 3 ; j ^g)
Tf^v-3,= -6 + 4D;^v'"^3Zz9-4D; ^v'"3,,= +3;j

of which the squares are

116±48d, 161±72d, 9; (229)

and we have now

H,g = 2-'3-'5«iri3, (230)

a value different from that marked (227). And, finally, with the arrangement
of the roots (198), we find instead of the quantities (225) or (228), the follow-
ing:

ipl8-8D, ±6, 0, (231)

of which the squares are

644±288d, 36, 0, (232)

and give still another value for the quantity h now under consideration, namely,

H,9 = 2' 3-» 5' 17. (233)

46. The twelve other expressions which have been referred to, as being ana-
logous to (a) and (b), are of the forms :

v\5 = H, + '/h8 + v^Hg-f/Hio-f v^H„- \/h,2; (a')

v'*364 = H, - /Hg -f \/h, - \/h,o + ^/h„ 4- /H,2 ; (b')

374 Sir William Rowan Hamilton on Equations of the Fijlh Degree.

v"\„ = H„ + \/h., + a/his + A/H,e + \/h„ - ^/H,8 ; (a")

534

V'"435 = Hj3 - /h,, + ^H,, - •/h,6 + a/h,, + ^H,8 ; (b")

and they give, as the simplest of the expressions deduced from them, the two
following, which are analogous to that marked (220) :

H. = i (V'^340 + ^'\. + V'\34 + V'^M + V'^«3 + V'\35) ; (234)

H,a = i (^"^345 + V"»4« + ^"^534 + v"^354 + V'^^a + ^'\^)- (235)

For the case of the equation (147), and the arrangement of roots (148), we find
the numerical values :

I v'3« = - 126b - 7c ; I v'453 = 202b - 11c ; f y\^ = 25b + 50c ; |
f v",3, = - 126c + 7b ; f v"^3 = 202c + 11b ; f v"3^ = 25c - 50b ; J ^

fv',35=-18B + 47c; fv'«3= 100b -175c; f v'3^ = -61b- 52c; ]
fv"3«=-18c-47B; fv%=100c + 175b; fv",3,= - 61c + 52b; i ^ ^

which may be obtained, either by the method of article 43., combined with the
values (221) (222) of the twenty-four functions x; or by the formulae (210),
combined with the following table :

fT,3,3= -175b-25c; |t^35=-150-11b-77c;

|t,453= +377b + 89c; fT^3 = 450 + 111b + 27c + 200d; • (238)

f T,53, = 150 + 77b - 11c ; f t^ = - 450 - 111b - 27c - 200d ; .

and with the condition, that, if we write for abridgment,

Ticde = T^°'jcde + Bt'jc* + CT" tcde + I>T'"4cde, (239)

we have in general the relations,

Tedcb = T^°^6cde — BT'jcde — CT"jc&, + 'DT"'icdt ', j ,

And hence, for the same equation of the fifth degree, and the same arrangement
of the roots, we find, by (54) and (55) :

H, = - 2-* 3-' 5* (10975 + 706d) ;
H,3= - 2-* 3- 5* (10975 - 706d).

I (241)

Sir William Rowan Hamilton on Equations of the Fifth Degree. 375

But, for the same equation (147), with the arrangement of the roots (192), we
find, by similar calculations, the values :

H, = - 2-^ 3-' 5^ (10975 - 1472D) ; |

h,3=-2-^3->5*(10975 + 1472d); J

and with the arrangement (198),

h, = -2-^3-'5^(10975 + 3832d); |

H,3 = — 2-'-3-'5^(10975-3832d). |

We see, therefore, that in this example, the difference of the two quantities
H, and H,3 is neither equal to zero, nor independent of the arrangement of the
five roots of the equation of the fifth degree. However, it may be noticed that
in the same example, the sum of the same two quantities h, and h,3 has not been
altered by altering the arrangement of the roots ; and in fact, by the method of
the 43rd article, we find the formula :

(244)

"5" V^7 "T H13) = (^2345 X5432) -\- (X2453 X3^.2) -j- (X2534 ^43Si)

"T (X3254 X4523) + (X4235 X3324^ + (,'^5243 ^3426^

I (,X2354 X4532) -J- (X2543 X3452) + (,X2435 X5342)

r i,X3245 X5423^ "T (.X5234 X4325^ + (X4353 X3J24^

of which the second member is in general a symmetric function of the five roots,
and gives, in the case of the equation (147), by (221) and (222), the following
numerical value, agreeing with recent results,

H, + H,3 = — 2-' 3-' 5" 439. (245)

47. It seems useless to add to the length of this communication, by enter-
ing into any additional details of calculation : since the foregoing investiga-
tions will probably be thought to have sufficiently established the inadequacy of
Professor Badano's method* for the general solution of equations of the fifth de-
gree, notwithstanding the elegance of those systems of radicals which have been
proposed by that author for the expression of the twenty-four values of Lagrange's

* Professor Badano's rule is, to substitute, in each h, for each power of x', the fifth part of the
sum of the corresponding powers of the five roots, x',.,x^ ; and he proposes to extend the same
method to equations of all higher degrees.

376 Sir William Rowan Hamilton on Equations of the Fifth Degree.

function If'. Indeed, it is not pretended that a full account has been given, in the
present paper, of the reasons which Professor Badano has assigned for believing
that the twenty-four quantities which have been called h are all symmetric* func-
tions of the five roots of the equation of the fifth degree ; and that those quanti-
ties are connected by certain relations among themselves, which would, if valid,
conduct to the following expression for resolving an equation of that degree, ana-
logous to the known radical expressions for the solution of less elevated equations :

<* = Ki + a/Kj -f V Kg -f \/k4 + V K3 — V'k4
+ V{Vi,-\- -/Kg + A/i74rVI^-|- Vk, - V'kJ
+ \/{k, 4- /Kg + 0V K, -f a/ Kg + e^V'lE^^T-T^}

+ v/{K3 + -v/k« + e^v'K, + 1/K3 + e^^^;:=wT,}.

But it has been shown, in the foregoing articles, that at least some of the relations
here referred to, between the twenty-four quantities h, do not in general exist ;
since we have not, for example, the relation of equality between h^ and Hg, which
would be required, in order to justify the substitution of a single symbol K4 for
these two quantities. It has also been shown that each of these two unequal
quantities, h^ and Hg, in general changes its value, when the arrangement of the
five roots of the original equation is changed in a suitable manner : and that h,,
•H,3, H,9, are also unequal, and change their values, at least in the example above
chosen. And thus it appears, to the writer of the present paper, that the inves-
tigations now submitted to the Academy, by establishing (as in his opinion they
do) the failure of this new and elegant attempt of an ingenious Italian analyst,
have thrown some additional light on the impossibility (though otherwise proved
before) of resolving the general equation of the fifth degree by any finite combi-
nation of radicals and rational functions.

* " Dunque le H sono quantita costanti sotto la sostituzione di qualunque radice dell' equa-
zione." To show that the constancy, thus asserted, does not exist, has been the chief object pro-
posed in the present paper ; to which the writer has had opportunities of making some additions,
since it was first communicated to the Academy.

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377

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XV. — On the Compensations of Polarized Light, with the Description of a
Polarimeter, for measuring Degrees of Polarization. By Sir David
Brewster, K. H., D. C. L., F. R. S., M. R. I. A., and V. P. R. S. Ed.

Read November 14, 1842.

In four papers, printed in the Philosophical Transactions for 1830, I have en-
deavoured to determine the general laws of the polarization of light, when reflected
from or refracted by the first and second surfaces of bodies, or when suffering
total or metallic reflexion. In opposition to the opinions of the most distinguished
philosophers, I was led to the conclusion — that when ligh^ was reflected at any
angle of incidence between 0° and 90° (excepting at the angle of complete pola-
rization), or was refracted at these angles, it did not consist, as they maintained, of
two portions, one of which was completely polarized, and the other completely
unpolarized or common light ; but that every portion of it had the same physical
property, namely, that of having approximated more or less to the state of complete
polarization. This general result, which enables us to compute all the phenomena
of polarization by reflection and refraction, has, in so far as I know, never been
called in question ; but as the investigation was conducted on the supposition,
that a pencil, composed of two pencils, polarized -{- 45° and — 45" to the plane of
reflexion, was equivalent to a pencil of common light, it became important to have
the general result confirmed by experiments made with common light itself; and
though the inquiries, the results of which I am now about to explain, had not
this object in view, yet it will be satisfactory to find in them a complete demon-
stration of my former views.*

In considering the condition of partially polarized light, it has always appeared
to me probable that some method would be found of distinguishing it from a

• Philosophical Transactions, 1830, pp. 69, 133, 145, 287.
VOL. XIX. 3 c

378 Sir David Brewstkr on the Compensations of Polarized Light.

mixture of polarized and common light ; and I have accordingly endeavoured at
different times, though without success, to obtain such a test. While studying,
however, the polarizing structure of the atmosphere, where it became desirable
to ascertain the degree and kind of polarization which light reflected from diffe-
rent parts of it experienced, I was led to a series of experiments, which furnished
me with the test of which I had been in search.

The comparative brightness of the two images in Iceland spar, directed to
different parts of the sky, afforded a very imperfect indication of its state of pola-
rization ; and I had, therefore, been in the practice of employing the uniaxal or
biaxal system of rings for this purpose.* Upon placing such a system between
light partially polarized in one plane, and light partially polarized in an opposite
plane, I found that the rings disappeared, the direct system being seen on one
side of the plane of disappearance, and the complementary system on the other side.
In this experiment, the polarization of the light in one plane was compensated
by the polarization of the samd light in the opposite plane, and consequently both
of the pencils that had undergone the two successive polarizing actions, had re-
ceived the same degree of polarization in opposite planes. In virtue of these two
equal and opposite polarizations, the light at the point of compensation, where the
system of rings disappeared, had been restored from partially polarized to com-
mon light, and the light on each side of this point of compensation was in oppo-
site states of partial polarization.

In order to have a more distinct idea of the nature of this experiment, let us
suppose that light reflected once, at 24° of incidence, from glass, whose index of
refraction is 1.525, is afterwards made to suffer one refraction at 80° by another
surface of the same glass.f In this case, the partial polarization produced by re-
flexion is exactly compensated by the equal and opposite partial polarization pro-
duced by refraction. In like manner, a second reflexion at 83^°, in an opposite
plane, will compensate the first reflexion at 24°, or the refraction in the same
plane at 80°.

Now, in these three cases of compensation, the quantity of polarized light in
the three pencils is very different, as appears from the following table :

• See my Treatise on New Philosophical Instruments, 1813, p. 349.

I The action of one refraction is obtained by using a prism of well annealed glass, as shown in
the Philosophical Transactions, 1830, p. 135, fig. 2.

Sib David Brewster on the Compensations of Polarized Light. 379

Angles of Incidence. No. of Rays, out of 1000 polarized by Reflection and Refraction.

24° 10.5

80° 158

83f 139.3

Hence, it is obvious that the compensation is not produced by equal quantities of
light polarized in opposite planes ; and it would be absurd to suppose that the
portions of common light existing in each of the partially polarized pencils per-
formed any part in the compensation. But even if it did, it could act only by its
quantity — that is, by the relation which it bore to the polarized portion of the
beam. Now, in the three cases which we have noticed, the ratio of the common
to the polarized portion of the pencil is not the same, although the compensation
is perfect, as the following numbers show :

Ratio of common and polarized Light.

Angles of Incidence.

Reflected Pencil.

Refracted Pencil.

24°

4.15 to 1

80°

2.8 to 1

83f

2.8 to 1

Hence, we are forced to the conclusion, that the compensation is produced neither
by an equality of oppositely polarized rays, nor by a proportional admixture of
common light, but by equal and opposite physical states of the whole pencil, whe-
ther reflected or refracted.

Let us now consider what takes place at the polarizing angle, or 56° 45', in
glass. The whole of the reflected light, or 792- rays, is here wholly polarized,
and the same quantity of oppositely polarized light, viz. 792- ^^Y^' exists in the
refracted beam. Now, this refracted beam is not capable of compensating the
reflected one, notwithstanding their equality in point of polarized light, and
though the reflected beam is not mixed with common light ; so that, upon the
old hypothesis, the refracted beam can owe its deficient power of compensation
only to the large quantity of common light which it contains.

But though in the compensations already mentioned the proportions of com-
mon to polarized light are different ; yet, in other cases of compensation, such
as the following, the proportion is pretty nearly equal ; but this equality is acci-
dental, and is not the cause by which the compensation is produced.

3 c 2

Angles of Incidence.

Reflected Pencil.

Light polarized.

15° 40'

43.4

4.5

56° 45'

79.5

79.5

87° 51'

80.9

70

380 SiE David Brewster on the Compensations of Polarized Light.

Ratio of common to
Refracted Pencil, polarized Light.

1/9.6
920 , 1/11.6
1/11.5

Hence, a pencil reflected at an incidence of 15° 40', compensates another re-
flected at 87° 51', and each of them compensates a pencil refracted at the
polarizing angle 56° 45', and the ratio of the common to the polarized light is
nearly the same.

In support of the same views we shall examine what takes place at other three
remarkable angles of incidence.

1. At 78° 7' where the quantity of polarized light is a maximum, or 158
rays, the power of compensation by reflexion is less than at every angle of inci-
dence between 78° 7', and 30° where the quantity of polarized light varies from
158 to 17 rays.

At 78° 7' the quantity of refracted light is double that of the reflected light,
and is equal to two-thirds of the Incident light, and the quantity of polarized
light is nearly one-fourth of the reflected, and one-half of the refracted, light.
Now, at this angle the power of compensation by reflexion and refraction is
nearly in the inverse ratio of the quantity of light in the reflected and refracted
beams, and not as the quantities of common light, which they are supposed to
contain. For the powers of compensation are as 6° 50' to 14° 7' ; the ratio of light
in each beam as 666 + 333, and the proportion of common light as 508 to 175.

2. At 85° 50' 40", when i — i' = 45°, when the refracted is one-half of the
reflected light, and the quantity of polarized light one-third of the refracted
light, one-sixth of the reflected light, and one-ninth of the incident light, the
power of compensation by refraction is nearly double of that by reflexion,* being
nearly in the inverse ratio of the quantities of light in the reflected and refracted
beams, and not of the quantities of common light which they contain.

At other angles of incidence beside these two, the powers of compensation
have no such relations.

3. At 82° 44', a very remarkable angle, where cos (i -\- i') = cos.'' {i — i'),
and where the reflected is equal to the refracted light, the compensation by re-
flection is equal to the compensation by refraction, and the ratio of the polarized

* The one is 9° 44', and the other 4° 48'.

Sir DxyiD BREVfSTEVL on the Compensations of Polarized Light. 381

to the common light, or to the total quantity in each beam, is the same ;* but this
equality is accidental, as appears from the fact already mentioned.

The remarkable phenomena produced at this angle in glass, and at the cor-
responding angle in all transparent bodies, where cos. (i-\-i') zz cos.'^ (i — i')
require to be more minutely stated, and lead us to the construction of what may
be called the compensating rhomb, which is shown in Plate, Fig. 1 . It consists
of a well annealed rhomb of glass, or of any other uncrystallized body abcd,
having, in the case of glass, the angles bad, bcd = 139° 25', and abc = 40" S5',
when the index of refraction is 1.525. If a ray of light Rr, is incident upon ab,
at an angle of 82'' 44', exactly one-half of it will be reflected in the direction rm,
and the other half refracted in the direction rN, having each the same quantity
of polarized light, as already stated. But the ray rN is again reflected at n at an
angle of 40° 35', and it will emerge from the face ad nearly perpendicularly,
without suffering any perceptible refraction, in the direction nm'. If we now ex-
amine this ray m'n, we shall find it to be in the state of common light, although
the incident ray rN contained 145 polarized rays, or nearly one-half of the pencil
rN. In order to be satisfied of this, the compensating rhomb should be made of
two equal and similar rectangular prisms, abc, ado, cemented to or nearly touch-
ing one another. By removing adc, the ray rN emerging nearly perpendicularly
from the face ac, will exhibit the state of its polarization, when it falls upon the
face DC at the point n.

We have now obtained by this experiment a very singular result. If the
pencil rN consists of 145 rays of polarized light, and 333 — 145 = 188, of com-
mon light, the effect of a single reflexion at n has been to unpolarize polarized
light ! and to produce no change at all upon common light ! a property of a re-
flecting surface hitherto unheard of, and incompatible with all our present know-
ledge of the polarization of light. After such a conclusion, it would be an un-
profitable task to adduce any further arguments ; and I shall therefore only state
that all the phenomena of polarization, by successive reflexions and refractions,
stand in direct contradiction of the views which I have been combating.

The restoration of the pencil rN to common light by reflexion at n, furnishes
us at once with the principle of compensation, in conformity with the laws of po-
larization deduced in my papers of 1830. The whole of the ray rN has suffered a
physical change by refraction at r, consisting of a rotation of Its planes of polari-

* This is the only angle where this equahty obtains.

382 Sir David Brewster on the Compensations of Polarized Light.

zation towards a plane perpendicular to that of refraction, and the subsequent
reflexion at n has exactly counteracted that rotation, by turning back the planes
as many degrees towards the plane of reflexion. The reflexion at n has, there-
fore, brought back the ray ra into the same state as the original ray Rr, that is,
the ray nm' is common light.

In order to ascertain if this principle is general, and to determine the laws
of the compensation of partially polarized light, I shall now describe the instru-
ment by which I have ascertained the physical condition on which compensation
depends, and the leading facts on which the doctrine rests. From its property
of measuring degrees of polarization, I have called this instrument a Polarimeter.
It is represented in Fig. 2, and consists of two parts, one of which is intended to
produce a ray of compensation, having a physical character susceptible of nume-
rical expression, and the other to produce polarized bands, or rectilinear isochroma-
tic lines, the extinction of which indicates that the compensation is effected. The
first part of the instrument consists of a goniometer ab, carrying on its axis mn, a
frame cd containing six or seven plates of glass, about the 70th of an inch thick,
such as are now used for holding microscopic objects. This frame can be taken
off and replaced by a black glass reflector highly polished, and free of all oxidation
on its surface, or it may be fixed permanently at ef, alongside of the frame cd.*

The second part of the Polarimeter is a combination of two plates of rock
crystal, or any other transparent doubly refracting mineral, such as I described
in 1819, in my paper on the Properties of Amethyst A The object which I had
in view by this combination was to exhibit the colours of polarized light in recti-
linear bands, and this is effected in the following manner. A plate of rock
crystal, ab. Fig. 3, from the fiftieth to the tenth of an inch thick, Is cut so that
its faces are inclined 45° to the axis of the prism, which is the axis of double re-
fraction. When the plate has been divided into two equal parts at the line cd,
the one is placed transversely above the other, and cemented to it by Canada
balsam, so that the two plates act in opposition to each other upon polarized
light. When this plate is fixed at the end of a Nicol's prism (or a rhomb of cal-
careous spar, with a circular aperture just sufficient to separate the two images),
as shewn in Fig. 4, the depolarizing axis of the plate being parallel to the prin-

* When much light is desired, a plate of a highly refracting substance, whose index of refrac-
tion is known, may be substituted for the glass,
t See Edinburgh Transactions, vol. ix. p. 148.

Sir David Brewster on the Compensations of Polarized Light. 383

cipal section of the rhomb, we shall observe in polarized light a beautiful system
of rectilineal bands, as exhibited in Fig. 5, where mn is a deep black neutral
line, with the usual coloured bands on each side of it. With light polarized oppo-
sitely, the central band mn is white, as shewn in Fig. 6, in which the tints are
complementary to those in Fig. 5.

Let us now suppose it required to determine the state or degree of polariza-
tion of any luminous surface from which light is reflected, or through which it is
transmitted, or of any illuminated medium from which both reflected and re-
fracted light are transmitted to the eye of the observer.

If the light is polarized in the plane of the meridian or a vertical plane, it
may be more convenient to use the glass plate at cd, and in doing this the ana-
lyser with the rock crystal is fixed between the frame cd and the eye of the ob-
server upon a pillar, or it may be held in the hand, so that the principal section
of the rhomb is in a vertical plane. The rectilineal bands will then be seen dis-
tinctly crossing the luminous surface, when cd is perpendicular to the axis of vi-
sion. But if we incline cd from 0° of incidence towards 90, by turning round
the goniometer, a position will be found when the rectilinear bands are inter-
rupted by a neutral line, as in Fig. 7, and the bands at a on one side of the neu-
tral line will be complementary to those at b on the other side. After marking
the indication of the goniometer, when this takes place, suppose 1 60°, turn back
the goniometer till the light from the luminous surface is nearly as much inclined
to the plates on the other side of 0° of incidence, and vary the angle till the bands
are interrupted as before, when the observer looks at the same point of the lumi-
nous surface. Having again observed the indication of the goniometer, suppose
10°, then 160° — 10° =. 150° will be the inclination of two rays equally inclined
to the plate, and the half of this, or 75°, will be the angle of incidence upon the
plates, at which the polarization of the light from the luminous surface is com-
pensated.

If the light from the luminous surface had been polarized horizontally, it
would have been most convenient to have used the rock glass, or other reflector
not metallic. In doing this, the luminous surface is reflected at the same angle
between the polarizing angle and 90°, and also between the same angle and 0°,
the analyser and rhomb being in each case interposed between the reflector and
the eye, as before, and the angle of incidence varied till the neutral line mn is
opposite to or seen upon the same part of the luminous surface. If the compen-

384 Sir David Brewster on the Compensations of Polarized Light.

sation takes place about 70°, it will also take place about 40°, and these angles
will afford measures of the degree of polarization necessary to produce the com-
pensation required.

In order to make these observations at different inclinations to the horizon,
the pillar which carries the graduated circle of the goniometer, and also the
pillar GH, must move upon a joint, as shewn in Fig. 2. By observations such as
those above described, the following angles of compensation will be obtained :

Compensations between two Reflexions, one above and one below the polarizing

Angle.

Below palarizing Angle.

Above palarizing Angle.

0°

90°

.5

89^

10

89

16

88

20

86

24

83

30'

81°

34

77

39

74

44

70

48

65

52

62

56|

56|

Compensations between one Reflexion below the polarizing Angle, and one

Refraction.

Reflexion. Refraction.

2° 10°

5 22

10 42

15 59

20 74

24 80

25 81
28 87
30 89^

Sir David Brewster on the Compensations of Polarized Light. 385

Compensations between one Reflexion above the polarizing Angle, and one

Refraction.

Reflexion. Refraction.

89^ ^ 22°

89 ' 42 •

88 59

86 74

83 80

82 87

81 89^

If we now compare these results with the experimental and calculated ones given
in my papers of 1830,* we shall find that one reflexion will compensate another
reflexion, or one refraction, when the inclinations of the planes of polarization
produced by the two reflexions are equal and opposite, or when the inclination
produced by one reflexion is the complement of the inclination produced by one
refraction ; or more generally, in both cases, when the rotations produced in the
plane of polarization are equal and opposite. Hence, it follows that the compen-
sations of polarized light are produced by equal and opposite rotations of the
planes of polarization.

Now, the inclination 0 of the plane of polarization by reflexion at any angle
of incidence i, is

cos (i-\-i')

tan 0 == tan. x ;. ..;,

cos (^ — J )

and the inclination 0' for refracted light, is cot <j} = cot x . cos (i — i'). In the
case of reflected light, the angles of incidence which compensate each other are
those where <j> has equal values ; and in the case of reflected and refracted light,
the one compensates the other, when 0 -j- 0' zz 90°, or tan 0 + cot 0' = 1, or
when

cos (i -\-i')

tan X

cos

;. .,, + cotar. cos (i — i') = 1.

{i — t) ^ '

Now, though we shall find that at the angles of compensation in the preceding

* Philosophical Transactions, 1830, pp. 74, 75, 78; 136, 138, 139, and 143.
VOL. XIX. 3 D

386 Sir David Brewster on the Compensations of Polarized Light.

table, the values of -|- 0 and — 0 in the case of reflexion, and of ± 0 and 90" —
0' in the case of a reflexion, and a refraction, are nearly equal ; yet it requires to
be proved, that when the planes of polarization are inclined at an angle, ± x, to
the plane of incidence, greater or less than 45°, another reflexion at another
angle, which would give ± 0, or 90° — 0', of the same value, will restore the planes
to their original inclination.

When X = 45°, and when one reflexion has turned the planes of a ray polar-
ized 45° into 37° 21', or given the planes a rotation of 45° — 37° 21' = 7° 39',
the action of a refracting surface which produces the same rotation, or
52° 39' — 45° = 7° 39' will bring the planes back to 45°, or restore the partially
polarized light to common light. Call x ■=. 37° 21', then in order that the
refraction may restore the ray to 45° we must have 0' = 45° or cot 0' = cot x
cos (^ — i') zz 1. Now, cot 0' = cot x cos {i — ^'), and when x = 45° and

0' = 52° 39', cot 0' = cos (i — i'). But x = 37° 21' = 90° - 0, hence — "— =

^ '^ cot .r

cot0', and = cos {i — i'), consequently cot x cot {i — i') = 1. In like

manner 0' will be restored to 45° by a reflexion which gives 0 such, that 0 + 0'
= 90°, or tan 0 = cot 0'. That is when x = 45°, and 0 = 37° 21',

cos (i "4— i I

tan 0 = tan x 7-7- ^r ^ 1 . The general formula

^ cos (^ — ^ ) °

cos (i -\-i') , 1

tan 0 = tan x ^. n^ becomes, when x zz 45 ,

cos (i — ^ )

cos (i + »■')

tan 0 = f-. ^,

cos (?. — I )

But when x zz 52° 39' = 90° — 0, we have
1

= tan 0, and
tan X

1 cos (^■ + i')

tan a; cos (i — i')'

cos (i -\- i) ,
tan X ■ — , . .;- = 1 .
cos (e — i)

Consequently,

Sir David Brewster on the Compensations of Polarized Light. 387

Having thus determined that light polarized in a plane whose inclination to
the plane of reflexion is + (p, will be compensated by oppositely polarized light,
whose inclination is — (p, if both the lights are reflected, or by refracted light
whose inclination is 90° — 0 or 0', we must next endeavour to discover at what
angle of incidence the polarized light submitted to the polarimeter, has suffered
reflexion or refraction, when we have the angle of incidence and the inclination
of the plane of polarization, by which we have effected the compensation.

Let us first take the case when light partially polarized by reflexion is com-
pensated by the polarization produced by refraction through one surface, at an
incidence i of 80°. The index of refraction being 1.525, we shall have when

or = 45°, cot 0' = cos (i — i'), and 0' = 52° 33'.

Now, the plane of the light polarized by reflexion must be inclined 90° — 0', or
37° 27' ; we must, therefore, find the angles of incidence above and below the
polarizing angle, or the two values of i corresponding to this value of 0, namely,
37° 27', at one or other of which the original light must have been reflected.
These values will be obtained from the expressions

cos (^ + i') , . ., sin i

tan 0 = -: 7pr, and sin i = .

cos (/ — I ) m

When ^ -|- i' is less than 90°, or when the angle of incidence is less than the po-
larizing angle, tan 0 is positive, and we have

sin i = ^/(m'^+l)a^tan 0)-^ / ^ ^/"~7~2';;r^~4T^^-(
8 tan 0 I "^ W* + 1 ;< -^ (1 -tan 0)U '

When i + i' is greater than 90°, and tan 0 negative, the formula becomes

smz-y _8tan0 l~^- ^ + V^^F+lJ ^ (l+tan0)^/ '

From these formulae, whem m = 1.525 and 0 =: 37° 27', we obtain i:= 24° 50',
and 83° 30'.

When the compensation of refracted light is effected by one reflexion, either
above or below the polarizing angle, for example, at 15° 40', and 87° 51', we
shall have

3d2

388 Sir David Brewster on the Compensations of Polarized Light.

tan 0 = ^^iiyi^ = 42» 31'.
cos (l — I )

But in the refracted light thus compensated, we must have 0' = 90° — 42° 31
= 47° 29', and, therefore, we must determine the angle of incidence i, at which
the original light suffered refraction. The expressions from which we obtain i

are cot 0' = cos (J, — i'), and sin i' = , which give

. . m /

sm t = - — -J J
tan f/> V

•^aJ

tan '0'
sm

tan 0 V ^2 _^ 1 _

2 m

from which we obtain, when 0' ^ 47" 29', i = 56° 45', the maximum polarizing
angle.

Hitherto we have supposed the compensation to be produced by one refrac-
tion, or by one reflexion ; but it may be effected by several. In the case of re-
flected light this is not necessary, because we have all degrees of polarization by
reflexion, from 0° of incidence to the polarizing angle, and from this again to 90°
of incidence.

When the compensation, however, is made by successive reflexions at the
same angle of incidence, or when light which is compensated has been so reflected,
we may find the angle of incidence ^, when n is the number of reflexions, by
means of the formulfe

^ , cos"(^■ + ^■') ■. ., sin z , «.- — - — co?, {i-\-i')

tan 0 = „;. .,;, sm i = , and v tan 0 = ~ :7^,*

^ cos"(z — z') m ^ cos{t — t')

which give

when i -}- i' is less than the polarizing angle, and tan 0 positive. But when i -f- i
is greater than 90°, and tan 0 negative, we have

sini- /K+l)(l+^tan0)^^ / ( 2m n^ 4^ta«0^

* See Phil. Trans. 1830, p. 80, 81.

Sir David Brewster on the Compensations of Polarized Light. 389

In the case of light polarized by refraction, the action of several surfaces may
and must often be necessary to produce compensation, and in this case, or when
the light compensated is polarized by successive refractions, we may find the
angle of incidence by means of the formulae

cot 0 r: cos" (i — i'), and sin i' z= .

m

And since v' cot0= cos (i — i'), we have for n refractions,f

.in,:-— "L_ / "-^;^^an0-]

Vtan0

When the light has passed through a prism whose angle is ^, then if the
angle of the prism is equal to the angle of refraction, or ^ = i', or sin -f =

SlH Z

, the incidence i will be found from the formula for one refraction, because

m

the ray will emerge perpendicularly from the second surface of the prism, and

suffer no change in its planes of polarization.

If the angle of the prism is double the angle of refraction, or -^ = 2i', and the
deviation i — i' a minimum, the incidence i will be found from the formula when n,
the number of refractions, is two ; the refraction, and consequently, the polari-
zation at each surface being equal, and, therefore, the same, as for a plate when
^ = 0.

Having thus determined the laws of the compensation of polarized light, I
shall conclude this paper by pointing out a few of their numerous applications.

1. The first and most important result of this inquiry is, that it aifords a
new and independent demonstration of the laws of the polarization of light by
reflexion and refraction, given in my papers of 1830. As this result has been
already referred to, I shall merely mention the following general proposition.

When a ray of common light is incident at any angle upon the polished
surface of a transparent body, the whole of the reflected pencil suffers a physical
change, bringing it more or less into a state of complete polarization ; in virtue
of which change, its planes of polarization are more or less turned into the plane

* See Phil. Trans. 1830, p. 137.

390 Sir David Brewster on the Compensations of Polarized Light.

of reflexion, while the whole of the refracted pencil has suffered a similar, but
opposite change, in virtue of which, its planes of polarization are turned more or
less into a plane perpendicular to the plane of reflexion.

2. As the light of the sky and the clouds is more or less polarized, the em-
ployment of the light which they reflect may, in delicate experiments, be a
serious source of error, if we are not aware of its properties. By the principle
of compensation, however, we may convert this partially polarized light into
common light, and thus make experiments with as great accuracy in the day-
time, as we can do with the direct light of a flame. If the light from a parti-
cular part of the sky is admitted into a dark room, or otherwise employed, we
have only to compensate its polarization either by reflexion or refraction, and em-
ploy, as unpolarized or common light, that part of the light which corresponds
with the neutral line.

3. The laws of the compensation of polarized light enable us to investigate
the polarizing structure of the atmosphere, and to ascertain the nature and ex-
tent of the two opposite polarizing influences, which I have found to exist in it,
and by the compensation of which the neutral points are produced. But, as I
shall soon submit to the Society the results of my observations on this subject,
I shall not add any thing further at present.

4. In every case where reflected or refracted light reaches the eye of the
observer, whether it comes from bodies near us, or from the primary or secondary
planets of our system, the doctrine of compensation enables us to obtain im-
portant information respecting the phenomena presented by light thus polarized.
The nature of the reflecting or refracting surface, the angles of reflexion or
refraction, and the nature of the source of illumination, may, in certain cases,
be approximately ascertained.

5. When the light of the sun, or any self-luminous body, is reflected from
the surface of standing water, such as the sea or a lake, it is polarized according
to laws which are well known ; but when the partially polarized light of the sky
(light polarizes in every possible plane, passing through the sun and the observer)
is reflected, a variety of curious compensations take place, which, when the
position of the observer is fixed, vary with the season of the year, and the hour
of the day. In some cases, there is a perfect compensation, the partially polar-
ized light of the sky being restored to common light by the reflection of the

Sir David Brewster ow the Compensations of Polarized Light. 391

water. In other cases the light of the sky has its polarization increased by
reflexion from the water in the same plane in which it was itself polarized ; and
in other cases, the compensation is effected only in particular planes. At sun-
set, for example, the light reflected from the sea at a great obliquity in two vertical
planes inclined 45° to a vertical plane passing through the sun and the observer,
is compensated in these two planes, or the plane of its polarization is inclined
about 45° to the reflecting surface. The same observations apply to the light of
the two rainbows when reflected from the surface of water.

6. When the light of the sky, or of the rainbow, is reflected from surfaces
not horizontal, such as the roofs of houses, sheets of falling water, or surfaces of
smoke and vapour, the compensations are more varied, and a perfect neutralization
of the light by the second reflexion is more frequently obtained.

7. When the compensating rhomb, whose properties I have already described,
is made of glass not highly polished, light that has suffered total reflexion is seen
through the face ad. Fig. 1. As the faces ab, cd, are parallel, none of the light
regularly refracted by the face ab can suffer total reflexion from cd. Upon
examining this curious and unexpected phenomenon, I found that it was owing
to light radiated, or scattered from the surface ab, which falling upon cd at

angles greater than that of total reflexion, whose sine is — , necessarily suffered

total reflexion. That this was the cause of the phenomenon, I proved by covering
the surface ab with a film of dried milk, which radiated light from every part of
its surface, and produced a beautiful zone of totally reflected light, increasing
in brightness as the incidence upon ab became more oblique. In examining
this totally reflected light, I was greatly surprised to find, that it was partially
polarized, and exhibited an interesting example of compensation.

Let MN, Fig. 8, be the luminous zone of totally reflected light with its blue
border. At the polarizing angle of the second surface of the rhomb, the polar-
ization is incomplete ; but at angles between that angle and 83°, the polarization
gradually diminishes, and at 83° it becomes common light, the rectilineal fringes
AB produced by the rock crystal passing into neutral light at cd, close to the
boundary mn of total reflexion. From 83° to 90°, which corresponds to a very
narrow space at cd, the light still appears compensated, though it is slightly
polarized, in a plane perpendicular to that of reflexion.

392 Sir David Brewster on the Compensations of Polarized Light.

At 83°, when this takes place, the totally reflected light mn is polarized, as
shown at ef. Fig. 9, in a plane at right angles to that of reflexion. But as the
angle of incidence diminishes, the polarization diminishes, till at an angle of
68° it becomes common light, the polarization produced by total reflexion at the
second surface exactly compensating, as at cd, that produced by refraction at the
first.

At angles less than 68°, the totally reflected light is partially polarized in the
plane of reflexion, the polarization increasing till the scattered light disappears.

The polarization of the light that afterwards suffers total reflexion, is pro-
duced by its refraction at the first surface ab, Fig. 1 of the rhomb, and the phe-
nomena above described arise from the opposite action of the reflecting surface
CD ; at one angle producing an inferior degree of polarization, at another com-
pensating it, and at another overbalancing it.

St. Leonard's College, St. Andrew's,
April 24th, 1841.

■>'?''\'''Uo

Trans R.I^.J&Z.X1X.

Tij. 3.

Fij.i.

k-—'-

393

XVI. On the Heat developed during the Formation of the Metallic Com-
pounds of Chlorine, Bromine, and Iodine. By Thomas Andrews, M. D.,
M. R. I. A., Professor of Chemistry in the Royal Belfast Institution.

j> : y^.' •

v Read December 12, 1842. ' . "Ir

*li

1. In pursuance of the train of investigation commenced in a preceding Memoir,
I propose, in the present communication, to advance to the consideration of the
more complicated thermal phenomena, which are accompanied by alterations in
the state of aggregation of the combining bodies. To deduce general conclusions
from such inquiries is extremely difficult, as the variation of temperature mea-
sured by the thermometer is in every instance the resultant of more than a single
cause, each of which must be separately eliminated, before the heat arising from
the chemical union can be determined. It has been my endeavour to furnish as
many data as possible, in the cases I have examined, for the solution of these
interesting problems.

2. That we may be enabled to measure with precision the heat developed
during a chemical combination, it is necessary that the reaction should be very
quickly completed ; and the experiment is also greatly facilitated, when the ac-
tion commences, by simple contact, without the application of external heat.
These conditions are completely fulfilled, when chlorine, bromine, or iodine are
brought into contact with zinc or iron, water being also present. To the success
of the experiment the latter condition is indispensable, as these elementary bodies,
at ordinary temperatures, and in the dry state, have no action upon one another.*

• The description generally given in chemical works of the rapid manner in which zinc, copper,
antimony, &c. enter into combination with chlorine gas at common temperatures, is only true when
the gas is in a moist state. Chlorine gas, when carefully dried, has no action whatever, at the ordi-
nary temperature of the atmosphere, upon fine filings of zinc or iron, or upon copper reduced from
VOL. XIX. 3 E

SO'i Dvi. Ai^BVLBWs on the Heat developed during the Formation of the

The relative proportion of water is also a matter of importance. The quantity
present must be suflScient to dissolve, with facility, the resulting compound, and
it ought not greatly to exceed that amount. In the following experiments I
usually employed about 2.4 gr. of water, for every 0.42 gr. chlorine, 0.9 gr. bro-
mine, and 1.5 gr. iodine, which entered into combination. If this precaution be
attended to, and the mixture briskly agitated, the whole reaction will be com-
pleted in the course of a few seconds.

3. As our object is to ascertain the heat due to the combination of the re-
acting bodies in an anhydrous state, and as we actually obtain the result of the
combination In a state of solution in water, It is obviously necessary, in the first
instance, to apply a correction for the heat arising from the solution. The
amount of this correction is easily discovered, by determining the heat evolved
during the solution of a corresponding weight of the dry compound in the nor-
mal proportion of water. If the combining bodies do not unite in more than
one proportion, there only now remains to be determined the heat evolved or
absorbed during the changes of aggregation which occur in the course of the
combination. Unfortunately we cannot attempt, by direct experiments, to dis-
cover the amount of this Important correction.

4. If we now make

A := heat evolved during the reaction of chlorine, zinc (in excess), and

water,
B zz heat evolved during the solution of Zn CI in a like proportion of

water,
X = heat evolved or absorbed during the change of the constituents

its oxide by means of hydrogen gas, although the action, as is well known, is most energetic if mois-
ture be present. On the contrary, the dry gas instantly combines with arsenic, antimony, and phos-
phorus. This striking difference appears to depend upon the circumstance that the compound*
formed by chlorine with the former substances are solid at common temperatures and very fixed,
while those formed with antimony and arsenic are fluid and volatile. The chloride of phosphorus
is also very volatile. If, however, the chemical affinity be very intense, combination will take place
although the resulting compound be quite fixed and solid. Thus potassium inflames in dry chlorine
gas, but the chloride which is formed terminates the action before the whole of the metal has entered
into combination. The fluidity of the metal also exercises an important influence in determining
the combination, — as in the case of mercury, which slowly combines with dry chlorine. The pre-
ceding remarks may be also applied to the behaviour of dry bromine when brought into contact
with the metals.

Metallic Compounds of Chlorine, Bromine, and Iodine. 395

of Zn CI, from the state of aggregation in which they exist, as
gaseous chlorine and metallic zinc, to that state in which they exist
in the dry chloride of zinc,
X =. heat due to the union of zinc and chlorine,
we shall have the following general equation :

:r = A — B ± X.

And, designating the corresponding values for bromine by a', b', x', af, and for
iodine by a", b", x", ar", we shall have

0/ = a' - b' ± x',

y'=A"-B"±x".

5. The class of metals forming more than one compound with chlorine, bro-
mine, and iodine is very numerous ; but none of them present the same facilities
for this investigation as iron, to which accordingly I propose to confine my atten-
tion in the present paper. It is usually stated in chemical works that when
chlorine, bromine, or iodine act upon an excess of iron filings, suspended in water,
a solution of protochloride, protobromide, or protoiodide of iron is formed. But
such a description gives a very imperfect idea of the successive series of pheno-
mena which actually take place. We have only, indeed, to watch carefully the
progress of the experiment, in order to discover that a sesquicompound (Fe^Clj,
Fe^ Brj, Fej I3) is formed in the first instance, which afterwards, by combining
with an additional atom of iron, becomes converted into the protocompound
(FcaCla-j-Fe, &c.) To prove this, we only require to filter the liquid be-
fore the reaction has terminated, when a red solution will be obtained, having
all the properties of a solution of a sesquisalt of iron, and yielding by evaporation
a red deliquescent mass. Whether the experiment be made with chlorine, bro-
mine, or iodine, the same results will be obtained. An elegant illustration of a
similar train of changes is afiPorded by the action of chlorine gas on metallic tin.
If we agitate an excess of tin filings with a little water in a glass vessel of chlorine
gas, till the colour of the gas has scarcely disappeared, and instantly filter, the
liquid which passes through will produce only a faint opalescence, when dropped
into a solution of the bichloride of mercury ; but if the agitation be continued for
only a few seconds after the disappearance of the chlorine, the filtered liquid will
give a dense curdy precipitate when added to the same solution.

3 E 2

396 Dr. Andrews on the Heat developed during the Formation of the

6. From these observations It follows, that the primary form of combination,
into which the molecules of chlorine, bromine, and iodine enter with iron, is that
represented by the formulas Fcj CI3, Ye^ Br 3, Fe^ I3, and that the so-called proto-
compounds are, in reality, secondary combinations, formed by the union of the
sesquicompounds with an additional atom of iron (Fcj CI3 + Fe, &c.). This con-
clusion is farther confirmed by the well-known fact, that when these substances
unite at elevated temperatures, the red or sesquicompounds are always formed.*

7. Let us now make

c =z heat evolved during the reaction of chlorine, iron (in excess), and

water.
D = heat evolved during the solution of Fcj CI3 in a similar proportion

of water.
E = heat evolved during the combination of Ye^ CI3 in solution with Fe.
Y = heat evolved or absorbed during the change of aggregation of the

constituents of Fe^ CI3.
y =: heat due to the union of Fej with CI3.
Let us also, as before, represent the corresponding values for bromine by c', d',
e', y', y, and for iodine by c", d", e", y",/'. The following equations will
then give the values oi y, y', andy.

y

=

c -

-D —

E

±Y,

y

—

c'-

-d'-

—

e'± Y

/
5

y"

—

:c"

-d"

-

-e"±

Y

8. Having thus endeavoured to lay down general formulas for the heat of
combination, I proceed to describe the experiments by which the values of a, b, c,
&c. have been determined.

9. The apparatus employed in these experiments consisted of several distinct
parts. The combination was effected in a thin glass vessel of the form repre-
sented in fig. 1. When chlorine was the subject of experiment, this vessel was

* If the view, which regards Fe CI as the primary form of combination, be preferred, it will be
necessary to suppose that three successive changes occur, — first, the formation of the compound
Fe, + Clj ; secondly, its conversion intc Fe, CI3 by combining with CI ; and thirdly, the reconver-
sion of the latter into Fej CI3 by its union with Fe.

Metallic Compounds of Chlorine, Bromine, and Iodine. 397

filled with the gas in a moist state, and two very flimsy glass balls, such as those
shown in fig. 4, were afterwards cautiously introduced. One of these balls con-
tained a large excess of the metal in the state of fine filings ; the other, a quantity
of water, whose weight had been adjusted nearly in the proportions before de-
scribed. On the other hand, when bromine and iodine were under examination,
the metal and water were introduced into the vessel itself, while the bromine, or
iodine, carefully weighed, was contained in one of the little balls. The vessel
was in all cases closed by a good cork, which was rendered air-tight by cement.
A small stud of iron wire was inserted into the cork to maintain the glass vessel
in its proper position in the interior of the apparatus. This vessel, thus prepared,
was agitated for some time in water adjusted to the proper temperature, and then
placed in the light copper vessel, fig. 2, which was immediately filled with water,
and its lid screwed on. In the top and bottom of the copper vessel, loops of cop-
per wire were inserted, by means of which it could be suspended, without contact
of the hand, in the centre of a cylindrical vessel of tin plate, fig. 3, having a de-
tached cover above and below. The complete arrangement will be readily un-
derstood from an inspection of fig. 5. In the lids of the tin cylinder and copper
vessel corresponding apertures existed, through which the bulb of a delicate ther-
mometer could be introduced into the water in the interior of the latter. On
withdrawing the thermometer the aperture in the copper vessel could be closed,
in the course of two or three seconds, without touching the vessel itself. By this
arrangement the copper vessel with its contents was suspended in a fixed position
in the centre of, but not in contact with, an outer cylinder of tin plate, while at
the same time the temperature of the water could be noted at any time without
removing it from its situation. A larger cylindrical vessel, capable of being ra-
pidly rotated round its shorter axis, completed the whole apparatus. It is shown
in fig. 6.

10. When an observation was made the copper vessel was suspended in the
cylinder, the opening in its lid closed, and the apparatus placed in a horizontal
position, and then cautiously agitated (lest the glass balls should break), till a
perfectly uniform temperature was established through the whole of the copper
vessel and its contents. This being accomplished, the cylinder was again placed
in the position represented in fig. 5, the temperature of the water carefully
noted, and the cork replaced. It was then suddenly shaken, so as to rupture the

398 Dr. Andrews on the Heat developed during the Formation of the

glasa balls within, and immediately afterwards secured in the interior of the
larger cylinder, fig. 6, where the whole was rapidly rotated, for the space of five
and a half minutes, from the time of observing the temperature. It was then
removed, and the temperature of the water again observed. In the case of bro-
mine and iodine, all that now remained to complete the experiment was to weigh
the water in the copper vessel, but, in the case of chlorine, the original volume of
the gas had to be determined. For this purpose, the glass vessel was placed in a
water-trough, and the cork withdrawn. From the quantity of water which rushed
in, the bulk of the chlorine was easily estimated. It is almost unnecessary to add,
that, in every instance, the whole of the chlorine had entered into combination ;
the small residue being atmospheric air, unavoidably introduced when the bulbs
were inserted.

1 1 . The accuracy of experiments of this kind greatly depends upon the heat
which is gained or lost by the apparatus during the course of the experiment.
In a vessel placed apart from other sources of heat, the losses and gains of heat
will evidently be equal to one another for equal diflPerences of temperature above
and below that of the surrounding air. But in the apparatus I have just de-
scribed, from the proximity of the person of the observer, and the necessity of
grasping the tin cylinder while placing it in, and removing it from, the rotating
machine, this middle point is no longer the temperature of the air, but 1°.4 above
that point. Direct experiments also showed that the water had nearly attained
its maximum point in 45", from the time when the glass balls were ruptured, and
15" usually elapsed from the observation of the first temperature to the latter
moment. We may, therefore, assume that the water is at the maximum tempe-
rature during 4-|-', and at the minimum during 15". If we put e for the excess
of the final temperature above the air, e' for the difference between the initial
temperature and the same, and r and r' for the corrections to be applied for the
cooling and heating of the apparatus, during periods of 4^' and 15" respectively, '
we shall have

R = + (e-r.4)X 0.049,

r' zz — (e + r.4) X 0.003 -fO°. 03.

12. The constant quantity 0°.03 is added to the correction for simple heat-
ing, as an allowance for the heat, transmitted by the hand through the apparatus,
while rupturing the balls. The temperature of the water being generally so ad-

Metallic Compounds of Chlorine, Bromine, and Iodine. 399

justed, that the mean point between the Initial and final temperatures was from
half a degree to one degree above that of the air, the entire correction required
was in all cases very small.

13. The value in water of the different parts of the apparatus was estimated
with as much precision as possible. The specific heat of the copper and brass of
the copper vessel was assumed to be 0.095, that of the glass of the glass vessel
and balls was determined by a careful experiment to be 0.140. The leather, cork,
and cement were found to be nearly equivalent to 1.1 gr. of water, and the spe-
cific heat of the solution formed in each experiment was also determined.

14. In the description of the experiments I have used the following abbre-
viations :

Bar. — The height of the barometer.

Th. air. — The temperature of the air.

T'. — The initial temperature of the water in the copper vessel.

T'. — The final temperature of the same.

Inc. c. — The increment of temperature corrected for heating and cooling,
according to the formulas given before.

Aq. — The weight of the water in the copper vessel.

Sn. — The weight of water equivalent to the solution of the compound formed.
This is found by multiplying the absolute weight of the solution by its specific
heat, which is also given.

Vss. — The weight of water equivalent to the vessels and other solid substances
used in each experiment.

15. The temperatures are given in the degrees of Fahrenheit's scale ; the
height of the barometer in English inches ; the volume of the chlorine in cubic
centimetres ; and the weight of the water, &c. in grammes. The volume of the
chlorine gas requires to be corrected for moisture, as well as for temperature and
pressure, and I have assumed the weight of 100 cubic centimetres of the dry gas
at 32°, and under a pressure of 29.92 in. to be 0.317 grammes.

COMPOUNDS OF ZINC.

16. Zinc and chlorine, Zn + CI -|- Aq.

Bar 29.47 in. . . 29.07 in. . . 29.97 in.

Th.air 50°.70 . . . 48°.50 . . . SO^.SO

400 Dr. Andrews on the Heat developed during the Formation of the

^ • • • • • •

rpf

Inc. c

Aq

Sn. (sp. heat 0.76)

Vss

CI

Heat of comb. .

45°.22 . .

. 49°.08

52°.18 . .

. 54M4

7°.03 . .

. 5M2

143.0 gm. .

. 143.6 gm.

2.4 . .

1.7

21.3 . .

. 21.3

141.0 c. c. .

. 100.4 c. c

2820° . .

. 2811°

47°.97 .
55°.20 .

7°.34 .
136.6 gm.
2.4 .

21.3 .
141.4 c. c.
2802° .

Mean heat referred to chlorine as unit, 2811°.
Mean heat referred to zinc as unit, 3086°.

The first number indicates the number of degrees through which a portion
of water, equal in weight to the chlorine, would be raised by the heat extricated
during the combination ; the second, the corresponding number of degrees for a
portion of water equal in weight to the zinc.

17- Zinc and bromine, Zn -|- Br -|- Aq.

Th. air

63°.40 . .

64°.10 . .

68°.3

T'

61°.30 . .

62°.07 . .

66°. 12

T^ ......

66°.94 . .

66°.91 .

71°. 12

Inc, c.

5°.70 .

4°.87 .

5°.03

Aq

. 152.8 gm.

155.0 gm.

158.4 gm.

Sn. (sp. heat 0.62) .

2.3 .

2.0 .

2.1

Vss

.' 19.4 .

. 19.4 .

. 19.4

Br

0.936 .

0.806

0.847

Heat of comb. . .

. 1063° .

. 1066° .

. 1068°

Mean heat referred to bromine as unit, 1066°
Mean heat referred to zinc as unit, 2586°.

18. Zinc and iodine, Zn + I + Aq.

Th. air

. 64°.0 .

. 63°.80 .

. 38°.4

T

. 61°.08 .

60°.50 .

. 36°.74

T^

. 66°.72 . .

67°.67 .

. 42°.42

Inc. c

. 5°.66 . .

7°.24 .

. 5°.77

Aq

. 159.5 gm. .

161.1 gm.

. 129.1 gm

Sn. (sp. heat 0.56)

3.8 . .

4.9 .

3.2

Metallic Compounds of Chlorine, Bromine, and Iodine.

401

Vss 19.7 . . 19.8 . . 21.6

1 2.372 . . 3.084 . . 2.000

Heat of comb. . . 436°.7 • 436°.2 . 444°.0

Mean heat referred to iodine as unit, 439°.
Mean heat referred to zinc as unit, 1720°.

19- To ascertain in the preceding cases the heat due to the solution of the
compound, portions of each, carefully dried, were introduced into the thin glass
balls, and the weight accurately ascertained, while the normal proportion of water
for their solution was placed in the glass vessel.

20. Chloride of zinc and water, Zn CI -\- Aq.

Th. air

. 36°.90 . .

37°.20

T'

. 35°.7l . .

36°.05

T

. 39°.00 . .

. 38°. 72

Inc. c

. 3°.29 . .

2°. 63

Aq

. 131.4 gra. .

129.9 gra

Sn. (sp. heat 0.76)

10.6 . .

8.4

Vss

21.7 . .

21.7

ZnCl

3.516 . . .

2.750

Heat of comb. . . .

292° . .

292°

Mean heat referred to chlorine as unit, 292°.
Mean heat referred to zinc as unit, 320°.

21. Bromide of zinc and water, Zn Br -j- Aq.

Th. air

T'

T

Inc. c

Aq

Sn. (sp. heat 0.62)

Vss

Zn Br . . . .
Heat of comb. . ,

54°.00

53°.86

56°.36

2°. 51

153.9 gm

9.1

19.4

5.077

127°

55°.50
55°.35
57°.4I

2°.06
154.9 gm.

7.7
19.4

4.310
122°

VOL. XIX.

Mean heat referred to bromine as unit, 124°.5.
Mean heat referred to zinc as unit, 302°.

3 F

402 Dr. Andrews on the Heat developed during the Formation of the

22. Iodide of zinc and water, Zn I -|- Aq.

Th. air

T'

J. • • • • • •

rpf
X ■ • • • • •

Inc. c

Aq

Sn. (sp. heat 0.56)

Vss

Zn I

Heat of comb. . .

58°.60 .

58°.02 .

59°.07 .

1°.02 .

159.1 gm.

4.8 .

19.1 .

3.52 .

66°.5 .

59M0 .

59°. 12 .

60°.21 .

r.06 .

159.6 gm.

5.0 .

19.6 .

3.92 .

62°.6 .

Mean heat referred to iodine as unit, 62°.8.
Mean heat referred to zinc as unit, 246°.

38°.4

37°.58

40°.12

2°.52
125.6 gm.

10.7

21.6

8.42
59°.3

COMPOUNDS OF IRON.

23. Iron and chlorine, Fe^ + CI3 + Aq + Fe.

Bar

. 30.07 in.

. 29.97 in.

29.08

Th. air

. 50°. 50 .

. 50°. 50 .

48°.00

V

47°.47 .

. 47°.67 .

4.5°.78

T^

53°.78 .

. 54°. 08 .

51°.93

Inc. c

6°.36 .

. 6°.47 .

6°.23

Aq

133.8 gm.

. 143.9 gm.

143.9 gm.

Sn. (sp. heat 0.74)

2.2 .

2.4 .

2.4

Vss

21.1

. 21.3 .

21.4

CI

131.7 c.c.

. 141.5 c.c.

. 141.5 c. c.

Heat of comb.

2503° .

. 2534° .

2505°

Mean heat referred t(

) chlorine as

unit, 2514°.

Mean heat referred t(

3 iron in Fcj

as unit, 4921°.

24. It must be carefully observed that the unit here taken is not the whole of
the iron dissolved, as in the case of zinc, but only two-thirds of it ; because the
remaining third does not enter directly into combination with the chlorine, as has
been already explained.

Metallic Compounds of Chlorine, Bromine, and Iodine.

403

25. Iron and bromine, Ye^ + Brj -\- Aq -|- Fe.

Th. air

. 64M0 .

T'

. 61°.81 .

T^

66°.89 .

Inc. c

. 5M0 .

Aq

155.3 gm

Sn. (sp. heat 0.60) .

2.4 .

Vss

19.4 .

Br

0.994 .

Heat of comb. . . .

909° .

49°.00
47°.52
53°.55
6°.14
147.4 gm.
2.7
19.4
1.145
909°

26.

Mean heat referred to bromine as unit, 909°.
Mean heat referred to iron in Fe2 as unit, 3933°

Iron and iodine, Fe^ + 13+ Aq -\- Fe.

Th. air.
T'

rpf

X • • • •

Inc. c. . .
Aq. . .

Sn. (sp. heat 0
Vss. . .
I. . . .
Heat of comb

63°.20 .

. 38°.10

60°.30 .

. 36°.32

65°.83 .

. 41.°44

5°. 55 .

. 5°.17

162.1 gm. .

126.1 gm

4.8 .

3.6

19.5 . .

21.6

3.151 . .

2.360

328°.3 .

331°.5

63°.40
61°.04
65°.99
4°.97
157.7 gm.
54) . 4.2
19.6
2.752
327°.8

Mean heat referred to iodine as unit, 329°.2.

Mean heat referred to iron in Fe2 as unit, 2299°.
27- The object of the experiments detailed in the three following tables was
to determine the heat evolved, when solutions of the sesquichloride, sesqui-
bromide, and sesquiiodide of iron are converted into solutions of the proto-
compounds by agitation with an excess of iron. The sesquichloride of iron,
obtained by the action of dry chlorine gas upon heated iron, was dissolved in
water (the quantity being adjusted as usual) in the glass vessel, and an excess of
iron filings was placed in one of the small balls. But I was obliged to have re-
course to a different method in order to procure determinate quantities of the
sesquibromide and sesquiiodide of iron in solution, from finding it impossible to

3f2

404 Dr. Andrews on the Heat developed during the Formation of the

obtain these compounds in the dry state. At first I attempted to add an excess
of bromine or iodine to solutions of known strength of the protocompounds ; but,
on endeavouring to expel the excess by heat, I found it difficult, even in the case
of the sesquibromide of iron, to avoid the decomposition of the sesquicompound
itself, when the solution was concentrated. The object in view was finally
effected in a very complete and easy manner, by adding weighed quantities of
bromine or iodine to solutions of the protobromide, or protoiodide of iron, con-
taining more than twice as much bromine or iodine, as the quantity added. The
object of employing a larger proportion of the proto-solutions than the bromine
or iodine added would be capable of converting into the state of sesqui-com-
pounds, was to prevent the possibility of any free bromine or iodine being pre-
sent ; and, as the results were the same, whether the excess of the proto-solution
was greater or less, it evidently in no way interfered with the success of the expe-
riment. In reducing the results we have, therefore, to remember that the sesqui-
compound formed, contains three times the quantity of bromine or iodine added,
designated in the tables by Br X 3 and 1x3.

28. Sesquichloride of iron and iron, Fcj CI3 Aq -|- Fe.

6r.80 .

61°.85 .

63°.34 .

1°.46 .

132.8 gm.

3.0 .

21.8 .

0.856 .

40(3 .

Mean heat referred to chlorine in CI3 as unit, 402°.5
Mean heat referred to iron in Fe^ as unit, 788°.

29. Sesquibromide of iron and iron, Fcj Br, Aq -\- Fe.

Th. air 44°.40 . . 46°.70 . .

T' 44°.46 . . 46°.23 . .

T^ ..... . 46°.68 . . 49°.02 . .

Inc. c 2°.23 . . 2°.81 . .

Th» air. .
T. . .

T^ . .

Inc. c.
Aq. . .

Sn. (sp. heat 0.73)
Vss. . . .
Fe^Clj . .
Heat of comb.

. 62°.50

. 43°.00

. 61°.35 .

. 41°.2I

. 64°.29

. 45°.45

. 2°. 92

. 4°.25

. 144.3 gm

. '. 151.4 gm.

6.8

. 10.4

. 21.4 .

. 19.9

1.895

2.900

402°

402°

47°.20

45°.77

50°.84

5°. 14

Metallic Compounds of Chlorine, Bromine, and Iodine. 405

xiq

Sn. (sp. heat 0.60)

Vss

BrX3 . . . .
Heat of comb. . .

152.6 gm.

6.3 .

19.6 .

2.163 .

184°.0 .

152.4 gm.

7.3 .

19.6 .

2.739 .

183°.9 .

152.1 gm.
12.9
,19.6

5.199
182°. 5

Mean heat referred to bromine in Brj as unit, 183°.5.
Mean heat referred to iron in Fe^ as imit, 794°.

30. Sesquiiodide of iron and iron, Fe^ I3 Aq -f- Fe.

Th. air. . . .
T'

X • • • • •

Inc. c. . . .

Aq

Sn. (sp. heat0..54)

Vss

1X3 . . .
Heat of comb. .

. 47°.40
. 46°.41
. 49°.22
. 2°.80
, 151.2 gm

9.1
, 20.0

4.497
112°.3

Mean heat referred to iodine in I3 as unit, 112°.l
Mean heat referred to iron in Fe^ as unit, 783°.

47°.00 .

46°.87 .

49°.24 .

2°.38 .
150.5 gm.

6.8 .

19.9 .

3.741 .
112°.8

51°.10
50°. 15
54°.66
4°.58
146.8 gm.
17.7
19.8
7.596
lllM

31. To complete this part of the inquiry, it only remains to determine the
heat evolved during the solution of the sesquichloride, sesquibromide, and sesqui-
iodide of iron in water. This I have been able to accomplish only in the case of
the sesquichloride of iron, from having failed, as has been already remarked, in all
my attempts to obtain the other two compounds in a dry state. Even a concen-
trated solution of the sesquibromide of iron allows bromine to escape during the
process of evaporation. If the evaporation be carried to dryness, and the dry
mass heated just to the point of fusion, a red substance remains, which is com-
posed of one atom of the protobromide and one atom of the sesquibromide of iron
(Fe^ Br^). An approximation, however, may be made to the heat which would
be developed during the solution of these compounds, by assuming that it will
bear the same relation to the heat developed during the solution of the sesqui-
chloride of iron, which has been already ascertained to exist in the case of the
analogous compounds of zinc (20, 21, 22).

406 Dr. Andrews on the Heat developed during the Formation of the

60°.5 . .

. 4r.4

60°.2 . .

. 41°.02

61°. 93 . .

. 42°. 10

r.68 . .

. r.04

132.8 gm. .

. 120.4 gm

2.7 . .

. 1.6

21.7 . .

. 19.3

0.856 .

0.504

466°. .

441°

32. Sesquichloride of iron and water, Fcj CI3 + Aq.

Th. air.
T. .
T. .
Inc. c.
Aq. .
Sn.

Vss. .
Fe,Cl3
Heat of comb.

Mean heat referred to chlorine in CI3 as unit, 453°.
Mean heat referred to iron in Fe^ as unit, 887°.

33. On the principle just stated, we may infer, as a rude approximation, that
the heat disengaged during the solution of the sesquibromide of iron would be
(referred to the iron as unit) 837° ; and that disengaged during the solution of
the sesquiiodide, 682°.

34. If we now substitute the numerical values, obtained by the preceding
experiments, for the known quantities in the equations given before, we shall
obtain

.r = 3086° -320° ±x
y= 2586° — 302° ±x'
.r"= 1720° — 246° drx"

y = 4921° — 887° — 788° dr y
y' = 3933° - 837° — 794° zb y'
y = 2299° — 682° — 783° ± y'

From these equations we deduce

w or Zn + CI = 2766° ± x
y or Zn + Br = 2284° ± x'
x" or Zn + I =z 1474° ± x"

y orFe2+Cl3 = 3246°±Y
«/' or Fe^ + Br, = 2302° dr y'
y" or Fe^ + I3 = 834° =t y"

(16, 20)
(17, 21)
(18, 22)

(23, 32, 28)
(25, 33, 29)
(26, 33, 30)

Metallic Compounds of Chlorine, Bromine, and Iodine. 407

35. It must be remembered that each of the letters x, x', &c. represents two
unknown quantities ; first, the change of temperature due to the alteration of
aggregation of the particles of the metallic elements, in passing from their ordi-
nary form to that form in which they exist in the dry salt ; and, secondly, the
change of temperature arising from the like alteration of aggregation of the par-
ticles of the electro-negative element. The actual value of these quantities can-
not be determined by direct experiments, but it is probable that for the combi-
nations of the same metal, the differences between x, x', and x", and between
Y, \', and y" will arise chiefly from the alterations of aggregation of the electro-
negative, and not of the metallic element. Now, as the heat arising from the
condensation of chlorine from the gaseous to what may perhaps be termed tlie
saline solid state, must be far greater than that arising from the change of fluid
bromine, or solid iodine, to the same state, it would be an object of great interest
to determine the heat evolved or abstracted during the changes of these bodies
from one physical condition to another, which would enable us to compare the
heat of combination of each body in the same physical state. This I have only
attempted yet to effect for the case of the solidification of bromine; and, as the re-
sult of a very imperfect experiment, it may be stated, that the heat evolved during
the passage of that substance from the fluid to the solid state, would be sufficient
to raise an equal weight of water through 24°. This amount of heat is evidently
far too small to account for the differences observed in the values of x' and oc" ,
and ofy andy ; from which it follows, that bromine and iodine, in the same
physical state, evolve very different quantities of heat when combining with the
metals.

36. On comparing the numbers deduced from the foregoing experiments
(28, 29j 30) for the heat developed during the conversion of the sesqul-com-
pounds of iron into the corresponding proto-compounds, by combining with half
as much iron as they already contain, the very interesting general principle re-
sults, that, referred to the combining iron as unit, the heat evolved in all these
cases of combination is the same. In fact, we have

. Fe^ClaAq-f Fe = 788°.
Fe,Br3Aq + Fe = 794°.
Fe, L Aq -f Fe = 783°.

408 De. Andrews on the Heat developed during the Formation, Sfc.

The slight differences between these numbers are fully within the limits of the
unavoidable errors of experiment, and leave no doubt of the truth of the prin-
ciple just enunciated.

37. On a future occasion I hope to have an opportunity of describing a more
extended series of experiments now in progress, on the heat developed during
the combination of other elements with chlorine, bromine, and iodine ; and, till
that opportunity occurs, I shall reserve any further observations of a general cha-
racter upon the preceding results. Meanwhile they may be thus recapitulated :

1. The heat developed during the combination of a given quantity of zinc
with chlorine gas is sufficient to raise an equal weight of water through 2766°,
while that evolved during the combination of the same metal with bromine, in
the fluid state, is 2284° ; and with iodine, in the solid state, 1474°.

2. The heat developed during the combination of iron with chlorine, bro-
mine, and iodine (which always takes place under the form FejClg, Fe^Brj,
Fcj I3) is sufficient to raise an equal weight of water through 3246°, 2302°, and
834° respectively.

3. When solutions of the sesquichloride, sesquibromide, and sesquiiodide of
iron become converted into proto-compounds by combining with iron, the heat
evolved in all is the same for the same quantity of iron dissolved.

POLITE LITERATURE.

VOL. XIX.

POLITE LITERATURE.

I. A Memoir of the Medals and Medallists connected with Ireland. By the
Very Rev. Henry Richard Dawson, A.M., Dean of St. Patrick's.

Read 16th March, 1838.

O, when shall Ireland, conscious of her claim,
Stand emulous of Greek and Roman fame ?

Pope.

1 HE increasing interest which has been of late years manifested respecting
collections of medals, affords a strong proof of the value justly attached to them,
both as commemorative corroborations of certain historical events, and also as
specimens of skill, ingenuity, and taste amongst artificers in that line. In
almost every country of Europe, excepting our own, its medallic history has at
successive periods occupied not only the attention, but the pens of learned indi-
viduals, and their lucubrations have greatly contributed as well to stimulate the
ingenuity of the artist, as to elucidate the facts connected with its exercise ; so
that many a political event, and many an heroic achievement, which had escaped
the notice of contemporary historians, has, through their instrumentality, been
rescued from oblivion, and brought under the notice of posterity in the almost
imperishable materials of the precious metals.

The northern States of Europe can boast of Beskrivelse, Mechel, and Brenner
illustrating and explaining their medals. Holland and the Netherlands have
Van Mieris, Van Loon, and Bizot, in ponderous folios, with plates and text,
describing each minute particular. In France, Le Blanc, Fleurimont, and
Bouteroue have engraved both coins and medals ; while in the later period of
the glorious era of Andrieu, Laskey and Millingen have elaborately pointed out

a2

4 The Very Rev. H. R. Dawson on the

their beauties, and detailed their intentions. Italy can point to Anthony Count
Caietani explaining the various works of the middle ages contained in the cabinets
of Mazzuchelli ; and to Venuti, Nobili, and Mollnet those of the Popes of Rome
are indebted for a great addition to these attractions. England can refer to the
works of Evelyn, Vertue, and Edwards noticing and illustrating the varied spe-
cimens of skill which have been produced by those artists whom the country
encouraged, and whose works have served to perpetuate the actions, good or
evil, of her devoted servants. I could refer to many other countries of Europe,
where the proud records of their fame have found studious chroniclers both with
pen and hand ; but no attempt has yet been made to record historically the
medals of Ireland ; and while some pains have enabled me to rescue the works of
her artificers from, I should say, undeserved oblivion, I venture to call the atten-
tion of the members of the Academy to some of the productions of the Irish
Coining Press, as well as to some medals connected with our country, and exe-
cuted by foreigi;! artists, in the expectation that their countenance may be the
means of eliciting some of the latent, and stimulating the neglected talents of
our countrymen.

For some few years past I have been endeavouring to collect and arrange in
historical order the medals connected with this part of the United Kingdom ; and
though with considerable diffidence I present these brief notices of my researches
to you, (brief, because I find these records of our national deeds very few,) yet
I am not without hopes that they may excite some interest even amongst those
who have not hitherto turned their attention to this pursuit. I purpose, there-
fore, to offer you some notices of such medallists, and such designs, emanating
from their studla, as have fallen under my observation. I regret to say my ma-
terials are scanty, owing, I believe, mainly to this, that the country has not
hitherto fostered nor encouraged that beautiful branch of art.

The earliest medal that I have met with, as connected with Ireland, is of the
time of Charles II. ; a small silver piece, of very beautiful execution, and I con-
sider it to be the work of some English or foreign artist, as both sides are
obviously taken from two medals which were struck to commemorate the mar-
riage of that Prince with Catherine of Portugal. It bears on the obverse a
figure of St. Catherine with her wheel, and the legend pietate insignis. The
reverse has Fame blowing a trumpet, and in her left hand she carries an olive

Medals and Medallists connected with Ireland, 5

branch. On the banner appended to the trumpet there is a small harp, the
arms of Ireland, and were not that sufficient to appropriate this medal as belong-
ing to our series, the inscription provincia connagh, decides the matter. Now
it is well known that Charles was married to Catherine of Braganza by Sheldon,
Bishop of London, May 21st, 1662; but many think the ceremony was pre-
viously performed by a Roman Catholic priest to satisfy the scruples of the
concealed as well as the avowed Romanist. This priest may have come from
Connaught, and it is not improbable that this piece was struck, that at least som»
obscure evidence might remain of the event.

The Roettiers, the celebrated Dutch medallists, worked for Ireland ; but
their skill was, I believe, less exercised to commemorate the heroic achieve-
ments of her sons, than to promote the purposes of their unfortunate master ;
and those pieces generally known as the gun money of James II. are sup-
posed to have been struck from dies executed by John Roettier. However
base the materials of these coins, their neatness and execution afford reasonable
grounds for attributing them to such a devoted follower as he was knovra to be
of the exiled king. I should here observe that James Simon, the author of an
essay on Irish coins, has engraved, Plate VII. No. 154, and described a silver
medal, which he conceives alludes to the landing of James in Ireland, and his
reception by his Irish subjects at Kinsale, March 12th, 1689. The obverse
represents the king crowned, and in his royal robes, holding a baton in his hand.
Behind him a ship, and before him a crowd hailing his approach, the legend
JACOBUS • II. DEI • GRATIA. The rcvcrsc, two sceptres in saltire behind a crown,
with the motto intemerata, and the legend mag. br. fra. et . hib. rex. 1689-
Simon saw only a drawing of this medal, which was sent to him by Mr. Charles
Smith of Dungarven ; I have not been so fortunate as to meet with it myself,
nor can I find any further record concerning it; but Simon is too accurate to
allow me to doubt its existence in his day.

When William III. came to fight the battles for our liberty and his own
sovereignty in this kingdom, his various victories were commemorated in Hol-
land by his own countrymen, and so many medals were struck with the intent of
perpetuating his renown, that it would be tedious here to enumerate them. The
engravings and descriptions published by Van Loon inform us, that neither the
Boyne nor Aughrim, nor Galway, nor Limerick, were considered undeserving
of commemoration by those who were most conversant with the events which

6 The Very Rev. H. R. Dawson on the

produced such an effusion of Irish blood. Nor were these memorials confined
to the illustrious hero himself, for similar records are also found of his victorious
generals, Schomberg and De Ginkle.

But in connexion with the history of this period, one medal only has been
discovered, struck in Ireland, and this bears reference to Van Homrigh, a fol-
lower of William's, who settled in Ireland about this period. And as this
medal has not been hitherto published, it may be interesting here to describe
it, and to show upon what occasion it was struck. It appears from the
records of the Corporation of Dublin, that in the year 1688 Sir Michael
Creagh was Lord Mayor of the city, and as such was in possession of the
parapharnalia connected with his office ; in the following year two persons,
Terence Dermot and Walter Motley, held the office, the one for nine, and
the other for three months. They, it is supposed, never received the usual
ensigns of dignity, but it is certain that in those troublesome times they were
either lost or purloined, and to this day it is usual, at the triennial perambulations
of the city boundaries by the Lord Mayor and his staff, for an officer to make
proclamation that Sir Michael Creagh should appear and restore the collar and
its appurtenances connected with the office, which he is alleged to have conveyed
away. In the year 1698 William III. presented to the city a new collar of
SS., to which is appended the noble medallion I am now about to describe, exe-
cuted by James Roettier. Obverse, gulielmus . tertius • d. g. mag. brit. fran.
ET . HiB. rex. Bust looking to the right, with flowing hair, in armour, with a
scarf over it. Reverse, gulielmus hi - antiquam et fidelem-hiberni^ me-

TROPOLIN - HOC INDULGENTI^ SU^ MUNERE - ORNAVIT • BARTH VAN HOMRIGH

ARM. URB. PRiETORE . MDCxcviii. This medallion is an important addition to
our series, as few impressions can possibly come under public observation.

During the reign of Anne, though Croker exerted his talents in England to
commemorate the distinguished events of her time, I have been unable to dis-
cover any medals immediately connected with Ireland ; and this appears strange,
since it is well known that Swift, then possessing great weight and authority,
exerted his influence to procure that change in the coinage which called forth
those pattern farthings, exhibiting records of remarkable circumstances, and
which also have encouraged the preposterous notions so widely diffused respecting
their extreme rarity and enormous value. He was a patriot, and it would appear
from some memoirs connected with him, to a certain degree, a collector of

Medals and Medallists connected with Ireland. ^

medals ; but his taste lay in a different line from that of encouraging artists or
scientific pursuits.

Connected with the times of George I., I am able to produce, I think, one
medallet, and that without any reverse. It is very small, and exhibits a three-
quarter bust of my celebrated predecessor in the Deanery of St. Patrick, in his
full wig and gown, with falling bands. It bears a strong resemblance to a por-
trait in my possession, which Swift is said to have given to Vanessa at the time
he quarrelled with her. The legend is, j-s dd d-s-p-d. (Jonathan Swift,
D. D., Dean of St. Patrick's, Dublin.) The execution is tolerably good, but I
have not been able to ascertain either the artist or the occasion upon which it
was struck.

In the succeeding reign, patronage or party feeling appears to have given
some stimulus to the art, for I find no fewer than five medals connected with the
period. As one only has been published, and that in a very incorrect and
slovenly form, and none hitherto described, I shall here attempt to give some
elucidation of them.

The first again refers to Dr. Swift, and exhibits his portrait three-quarter
face to the left, with wig and gown, in a small oval frame, supported by a winged
child upon clouds. To the right of Swift is Minerva seated, in armour, with
spear and aegis, pointing with her right hand to a shield resting against her
knee, and bearing the arms of Ireland. To the left a female also seated, lean-
ing on a pile of books, and with her right hand holding a laurel crown over the
Doctor's bust. Above there is a winged figure of Fame, and below a scroll
inscribed rev. j. swift, d. s. p. d. The reverse displays Hibemia seated, in
her right hand an olive branch, and her left is supported by a harp. In the back
ground a shepherd tending his flocks, and a view of the sea covered with
ships. On the exergue is the date mdccxxxviii., j. b. fecit. This medal, I
conjecture, was intended to commemorate Swift's exertions for the advance-
ment of commerce, manufactures, and agriculture. He was at that period in
the zenith of his glory ; and it cannot surprise us that the zealous friends, of
whom he had many, should thus endeavour to perpetuate his fame. Of the
artist I know nothing, and the execution is so rude, that I am indisposed to
conjecture it to be the work of any artificer of eminence. The next in the
suite gives better hopes for the progress of improved taste in the medallic

8 The Very Rev. H. R. Dawson on the

art as connected with Ireland, and the subject is very interesting. The artist,
T. Pingo, has not hesitated to put his name upon the work, and it fully sup-
ports the character he has obtained. The obverse presents three figures,
on the right a female thrown upon the ground, emblematic of Ireland ; at her
feet a cap of liberty and a spear. A male figure in the centre is represented
seizing her by the hair with his left hand, and with the right holds a dagger over
her. 'On the left stands Justice, with her emblems, averting his uplifted arm, and
the inscription reads, may geokge protect what justice trys to save. On
the reverse, at the top, is the harp of Ireland, with some of the strings broken,
and at the bottom a shield, bearing the arms of the city of Dublin, the sword,
mace, cap, and collar of the city lying near it on the ground. Across the field
is the legend, the glorious - attempt - of lxiv-to preserve the- consti-
tution - MDCcxLix. There is every reason to presume that this medal was struck
to commemorate the defeat of the efforts put forth by the celebrated Charles Lucas
in favour of the liberties of the Corporation of Dublin, as it was in this year he
addressed his memorable letter to George II. on the charter of the liberties of
the city of Dublin, complaining that the freemen and common council were
defrauded of their rights and privileges by the Board of Aldermen, who, he
alleged, were mere usurpers, and arrogated to themselves too much power in the
election of the Lord Mayor.

I am now about to call your attention to a medal in the possession of many
families in this country, which, in design and execution, will not be easily sur-
passed. As it has not, I believe, been published, and as it relates to an event
considered very remarkable in the history of the Irish Parliament, I shall be
excused for recording some details respecting it while they are yet attainable.
By the Commons' Journals it appears that from the year 1692 the practice of the
house was to call for and examine the public accounts. If there appeared a
deficiency in the treasury, they provided for it ; if a surplus remained after the
purposes were served for which it had been granted, they proceeded to dispose of
it for the public advantage, without asking permission from the Crown, or re-
ceiving any intimation that the king's prerogative was thereby invaded. It
happened that in 1Y49 a considerable sum remained in the treasury, and upon
the circumstance being reported, the Commons of Ireland framed the heads of a
bill, according to the powers heretofore exercised by them, for applying a portion

Medals and Medallists connected with Ireland. 9

of it towards the discharge of the national debt. They were sent to England,
returned without alteration or objection, and the same course would have conti-
tinued, had not some mischievous intermeddling courtier discovered what he
considered an invasion of the rights of the Crown, which it was determined by
those in authority to repel. In the year 1751, the Lord Lieutenant, acting upon
this suggestion, in his speech from the throne at the opening of the session,
informed the House of Commons, " That he was commanded by the king to
acquaint them, that his Majesty, ever attentive to the ease and happiness of his
subjects, would graciously consent and recommend it to them, that such part of the
money then remaining in the treasury, as should be thought consistent with the
public service, should be applied to the further reduction of the national debt."
This was assuming that the king had an exclusive property in it, and might, as
an act of favour, permit the Parliament to dispose of it. The Commons in their
Address paid no regard to this unprecedented claim. The heads of the bill were
framed as usual, it passed the Commons and Privy Council, was sent to England,
but returned with the word "consent" inserted in it. Then, though many
members were dissatisfied with this infringement of their rights, it passed unani-
mously, and thus a precedent was made which was attempted to be used on the
event which produced the present medal. In the year 1753 even a larger sur-
plus was reported in the treasury. The Right Hon. Thomas Carter, Master of
the Rolls, presented, on the 13th of December, a bill, entitled " An Act for the
payment of £77j500, or so much thereof as shall remain due on the 25th of De-
cember, 1753, in discharge of the National Debt." This was read a first time
on the following day, and a committee was appointed to inquire if any, and what
alterations had been made in the preamble and enactments of the bill. On the
15th, Mr. Upton reported that an alteration, or rather an addition, had been
made, by inserting in the preamble the following words : " And your Majesty,
ever attentive to the ease and happiness of your faithful subjects, has been gra-
ciously pleased to signify that you would consent, and to recommend it to us,
that so much of the money remaining in your Majesty's treasury as should be ,
necessary, be applied to the discharge of the national debt, or of such part
thereof as should be thought expedient by Parliament." The house was again
aroused to jealousy respecting an invasion of its privileges, and on the 17th it
resolved itself into committee, when the Master of the Rolls reported from it,

VOL. XIX. B

10 The Very Rev. H. R. Dawson on the

that they had agreed to the enacting paragraphs of the bill, but disagreed to the
preamble; a division took place, and the bill was rejected by a majority of five
voices.* Although the numbers on each side are not given in the Commons'
Journals, I conceive, from the record of this and another medal, that the dissen-
tients amounted to 124, a strong testimony to the feeling of parliamentary pri-
vilege that pervaded the house. I should add, that this bold assertion of right
by her representatives produced no immediate advantage to Ireland, whatever
may have been its future consequence, for his Majesty, by his letter, took that
money out of the treasury which had been the subject of dispute. On the
obverse of the medal the legend reads, utcunque ferent ea facta minores
viNCiT amor patri^. In the centre stands Hibernia, with a harp in her
left hand, and behind her another figure holding a distaff, emblematic of
the staple trade of the country. On her right stands another female grasping
her hand, and holding in her right hand a roll inscribed leges. To her left is
the Speaker of the House of Commons in his robes, placing a cap of liberty on
her head, and holding in his left hand a heavy bag inscribed vindicata, and
behind him three senators stepping out from a portico. Over the figures is Fame
flying, and blowing a trumpet, with a banner appended, and inscribed cxxiv ;
she holds in her left hand a ribbon or band bearing the inscription, ergo tua
JURA MANEBUNT. On the cxerguc are two human figures naked, the one with
the head of a bird of prey, clutching at a quantity of money scattered on the
ground, which the other with the head of a wolf, and loosed from a chain fastened
to a rock, guards ; behind them some open rolls. The legend on the reverse reads,

QUIQUE SUI MEMORES ALIOS FECERE MERENDO. AcrOSS the field, SACRUM - SENA-
TORIBUS CXXIV - QUI TENACES PROPOSITI - FORTITER AC PRUDENTER - JURA
PATRI^ RITE-VINDICARUNT XVII - DIE DECEMBRIS ^R^ - CHRISTIANS MDCCLIII

- QUociRCA viviTE - FORTES. I conjectuTc a medal in gold was given to each of
the members who voted on the popular side, as I have seen several, and the one
before me is engraved on the edge THO^ Montgomery, ESQ^ 8 b". 1755. He
was Member for the Borough of LifFord in that Parliament.

Another medal and medallet, both of similar type, were also struck upon the
occasion of this triumph. Obverse, the speaker . and liberty. Bust three-

* In the "Universal Advertiser," Dublin, 1754, there is a list of the members \»ho voted for
and against the Altered Money Bill.

Medals and Medallists connected with Ireland. 11

quarter face to the left, in wig and robe of office. The portrait is that of Henry
Boyle, afterwards created Earl of Shannon, under whose banner the patriots
opposed the corruption and tyranny practised by Primate Stone and the Court
party. Reverse, the 124 patriots of Ireland; in the field a harp with the
royal crown over it. Exergue, December 17- 1753. The execution of both
is indifferent, and the metal brass ; they were probably struck immediately upon
the occurrence of the event.

The next piece, and that too upon the same subject, refers to the Kildare family ;
on the obverse is seen a table covered with money, to the left a hand and arm
stretched out from above grasping at it; to the right a man in full dress, in an
attitude of defiance, with a drawn sword over the table, as if guarding the money,
with the inscription, touch not says • kildare. Exergue, mdcclv. Reverse,
a harp with a crown over it; legend, prosperity to old Ireland, 1754.
This commemorates the celebrated memorial presented to the king by James
Fitzgerald, Earl of Kildare, remonstrating against the withdrawal of money from
Ireland, and the removal from public employment of those who favoured the
popular cause.

The last medal but one connected with this reign had reference to a con-
tested election for a member for the county, which took place in Louth in the
year 1755. At that time a number of persons formed themselves into what they
called an Independent Club, for the purpose of giving opposition to the gentlemen
of the county of the high influential interests, and resolved to try and obtain
the return of the members. In one instance they were successful in ousting
Mr. Bellingham, and succeeded in returning Thomas Tipping, Esq., in con-
junction with the Hon. W. H. Fortescue, to serve in Parliament. This medal
commemorates their triumph. Obverse, firm to our country as the hock
IN THE sea. a large rock standing boldly in the sea, the four winds blowing
against it, and on the top a figure of Hibernia, with her left hand resting upon a
harp, and her right pointing upwards. Reverse, may the lovers of liberty
NEVER LOSE IT. Two hauds United, with a heart over them ; and underneath,
in the field, by our strict - union in louth - we disappointed the - hopes

OF OUR enemies - ON THE 1 OF NOVEM - 1755 IN THE 29 YEAR -OF THE
REIGN OF - K • GEO • THE II - WHOM GOD LONG - PRESERVE. The artist has not

given his name, but from the execution of the work he could not have been one

B 2

12 The Very Rev. H. R. Dawson on the

of any note ; and I may observe, that the design of the obverse seems to have
been very closely copied from a medal by Dassier, to the memory of Dr. Samuel
Clarke.

About the year 1756, there existed an Association of Painters and Sculptors
in Dublin, who exhibited their works at a house in William-street, which they
built as an Exhibition Room, with the assistance of a parliamentary grant ; but
not being incorporated, they were unable to hold the premises, and were even-
tually ejected from them by some persons who had advanced them money towards
the completion of the building. They had a medal struck as an admission ticket,
bearing on the obverse a boy sculpturing a bust, behind him another with pallet
and colours, and in the back ground a column and a capital. The reverse is
merely inscribed exhibition ticket, with a space left for the proprietor's name.
This, I am aware, cannot legitimately be classed as a medal, but as it occasionally
appears in collections, I have thought it desirable to record it here.

That I may not interrupt the course of this memoir, I shall here insert an
account of a very remarkable medal which has been sent to me, (though I have
been unable to procure an inspection of the piece itself,) and extracted from
Faulkner's Dublin Journal of August 6th, 1768, which precludes the necessity of
any further remark for its elucidation. " On Saturday last ended the poll for
the election of Knights to represent the County of Westmeath in Parliament,
when the numbers stood thus : for Lord Bellfield, 475 ; for the Hon. Colonel
Rochfort Mervyn, 387 ; and for the Right Hon. A. Malone, 469, of whom 377
were single votes ; when Lord Bellfield and Mr. Malone were declared duly
elected, the latter by a majority of 82 over Colonel Rochfert Mervyn. After
the return the free and independent electors, consisting of a most respectable
majority of the gentlemen of the county, met together, and they (in testimony of
the singularly constitutional conduct of their candidate, who stood forth at their
call and nomination, with an exertion of his usual dignity and spirit,) formed a
subscription for a gold medal with the following device : Liberty embracing with
her right arm a pillar, and supporting herself by it, her left arm resting on her
shield, her spear, casque, and other ensigns lying at her feet ; the motto vincit
AMOR PATRiiE, ANNO 1768. On the revcrsc, a hand presenting a civic crown,
and underneath, presented to the right honourable a. malone by the

FREE and independent ELECTORS OF THE COUNTY OF WESTMEATH, IN ACKNOW-
LEDGMENT OF HIS STRENUOUS AND SUCCESSFUL SUPPORT OF THEIR INTERESTS

Medals and Medallists connected with Ireland. 13

ON THE 25th of JULY, 1768," I am pleased to have the Opportunity of preserving
this record of any testimonial to the merits of so celebrated a man as Malone,
and the more so as I had vainly sought from the gentlemen of Westmeath any
account of the occasion on which the medal was struck, as in fact it appeared
totally unknown to those of whom I made the inquiry.

The reigns of the two last Georges constitute an aera in the medallic art, of
which Ireland may be justly proud, as it produced two artists, who, notwithstand-
ing the difficulties under which they laboured, were the authors of some speci-
mens in the art, that will not lose by comparison with those of the most skilful in
that line in any country. They were both natives of Dublin, and when I men-
tion the names of William Mossop, father and son, every admirer of medals will
justify me in endeavouring to rescue from oblivion such memorials of them as I
have been able to obtain. Through the kindness of Edward Hawkins, Esq. of
the British Museum, I have been put in possession of, and allowed to use, several
letters and pieces of autobiography from William Stephen Mossop, jun,, which
give the Academy a security for their authenticity, but I shall state them very
briefly, as they might otherwise extend this memoir to an unreasonable length.
The series published by these two artists amounts to more than seventy pieces.

William Stephen Mossop, the elder, was born in Dublin A. D, 1751, and
about 1765 was placed with Mr, Stone, at that time regarded in Dublin as a man
possessed of considerable ingenuity as a die sinker, but whose talents never carried
him higher than making a steel letter, or some other mechanical work. Here
Mossop's time was thrown away, and his term of apprenticeship passed in the mere
drudgery of a trade. Stone was employed in making seals for the Linen Board,
and upon this work Mossop was chiefly engaged, and by his exertions mainly con-
tributed to the support of his master's family. Stone soon fell a victim to intem-
perate habits, and was succeeded by his son, who following his lamentable example,
died in the same wretched way. Mossop was then engaged to work for the
Linen Board on his own account, and continued to execute their orders until
1781, when a change in the system of the Board threw him out of employment,
burthened with a wife and growing family. At this period he was induced,
from an accidental circumstance, to undertake some higher works of art. A per-
son intending to purchase some medals, submitted them to the judgment of
Mossop, who then, for the first time, had an opportunity of contemplating those

14 The Very Rev. H. R. Dawson on the

beautiful results of human Ingenuity. He gave an opinion in accordance with
the impression produced on his own mind, recommended the purchase of them,
but for some reason it was never completed, and eventually he bought them on
his own account. From this hour his destiny was fixed ; the flame had been
kindled, and every moment he could spare from his other avocations was em-
ployed in the study of what was now become an absorbing pursuit. From admiring,
he desired to imitate, and persuaded himself that though he might not succeed
in the first or second attempt, he would ultimately accomplish something similar.
In the year 1782 he produced his medal of Ryder the comedian, his first work,
which as a debut in the arts will always be esteemed. When publicly announced,
it attracted crowds to inspect and admire it : and yet, after a lapse of several
months, but one was sold, and empty praise was for some time his sole reward.

At this period he executed a medallion, of which, I believe, only very few
impressions remain. It represents the busts of the Right Hon. John Beresford
and his wife. Miss Montgomery, side by side, and was engraved for a person who
passed himself as a Turk, and kept baths in Dublin : he was called Solyman
Achmet, but his real name was, I believe, Kerns. Having received some favour
from Mr. Beresford, he caused this medal to be engraved, and set in the side of
a silver cup, which he presented to him. The work is extremely delicate, and
gives a faithful resemblance of his patron and lady.

Amongst those who were distinguished as encouragers of genius, Mossop
found a friend and protector in the late Dr. Henry Quin. The first work he
executed after his acquaintance with that gentleman was a head of his patron,
and in it the artist had given an expression so true to nature, and had finished
the whole with an air so closely resembling the antique, that it met the unquali-
fied approbation of the excellent judge whose portrait it gives. The immediate
occasion of this medal was as follows. Robert Watson Wade, Esq., first clerk of
the treasury under Wm. Burton Conyngham, Esq., was affected with a violent
imposthume in his side, which had baffled the skill of the faculty in Dublin, but
having fortunately called in Dr. Quin, he obtained almost immediate relief, and as
a token of gratitude presented him with this medal in gold, and inscribed on the
reverse, ob sanitatem restitutam excudit r w wade. This was followed by
orders for medals of Mr. La Touch e^ Mr. Alexander, Mr. Deane, and Viscount
Pery. Of this nobleman it may not be unsuitable to record an anecdote, which

Medals and Medallists connected with Ireland. 15

affords an example worthy of imitation amongst those who may have an oppor-
tunity of patronizing arts and artists. When Mossop had finished the head of
Lord Pery, he waited upon him with the work. His Lordship expressed him-
self highly pleased with the performance, and inquired what remuneration he
expected ; on Mossop's replying twenty guineas, the nobleman's surprise gave
every reason to imagine that he conceived it an exorbitant demand; coldly
remarking, that he thought the artist had not put a fair price upon his work, he
observed, he hoped he would be satisfied to accept what he thought proper to
give. With these words he presented Mr. Mossop with a paper, which he put
into his pocket without examination, and in some confusion bowed and withdrew.
If the artist was mortified under the impression that his price was to be reduced,
we may imagine his gratification at finding he had been presented with an order
for double the sum he had demanded.

Shortly after, in 1786, Mossop was employed to execute the Prize Medal of
our Academy. The side with Hibernia and the emblems of art was the original
device, to the other side was added the head of the Earl of Charlemont when
he became our president. As this work may be justly considered the chef
d'ceuvre of the artist, and is, I regret to say, in the hands of so few of our
members, it will be proper here more particularly to describe it. Obverse,
JACOBUS • COMES • DE CHARLEMONT • PR^s. The Earl is represented in the
uniform of the Irish volunteers ; the resemblance is most correct, and the exe-
cution of the head beautifully soft and fleshy ; the modem costume, so ill
adapted to classical art, is rendered agreeable by delicate and judicious ma-
nagement. Reverse, veteres revocavit artes. Hibernia seated on a pile of
books, surrounded by emblems of astronomy, chemistry, poetry, and antiquities.
Exergue, acad • reg • hib • inst • jan . 28 - mdcclxxxvi. The figure is bold and
masterly, the drapery broad, and the drawing correct ; while the disposition of
the emblems is so tasteful, that in the variety of subjects embraced, nothing ap-
pears crowded or confused. The noble Earl was so pleased with this specimen
of his skill, that he allowed the artist the use of his library, and free access to
all his valuable collections.

Soon after the execution of this work Mossop received orders for the
medal of Lord Rokeby the Primate ; for that given at the Commencement in
Trinity College ; for the badges worn at various societies ; and for tickets of ad-
mission to sundry institutions : in fact, he had arrived at the top of his profession.

16 The Very Rev. H. R. Dawson on the

>

and in every thing connected with it in this country he was employed. His
fame had reached England, so that Mr. Boulton, the intelligent proprietor of the
Soho Factory at Birmingham, was induced to give him an invitation to go over
to his employment in 1791? expressed in the most flattering terms, which, how-
ever, he thought proper to decline.

During the administration of the Marquis of Buckingham he produced a
pattern piece, which he denominated the Union Penny, engraved after a design
by Sir Joshua Reynolds. Only six impressions were struck before the die was
destroyed, but so admirable was the execution, that two were thought worthy of
a place in the cabinet of the reigning monarch. Afterwards he was employed
to superintend the coinage of the copper money issued by Messrs. Camac, Kyan,
and Camac, until the failure of the concern, by which he sustained considerable
loss ; and then he resumed his former pursuits. These led him in 1797 to com-
memorate the destruction of the French fleet atBantryBay by a beautiful medal,
which is still worn by the members of a club established on the occasion in the
neighbourhood ; and he was further employed by the Orange Association and
by the Farming Society, to design and make their badges and premium medals.

The Rebellion, and subsequently the Legislative Union in 1801, diverted
the public mind from any consideration of the fine arts, and the medallic art, the
object of our inquiry, shared the common neglect. With the exception of a
medal for the Dublin Society, and a Premium Medal for the Navan Farming
Society, no other work of importance was executed by Mossop ; and when the
former was undertaken, it was proposed that it should have an appropriate reverse
for each of the objects which that Society was embodied to encourage. From the
eminent skill exhibited in the part of the work which was completed, it is much
to be regretted that the original plan was not persevered in. This medal, when
at present used, is struck with a blank reverse, upon which is engraved the name of
the person obtaining it, and the object for which it is adjudged.

In 1804 a paralytic affection, followed almost Immediately by apoplexy, ter-
minated in a few hours the life of this ingenious artist. Though his works are
not numerous, they are interesting, and as the first of the kind produced in Ire-
land, are a lasting evidence of his natural ability in this department of art. Had
he received the advantage of early preparatory study, there can be no doubt that
he would have equalled any modern medallist, and rivalled those in former times
of whom other countries are so justly proud. Besides his medals, he engraved

Medals and Medallists connected with Ireland. 17

several large official seals for corporate bodies in Dublin and elsewhere. He also
executed a head in carnelion, and a small copy in ivory, from the celebrated gem
of the marriage of Cupid and Psyche. In the domestic relations of son, hus-
band, and father, he was most exemplary, and obtained respect wherever he was
known.

William Stephen Mossop, jun., also a native of Dublin, was born in 1788,
and after receiving a liberal education at the celebrated school of Samuel Whyte,
he commenced in 1802 his studies in the fine arts at the academy of the Royal
Dublin Society, under the care of Mr. Francis West, then master of the Figure
School. The progress he made not proving satisfactory, he was placed amongst the
private pupils of Mr. West, with whom he continued until his father's death left
him, at the age of sixteen, very inadequately prepared to commence the practice of
his profession ; and the first work he produced was the medal for the Society
incorporated for promoting Charter Schools. It was commenced in the life-time
of his father, and finished shortly after his death, when the artist was not seventeen
years of age. In 1806 he was employed by the Farming Society to execute a badge
to be worn by such persons as were life members ; and in 1809 he commenced a
medal of considerable merit, for the purpose of commemorating the fiftieth year
of the reign of George III. By his own account I find that in the following
year he visited London for the first time ; but, as he expresses it, " his stay was
so short, and he was so much bewildered by the variety that surrounded him, that
he did not derive all the advantages from it he might have done." However,
his spirit was greatly aroused, for though after his return to Ireland he was
much occupied in working at medals for various branches of the Farming So-
ciety, then in active operation, he found time to execute a medal, the die of
which was afterwards purchased by the Feinaglian Institution as a Premium
medal, and for which he obtained a premium himself from the Society of Arts at
the Adelphi. In 1814 he obtained another premium from the same body for a
head of Vulcan, which he engraved in compliance with an advertisement from
that Society, who promised to purchase the die, but left it, through neglect, on
his hands. Thus it appears his merit was acknowledged, but his works were
very inadequately remunerated.

In 1820, I find from his letters, that he projected a series of medals of dis-
tinguished Irish characters, but I cannot discover that he put his design fully

VOL. XIX. c

18 The Very Rev. H. R. Dawson on the

into execution, though medals of Ussher, Swift, Charlemont, Sheridan, and
Grattan afford some evidence of a commencement. Their execution, and the
fidelity of the likenesses they exhibit, are such as to make us regret the design
was allowed to fall to the ground. The last die that I can discover of his work-
manship is one of a noble medallion of the illustrious Wellington ; it appears as
jf the subject, as well as the country of the hero, had sharpened his graver, and
directed his hand, for it is in truth a spirited performance, having on the obverse
a bust of the Duke to the left, and on the reverse the appropriate emblem of
Victory crowning a warrior, who is seated, leaning upon his shield. There is
also, by the same hand, a small medallet of the hero, a perfect gem ; the die
came into the hands of the late Mr. West of Skinner-row, and impressions from
it are very rare. On one side it exhibits a bust inscribed duke of Wellington,
and on the other the simple but expressive word Waterloo, inclosed in a v«-eath;
this reverse however was executed by another artist. Mossop died in 18275
having for some time previous been afflicted by mental aberration, brought on
probably by intense application, and increased by those disappointments con-
comitant with unrequited genius and professional assiduity.

Unwilling to break in upon the account of the two Mossops, I must here
insert a reference to some medals struck in the years 1 797-8. Kirk, an artist
well known in England, thought it no disparagement of his own talents to copy
from Mossop's medal the head of Primate Robinson, and place it on a smaller
one with his name, and bearing on the reverse an elevation of the library at
Armagh, as a memorial of the liberality of that munificent prelate. The two
next are miserable in point of design and workmanship. They were executed
under the direction of a person named Brush, who was a silversmith, and as
appears from them totally devoid of skill and judgment in that line. One I
imagine to be the original badge of the Orange Society, and bears a figure of
William III. on horseback within a border of orange lilies. On a scroll above,
THE glorious MEMORY, and below, KING AND CONSTITUTION. Rcvcrsc, a
sword and sceptre in saltire through a crown, in a wreath of orange lilies, and
below on a scroll, god save the king. The second bears the legend, corpo-
ration AND citizens OF LIMERICK, — a castlc, with the armorial bearings of the
city in a wreath of laurel and palm. Reverse, a crown within a laurel wreath
inscribed to the heroes of coloony, 5th • sep*. 1798. It was designed to

Medals and Medallists connected with Ireland. 19

commemorate the successful battle fought by the Limerick militia under Colonel
Vereker, against General Humbert and the French, at Coloony, near Sligo.
Another medal of this year, of beautiful workmanship, and executed by Hancock
in England, commemorates the. decisive victory obtained by Sir I. Borlase Warren
over the French fleet off the coast of Donegal, on the 12th of October, 1798.

The visit of George IV. to his Irish dominions naturally called forth the
emulative talents of various artists, both in this and the sister kingdom. On this
occasion a medal was published by Mossop. Obverse, georgivs iv d . g . brit .
ET HiBERNi^ REX F • D. The king's head laureated to the left. Reverse, advenit
REX CONCORDAT civiTAS. Hibcmia standing with a cornucopia in her right hand,
and an Irish harp in her left ; at her feet, on the right, a child with a lighted
torch, setting fire to a pile of armour and military weapons ; on her right a square
altar, with a small flame arising from its top ; in the exergue the arms of the city
of Dublin, with the city mace, sword, and cap, mdcccxxi. The die of the
reverse of this medal was broken after a few impressions were struck off, and the
artist speedily executed another, which differs a little from the one just described,
having in the exergue, xii , aug : mdcccxxi.

Connected with his Majesty's visit, another medal was executed by Isaac
Parkes, an artist still living, to commemorate the Installation held at St. Patrick's
Cathedral. Obverse, georgius mi . D : G : britanniarum rex -fid: king's
head laureated to the left, encircled by the collar of the order of St. Patrick.
Reverse, south-east view of St. Patrick's cathedral ; in the, exergue, royal

installation - AT S^ PATRICK' DUBLIN - AUGUST XXVIII - MDCCCXXI. The vicW

of the cathedral is very correct, and executed with ability.

There is a medal connected with this period, which, though executed in
England, as it purports to be struck on Irish metal, it may be fitting to allude to.
Obverse, georgius iiii d : g : britanniarum rex f : d : Bust to the left, with a
laurel crown. Reverse, Hibernia with a harp, and a wolf dog at her feet,
receiving the king, who is just landed from a boat bearing the royal standard.
Howth, and some of the most conspicuous buildings of the city in the back
ground. In the exergue, in commemoration op his majestys - most gra-
cious visit to IRELAND - 1821. w • HAMY DiREX. There is engraved on the
edge, IRISH COPPER from the mines in the county of wicklow. This is a
work got up by Hamy and Mann, silversmiths in Dublin. The bust was exe-

c 2

20 The Very Rev. H. R. Dawson on the

cuted by Benjamin Wyon, and the reverse by Mills, both artists of eminence,
and are creditable to them.

I have but few medallists more to notice ; as they are still living, and work-
ing in their profession, I should prefer finding that the Academy was about to
take them under its fostering care, to occupying your time in criticising their
performances. John Jones was employed in the establishment of the younger
Mossop until the death of the latter, and has since produced some works from
his own graver connected with the political events of these busy times. They
speak for themselves, and I only regret that he has not been more employed, as
his Premium Medal for the North East Agricultural Society, is, in taste and
execution, a very beautiful performance. His tools and presses are now rusting
in his workshop ; and a talented professional native, educated in an excellent
school, has the mortification of finding himself neglected, and English artists
employed to record Irish events.

William Woodhouse, who is a native of England, and received his education
at Birmingham, has also struck some few medals. I have no doubt, from the
specimens I have seen, that were he to receive due encouragement, his talents
would be well employed in the service of our country.

The last with whom I am acquainted is Isaac Parkes, a native of Birmingham
also, but who came to this country in 1807, and served his apprenticeship to his
brother, an eminent button manufacturer in this city. We are justified in con-
sidering Parkes as our own ; for, here he served his time ; here he received
instructions in modelling from Sherwin, the pupil of Smyth, whose chisel-
lings and figures adorn so many of our public buildings ; and, here whatever
proficiency he has attained to in the art has been elicited and nourished. If
diligent attention to business, access to a well-chosen collection of models, and a
considerable share of ingenuity and taste, can secure public patronage, Parkes
well deserves it ; and his large medallion of the late Duke of York is an evidence
of his boldness and power in the art of die sinking, — for amongst all those of the
middle ages, I have scarcely seen one that exceeds it in relief, and it has this
superiority over them, that while they were invariably cast, this was raised out
of the solid metal by the power of the screw.

The comparatively small number of medals I have been able to record from
the time of Charles II. to the present day, affords a lamentable and humiliating

Medals and Medallists connected with Ireland. 21

proof of the small encouragement both arts and artists have hitherto received
in Ireland. Our medallists, while labouring under great discouragements, have
shown themselves capable of performances worthy a place in any cabinet ; what
might we not then expect if the liberal, the enlightened, the classical were once
aroused to patronize an art which formed the boast of Ancient Greece and Rome
in the days of their greatest power and highest civilization.

P. S. — It was my intention to have accompanied the preceding Memoir with
an Appendix, giving a particular description of many other medals connected
with Ireland, as well as those which have been noticed already, together with
engravings of the most rare and interesting. But since I have more particularly
directed my attention to the subject, my researches have led to the discovery of
so many medals, of the existence of which I was before ignorant, already amount-
ing in all to more than two hundred, that I shall for the present defer the pub-
lication of the appendix and engravings till I am enabled to present it to the
Academy in a form as complete as I would wish, and as the subject deserves.

22

II. On the Antiquity of the Kiliee or Boomerang. By Samuel Ferguson,

Esq., M. R. I. A.

" Forte tamen aliquis erit qui de Aclide certius aliqnid in medium ferat." — Pierii in ^neid, 1. vi.

V. 730, Comment.

Read January 22, and February 12, 1838.

I.— OF THE CATEIA.

1 HE Kiliee or Boomerang, at present the peculiar weapon of certain Australian
islanders, several varieties of which are represented in Plate I., appears to have
been known to European and other Continental nations from a very remote
period.

The name by which the Boomerang is most readily recognized in the works
of Roman writers is Cateia. Of this, the earliest notice is found in the MnexA
of Virgil, where, among various tribes who joined themselves with Tumus,
mention is made of a people accustomed to whirl the Cateia after the Teutonic
manner,

" £t quos maliferse despectant m^enia Abeli%
Teutonico ritu soliti torquere Cateias."

Virg. Mneid. 1. vii. v. 740.

The next mention of the Cateia occurs in the Funics of Silius Italicus, where
the poet describes an individual of one of the Lybian tribes, who accompanied
Hannibal to Italy, as being armed with the bent or crooked Cateia :

" Tunc primum castris Phcenicum tendere ritu
Cinyphii didicere Macae : squalentia barba
Ora viris : humerosque tegunt velamina capri
Setigeri : panda manus est armata Cateia."

Sil. Ital. Punic. 1. iii. v. 274.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 23

A third notice of the Cateia is found in the Argonautics of Valerius Flaccus,
where, in an enumeration of the Maeotic nations which rose in arms against
Jason, a people are described whose tents of raw hides were carried on waggons
from the extremities of the poles of which their young men whirled Cateias.

" Quin et ab Hyrcanis Titanius expulit antris
Cyris in arma viros : plaustrisque ad prselia cunctas
Coraletae traxere manus : ibi sutilis illis
Et domus, et cruda residens sub vellere conjunx,
Et puer e primo torquens temone cateias."

Val. Flac. Argonaut. 1. vi. v. 83.

From these notices it may be collected,

1st. That the Cateia was an instrument of a curved shape, for this is the
constant meaning of the adjective pandus. " Carinas pandae," ( Virg. Georg.
1. ii. V. 89.) — " Delphines pandi," (Ovid. Trist. 1. iii. v. 9.) — "Fauces pandae,"
{Stat. Sylv. 1. iii. V. 15.) — " Rostrum pandum," {Ovid. Metamor. 1. iv. v. 57.)
— "Rami pandi," {Ovid. Metamor. 1. xiv. v. 37.) — "Juga panda bourn,"
{Ovid. Amor. 1. i. and Eleg. 1. xiii. v. 4.)

2nd. That it was a projectile — "e temone torquens."

3rd. That it was dismissed with a rotatory motion — " torquens," — " soliti
torquere." For, although the verb torqueo is frequently applied to the projec-
tion of the straight missile, it is always with reference to the rotatory motion
either of the amentum, by which several sorts of straight missile were thrown, or
of the weapon itself round its own axis.

These marked characteristics of the Boomerang would, perhaps, furnish
sufficient grounds for inferring an identity between it and the weapon under
consideration ; for, from recent experience, it might safely be asserted that no
instrument having the peculiar shape ascribed to the Cateia could be projected
with a rotatory motion, without also exhibiting the great distinguishing property
of the Boomerang by a reciprocating flight. But the description of the Cateia,
given by Isidore, Bishop of Seville, a writer of the end of the sixth and beginning
of the seventh century, renders this line of argument unnecessary. He describes
the Cateia as a species of bat, of half a cubit in length, 'which, on being thrown,
flies not far, on account of its weight, but where it strikes, it breaks through
with excessive impetus. And if it be thrown by one skilful in its use, it returns

24 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

hack again to him who dismissed it. The passage occurs in the " Origines,"
under the head Clava, viz. :

" Clava est qualis fuit Herculis, dicta quod sit clavis ferreis invicem reli-
gata, et est cubito semis facta in longitudine. Haec et Cateia, quam Horatius
Caiam dicit. Est genus Gallici teli ex materia quam maxime lenta; quae,
jactu quidem, non longe, propter gravitatem, evolat, sed ubi pervenit vi nimia
perfringit. Quod si ab artifice mittatur, rursum redit ad eum qui misit. Hujus
meminit Virgilius dicens

' Teutonico ritu soliti torquere Cateias.'

Unde et eas Hispani Teutones vocant." — Isidor. Origin. 1. xviii. c. vii.

Thus, all the characteristics of the Boomerang, its use, its shape, its mode of
projection, its extraordinary impetus, and its peculiar reciprocating flight, belong
to the Cateia, from which it cannot but be concluded that these were the same
weapon.

II.— OF THE ACLYS.

Another name by which a weapon of the same character would appear to
have been known to Roman writers is Aclis — aclidis, and Aclys — aclydis. It
is first mentioned by Virgil, speaking of the aborigines of Campania.

" Oscoruinque manus : teretes sunt aclides illis

Tela ; sed haec lento mos est aptare flagello."

ViTg. JEneid. 1. vii. v. 730.

From which it appears that the Aclys was originally a hand weapon, as its
discharge by means of a thong is mentioned as something unusual.

Silius also mentions the Aclys, after enumerating those tribes of Campania
who allied themselves with Home before the battle of Canns.

" Formabat Scipio hello.

lUe viris pila, et ferro circumdare pectus
Addiderat : leviora domo de more parentum
Gestahant tela ; amhustas sine cuspide cornos ;
Aclydis usus erat, factseque ad rura bippennis."

Sil. Ital. Punic. 1. viii. v. 553.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 25

And again, among the forces of Hannibal :

" Jamque Ebusus Phcenissa movet, movet Artabrus arma
Aclide vel tereti pugnax instare veruto."

Sil. Ital. Punic. \. iil v. 362.

Mention of the same weapon is found in the rescript directed to Zozimio, Pro-
curator of Syria, empowering him to pay a certain annual stipend to Claudius,
at that time tribune of one of the Roman legions, and afterwards Emperor,
which document is embodied in the life of Claudius, by Trebellius PoUio.
Here, among various articles of value, such as mantles, belts, and various sorts of
weapons, are specified " Lancea2 Herculeanse duse — Aclides duse — falces duae,
&c. (Hist. Aug. Scrip. Minor, v. ii. p. 149.)

These passages, although they may appear to distinguish the Aclys from
straight missiles in general, yet do not afford more than a negative inference.
A more satisfactory evidence of the shape of the weapon, may, however, be
obtained from a passage of Valerius Flaccus in the above-mentioned enumera-
tion of the Mfflotic nations.

" Nee procul albentes geminS, ferte aclyde parmas
Hiberni qui terga Nose, gelidumque securi
Eruit, et tota non audit Alizona ripa.

Fal. JFlac. Argonaut. 1, vi. v. 99.

For " fert," Burmann reads " ferit," and considers the double Aclys as the
instrument in eliciting a warlike sound from the struck shield. He also takes
" albentes" to mean white, as having no device, in the same sense as " albus"
in Virgil, " parma inglorius alba." But " fert" is the reading of all the MSS.,
and, as "fert" cannot take an ablative to complete its meaning, "gemina
aclyde" must be referred to "albentes." Again, had Valerius intended to
convey the same meaning with Virgil, he would have used "albas," or perhaps
" albatas," but never " albentes," which means growing white from some other
colour, and implies a proximate cause. — " Campique ingentes ossibus albent,"
(Virg. ^neid.\.x\\. v. 36.) — "Caput quod videam canis albere capillis,"
Ovid. Heroid. Ep. xiii.) The meaning of the passage would, therefore, appear
certainly to be, " close to him, the hewer of the crust of wintry Danube, who

VOL. XIX. z>

26 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

draws his water with his axe" (a quaint phrase parallel to that of Sidonius Apol-
linaris, " Ligerimque securi exclsum, per frusta bibit. — Carm. v. v. 209.)
advances shields charged with the white blazonry of the double aclys." Now,
the general family to which this tribe belonged, appears as well from their being
brought from the Alazonian or Amazonian river (it is also fi'om the banks of
the Danube that Seneca brings the Amazons in his Hyppolitus) as from some
markedly Amazonian characteristics attributed to them. Of these the most
striking is the adoration of pillar-stones, an Amazonian trait not to be mistaken.
For, however fabulous that story was which appears to have originated in a
vulgar etymology of the word Amazon, it is certain that there were nations of
such a family, among whom the women took an active part in war, and that the
worship of pillar-stones has been very generally ascribed to them by ancient
writers. Plato mentions an amazonian pillar-stone at Athens. IlXrja-iov cokci
Tcov TTvXcov Trpo^ rrj Afia^oviSi crrvXr) (Plato in Axiocho. v. iii. p. 365.) And
the Argonauts of Apollonius are represented as finding a similar one in Pontus,
near the Amazonian Temple of Mars.

'Itpog (^ VOTE nacrai Afia^oveg £V)(sraovTai,"

Apollon. Argonaut. 1. ii. v. 1177.

" Wherein was set up a black holy stone to which all the Amazonians offered
their prayers." A stone of the same sort was shown in Colchis in the time of
Arrian, and was said to have been the anchor of the Argo, (Arrian. Peripl.
p. 9 ;) and even down to the thirteenth century, pillar-stones were of frequent
occurrence throughout the plains bordering on the north of the Euxine, (^Rubru-
quis apud Hackluyt. vol. i.) So that, in reference to the bearers of the shields
blazoned with the double aclys, the following passage from Bryant's Analysis of
Ancient Mythology may safely be submitted.

" The Amazonians were Arkites ; hence it is, that they have ever been
represented with lunar shields ; many have thought that they were of a lunar
shape, but this is a mistake, for most of the Asiatic coins represent them other-
wise. The lunette was a device taken from their worship. It was their
national ensign which was painted on their shields ; whence it is said of them,
* Pictis billantur Amazones armis,' and in another place ' ducit Amazonidura

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 27

lunatis agmina peltis, Penthesllea furens.' The Amazonian shields approached
nearly to the form of a leaf, as did those of the Gothic nations. Pliny says of
the Indian fig, ' Foliorum latidudo peltae eflSgiera Amazoni?e habet.' Upon
these shields they had more lunettes than one ; and from them the custom was
derived to the Turks and other Tartar nations." — (Anal. Anc. Myth. v. iii.
p. 472.)

Whether or not the lunette, which is still the ensign of a very numerous
nation, was an Arkite emblem, as this learned, but somewhat fanciful writer
supposes, it is extremely probable, that if his interpretation of " lunatse peltse"
be correct, this is the same blazonry described by Valerius Flaccus, whose
omitting so marked a characteristic would otherwise be singularly inconsistent
with the propriety observed throughout the remainder of his poem. " Albentes
gemin^ fert aclyde parmas" may then be rendered — " Advances shields charged
with the white blazonry of the double lunette" and thus the curved form of the
aclys, if this argument of Bryant be correct, will become as apparent as that
of the " panda Cateia."

This view is strongly confirmed by the description given of this weapon by
Servius. " The aclys," he says, " is a weapon of so great an antiquity, that the
use of it in war has not been recorded (meaning probably, not otherwise than by
poetical writers.) We read, however, that these were bats, of half a cubit in
length, with horns projecting at either side, {eminentibus hinc et hinc acumini-
bus,) which were so cast against the enemy attached to a line, as to be capable of
being retracted after having inflicted the wound;" (Sertnus in JEneid. 1. vii.
v. 730.) Here, while Servius clearly describes the shape, and refers to the
peculiar flight of the Cateia, he seems to consider the latter as produced by the
retraction of thongs to which the weapon was attached ; and in this view he has
been followed by all the commentators down to our time. He admits, however,
immediately after, that this was but a guess, and refers to the tradition which
appears to have preserved the true account ; " putatur tamen esse teli genus
quod per flagellum in immensum jaci potest," which will safely bear this
translation, •' some, however, are of opinion, that the thong was only used in its
projection, and that by its means it could be cast to an immense distance."

Such was the Aclys, according to the uncertain report of Servius, and,
whatever it may have appeared to him to be, he identifies it with the Cateia,

jd2

28 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

making only this distinction, that the latter was a weapon of double the dimen-
sions ; " Cateiam quidam asserunt teli genus esse, tale quale Aclides sunt, ex
materia quam maxime lenta, cubitus longitudine, tota fere clavis ferreis illigata,
quam in hostem jaculantes, lineis quibus earn adnexuerant, reciprocam faciebant ;"
(Servius in ^neid. 1. vii. v. 741;) where it will be still observed, that he
leaves it uncertain whether the reciprocating flight arose from the retraction of
the lines, or was a consequence of the mode in which the weapon was thrown by
their instrumentality.

To these we may add a testimony of considerable force, if the translation
suggested should be deemed the true one, from Sidonius ApoUinaris, Bishop of
the Arverni, a writer of the fifth century. The passage occurs in that panegyric
which Sidonius recited before the Emperor Majorian on his arrival at Lyons in
the year 457. In this piece the Acquitanian prelate gives an interesting, though
inflated account of a victory obtained a short time previously by Majorian over a
predatory band of Vandals and Moorish slaves from Africa, who had attempted
to carry off a prey from the coast of Campania. He depicts the fat Vandal
starting from the benches of his galley, and arming himself for the support of
his emissaries on shore, with certain poisoned missiles, which, according to what
appears the most obvious translation,* strike twice when once discharged ; and, in

* It may be argued that the words, " quae ferlant bis missa semel" have reference to the poison
of the arrows alluded to in the preceding Une, and mean, " vfhich injure doubly by a single dis-
charge." The other translation has, however, been preferred on the following grounds.

Both interpretations go on the assumption, that in the words " quae feriant bis missa semel," the
poet intended an antithesis between his and semel ; and the diflference between the two interpreta-
tions consists in this, that in the one the antithesis is held to lie between the one discharge and the
two successive effects ; while in the other, it is held to lie between the one discharge and the two
simultaneous effects.

It is true, bis, under certain circumstances, will mean double in simultaneous operation, as " bis
periit amator," &c. ; but never, it is submitted, when in opposition to semel, for semel has but one
meaning, " once, in point of time" and to be in opposition to it, bis must necessarily mean " twice,
in point of time," The interpretation which refers his to a succession of blows, would, therefore,
so far appear preferable to that in which his is made to have reference to the double simultaneous
operation of cutting and poisoning by one and the same blow.

Again, where the actions of two or more agents unite in one verb, the verb employed ought to
be such as is proper to both or all. Thus, in expressing in English the idea supposed by the

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 29

the subsequent account of the engagement, represents some as slain by pikes,
some by arrows, and others by the Aclys.

" Turn concitus agmine tot&
In pugnam pirata coit ; pars lintre cavata
Jam dociles exponit equos, pars ferrea texta
Concolor induitur, teretes pars explicat arcus,
Spiculaque infusum ferro latura venenuin
Quce feriant his missa semel ; jam textilis anguis
Discurrit per utramque aciem, &c. &c."

And again, after the battle joined :

" Hunc coiiti rotat ictus equo, ruit aclide fossus
Ele, veruque alius, jacet hie simil alite telo
Absentem passus dexteram."

Sidon, Apollinar. Carm. V. v. 328-413.

Thus, then, the notices which can be collected concerning the Aclys furnish
evidence nearly as strong as that adduced in the case of the Cateia, shewing that

suggested interpretation to be conveyed by these words, we do not say, " which poison twice when
once discharged," on the one hand, nor " which cut twice when once discharged," on the other ;
but select some equivalent for Jeriant, which is equally applicable to the infliction of a hurt by the
incision of a cutting instrument, and by the operation of a poison, such as " wound," " hurt,"
" injure," &c.

But it is conceived thaX ferio is not capable of such an equivalent. It means essentially to
" hit," to " strike," to " illide against," and is quite inapplicable, without a very strong metaphor, to
the operation of a poison. But if there be two agents, as in this case, the common verb cannot be
employed metaphorically, unless the metaphor be equally applicable to both agents. The meaning
of the common verb cannot be split, so as to suggest two ideas, one metaphorical, and one simple,
having reference severally to the respective agents. Had the poet intended the meaning suggested,
he might properly enough have made use of either " noceo" or " laedo," both of which are applica-
ble, as well in point of rythm as of meaning. Thus, "namque ut refecta est coluber, nocuit hominem
protinus," (Pheedn, 1. i. fol. 18 ;) " Lcedere aliquam vulnere," {Ovid, in Jbin, v. 484,) &c.

Further, missa seems to imply progressive motion, such as is more proper to successive than to
simultaneous effects ; and, therefore, had Sidonius intended the meaning suggested, he would pro-
bably have employed, not missa, but some such word as acta, impacta, or the like, which would
carry the agents to their locus in quo, and leave them there.

To express the meaning suggested, the fittest words would be " quae noceant dupliciter simplici
ictu," which are all different from the words employed ; but, to express the meaning adopted, it
would be impossible to find apter words than those employed themselves.

80 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

all the chief characteristics of the Boomerang belong to this weapon also ; whence
it is concluded, that the Aclys was a weapon which differed from the Cateia only
in dimensions.

Ill— OF THE ANCYLE.

The etymology of the word Aclys points, in the third place, to another name
by which a similar weapon seems to have been known to the Greeks. " Ego
jacula crediderim, (says Turnebus, in his commentary on the 'duas Aclydes' of
Trebellius, Adversar. lib. xxx. c. xi.), an sata, an amenta. Ay/cuAat autem
Graeciae jacula quaedara sunt ; et per diminutionem inde AyKvXiSes — inde
Aclydes." And this etymology is generally adopted by subsequent commenta-
tors. There exists, indeed, a remarkable connexion between the sounds ak and
ank, which strongly supports the conjecture of Turnebus. Thus, as Vossius
observes, from KLKiwo^y cincinnus ; from Xei\(o, lingo ; from cx'^j anguis. In
like manner ank, in the present of some verbs, assumes the form ak in the pre-
terite, as stringo, «^rm ; ^ngo, Jixi ; £rango, Jregi ; x'mco, vici ; i^ango, pcBxi,
pegi, pepigi ; pactum, &c., (old praeterite.) Thus, also, the ayKvpa of the
Greeks, and anchora of the Latins, is found in the form akkeri in the Islandic,
and akkjeri in the dialect of the Feroe islands. — (Antiq. Americ. ante- Columb.,
p. 328.) So also in topographical nomenclature, the Sangar river, called by the
barbarians Sagaris ; the Ogygian gates, stated by Hesychius to be called the
Oncaian gates by the Athenians, &c. Numerous similar instances may be had
in the modem languages of Europe, as against, in the Anglo-Saxon onjean,
{Skinner, Etymol. Mag. Ling. Ang.) ; aguillon, the French needle, in the Teu-
tonic, angel, (do.) ; ache, a pain, from the Anglo-Saxon anje, vexatus, (do.), &c.

Now the KyKvkrj of the Greeks, though commonly used synonymously with
the Latin Amentum, meaning the thong or attached sling by which various sorts
of missiles were discharged, has an independent signification as a distinct species
of missile, as in that passage of the Orestes of Euripides, where certain Phry-
gians, speaking of their weapons, are made to say :

'O fif.v irtrpovc 6 Ss ayKvXag,

'O Se %i(pOQ irpoKWTTOv ev x^potv ex^v.

JEurip. Orest. v. 1438.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 31

On which the scholiast observes, ayKv\as — ra aKovria avo tov eTrrjyKvXtaa-Oai ;
j) 8coTi airo rrjy Kara fX€<rov ayKvXrjs Xafi^avo/xevoi pnrTOvaiv. — *' Ancyles,
certain missiles, so called from being of a curved shape, or because weapons of
that sort are thrown by means of an ancyle fastened to their middle." The
ancyle is also given in Hesychius and Suidas, as ubos aKovriov, " a species of
missile," along with its other significations.

If, then, the Aclys be truly a derivative of this name of a weapon known to
Greeks as a missile of a curved form, there appear good grounds for considering
the Ancyle also as belonging to the family of the Boomerang. These conclu-
sions will receive further corroboration from an investigation of the meanings of
the names so far sought to be identified.

IV.— OF THE RADICAL MEANINGS OF THE NAMES CATEIA, ACLYS,

ANCYLE, AND TEUTON.

That Cateia means literally something curved, might be inferred from the
application of the word in the Basque language to signify a reaping-hook, —
Iguiteia., /alx, {Lhuid Archceol. Brit.) ; and this inference is very amply borne
out by an inspection of those words involving the idea of curvature, into which
the element kat enters radically. Thus the Latin catena, a chain made up of
twisted links, appears rather a derivative from, than the parent of the Belgic catte,
a chain. That both signify something crooked or twisted, appears clearly from the
application of the synonymous Welsh kaduen to mean both a chain and a hook.
Catte also is the old Belgic anchor, whence our cat-head, that piece of timber,
namely, from which the cat or anchor is suspended. Guet, again, in the Cornish,
means a turning. In like manner, the Welsh kad-\y% is found synonymous with
the Irish uir-Xi?,, or circular enclosure ; an instance which may be considered
conclusive in settling the meaning of the element kad, or kat, in the Celtic.
Hence it appears, that the idea of rotundity or circularity, which is shewn in the
Ordnance Memoir of Londonderry to enter into the signification o£ gort, gard,
villa, bally, urbs, as applied to early cities, is also radically involved in the synony-
mous caiha.iv, whether spelled as in the Punic gadera, or as in the Gallic cattur
of Ptolemy, or as in the Welsh and Cornish cader of the present day ; and hence

32 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

a curious illustration of the TaSepa, ra irepK^paynara of Hesychius, as well as
of the other testimonies adduced by Bochart to shew that this word literally
means a fenced enclosure. — (^Bochart. in Georg. Sac.) It is worthy of observa-
tion, that the kraals of savage nations still retain this primitive form, which we
see thus indicated in almost all the names used by European nations to signify
a collection of habitations. These will be sufficient for the present to establish
the necessary meaning of Cateia.

If the conjecture as to the etymological relation between the words Aclys
and Ancyle be correct, it will only be necessary to investigate the radical mean-
ing of the latter; and here we are introduced among a numerous family of
words in which the idea of curvature is uniformly inherent : ayKcov, ayKvXrj,
ayKvpa ; unguis, unguis, ancus, uncus, angulus, ango, angor, anxius, angle,
ankle, hang, hank, hanker, (synonymous with the hake of Lincolnshire, Skin-
ner,) hunkers, haunch, (the Italian and Spanish aiica, synonymous with hough
or hock,) hunch, hunch-hacked, (the Belgic huckschoulderen, from the Belgic
and Teutonic hucken, to bend down,) in which last the connexion above con-
tended for is strikingly manifested. These examples might be swelled to a
great extent, but it is conceived that enough has been done to determine the
essential meaning oi Ancyle, and to shew a high degree of probability that a like
signification is also involved in Aclys ; so that as Ancyle appears to be nearly
identical with the Sicilian zancle, a reaping-hook, Aclys may, in like manner,
be the representative of our own sickle.

With regard to the passage from Isidore, which states that the Gauls and
Spaniards of his time called the Cateise Teutones, as indicating the Teutonic
origin of the weapon, it is to be observed, that the proper name of the Teutonic
people is Tuitschen, or Duytschen, and that the word Teutones of the Latins
was only a softened representation of that sound. Now Grial, commenting on
this passage of Isidore, states that the Spaniards of his time continued to use
certain instruments, which he conjectures to be the same. These he does not
farther describe than by observing, that the name they then went by was
Chochones ; but Chochono in the Basque language is equivalent to the Castilian
Concavo, {Dictionar. Triling. ad verb.) ; and hence it appears very probable,
that the name Teutones was imposed on these weapons, not as indicative of their
origin, but as descriptive of their shape.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 33

It may, then, be concluded, with a strong degree of confidence, as well from
the testimonies of ancient writers, as from the necessary signification of the names
by which these weapons were known, that the Cateis, Aclides, Ancyls, and
Teutones, of the classic authors, were true varieties of the Boomerang. The
consideration of the name Caia, which also occurs in Isidore, but with marks of
a corrupt reading, is reserved for another place.

v.— OF THE JAVELIN OF CEPHALUS AND AQUIFOLIA OF PUNY.

So far of the name or names by which weapons of this species were, or may
have been, known to the ancients. That their peculiar flight was known, and
has been markedly alluded to without the specification of any name, appears also
from the classic writers, Ovid, in the fable of Cephalus and Aurora, has attri-
buted the distinguishing property of the Boomerang to the weapon of Cephalus.
" It pursues whatever it is aimed at : chance does not govern its flight ; but it
flies back of its own accord bloody from the wound it has inflicted."

" Consequitur quodcunque petit ; fortunaque missum
Non regit, et revolat, niullo referente, cruentum."

Ovid. Metamor. 1. vii. v. 684.

From the context, however, it appears that Ovid does not ascribe any of the
other characteristics of the Australian weapon to the one in question ; on the
contrary, he represents it as a straight and pointed dart.

"jaculum cujus fuit aurea cuspis." (v. 675.)

" Qua tamen e sylva teneas hastile recisum
Jamdudum dubito." (v. 677.)

Which would argue rather a hearsay acquaintance with the properties of the
weapon, than any accurate knowledge of its shape or structure.

A passage, also, in the works of the elder Pliny, gives evidence of some
acquaintance with the distinguishing properties of such missiles ; though his
attributing the peculiarity in question to an innate virtue of the wood will
probably excite a smile. Speaking of the Aquifolia or Agrifolia, a species of

VOL. XIX. E

34 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

holly, he says, a bludgeon of this wood, if thrown at any beast, and falling short
of it, will glide nearer (query, to the beast or to the thrower ?) in its rebound or
descent. " Item baculum ex ea factum, in quodvis animal emissum, etiam si
citra ceciderit defectu mittentis, ipsum per se recuhitu proprius adlabi, tam
praecipuam naturam inesse arbori." — (Plin. Nat. Hist. 1. xxiv. c. 73.) On
which the naturalist Bauhin observes : " At nos praecipuam in iis inesse supersti-
tionem censemus qui istas nugas credant." — (Hist. Plant. 1. viii. c. 3.) And
indeed it is not surprising that properties so extraordinary should excite the
ridicule of commentators not practically acquainted with the peculiarities of the
weapon. Thus, Cerda, commenting on the words of Isidore, " Quod si ab
artifice mittatur rursum redit ad eum qui misit," considering the alleged result
as a consequence of some mystical sympathy between the weapon and a particular
person, falls into the error of taking artifex to mean the maker of the instru-
ment, and exclaims, " Nam cur non etiam redibit si mittatur ab alio quam ab
artifice ?"— ( Virg. Not. Var.)

So far, then, it may be concluded that the Latin writers of the Augustan
age were acquainted with weapons possessing all the characteristics of the Boome-
rang, but with that degree of uncertainty which would imply that their know-
ledge of them had been derived from a source very remote, either in point of
distance or of time. This partial ignorance on the subject will account for any
apparent discrepancy that might be charged against those evidences in which
notices of the Cateia and Aclys, argued to be the same, are drawn from different
passages of the same authors, who would thus appear prima facie to put a
difference between them. That it was the extreme antiquity of the weapon
which caused this uncertainty will appear the more probable from further con-
siderations.

VI.— OF THE CLAVA OF HERCULES AND HAMMER OF THOR.

Isidore identifies the Cateia with the Clava of Hercules : " Clava est qualis
fuit Herculls — haec et Cateia ;" an identity which, most probably, would not
have been argued by one so well acquainted with the peculiarities of the Cateia
without good grounds. That the Herculean weapon was a missile, appears from

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 35

Sextus Pompeius, " Clava, teli genus qua Hercules utebatur ;" for although, by
a poetic license, Virgil has applied telum to a sword, yet the exactness necessary
to a lexicographer like Festus precludes any uncertainty that might arise from
his supposed adoption of this precedent. That his opinions, and those of Isidore,
were recognized down to the tenth century, appears from the Anglo-Saxon
Glossary of -^Ifric, " Clava, vel Cateia, vel Teutona, annej- cinnej- jej-ceoc," i. e.
" the Clava, Cateia, or Teutona, are missiles of one sort ; — {JElfric. Glossar. ad
calcem Dictionar. Somneri ;) — there are, therefore, sufficient grounds to justify
some further inquiry into the truth of this assertion, although at first sight it
may, perhaps, have appeared too startling for serious consideration.

That the idea of curvature is Involved in the word Clava, as well as in those
hitherto investigated, may be inferred from the application of numerous words
of the same family. Thus Clava itself is used synonymously with unguis, to
signify the twisted tendril of a vine ; claw, our English for a hooked talon, is
equivalent to unguis in another sense ; and clavus, a crooked holdfast, or clamp,
is another equivalent of unguis, as is Indicated by our use of the synonymous
nail. Thus cluif, in the Lowland Scottish dialect, is synonymous with ungula ;
and the word clams is still used in the same idiom for crooked forceps. Thus,
also, glomus, our clew, or round ball of thread ; glomero, to gather in a circle ;
clavicula, the crooked key-bone of the shoulder, &c. Another confirmation may
be drawn from the application of the Latin clavis, to signify a key ; for, that the
key was originally a crooked instrument appears clearly from all that can be
collected from the works of the ancients concerning it; ( Salmasius in Exercitat.
Plinian.) ; and the very word key, by which this instrument is now known to
us, is still the identical word used to express a club by the Sclavonic nations,
{Cluverius in Germ. Antiq. p. 304,) and is very probably the same caia to
which Isidore alludes in that description identifying the Clava and Cateia.
Hence this conclusion seems quite legitimate, that the original form of the
Clava, or artificial club, was like that of the clavus, or original holdfast ; or like
that of the clavis, or original key.

Hence the report of Servius concerning the Aclys, " Quod sit clava, cubito
semis facta ;" and the statement of Johannes de Janua, " Cateia — hasta qua ute-
batur Hercules," appear by no means inconsistent with probability.

On these grounds, it may be expected that the club of Hercules will be

e2

36 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

found represented in ancient sculptures, drawings, or impressions on coins, of a
curved shape. It appears, however, from an extended examination of glyptical
and numismatical antiquities, as well as of the drawings which remain in the
chief collections of Etruscan vases, or on sepulchral monuments, that the poetical
Hercules is almost invariably represented with the straight, knotted weapon.
The only marked exception which has been observed is in the contest of Hercules
with Achelous, (PI. I. fig. 9?) in the " Museum Etruscum," where the club
in the hand of Hercules is represented of a form somewhat approaching to that
of the common "hurl" of this country. It is apparently of an untrimmed stem
of palm-tree, which, growing naturally straight, must have been reduced by
artificial means to the curved shape ; suiting well with the description given
by Statius of the first attempt at forming an artificial weapon among a rude
people.

" Arcades hi : gens una viris, sed dissona cultu

Scinditur ; hi Paphias rayrtos a stirpe recurvanf

Et pastorali meditantur praelia trunco."

Stat, Thehaid. 1. iv.

Where it is observable that the writer does not seem to consider the mevefustis^
or stake, to be a legitimate weapon till bent into the curved form of the Clava.
But although the weapon with which Hercules almost universally appears
armed in these poetical representations be undoubtedly a mere Jiistis, or knotted
staff, there is one instance of a very differently shaped weapon, which appears
certainly intended for the club of Hercules, being represented in ancient sculp-
ture. The original is in the French King's collection, and has been described,
and a drawing of it given, by Millin, (PI. II. fig. 3.) The subject is a throne,
on one side of which two young genii appear playing with a large, flat, curved
instrument, which they seem with difficulty to support. Millin, following
Viscenti, considers this instrument to be the harpe, or falciform weapon peculiar
to Saturn and Perseus. This assumption is, however, quite gratuitous on the
part of both. The sculptured instrument is blunt on the inner edge, and square
at the broader extremity ; whereas the harpe of Saturn is invariably represented
as being sharp on the inner edge, and terminating in a point, (PI. II. fig. 5;)
while the harpe of Perseus (PI. II. fig. 4) was a poetical combination of the
sword and the Saturnian weapon, having a falciform projection at one side of a

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 37

straight blade, and bears not the least resemblance to the sculpture. The
sculptured instrument is, on the contrary, identical in shape with weapons repre-
sented in the hands of certain figures in the collection of Egyptian monuments
published by Signor Rosellini ; and these weapons are manifestly clubs, (PI. I.
figs. 10, 11.) It is clear, then, that the weapon in the sculpture is a Clava.
That it is also intended to represent the particular Clava of Hercules may be
inferred with a pretty strong degree of confidence from the accompaniments.
It was a favourite practice with ancient artists to represent the influence of love
over the sterner deities ; as in the case of Mars, by young genii playing with his
sword and helmet ; in that of Jupiter, by their sporting with his thunderbolt ;
but particularly, and as a favourite study, they shewed the triumph of the softer
passion over Hercules, by Cupids represented masquerading in his lion's skin,
or tolling under the weight of his club. An inspection of any collection of
ancient gems will give abundant evidence of the favourite character of the sub-
ject among classic artists. That the weapon in the sculpture is, therefore, the
Clava referred to by Isidore, appears, on these considerations, highly probable.

There remains, besides, the practical test. If this weapon truly represent
the club of Hercules alluded to by Isidore, an instrument formed on the model
of it will exhibit the peculiar flight of the Cateia. The experiment has been
tried, and the practical result confirms every induction drawn from the written
testimony. Such an instrument exhibits the reciprocating flight almost, if not
fully, as perfectly as the regularly shaped Boomerang. Indeed It Is Identical in
shape with one variety of the crooked implement at present used by the inhabi-
tants about Swan River, (PI. I. figs. 5, 6, 8.)

It may, therefore, be concluded of this famous weapon, that the knotted
fustis of ancient monuments is only Its poetical representative ; but that the true
shape of the Herculean club, as understood by Festus, Isidore, ^Ifrlc, and
Johannes de Janua, is found in one variety of the Boomerang.

This conclusion is further corroborated by the fact, that a reciprocating flight
has been ascribed to the weapon of Thor, who, it is well known, represents Her-
cules In northern mythology. " Lock gave to Thor a hammer, (says the Edda,)
which he told him would be serviceable in combating giants ; that it would
never miss its mark ; and that, though it should fly never so far off, it would
return forthwith into his hand as often as he threw it." " Hammaren gaf hanu

38 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

Thor og tuad ai mundl blla throl ad llsta og if hann yrpi hunum til tha mundi
hann aldri missa og aldri fliuga so longt ad ei mundi hann soetia hond heim." —
{Edda Mythologica lix. Apud. Stephan. in not. uherior. in Sax. Gram.) The
name of this weapon was " Miolner," which means "the crusher," and with it
Thor accomplished labours quite as wonderful as those of his southern prototype.

Now this weapon, although called Clava by Saxo, appears to have been
regarded as of a hammer shape from a very early period ; for it is related by
Snorro, that when Haco, one of the first Christian kings of Scandinavia, was
presented by his pagan subjects with the horn of Odin, and made upon it the
sign of the cross, Sigurd, one of his counsellors, excused the apparent profana-
tion, by telling the people that this was the sign of Thor's hammer, which the
king had drawn upon the sacred vessel. — {Snorro Sturl. \. iii. c. 18.) Accord-
ingly it is found that a T, or hammer-shaped instrument, exhibits the peculiar
flight of the Cateia in a very perfect manner. The cross on many Scandinavian
monuments, of an age apparently anterior to the introduction of Christianity,
has been long since conjectured by Keysler and others to be a representation of
this instrument. Hence it appears very probable that those double crosses which
appear on the British coins of Cunobeline, and the single crosses in the hands of
some of the Anglo-Saxon kings, (see Ruding,) are intended for weapons of
the same description, (PI. II. figs. 7, 8 ;) especially as it is found that instru-
ments formed on the same model exhibit the reverse flight equally well with the
common Boomerang ; and as the tradition of cruciform missiles, called cpioy^ac,
having been used in war, is still preserved in some of the older Irish remains
relating to Cuchillin and the Finns. It is true there is no peculiar flight
ascribed to these weapons in the romances, at least so far as has been ascertained ;
but it is a remarkable fact, that the throwing of wooden crosses, having all the
properties of the Boomerang, became a general amusement among the children
of the lower orders here, immediately after the first introduction of the Australian
instrument ; and that this practice cannot be traced to any inventor among them,
but appears to have sprung up spontaneously, as the revival of something that
had been long disused, but was not altogether forgotten.

The ascertaining of these varieties in shape may, perhaps, prove useful in
furnishing data for an investigation of the law which governs the flight of such
missiles. For although, generally, any flat lamina, dismissed with a rotatory

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 39

motion, will descend nearly in that plain at which its projectile force leaves it,
and will, therefore, if projected upward, exhibit a reverse flight, yet the peculiar
ascending flight of the Boomerang is found only to belong to varieties of the
curved or angular instrument. To the property first alluded to, Plutarch appears
to refer, in a remarkable passage in his inquiry, " Why the Pythian ceased to
deliver her oracles in verse," a passage which would lead to the supposition that
he had himself witnessed the flight of some such missile. "For, " he says, "as
the whirling of bodies that fall circularly downwards is nothing violent, but when
upwards, forced by a preternatural circumgyration and whirlwind violence, two
curling impetuosities become incumbered in one irregular circumrotation ; so
that divine rapture which is called enthusiasm," &c. — (Phillips'' s Translation.)

Here, again, as in the classic tradition, the evidences are accompanied by
such marks of uncertainty, as imply a source in the most remote antiquity.
Thus, while the form alone of the crosses of the Irish romances has been noticed,
the peculiar flight, which ought to have been attributed to them at the same
time, is transferred to a fabulous javelin like that of Cephalus, called the plac
lugaid, or spear of Lewy, which is the subject of other and separate legends.

Thus, also, in Scandinavian history, the property of the hammer of Thor
must have been considered fabulous in the time of Saxo, who regards the similar
flight of a javelin as something preternatural. In describing a battle between
Hacquin and King Harold Blaatand, he gives the following account. " A won-
drous prodigy suddenly befel in the fleet of Hacquin ; a javelin was observed to
fly overhead, with so irregular and wandering a course, as to fill the minds of
the beholders with no less awe than astonishment : for, carried hither and thither,
with uncertain doublings, (in diversas partes dubiis reflexibus agitatum,) it
appeared to be exploring a place for inflicting its wound. Which miraculous
sight, while all were gazing at in horror and suspense, uncertain what a circum-
stance so extraordinary might portend, descending suddenly, it transferred the
common danger to the sole head of Hacquin. Some think it was Gunnilda, the
mother of Harold, who had procured the javelin by witchcraft, and thus took
vengeance on the conquerer of her son," — (Sax. Gram. 1. x.)

40 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

Vir.— OF THE REMAINING NAMES OF THE CATEIA,— CAIA AND KAILE,

AND OF ITS ORIGIN.

Among the different names by which weapons of this species have been so
far sought to be identified, viz. Cateia, Teuton, Aclys, Ancyle, and Clava, there
is none which approaches either of the appellations by which the Australian
instrument is at present known. Now, however, that the close connexion of the
crooked implement and club has been established, the following very remarkable
testimony of Cluverius, regarding the latter, may be adduced. " The club,"
he says, " is still the only weapon known to many nations of the new world.
Where Horace has called it Caia, as Isidore states, I cannot tell. This, how-
ever, I know, that at the present day, the Lusatians, a Sclavonic nation of
Germany, call the club Kai,; and that the Poles, also a people of Sclavonic
stock, call it Kiy ; but the Germans call it Kaile, and Keile, and Kiele,
according to their different dialects : and whether these be all of one and the
same original, I know not." — {Cluver. Germ. Antiq. p. 304.)

With regard to the apparently corrupt passage from Isidore, Lipsius well
suggests, that for " Horatius," we should read " Dorcatio," a lost writer quoted
elsewhere by Isidore. That Caia, the Latinized Kai of Cluverius, is the true
reading, appears beyond question, whoever the writer may be that Isidore refers
to. As to the meaning of Kai, it seems to be the radix of the entire family of
words hitherto investigated, and to signify essentially something crooked.

Kay and kayol are the Welsh cavus ; kae is the German hallium, or circular
enclosure ; key, jetty, and wharf have all their origin from verbs, of which
torqueo is the common equivalent : hence it might, perhaps, be inferred that /cat
in the Greek has the same force as vau in the Hebrew, the link, namely, by
which one part of the subject is connected with the other.

As to the kiele of Cluverius, it also is clearly of the same stock ; we have
it in our keel of a ship ; the ceola, or curved vessel itself, of the Anglo-Saxons;
the galleon of the Spaniards ; and the English yawl and galley. We have it in
the Latin qualus, and Welsh kailh, synonymous with the Irish kliav, the Belgic
kit, and the Latin carina and lancet., in all which, the same signification is con-
spicuous. Without a needless accumulation of examples, kiele may be taken as
likewise descriptive of a crooked weapon ; and when it is considered that this

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang, 41

appropriate name is almost Identical with the word kiliee, at present used by the
natives about Swan River to indicate the same weapon, it cannot but excite spe-
culations of great interest. And, wide as the difference is between the cultivated
Germans of the present day, and the savages of Australia, it may not, perhaps,
be too much to hope that this very striking point of coincidence may yet lead to
the. development of a perfect link between this widely and long separated race,
and their kindred of the human family elsewhere.

We are now in a condition to form a conjecture as to the origin of the wea-
pon. We have seen the ^Xvait fustis bent into the crooked clava ; then flattened,
and used as a reciprocating missile : the elongation of the shorter limb of this
clava would give the perfect Cateia, " Eminentibus hinc et hinc acuminibus,"
and thus the Boomerang would appear to be immediately sprung from the first
offensive weapon used by man. Its place in the order of the invention of other
weapons may be now investigated.

VIII.— OF THE COMPARATIVE ANTIQUITY OF THE BOOMERANG AND

SPEAR.

It is a remarkable fact, that the names of the straight spear, in various lan-
guages, are either identical or radically connected with the names under which
the weapons of this family have been hitherto found.

Thus, identical with Cateia are the straight Tudesque Cateice of Servius,
" Cateice autem lingua Teuthisca hastas dicuntur," (Serv. in ^neid. 1. vii.
v. 741 ;) the straight Persian Cateia of Johannas de Janua, "Cateia telum dicitur
lingua Persarum et ut dicunt, lancea vel hasta," (Catholicon ;) and the kaduayu
of Lhuid, whiph is the word still in use among the Welsh for a straight spear.
To these may be added, as evidently looking to a like origin, the chcBts of the
Hebrews, the kadmos. of the Cretans, (Megisser,) and the got of the Irish, all
having a like signification.*

• An instance of the use of the word Cateia in the sense, as there would appear reason to

believe, of a straight projectile, is furnished by the poem of Abbo, " De Obsessa a Nortmannis

Lutetia Parisiorum," printed with the works of Aimoinus, " De Gestis Francorum." The siege

described in the poem took place in the year 885, and Abbo was an eye-witness. The word Cateia

vol,. XIX. F

42 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

The only names of the straight spear which appear to be connected with the
word Aclys, are the Latin jacw^Mm, and the Sclavonic ^iA^e/. To the radix of
Ancyle are clearly referrible Xayxos, fyx°^) cyx^'^j among the Greeks, and
lancea among the Gauls. It is worthy of remark, that iyyps has been applied
to the sword, and that the Latin equivalent, ensis, properly means the curved
cimeter.

Clava, also, Is a name common to the two classes of weapons, glavea in the
old Latin signifying a straight spear : to this also, by a return to the original
element cam, (from which clam and all its derivations are formed,) may be
referred the Irish gavla, and the English jauefow.

Identical with Caia are the Irish gai, the Welsh guayu, and the Cornish
and Armorican guayu; and perhaps to the same root may be traced the Gaulish
gcBsa, the Irish keis, and the German speiss.

The Irish cuaille, signifying a straight javelin, is in like manner identical
with one of the present names of the crooked weapon ; and it is not impossible
that, as the Oscans and iEolic Greeks said pedor for quatuor, pilum itself may
be a form of kilum, especially as we find several words of this family, pile, pole,
pill, pale, pail, for example, applied indifferently to signify a straight instrument,
and a spherical body or vessel.

occurs in three different passages : first, where Abbo, personifying one of the towers of the city,
represents it looking abroad over the hostile array brought against it.

" Prospiciens turrisque nihil sub se nisi picta
Scuta videt, tellus ab els obtecta latebat :
Inde super cernens lapides conspexit acerbos
Et diras, ut apes, dense tranare Cateias."

Again, in the same book ;

" Pila dabat, rupesque simul, celeresque Cateias
Plebs inimica deo."

1. i. p. 409.

1. i. p. 416, G.

And again, in the second book, speaking of Count Otho, one of the defenders :

" Fossata volatu
Transiliit propero, clypeum gestensque Cateiam."

1. ii. p. 419, C.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 43

Hence the inference seems unavoidable, that, as the same names, and names
radically connected, are found applied to those two distinct classes of weapons,
and as these names are all radically and properly descriptive of the one class, but
not at all descriptive of the other, that family of crooked missiles, the charac-
teristic names of which are thus applied to the family of straight projectiles, must
necessarily have been the older of the two, and the other must have originated
from it. In other words, we must conclude that, as the club appears to have been
the parent of the Boomerang, so does the Boomerang appear to have been the
parent of the spear.

This conclusion, startling as it is, receives further confirmation from the fact,
that the invention of the spear has been attributed to the Etruscans, who, although
a very ancient people, were never looked on as the aborigines of their country ;
and it is very remarkable, that the name coris, which they are stated by Festus to
have given to the weapon, (the quiris of the Sabines,) is so evidently associated
with the idea of curvature, that the Quirites, Curetes, and Coryhantes, have
been argued to be the same, on the common affinity of these titles with the x^poy,
or circular dance of the priests of Mars. — (Pezron, Antiq. of Nations, c. iii.)
Again, this coris of the Etruscans is one of the few words of their dialect which
correspond with any part of a known language, being clearly identical with the
Irish corr, still signifying a straight spear, and hitherto offering an unaccountable
anomaly, as being the only one of a very numerous family which is not palpably
applied to something curved or circular. For example, the Ordnance Survey of
Derry contains a list, from O'Brien's Dictionary and Cormac's Glossary, of
upwards of thirty words having cor for their radix, every one of which involves
this peculiar meaning. A few of the most striking are subjoined.

" Cor, a twist, a round or circular motion, a round hill ; Latin, curvus.

Cor, a choir ; Latin, chorus ; chorea, the circular dance.

Cor, a round pit of water.

Coire, a c.auldron, a whirlpool.

Caor, a berry.
- Cuar, crooked.

Corran, a reaping hook," &c. &c.

Ordnance Survey of Londonderry, p. 212-13.

f2

44 Mr. FERausoN on the Antiquity of the Kiliee or Boomerang.

IX._OF THE TRANSIT OF THE NAMES OF THE CURVED MISSILE TO THE

STRAIGHT WEAPON.

It has been seen that the Aclys and Ancyle, two varieties of the curved
weapon, were thrown by means of an amentum or attached thong ; and that the
Clava, also, was thrown in this manner, appears from various representations both
of the straight and crooked club having such an appendage, (PL II. fig. 11.)
Now this, also, was the mode in which several varieties of the spear were thrown
among the ancients, and in which a species of it is still thrown among the
Australian savages. — (Cooke's Voyages towards the South Pole.) The word
lancea itself has been derived by Isidore from this peculiarity, and ey^os quasi
Xay^os is a received etymology for the Greek weapon. The tragula appears
to be so thrown in Caesar, {De Bell. Gall. 1, v. cxlvi.) ; and the frequent allusions
of other classic writers shew that the amentum was an usual appendage to the
spear in general. Hence there would appear a probability, that the common
name may have passed from one weapon to the other, through the medium of
the common apparatus by which both were thrown ; a probability which is con-
siderably increased by the fact, that the amentum itself among the Greeks was
also called ayKvXr], whence their ixeaayKvXov, or spear thrown by the ancyle
attached to its middle. Whether this have anything to do with the vinculum
of the Latins ; and whether aclys may, in like manner, have given name to the
Belgic schacckel, our shackle ; cateia to the Belgic catte, a chain ; and caia to
our guy, or attached rope, I leave to the consideration of the curious.

X.— OF THE MODES OF THROWING THE CATEIA, Etc., AMONG THE

ANCIENTS.

Whatever uncertainty may attend this portion of the inquiry, it is certain
that the curved weapons under consideration were thrown by divers apparatus ;
and a consideration of what can be collected respecting these may, perhaps, fur-
nish some practical hints towards devising similar appendages to the weapon
as we have it at present.

The passages always quoted shew that the Aclys was thrown by means of a

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 45

thong, and the expression of Servius, " teli genus quod per flagellum in immen-
sum jaci potest," proves that this was not used in the retraction of the weapon,
but must either have left the hand of the thrower along with the Aclys, or have
been used as a sling, from which it may have been let slip, when it had acquired
sufficient velocity. A horseman is represented on one of the British coins given
by Ruding, (PI. II. fig. 9,) who appears to be whirling an instrument of this
sort round his head by a similar appendage. The same collection, also, affords
a curious illustration of the use of the cruciform missiles already alluded to,
(PI. II. figs. 7, 8.) Here the ancient Briton is represented throwing his
criosach from a sling, such as we may suppose CuchuUin, and the other heroes
of Irish romance, to have done. The sling appears to be attached ; but from the
application of the epithet "eyed," or perforated, to the weapons of the Irish
poems, there is reason to suppose that the artist intended to represent the missile
here as on the point of slipping from the extremity of the thong.

Another apparatus used in hurling the Clava, if we are to credit the testi-
monies of northern mythology, was a haft or manubrium. It was by means of
a haft of this sort Thor threw the miolner ; and the efficacy of the apparatus is
attested by various mythi, one of which, preserved by Saxo Grammaticus, gives
the following characteristic account of a battle between Balder and Hother, in
which a band of the Scandinavian deities took part with the former. " Then
might be seen a battle waged by human against divine belligerants ; for Hother,
grit in his impenetrable mail, fearlessly assailed the thickest battalia of the gods,
doing all that mortal man might against immortals. But Thor, upon the other
hand, with such whirls of his club as had not been experienced till then, (inusitato
clavcB libratu,) swept through every obstacle presented against him. There was
no armour which did not yield before his strokes ; no warrior who could sustain
them, and live. Down went all he touched, the hurled oak bursting through
helmet and shield. Bulk of body, and stoutness of heart, alike availed not.
Then, indeed, the victory had fallen to the gods, had not Hother, perceiving the
day to go against him, run, and rendered the club useless by cutting off its haft,
(clavam prceciso manubrio inutilem reddidisset,) deprived of which weapon,
the gods betook themselves to sudden flight," &c. — (Sax. Gram. Hist. Dan.
I. xvi.)

Now, it is stated in the Edda, that among the most precious things possessed

46 Mr. Ferguson on the Antiquity of the Kiliee or Boomerang.

by Thor was his gauntlet, which he always put on when he would throw the
miolner. And there appears some probability that this and the manubrium of
Saxo are one and the same, for the haft is not mentioned in the Edda, nor the
gauntlet in the works of Saxo, while both describe the miolner. If so, it might,
perhaps, be inferred that this was a sheath not for the protection of the hand, but
for the reception of one limb of the weapon ; and hence it is suggested, that an
elastic haft, having a sheath attached, might also be found serviceable in throwing
the Boomerang.

Many of the foregoing inferences will, doubtless, appear in a high degree
speculative ; and the writer is conscious, that, in pushing the inquiry in some
directions to the length it has gone, the bounds of strict induction have been
very closely approached ; still it is submitted, that if the first step of the argu-
ment, namely, the identification of the Cateia with the Australian weapon, have
been taken on sure ground, it will not be possible to stay the subsequent progress
of the inquiry. And, that this step has been taken with great, indeed with
extraordinary, certainty, appears as well from the minuteness with which all the
peculiarities of the weapon in question are described in the passages already
quoted, as from the fact that unquestionable representations of the Boomerang
are found on ancient monuments. The representations in PI. II. figs. 1 and 2,
taken from Sig. Rosellini's " Egyptian Monuments," cannot be mistaken ; and
the reader who will take the trouble of referring to Mr. Wilkinson's work on the
same subject, will there find still further confirmation of the acquaintance of this
most ancient people with the very implement in question. In the latter instance,
parties are represented throwing missiles of a form which, from experiment it is
now certain, must have produced a reciprocating flight, at birds, reminding us
strongly of that passage of Strabo, (1. iv. pp. 196, 7, Ed. Causab.,) where he
describes the Belgae of his time as using " a wooden weapon of the shape of a
grosphus, which they throw out of the hand, and not by means of an ancyle, and
which flies faster than an arrow, and is chiefly used in the pursuit of game."
So, also, it is difficult to assign any other use to the instrument appearing in the
hand of the Belgic Briton represented in PI. II. fig. 6.

Mr. Ferguson on the Antiquity of the Kiliee or Boomerang. 47

If any certainty could be had that the notices so far collected were all that
antiquity could furnish on the subject, a new and very wide field of speculation,
of perhaps a still more interesting character, would be opened, in the endeavour
to trace the international resemblances between those people known to have
used such weapons in the old world, and the tribes who still retain the use of
them in the new. Even on the scanty materials here brought together, there is,
however, sufficient to excite serious attention, in the fact, that amongst the ancient
nations using the Cateia and its cognate weapons, certain peculiar characteristics
are distinctly traceable, such as the prevalence among them, from the earliest
periods, of Amazonian habits, and their being in almost every instance of the white
variety of mankind, and of the Xanthoiis family of that variety, characteristics
which point, in a very marked manner, to an Indo-European origin.

Now, there are in Australia two distinct races of men, one of which is clearly
of the white variety, as appears from the coloured drawings which accompany
M. Peron's Voyage to Van Dieman's Land and New South Wales, in 1824.
What, then, shall we say ? Has the European or Indo-European weapon, with
its characteristic name, been introduced into Australia by these lighter-com-
plexioned islanders ; and are these far-separated savages members of the same
great Japhetic stock of whom we have this testimony from the oldest and most
authentic of human records, *' By them were the isles of the Gentiles di-
vided."— ( Gen. c. X. v. 5.)

49

III. On the Egyptian Stele, or Tablet. By the Rev. Edward Hincks, D. D.
{Communicated by the President.)

Read June 28, 1841.

Of the Egyptian monuments that are collected in European museums, there
are none which ought to attract more attention than the steles, or funeral tablets ;
and yet I suspect that there are none which are more generally overlooked.
They are certainly not so well calculated to arrest the attention of the uninitiated
observer as many other objects ; but they are much more likely to afford infor-
mation. They in general record facts ; and it not unfrequently happens that the
facts recorded throw light on the history of the country, or on the state of society
in it. Sarcophagi, on the other hand, mummy cases, sepulchral figures and
cones very seldom determine any thing but the name and parentage of the
deceased person whom they commemorate. The copious inscriptions, with which
the former are often covered, contain merely extracts from the Ritual, or other
general formulas, in which the names and offices of the deceased and of his
parents are alone peculiar. There are some scarabaei, on which historical facts
are recorded, and which are somewhat of the nature of medals. There is one,
for example, in the museum at Liverpool, of which there is a duplicate at the
Louvre, which records the name and parentage of the Queen of Amenothph III.,
and the northern and southern limits of his kingdom. These were probably
sculptured in considerable numbers on the occasion of the marriage of that prince,
which must have taken place when he was a mere child ;* and which was in all
probability an important political event, as transferring the actual government

s

• At the death of his father, this Amenothph and a twin brother, who shared with him the
nominal sovereignty, were infants in arms ; yet the scarabaei recording his marriage, are dated in the
eleventh year of his reign.

VOL. XIX. Gf

50 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

from his mother to his wife or her father. There are other scarabaei of a similar
nature ; but the great majority of them are funereal, containing the name of a
deceased person (or sometimes a blank for a name, the scarab^cus having never
been appropriated), followed by a speech from the Ritual respecting the heart of
the speaker. The tablets, on the contrary, though essentially funereal, and con-
taining much that is of a general nature, have, for the most part, a great deal
which is peculiar to the deceased person. In this, they resemble our tombstones ;
and it is curious that they are of the same shape as those which we set up at the
head of graves, and that they were set up in similar positions. Some tablets
mention the King of Egypt whom the deceased person served, and the capacity
in which he served him ; some record the more important events in his life ;
some are dated either in the body of the inscription or at the top of the tablet,
with the year of the king's reign, and often with the month and day of the
month; and in some rare instances (would that they were more frequent!) the
dates of the birth and death of the deceased person and the length of his life are
all stated. I am aware of but two such tablets ; but among the many which are
in existence, that have not yet been examined, it is likely that there are others ;
and the immense importance of such tablets, which are probably the only means*

* Another means of equal value would exist, if we had records of the years of kings' reigns, in
which the cyclical panegyries were held. These panegyries occurred at intervals of three years; ten
of them forming a series, the TpiaxoyTasTupi; of the Ilosetta stone. A tablet has been found at Silsilis,
stating that a certain person presided over the first or grand panegyry in the thirty-first year of
Rameses the Great, the second in his thirty-fourth year, the third in his thirty-seventh year, and
the fourth in his fortieth year. Another tablet records that another individual presided over the
sixth panegyry, in the forty-sixth year of the same king. Any of these records would prove that
the first year of Rameses the Great was the first year of a Tfiaxo>-asT>ipK ; and, of course, if the prin-
ciples which Ihave endeavoured to establish elsewhere be correct, in a year B. C. of the form 1767 —
30 k. If now a record should be found of any given panegyry of the series occuring in any given
year of any other king, the exact interval between the commencement of the two reigns could be
determined from an approximate interval. Suppose, for example, that a record should be found of a
grand panegyry occurring in the twenty-sixth year of Amenothph III. Knowing that the commence-
ment of his reign was above 100 years before that of Rameses the Great, we should infer, that the
interval between his twenty-sixth year and the first of Rameses, was ninety years ; and, of course,
that the interval between the beginnings of the two reigns was 115 years. Unfortunately, with the
exception of the two tablets at Silsilis, I believe no record of this kind has been discovered.

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 51

by which the chronology of the Egyptian kings can be settled with accuracy,
renders it highly desirable that they should be sought after.

In order to show the utility of tablets of this description, I will enter into
some details respecting the two that are known ; and I am the more disposed to
do this, because a false inference has been drawn from one of them, and 1 believe
the other has not been noticed by any one conversant with hieroglyphics.

One of these tablets, which is in the museum at Florence, records, that a per-
son named Psammitich, was born in the third year of Necho, the tenth month,
and first day ; that he died in the thirty-fifth year of Amasis, the second month and
sixth day ; and that he lived seventy-one years four months and six days. When
this tjiblet was first noticed, it was carelessly stated, that it counted seventy-one
years from the third of Necho, to the thirty-fifth of Amasis ; and from this it
was inferred that there were thirty-nine years between the first of Necho and
the first of Amasis. If, however, we take into account the months and days, we
shall see that the true interval was forty years. This interval comprehends the
reigns of three kings, the joint length of whose reigns is stated by Herodotus to
be forty-seven years ; by Africanus, from Manetho, to be thirty-one ; and by
Eusebius, who professes also to follow Manetho, to be forty-eight. We may
judge of the degree of credit due to the Greek authorities by the gross blunders
which they have, all of them, been detected in making, in this instance, where
the truth is known from a cotemporary monument. We may likewise test their
accuracy by the length of reign which they assign to Cambyses in Egypt.
Herodotus, Diodorus Siculus, and Eusebius, are all agreed that he conquered
that country in the fifth year of his reign ; and of course that he reigned over it
only three or four years. Africanus alone gives him a reign of six years ;* but
in this he is corroborated by the express testimony of a cotemporary monument,

* Ka5ft|Si/cr>){ IT» t T?5 iavTov ^owiXEia; Xlef(ra» iPeu/iKivait, Alyuirvov eri) r'- So the text of Africanus
exists in all MSS. and editions ; but for i I would read 9' ; correcting a mistake, into which a trans-
criber might easily fall, and rendering the statement perfectlj' consistent with truth. I would also
correct the text of Africanus, by substituting ir for j-', as the length of reign of Necho II. This
mtdces him agree as to the length of that reign with Herodotus ; and as to the sum of the three
reigns with the Florence tablet ; for, where reigns are reckoned by complete years, months
and days being neglected, the sum of sixteen, six, and nineteen years may be very well reduced to
forty.

c2

52 Rev. Edward Hincks on the Egyptian Stele, <yr Tablet.

published by Mr. Burton ;* and also by an obvious inference from the narrative
in 2 Kings, xxiii, taken in connexion with the tablet above mentioned. Necho
was king of Egypt before the death of Josiah, in 610, B. C. ; but this could not
have been the case, if Cambyses had only conquered Egypt in 525, B. C, as
Amasis only reigned forty-four years, and Necho and the intermediate kings only
forty. The true date of the death of Amasis, and of the conquest of Egypt by
Cambyses, must therefore be 527, B. C.

The other tablet to which I have alluded is of the Ptolemaic age ; and its
dates are useful, not in determining the chronology of the reigns, which is
already known from other sources.f but in ascertaining the power of a numeral
character, which occurs for the first time in inscriptions of this age ; and in de-
termining to which of the Ptolemies a cartouche with certain titles belonged.
This tablet belongs to Mr. Harris, of Alexandria, and it has been published by
Mr. Sharpe, in the seventy-second and seventy-third Plates of his Egyptian in-
scriptions.

The person commemorated by this tablet was a priest at Memphis, named
Psherin- phthah, son of a priest, who held a very high sacerdotal office, the name
or precise nature of which I have not yet been able to ascertain. He is said to
have been born in the x -j- 5 year of a Ptolemy, whose cartouche is

:i: ^ m

I have used the letter x to represent the unknown numeral, a bird's head, which
is here accompanied by five vertical lines. He was born in the second month
of this year, on the twenty-first day. When he was thirteen years old, his father
died. He was promoted by Ptolemy " the new Osiris" (the Neo-Dionysus of
the Greeks), in the tenth year of his reign, to the sacerdotal office which his
father had held. After he had completed his forty-third year, he had his first

* An Egyptian functionary is said to have served under the Persians for six years of Cambyses,
thirty-six of Darius, and twelve of Xerxes. — Burton Exc. Hier. 8.

f It appears from Ptolemy's canon, that the first year of Lathyrus was the 632nd of Nabonassar ;
the first of Neo-Dionysus, the 668th of Nabonassar ; and the first of Cleopatra, the 697th of Nabo-
nassar. Alexander's first year was 635, when his brother Lathyrus was driven to Cyprus ; and the
latter was restored to the throne of Egypt about 660.

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 53

son, who was named Imotlipli. He died, aged forty-nine years, in the eleventh
year of Cleopatra and her son Caesar, the eleventh month and twentieth day ;
and he was buried in the twelfth year on the thirtieth day of the first month.
The usual interval between the death and burial was seventy days, and we see
here that the Epagomena3 were not counted, being strictly dies non. His death
took place, as appears from Ptolemy's canon, at the close of the 707th year of
Nabonassar ; and as he lived about forty-nine years, and was born at the beginning
of a year, the year of his birth must have been the 659th of Nabonassar. This
was the 25th year of Alexander, and certainly before the restoration of Lathyrus ;
as there is a papyrus at Berlin (Kosegarten, Plate XH.) dated in the twenty-sixth
year of Alexander, the fourth month and nineteenth day ; it is therefore certain
that the cartouche above given, belongs to Ptolemy Alexander, though it does
not contain his surname ;* and that the bird's head, when used as a numeral, sig-
nified twenty.

It is a curious circumstance, that the tablet of the wife of this person, who
was also his half-sister, is in the British Museum. It has been published by Mr.
Sharpe in his 4th Plate ; and by combining the information which the two
tablets afford, we obtain much insight into the history of this family, which is
perhaps not a bad illustration of Egyptian family history in general. It appears,
that, after the death of the father of Psherin-phthah, his mother, Ho-onkh,
married another priest named Hapi, by whom she had a daughter, Te-imothph,
and a son, Imothph, who survived his half-brother and sister, and erected both
their tablets. The first husband died when his son was thirteen years old, and
therefore in the fifth year of Neo-Dionysus. Five years after, in his tenth year,
and in the fourth month, Te-imothph was born ; and in his twenty-third year,
and in the eleventh month, she married her half-brother. The birth of their
son, Imothph, is recorded as having taken place in the sixth year of Cleopatra,
and in the eleventh month, just twelve years after her marriage ; and she died
in the tenth year of Cleopatra, the eighteenth day of the fifth month. Her age
at her death is not stated on the tablet ; but it must have been twenty-nine

* Unless indeed the sculptor committed the mistake of using the cartouche of the exiled, but
afterwards restored king, de jure, instead of that of the intrusive king de facto. He might easily
have done this after an interval of about fifty years.

54 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

years and a few weeks. By comparing the dates of the births of her son and of
his father, the interval between them is found to be forty-three years and eight
or nine months. This accords with the statement on the father's tablet : " I
lived forty-three years before a son was born to me." Whether he had or had
not daughters previously, is not stated. As they could not fill his sacerdotal
office, the existence of such would be considered unimportant. That office was
not strictly hereditary ; for it appears from this tablet, that it was conferred by
the sovereign. It is probable, however, that if it was not conferred, as a matter
of course, on the heir of the former possessor, as soon as he attained a suitable
age, it was limited to the members of a few particular families ; and a desire to
preserve the purity of the priestly stock, as well as to prevent it from becoming
too numerous, may have led to such unnatural marriages as that of Psherin-phthah
and his sister. Similar marriages were, however, common among all ranks of
the Egyptians. It appears that the sacerdotal office, whatever it was, was con-
ferred on this person, when he attained the age of eighteen. This may have
been the age at which he was considered capable of filling it, and it may have
been kept vacant for him ; but it is also possible that it may have been held in
the interim by some other person, on whose death it reverted to the son of the
former incumbent.

In the remainder of this paper, it is my intention to resolve the inscription,
which usually occurs on these tablets, into its several parts. I will treat of all
these parts in succession ; pointing out, as I go along, the criteria derived from
each, by which the age of undated tablets may be ascertained ; and likewise
directing the Egyptian student to the parts in which he is to look for informa-
tion respecting the person commemorated.

The following is the skeleton of an inscription in the most usual form :

/wwv

\-lJ „ Pronoun, / \ « / \ ♦ *

/W\/y " 3rd person, f ■ \ -^ / » \ Mil ▼*

which I translate : " An act of homage to A ; he has \or, as the case may be"]
given B unto C, who says D." The blank at A is filled up with the names
and titles of deities ; that at B with an enumeration of gifts ; that at C with the
name and description of the deceased person ; and at D is the speech attributed

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 55

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

I now remark, in the first place, that no record of facts, and, in short,
nothing which would not answer equally well for any tablet, is to be expected
till we come to C. The part before this is only valuable, as it may aid us
in the study of the language, and as it may lead us to know the age of the tablet,
supposing it to be without a date. To assist in this, I propose the following
criteria, the result of a careful examination of a great number of tablets of
known age.

1. If the lowermost of the two central introductory characters be omitted, the
semicircle being placed over the triangle, the tablet may be presumed to be of
the most remote antiquity. This is the case in the tablets, which have been
found in the neighbourhood of the pyramids, and which bear the names of their
builders, Cheoph (p]ln) ^^^ Kephren (i^ioy!^). But if the introductory charac-
ters, being all present, be grouped in a different manner from what I have
represented above, the tablet is not of very great antiquity. I speak, of course,
comparatively. I mean, that I have met with no tablets, in which the initial
group was differently arranged, which there was any reason to suppose anterior
to the so called eighteenth dynasty.

2. If the initial group be followed by the preposition N to, the tablet can
have no pretensions to antiquity : it is probably Ptolemaic or Roman.

3. If the names of more than one deity are combined in the space A, the
tablet is not of the most remote antiquity. The earliest dated tablet, in which
I have met this combination of divine names, is of the thirteenth year of
Amenemhe II., the king whose cartouche was the first on the second line of
the tablet of Abydos, at the time when that tablet was first copied. It has
since, I believe, been broken off. If more than one deity be mentioned in
tablets more ancient than this, the initial group is repeated for each ; being,
however, sometimes mutilated at its commencement for all after the first.

4. The mention of Osiris- Apis, or Apis-Osiris, the Serapis of the Romans,
among the deities enumerated in A, is a proof that the tablet is Ptolemaic or

56 Rev. Edward Hincks on the Egyptian Stele or Tablet.

Roman. I do not think that any other inference can be safely drawn from the
names of deities introduced.

5, The mode of writing Pente-pamente, a common title of Osiris, which
occurs very frequently in A, furnishes more than one criterion. The use of a
nose (the old Egyptian name of which was Phente) for the former part of this
title was not introduced till the latter part of the eighteenth dynasty; and it is,
of course, a proof that the tablet on which it occurs is not of very great anti-
quity. In the most ancient tablets, but not in them exclusively, this is written

/WV TTT

PNT

which is often reduced by abbreviation to the first character, a combination of
water jars ; either alone or with the small semicircle, which so commonly accom-
panies a single character when It stands for an entire word. The use of the
square for P in this word is, comparatively speaking, modern.

6. The absence of a bird from the usual group representing Amente, whether
in this title or elsewhere, is a proof that the tablet is not more ancient than the
middle of the eighteenth dynasty. Anciently, the group without the bird, or
the single character to which it was frequently reduced, signified " the west ;"
and the bird restricted the signification to "the divine west," or "the west of
souls," that is, the Amente or Hades. About the middle of the eighteenth
dynasty the bird was omitted. I have observed that, during a short interval of
time previous to its omission, it had the usual sign of the plural number annexed
to it. Should the word Amente occur on any tablet In that particular form, I
should scarcely hesitate as to its being of the reign of Amenothph II., or one of
his immediate predecessors or successors.

7. The omission of the connecting verb between A and B Is, I think, a
positive proof that the tablet is very ancient. We must not, however, conclude,
that the insertion of the verb is a proof of the contrary ; as it is found in tablets
of the earliest age. The fact seems to be, that so long as the initial characters
were grouped in ihQ primitive manner (see 1), they might be translated in two
ways ; either " an act of homage for bounty to A," in which case the verb and
pronoun were required before B; or "an act of homage ; A has given," in which

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 57

case B should follow at once. It is well known, that the subject of an Egyptian
verb, whether noun or pronoun, was always placed after it.

The connecting verb is followed by the pronoun of the third person, required
by the contents of the space A. If a single male deity be there mentioned, the
horned serpent, corresponding to the Hebrew i, is invariably used ; if a single
female deity be mentioned, one of the usual characters for S is used ; and if two
or more deities be mentioned, the plural pronoun SN, with three small lines as
a determinative sign, is employed. For convenience of grouping, a hand hold-
ing a small triangle is frequently substituted for the triangle itself. Thus, we

liave ^ y\

" he has given."

The contents of the space B were supposed by Dr. Young to be offerings to
the gods, instead of gifts of theirs to the deceased person ; and I believe the
nationality of some English antiquarians leads them still to persist in this mis-
take. That it is such must be evident to any one who admits the first prin-
ciples of hieroglyphic interpretation, from the use of the preceding verb and
pronoun, as just explained. It is also evident from an examination of the con-
tents of B ; for, though many things there enumerated may be supposed to be
given to the gods, as well as by them, this is by no means the case with all.
We frequently meet among the gifts " a good burial ;" — " that he may go in
and go out in Noutehir, without being turned back at the gate of the abode of
glory ;" — " that he may adore the Sun in Heaven ; that he may give aid in battle
to Sebh upon the earth ; that he may speak the truth (i. e. be justified or pro-
nounced righteous) before Osiris in Amente." These are not the kind of gifts
that a man would offer to a deity.

It may be asked, why I have translated the verb between A and B in the
past tense, rather than in the optative mood. The latter appears more natural ;
and, as the letter N, the usual sign of the past tense, is not affixed to the verb,
I should certainly have preferred " may he give ;" did I not feel myself con-
strained by the authority of the Rosetta stone to adopt the other translation. In
the fifth line of the hieroglyphic text of that inscription, we have an expression
precisely similar to that in the tablets, in which the N of the past tense is equally
wanting ; and in the thirty-fifth line of the Greek version the verb is translated
in the past tense. This appears to me decisive on the subject. The objection,

VOL. XIX. H

58 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

which may occur to some, that the gifts enumerated were, in part at least, to
he enjoyed hereafter, appears to me to have no force ; and in truth the same
objection might be made against the passage on the Rosetta stone ; for among
the "ifts of the gods and goddesses there mentioned is " a kingdom estabhshed
to him and to his children for ever." The answer is easy. The gift was past,
though the enjoyment of it was future.

8. Very little dependence can be placed on the contents of B as determining
the age of a tablet. It may, however, be stated that the abbreviated group.

,i

I

which I believe means "the appointed nourishment of meat and drink," and
which begins B in almost all tablets of the reign of Osortasen I., and of his suc-
cessors to the very latest period, has not been met with, so far as I am aware, in
any tablet of an earlier reign. Before his time the characters for meat and drink
were placed after the words Hre taoue, " the appointed provision," or their abbre-
viation as above given ; and accompanied either by a circle, representing a cake
of bread, or by a long figure, resembling the prismatic spectrum, representing
a number of such cakes. This character, however, is not to be translated in the
present instance "bread" or "cakes," but "of all sorts." The Egyptian word
having that meaning, being homophonous, or nearly so, with the word signifying
bread, is often represented by the symbol for the latter ; and it is so, I conceive,
in this connexion.

The group which occurs between B and C was naturally translated " for the
sake of" by those who imagined that B were offerings to the gods. As the
deceased person could not make these offerings himself, they conceived that the
survivors made them for his sake. It appears to me unaccountable that any
should have retained the old translation of this group, who perceived the mistake
in which it originated. I take the literal meaning of the group to be "to the
receiving of," a compound proposition, more definite in its signification than
the single N, which admitted a variety of meanings ; and probably also more
solemn, as being confined to the forms of religion. The middle character is a
pair of arms held up, as if to receive a gift,* which ideagraphically denoted the

• This may derive confirmation from the speech of the ancestors of Rameses II. to that king, at
the conclusion of the tablet of Abydos, — " We hold up our arms to receive offerings." It is true,

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 59

verb " to receive," and its derived noun ; and which also denoted the same verb
phonetically, according to the well-ascertained usage of the Egyptians, being
the letter K, the first letter of the old Egyptian verb ki " to receive ;" whence
we have in Coptic 2fl and (TT. After this character a small vertical line is
frequently placed, signifying that it represents a word, and not a mere letter.
Compound prepositions of this sort are of common occurrence in the Coptic
language ; and there are some well-known instances of them in Hebrew.

9. Now, I observe that, though this compound preposition en-ki-en, was
substituted for the single preposition en, at a very remote period, it is not so
remote a one as that instances to the contrary do not occur. The earliest dated
tablet that I have seen, containing the compound preposition, is of the twenty-
ninth year of Amenemhe II. In all tablets sculptured in the early part of the
reign of this king, as well as in all those sculptured under his predecessor Osor-
tasen I., or any of the preceding raonarchs, the simple waved line, en, " to," is
invariably used ; if, indeed, the preposition be not omitted altogether.

The part of the inscription, which follows this simple or compound preposi-
tion, contains the name of the deceased person, preceded by an enumeration of
the offices, sacerdotal, civil, or military, which he held, and followed in most
instances by the names and offices of his father and mother (or at least one of
them), and sometimes of his grandfather or other relatives. It is but seldom
that the exact nature of all the offices held by the deceased person can be satis-
factorily discovered. We can perceive, however, that the Egyptians in general,
and especially the priests, were great pluralists. Occasionally, but very rarely,
we meet in this part of the inscription with the name of a king, whom the
deceased person served, and even with a fact respecting him of historical interest.
Thus, in a tablet of the reign of Thothmos IV.,* belonging to Mr. Harris (Eg.

that the verb here used for " receive" is not ki ; but is the equivalent verb chop, ^n> preserved in
the Coptic jy6n or UJUJIT, and corresponding to the Latin cap-ere.

* I mean the king, who is called Thothmos V. by Rosellini. The Italian antiquarian has
imagined a king of this name, whom he calls Thothmos III., but who had no real existence. Having
taken it into his head that Queen Amouneth ente heou, who erected the Karnac obelisks, was the
mother of Thothmos Mephre, and finding that the name of the father of this king was Thothmos,
he assumed the existence of a husband of the queen, whom he called Thothmos III. ; and he styled
Mephre, Thothmos IV. The fact is, however (as I conjectured in a note to my paper on the years
and cycles of the ancient Egyptians, and as has since been completely established), that this queen

if 2

60 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

Ins. 93), the deceased person is called "the attendant upon the king in his
journeys to the southern and northern countries, who went from Naharina
(Mesopotamia) to Karai in the suite of his majesty." It is worthy of observa-
tion, that these are the identical limits of the Egyptian empire, which are
recorded on the Liverpool and Paris scarabaei (as already noticed), in the eleventh
year of Amenothph III., the son and successor of this king. This deceased
person, whose name was Amenothph, was also "first prophet of Empe" and
" superintendent of his Majesty's cattle stall ;" and he held another office under
the crown, the nature of which I do not understand.

After the name of the person commemorated by the tablet, there occurs very
commonly, in inscriptions of all ages, an addition on which I will make a few
remarks. It commences with the word Me (yo) " truth," expressed either
symbolically, by an ostrich feather or a measure ; phonetically, by the sickle and
arm, which represent the two component letters of the word ; or in both ways
combined, the measure or feather, the sickle and arm being all used. This is
followed by a club, T, representing the word Taoue, " speaking," the subsequent
or complementary letters of which are but seldom expressed. And after this we
occasionally meet characters which I consider to belong to the sentence; namely,
Chal, (^n) a preposition, answering to the Hebrew ^a or ■?, " to," and either
the name of Osiris, or the two N's, the hatchet and the pike, with which the
words Nter, " god," and Naa, " great," are written, and which are commonly
used as abbreviations of those words. I would then translate the entire addition,
not as ChampoUlon has done " the truth-speaking, le veridique,"* but " who has
spoken the truth to Osiris," or " to the great god."f This expression I under-
stand in a forensic sense, as meaning "who has been justified, or pronounced
Innocent, by Osiris." It has been expressly stated by Diodorus, that the presi-
dent of every Egyptian court of justice wore a badge, which was called Truth,

vias sister to Thothmos Mephre, and that they were children of King Thothmos II. It is there-
fore Mephre that we should call Thothmos III. ; and his grandson, under whom this tablet was
sculptured, must be Thothmos IV.

* I do not deny that the two former words would have this meaning, if they stood alone; as they
do in the praenomen of the successor of Amenemhe III., whose phonetic name has not yet been
ascertained, " The sun who speaks truth." But I conceive that in the addition of which I am speak-
ing, the subsequent words, if not expressed, are always to be understood.

t Or as I have observed in one place, " To the lords of the abode of glory."

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 61

and which the monuments show us to have been an image of Thme, the goddess
of Truth or Justice, who is represented sitting, with an ostrich feather on her
head, and a bandage over her eyes. With this figure he touched the successful
party in the suit; thus announcing to him that the decision of himself and his
assessors was in his favour. This was as much as to say to him that " he had
spoken the truth ;" that his plea was true. In accordance with this, the unsuc-
cessful accuser, the adversary of the deceased, is called in the ritual "the liar."

Here I cannot refrain from noticing the extraordinary mistake, into which
Sir J. G. Wilkinson has fallen with respect to this badge, which he supposes to
have been the same as that worn by the Jewish high priest ; arguing from the
similarity of the words Thme and Thummim. The resemblance between these
words is merely apparent, and disappears when we reduce them to the radical
forms. The initial Th of the Egyptian word is the feminine article, while the
j^ of the Hebrew word is radical ; and, on the other hand, the Egyptian word
has at the end of it a letter having the force of the Hebrew y, to which there is
nothing equivalent in the Hebrew word that has been supposed to correspond
with it. The resemblance, then, between the names (yo and dji) it not real;
nor were the purposes for which the two badges were worn at all similar.

The addition, of which I have been speaking, which is commonly abbreviated
to two characters, such as

W

or

appears to belong to deceased persons exclusively ; so that it might be translated
" deceased," or " the late." It is contrasted with the characters,

1^

which, when they follow the name of a man, imply that he is alive. Thus,
on a broken tablet, in the British Museum (Eg. Ins. 27) the person comme-
morated is called Imothph, deceased, son of Hapi, still alive ; and of a deceased
mother, daughter of a deceased person, and sister to a living person. It was,
however, in most cases, considered sufficient to express that a person was
alive, if the characters for deceased were omitted after his name. Now, as

6i Rev. Edward Hincks on the Egyptian Stele, or Tablet.

these characters are wanting after the names of many persons commemorated
on tablets, a question arises, whether these tablets were always funereal ;
whether they may not, in many instances, have been erected by individuals out
of gratitude to the gods, for gifts conferred on them during their lives. That
this was the case, in some instances, is highly probable ; but I would by no means
affirm that it was the case whenever the characters expressing death were wanting.
It is, however, a question, which I do not feel myself called on to decide. One
thing appears to me clear ; namely, that the presence or absence of this addition
is no criterion of the antiquity of the tablet.

10. It is otherwise with certain prefixes, which are found on very early and
on very recent tablets, immediately after the preposition en, or enkien. Tablets
of the Ptolemaic and Roman ages, and, perhaps I should add, tablets sculptured
under the latest dynasties, have after this preposition the title " Osiris," which
is never found on the more ancient tablets. I do not, by any means, intend to
deny that it was customary, in ancient as well as in modern times, for the Egyp-
tians to identify deceased persons with Osiris. I am aware that on that most
ancient record, the coffin found in the third pyramid, this identification is
distinctly made. What I mean to assert is simply this — that the title is not
given to deceased persons on ancient tablets.

11. On the other hand, a title, which I interpret "the blessed," or "favoured,"
sometimes followed by a preposition, and the name of a deity, is almost pecu-
liar to very ancient tablets. Instances, may, perhaps, occur, in which this title
may be found on recent ones, or in which it may be wanting on ancient ones ;
but we may infer with tolerable certainty, that if this title be found on the stone,
it is more ancient than the reign of Amenemhe III., and if it be not found on it,
it is of that or some subsequent reign. I would be understood as speaking with
the same qualification as I did with respect to the title Osiris. Deceased persons
of all ages are spoken of as "blessed," or "possessed of blessing;" but it is only
on ancient tablets that gifts are said to be given "to the blessed superintendent,"
&c., or the like.

The essential part of the title, to which I allude, is the character.

representing an object unknown to me. How this character came to signify

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 63

" blessed," I cannot say; but Mr. Sharpe assigned this meaning to it by decipher-
ing ; and though I do not often assent to that gentleman's conclusions, I cannot
avoid doing so in this instance. It may possibly represent the idea expressed by
the word "blessed ;" but it is possible also, and 1 think much more probable, that
it represents some object, the name of which was pronounced in the same manner,
or nearly so, as the Egyptian word for " blessed," or as the first syllable in this
word. Along with this unknown character, there occur in this title, when
written in full, the leaf, answering to the Hebrew Aleph, and which may be
read by any vowel ; the sickle M, the sieve CH, and either the pair of leaves
EI, or the quail OU. The two latter characters are equivalent to our termina-
tion ed ; and have the same effect as the corresponding Hebrew vowels '' and \
when placed before the last radical, in the participle Pahul or the verbal noun
of the form Pahil. Rejecting then these servile letters, the Egyptian verb con-
sists of three letters nOJ^j in addition to the unknown character ; which I regard
as merely determinative, unless it be used as a substitute for the whole word, or
for its first syllable, or for the consonant M. To show the manner in which this
peculiar character is introduced, I will set down a number of varieties which I
have met with ; putting for the common phonetic characters their Hebrew equi-
valents, and for the peculiar character an asterisk ; and, for the sake of compari-
son, I will do the same thing with the word me, " truth," already mentioned ;
the asterisk in it representing its peculiar character, the ostrich feather or the
measure.

Amach, to bless, is written, *n?l3N ; n*50N; T\*ii'i PI*; *
Me, truth, is written, *y;a ; i?)D* ; y* ; *

The peculiar characters belonging to the word me, " truth," are known to
be ideagraphic ; but that which distinguishes the word amach, is unknown ; and,
as I have already observed, it may be significative of sound. If I must hazard a
conjecture, it would be that it represented a vessel holding mud, with the mud
flowing out of it ; omi, or ome, is the Coptic for " mud ;" and the old Egyptian
word for it probably only differed from this in its vowels.*

* On communicating my views respecting this word to Mr. Birch, he proposed an objection to
them, which I think it right to notice, as I trust I shall be able satisfactorily to remove it. He ob-
served that the preposition used between this participle and the name of a deity was " to," not
" by," as according to my views it should be. The proposition is bn, answering to the Hebrew

64 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

I now come to the most important part, as I think I may safely call it, of the
inscription on a tablet, namely, the speech put into the mouth of the deceased
person. It may be known by the group of hieroglyphics which precedes it, as
in the skeleton inscription given above. These characters are in^, " he says,"
that is, " who says ;" for the Egyptians had no relative pronouns. If the person
commemorated be a female, the broken line D, " she," is used for the horned
serpent, "i, " he." It must not be supposed that these speeches are always of im-
portance, or even that they always convey information respecting the deceased
person. Sometimes, the speech is a prayer addressed to Osiris, or some other
deity ; sometimes it is a statement of the happiness enjoyed by the deceased in
Amenta ; sometimes it is an Invitation to mankind in general, or to the priests, or
to those who may approach the burial place, to pray for blessings to the deceased ;
but it is, in many instances, a brief narrative of the most important events in the
life of the deceased person ; and it is here, if any where in the body of the
inscription, that we may expect to find the time when he lived, or his age,
stated.

It would be impossible, in such a paper as this, to describe at any length the
varied contents of this portion of the inscription. Nor is it necessary for my
purpose, which is merely to direct attention to this class of Egyptian antiquities,
and to guide the purchaser or student to those which are of most value, either
from their age or from their contents. It is a rule, which admits few excep-
tions, that very little information is to be derived from any tablet which does not
contain a speech ; but the converse of this is by no means true ; many speeches
contain no information whatever.

I have mentioned, as I went along, several criteria of the antiquity of tablets.
It remains for me to notice one, the most striking of all, which lies not in the

bH or b ; and, no doubt, it signifies most commonly " to." It, however, has other meanings, just
as the corresponding h has. It is used before the name of a king, when the year of his reign is to
be expressed. So is the Hebrew b. And why may it not be also used for "of" in such expres-
sions as " the blessed of Osiris," « the favoured of his master ?" In that very ancient Hebrew
passage. Genesis, xiv. 19, a document, which is probably of the same age with the tablets which
contain this formula, the proposition b is used for "of" in the similar expression, "Blessed be
Abram of the most High God," ]^>b^S bwb. The Hebrew and the ancient Egyptian languages
throw great light on each other ; and it is not unreasonable to expect that the study of the Egyptian
monuments will elucidate many passages of the sacred text that are now obscure.

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 65

inscription itself, but in the sculptures which accompany it. In the more ancient
tablets, the figures which occur are exclusively those of the deceased person and
his relatives ; figures of deities are never introduced. On the contrary, a tablet
of the eighteenth dynasty, or of any subsequent period, is seldom without the
representation of some deity or deities. I must, however, remark, by way of
caution, lest anyone should infer from this that the Egyptians of the earlier ages
did not represent their deities in a visible form, that in the inscriptions on these
ancient tablets small images of the deities are used, either to represent their
names, or as determinative signs after them. The difference between the two
classes of tablets is not to be attributed to any change in the religious notions of
the people ; it seems to have been merely a difference of taste or fashion ; the
more ancient Egyptians representing the deceased person as entertaining his
relatives at a feast, while those of after ages represented him as doing homage to
the deities.

The dates of some tablets are conspicuously placed at the tops ; the royal
name and titles being inclosed in a cartouche, and the year of the king's reign,
and sometimes the month and day, being prefixed. It is from a comparison of
these dated tablets, the relative ages of which can admit of no question, that I
have derived the criteria of antiquity which I have mentioned.

I say the relative ages, because there are gaps in Egyptian chronology, which
render it impossible for us to assign as yet the years, or even the centuries, before
our era, at which the earlier kings lived. We know that the eleven kings, who
appear as the predecessors of Rameses II. in the tablet of Abydos, with the inter-
vening kings and queens whose names are omitted, reigned together for about
300 years. These are included in the eighteenth dynasty of Manetho. We
know also that from the commencement of the reign of Sheshonk I., who com-
menced the twenty-second dynasty of Manetho, to the Persian conquest, is within
a trifle, in excess or in defect, of 450 years. But as to the interval between the
accession of Rameses II. and that of Sheshonk I., we have as yet, so far as I am
aware, no satisfactory evidence. We know both from Manetho, and from the
royal tombs at Thebes and other monuments, that a great number of kings
intervened ; but we have no certainty, that they did not belong to two or more
contemporaneous dynasties ; or that in the same dynasty two or more brothers did
not occupy the throne together. This interval, then, which is by some extended

VOL. XIX. /

66 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

to 550 years, is reduced by others to less than the half of that period ;* and
thus an uncertainty to the extent of about 300 years exists as to the reign
of each monarch of the so called eighteenth dynasty, when the date of its com-
mencement is compared with any given era ; although the order of most of the
reigns is perfectly well ascertained, and the length of many of them is known
also.

, I have spoken of kings and queens belonging to this dynasty, whose names
are omitted in the tablet of Abydos. That this should be the case should excite
no surprise, because that tablet was only intended to include the royal ancestors
of Rameses II. The non-appearance of a king's name in it is no evidence that
he did not live during the interval of time which it comprehends. In point
of fact, the monuments in existence exhibit to us no less than four royal per-
sonages, who lived between Thothmos IV. and Rameses I., the twelfth and
fifteenth kings on the tablet, in addition to the two who appear as the thirteenth
and fourteenth, viz., Amenothph III., and Horus (Har-em-hebee). The names
of three of these kings are Amuntuonkh, Amunmes, and Amenothph IV. ; that
of the fourth, whose tomb is in the western valley at Thebes, is yet undetermined.
There can be little doubt that Amuntuonkh was the brother of Amenothph III.,
who shared the sovereignty with him for a time. This was pointed out by Sir
J. G. Wilkinson, who has, however, confounded this king, who probably died
in his childhood, with Amenothph IV. This last king has deservedly excited
much interest ; and strange mistakes have been made respecting the age when
he lived. M. Letronne, and other French writers, have supposed him to belong
to a dynasty anterior to the shepherds, the immediate successors of the gods !
Colonel Vyse, on the other hand, imagines him to be one of the Persian kings
of the twenty-seventh or thirty-first dynasty ! The monumental evidence is,
however, conclusive as to his belonging to the Thothmos family. It appears,
that having become a proselyte to sun worship, he changed his original name of
Amenothph, which implies devotion to Amoun, for Vach-en-aten (jn{^3n3)»

• The most probable supposition appears to me to be that, which makes the date of the ceiling
of the Memnonium about 1322 years B. C. ; and which, to accord with this, assumes that the twen-
tieth and twenty-first of Manetho's dynasties reigned contemporaneously after the nineteenth. If
this be so, according to the principles laid down in a former note, Rameses the Great must have
ascended the throne in 1347 B. C, about 400 years before Sheshonk.

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 07

" the adorer of the sun's disk."* The latter name is found at Karnac, cut over
the former, the praenomen attached to it remaining unchanged. Not content
with this, in the fervour of his religious zeal, he made war against the name of
Amenothph, wherever he found it. It has been defaced in innumerable instan-
ces in the second cartouche of his grandfather (or perhaps his great grandfather),
Amenothph III. In general, the name has been merely chiselled away ; but in
several places, a repetition of the praenomen has been cut over it ; a plain proof
that his hostility was not directed against his ancestor, but against the name
which he bore. There is also a tablet of Mr. Harris's of the age of Thothmos
IV. (already referred to in this paper), relating to a deceased Amenothph, the
former part of whose name has been rudely defaced in every one of the four
places where it occurs. A like hostility appears to have been directed against
the goddess Mouth, the wife of Amoun. In a curious statue of the reign of
queen Amuneth, in the collection of Sign. Athanasi, representing (as I conceive)
this queen, when an infant, in the arms of her nurse, and commemorating the
father of the nurse, whose name was Sen- Mouth ; the latter part of this name,
which occurs very frequently in the inscriptions, has been, in the majority of
instances, more or less defaced. This statue is curious, not only on account of
its subject, but on account of its exhibiting traces of two defacers ; a political
one, who obliterated the name of the queen on the accession of her brother; and
a religious one, at a later period, who made war on the name of the goddess. I
mention these facts, because they are not unconnected with the subject of the
present paper ; they furnish a criterion of the age of a tablet which may some-
times be applicable. If the name of Amoun, or Mouth, appears on a tablet with
marks of a hostile tool, it may be considered as certain that it was anterior to the
reign of Rameses I., perhaps to that of Horus ; and as highly probable that it was
not very long anterior to it. Very ancient tablets, which are now in existence,
were in all probability buried in the days of the sun-worshipper.

* In an article in the Foreign Quarterly Review, which has appeared while these sheets were
passing through the press, this king is called Oubasheniten, which is interpreted "the splendour of
the disk." The Coptic word oubash, splendour, is in Egyption 2723?, and can have no connexion
with nS; the Coptic corruption of the latter might be bash or ouash, but it certainly could not be
oubash. It has been demonstrated by Salvolini that this root signifies " to adore." Ouasht has
this signification in Coptic, iu which language a T is often paragogic.

/2

68 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

Before the commencement of the eighteenth dynasty, the tablet of Abydos
furnishes us with five royal names, to which we may add a sixth, ascertained from
other monuments, who appear to have constituted the twelfth dynasty of Manetho,
and to have reigned for about 1 60 years. These sovereigns have been commonly
classed under the sixteenth and seventeenth dynasties of Manetho ; but that
writer's catalogue of the twelfth appears to me to be intended for them, though
we must suppose it to be grossly corrupted. The five dynasties intervening be-
tween the twelfth and eighteenth, I conceive to have been either contemporaneous
with the twelfth, or altogether imaginary.

The first two monarchs of this twelfth dynasty were Osortasen I.* and
Amenemhe II. ; the former of whom appears to have reigned forty-two years,
and the latter thirty-two, before they took their respective successors into part-
nership with them. A great number of dated tablets are in existence, belonging
to these two reigns. The first year of Amenemhe II. corresponded with the
forty-third year of Osortasen I. ; and the first of Osortasen II. with the thirty-
third of Amenemhe II. ; after whose death he appears to have reigned a very
short time. We cannot, then, expect to have many monuments of his. After
him comes Osortasen III., and then Amenemhe III. The first Amenemhe
preceded Osortasen I., and belonged, according to Manetho, to the eleventh
dynasty.

I have made the preceding statements advisedly, and on what I consider
perfectly sure grounds, though they are at variance with the received opinions.
Major Felix produced a supposed succession from Benihassan, from which
he inferred that Amenemhe the First intervened between Osortasen I. and
Amenemhe II. This error, for such it demonstrably is, has been adopted
by Sir J. G. Wilkinson, and by Rosellini ; and Mr. Cullimore has grounded
upon it a restoration of the obliterated portion of the tablet of Abydos, which has
been published, under the title of" Chronologia Hieroglyphica," by the Royal
Society of Literature. I have the highest respect for the learning and ingenuity
of Mr. Cullimore, but truth obliges me to pronounce this restoration to have
been made on erroneous grounds, and to be of no authority whatever. The sole
ground for supposing that the royal names at Karnae formed a connected series,

* Or Gesortasen, if the initial letter corresponding to V be sounded in Greek as a G, as it is in
Gaza, Gomorrah, &c. Hence, probably, the grossly corrupted reading of Manetho, Gesongosis.

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 69

like that of Abydos, was that the names of the three kings in question occurred
among the names at Karnac ; and that they might be read with a little manage-
ment in the order, in which the Benihassan inscription was supposed to indicate
that the kings reigned. It is quite impossible, however, that the names at
Karnac can be read with any management in the true order of succession, as indi-
cated above ;* and therefore I conclude that the names at Karnac must have been
set down without order, the inscription there having never been designed to
be historical. Nor do I think that it at all follows, that these were names of
Egyptian sovereigns exclusively. If Thothmos reigned over the country about
Meroe, as 1 believe he did, his predecessors in that region might very well be
represented as receiving homage from him, as well as his predecessors In Egypt.
I will now state the grounds on which I pronounce the received order of
succession of these three kings to be erroneous. In one of Mr. Harris's ta-
blets figured by Mr. Sharpe (Eg. Insc. 73), which Is dated in the third year of
Amenerahe II., the deceased person is made to say, that he was born in the reign
of Amenemhe I., and was appointed to certain offices by Osortasen I. When
first I saw this, I was lost in astonishment, having never doubted, after the con-
fident statements of Mr. CuUimore, Sir J. G. Wilkinson, and Rosellini, that
there was a clear indication at Benihassan of an order of succession inconsistent
with this. To settle the question, however, I referred to the Benihassan inscrip-
tion itself, which I found copied by Mr. Burton (Exc. Hier. 33). I certainly
found the three royal names occurring there in an order, which might not unnatu-

• This remark has led to a friendly correspondence with Mr. CuUimore, the result of which I
have been requested to communicate in a note. Mr. CuUimore and I are agreed, that there is a way
of reconciling the facts above stated, which he does not dispute, with the authority of the Karnac
tablet, namely, by supposing that Amenemhe I. usurped the government in the hfe-time of Osor-
tasen I., but that he died before him, and the latter then resumed his authority ; so that he was, in
fact, the predecessor both of Amenemhe II., as is testified by contemporary monuments, and of
Amenemhe I., in accordance with the Karnac tablet. But Mr. CuUimore and I differ as to the
claims of this tablet to be received as an historic document. He considers it to carry with it its own
evidence that it is such, and to be sufficiently corroborated by other monuments. I, on the contrary,
conceive it to be totally destitute of internal claims to be received as an authentic catalogue of
kings ; I consider the evidence on which Mr. CuUimore relies, as corroborating it, to be inconclusive ;
and I think that other parts of it, as well as the Osortasen succession, are inconsistent with contem-
porary monuments. Mr. CuUimore's services to the cause of literature have been great ; and while
I am compeUed to differ from him on this point, I readily acknowledge them.

70 Rev. Edward Hincks on the Egyptian Stele, or Tablet.

rally be supposed to be the reverse order of their reigns. Amenemhe II. occurred
first ; it was followed by Amenemhe I., and that by Osortasen I. I observed,
however, that there was a great deal of matter intervening between these royal
names ; and I found, on examination, that this intervening matter was of such
a nature as completely to disprove the order of succession, which it had been
supposed to prove. The inscription stated that Nebhothph had been appointed
by Amenemhe 11., in the nineteenth year of his reign, a " Repha-He," with the
military government of a certain district ; the same rank and government having
been conferred on his father by Amenemhe I., and on his elder brother by
Osortasen I. Of course, Osortasen I. intervened between the two Amenemhes.
After this I became acquainted with a tablet in the Leyden Museum, the date
of which made " assurance doubly sure ;" being " the forty-fourth year of Osor-
tasen I., which is the second year of Amenemhe II."

The importance of this inference, as setting aside the supposed series of
kings at Karnac, will, I hope, be accepted as an excuse for this digression. I will
only add, that of the kings preceding Amenemhe I., we know very little as to
the order, and nothing as to the length of their reigns.

I have now completed the task which I had marked out for myself; and it is
my earnest wish that what I have said on this branch of Egyptian antiquities may
induce others of my countrymen to engage in the study of this interesting and
Important branch of literature. I trust that no preconceived opinion of the
Impossibility that hieroglyphic characters in ancient inscriptions should express
phonetically the words of a language will cause them to shut their eyes against
the fact that they do so. And I trust also that no unworthy national prejudice
will lead them to undervalue this field of discovery, because, though it may be
said to have been opened in England, its most successful cultivators have been
hitherto foreigners. I well remember the time, when the current of national
prejudice ran strong against what were contemptuously called " French Mathe-
matics ;" but the good sense of our countrymen at length prevailed, and those
branches which were once regarded as exclusively French, have been pursued
with as much success in England, and, I will add, in Ireland, as ever they were
in France. Let us adopt the same course in respect to hieroglyphical literature ;
and, in place of decrying the labours of Champollion, and undervaluing his won-
derful discoveries, let us apply ourselves to follow them up ; correcting, as we go

Rev. Edward Hincks on the Egyptian Stele, or Tablet. 71

along, his errors where we find that he has committed them ; but candidly
acknowledging that he himself corrected most of his early errors in his grammar,
and that those which remain are few and unimportant, when we take into account
the number, the magnitude, and the importance of his discoveries.

72

IV. On the true Date of the Rosetta Stone, and on the Inferences deducihle
from it. By the Rev. Edward Hincks, D. D.

Read May 9, 1842.

IN investigating the affairs of ancient nations by the help of the contemporary
monuments that are yet in existence, there is no knowing beforehand how prolific
a single truth may be ; what a train of interesting and even important facts may
be brought to our knowledge by combining that one truth with those that are
already known. This should lead us to prize every new fact that can be ascer-
tained, however unimportant it may appear in itself. And, on the other hand, a
similar consideration should lead us to endeavour to correct every falsely assumed
fact, no matter how trivial the error may appear ; for falsehood is unfortunately
as prolific as truth ; and one falsehood, assumed as a fact, may give birth to errors
without number.

A striking illustration of these general principles has lately occurred in M.
Letronne's Edition of the Greek Inscription on the Rosetta Stone ; in which,
with the most perverse ingenuity, he draws inference after inference from the
false date, which Dr. Young assigned to that monument ; which inferences are
all erroneous, and are in most cases the very reverse of those which should have
been drawn.

The date, which Dr. Young erroneously assigned to that monument, was the
27th March, 196 B. C, according to the proleptic Julian reckoning ; the true
date was, according to the same reckoning, the 27th March, 197 B. C. I will
first contrast the inferences which M. Letronne has drawn from Dr. Young's
date, with the inferences that he would have drawn had he adopted the earlier
date ; placing, for greater clearness, the corresponding inferences, which are ge-
nerally contradictory, in parallel columns. Having done this, I will bring for-
ward reasons, on which I confidently pronounce it to be impossible that Dr.
Young's date was the real date of the monument.

Rev. Edward Hincks on the true Date of the Rosetta Stone. 73

M. Letronne's inferences relate to the history of Epiphanes and to the mode
of computing the years of his reign, and that of other Egyptian kings ; and to
the various priesthoods of royal personages that are mentioned on the Ptolemaic
monuments. He begins with the latter of these ; but it will be more convenient
to take the former first. I will only premise that the ninth year of Epiphanes,
according to Ptolemy's canon, and the Egyptian mode of dating, is admitted to
have been that, the first day of which coincided with the 1 1th October, 197 B. C.

Assuming the Rosetta Stone to be dated in
March, 196 B. C, M. Letronne infers:

1. That Philopator died in March, 204 B. C.

2. That Epiphanes was born in October, 209
B.C.

3. That the interval between Philopator's
death in March, 204, and the 1st Thoth in the
following October, was counted as the first year
of Epiphanes.

4. That, as a general rule, the portion of a
year which elapsed between a king's death and
the 1st Thoth following, no matter how small it
might be, was counted as the first year of his suc-
cessor.

If, however, it were dated in March, 197
B. C, the inferences woyld be :

1. That Philopator died in March, 205 B. C.
The decree bears date the day following the an-
niversary of his death ; and, as it is said to be in
his ninth year, while, according to the Egyptian
computation, it was in his eighth, it must have
been made on the day after the eighth anniver-
sary of his death, when he had reigned eight
complete years. It should be observed that the
mention of the ninth year is in the Greek part
of the inscription ; the Egyptian date was on a
part of the stone which is broken off.

2. That Epiphanes was born in October, 210
B. C.

3. That the interval between Philopator's
death and the 1st Thoth following, was counted
as a continuation of the 17th of Philopator, which
began on the preceding 1st Thoth ; and that the
first year of Epiphanes did not commence until
the 1st Thoth after his father's death.

4. That, in the case of a king succeeding
peaceably to the throne in the latter part, or
even in the middle of a year, the remainder of
that year was called after his predecessor; and
that his first year was not reckoned to begin till
the 1st Thoth after his accession.

Previous to considering M. Letronne's inferences respecting the various royal
priesthoods that are mentioned in Ptolemaic inscriptions, it will be right to men-
tion the data which he uses in conjunction with the Rosetta Stone. There are

VOL. XIX. K

74 Rev. Edward Hincks on the true Date of the Rosetta Stone.

three papyri in the Egyptian Museum at Paris, bearing date in Epiphi of the
seventh year of Philopator, i. e. in August, 216 B. C. ; in Pharmuthi of the 8th
of Epiphanes, i. e. in May, 197 B. C. ; and in Paophi of the 21st of Epiphanes,
i. e. in November, 185 B. C. The important point, in which M. Letronne has
erred, is that he supposes the second of these papyri to be dated ten months be-
fore the Rosetta Stone, when it is really dated two months after it.

On the first of these papyri and on the Rosetta Stone, Aetes or Aetos is
mentioned as priest of Alexander and of the other deified kings ; while on the
second of the papyri Demetrius is mentioned as filling that office. On the second
and third papyri, as well as on the Rosetta Stone, Hirene is mentioned as priestess
of Arsinoe Philopator ; but the Athlophora of Berenice Evergetis and the Cane-
phora of Arsinoe Philadelphe are different in all the documents ; Aria, however,
the Canephora of the Rosetta Stone, being the Athlophora of the second papyrus.
The inferences then are as follows :

5. Demetrius being priest of the kings before
the decree recorded on the Rosetta Stone, while
Aetos was priest at the time of that decree, and
also at a period previous to it, the office of priest
of the kings was not a permanent one, but was
probably annual.

6, The offices of Athlophora, Canephora, and
Priestess of Arsinoe, were all annual. It would
be highly improbable, if this were not the case,
that the persons holding them would in two out
of the three cases, be changed during the short
period of ten months.

7. The office of Athlophora was not placed
first, as being a more important office than that
of Canephora ; for Aria held the former office in
197, and the latter in the following year. M.
Letronne conjectures that the reason for the for-

5. Demetrius not being priest, so far as we
know, till after Aetos had ceased to be so ; there
is no ground for supposing the office to be an-
nual. Aetos probably held it from the com-
mencement of the reign of Philopator till after
the Rosetta decree. In the course of the next
two months, he either died or was removed by
the new sovereign, who, it will be recollected,
assumed the reins of government at the date of
that decree.

6. There is no reason as yet for supposing
that any of the royal priesthoods was annual.
The changes which took place between the dates
of the Rosetta Stone, and of the second papyrus,
were such as it was highly probable would take
place, if the office were held during pleasure, in
the two months next following the attainment
of his majority by a minor sovereign.

7. The office of Athlophora, being always
placed before that of Canephora, was a more im-
portant office. Aria, who held the latter in
March, 197, was promoted to the former before
May in that year, the former Athlophora dying.

Rev. Edward Hincks on the true Date of the Rosetta Stone. 75

mer beinw always named before the latter was, or being removed by the new king. The idea
that Epiphanes, or those who acted for him in of these offices being annual ones appears to have
his minority, had a particular regard for the me- first occurred to M. ChampoUion Figeac ; but it
mory of his grandmother. is not necessary to suppose them to be so, in or-

der to explain the observed facts ; and the con-
trary supposition seems on every account prefer-
able.

I come now to state my reasons for maintaining, that the Rosetta Stone re-
cords a decree which was made in March, 197 B. C. The date of the decree is
given according to the Greek and Egyptian computations, so far as respects the
month and day. It was the 4th of Xanthicus, being the 18th of Mechlr. Now
I am going to show that these dates could not possibly coincide in the year 196
B, C. ; but that they could and did coincide in the preceding year.

It has been proved by Archbishop Ussher, that the Macedonian year was a
solar one, similar to that which was introduced at Rome by Julius Cassar. As,
however, some may doubt whether this solar year was in use at so early a period
as the date of the Rosetta Stone, and as it is generally believed that the Mace-
donians had also a lunar year ; it will be necessary to show in the first place, that
the 18th Mechir, that is, the 27th March, in the year 196 B. C, could not be
the 4th of a lunar month. To do this, I need only quote M. Letronne's own
words : " This year the full moon fell on the 29th March, or the 6th Xanthicus.
The first of this month was then about the ninth day of the moon's age ; whence
it would follow that the calendar to which it belonged was not lunar, unless this
month was this year an intercalary one (a moins que ce mois ne fut embolimique
cette annee)." The learned Frenchman has not explained how this removes the
difficulty ; though it is evident that he supposed it to do so. It is not very ob-
vious how in any lunar calendar, whether the month was intercalary or not, the
full moon could occur on the sixth day. In the preceding year the full moon
fell on the 9th April ; so that if the 27th March had been the fourth of a lunar
month, the full moon would be on the 17th day of it. This is so much less
astray from the correct time than in the year 196, that if it were certain that the
Macedonian year were lunar, I think there could be no hesitation in fixing on
the year 197 B. C, as that in which the fourth of a lunar month would coincide
with the 18th Mechir. I am, however, decidedly of opinion, that the Macedo-

K 2

76 Rev. Edward Hincks on the true Date of the Rosetta Stone.

nian year was solar ; and I find that, by supposing it to have been so, an exact
coincidence between the two dates occurred in the four years 200, 199, 198, and
197 B. C, but not in 196, or in any other year.

That the Macedonian year was a solar one, subsequent to the Julian reforma-
tion of the Roman calendar, is unquestionable. What I contend for is, that it
was so at the time of the Rosetta Stone, more than 150 years before that refor-
mation ; and the double date of that monument appears to me to establish this
interesting fact in chronology. The mode of proceeding, in order to investigate
this matter, is a simple and obvious one. I will take those dates of the Macedo-
nian solar year, as it existed under the Romans, which are recorded as being co-
incident with dates of the Julian year, or of the fixed Alexandrian year, the cor-
respondence of which with the Julian is known. From these dates, and the
known lengths of the Macedonian and Julian months, it is easy to ascertain with
what day of the Julian year any given day of the Macedonian year, say the 4th
of Xanthicus, coincided in each of the four years of the Julian cycle ; and it is
obvious that this coincidence must remain unaltered, if we compare Macedonian
years, actual or proleptic, at any period, with proleptic Julian years.

Now it has been shown by Archbishop Ussher, that the Macedonian year, as
used in Asia generally, differed in certain respects from the Macedonian year, as
used in Macedonia. The commencement of both years was at the autumnal
equinox ; but the first month of the Asiatics was Hyperberetaeus, while that of
the Macedonians proper was Dius. The same difference remained through the
other months, Xanthicus being the sixth in Macedonia, but the seventh in Asia.
It is natural to suppose that Egypt would follow the Asiatic system in preference
to that of the Europeans ; and this is confirmed by the Egyptian date, with which
one of these Asiatic dates which I am going to produce is stated to correspond.
These dates (which I take from the treatise of Archbishop Ussher, " de Macedo-
num et Asianorum anno solari ;" a valuable work, with which neither Dr. Young
nor M. Letronne could have been acquainted) are, first, that of the martyrdom
of the Apostle St. Paul ; which is stated by Euthalius to have occurred on the
29th June, A. D. 67, being the 5th Panemus. Xanthicus, Artemisius, and
Dffisius had the same number of days as March, April, and May. Therefore the
29th March in that year coincided with the 5th Xanthicus, and, of course, the
28th March with the 4th Xanthicus.

Rev, Edwakd Hincks on the true Date of the Rosetta Stone. 77

The second date is that of the martyrdom of St. Polycarp, which is shown by
the learned Archbishop to be assigned by the most correct copy of the Acts
thereof to the 2nd Xanthicus, and 26th March, A. D. 169 ; being the day of
the great Sabbath, or that Sabbath which occurred at the Passover. In that year,
therefore, the 4th Xanthicus also coincided with the 28th March.

The third date is that of the burial of the younger Valentinian, which is
stated by St. Epiphanius to have fallen on the 23rd Artemisius, being the 21st
Pachon (of the fixed Alexandrian year) and the 16th May, A. D. 392 ; the latter
days are known to correspond. This correspondence gives us for the 4th Xan-
thicus in that year the 27th March. It is, therefore, evident that in bissextile
years, the 4th Xanthicus corresponded with the 27th March, and in the other
three years of the Julian cycle with the 28th March. This is, in truth, nothing
more than what has been expressly asserted by the Archbishop, who shows in his
treatise (pp. 46, 47» Ed. 1648), that in bissextile years the month of Xanthicus,
which he specially notices on account of its connexion with Easter, began on the
24th March, and in the other three years on the 25th.

Now, as the year 197 B. C. was proleptically bissextile, according to the Ju-
lian computation, the 4th Xanthicus must in that year have coincided with the
27th March, and therefore with the 18th Mechir. In the three preceding years
it would also coincide with the 1 8th Mechir, both dates coinciding with the 28th
March ; but in the following year, 196 B. C, and those after it, the 18th Mechir
would coincide with the 27th March, while the 4th Xanthicus would coincide
with the 28th.

It appears to me that this amounts to a complete demonstration, that the true
date of the Rosetta Stone was 197 B. C, and that the date assigned to it by M.
Letronne after Dr. Young was erroneous. Consequently, the seven inferences
drawn by M. Letronne must be rejected ; and the seven others, in most cases
contradictory, which I have placed in the parallel columns, must be substituted
for them.

78

V. — An Essay upon Mr. Stewarfs Explanation of certain Processes of the
Human Understanding. By the Rev. James Wills, A.M., M.R.I. A.

Read February 14, 1842.

CHAPTER I.

ARGUMENT STATED, AND MR. STEWART's EXAMPLES ANALYZED, WITH A FEW
ADDITIONAL CASES WHICH PRESENT THE SUBJECT UNDER A DIPEERENT ASPECT.

It is some years since I was very much struck by an argument of Mr. Stewart's
with which many here are likely to be famiKar : he endeavours to prove from
several cases, that the mind, from habit, acquires a rapidity in the succession of
distinct thoughts, so great as to escape the consciousness, a proposition which he en-
deavours to prove by examples, and from which he draws some important conclu-
sions. Considering that all his instances are such as seem essentially to involve the
principle of consciousness, I found it hard to acquiesce in his theory. But it was
impossible not to admit that if Mr. Stewart has correctly stated his facts, the in-
ference is in no way to be avoided. And I failed at the time to observe, that all
these facts (as I shall presently show) are themselves results of a very complex
nature, and requiring a minute analysis, before they could become the fair
grounds of such inferences as Mr. Stewart's : I, therefore, with some reluctance,
dropped a subject which seemed to offer some curious approaches to a more inti-
mate knowledge of our intellectual nature. The popularity which Mr. Stewart's
theory has acquired (chiefly owing to his very curious and interesting exposition
of the phenomena of dreaming) has led me to reconsider the subject with more
deliberate attention : and I now venture to advance a statement of the inferences
which I propose to substitute for Mr. Stewart's.

To express Mr. Stewart's theory in his own language, it is this, " The won-

Rev. J. Wills on certain Processes of the Understanding. 79

derful effect of practice, in the formation of habits, has been often and justly
taken notice of, as one of the most curious circumstances in the human constitu-
tion. A mechanical operation, for example, which we at first performed with
the utmost difficulty, comes in time to be so familiar to us, that we are able to
perform it without the smallest danger of mistake, even while the attention appears
to be completely engaged with other subjects. The truth seems to be, that in
consequence of the association of ideas, the different steps of the process present
themselves successively to the thoughts, without any recollection on our part,
and with a degree of rapidity proportioned to the length of our experience ;
so as to save us entirely the trouble of hesitation and reflection, by giving us
every moment a precise and steady notion of the effect to be produced." Ac-
cording to this statement, a succession of acts of attention and volition are sup-
posed to pass through the mind with a rapidity too great to be perceived, and
for which, therefore, there can be no argument but the necessity of the thing ;
because, according to Mr. Stewart, no other will explain the phenomena. These
notions are so involved in the entire of Mr. Stewart's Theory of the Mind, that
were I to attempt a full analysis of his reasoning It would necessarily lead me
into a very prolonged discussion, which should commence by a systematic expo-
sition of those elementary views of the mind and its functions, which I conceive
to be entangled with many errors by Mr. Stewart. The difficulty attendant on
such an undertaking would be enormous : for 1 must confess that I cannot so
easily satisfy myself as Mr. Stewart and other writers on the same subject seem
to have done, with any definition of those elementary processes of the mind, on
which so much reasoning is built.

The elementary fallacy in which I conceive Mr. Stewart's error to have
originated, is comprised in his very first step. It is difficult to speak satisfacto-
rily of a function so purely elementary as consciousness. Like light, it is chiefly
apprehended by reflection from surrounding things : but it is not hard to
point out the mistake which Is Implied in Mr. Stewart's view. He fails to observe
that the mind apprehends by wholes before it perceives by parts. Consciousness,
as it may be described (I do not pretend to define), appears to be the sum of
sensations and apprehensions of whatever nature, which constitute the whole
state of mind at any moment. The fallacy contained In Mr. Stewart's first ex-
amples, consists in an Implication that every part of this aggregate is separately

80 Rev. J. Wills on Mr. Stewart's Explanation of

perceived. Had he distinctly asserted this proposition, he vpould have quickly
seen his error, but he takes it for granted, and goes on to applications in which
it misleads him. There is, in those who are in a state of consciousness, at all
times a certain aggregate of things presented to the perception. Of these, some
may become more prominently the objects of attention, and the rest will invariably,
in the same proportion, become vague and indistinct. The perception of indi-
vidual parts of this vague whole will, in general, not be separately recollected,
because they have not been separately observed; and not, as Mr. Stewart assumes,
because the observation has been too rapid. There is a process, it is true, by
which, in a certain class of cases, the mind can recal and analyze a large combi-
nation of things ; but this is not what Mr. Stewart has in view.*

I shall presently be in a condition to examine more closely some of Mr.
Stewart's reasonings on this point, but I shall now proceed by a more simple and
far shorter method, which Mr. Stewart himself has the great- and signal merit of
having pointed out, and in some measure exemplified. Instead of adopting de-
finitions, and launching out upon the vague ocean of pure reasoning, I shall essay
the humbler adventure of a coasting voyage along the safe shore of known and
familiar facts ; the only method that I suspect will be ever found to lead to any
satisfactory result, in a science of which the first elements are so little tangible
to strict observation as those of the mind.

The nature then of the analysis to which I beg to call the attention of the
Academy is strictly this ; I shall state in order a numerous train of well known
and most common facts, in all of which the same process can be easily observed,
and which will exhibit this process in a variety of aspects, so that it may thus
appear what method of explanation will best agree with all. Among these I
shall include Mr. Stewart's cases, and endeavour to show that his explanation,
which is specious enough on a confined view of examples selected for the purpose,
is negatived entirely when referred to other cases which cannot be regarded as
specifically different.

The first case which Mr. Stewart states, with an explicit reference to the
subject of this essay, has the advantage of offering a passing view of another

• Some of the examples by which Mr. Stewart illustrates his views concerning consciousness,
perception, and attention, cannot be here satisfactorily discussed, until I shall have first fully ex-
plained the principle to be asserted in this essay. I shall, therefore, revert to them further on.

certain Processes of the Human Understanding. 81

philosopher, who, though far less reasonable than Mr. Stewart upon the subject,
offers the advantage of a different observation of the same phenomena.

Mr. Stewart quotes from Hartley his first example, which is that of a person
playing upon the harpsichord. The fingers of the player perform a variety of
movements from key to key, each of which, as Hartley observes, is at first an act
of distinct volition. By degrees, however, the motions (according to his lan-
guage) cling to each other, and the acts of volition grow less and less, until at
last they become evanescent. On this case Mr. Stewart says, " thus in the case
of performance on the harpsichord, I apprehend that there is an act of the will
preceding every motion of the finger, although the player may not be able to
recollect these volitions afterwards, and although he may, during the time of his
performance, be employed in carrying on a separate train of thought."

In supporting this proposition, Mr. Stewart observes, that the " player may
vary his rate of movement, and play so slowly as to be able to attend to every
separate movement :" and on this very justly observes Hartley's unreasonable-
ness in assuming two different rules of mental action for the quick and the slow
playing.

It is remarkable that Hartley's reasoning actually terminates in the vulgar
notion upon that class of acts commonly called mechanical, from which his in-
stance is drawn ; a circumstance which at least seems to show that he has carefully
observed, and correctly described the pAewomena, though in his attempt to explain
them he was (as usual) misled by a theory. The fact that the distinct acts are
not separately the object of any conscious volition or attention, he recognized by
direct observation : it was perhaps rash to infer the absence of these elements :
but if Hartley knew any thing about the art from which he exemplified his rea-
soning, he must also have observed, that these separate attentions and volitions
were in certain movements of the player necessarily impossible, and that, there-
fore, some other law must be sought for : the automatic movement is very like
the truth, and though liable to Mr. Stewart's objections, would be far easier to
support than his own solution. I trust to convince the Academy that there Is no
proof of the separate volitions assumed by Mr. Stewart, in either quick or slow
movements. Volitions there must be, but executed under the intervention of
another process ; a process, it js true, still to be referred to the effect of habit,

VOL. XIX. L

82 Rev. J. Wills on Mr. Stewart's Explanation of

but carried on in the progress of its operation to a much more complete result
than that contemplated by Mr. Stewart.

Let me call your attention to the actual Instance : two or more notes are
marked for the right hand to strike together, and perhaps as many more for the
left, all at the very same time, and by one movement in which several others, all
distinct in their effect and intent, are absolutely and indivisihly combined into one
act: a single impulse giving simultaneous movement and synchronous directions
to several members, and constituting, therefore, one conception in the mind of the
mover. The difference between such a process and the most rapid succession that
the nature of the thing can admit of, — say the vibrations of sound, — is as great
as the difference between the mere confusion of substances called mixture, and
the substantial union caused by chemical affinity : as that substance is one, so is
the effect in this case absolutely one, executed by one act, governed by one con-
ception— a single complex idea, the result of association. I agree with Mr.
Stewart, or rather with the common notion, in assigning this complex act to habit ;
but habit acting, not by mere acceleration, but by a maturer process to which it
is always tending, and which forms its main department of the mind; the combi-
nation of ideas which have been frequently presented, into recogiiized groups, of
which each, losing its features of aggregation, acquires an integral and distinct
identity of its own. Though I am anxious to avoid the adoption of any system
of metaphysical language, yet it will be convenient to keep in view, that the re-
sults here described are the same which are called complex ideas by Mr. Locke,
which term I shall retain through this Essay.

Let us dwell for a moment longer on this first case, and take one glance at
the general progress of the performer in the acquisition of the art by which those
complex movements are effected.

At first those signs must be separately observed by the learner, and the an-
swerable movements separately made ; two notes cannot be at the same instant
observed, still less their movements (altogether amounting to four distinct acts of
thought for one simultaneous act of the hands), be performed; though all are fully
recognized, no velocity of will and attention can impart the simultaneous execu-
tion required : the movements can only come separately, and, therefore, cannot
operate together. Slowly, however, and by continual repetition of the same
efforts of attention, the combinations begin to be seen as combinations, and be-

certain Processes of the Human Understanding. 83

coming virtually single conceptions are executed by single movements. One
act of volition can direct the most complicated movement when it is once thus
conceived. And it is a very remarkable and highly confirmatory fact, that the
slightest attempt to direct the attention to any of the separate components or
signs, would instantly disconcert the most practised skill. This Mr. Stewart
would have seen and profited by seeing, had he not selected examples of which
the component acts are not necessarily simultaneous. A performer on some kind
of instrument requiring a succession of uncompounded movements, may un-
doubtedly, by playing more slowly, attend to his separate touches, but then he is
not a case in point : for that species of acceleration of the mental processes
which can be actually observed, is not that for which Mr. Stewart would contend.
The point here to be established, is not that the mind may not operate with any
imaginable velocity, but that the assumption of an acceleration so great as to es-
cape all consciousness, is unnecessary for certain purposes, and a departure from
an observable and well known process. It is one thing to assert that the mind
can by distinct steps follow and regulate certain rapid changes of motion, and
another to assume that this process may become so rapid, as to be impossible for
the apprehension to follow it distinctly. The real difficulty which I shall have to
surmount is this, that there appears in this case, and some others, to be two dis-
tinct trains of thought going on. I mean, further on, to show that this is but
apparent, and I shall at the same time show that Mr. Stewart's assumption vastly
aggravates this difficulty.

A curious instance of the effect of separate attentions and volitions in cases
of complex action is not very uncommon. When a person of a very anxious
temper is called on for an exhibition of skill in some act which requires very
complex acts of mind, it sometimes occurs, that extreme anxiety to succeed forces
the attention from the common process, as here described, to an intimate notice
of the separate acts of the combination : and the links of complex volition are
thus broken, so that embarrassed movements follow. The best illustration of
this will occur farther on.

This last circumstance is most frequently observable in that extensive class of
acts, which, in popular phrase, we call mechanical. They are, indeed, nearly de-
cisive against Mr. Stewart; for, while they consist, for the most part, of complex
movements, the separate acts of which they are framed have never been recognized

L 2

84 Rev. J. Wills on Mr. Stewart's Explanation of

in separation, and cannot be taken asunder by any power of attention. Of these,
every person has his own share — one instance will be enough ; that, suppose of
unlocking some well known lock, which has become, by habit, so familiar, that it
can be effected in the dark. Now let any person who is conscious of any such
habit try to substitute his reason for the habit ; he will at once, and I would say
inevitably, fail ; his volitions and attentions will put his hand astray. In fact, the
operation of habit was to frame the conception of a movement, out of an actual
movement which, by the help of the sight, was first repeatedly performed. Of
such movements of frame and thought, are composed the entire actions of the
player's hand, the dancer's foot, or the reader's eye. And here it may be useful
to observe and bear in mind, that in all these cases, of every description, there ex-
ists at the same time a distinct succession of acts of will and attention, sometimes
continuous and sometimes changing, but always fully apprehended by the con-
sciousness ; and that the mind is in fact thus guided from change to change, and
from one complex act to another ; while these latter alone are the processes in ques-
tion here. According to Mr. Stewart, both must be going on together without
intermission, at different rates, and having different objects ; taking, for instance,
the player on the harpsichord, we have the movements of the hands, the interpreta-
tion of the notes, the relative intent of each to a certain whole harmony, the moral
sentiment belonging to the melody. Now had Mr. Stewart been asked to explain
this medley of concurrent processes, he must have been forcibly conducted to the
very theory which is here proposed to be substituted for his.

But I turn to Mr. Stewart's next example, suggested by a passage in the
Latin writings of Doctor Gregory, who applies a similar example to prove or
illustrate the rapidity of muscular action, for which he refers to the vast num-
ber and variety of intonations produced by muscular movements in the pronun-
ciation of words. With the Doctor's application I am not concerned. Mr.
Stewart says, " when a person, for example, reads aloud, there must, according
to this doctrine, be a separate volition preceding every letter." Now, I do not
here state Mr. Stewart's very indirect reasoning, because it consists altogether in
combating objections which have not, I believe, been advanced, viz., objections to
the possibility of the extreme rapidity of mental action required by the process
he assumes. I do not, for my part, deny the fact of such possible velocity of the
thinking power, though I see no force in Mr. Stewart's reasons for it. I only

certain Processes of the Human Understanding. 85

affirm that it is not proved by any of the alleged examples, and is not necessary
for their explanation ; and into the assumption of such a necessity, the entire
argument of Mr. Stewart may be resolved.

This example is very convenient for illustration ; I will, therefore, examine
it fully. Now let it be distinctly kept in view, that though the process of reading
is in both systems inferred to be the result of a power attained by habit, the dif-
ference is as to the nature of that attainment. Mr. Stewart's solution requires
that it should be by accelerating that succession of acts, by which every letter
of the word is separately noticed. If this be true, then, it is evident that the
facility can in no way depend upon perceiving the combination, as it is the prin-
ciple that every separate part must be antecedently recognized, and the perception
of the combination is but consequent. Therefore, it is quite immaterial how
strange the order in which letters are combined, when they are separately so far
known as to be instantaneously recognized. Now this can be tested. If any reader
who is sufficiently interested in the matter for an experiment, will take the trou-
ble to write out a few lines of new combinations of letters, forming words of the
ordinary number of letters, or get it done by another, and then try his skill in
reading those words with the usual rapidity ; he will immediately discover that,
however expert he may consider himself to be, he will be compelled to go back
to the old nursery discipline of spelling. Those extremely rapid attentions and
volitions will be found to fail when they should be efficient, if the assumption
of Mr. Stewart (for, after all, it is no more) be correct. Here, again, I might
pause to dwell on the consequences of Mr. Stewart's assumption. The same law
which demands successive distinct notices of the letters, essentially requires an
equally distinct and separate succession of perceptions of the several parts which
form the shape of the letter. The letters taken separately have each a sound
different from their syllabic effect, and this again is variously modified according
to the combination. Then comes to be recognized the sense which a word ac-
quires from context ; and lastly, the train of reason in which the intellect seems
to be wholly engaged. If all these several trains are to be separately noticed,
according to Mr. Stewart's law, it is evident what a complication of wholly distinct
trains of thought must be simultaneously proceeding ; but if Mr. Stewart should
stop at any point short of this, it is plain that his whole theory fails ; the explana-
tion he must substitute at that point may serve as well for the whole ; the neces-

86 Rev. J. Wills on Mr. Stewart's Explanation of

sity of the assumption no longer exists. Let me now call the attention of the
Academy to the law of progress, by which the requisite facility is actually attained,
both in this and all the other cases to which Mr. Stewart's theory of acceleration
can be applied.

So long as a direct and separate conscious attention is required to each of the
several letters forming a word, the process is that of spelling only ; the compo-
nents are separately and successively noticed, but the result (a wholly different
object of thought) is not perceived.

How, then, does the mind proceed ? It slowly, and by much discipline of
thought and repeated efforts, acquires a stock of syllabic and vocal associations ;
that is, it acquires a set of complex ideas and represented sounds. In these, it no
more separately notices the separate parts of the syllable than the separate parts
which constitute the form of the letter. And let it be observed, that in difficult
handwriting, it is hy the syllable that the letter is known, rather than the converse
process. Again, it is pretty well known, that in correcting the press, it is exceed-
ingly difficult to acquire the habit of perceiving literal errors ; while compositors
in printing offices have been heard to remark an occasional difficulty in readiilg
words and sentences, from their habit of attending to the letters.

Just in proportion to the expertness of the reader, and his intimate acquain-
tance with written language, the combinations become more extended ; and, in
consequence, the number and extent of the parts which escape notice also in-
crease ; as the letter became lost in the syllable, so the syllable becomes lost in
the perception of the word. Words acquire their visible symbols, and are dis-
cerned in such ill-formed scrawls, that no letter could be separately recognized ;
here it is evident that the general form of the word is enough for the mind. Even
common conventional forms of sentences are read with one single act of thought,
forming but one idea, registered by use ; and if any one wants an illustration, I
will refer him to the familiar fact, that in reading easy and idiomatic language,
the omission of words is often unperceived. The omission is supplied by the men-
tal eye ; it has become a portion of a known whole. To complete our view of
this case, a written word becomes identified with the meaning of which it is the
'visible symbol. By a further extension, a sentence becomes similarly identified
with a process of thought. Every one possesses a certain range of thought, all
of which habit has thus symbolized. And this range is various in its scope and

certain Processes of the Human Understanding. 87

breadth in different minds. Present any one with a wholly novel combination,
and he must pause to analyse.

The facts so far observed are no more than an analysis of the process of learn-
ing. The scholar slowly acquires a class of complex ideas, called syllables ; from
these he acquires another more compounded, as they coalesce into another class
called words. To this I may add, that, as ordinarily takes place in our complex
ideas, the combination is entirely (or, to a great degree) different in character
from the parts of which it is primarily composed. But, of this there are better
examples ; the sounds of the letters are to some extent preserved in most words.
Another reason why the example was calculated to mislead is worth notice, — in
speech, the sounds of most words are necessarily successive ; and this alone might
tend to conceal the simultaneousness of the mental act. But it will be at once
recollected that, in reading, the eye has commonly passed over many words, before
the tongue has performed its office.

The general inference is this, — that by habit, groups of signs, of movements,
oi facts, thoughts, sensations, or phenomena, acquire certain relations to each
other ; and these being acquired, it is the combination alone that becomes the
object of thought.

The parts come simultaneously to the apprehension or sense ; they do not_
even necessarily require to be complete ; it is enough if the character is kept.
Hence the deceptions in drawing — the faces in the fire, and the innumerable illu-
sions of the eye and ear; and, perhaps, all the senses.

I think that some more simple illustration of these facts may be satisfactory.
Mr. Stewart employs several, but for the most part they are not sufficiently fa-
miliar to convey much in the way of illustration. Before I proceed to their
analysis I shall, therefore, endeavour to apply the same investigation to some
very common and familiar acts, with which most persons must be acquainted.
In first learning to ride, there are certain niceties of posture and action, but still
of a very simple and easy nature, to be simultaneously attended to. These the
finished equestrian (unless he be a riding master) performs unconsciously, and
perhaps has forgotten in their separate forms. A simple volition executes for him
a compound posture of movement. But, look at the tyro, he learns in a few
minutes all the simple rules that are to be taught ; but he cannot govern the
gallop, or ride skilfully and with a firm and graceful seat over the bar or wall.

88 Rev. J. Wills on Mr. Stewart's Explanation of

He forgets the leg, while attending to the inclination of the body ; and the hand
neglects its office, while he thinks of his feet ; the saddle, bridle, stirrups, whip,
and spurs belong to different systems, and war with each other, and the idea of
preserving a graceful balance obliterates them all. Now, as the idea of succes-
sion is here excluded, and as the equestrian must keep all together, or roll in the
dust, the process becomes more clearly indicated ; he must necessarily acquire a
position of will or attention, of which all these minutias are the components.

In shooting, there are three acts to be executed simultaneously — the motion
of the gun, of the eye, and of the finger ; they separately present no difficulty ;
the young sportsman is, however, aware how hard it is to think of them toge-
ther ; the veteran executes them as a simple act conceived by the will, and per-
formed by the members. But this example offers a side-glance at the process :
for in shooting there is an obstacle very often found from the operation of ex-
treme anxiety to hit : the immediate effect of this is to cause a minute attention
to the means, so that the ordinary act is thus interfered with. The complex
volition is resolved into its component parts, and while the anxious marksman is
securing some part of accuracy, he neglects some other. The sure marksman does
not think of any methods ; but hits without knowing how it was done : his gun
seems to have learned its part, and comes up to his mark : he may tell you, if
you ask, that he never takes an aim. The fact is, that men do not recollect, and
often cannot find out the component ideas involved in their commonest acts : they
act with a single effort complex in its motions, but uniform and one in the im-
pulse of the mind.

It would be tedious to apply, at detailed length, the same reasoning to all
the examples given by Mr. Stewart : but it is fit and just to touch upon them ; in
order to indicate at least their connexion with the general process. They m^
all indeed suggest much, which I shall not notice until further on, when I shall
reach the more general statements which I think to be the results of this view.

The case of an expert accomptant is easily apprehended. The constant habit
of arranging numbers into groups, each group indicating a certain sum, is the
same process as that by which letters combine into words having each word a cer-
tain sense. This is too simply obvious to dwell upon.

But I would here call your attention, by the way, to the obvious difficulty, which
makes the conception of all unhabitual operations very nearly impossible to the

certain Processes of the Human Understanding. 89

human mind. In truth, it is only when the habit is actually acquired that any
idea of the act can be realized to conception ; and it then escapes the powers of
distinct analysis. But on this point I shall only need to remind you that the
same difficulty must exist, however the matter be explained. It belongs not to
the solution, but to the fact.

There is perhaps more real difficulty affecting the case of the jugglers, which
is noticed by Mr. Stewart. And the more, because, as in many acts of the mind,
it is in some degree entangled with other laws of action. Yet, so far as the
main point, it is not really difficult to explain. The eye and hand, with all their
involved rapidity, are still kept under the unerring government of a single con-
ception of a complex continuous movement, every part of which is together pre-
sent to the mind. Were it not for this, indeed, it would not be difficult to prove
that this, and all other similar feats, would be utterly impracticable. A distinct
interference of volition would arrest the juggler's flying and circling balls; as
it would precipitate the rope dancer, another of Mr. Stewart's cases, from his
dangerous height. In this case the movement and the balance are preserved by
not thinking of the emergency of the instant : but yielding to the constant action
of a conception and habitual impulse, which have been called mechanical, with a
just regard to analogy, because they exclude the uncertainty of the deliberate
and voluntary processes of the mind.

There is withal a distinction which I have hinted, but with which I did not
wish to complicate the subject, which demands notice. The cases which I have
referred to, as well as the numerous ones which might be mentioned, all fall into
two general classes : that oi instantaneous acts which present no difficulty, and lead
the investigation with the simplicity of self-evidence to the nature of the opera-
tion ; and those which, being continuous, appear at first less reconcileable to the
solution which explains them into a single idea. This difficulty (if such it should
be called) is but specious : there is no reason against the supposition of one idea
being held for any length of time, which the purposes in question require. I am
no more bound to the asssumption of a single instantaneous process than Mr.
Stewart. I am not bound to disprove, that habit facilitates, and therefore accele-
rates any constant succession of ideas : but the inference is as to the result, when
this succession has apparently ceased. And this result, according to the view
here explained, is simply this, that the limit of such acceleration is a coincidence.

VOL. XIX. M

90 Rev. J. Wills on Mr. Stewart's Explanation of

A result whieh, if this very faulty method of statement were to be allowed, would
amount to something different from the metaphysical asymptotes, involved in
Mr. Stewart's indefinite acceleration.*

There is one example brought forward by Mr. Stewart among the statements
by which he is first led to the conclusion which I have been examining in this
essay. I could not have noticed it much sooner without anticipating the infe-
rences at which I have now arrived. The following is Mr. Stewart's statement :
" It has been proved by optical writers, that in perceiving the distances of visible
objects from the eye, there is a judgment of the understanding antecedent to the
perception. In some cases this judgment is founded on a variety of circumstances
combined together, — the conformation of the organ necessary for distinct vision ;
the inclination of the optic axis ; the distinctness or indistinctness of the minute
parts of the object; the distances of the intervening objects from each other, and
from the eye ; and, perhaps, on other circumstances besides these : and yet, in
consequence of our familiarity with such processes from our earliest infancy, the
perception seems to be instantaneous ; and it requires much reasoning to convince
persons unaccustomed to philosophical speculations that the fact is otherwise."
I shall not here dwell on the very equivocal language used by Mr. Stewart. The
purpose for which he uses the example is, however, such as to imply the more
objectionable of two senses in which I might take his assertion of a "judgment
of the understanding antecedent to the perception ;" that is, that antecedent to
the perception some distinct exercise of reason, referring to the separate inci-
dents of the actual perception, occurs. In this sense, the mere statement is a suf-
ficient reply ; the notion conveys an utter absurdity. If, however, Mr. Stewart
simply means the process of the understanding, by which inferences respecting
the distances of visible objects have been gradually obtained; so that a judgment,
grounded on such reasonings as he has stated, goes before and modifies the per-
ception, forming, in accordance with his views, an antecedent part of it ; while the
extreme rapidity of the mind prevents any consciousness of the distinctness in
time between the two processes ; his fallacy is certainly less glaring, but I
must observe, that it only becomes so by simplifying the assumed process. Now,

• The method is faulty, because it confuses two very distinct classes of phenomena: the aggre-
gate perceptions of mere consciousness, and the complex formations of association.

certain Processes of the Human Understanding. 91

the fact is, that the species of reasoning to which Mr. Stewart refers the judg-
ment has no existence in any case. The reasons not only never occur to the
understanding, but are not to be found by it, unless in the case of opticians, who
are themselves so little aided by their reasons, 'that they have long disputed as to
the means according to which vision is accompanied by a judgment of distance.
The theory here stated reduces this question to a very simple and obvious law —
the same long ago stated by Mr. Locke in his chapter on the Association of Ideas.
By habit we are enabled to understand our perceptions as the indications of ex-
ternal things ; the import of a habitual perception demands no reasons of any
kind ; it is become a part of it.* As the eye approaches or recedes, the appear-
ances of things uniformly alter ; and as the mind grows accustomed to these altera-
tions, it insensibly learns to translate them into the constant fact. Should any
occasion of doubt arise, the reasoning then steps in ; it is, however, seldom derived
from the laws of vision. When the judgment is not involved in the perception,
it Jbllows it. The artist whose business it is to imitate the appearances of things,
imposes on the perception, by producing the same indications in a different way ;
it is then that the judgment becomes antecedent, and that the law of the appear-
ances must be ascertained. In the common exercise of vision, distance is recog-
nized as every other object of sight which constant recurrence has made familiar.
By habit, the eye, ear, and all the senses acquire their proper scales of adaptation
— a law involved in every movement of the frame, in every living thing.

There is another class of common facts, very curiously illustrative of the con-
clusion hei*e aimed at. I mean the numerous errors arising from our tendency
to combine, or from the habitual combinations of every individual. These, from
their nature, must be mostly peculiar, and even singular. Every one may recol-
lect some case in his own experience, and it is but a chance if any instance which
one person may offer will have come within the observation of another. An in-
stance may, however, be good for illustration. I recollect that once, on looking
at a picture which represented the interior of a cottage, with very unusual force and
truth, to have observed that the flame of the fire seemed to have the same quiver-
ing motion always accompanying the kind of flame represented. Now this could

• The perception is itself a complex state of mind ; it is composed of certain sensations, and
certain judgments.

m2

92 Rev. J. Wills on Mr. Stewart's Explanation of

not be the result of any real perception, but is easily explicable by the process
already described ; the form, hue, and motion of the flame had been so associated,
that the incident wanting in the representation was supplied, before the judgment
could come into operation.* Of this nature are those cases also, already slightly
adverted to, of faces framed by the imagination out of accidental lines. Let me
dwell a moment on this, for it is one of a large and diffusive class of results, to
all of which the same explanation will apply. I mean that class of expressions
and effects which must in part be referred to the fancy of the observer. The
expression of the human countenance offers an instance in which several varied
qualities of human character seem combined with certain dispositions of form, in
such a manner, that while the expression is instantly presented to the observer, he
can in few instances, and then but partially, and by much nicety of observation, as-
certain the precise arrangements of feature to which the characteristic expression
is due. I shall not encumber the case by an analysis of the origin of such combi-
nations ; it will be enough for the present purpose to observe, that the acquired
tendency to read such undistinguished elements into meaning must be very
deeply fixed ; to all purposes, it might be considered as instinctive. For, while
all can at once see and designate an ordinary expression, which is the result of cer-
tain lines of feature, the artist alone can discriminate the characteristic curve, and
reproduce the effect on his canvass. But now observe the consequence of the
associating tendency, — the strong prepossession which conveys ideas of expression
from lines Indistinctly discerned, will actually select and attach similar expression
to similar lines, when they appear in any mass of confused and indiscriminate
lines. The instant the eye rests on a single characteristic curve, this will be the
key to all the lines in the mass which (if I may so speak) belong to the same face.
The fierce eyebrow will impose on the eye a mouth of the same character, which
will be seen in its proper place. This case is the plainest of its class ; but all
the forms of familiar things are similarly traced by the vacant eye, out of formless
elements ; for these alone leave it free to the stream of association. From this,
I might proceed to the phenomena of dreams ; but the subject demands a separate
treatment, and must be referred to the conclusion of this Essay.

The cases so far stated to the Academy have exhibited the simple continua-

* The picture alluded to is the " Arran Fisherman's Drowned Child," by Burton.

certain Processes of the Human Understanding. 93

tion of a process which we can trace, to further phenomena of the same appa-
rent nature in which it cannot be so easily traced : but from which there seems
no reason to exclude it, unless one which should be noticed before I venture to
extend my theory to the explanation of some of the more complex operations of
the intellect. This objection consists in the difficulty of attributing so many
varied and continuous acts to one single conception, or moment of time. My
answer to this objection (here) shall be very brief indeed, being no more than
this, — that the self-same objection applies to Mr. Stewart's explanation of every
example he adduces. If twenty acts of will, or attention, or reason, or any other
mental process, take place in the time of one, the difficulty is not much dimi-
nished by saying they are successive, instead of simultaneous. In truth, no
power of intellectual comprehension or resolution can distinctly conceive either
one or the other ; they are creatures of reason only. I am aware of the infinite
divisibility of time, which is easily proved by the same argument which demon-
strates the same proposition of a line, on the parts of which it is only necessary to
conceive the idea of motion. I am also willing to assent to any proposition assert-
ing the infinite velocity of the thoughts ; I do not pretend to deny any thing on
the mere ground of not being able to explain it ; but I say that, so far as I can
venture to assert, the proof has entirely failed. The necessitas rei of Mr. Stewart
has no existence ; and if any solution is to be tolerated of those processes of the
mind which are so subtle, or so compounded, as to escape all direct analysis, there
is none more likely to apply, than that which, in simpler cases, is plainly and mani-
festly applied to the same offices. On this point, let me recal your attention to
Mr. Stewart's own argument against Hartley's theory, as I think we may now be
better enabled to perceive that it equally destroys his own, while it is not applica-
ble to that here offered. Hartley supposes the same processes, which are volun-
tary up to a certain rate of velocity, then to become automatic. Stewart very
justly remarks the disadvantage of assuming two wholly different laws of action
for the same processes, in different degrees of action. Now Mr. Stewart only
escapes the same objection, by giving the same name to different things ; this I
have already shown. But in my own solution alone the same law is manifestly
carried through, without the least abatement of its identity. Not being a sum-
mary operation, but the result of numerous operations, it does not in any way
involve the principle of consciousness, more than the growth of the body involves

94 Rev, J. Wills on Mr. Stewart's Explanation of

sensation. Unconscious from tlie very commencement, the combining process is
no worse than unconscious at the height and depth of its remotest combinations.
And if — in the indefinite progress of intellectual power, which no thinking per-
son will venture to limit — the elemental process which generates all our registered
and tangible combinations should give birth to combinations more broad, or
subtle, or varied, there is no reason why we should think it necessary to say that
these are beyond the limits of its office.

It is easy to perceive, as a direct consequence, that the operation which I have
explained by so many examples, must react upon all our perceptions, and there-
fore modify the very consciousness. All that we see or hear, and every intima-
tion of the senses, must become variously involved with suggestion, — or combined
Into these complex notions which I have stated as an ultimate result. This pro-
cess not only supplies the successive trains of recollection, which will arise at the
sound of a name or the sight of a place : but it will, under circumstances, identify
them into that indissoluble connexion, that often gives to place Its peculiar aspect,
or to countenance its familiar expression. Thus it is, that to different persons,
the poet, painter, geologist, or agriculturist, the same prospect of a country pre-
sents so different a scene. The whole frame of intellect and perception are al-
tered, and all that meets the sense formed into different combinations.

In the same manner, the moral structure of the mind is affected by the same
law. It would demand a separate essay to shew the precise operations by which
principles recognized by the intellect, and tendencies Implanted in the nature,
become variously involved, so as to become Inseparable in thought from circum-
stances, acts, and courses of conduct. For a dissertation admirably illustrative of
this, I would refer to Bishop Butler's chapter on Moral Habits. I shall here
content myself with pointing out an Important bearing of the principle. In pro-
portion as we act upon a determining motive, there takes place and grows a com-
bination which identifies the motive and the action, so that the principle becomes
Incorporated with the moving impulse. On the other hand, the converse process
takes place, when a separate attention Is frequently directed to laws of conduct
which are rarely carried into effect. The habit of distinctly regarding those
principles and observances, in proportion as it is cultivated, tends more and more
to give them separate identities in the mind ; so that the exercise of the reason
becomes less and less capable of moving the active tendencies of our nature.

certain Processes of the Human Understanding. 95

Hitherto the examples discussed have been more viewed as means of ascer-
taining a result, than for any interest of their own. I should, however, not have
pursued them into so detailed a discussion, were there not applications to be made
of more general interest and importance.

Before entering upon the application of the theory thus arrived at, to the ex-
planation of more complicated phenomena, it may be advisable to clear away a
slight difficulty which may otherwise appear to embarrass the language which
I am compelled to use in common with other writers who have taken different
views. Had I adopted a purely theoretical method, this explanation must have
commenced my statement, in the regular form of definitions : the method here
adopted has necessarily transferred these definitions to the conclusion : they are,
m fact, the questions under discussion.

In common with Mr. Stewart's, the theory here explained involves the as-
sertion of one law of operation pursued through different stages, in each of which,
its results, though in principle the same, are apparently different, and actually tend
to different uses. In these different stages, this operation has acquired different
names ; a circumstance which, while in ordinary language it undoubtedly contri-
butes to clearness, tends, at the same time, to baffle the metaphysical inquirer.
The river which winds through a hundred realms, is distinctly referred to these
varied localities, by the hundred names, which only help to confuse the general
map.

The term, association, is here used to signify the process by which ideas are
combined, through all the stages of this operation. It is assumed to be the ten-
dency of the mind to recal together, and permanently combine, oft recurring ideas
or phenomena. As by repetition the effect of this tendency is increased, a conse-
quence is that it must be experienced in different stages of progress : of these are
the several classes of suggestion, in which one idea leads to the successive recur-
rence of another, which has been in some way associated with it. The next dis-
tinguishable stage, is that which it has been the purpose of this Essay to illus-
trate, and which, for distinctness, I have called combinations, or complex ideas
of that kind which are formed by association*

* There are two distinct classes of complex ideas; viz., those framed by association, and those
acquired from the immediate constitution of things.

96 Rev. J. Wills on Mr. Stewart's Explanation of

CHAPTER II.

THE SAME ARGUMENT ILLUSTRATED BY A MORE EXTENDED APPLICATION — THE

ORATOR.

In passing from cases in which the mental process approaches nearly within the
ordinary range of that class of ideas, of which no one doubts the unity, it may
be necessary to proceed with new caution. Hitherto our instances have had the
advantage of the important character of being free from any element, not com-
monly recognized in single ideas : no difficulty has arisen from their duration, or
apparent variation ; all, as I have endeavoured to show, being comprehended toge-
ther within the limits of duration which appertain to single acts of thought. This
last fact is especially important to be borne in mind ; as it offers the essential
characteristic by which I would ascertain the unity of the mental process. But
when I distinguish the instances now to be explained from those already offered,
the distinction is only apparent. The difference in this respect is only just such as to
present a difficulty to the apprehension : the intellectual processes are the same,
and the reasoning, were it to be distinctly followed out, would be the same. This
will now, however, be the less required, as I have some trust that the elementary
process has been satisfactorily ascertained ; and the far more complicated nature
of the example now to be noticed would render the same method hitherto fol-
lowed, both tedious and difficult, and occupy an unwarrantable length of the
Academy's time.

I have already endeavoured to shew, that there can be no reason for fixing
any limits to the operation of the function which is known to be so active, or
which has so large an ascertained compass, as the associating faculty. From the
simplest commencement of its operation, where it is merely suggestive, to the
completion of its task, when oft-repeated association is lost in the simultaneous
unity of combination : from the simple combination which invests three or four
letters with a mora^ or physical existence, to the wide and varied array of remotely
related, or even discordant notions, forms, reasons, and abstractions, which, from
their compass, variety, number, and even inconstant and fleeting connexions, re-
ject the identifying stamp of a name ; all are still subject to the operation of a

certain Processes of the Human Understanding. 97

subtle process which is for ever going on, the most constant as well as the most
powerful of the mental functions. In this, also, essentially different from all other
mental functions of which we have any distinct notion, that it is independent of
all volition and consciousness ; and if the illustration be allowed, that it bears to
the recognizable and conscious operations of the mind a relation analogous to that
which the digestive and assimilative processes bear to the voluntary powers of the
frame.

There is no discoverable limit to the operation of the process here described,
though it only becomes distinctly cognizable as it comes within the province of
language. But before this condition is attained, and beyond the bounded compass
of language, there is an endless range of unfixed, local, and transitory combina-
tions of ideas ; some belonging to real existence, and some in their nature arbi-
trary and unreal : all, still, in some way connected with the ordinary operations
of the mind. Of this vast stock of ideal elements, the wrought and unwrought
materials of thought, there is a continuous transition in the progress of association :
some are connected no further than the first stage of mere suggestion — these are
the ordinary masses of our casual associations, and are, by the nature of things, un-
limited ; some have local relations, and are peculiar to times, places, individuals,
and professions — these may acquire the form oi combination in individual minds ;
others, lastly, from their uniform juxta-position in reality, acquire a permanent
unity, and the indissoluble stamp of a name. These last alone are universally re-
cognized in their real character; while the unlimited multitude of casual and transi-
tory associations, appearing in the various stages of the common process, from
the remotest suggestion to the most constant identification of an inseparable
unity, thus afford a seemingly wide scope for metaphysical discriminations and
classifications — while the process throughout is uniform. In following out this
varied succession of changes, there would be, however, the utmost complication,
as at every point the process becomes variously subjected to the active operations
of the understanding, which derives from it the entire stock of its ideas. I shall
now, therefore, aim to be compendious, and for this purpose select an example
which involves the utmost difficulties to which this inquiry is liable.

The intellectual habits of the public speaker have been explained by Mr.
Stewart, according to the theory which I have been endeavouring to supersede.
Lord Brougham has described them with the accuracy of a philosopher, and the

VOL. XIX. ^

98 Rev. J. Wills on Mr. Stewart's Explanation of

eloquence of a consummate orator. I quote this description, which is the more to
my purpose from the metaphysical propriety of the language, which seems to in-
dicate that Lord Brougham, had his attention been specially directed to the topics
here discussed, would have followed it out to the same conclusion.* " Whoever
(his Lordship writes) has observed the extraordinary feats performed by calcula-
tors, orators, rhymers, musicians — nay, by artists of all descriptions, can want no
further proof of the power that man derives from the contrivances by which
habits are formed in all mental exertions. The performances of the Italian Im-
provisatori, or makers of poetry off-hand upon any presented subject, and in
almost any kind of stanza, are generally cited as the most surprising efforts in this
kind. But the power of extempore speaking is not less singular, though more
frequently displayed, at least in this country. A practised orator will declaim in
measured and in various periods — will weave his discourse into one texture — form
parenthesis within parenthesis — excite the passions, or move to laughter — take a
turn in his discourse from an accidental interruption, making it the topic of his
rhetoric for five minutes to come, and pursuing in like manner the new illustra-
tions to which it gives rise — mould his diction with a view to attain or shun an
epigrammatic point, or an alliteration, or a discord ; and all this with so much
assured reliance on his own powers, and with such perfect ease to himself, that he
shall even plan the next sentence while he is pronouncing off-hand the one he is
engaged with, adapting each to the other, and shall look forward to the topic
which is to follow, and fit in the close of the one he is handling to be its intro-
ducer ; nor shall any auditor be able to discover the least difference between this
and the portion of his speech he has got off by heart, or tell the transition from
the one to the other."

In noticing the theoretical justness of the language here used, I overlook the
fact that, notwithstanding his theory, Mr. Stewart's language is equally accom-
modated to what I consider the truth of nature ; a fact which, indeed, leads to
the reflection — how much on the surface this truth is, had it been let alone. Mr.
Stewart's common sense and sagacity intrude upon his ingenuity, which I must,
in fairness, observe is not the characteristic of his sound understanding, and seldom

* The slight discrepancy will be accounted for by observing, that the subject occurs but inciden-
tally in his Lordship's discourse, and that probably the outline is suggested by the perusal of Stewart.

certain Processes of the Human Understanding. 99

leads him far astray from the track of observation. And it is, indeed, almost
apparent from his language, that a second and more deliberate consideration
would have led him to an inference, which, though opposed to his propositions, is
directly involved in all his language. He had only to ask himself the question,
why — having assigned so much of the very same operations to habit and associa-
tion as he manifestly does — ^he should stop at a certain point, and not observe the
strict analogy that pervades the entire work of the mind from first to last.

As the accomptant has insensibly treasured all the usual combinations of figures ;
as the fluent reader similarly possesses all the usual groups of letters, syllables
with their wonted sounds; as the musician has the same possession of the two
classes of simultaneous and successive indications of sound ; so, in the separate
pursuits of life, there is, incidental to every one, a peculiar range and grouping
of the materials of professional avocation, all so ready at command, and so inde-
pendent of separate attention and voluntary effort, as to admit to some extent of
other trains of thought being at the same time engaged in. The poetical land-
scape painter can, with one glance of his imagination, throw together into one
single whole, all the vast and boundless varieties of observed nature ; the modi-
fications of form, colour, light, and distance are at his command : sky with its
blue depths and fantastic pageantry of cloudwork, earth with its varieties of hill
and dale, forest and lake, from the mountain receding into etherial distance, to
the flowers and weeds which diversify and animate his foreground. These,
without conscious eflbrt, roll together like new creations, at the very caprice of a
moment. Nor is this all ; with equal facility the groups of life, armies, proces-
sions, and all the bustle and pageantry of civil life start up in the conception,
or fill an imaginary canvas with the additional incidents of representation, the
adaptations of life and proportion which deceive the eye. These combinations, —
and let me say, that I would not here dwell upon such a fact, did I not believe
it, in different degrees, common to all minds, — offer a wide range of the most
complicated conceptions of that kind which the mind most rapidly and easily
throws together with the fertility of a kaleidescope, because being mainly con-
versant with visible images, they demand less attention and study in their acqui-
sition, and form a great portion of the common stock. Every one is master of a
certain stock of intellectual maps of familiar places and accustomed roads, as well as
pictures and portraits, which supply the ofiice of terms. From the same compen-

n2

100 Rev. J. Wills on Mr. Stewart's Explanation of

dious source arise the similarly combined groups of our more purely intellectual
stores. The lawyer, together with the stock of precedents, maxims, and forensic
conventions and technicalities, which are to him an habitual language and rule of
reason, is also possessed of his treasury of phrase, adapted to the exigency of his
profession ; as he increases in practice, they grow together by the process of as-
sociation, as insensibly as the muscles of the Athlete, and acquire command by
training. With these he similarly obtains the habitual command of trains of
considerations, which being variously adapted to the questions that engross his
understanding, offer various and new points of relation to each other. These,
however varied, subtle, and remote, must, in proportion as they are liable to re-
cur in practice, become gradually arranged by some certain index of the mind
with more or less familiar combinations, and, therefore, demanding a greater
or less degree of separate attention to bring them together ; the less familiar de-
manding more distinct and separate efforts of thought, because they are either not
at all, or less, involved in the common process. But still, only in proportion
as the combining processes have taken place, will the operation, so lucidly '
described by Lord Brougham, be performed. To the more experienced mind,
or the more powerful and richer intellect, vast and seemingly boundless galleries
(if I may use the metaphor) of views, combined in order, and ranged in their
due subordination and distance, will start at every suggestion ; and trains of rea-
soning, which hours are insufficient to express, will be placed like a picture before
the mind. Of this, too, every mind possesses its share, but it is not given to all, or
even to many, to look with a length and breadth of intellectual range that might
well pass for inspiration along the chain of consequence to the remote conclusion.

Every pursuit and every character of mind has its own range, in which it
gathers intellectual combinations of its own, incomprehensible to most others.
It is needless, and would occupy a long discussion, to dwell on these unconscious
commonplaces, the ideal or verbal associations of politicians and poets, moralists
and preachers. I should use one description for all ; the science does not exist,
nor perhaps the intellect to produce it, which could reduce so wide a scope of
method, arrangement, and material, into a practical compendium. It would hold
the place to thought which logic does to reasoning, or rhetoric to language.

But here it may be useful to guard against the suspicion that two distinct
processes are confused. Let it be observed, that in the whole of the operations

certain Processes of the Human Understanding. 101

to which I have adverted, I do not exclude the operation of any other process
that may be insisted upon. I simply have endeavoured to place due bounds to
an usurpation in favour of some known faculties, and to restore to another its
own due jurisdiction. I am not to be understood as excluding the separate work-
ings of attention and volition from their very observable place in every one of
the operations just noticed. But what I have contended for is reducible to the
nearly self-evident fact, that in the course of all habitual thoughts, there is a point
where the separateness of associated ideas ceases to be perceived, and I say, that
at the same point these separate acts of attention and volition also cease ; they
are neither necessary nor conceivable, or indicated by any sign, and their as-
sumption is, therefore, altogether gratuitous.

The orator, as he follows out the details, which appear in the perspective of
his ideas, will direct the minutest attention to each as it passes in array: while he
is following out this long chain, he is obviously exerting a voluntary and con-
scious attention to the verbal evolution of its parts. And the very same law of
association which offered the first summary glance of his whole argument, operates
as he proceeds, and presents similar combinations at the separate stages. With
this, suggestions, which are no more than imperfect associations, are starting
up in proportion to the range of the speaker's mind. But reflect what an absurd
medley of processes there should be, if we admit that throughout this lengthened
operation the whole chain is still retained before him by a continued succession
of iterations of the same rapid series of separate attentions and volitions ; the ne-
cessary consequence of Mr. Stewart's assumption, that this chain is put together
by this inconceivable operation : whereas, by the explanation which has been here
offered, the formed combination is already there, lying like a text-book before a
lecturer, and needing no jarring dance of imperceptible volitions and attentions ;
volitions unwilled, and attentions unattended to : no inconceivable analysis to
supersede and frustrate those fundamental operations to which, by Mr. Stewart's
own repeated admissions, direct or implied, the very power of thinking at all is
due.

The view here oflTered may be illustrated with some precision. Every one
may be supposed to dwell within some circle of familiar localities which are va-
riously combined in his memory. Within this compass a hundred roads and by-
paths are within the instant command of his recollection, and as in conception

102 Rev. J. Wills on Mr. Stewart's Explanation of

he places himself in each successive point, a wide variety of scenic combinations
spontaneously arise on his mental vision, each of them filled with different succes-
sions of locality. Strictly analogous is the intellectual horizon of the practised
professional speaker, within the range and compass of his habitual associations.
The analogy may be further pursued even in the failures to which either is liable,
when his thoughts attempt to travel out of the accustomed range : though he may
possess a general knowledge of his line of road, the traveller must lose the chang-
ing combinations, the side views, and the shifting backgrounds ; while the orator,
in like manner, must want the varied suggestions, and the rapid transitions, so ex-
cellently described by Lord Brougham.

His language, supplied as language is by habitual combination, will become
less appropriate, flowing, and effective ; and should he not have the good sense
to perceive quickly the really narrow limit of his power, and take due care to
keep within its scope, he will soon become embarrassed by an effort to maintain
his usual superiority.

There is another not unfamiliar affection to which unaccustomed speakers
are occasionally subject, which may be considered to illustrate the elementary
process in a different way. When a young speaker, in his great and earnest
anxiety, instead of yielding his mind to the spontaneous processes already de-
scribed, begins to exert an enforced voluntary effort, and to look for that lan-
guage in one way which should be obtained in another ; a total embarrassment
often seizes him, he begins to look for the path on which he should be moving,
and he can see nothing more than the preconceived outline, which it had been his
design to clothe variously in effective language, and with all the popular artifices
of rhetoric.

In thus dwelling on the example offered in this section, I cannot but observe,
that I could have selected others far more illustrative of the argument; but I have
thought it fairest and most satisfactory to pursue the subject as it has been argued
by Mr. Stewart and others who have fallen into his views.

certain Processes of the Human Understanding. 103

CHAPTER III.

APPLICATION TO DREAMS.

In dreaming, the ideas which press themselves are either such as have been pre-
viously connected by association, or not. If they have not, Mr. Stewart's theory
cannot be applied, nor will such cases be found illustrative of the mode of expla-
nation adopted in this essay. Both, though in very different ways, involve the
principle of association.

Cases of dreaming occur in. which the succession of thought appears too ca-
pricious to be easily referred to any of the waking habits of most minds, and
though even these may be, to a considerable extent, explained according to the
law of suggestion, yet it will be apparent enough that they cannot be considered
as cases of that succession of thoughts, which has become accelerated from the
effect of frequent iteration. In these it must be observed, that the process is
directly contrary to the process of waking reason. Awake — certain ideas are ac-
companied by a rapid combination (or acceleration), such as not only to facilitate
the course of the thoughts in some established direction, but to prevent any other;
whereas, in sleep, the occurrence of the same idea leads mostly to a different train,
which could not well take place if the same associative (or accelerating) faculty, in-
stead of being more alert, were not itself asleep, or nearly so; and it is very curious
to observe, how the suggestions of the waking faculties change in the very process
of falling asleep, so as, indeed, to indicate very clearly that the faculty which
governs the connexion of our thoughts has partially at least resigned its office.
The most familiar things take monstrous forms, and begin to play strange an-
tics, which are to be noticed as tending to show that particular operation of
habit, on which Mr. Stewart relies for his solution, to be diminished, and ren-
dered comparatively inert in sleep, just as the other faculties are.

Now, let us see what Mr. Stewart's notion Involves. The associating faculty
acts in sleep with increased energy, and according to a new law.

First, it acts with increased energy, or in other words, is more awake in sleep.
When awake it can only read, play the piano, or execute such operations as it has
learned from repetition; but asleep it acquires the power of accelerating all those

104 Rev. J. Wills on Mr. Stewarfs Explanation of

thoughts over which it has no such power when awake ; it can compose new
novels with a rapidity unknown to Scott, and dramatize them with a facility be-
yond the joint efforts of Shakspeare and Garrlck. No matter with what lumber-
ing incapacity, or what inert and floundering dulness its waking thoughts may
be combined, all at once in sleep, it can take the wings of Ariel and " Put a
girdle round about the earth in forty minutes," or rather in the twinkling of an
eye. — So much for increased energy.

But it acts according to a new law. Mr. Stewart says not. He meets the
objection by those solutions which I have already gone through. But if these were
even granted, the matter is not mended. For a moment, assuming Mr. Stewart's
explanations to be all correct, it will yet appear that the sleeping and waking
processes have the essential difference of a new law.

According to Mr. Stewart, the process of the mind, when awake, becomes so
rapid that separate attentions and volitions grow imperceptible ; if so, how does
it happen that in a case of the same supposed process in sleep they all become dis-
tinctly perceptible and conscious ?

The romance comprising a long succession of events, occurs in an Instant,
but all the parts of which it is composed are (according to Mr. Stewart) so sepa-
rately attended to that they could not be more observed assunder, if they actually
took a long period of time. Here, then, is one difference ; there is not only an
increase of power, but a different mode of action.

But I have another question to ask — if the assumed rapidity of ideas does not
escape the attention, when asleep, and does when awake, why is not this character
at least uniform ? why, in fact, is it reversed ?

Why, in sleep, do not all the other operations of habit become similarly re-
solved, by separate acts of attention, into their constituent parts ? If this law were
to be followed out into its consequences, there could be no such thing as a dream
at all ; thoughts would be thus resolved into their elements, and the mind could
not think even for the purpose of dreaming. The case amounts to this ; when awake,
the effect of habit enables the mind to pursue a succession of musical notes, so
fast that it cannot have a conscious perception of their separate occurrence: when
asleep, it seems to have acquired a faculty the converse of this ; that is, it accele-
rates a succession of slow operations, which, when awake, no power of conception

certain Processes of the Human U?iderstanding. 105

could so compress together in the mind ; and then it actually does perceive their
separate occurrence. Now I will not undertake to deny the possibility of this
mode of operation, because I do not think that any thing should be denied or
affirmed without proof; but I say the case is clearly different from the former

•

examples with which Mr. Stewart has attempted to illustrate and explain it.
The attention which follows and dilates into a history, the rapid phantasmagoria
of the dream, should, by the same power, separate the letters of a word, and the
components of all our perceptions. It is plain that any acceleration supposed in
the former cases, must involve some process different from the latter, and that the
result also is opposite.

But it is needless to grapple with a theory which rests on nothing at all; the
difficulties inseparable from Mr. Stewart's solution, entirely disappear when the
process of habit is rightly comprehended, and directly applied.

When a complex conception, formed, as I have already explained, by the or-
dinary law of habit, offers itself to the mind, it presents one undivided and simul-
taneous combination. I am now to apply this principle to that class of dreams
which can be considered instantaneous : to such alone the argument of this Essay
extends.

I shall here for the present assume, for the assumption does not affect the argu-
ment, that there are two classes of dreams ; those which are instantaneous, and
those which are not. It is of the first I .am here to speak. The first and
greatest difficulty affects me in common with Mr. Stewart, for whether the
aggregate of ideas which passes during the explosion of a pistol shot is succes-
sive or simultaneous. It is equally hard to comprehend. They take place in the
time of a single act of thought, and I say, that they constitute but a single act ;
the nature of this I have fully explained, and it only remains to point out its
probable application to this case.

In looking at a familiar combination of words, the intellect receives both the
ideas of their appearance and their sense, long before the eye could have noticed
all the separate letters, syllables, and words. In fact, only a part is looked at ;
but the mind, which is slow to analyze its own operations, is impressed with the
sense of having separately noted all. Now such is the case of the dreamer ; to
understand it, no more is necessary than to recollect the observed fact, of which
every one who dreams is aware, — I mean the tendency of the mind to realize its

VOL. XIX. 0

106 Rev. J. Wills on Mr.. Stewart's Explanation of

ideas in sleep. Think of a person, and he stands before you, and with him all
the most prominent associations connected with him ; these, too, appear as objects
of sense, being realized to the imagination. This fact is, indeed, well worthy of
attention from those ingenious writers who have investigated the subject of
dreams ; and if I do not greatly err, it will be found to offer the specific principle
from which all its peculiar phenomena arise. The effects of imagination cease to
be distinguished from the effects of sensation. The conception, or intellectual
sign, is in the dark isolation of sleep confounded with that thing, the presence of
which it liabitiially signifies ; for though the intellect is obscured, and its action
partial, yet so far as it does act, it follows the same laws of action as when awake ;
but the direct and manifest result is an illusion easily understood. The shadows
of things being thus invested with the conditions of seeming reality, and exempted
from the interference both of sensation and will, lead to a natural illusion. The
mind, deceived by the whole combination, judges as we judge in looking at a
perspective deception ; the whole of the accessory ideas becoming similarly rea-
lized, modify the process. It is not the person only who appears, but the person
doing some characteristic act ; which act carries with it the supposition of other
accessories, in which may be involved the ideas oi distance and succession. Thus
a few characteristic facts may compose the illusory perception of a story, just as a
few characteristic touches convey the illusion of a picture to the eye. The sole
difficulty, indeed, which may seem to affect the entire process, is the apparent suc-
cession and duration ; the duration we know to be an illusion, and the succession
(without duration) is resolved precisely into the common analogy of all the other
examples 1 have noticed. There is, indeed, no reason why the idea of duration
should not follow the common law of all our ideas. When awake, there is a
real perception which is contradictory to the illusory perception. Asleep, the
idea is subject to the general effect already stated as a common condition of the
mental operations in dreaming ; with the conception in which it happens to be
involved, it becomes seemingly realized, and consequently becomes a distinct fea-
ture of the illusion ; the moment has expanded into an age, because it seemed to
embrace the occurrences of an age. If the thought of eternity should present
itself, or of infinity, the imagination becomes oppressed with some vast field of
darkness, or the burthen of some endless endurance. The idea of duration is sub-
ject to the same conditions by which all other ideas are affected. There is, per-

certain Processes of the Human Understanding. 107

haps, no idea so apt to be held in due subordination to the reality of things ; and
yet every one can at once recal cases enough in which it is liable to be variously
falsified in the perspective of thought. The case of dramatic fiction may, perhaps,
be considered most apposite ; a train of occurrences, which involves the idea of
time, is presented ; and though the waking man is quite cognizant of the actual
state of the case, yet a latent but operative impression follows the law of habit
more quickly than the judgment of the reason ; and the conditions of a fictitious
succession are sufficiently realized, to affect the imagination. To produce such illu-
sions, in the highest perfection, is indeed the end of a subtle art, by which the
poet can impose his waking dream upon the reader.

" Qui pectus inaniter angit,
Irritat, mulcet falsis terroribus implet,
Ut magus: et modo me Thebis, modo ponit Athenis."

But when, in sleep, a complex conception or train of ideas (for I suppose
either case), involving the idea of succession, is presented, the idea then not
mei'ely alfects the imagination with a latent impression — the impression takes the
form of reality, and the conception becomes affected by the elements of time and
space. A picture when dreamed of is likely to assume the appearance of reality,
because the artifice of perspective suggests the impression of distance ; and every
♦ other combination may convey similarly some impression, which, once received as
real, alters the condition of the case. And here let it be observed, there can be
no controversy on the point ; however it may be explained, the idea of duration
is unreal ; it must at once be admitted to be but a component idea — involved,
to be sure, in a very curious manner well worthy of attention, but offering abso-
lutely no obstacle to any theoi'y in question. But having gained this point, it
suggests a good deal.

First, were we to look no farther, it seems plain that the same explanation may
be applied to any other ideas which may seem to form parts of a dream ; that (to
use the short cut of illustration) the dream was but as a face seen in a fire, in
which a few leading lines take the shape of a familiar combination, and, though
imperfect, carry with them the entire of that which they partially represent. The
same process (whatever it may be) which gives visible appearance to a mere idea,
may be well supposed to give visionary completeness of outline to a few random
touches of thought. This, let it be observed, has a very distinct parallel in the

o2

108 Rev. J. Wills on Mr. Stewart's Explanation of

known illusions of the pencil ; a few imperfect, but characteristic, lines can be so
placed, as to convey as much as the most complete representation. But sleep
seems to carry the process of deception much farther. I have, for instance, fre-
quently observed, what must have occurred to many to notice, that in sleep the
mind is strangely imposed on as to resemblances. The absurdity of the most fan-
tastic changes and representations is seldom, if ever, noticed ; and if a dream of
any supposed incidents be attentively called over after waking, it will be observed,
that in many instances the impressions were not only unreal but false.

Little now remains to be said, so far as the topic of dreaming is involved in
this inquiry. Our thoughts, as I have shown, present themselves in varied aggre-
gations. In different minds the constituent ideas of the aggregation are diversi-
fied by the habits and intellectual constitution of the individual ; but while these
aggregations are liable to be presented in sleep as in waking, there is j ust one
condition of difference, which, without altering any of the primary laws of thought,
by direct consequence changes the entire character of the result. This condition
is simply the realizing of the idea. Under this operation, the slightest and most
latent impression which constituted any part of the waking association, in sleep
starts into shape, and becomes an efficient and distinguishable feature of the
dream. A dream may thus be considered as a picture presented to the sleeper's
fancy, sometimes full of meaning and orderly subordination, sometimes strange, •
fantastic, and unaccountable ; at times the object is some preconceived associa-
tion, and occupies the ordinary duration of thought, but still undergoes the effect
of being dramatized in all its parts, because, in fact, such a consequence is abso-
lutely involved in its being realized ; and it Is thus also that those seemingly in-
stantaneous successions arise. Again, the actually present scene, or circum-
stances, may be part of a dream : and the sleeper will then awake under the
sense of reality.

I shall now end with a few remarks upon the manner in which the ordinary law .
of association, considered simply as suggestive, may be supposed to operate in a
state of sleep. For this purpose it must be observed, that the action and reaction
of associations are mutual, and that, therefore, in sleep, if any moral affection of the
mind is, as may happen to be, induced by some fantastic cause, it will, according
to the known law of habit, immediately suggest some such occurrence as would
ordinarily have caused it ; suppose, for example, the parts of the frame which

certain Processes of the Human Understanding. , 109

would be affected by violent weeping to be acted on by some cause purely physi-
cal : now, even when awake, the moral frame of mind is in some small degree
liable to the species of external action here supposed ; and the fact is general ;
there is no train of correlative affections either between mind or body, or between
the thoughts and affections of the mind, that is not liable to commence at either
end of the chain. When we are awake, this liability is regulated by the action
of other causes ; the processes of the mind are subject to both the will and the
senses, there can, therefore (generally speaking), be no illusion ; the scenes and
occupations of reality are before us, and all the control of the active faculties is
in operation. Now, to recur to the examples just given, a person, if he is of a
delicate frame, may, under the influence of some nervous affection, be, even while
awake, disposed to gloomy views of affairs ; but let him fall asleep — he is instantly
head and ears plunged into a bottomless abyss of perils, distresses, and labours,
defined or undefined, taking form in the shape of some gigantic calamity, or cloud-
ing the prospect with the obscurity of terror and inconceivable ruin. It becomes
a dream, or that species of oppressive consciousness which is called a nightmare.
Now, if the images of a dream are supposed to be presented in succession, a
very different order of phenomena from those hitherto contemplated takes place;
all, however, the result of the two main principles now stated, viz., the apparent
realization of the idea, and the governing law of suggestion. The general con-
dition will be best conceived by an illustrative method of statement ; but first let
me impress the two points to be illustrated. The moment the thought occurs, the
thing appears : and as every thing is likely to present some suggestion, no sooner
does it appear than some new fancy starts to mind, so as to place the whole in a
new relation to the dreamer. This may be exemplified : a person dreams of some
friend who lives in a distant city ; the individual at once becomes present : this
individual exercises some particular calling, or has habits which characterize him;
these at once are suggested and realized ; they absolutely imply the notion of
some locality, and the locality becomes present. This implies a change of place,
and at once, as if his night-cap were the wishing-cap of the fairy tale, the dreamer
is transported with a thought over the intervening billows or mile-stones, and
without any interruptions from collisions, explosions, or upsets, is set down in the
well remembered street. No sooner is he there, than his friend, who is, perhaps,
a great traveller, begins the story of some adventure in returning from the con-

110 Rev. J. Wills on certain Processes of the Human Understanding.

tinent ; or not being very hospitably disposed, asks him by what road he means to
go home. Instantly at the word, a rush of waters, and the wind roaring in the
shrouds, salutes his ear ; or he is hurled away on the Liverpool railroad ; and if
he had the ill luck to have looked into any of the public journals that evening,
he is startled into a terrified consciousness by the explosion of a boiler, or the shock
of trains rushing into collision. Such is the fantastic chainwork, in which the
same laws which contribute to maintain the coherence of our waking thoughts,
operate to disarrange and confuse them into the obscure phantasmagoria of
dreams.

CONCLUSION.

The subject of dreams has led me somewhat beyond the strict argument of
this Essay. There is, perhaps, no class of affections to which the mind is liable,
so adapted for the purpose of investigation on the elementary laws of association.
Mr. Stewart's chapter on the subject of dreams offers also a singularly pleas-
ing and Instructive example of that just method of philosophical induction, of
which there is generally so lamentable a dearth in all inquiries respecting the
intellectual faculties.

But Mr. Stewart set out with a notion, which was not merely adapted to lead
him into some important errors, but altogether to shut from his view the actual
law which regulates the succession of thoughts in dreaming.

I regret this the more, because. If I am not very much mistaken, I shall here-
after show, that the elementary facts illustrated In this Essay would have other-
wise offered to this sound-minded Inquirer, a simpler and better evidenced foun-
dation for the whole structure and action of human reason, than has yet been
fully noticed by any of those who have turned their thoughts to the subject : this
1 trust to be enabled to explain satisfactorily hereafter.

Ill

yi. — Memoir of Researches amongst the inscribed Monuments of the Grceco-
Roman Era, in certain ancient Sites of Asia Minor. By James Kennedy
Bailie, D. D., late F. T. C. D., and Lecturer of Greek in the University.

Bead May 9 and 23, 1842.

PART I.

THE APOCALYPTIC CITIES.

I. IHERE are few departments in the extensive field of classical antiquities
which have excited greater interest, or to which scholars have applied themselves
with more zeal, than the philology of inscriptions ; those memorials of past ages
which, more intimately than perhaps any other monuments, bring us into con-
tact with the laws, the institutions, the manners, and, it may in a certain sense
be added, the languages of the civilized nations of antiquity. On this point I
feel assured, that it is quite unnecessary for me to enlarge at any great length
in the hearing of my present auditory, composed as it is of persons who are fully
prepared by their respective studies and accomplishments, to acquiesce in the
truth of what is here stated; but as it has fallen to my lot, recently, to be placed
in circumstances peculiarly favourable to the giving me a somewhat clearer in-
sight into the various details of this branch of literature than I had ever possessed
before, to a juster appreciation of its value, and to the improvement of my know-
ledge of it, by enabling me to prosecute my studies and my researches at the very
fountain-head, it will not, perhaps, be regarded in the light of a presumptuous
attempt on the part of the writer of the present memoir, to endeavour, by sub-
mitting it to their consideration, to awaken a spirit of inquiry commensurate to
the importance of the subject. This, in the present state of literature and literary
research, it would be difficult to overrate.

VOL. XIX. P

112 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

The Continental philologists, particularly those of Germany, have long since
devoted their attention, proverbially so unwearied, to the elucidation of these
* remains. Their profound and exact learning has contributed in a pre-eminent
degree to its establishment, as a most valuable and interesting department of
literature. They have travelled with the zeal, and deciphered with the acumen, of
devoted students ; or from the professor's chair have poured fresh streams of
light on the sense and construction of the monumental language. I here refer
especially to the Germans ; and, for evidence of what I state, I deem it sufficient
to mention the names of Thiersch and Creuzer, of Miiller and Bockh. The
" Corpus Inscriptionum Graecarum," of the last of these scholars, will long re-
main a monument of his industry, learning, and profound research ; it affords,
at the same time, a convincing demonstration of the utility of this branch of
philological science ; for by his exact acquaintance with it, he has been enabled
to clear up many points of extreme interest in the social economy of the ancient
inhabitants of Greece, which had been involved in much obscurity before. It
has supplied him with an extensive and a solid basis for the construction of his
most valuable work, " Uber die Staatshaushaltung der Athener," an attentive
perusal of which is of such essential importance in the investigation of the Attic
monuments, and the study of the Attic literature.

To the third of the abovementioned names, the deceased and lamented
Miiller, I cannot refrain from paying the tribute of a well-merited eulogium.
He also was distinguished amongst the foremost in this, as well as in other de-
partments of Greek learning. With the genuine ardour of a Philellenist, he
visited the shores of Greece, penetrated into her territory, mixed with her
children, disinterred from the sepulchres in which they had lain so long en-
tombed, the sculptured monuments of her pristine magnificence, and gave them
once more meaning and life. I shall not soon forget the impressions which were
made upon me when visiting one of his favourite scenes. It was at Castri, the re-
presentative of the ancient Delphi. I was conducted by his host to the site of
the ApoUoneum, and within an enclosed space to which he directed my attention^
on the very ground of the Peribolus, I found ranged the huge masses of en-
graved and sculptured blocks, which by Miiller's perseverance had been laid
open to view. Here was labour for months ; I might say more truly, for years ;
for the entire extent was one continued series of engraved characters ; the re-

of the Grceco- Roman Era in certain ancient Sites of Asia Minor. 113

cords of the Pythian shrine for generations on generations ; and yet the part
which had been exposed, formed, in all probability, but a small proportion of the
monuments which still remained under ground ; and which the deceased scholar
would doubtless, had his life been spared, have rescued, as he had done their
fellows, from their present state of oblivion.

The efforts which Miiller made cost him dear. A few months before ray
arrival at Delphi, he had been carried off by a malignant fever, which had been
brought on by his incessant labours. It is said that he was engaged in preparing
a history of Greece, and that this visit to her shrine had been paid in the hope
of discovering amongst its vast mass of inscribed monuments, inedited materials
for his projected work. Nor would his expectations have been disappointed :
for the little which I was enabled to observe, and the less to glean, amongst
those treasures, sufficed to convince me that a rich and abundant harvest awaits
the student in that spot, whether his attention be devoted to the sacred annals of
Greece, or to researches into her dialects.

The great work of Professor Bockh to which I have referred, leaves, it is
true, all other publications of the same class at a vast distance behind it. It may
most justly be styled a national performance, and has beeh executed with talent
proportioned to the munificence of the government under whose auspices it has
been published. It is impossible to read a page of that work without being
impressed with the highest admiration of the learning and critical acumen of the
author. It is a vast repertory of political and philological learning. Under the
first of these heads, I comprehend all subjects which relate to civil economy, all
hieratic details, all private or domestic contracts ; under the second, the phi-
lology of archaic forms, as well as the more known usages of the refined dialects
of Greece and its dependencies.

But justice to the merits of British scholars demands a meed of praise to be
awarded to them, for having contributed in no ordinary degree to the advance-
ment of this literature. We all are acquainted with the names of Pococke,
Chandler, Chishull, Clarke, and Rose. I mention these amongst a great num-
ber of others, as the representatives of their class, but not by any means as en-
titled to a monopoly of the honour which is due to talent, labour, and research.
The " Antiquitates Asiaticae" of the third of these, Edmund Chishull, was a pub-
lication in all respects worthy of the character which he had already acquired by

p2

114 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

his work on theBustrophedon Inscription of Sigeum, and which had brought him
into a certain degree of collision, not derogatory to his scholarship, with the illus-
trious Bentley. This, and the publication which succeeded it, I reckon to be, on
the whole, the most important of any which had appeared on palteography before
the volume of Rose, who, in redeeming the pledge which his abilities and learning
had given, had the advantage of an improved state of antiquarian knowledge,
and of literary correspondence of the highest order.

His learned volume, entitled " Inscriptiones Grsecae vetustissimae," was pub-
lished in 1 825, at the expense of the University of Cambridge, and is enriched
with prolegomena and notes, evincing considerable research, a great part of them,
moreover, the fruits of his intimacy with Professor Bockh.

A kindred spirit has animated the scholars of other nations ; for example,
Italy and France ; the first of which can recount such names as Maffei, Lanzi,
Visconti, amongst her contributors to this department of learning ; whilst
France has had her Spon, a traveller, — and amongst her antiquarians, a Bar-
thelemy. a Raoul de la Rochette, and a Boissonade. I refrain from naming
another who certainly made considerable noise in his day, but whose archaso-
graphical exploits in the Peloponnese have handed down his name to posterity
with a somewhat worse than an equivocal reputation attached to it : for it is, I be-
lieve, a matter of notoriety, that the researches of Fourmont have not benefited
scholars so much as his vain and dishonest pretences have occasioned them
trouble in disengaging the ore from the dross, what was truly classical and
authentic from the unlearned and spurious admixture.

The character of this traveller may be sufficiently estimated from the fact,
that Professor Biickh has devoted an article of much length, in his great work,
to the exposure of his forgeries. Nay more, it is even reported of him, but
with what truth I can only judge from hearsay, that, such was his narrow-mind-
edness and illiberality, he caused, in many instances, monuments to be defaced,
lest succeeding travellers should profit by their inspection. This at least I can
state with certainty, that some instances of this ungenerous temper have been
pointed out to myself during my tour in Greece.

In concluding this part of my subject, it may be interesting to my audience
for me to remark, that the educated classes of Modern Greece are directing
their attention to this amongst other branches of Hellenic literature. It was

of the GrcBco- Roman Era in certain ancient Sites of Asia Minor. 115

my good fortune, during my stay at Athens, to become acquainted with the
gentleman* who is at present employed by the Greek government as Curator
of Antiquities in that metropolis, and to benefit by many interesting conversa-
tions with him on the present state of learning in Greece, and the progress of his
researches. He is himself an author, having given to the public a topographical
account of ancient Athens, which has been translated into several of the modern
languages. He has collected, moreover, in the Acropolis and the Theseium
(which were the principal scenes of my labours), a considerable number of
statues, busts, reliefs, and inscribed tablets, most, if not all of which, have
been published in Ephemerides, and in his own work. This consideration,
however, did not deter me from prosecuting my researches in the same field, and
holding a converse on Minerva's height, or within the sanctuary of the hero-god
of Athens, with her jurists, her priests, her statesmen, and her warriors.

But I press forwards somewhat too rapidly. Greece, though the principal
scene of my labours, was one of the last ; and it is my present intention to lay
before my fellow-academicians, with all the respect which is due to so learned and
distinguished a body, a summary of my researches in the order in which they
were conducted. I might have observed a different, and, for some purposes,
perhaps a more convenient arrangement ; I mean by this, a classification of the
documents which I have collected, according as they related to public or to private
concerns, to secular or religious, to the historical or the purely legal. Of all these
I possess examples, viz., treaties, lists of magistrates, treasury accounts, temple
inventories, epitaphs, with a great variety of others, which have unfortunately
been so mutilated and defaced, as to afford a wide scope to the student in such
matters for the exercise of his palaeographical sagacity.

Now, an arrangement under these several heads presents many advantages,
when the subject is made a study : and a more convincing proof of its expediency
cannot be cited than from the great work of Professor Bockh, wherein the reader
is at a loss which to admire most, the lucidity of the disposition or the accuracy
of the details. But as the circumstances under which I appear before the
Academy, and hope shortly to present myself before the public, are somewhat
different from those of the mere editor, I have deemed it best to be guided in a

116 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

great measure by them, that is, to follow the course of my recent travels ; to
conduct my hearers over the ground which I have traversed ; and at my halting-
places to share with them my palace, my hovel, or my tent, as the case may be ;
and then to unpack before them my treasures of by-gone ages, whether sought in
the desert, or amidst the habitations of my fellow-men ; whether surrounded by
the ruins of ancient splendor, or the tombs of departed greatness ; whether ex-
posed to the chilling blasts of the alpine region, or fanned by the zephyr of the
valley, or scorched with the rays of a tropical sun. Limited as I was to a certain
period of absence, it was quite impossible for me to consult my ease, or the state
of the weather, in making my visits to ancient sites. With but rare exceptions,
I was in constant motion; I was in consequence subjected to innumerable hard-
ships and inconveniences, from which travellers in those imperfectly civilized
reo-ions, who have time at their command, are enabled to exempt themselves. I
was accordingly forced to traverse the burning plains of Asia Minor in the dog-
days, and to make my visit to Greece during mid-winter, in which region I shall
not soon forget the perils my health and person encountered, more especially in
the interior of the Morea, where the country has been, until very lately, a per-
fect wilderness ; and the more civilized districts of which are but slowly emerging
into social life, after the terrible vengeance wreaked upon the Moreotes by the
hordes of the Egyptian Pasha. Roofless dwellings, wasted fields, ruined villages,
and an Impoverished people bade mournful welcome to my retinue and myself,
after many an hour's exposure to "the pelting of the pitiless storm" in the
alpine solitudes of the Peloponnese. Nor has that scourge of Greece, under the
Musulman rule, the pestilence of the Klepts, been wholly banished from the
country ; although, thanks to an improved system of police, and some vigorous
measures adopted lately by the government, the evil has been materially dimi-
nished.

The researches of which I propose to give the Academy some account at
present, commenced in Asia Minor, and embraced the following sites ; Ephesus,
Gheyerah (the representative of Aphrodisias), Ailah Shehir (the ancient Phila-
delphia) ; Sart, that is, Sardes ; Kirkagatch, a Turkish town on the road from
Thyatira to Pergamus, and which the inscriptions found there seem to prove to
have been in some way connected with Stratonicea : Ak-Hissar, which occupies
part of the site of the ancient Thyatira ; Pergamus ; Eski-Stanpiil, the site of

of the Grasco- Roman Era in certain ancient Sites of Asia Minor. 1 17

Alexandria Troadis ;* Beeram, the representative of Assos ;f and one or two
other places of minor importance, in the Troad, on the site of Roman military
stations, where I collected a few Latin inscriptions.

This list, to which is to be added a small collection which I made at Smyrna,
comprehends my labours in the department of inscriptions during two excursions
which I made from that city ; one around the churches of the Apocalypse ; and
another to the Dardanelles, returning by the coast to Smyrna.

Of these sites, Aphrodisias and Thyatira furnished me with by far the
greatest number of inscriptions. Indeed, so numerous are the inscribed monu-
ments in the first of these places, that the principal trouble devolving upon the
traveller is a selection of the most important, or those which illustrate best the
ancient records of the place. I find fifteen of these inscriptions in my note-
book ; but at least ten times that number solicit the attention of the antiquarian :
and accordingly the curious in such matters will find, in the last published volume
of Mr. Fellows' travels in those regions, a much larger collection of the inscrip-
tions of Aphrodisias than I have made. It will be borne in mind, however,
that that gentleman worked at a great mechanical advantage, for, avowedly un-
acquainted with Greek literature himself, he adopted the plan of what may be
termed mechanical copying ; in which way two or three sheets of the soft Turkish
paper will perform in a few minutes as much work as would cost ordinary drudges,
who have the misfortune to know something of the language, as many hours to
get through. Any one, however, who has seen his first volume, will clearly ap-
preciate the advantages of this method. Whenever an inscription is at all de-
faced, and the most valuable are generally not the least so, the thousand lines
which the chisel of time has indented in it, are as faithfully represented in the
mechanical counterpart, as those of the epigraph itself; a source of error most
prolific, as well as vexatious, to the decipherer afterwards, when threading his
way through the palaeographical labyrinth.

The strangest readings have, in consequence, found their way into that part
of Mr. Fellows' first volume which relates to Inscriptions. His second, which has
recently made its appearance, I have not had time to examine with the minuteness
which it seems to deserve.

• Acts, xvi. 8, 11. t Ibid. xx. 13, 14.

118 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

Rejecting, therefore, all such contrivances for facilitating or expediting
labour, my uniform method was, to make myself acquainted, in each instance
which presented itself, with the import of the words, when it was at all possible
for me to do so. This, after some practice, was of great utility in enabling me
to abridge the trouble of a repeated inspection, as established formulse were of
constant recurrence, and the known succession of words thus at once suggested
itself to the mind. In cases, where the characters were so defaced or mutilated
as to afford no clue, or next to none, to the sense, my practice was to read
the several tituli orthographically, that is, to resolve them according to the
known laws of termination of their components ; I mean, according as they were
nouns, verbs, or particles, thus to establish what may be termed resting-places
for the eye, while the hand was occupied with the task of committing the record
to paper.

This method, or rather what was consequent upon it, dexterity of trans-
cription, effected often somewhat more than a mere abridgment of labour : for
it is clear, that the same law of sequence which enabled me without actual in-
spection to anticipate sentences, supplied me also with the means of restoring
them when broken off or effaced. I have thus been frequently guided to the
general import, at least, of a document, the first appearance of which was most
unpromising to the copyist.

An example, or two, may not be uninteresting.

There are few formulae of more constant recurrence, particularly in the
ancient sites of Asia Minor, than epigraphs on the coffers {<ropo\) in which
families of distinction laid their dead. By far the finest of these I met with
was one in the upper quarter of Akhissar, the ancient Thyatira, it wanting only
the operculum, but the body of the sarkophagos being in perfect preservation.
The name of the individual who had caused it to be constructed is recited, the
spot where he had it placed, the purposes which he had in view ; and then fol-
lows a prohibition to all others meddling with, or in any way making use of,
the soros, under a heavy penalty, which might appear to have been twofold ; but
this I shall explain more fully in its proper place.

The titulus concludes with stating, that the customary formality was observed,
of a copy (dvTiypa(j)ov) being deposited in the office of the registries, (to dpxelov,)
in this case, perhaps, the senate-house ; with the name of the pro-consul for the

of the GrcBco- Roman Era in certain ancient Sites of Asia Minor. 119

time being, the date of entry, and the name of the scribe (drj/xoaios,) or registrar,
by whom the document was entered.

The study of this most valuable monument enabled me to restore, in con-
siderable part, three inscriptions to the same effect, which I found also at Ak-
hissar, but in a different quarter of the town, namely, the Armenian cemetery.
The extent to which they had been mutilated would otherwise have made it a
hopeless task, as it is the custom of that people to re-work the ancient soroi for
their own sepulchral purposes, and to provide room for emblematical devices,
and epigraphs in their own dialect, without much respect to the Grseco- Roman
monuments. Of this I observed more than one example at Akhissar : but the
most remarkable instance I met with, was in a tomb at Kutaieh, the represent-
ative of the Cotyaion of Pliny.* The soros from which the Armenian selected
his materials had belonged to a Greek family of the highest distinction, as is
evident from the style of embellishment which it still exhibits. It is now covered
with Armenian devices and characters, the former of which are easily distin-
guished from the reliefs of the more classical era.

The possession of this epigraph (to remark in passing), has enabled me to
correct one of the oversights in Mr. Fellows' first volume, which was doubtless
the result of his expeditious mode of transferring inscriptions abovementioned.
This it has done by furnishing me with an important name, which had un-
questionably been recited in that gentleman's inscription, but has been left out
by him in his appended explanation as unintelligible. But this is not all. The
consideration that this name was connected with Cotyaion restored another, and
an important, reading in the same inscription, a geographical one, which had
been totally disfigured by his mechanical process.

One of the inscriptions which I have brought home from Smyrna, supplies an
excellent example of the mode of dealing with such as have reached us in so
mutilated a state, as to preclude all hope of our arriving at a knowledge of their
exact import. Such titull as these are best studied in situ ; and the resolution to
which I have adverted above, should precede the process of copying, otherwise
the chances are, that the most embarrassing mistakes will ensue.

The epigraph to which I now refer, was copied by me from an irregularly

* Histor. Nat. v. 41, 1.
VOL. XIX. Q

] 20 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

fractured block of marble, which has been built into the east wall of the Venetian
fort of San Pletro, and consists of ten lines, each numbering from seven to ten
letters. It is plain, therefore, that but a meagre fragment of the entire monu-
ment remains, and, unfortunately, without any word of so precise an import as to
throw light on its subject-matter or date. This is the more to be regretted, as there
is something in the air of the inscription, which informs us that it was of a good
era ; and that the monument had been destined to perpetuate some remarkable
event in the history of the town, perhaps the earlier, or that previous to the
Roman dynasty. There is an allusion, in the first line, to an embassy, either to
or from Greece ; one, in the second and third, to the free constitution of
Smyrna : another reference of the same import perhaps, in the fourth and fifth ;
in the remaining lines, more especially the ninth and tenth, the allusions are to
its allies and confederates, but whether states or personages we have no means of
determining. It may be, that the concluding expressions comprise both.

The learned Society which I address, will apply these hints to specific events
in the Ionian history, in which the city of Smyrna was prominently engaged.
We know, in general, that intercourse with Greece Proper was constantly main-
tained by the Asiatic confederation ; in particular, that the games formed a most
important centre of union.* Again, there was the treaty with Seleucus, which
is not obscurely hinted at by the abbreviator of Trogus ; f lastly, there was the
league formed by the citizens of Lampsacum, Alexandria Troadis, and Smyrna,
in favour of the Romans against Antiochus.|

To which of these, if to any, the fragment under consideration refers, we
have but scanty materials for determining. The terms in which it concludes,
TOYSEYNOI AS^YNEP that is, cooperators in offices of good-
will, S)C., should lead us to infer, that the states of the Ionian alliance, either in
whole or in part, had been mentioned in the document : but unfortunately, not
a trace of their names has been preserved. It occurred to me, when studying
the inscription on the spot, that possibly it had formed part of a supplement to
the provisions of the treaty with the citizens of Magnesia (ad Sipylum), in
support of the interests of Callinicus, which has been brought over to England
by the Earl of Arundel, and the student of such matters will find published at

• Pausan. v. 8, 2. f Hist, xxvii. 2. % Liv. Hist, xxxiii. 38 ; xxxv. 42.

of the Grceco-Roman Era in certain ancient Sites of Asia Minor. 121

length in Prideaux's volume.* The characters are certainly sufficiently antique
to countenance this, or even the supposition of an earlier date : but beyond con-
jecture we have no data for proceeding.

Its allusions however, general as they are, cannot fail of inspiring much
interest. In the hope of eliciting something more definite, I searched, in com-
pany with a gentleman of Smyrna, who most kindly attended me through the
city, in every accessible quarter of the building, for the remainder of the monu-
ment, but without success. The rude hands of the semi-barbarous constructors
of the fortress had, in all probability, consigned it to perpetual obscurity in
laying the under-courses of the masonry. The portion which they had placed
within sight, had been so chipped and otherwise defaced in the progress of the
work, that it is probable, had the expeditious process of copying it been resorted
to, the result would have exhibited an unintelligible mass of confusion.

There was some degree of inconvenience attendant on the study in situ, as
the marble was at least five-and-twenty feet above the street-level, and I was
obliged to employ a ladder placed against one of the buttresses, in order to obtain
a sufficiently close inspection of its contents. This was in a densely inhabited
quarter of the town, next the market-place ; and in a very short time I had
more company with me than I could have desired. The generally received idea
amongst the Turkish population is, that we explorers of ancient monuments can
have no other object in encountering so much trouble for the sake of such ob-
solete reminiscences, than a vague notion that they point to some hidden
treasure. Their cupidity is accordingly, still more than their curiosity, aroused ;
and this has proved a fruitful source of the injury done by the Mahommedans to
the finest treasures of the classical period :

« Hoc fonte derivata clades
In veterum monumenta fluxit."

My collection of inscriptions commenced, as I have said, at Ephesus. When
I first reached Smyrna, having been limited by my diocesan, the Lord Primate,
to an absence of but six months, it was my intention to visit the Apocalyptic
sites alone, and that being effected, to return straight home. A period of sojourn

• Marraor. Oxon. p. 4, § 94, 95.

Q 2

122 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

so brief, would evidently not have admitted my forming any collection worth
mentioning of such treasures. I was soon, however, relieved from my fetters,
by the extreme kindness of his Grace, who, in consideration of the object which
I had in view, relaxed his parting injunction : for a letter that awaited my return
from Pergamus, announced the gratifying intelligence, that my term of absence
had been doubled; a great boon to a traveller in those regions, in which
twenty-five or thirty miles is the ordinary length of a day's journey, and no faci-
lities exist for expediting his movements beyond that limit ; and, I must add
also, eminently characteristic of the personage who conferred it.

I now proceed to enter somewhat more precisely into my details. I believe
I have already mentioned, that the order which I mean to observe is that of my
visits to the respective sites ; a choice more agreeable to my recollections, and
as fit as any other, perhaps, for presenting my acquisitions to the Academy. I
now speak with reference to the Apocalyptic cities, reserving to myself the
liberty of deviating from this rule in the case of others of less moment. I mean,
however, in all cases, to classify each separate series, so as to avoid the chaotic
jumble which one meets almost invariably in travellers' collections, as also,
where the state of the monument at all admits it, to give a general outline of
its contents.

II. Ephesus, at which celebrated site I arrived on the eighth of September,
1840, and where I commenced my labours in this department of research, fur-
nished me with three. I could have had more, but I made choice of those
which I had some reason to suppose had been little known or noticed before. I
copied them from a cubical block of marble which lay half concealed in the
midst of some agnus castus on the left-hand side of the road that skirts the cita-
del (called by the Turks Alasaluk), and conducts to the lower town, if it be
not a misnomer to apply the term to that wretched vestibule to the splendid ruins
which overspread the valley of Coressus.

Each of the three inscriptions to which I now refer is mutilated, the intro-
ductory matter, or, as they may be termed, the preambles, being in a great
measure wanting. This defect has arisen from the block of marble, on three
faces of which they had been engraved, having passed, most probably, through
the hands of some mason ; I shall not say Turkish ; for I regret to be obliged to
remark, that the degenerate representatives of the ancient possessors of the

of the Grceco-Roman Era in certain ancient Sites of Asia Minor. 123

country, are, for the most part, quite as ready as their masters, to appropriate to
less worthy purposes the records of the civilization and the taste of their fore-
fathers.

All these Ephesian inscriptions illustrate in the strongest manner the ex-
pressions of the sacred historian, Ti? yap iariv avdpcowos os ov yivcocTKet ttjv
i(f)€(ricou ttoXlv uecoKopou odaav ttjs fieydXrjs deas apre/MiSos ; * the first two
having been framed with the avowed intention of enforcing and perpetuating the
worship of the tutelary goddess of that celebrated emporium. Sufficient of the
preliminary matter of the longest of these remains to inform us as to the grounds
on which the ruling powers of Ephesus founded this and similar decrees ; the
document forming part of a Psephism which had been enacted by the senate and
people. Its purport was to command the strict observance of the entire month
Artemision, by a succession of festivals and assemblies, which are termed
iopToi, lepofjirjuiai, Travrjyvpeis ; the second being Introduced, as appears evi-
dent, with a special reference to the Artemlsiac solemnities which were ordained
for a particular month. Thus the sacred month of the Nemean games, or rather
the collective series of solemn observances which were enjoined as appropriate to
that period, are termed by Pindar Upo/xvla vefied^.f

There are curious and interesting allusions in the preamble of this decree to
the circumstances which we know from other sources to have existed amongst
the Macedonians, the Egyptians, and the people of Laconia, namely, of their
having had sacred months ; the first and third, their Artemisius, for holding
assemblies and celebrating feasts, called in this section of the Psephism einixrfvia.
I regret to observe, that the passage which completed the argument from ex-
ample, by citing that of the Egyptians, has been exceedingly defaced ; but
sufficient has remained to enable me to determine with tolerable certainty, that
this had not been forgotten, as, fortunately, the first syllable of the sacred month
has escaped the ravages of the destroyer. Now, the names of the Egyptian
months are perfectly well known, as are those also of the Macedonian, of which
the learned Ideler has given a catalogue comparatively with the Athenian and
the Syro- Macedonian. J In this, the Artemisius of the second of these peoples
corresponds to the Munychion of the third, at least on Plutarch's authority ; and

* Acts, xix. 35. , f Nem. iii. 4.

% Handbuch der matheniatischen und technischen Chronologie, Th. i. ; p. 39 in Passow's Lexicon.

124 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

this again to the third of the Aratorial months, as represented in the sculptures
which I saw in the Memnonium, and of which Sir Gardiner Wilkinson has
given us an account in the first volume of the second series of his invaluable
work.* Its name, both in his book and elsewhere,f is written Phamenoth. The
query suggests itself, could this have been a contraction for Phtha-Amon-Thoth,
a triad of Egyptian deities, and expressive of the conjunction of the intellectual
with the generative and demiurgic powers ? Two of the months of the season
of the water-plants have been named after single divinities, Athyr and Thoth ;
why should not the same custom be observed in the case of a greater number,
particularly as we know that it was usual for the Egyptians to form such groups ?
Thus, we have the triads of Thebes, Syene, Philae, &c., the especial objects of
adoration in those districts. J

However this may be, it is certain that in the Ephesian inscription, the ini-
tial syllable of the desiderated month, which Is expressly stated to correspond
to the Macedonian Artemisius, is HTA, and that the letters which are now
effaced therefrom occupied a space about equal to its last two, supposing them to
have been MOYNQG.

Here, however, a slight difficulty arises from the representative of Artemis in
the Egyptian Pantheon having been Pasht, or as the Greeks expressed it,
Bubastis. This may be met in two ways ; firstly, by supposing that the framer
of the decree merely intended to express the coincidence between the Artemisius
of the Greeks and the Egyptian Phamenoth ; for his words are, Jnd the most
convincing proof of this religious veneration is, that the month denominated

Pta (by all the Egyptians) has been called by the Macedonians and

the rest, the Laconians, and the cities in their territory, Artemisius. In the
second place we may add the fact, that Pasht was a member of the great triad of
Memphis, and the usual companion of Phtha, or Hephsestus, by whom she is
stated in the hieroglyphic formulae to be " the beloved."§ This makes it highly
probable, that the great festival which Herodotus || mentions as having been
celebrated at Bubastis in honour of Pasht, took place in the month of which we
have been treating ; and if this supposition be correct, the author of the Psephism

• Vid. pp. 377, s. f Rosin. Antiqq. Rom. p. 954.

t Vid. Sir G. Wilkinson, vol. iv. p. 231. § Ibid. vol. iv. p. 280.

II Ibid, ubi supr. p. 279. Herod, ii. 39, s.

of the Qrceco-Roman Era in certain ancient Sites of Asia Minor. 125

shewed great judgment in thus enforcing its provisions by an appeal to the
religious usages of those who were the undoubted founders of the Greek mytho-
logical system.

I am now conducted to the second of these tituli, which is, as I have already
observed, decapitated. Part, however, of the preamble remains, which was con-
ceived in the same spirit with that of the foregoing. The observance of the
Artemisiac festival is enforced by an appeal to the piety and the devotion of their
predecessors; and then the decree concludes with consecrating certain days,
doubtless, of the month Artemision, perhaps indeed the entire thereof, to the
solemnities of that festival, during which Armistices (e/cexet/j/ai) in particular
were to be observed. We are further informed, that this was a decree of a
grand convention, {wavqyvpLs), the same which Thucydides terms a synodos,*
and the whole concludes with the names of the Prostates, or president of the con-
vention, and of the Agonothetes, or director of the games. f These are, Titus
Aelius Marcianus Priscus, and Titus Aelius Priscus.

The next inscription, which also has been mutilated, comprises the latter half
of a resolution or decree of a Panegyris in favour of some distinguished citizen,
ordaining a statue (termed in the conclusion TLfxi]) to be erected in his honour.
This is prefaced with an enumeration of his public services in the following
instances ; in matters which related to the panegyrical assembly, and the
solemnities of the sacred month ; in the establishment of what is here termed
the Artemisiac Judgment {rj dpTefiia-iaK^ Kpiats), by which I understand either
the games themselves, or the court for the regulation of their details, over which
the Asiarch for the time being presided ; in augmentation of the prizes of the
Athletes ; lastly, in the erection of statues in honour of the successful candidates.

The only name preserved in this titulus is that of the individual to whom
the convention had confided the office of providing for the erection of the statue,
viz., L. Faenius Faustus. It might indeed be supposed that this individual had
undertaken the office, of himself, and at his private cost ; but I choose rather
to think that he was the agent of the Panegyris, notwithstanding the use of
dvaa-TTjcravTOs, not €7n/jLeXr]deuTOs rrjs dvaaracreco^, as in an inscription of a si-
milar purport which I copied at Philadelphia.

• Hist. iii. 104, fcty»x„ |iroS<.{ tS> iuiui. t Hist. i. 127; ii. 179; vi. 127.

126 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

These Epheslan monuments cannot but be regarded as possessing much to
interest us, from the notices which they contain of a prominent idolatry of the
Panionian Confederacy. But interest of another order attaches to them also in
the eyes of the Christian antiquarian, who will not fail to perceive in these
strenuous efforts of individuals and bodies of men, marked indications of a de-
caying worship, and melancholy forebodings. The address of the silversmith of
Ephesus* is familiar to all here, which presents so remarkable an instance of the
admixture of low and sordid motives with the more elevated feelings of national
vanity and pride : and doubtless, Demetrius was not only a skilful artist, but a
sharp-sighted spectator of passing events. He well knew the versatile character
of his fellow-citizens, and trembled for his craft ; with what justice, these docu-
ments of a somewhat later era sufficiently attest : for to what are we to attribute
these efforts of the heathen priesthood to reconstruct, to invest with additional
solemnity, to fortify with more stringent sanctions, the worship of their tutelary,
but the astounding fact, that the temple of the great goddess was fast falling
into contempt, and that the magnificence of her, whom all Asia and the world
had worshipped, was about to be destroyed ? How truly the illiterate artisan
predicted coming events ! What a contrast his misgivings present to the as-
sumed tone of confidence with which one of the state documents described above
concludes ; inasmuch as this will conduce to the promotion of the honour of the
goddess, which will continue more glorious and in higher repute, on those days,
for all succeeding time ! The vaunted magnificence, and with it the decrees, of
the proud Asiarchs of Ephesus, have crumbled, and are still crumbling, into
dust, whilst the anticipations of her humble mechanic are inscribed in indelible
characters on the ruins of her palaces and her shrines !

Between Ephesus and Laodicea, which was the next site that I wished par-
ticularly to visit, I took the road which included the towns of Aidin, Nazeleh,
Yeni-shehir, Gheyerah, and Serai-kui, which represent in their order the ancient
names of Tralles, Nysa,f Antiocheia, Aphrodisias, Karoura.J Of these, the

* Acts, xix. 24, ss.

t Viz. according to D'Anville. Vid. Ansart, Not. in Plin. v. 29, 6. This, however, is ques-
tioned.

X Vid. "Visit to the Seven Churches," &c., by the Rev. Fr. V. J. Arundell, p. 73, and accom-
panying Map. Strab. xii. c. 8, p. 75. Tauchn.

of the GrcBco- Roman Era in certain ancient Sites of Asia Minor. 127

fourth, or Gheyerah, presents highly interesting remains of temples and other
public buildings, whilst inscribed monuments lie scattered on all sides in such
profusion, as to render a judicious selection of their contents the chief difficulty
of the traveller. I remained there for three days, during which interval I copied
a considerable number of inscriptions in different quarters of the ancient site.
The labour and difficulty of this operation was much enhanced by the extreme
heat of the season, and my disinclination to adopt any mechanical device for cur-
tailing either.

It is not my intention, at least for the present, to submit to the Academy the
result of my sojourn at Aphrodisias, but to connect it with another series, and
make these the subject of a separate memoir. I mean now to treat of those in-
scriptions alone which I have brought from the Apocalyptic sites, and one or two
other places which lay in my road. The Aphrodisian Tituli, I mean the whole
number which I found existing, would be sufficient to form a large volume of
themselves.

The site of Tralles supplied me with none. I made anxious inquiries re-
specting them of the person who accompanied me in my excursions through the
Acropolis and other quarters of the ancient town, but received the discouraging
answer that all such monuments had disappeared. This gentleman (who was
the Pasha's physician) chose, for obvious reasons, to convey his sentiments on this
subject to me in Latin. I have a vivid recollection of his concluding words,
which were uttered with strong emotion : " Lege Strabonem : ille omnia con-
spectul dabit : sed monumenta delevit barbara manus."

I pass over Eskl-Hissar, the representative of Laodicea, and Pambuk-Kalessi,
that of Hierapolis, as barren in the immediate materials of my present research.
Desolation more utter and more disheartening can scarcely be conceived than
that of Laodicea ; and the extraordinary vision which met my eyes at the second
of those places, wholly engrossed my attention during the brief period of my stay.
The remains of its baths, its temples, its amphitheatre, and more than all, the
singular phenomena of its stalactitic concretions, render it one of the most inte-
resting sites in the whole extent of Anatolia. But the feeling of utter loneliness
and desolation is the same there as in the neighbouring locality of Laodicea. Not
a habitation is to be seen, after the adventurous traveller has crossed the narrow
ledge of rocks by which the ruins are approached from the plain of the Lycus.

VOL. XIX. B

128 Dr. Kennedy Bailie's Researches amongst the inscribed Monumetits

The solitary Turkoman tending his charge, the jackal, and the viper, are now
the only tenants of this once celebrated resort of the masters of the world and
their Asiatic tributaries ; for the saline baths of Hierapolis made it one of the
most frequented watering-places in the Roman dominions.*

We shall now recross the Maeander, and penetrate the defiles of the Mesogis,
on our way to A'ilah-shehir, the fair city, as it is called by the present possessors
of the country, the representative of Philadelphia. It is usually set down In
maps as AUah-shehr, that is, the city of God ; a coincidence with its former eccle-
siastical status, which, were it well-founded, would be remarkable, and which has
been noticed :f but this is a mistake: the Turkish name of Philadelphia is but
a variation of another which has been given by the present possessors of Asia
Minor to other celebrated sites, distinguished, as the town of Attains is, by the
natural beauty of their position. I refer to the name Ghiuzel-Hissar, or beau-
tiful castle. Thus, they call Tralles, and with the greatest justice, A'idin-
Ghiuzel-Hissar ; and Temnos, In the fine coast-country between the chain of
the Sipylus, and the river Hermus, Menamen- Ghiuzel-Hissar. Philadelphia,
which lies in one of the most beautiful recesses of the Tmolus, over the rich
plain of the Katakekaumene, amply merits its present name.

But I must not forget my more immediate concern at present, the inscrip-
tions of the ancient town. In these Philadelphia Is by no means rich. I could
discover but four or five : one on a block of marble, which now serves the town
porters as a support for their loads, but had once been part of the pedestal of a
statue erectedlnhonour of a personage of consular dignity ; two entaphial, and a
fourth, which I discovered on the outer angle of one of those massive supports

* Vid. Plin. V. 29, 3. Strab. xiii. 4, p. 157. Tauchn.

t See the Rev. Mr. Arundell's Visit, Sfc, p. 169. There is a strange confusion here. The
author has written the name Allah Sher, and seems to think it capable of the double meaning : this
is not the case : there are, in effect, three Turkish names, which closely approximate to each other
in sound, but in meaning are quite different, which may be applied to Philadelphia, viz., Allah Shehii;
the city of God ; Aildh Shehir, the fair city ; Alia Shehir, the red city. The second of these is
the true Turkish name.

Were my classical associations to get the better of my veracity, the aspect of the Buz-dagh
(Tmolus) and of the bed of the Pactolus, would incline me to adopt the last of these. The stream
still remains, at least in one sense, the Chrysorrhoas of the ancient naturalist.

of the GrcBCO-Roman Era in certain ancient Sites of Asia Minor. 129

that attest the former magnificence of the edifice to which they belonged, the
church of St. John.

In the first of these, the name of the consular has been preserved, Flavius
Archelaus Claudianus, as also that of the person to whom the erection of the
statue had been confided, Glyko (or Glykis) Papias, whose rank as Bularch* is also
mentioned.

The last cost me infinite pains to acquire, from its very elevated position,
and the inconvenient manner in which the builder had placed the stone on
which it had been engraved : I mean to explorers such as I am ; for his own exigen-
cies had compelled him to place the lines in a vertical position at the outer edge
of the building. To add to my dissatisfaction, it turned out, after all the trouble
I had taken to obtain possession of its contents, but a fragment, and that a
meagre one, of the original composition. Sufiicient, however, remained to direct
my subsequent researches to its probable import. A name has been most fortu-
nately preserved unmutilated, which is familiar to every reader of Claudian ; and
from the pages of his vindictive satire on the discarded favourite of Arcadius, I
have been enabled to fill up the imperfect outline which the quoin of St. John's
has supplied.

The name here alluded to is Eutropius, one most convenient to the purpose
of the author of this epigraph, which was to bequeath to posterity a marble-
graven record in verse, of the courage and generalship of an officer whom that
courtier had employed in an important military operation. It occurs twice in
the course of the inscription, which was composed in lines alternately hexameter
and pentameter. Of eleven of these but the initial fragments remain, presenting
only the first, or (and this in two instances alone) the first and second feet.

The historical fact which I brought to bear upon this monument, with a
view to its elucidation and, if possible, restoring it, was that which has been de-
tailed so amusingly and with such power of ridicule by Claudian, in the second
of his poems against Eutropius, namely, the ill-concerted expedition of his gene-
ral, the woolcomber Leo, against Trlbiglld, or as he is called by Claudian, Tar-
glbilus, the Ostrogothic leader, who had invaded Asia Minor, and was then
occupied in devastating Pamphylia, where he had taken up a disadvantageous

* I have fully explained the import of this term (BovAajpijof) in the commentary subjoined to my
series of inscriptions of the Apocalyptic sites.

R 2

130 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

position between the Melas and the Eurymedon. By this, however, Leo failed
to profit, and the result of the conflict was as might have been anticipated : he
was defeated by Tribigild, and his army slaughtered or dispersed.*

The feature of the struggle which has, in my opinion, been drawn by the
author of the inscription, is that where Leo terminates his career in a morass
into which he is pursued, and where the poet has represented him as expiring
from the mere influence of terror. This closing scene of the drama is described

as follows :f

" Ast alios vicina palus sine more ruentes
Excipit, et cumulis immanibus aggerat undas.
Ipse Leo dama cervoque fugacior ibat,
Sudanti tremebundus equo ; qui pondere postquam
Decidit implicitus limo, cunctantia pronus
Per vada reptabat, coeno subnixa tenaci.
Mergitur, et pingui suspirat corpore moles,
More suis, dapibus quae jam devota futuris
Turpe gemit, quoties Hosius mucrone corusco
Armatur, cingitque sinus;

Ecce levis frondes a tergo concutit aura ;

Credit tela Leo : valuit pro vulnere terror,

Implevitque vicem jaculi, vitamque nocentem •, • ,

Integer, et sola formidine saucius efflat."

« The rest, in rude disorder hurrying, wild,
A marsh receives, full soon with corses pil'd.
Leo himself, more fleet than timid deer.
Flies on his panting steed, half dead with fear :
Anon his weight o'erpowers his courser's strength,
' Who, 'tangled in the mud, with tottering length

Falls prone, and struggling in the slimy shoals
Wriggles in reptile effort, snorts and rolls,
Whilst the unwieldy bulk he bore, the pride
Of chieftains ! wallows in the slimy tide,
Panting, expiring, as a well-gorg'd swine
Its gutturall screams when Hosius means to dine.

»»•»•»»«♦ ,

• Vid. Suid. in Xitn, ii. p. 428. Ed. Kust. Gibbon, Hist. c. xxxii. p. 181.
j- Lib. in Eutrop. ii. 438, ss.

of the Grceco-Roman Era in certain ancient Sites of Asia Minor. 131

The light breeze stirs the foliage in the rear ;
The clash of weapons bursts on Leo's ear!
Affright performs the dreaded javelin's part,
And deals the blow which rives his dastard heart :
To vain affright he yields his parting breath,
Unconscious of a wound, and sinks in death !"

The author of the inscription has, as I conceive, availed himself of the inci-
dent of the discomfited army's betaking itself to the marsh, to represent its leader
as desirous of visiting the water-nymphs of the district, whom he appears to
have addressed in a mock style of supplication on behalf of this Ajax of the
East.* Nor should I omit to observe, that a very unusual epithet occurs in the
last verse but one, the nearest approximation I have found to which is the epithet
of the hare, in a poemt of Nicander, BepKevvrjs, so beautifully descriptive of the
particular habit it expresses.

AepK€OKprj8efivoi is that to which I now allude, and which I beg permission to
translate, ogling through your veils ; for I regard it as applied to the nymphs, and
as intended to express a not unusual attribute of the sex, in which the classical
mythics have been pleased to rank these offsprings of their fancy. If this con-
jecture be well-founded, the restoration I have ventured to offer may, perhaps,
not be regarded as very far from the sense of the original composition. But
however this may be, there can be no question of the felicity of the epithet under
consideration.

The inscribed monuments of Sardes, which was the next site I visited, are
not more numerous than those of Philadelphia. I am confident, however, that
excavations in the vicinity of that once splendid structure, usually called the
temple of Cybele, but of which only two columns have been left standing, would
bring to light much curious and interesting information ; I may add also, near
the Gerusia,J or Old Man's Asylum, in the ancient city. I must, however,
here remark, that I apply this name to the ruin to which I at present allude,
rather in accordance with the presumptions of most of those who have preceded
me in this route, than with my own belief. Mr. Arundell very naturally puts

* Vid. Gibbon, ubi supr. Claudian. in Eutrop. ii. 386. Tunc Ajax erat Eutropii, S^c.
f Alexipharm. v. 67. J Vitruv. de Architect, ii. 8, p. 64.

132 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

the question, after stating the measurement of the walls, and one of the rooms,
" Might not this have been the Gymnasium ?" *

It was in the neighbourhood of this ruin that I discovered the inscription
which is numbered the eighth in my collection. The cubical block of marble
on which it was engraved lay, with the inscribed face undermost, in the open
ground to the east of this edifice, and had originally, I am persuaded, been set
up within the precincts of the treasury of the ancient city. It is now, as I have
said, prostrate, and is used by the Turkoman herdsmen and the villagers of Sart
as a seat, in consequence of which it has been worn down to such a degree as
almost to have ceased to attract the notice of the traveller. Mine it certainly
would have escaped, had it not been pointed out to me by the suruji (or groom),
who had the care of my horses, and attended me over the ground. I lost no
time in making myself acquainted with its contents, but the labour of trans-
ferring them to my note-book was very considerable, and occupied nearly the
whole of the time I could spare from visiting the other objects of interest in and
around the site of Sardes.

The inscription numbered the ninth was copied by me from a Turkish grave
which I observed when approaching the town. It was well chosen by the Mahom-
medan who had pressed it into this service, as the marble fragment on which it
is inscribed, had itself once formed part of a soros, or sarcophagus ; but the pro-
cess which it has thus undergone has deprived it of its chief interest, the names
and dates having been cut away to adapt it to the dimensions of the grave.

Such, however, is not the case with first-mentioned titulus, that near the Ge-
rusia. Sufficient of this as yet remains to acquaint us with its general import. It
supplies us in its names and historical references with data of no common interest
to the classical antiquarian. It appears to have been a decree, or public act of the
senate and people, directing a monument (fivrjfielov) to be raised in honour of
one of the imperial benefactors of Sardes, with whom there is some reason to
suppose a lady of Lampsacus, Publia, or Papia Patricia, to have been connected
in his offices of kindness and liberality towards the distressed citizens. There is,
as appears to me, distinct mention made of the names of Tiberius and Trajan :
and, perhaps, in the portions which have been defaced or broken off, that of

* Visit, &c. p. 180.

of the Grceco- Roman Era in certain ancient Sites of Asia Minor. 133

Hadrian had also been introduced; for it is matter of history, that this great
emperor had emulated his predecessors in the succour which he had afforded to
the Sardians in their emergency. This monument, therefore, refers chiefly to a
period, in which this metropolis had emerged from a dreadful national calamity,
or rather a succession of calamities, in consequence of the earthquakes which so
frequently devastated the volcanic region of the Katakekaumene. Those which
had taken place during the reign of Tiberius are expressly recorded by
Tacitus,* and Dio Cassiust I'cfers to those which had occurred in Trajan's time,
but in a general way, as the attention of that historian was more especially
directed to Antiocheia, where Trajan was sojourning during the season of the
catastrophe. The generosity of his successor, on a similar occasion, procured
him, by a decree of the Sardians, the title of Neocorus, | one of great honour,
and much sought after during the dynasty of pagan Rome, as well by commu-
nities as by individuals. It may be translated, Temple-warden.

The conclusion which appears, from the indistinct notices at the close of this
titulus, to be probable is, that the funds at the disposal of the priesthood had
mainly contributed to the erection of this testimonial.

We are informed also in the fifth, and as appears to me, in the thirteenth line
also, that Sardes enjoyed, like Pergamus and a few other cities of principal note,
the title of 5ty vecoKopos, This expressed a much higher grade of honour than
the single Neocore,§ to which, even by itself, the generality of cities esteemed
themselves fortunate in being: admitted.

The characters are, it is true, considerably effaced in both the instances to
which I refer, and I did not venture to supply the Lacunse until after a most
careful consideration of the text, which points at once to the readings which I
have introduced.

The simple epithet, vecoKopo^, appears to have occurred towards the close,
namely, in the twenty-third line. This, however, might have been 8ls vecoKopos
also, as a very considerable hiatus precedes the first syllable, which, together
with the last, is the only remaining portion of the word.

There is a fragment preserved in the eighteenth line, belonging to a word

* Annal. ii. 47. f Hist. Rom. Ixviii. 24.

X Vid. Rees' Cyclopaed. Art. Sardis. § Vid. Vaillant. de Numism. Graec. Rom. pp. 266, ss.

134 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

which I have not met elsewhere, that is, ya^eiov. The question is, what does this
mean ? We know what ya^a or yd^r], adopted from the Persian, was,* and that
from it was derived the well-known ya^o^uAa/cioi/.f We have, likewise, the ana-
logy of apx^lov, a registry/ office, Ta/jLehv or Tafiielov, a treasury, formed from apyj)
and ra/ttay, and the like. If then ya^ehv be the legitimate restoration in this pas-
sage, the conclusion appears at least to be probable, that the public building in
which this monument was directed to be set up, was none other than the cele-
brated treasury of Croesus, and therefore (supposing it to have been found in situ),
that the spot it occupies was within the precincts of that building. I mention this,
because, as I have remarked already, it has been very generally supposed that the
Gerusia is represented by a considerable pile, which arrests the traveller's attention
somewhat further on towards the west, and in the direction of the Pactolus.

However this may be, the propriety of the use of the term ya^eiov is quite a
distinct question. Tafiecov is that which I have found elsewhere, as, for example,
in the Thyatirene Tituli. But the Persian invasion, and subsequent dynasty,
account so satisfactorily for the former, that we may well allow the Sardian scribe
the use of the term, without supposing him to have affected singularity.

I hasten, however, to conclude my remarks on this document, reserving more
detailed ones for a fitter opportunity. The last I shall now offer is on the use of
drropiav, of which almost the entire has been preserved in the eighth line, to
which I may add that o{ evSeiav (but of this I am not equally certain), in the
seventeenth. These expressions illustrate very forcibly the picture which the
Roman historian of those times draws, in his own brief yet graphic style, of the
depth of misery into which the Sardians had been plunged by the catastrophe
that had laid waste their devoted region.

The words of Tacitus are : " Eodem anno duodecim celehres Asia urbes
coUapscB nocturno motu terra: quo improvisior graviorque pestis fuit. Neque
solitum in tali casu effugium subveniebat, in aperta prorumpendi, quia diductis
terris hauriebantur : ' Sedisse immensos montes : visa in arduo quae plana
fuerint: effusisse inter ruinam ignes,' memorant. Asperrima in Sardianos
lues plurimum in eosdem misericordice traxit."X

* Vid. Reland. Dissert. Misc.ii. p. 184. f Comp. S. Mark. xii. 41 : S. Luke, xxi. 1.

X Annal. ii. 47. Comp. Strab. xiii. 4, p. 15+. Tauchn.

of the Grasco- Roman Era in certain ancient Sites of Asia Minor. 135

The historian then proceeds to an enumeration of the other cities which had
shared in the general calamity, as also in the imperial bounty : all had their
tributes remitted to them for the time, and deputies of senatorial rank appointed
to visit them, and take such measures for their relief as the exigencies of their
cases demanded. The Sardians, in particular, exclusively of a temporary remis-
sion of their taxes, had a large grant from the imperial treasury.

My present circumstances forbid more than brief allusions to authorities. I
therefore conclude this part of my subject with referring my learned audience to
Pliny,* StrabOjf the medals of Tiberius which were struck in commemoration of
this event, I and the Marble of Pozzuolo,§ for illustration of the historical
document here noticed.

My road to Ak-Hissar, the Turkish town which occupies the site of the an-
cient Thyatira, lay through the battle-field of Cyrus, the Lydian tumuli, the
western side of the Gyga;an lake, and the town of Mermera, or Marmora, which
some travellers suppose to be the representative of Exusta.|l Whilst amongst
those monuments of the Alyattic dynasty, the sepulchral mounds, I did not fail
to visit in particular the largest, the tomb of Alyattes, of which Herodotus has
left us an account.** The view which presented itself from the summit, of the
lovely region beneath, of the long range of the Tmolus, the acropolis of Sardes,
the lake of Koloe, and the plain of the Hermus studded with the monuments,
in an endless profusion, of the remote age of the Merranadse, was one which will
not soon be effaced from my memory.

Whilst on the summit of the Alyattic tumulus, I recalled to mind, in parti-
cular, that part of Herodotus' description, in which mention is made of the five
odpoi, or termini, which he affirms to have been placed there, with epigraphs
inscribed upon thera,f f specifying the amount of labour which the classes who
had been employed in the task of erecting it had severally contributed. My
curiosity was accordingly much excited, when I beheld on a narrow platform on
the top of the mausoleum, and imbedded in a cavity in the centre thereof, an

• Hist. Nat. ii, 86, 1. f Vid. xiii. p. 154. Tauchn.

J Spanheim. de Usu et Pr. Num. Diss. ix.
§ Vid. Gronov. Dissert, viii. Ernesti, Not. in Tacit, ubi supra.
II Vid. Smith, referred to in Mr. Arundell's work, p. 187. •* Vid. i, 98.

'j"!' Herod, u. s. k»i a-fi yfdfiiiscra iyixiKi\»itr».
VOL. XIX. *

136 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

irregularly formed, oblong stone, to the best of my recollection, of granite, and
on which I thought that I could trace certain marks, or indentations. These,
however, may have been the effects of atmospheric influences : I could form no
certain conclusion respecting them : still less am I enabled to assert with any
degree of confidence tliat" the rude block which I then saw before me had been
also beheld by the Father of history : I wished, however, to believe the fact, and
having travelled so far to test the accuracy of Herodotus, I found it no difficult
matter to enlist my convictions under the banner of my imagination.

Thyatira, to which I am now conducted, furnished me with nine inscriptions,
most of which were copied by me in a cemetery of the Armenians, lying a little
off the road to the right, as the modern town is entered from the south-east.
But by far the most perfect of the number is one which I had from a sarcopha-
gus in the upper part of Ak-Hissar, where it lies in a field belonging to the
Agha, who kindly granted me an escort thither, and his permission to examine
the monument. Scarcely a letter of this has sustained any injury ; and as the
soros itself exists in all probability in situ, we may infer with some degree of
confidence, that certain names which it supplies, designated of old the quarter in
which it is now seen by the traveller.

I have already adverted to this titulus,* but in so general a way as to afford
room for a more particular specification of its contents.

The erector of the soros was a person of the name of Fabius Zosimus. The
spot which he selected was an unoccupied one before the city, contiguous to the
Sambatheion, within the Peribolus, or precinct of the Chaldaron (perhaps Calda-
rium), and alongside of the public road.

These are local designations which it would, of course, be impossible for us,
possessing as we do no notices whatever of the astygraphy of Thyatira, to ex-
plain satisfactorily. We know that Trepl^oXos means what I have stated above,
a precinct of any kind, whether wall, hedge, or rampart. We also know from
Seneca,t Vitruvius, % and the younger Pliny, § what the Romans termed Calda-
rium, or Caldaria Cella. The conclusion, therefore, to which we are conducted,
is, that this opulent citizen of Thyatira had chosen a place of public resort
wherein to erect this family monument ; perhaps, from circumstances of owner-

' *Vid. p. 118. t Epistol. Ixxxvi. 9.

X De Architect, v. 10, p. 152. § Epistol. v. 6. 26.

of the Grceco-Roman Era in certain ancient Sites of Asia Minor. 137

ship, or because he was prompted by his vanity* to a public display of so beauti-
ful a monument as even the relic which I saw proves the tomb to have been when
as yet uninjured by time or barbarism.

The inscription proceeds to inform us, that this soros was destined to his own
use and to that of his sweetest spouse (yXvKVTaTrj avTov yvvaiiu) Aurelia Ponti-
ana, exclusively, no other individual being privileged to make use of it for the
purpose of interment : that any infringement of this notice was to be attended
with a forfeiture to the most illustrious city oftheThyatirenes, of one thousand
five hundred denaria, and to the most sacred treasury {to lepcoTarov rafjulov)
of two thousand five hundred:^ in addition to which, the parties so offending
were to incur the penalties of the law against breaking into tomhs (rvii^wpv^ia).
It is then added : two fair copies of this inscription have been made, one of'
which has been entered (ereOr)) in the registry office {ap^eiov). Done in the
most illustrious city of the Thyatirenes, in the proconsulship of Catillius Severus,
on the thirteenth of the month q/AudncBUs, in presence ofMenophilu^sJulianus,
Registrar.

The following observations are suggested by this extract : firstly, that there
were two classes of penalties to which tomb-breakers {TVfijBcopvxoi) were made
liable, one affecting their property, the other their persons, or, it may be, their
civil rights. We know that amongst the Romans there were express laws against
the violation of the receptacles of the dead, J as also that this department of legis-
lature was not neglected by the Greeks : for Cicero's words, when treating of
Solon's enactments on this and other matters relative to the common weal, are,
" Posnaque est, si quis bustum (nam id puto appellari Tvp.fiov), aut monu-
mentum, aut columnam violarit, dejecerit, fregerit. §

Secondly : that the framer of the inscription defines with great exactness the
legal formalities which were observed, giving also names and dates.

Of these the proconsulship of Catilius Severus is the first. This name is

* The expressions of Rosinus prove that Zosimus shared this feeling in common with his
countrymen : " Communis Romanorum sepullura in viis publicis erat ut ex epitaphiis apparet, <^c."
Antiq. Rom. v. 39. fin.

■f The value of the denarius wras different at different times : but fixing it at a medium of eight-
pence halfpenny, these suras correspond respectively to £53 2s. Gd., and £88 10s. lOd. of our money.

I Vid. Rosin. Antiq. ubi supr. § De Legibus, ii. 26.

S2

138 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

found in the Consular Fasti in conjunction with T. Aurelius Fulvus, during the
reign of Hadrian, and in the year U. C. 873. He had been sent previously into
Bithynia, and filled shortly after the important office of Proconsul in Syria.*

The next date is given according to the Macedonian reckoning, and corres-
ponds, in our's, to the fifth of December, that is, supposing Ussher's computation
to be correct, which agrees sufficiently well with Ideler's table referred to above,f
if we take the list of congruous months in the Calendars of Macedon and Athens
with which Plutarch supplies us : but here there exists some diversity of opinion,
a discussion of which I postpone to a more suitable occasion ; contenting myself
at present with stating the Athenian Poseideon, that is, half December, half
January, to be the month I have selected as answering to Audynaeus.

I have been induced by the value and fine state of preservation of this se-
pulchral inscription, to diverge somewhat from my regular course, as it is the
sixth in the order of those from Thyatlra. But it has saved me the trouble of
commenting at any great length on most of the others, as of the nine which I
have brought away from thence, perhaps five, certainly four, are entaphial re-
cords.

The following is a list of these, and a concise account of their contents.

a. A fragment of a Latin inscription, which I am inclined to think was the
titulus of a statue erected by the citizens of Thyatira in honour of the proconsul
Severus, the same who is mentioned in the foregoing. The high terms of
eulogy in which the historian DioJ has written concerning this functionary,
makes it at least probable, that his administration should have been distinguished
with this mark of honour. I have accordingly ventured to restore it, and in
conformity with the known rules of the Roman Sigla, on this hypothesis.

The marble on which it was engraved has been built into one of the walls of
the old Greek church of St. Basil in Ak-Hissar, which is now used as a mosque.
The entire thereof, with the exception of the part containing my inscription, has
been covered in the Turkish fashion with a coarse plaster. I attempted to dis-
lodge as much of this as might have enabled" me at least to test the accuracy of
my conjecture, but the fanaticism of the Imam was aroused, and I judged it my
most prudent course to forbear.

* Dio. Hist. Rom.kix. 14. f Vid. p. 123. % Hist. Rom. ubi supr.

of the Grceco-Roman Era in certain ancient Sites of Asia Minor. 139

b. The next inscription was copied from a mortar, formerly part of an altar,
lying in the court of the Agha's residence in a village* through which I passed
on my road from Pergamus to Magnesia (ad Sipylum). I was informed that it
had been brought by the servants of that magistrate, Kara-Osman-Oglu, from
Ak-Hissar, and I have therefore given it a place in the present series.

It records an honour which had been conferred by the senate and people (of
Thyatira) on a distinguished matron, named Glykinna, in consideration of the
public services of her husband, Publius Aelius Aelianus.

c. The third in order is also an honorary Titulus, commemorating the
deserts of a victorious prize-man in the public games. It records the erection of
a statue to his honour in a conspicuous position in Thyatira. The document
having been mutilated in this part, I am unable to determine the name of the
place with any degree of certainty ; but I am disposed to think it was the Asium,t
{to acrelou,) and very probably one of the gymnasia, of which there were several
in the ancient town. Apollonius Justus (of the first of these I am certain, but not
equally so of the last) was the name of this fortunate candidate for so envied
a distinction. The inscription mentions him as having been a victor in the torch-
race (XafJLTradapx^cTavTa), as having been crowned (crTe(f)avcodeuTa), and, in
general, as having excelled all other competitors (TrpcorevcravTa.)

d. The fourth inscription commemorates a similar testimony in favour of a
successful athlete, Menander the son of Paullus, and on the part of the youths of
the first HeracleanJ gymnasia. This I copied from a beautifully sculptured
marble slab in the Armenian cemetery mentioned above. It had once, perhaps,
formed part of the pedestal of a statue, out of which it had been cut to adapt it
to its present, or some other position.

e. The fifth cost me much trouble to decipher, nor am I yet assured of its
real import. At first I regarded it as sepulchral. This opinion I have since
abandoned for another, namely, that the marble fragment on which it appears,

* Yaia-keui.

I The reading ao-rsiov, which I have conjectured in a note on this inscription, is not by any means
so probable : nor is there an^ authority for the use of the word, as for ?rf o«Vt8io» in Herodian. Hist.
Rom. i. 12.

I Or, dedicated to Sercules. The words are, »i Trtfi t«» ifccxxix rut a-p«'T«» yv/*»xrtei» »g«>iVxo(
irifiriirxf.

140 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

formed originally part of an altar, which had been erected by a lady named
Aurelia Matria, in commemoration of the issue of a suit (probably for disre-
garding her rights of sepulture), between her and a person of the name of Julius
Atticus. If this conjecture be well-founded, it may follow that the altar in
question was one of that class which the Romans styled Arce amicitice, for men-
tion of which my audience is referred to Tacitus.*

/. The sixth is sepulchral, that of Fabius Zosimus, to which I have already
adverted, f The soros in which it appears wants the operculum, or cover, but
in all other respects is in complete preservation. It is of greyish coloured and
very fine grained granite. The ornamental sculpture is of a very simple kind,
and there are no figured devices ; but the chiselling of the cornices is in the
best style of art, and the characters of the inscription deep, sharp, and beautifully
even.

g. The seventh inscription is also entaphial. This I found on a flat and
highly-ornamented stone covering an Armenian grave, intermixed with the de-
vices of that people, and epigraphs in their language. It formed three columns,
each making a consecutive sense with that which went before, and separated from
it by highly ornamented sculptures in low relief. The names of the erectors of the
monuments have been abstracted by the process of adapting the slab to its pre-
sent position, but in the second and concluding compartments, I have found
means to restore the names, firstly of the proconsul, J during whose tenure of
office the monument was erected ; secondly, of the emperor § who then reigned ;
and thirdly, of certain Romans of distinction who were, by the provisions of the
inscription, either admitted to a right of sepulture in the soros, or who witnessed
the execution of the instrument ; or, lastly, who contributed to the decoration of
the monument. These were of the family of the Annii, of which Tacitus and
other writers II make frequent mention.

The hand of time, and the liberties taken by the Armenian owners of this
grave, have rendered any elucidation of this inscription almost a hopeless task.
On certain points I am not as yet satisfied : but I hope much from the coope-

* Annal. iv.74. t Vid. pp. 118, 136.

i LoUianus, or Julianus. I incline to the former, on the evidence of an inscription which I
copied in the Troad. § Trajan.

U Ex. g. Josephus, Antiqq. Jud. xviii. 2, 2. Compare Rosin. Antiq. Elect, p. 904.

of the GrcBCO- Roman Era in certain ancient Sites of Asia Minor. 141

ration of those who are best qualified to decide on the criticism of inscriptions,
when my first part shall have made its appearance.

/*. The next in order is also entaphial. A lady named Aurelia Tycha
erected the soros for her own use, for that of her husband Aurelius (Rufus?)
for that of their sons and daughters-in-law, and lastly, of the Olnetizi, a family
of distinction, most probably, at the time of its erection, in Thyatira. At the
close we again meet evidence of the Macedonian origin of that town in the date
which is given, namely, the eighth of Dassius, answering to the sixth before the
Nones of May in the Roman reckoning, and to the second of that month in our
calendar.

i. The ninth, and last of my Thyatirene tituli, also a sepulchral docu-
ment, wants the name of the founder of the monument, but compensates
for this by its mentioning at the close the existence in Thyatira of a public
building for registries, called the Panionian Archium (to apx^lov iravLcoviov),
thus hinting some connexion with, or It may have been, a memorial of, the cele-
brated confederacy which bore that name. We observe in this also the name of
Trajan as designative of the month which was called after that emperor, but in
a part of the stone which had sustained so much injury as to be almost illegible.

It is proper, however, to apprize my audience, that my proofs for what has
been here advanced, are by no means so satisfactory as to supersede other at-
tempts to restore the true readings. I have accordingly, in my commentary on
this part, proposed another series of these, and have accompanied it with a tran-
script of my original copy, to enable such inquirers as may feel an interest in the
present subject to judge for themselves.

Of other remains of antiquity I could discover none whatever in Ak-Hissar,
with the exception of capitals of columns, friezes with architectural sculpture,
and pediments, the former of which have been employed for the most part in the
construction of wells, which the traveller meets in every part of Asia Minor.
Altar-pieces and capitals — the latter when of sufficiently massive proportions to
admit of their being used for such purposes, are the materials one chiefly finds ap-
propriated to these works of public utility ; In one respect a fortunate application
of those treasures of ancient art, and infinitely preferable to using them as street-
pavement, or for the substructions of dwelling-houses. The most valuable in-
scriptions have thus been often preserved : but woe to the luckless monument

142 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

which has had the misfortune of being decorated with reliefs of the features of
the illustrious dead, or of embodying an artist's ideas of a superhuman beauty !
On such as these the Musulman Iconoclast has invariably been sure to wreak his
fanatical wrath, and often the very circumstance of their attracting the admira-
tion of the dogs, the polite appellation generally bestowed on Ghiours, or
Infidels, by all true disciples of Islam, has proved a powerful auxiliary of this
principle. An anecdote which has been related by the accomplished Cockerell,
places this in a strong light.

It is thus that the work of demolition is, I fear, in rapid progress amongst
the beautiful ruins of the temple of Aphrodite, in the vicinity of which the mud
huts of the villagers of Gheyerah have been clustered, with large contributions
from the sculptured relics of the ancient Aphrodlsias.

My road to Pergamus lay to the north-west, through Bakir, Kirkagatch, and
Soma, leaving Bulleneh (the representative, as I think, of the ApoUonia men-
tioned by Strabo*) to the left, in a direction south by west. I crossed the
Ghediz (the ancient Hermus), at a point a little less than half way between
Ak-Hissar and the first of these towns. The second, Kirkagatch, was my resting
place for two days ; and here I found some memorials of the Carian city Strato-
niceia, which have led me to believe that the Turkish town has been in some
way or another connected with the Macedonian colony, most probably through
immigration of Greek families.

The memorials to which I here refer, are two of three inscriptions which I
copied at Kirkagatch.

a. The first commemorates the deserts of a citizen named Dlodorus Philo-
metor, son of Nicander, who had entitled himself to the honour thus conferred
upon him by his patriotism and private benevolence. It was a public act or
decree of the senate and people of the Hadrlanopolitan Stratoniceans on behalf
of this eminent person, who is mentioned as having discharged every magisterial
office (iraaav dpxv'^), as well as public service (XeirovpyLav), on the distinction
between which it is unnecessary for me to dwell, in the hearing of those whose
classical remembrances will immediately suggest to them the offices of the Archon
and the Trierarch amongst the ancient Athenians.

* Tlpoiitri V am rev iri3(ou tea) T?{ ■xixiut (Pergamus) s?r» ftii t« jrposjs'a fiifA, xoAij 'nrrit MoXhutU.

Strab. xiii. 4, p. 150. Tauchn.

of the GrcBco- Roman Era in certain ancient Sites of Asia Minor. 143

I found this inscription in the court of a private dwelling, belonging to a
Greek family, in the higher quarter of the town. It was engraved on the upper
part of a small column of verde antico, which served, as I conceive, to support a
statue of the distinguished Stratonicean whose memory has thus been preserved.

b. The next inscription was found by me in the garden of the schoolmaster
(SiSda-KaXos) of the Greek church, supporting a Maltese flower-stand. From
its supplying no information with respect to the site from which it had been
brought to its present position, I am not as confident of its being a relic of Stra-
tonicea, as of the one just mentioned. Some may suppose it to have been from
Athens ; but then the difficulty of transport from a place beyond sea is to be
taken into account ; yet, on the other hand, it must be acknowledged, that immi-
gration into Asia Minor from the part of Greece over which King Otho bears
sway, has been going on to a considerable extent since the accession of that
prince, whose policy has been, to say the least, very generally distasteful to the
proud and versatile people over whose regeneration he has been called upon to
preside. This I can vouch for from experience, having frequently, during my
sojourn in his majesty's dominions, involved myself in rather unpleasant alterca-
tions with my travelling companions, whilst reading them for their good, lessons
of loyalty and subordination. Changes have, however, taken place since that
time ; amongst these the accession of Prince Mavrocordato to the councils of the
Greek government, which may check this spirit of discontent, and operate bene-
ficially for the future.

But to leave political matters to take care of themselves, and to return to my
subject. The inscription at present under consideration was in honour of the
emperor Hadrian, whose titles are enumerated, namely, C«sar, August, Pan-
Hellenian, and, I believe (but here the marble has been broken), Archon. The
last two are specially illustrative of this great emperor's history, to whom, for his
munificence towards them, the Greeks dedicated their Pan-Hellenium, and the
Athenians, in particular, paid the compliment of an investiture with their chief
magistracy.* I find moreover, amongst the Inscriptions which Mr. Fellows has
brought from Azani, one styling Hadrian the god and Fan-Hellenian.f

* Vid. Casaub. ad Spartian. Hadrian, p. 7, 4. Salmas. in Spartian. p. 34, e.
f Travels in Asia Minor, vol. i. p. 144.
VOL. XIX. T

144 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

It was this occurrence of a part of the word ap^ovra in the monument now
under consideration, which induced me to suppose it of Athenian origin. But
as the title in question was one of which Hadrian was deservedly proud, as it was
a purely honorary distinction, there may hardly seem to exist sufficient reason
for considering it as designative of place, at least in any such sense as to fix that
of the monument. It is quite as reasonable to suppose, that the gratitude of the
people of Stratoniceia, whose city had received substantial benefits from Hadrian,
and had been dignified with his name, would lead them to select whatever title
they judged would be most agreeable to that emperor's vanity.*

The erector of this statue (for the marble I saw is a fragment of what had
once been a pedestal), was Julia Menylleina ; and her special motive has been
duly recorded, namely, to express her gratitude to Hadrian for his private acts
of liberality towards her father, Julius Paterculus. The inscription concludes thus :

rAIOYIOYAIOYHATEPKAOYnATPOSIAIOYA lAIONf EYEP-

PETHN.

I should have remarked, in connexion with this subject, viz., the intercourse
in kind offices which subsisted between Hadrian and the citizens of Stratoniceia,
the designation of the latter in the first of these two inscriptions : they are styled
Hadrianopolitan Stratoniceans. Their city was one of the considerable num-
ber which, as having experienced their master's bounty, he had decreed should
perpetuate the memorial thereof in their names. Thus, to cite another instance,
Athens, at least that section which included within its precincts his gigantic
structure, the Olympium. But in these, as in other instances, first associations
overruled emotions of a more recent date, and their inhabitants soon recalled
the ancient designations. In the case before us we observe a sort of transition
state ; a species of compromise effected between the old and the new. The
additional title may have been imposed also for the sake of distinction. |

c. Having travelled so far out of my course — for these inscriptions interfere
with the regular series of the other from the Apocalyptic sites — I may as well
conclude my notice of them with one which I had from the mosque Yeni-Oglu,
formerly a Greek church. It is evidently of the Byzantine era ; and appears,

* Anc. Univ. History, ii. 6, p. 503. t Or lAIHN.

J 1 have enumerated in my Commentary ten cities which bore the name of Hadrianopolis.

of the GrcBco-Roman Era in certain ancient Sites of Asia Minor. 145

from all that I have been able to decipher of it, to commemorate the erection of
a church by a pious Greek, named Evander, whose virtues, as well as the character
of his spouse, Aurelia Echneea, are eulogized in language made up of extracts
from the Iliad and Odyssey.

Whilst at Soma, on my road from Kirkagatcli to Pergamus, I met with a
few inscriptions, but of such little importance as by no means to repay the
trouble of committing them to my note-book. Some of these may be found in
the first of Mr. Fellows' volumes of his recent travels in Asia Minor. I may
say, indeed, that for this time at least my search after these remains had been
arrested, as during my stay at Kirkagatch I had been incapacitated for carrying
my first design into execution, which was to include the Troad in my tour, by one
of those mishaps which are ever likely to betide a traveller amongst the Greek
population whether of Asia Minor or Greece Proper, In short, I was deprived
of the means of doing so by the dishonesty of the persons with whom I lodged ;
to make the matter worse, Zantiote Greeks, and, therefore, in some sort fellow-
subjects, and residing within the district of the Mutsellim of Pergamus, under a
protection from the British Consul at Smyrna. I was accordingly forced to re-
trace my steps to the latter place as speedily as I could, to replace the funds of
which I had been deprived.

This little disagreeable remembrance I may be pardoned for noticing for the
sake of my motive in doing so, which is, to beseech those of my auditory, if such
there be, who may entertain a design of penetrating into these regions, to take
warning by my example, to confide less than I did in the integrity of their hosts,
and keep constantly before their eyes the Grceculus esuriens, and the Grcecia
mendax of the satirist of Aquinum.

I was not, however, prevented from visiting Pergamus, and thus completing
my tour of the Apocalyptic sites. I then returned to Smyrna by the coast-road,
leaving Magnesia (ad Sipylum) to the left. But a second excursion which I
made from thence, namely, to the Dardanelles, and round by Bunar-Bashi
(usually regarded as the site of Ilium), and the Ida;an region, to Pergamus, en-
abled me to fill up this blank. During the interval of which I speak, I visited
also Alexandria (of the Troad), Assos, some Roman military stations, Lectos
(the extreme point, to the south, of the Pnameia regna), A'ivali (a town of
recent date, and a conspicuous scene of action in the Greek revolution), Temnos

r2

146 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

(at least what has generally been supposed to be its site*), Magnesia (the Sipy-
leian), and added very considerably to my stock of inscriptions. Those of Per-
gamus which I now have the honour of submitting to the notice of the Academy,
were, in a great measure, the fruits of this excursion. I propose, with the per-
mission of the Council, to reserve for some future meeting, an account of my
researches during this period amongst the other sites I have mentioned. Of this
number, Yaikli, a village on the road from Bunar-Bashi to Eski-Stanpul, where
evident indications of Roman colonization meet the traveller's view on all sides,
Eski-Stanpul itself, the representative of Troas, and Beeram, that of Assos, fur-
nished the greater part.

a. The Pergamene inscriptions are seven in number ; four of the antebyzantine
age ; two of that period ; and one of comparatively very recent date, in the
modern language and style of writing. I copied it from the upper part of the
architrave of the church of St. Theodore solely as a matter of curiosity, and sub-
mit a fac-simile which, I may observe, it was exceedingly difficult to take, from
the intricacy of the character and the abbreviations employed by the engraver.
The date of this is 1653, A. C. Those of the inscriptions of the Byzantine period
are, respectively, 1433 and 1461.

h. One of these, the latest, was a testimony of affection on the part of a lady
named Aelia Noma, towards a person of the other sex, of the name of Aelius
Isidotus, but whether her husband, or in what degree related, is not mentioned.
The just tribute to the virtues of his private character is not forgotten : and
here, we may remark In passing, the peculiar and vitiated taste of the age is
manifest. From the commencement of one of his names, Isidotus, and the ter-
minating syllables of his professional title, Geometres, a sort of medley is formed
to express his moral accomplishments, as will be evident to any one who compares
the fourth with the two preceding lines.

c. Indeed, something analogous to the same taste may be observed in the
other nearly coeval inscription which accompanies it. The subject of the eulo-
gium in this case was Nicodemus, an architect, who had at his private cost re-
paired and embellished a public thoroughfare in Pergamus, called the Aediles'
walk, or mall (dyopavofiios irepiiraTos). The hint afforded by the name of

* Compare Plin. v. 31, 8. Arundell's Visit, SfC. p. 297.

of the GrcBCO- Roman Era in certain ancient Sites of Asia Minor. 147

this public-spirited individual was too obvious and too tempting a one not to be
fine-drawn, and accordingly we find subjoined to it the words a/ia Stj 6 kol viKcoueof,
thus making the following sentence. To the divine and ever-sacred artists, the
architect (Julius ?) Nicodemus (that is, people-vanquisher), and who has at the
same time approved himself Niconeus (that is, youth-vanquisher), S^c, an
attempt at paronomasia whereby I conceive were intended to be expressed his ad-
mirable fortitude and strength of mind in contributing of his substance to pro-
mote the comfort and ensure the safety of his fellow-citizens of Pergamus.

, It will be perceived, that the writer of this encomiastic sketch was also a poet,
on a small scale, as he terminates it with a catalectic tetrameter of the trochaic
metre : but in judging of its merits we must exercise a little charity, and suppose
that the gross blunder in the sixth foot is due to the oversight of the sculptor.

One additional observation, and I shall dismiss these inscriptions. It will be
noticed, that series of the same letters range in one, with the first, fourth, and
last lines ;* in the other, with all.f What these mean, is the question. In the
grave-yard of the church of St. Theodore, already mentioned, I observed similar
series in all the epitaphs. I conceive them to be numerals. In the inscription
of Isidotus, I think it is clear that they point at once to the year of our era ; but
in that of Nicodemus, the case appears to be otherwise, as the letters, supposing
them to be numeral marks, correspond to 2000, 100, 80, 6. I conclude, therefore,
that the reckoning in this last is the old Roman one, ab urbe condita, as in the
Consular Fasti : and this agrees extremely well with the internal evidence which is
supplied by the similarity of their style, this showing that their dates cannot have
been very far asunder. I have, therefore, referred them, in my Commentary, to
the years 1433 and 1461 after our Lord. J

d. I now proceed to the earlier tituli, the first two of which concern the Em-
peror Hadrian. I have placed the more perfect one, though later in its date, the
first, on account of its state of preservation. It was copied by me from a large
cubical block of the finest Parian marble, which I found in the possession of a
Greek resident in the upper quarter of the town, and which originally supported

» Viz. ATSA. f Viz. BPnS.

t I have referred inscription b to the Byzantine period, notwithstanding its dating eight years
subsequent to the fall of the empire, as so brief an interval was not sufficient to produce any per-
ceptible change in the style of these documents.

148 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

a statue o^ the lord of the earth and sea, as Hadrian Is styled in this fine monu-
ment. If the execution of the sculptor was at all in proportion to that of the
engraver, the whole work must have been in the highest degree splendid. The
inscription is in every respect perfect, unless a critical eye would object to the dimi-
nutive size of the O, both long and short, which was, perhaps, intentional on the
part of the lapicide, and designed to produce a better effect in the ranging of the
lines. Perhaps he was apprehensive of not having sufficient space in some of the
lines, which certainly approached very closely to the edge of the stone, even with
the precaution he used, were he to engrave the full letters. It may be, that a
little negligence contributed its share to this curtailment of the fair proportions
of the letters in question : it certainly somewhat offends the eye.

This titulus informs us, that the honour, that is, the erection of the statue,
was confided by the senate and people of the twice Neocore {Bis vecoKopoou)
Pergamenians to the prtetors {aTpar-qyols) of the time being, whose names are
recited ; and this is preceded by a very full list of the titles of the imperial object
of their gratitude, who is styled August, Chief Pontiff, seven times of Tribuni-
cial Authority, four times of Consular, the Lord of the Earth and Sea. His
adoption also by Trajan, on which Dio Cassius* has thrown so much doubt, is
implied in his being intituled the grandson of Nerva.

It is well known, that the learned Dodwell has introduced into his historical
Prelections f an elaborate refutation of Dio's statements on this point: as also,
that more recently, the eloquent author of the Decline and Fall of the Roman
Empire has attempted a solution of the problem, by supposing that Trajan had,
in a season of imbecility and irresolution, yielded to the entreaties of Plotina,
and by a formal act of sonship, nominated her favourite his heir. | This is, in
effect, deciding the question against Dio, with whom it is abundantly evident,
notwithstanding the sentence of encomium of her he had before penned, § that
Plotina was no especial favourite : for to her efforts on behalf of Hadrian he
applies the highly equivocal expressions ipcoriKT] ^iXia. Yet the Greek histo-
rian speaks in the most positive tone, stating, moreover, that he had his informa-
tion from his father, a grave authority unquestionably, but yet not inaccessible,
constituted as the imperial court was, to the influence of less worthy motives.

• Hist. Rom. Ixix. 1. | Prselect. xvi. pp. 506, ss.

} Vid. Gibbon, ch.iii. p. 89. § Dio. u.s. kviii. 5.

of the GrcBco-Roman Era in certain ancient Sites of Asia Minor. 149

Now, it is certain, that the document of which I have just now given an
account, proves nothing : it informing us only of an act of the Pergamene
authorities, at a period when there existed every possible inducement to pay
court to Hadrian, without the slightest risk attending the flattery. But with
what an argument would Dodwell have been furnished, as well as Gibbon,
who inclines to his opinion, had he been in possession of a document of import
almost precisely similar to the one I have described, a public act of the authorities
of Pergamus, passed during the life-time of Trajan, and conferring an honour
on Hadrian : an act wherein he is styled the son of that emperor, virtually,
under the title of the grandson of Nerva ?

e. Such an act is the inscription to which I now beg to direct the at-
tention of my audience, or rather somewhat more ; for I have abundant
reason to believe that, independently of being styled the grandson of Nerva,
Hadrian is described in the very commencement as Publius Aelius Trajanus
Hadrianus.

I found the marble on which it was engraved in the court of an obscure
dwelling belonging to a Greek of Pergamus, set into one of the side-walls, and
half-buried in the pavement of the yard. I was obliged, therefore, in order to
copy it more perfectly, to employ persons to displace the stones. It was con-
siderably defaced, as may be observed by the frequency of the dotted lines in my
copy, which mark the passages where time and accident have impaired the dis-
tinctness of the characters : but of the substantial accuracy of the translation
which I now offer, I am of opinion that no reasonable doubt can be entertained.
It is as follows :

Publius Aelius Trajanus Hadrianus, Pro-consul of Pergamus, and Pro-
prcBtor to the Emperor Nerva Trajanus, Caesar, Augustus, Germanicus,
Dacicus, of Syrophoenicia, Commagene ; Grandson of the August Nerva ;
Curio of Nerva ; late Demarch of the Antiocheans in the territory of the
Chrysorrhoatce ; the Senate and People of the Pergamenes {have honoured)
through Apollonius Dionysius .... and Malchio, and Cephalo Artemidorus,
and Dionysius Demetrius, son of Amyntas

Such is the document : the questions which involve critical inquiry, it
would not be expedient under present circumstances to enter into, or discuss,
with any degree of minuteness : this I have reserved for a more suitable occa-

150 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

sion : I content myself at present with giving the result, and conclude with ex-
pressing it as my firm belief, that this titulus goes far to establish Dodwell's
opinion, and Hadrian's succession to the imperial purple jure hcereditario. It
implies the fact, that there had been some public and recognized expression, at
the least, of Trajan's intention ; one of superior stringency to a mere sponsio
adoptionis which Dodwell supposes, and suflficient to authorize both the citizens
of Pergamus to bestow, and Hadrian to accept, the highest title which could be
conferred on a subject of the empire.

f. The inscription which I have placed next in order, was copied by me from
a cippus in the finest state of preservation in one of the by-streets of the town.
This also I was obliged to get cleared of the rubbish which had accumulated
around it, so as almost entirely to conceal it from view. The inscribed face lay
undermost, and it was with much difficulty that I succeeded in my object of ac-
quainting myself with its contents, in consequence of the uneasy position I was
forced to assume.

This monument decorated at one time the tomb of a citizen of considerable
rank, M. Julius Major Maximianus, Qusstor, Propraetor, and Aedile (ayopavofios)
of the Romans, and is a curiosity in its way, from its being accompanied with a
brief description of the personal appearance of the deceased functionary, namely,
that he was well-favoured and of a ruddy complexion [eva^rjiifov kcu irvpaos.)

g. The last of the series at present under review was copied by me from a
marble near the ruins of the church of St. John. This also had been sepulchral ;
but farther than its general import, it conveys no information whatever, from its
having been so completely mutilated. I copied it, however, as a memorial of
the Acropolis, from a most fatiguing excursion through the remains of which I
had just then descended : it had been brought down to its present position by a
Turkish mason, and built into the upper course of his garden wall. It was,
moreover, the only monument which I found in the city of Attains, in the lan-
guage of his self-constituted heirs.

I regret to mention, that Magnesia {ad Sipylum), in which I remained for
two days, furnished me with no documents of this kind. Not but that I am
convinced it contains some, but because the general alarm which seemed to have
pervaded at that time the Greek population, rendered all my inquiries fruitless.
On one occasion, indeed, I was conducted by a Greek to a fountain, on the

of the GrcBco- Roman Era in certain ancient Sites of Asia Minor. 151

upper part of which the word Karaa-Kevacras gave some promise of a reward to
my perseverance ; but no sooner did I stop to copy it and examine the ground
adjacent in the hope of making a fresh discovery, than my guide made so preci-
pitate a retreat, as in a few moments to be out of sight.

Thus began, and thus ended my search after tituli in the city of Antiochus :
but in other respects I was amply rewarded for my visit to it, for the Sipyline
Magnesia is, beyond all comparison, the most beautiful city I beheld in Asia
Minor.

As I am not now writing a detail of my travels, I shall conduct my audience,
by a far speedier and less rugged path than I was forced to traverse, over the
heights and through the defiles of the giant Sipylus to the lovely Smyrna, the
place of my first sojourning and of my last, in those regions of the myrtle and the
zephyr. In Smyrna it was that I enjoyed the solace of refined society and
Christian fellowship after many an arduous wandering beyond the pale of Euro-
pean civilization.

Of its ancient splendor Smyrna possesses now but scanty remains : of the
monuments, which I am at present discussing, still fewer. A fragment of a de-
cree or treaty, for it is impossible to decide which ; a custom-house regulation, a
votive thanksgiving, an epitaph, the name of the dedicator or of the architect of a
temple, with about a half dozen other tituli, and some of these of the age of the
lower empire, are all that I have been hitherto enabled to procure.

a. I have already ventured a few observations on the first of these,* since I
penned which I have come to the conclusion, that it related to certain negoci-
ations between the Romans and the cities of the Ionian Confederacy which are
detailed by Polybius and Livy. Yet as I have mentioned before, the evidence
for this is extremely vague and uncertain, from the meagreness of the document.

b. The next in order is a titulus which related to the department of the
customs of ancient Smyrna, and by the position of the marble from which I
copied it, I think myself justified in fixing the locality of the Telonium of the
port. It is now in the garden of an Armenian merchant, about five hundred
yards eastward from the sea shore.

* Vid. page 119.
VOL. XIX. U

152 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

Smyrna is styled, in the commencement of this inscription, The Neocore city
of the SmyrnceanSi rj vecoKopos (r/iypvalav ttoXis. This serves to fix the limits
of the date of the monument, namely, that it was subsequent to the reign of
Tiberius, in whose time the city became a Neocore, and prior to that of Hadrian,
when it was admitted a second time to the honour, and was accordingly intituled
twice Neocore (5iy vecoKopos.)

Caracalla conferred subsequently a third Neocoria on this favoured town, as
he did also on Ephesus.*

c. The third of my Smyrneean tltuli was copied from a column in the mosque
at Burnabat, a country retreat of the Frank merchants to the north-east of the
city, and is said to have been brought from the ancient temple of ^sculapius.
It was the votive offering of a convalescent, whose recovery is attributed to the
favour of the deity Meles. The word with which it commences, vp-va, implies
evidently, that it was intended as a metrical composition ; and in effect, by
merely retrenching the last word (7roTap.ov) of the second line, which was, in all
probability, the gratuitous addition of an ignorant engraver, it forms two trimeter
iambic lines. Superadded to this blunder, if I may be allowed to call it such, a
second has been committed by my predecessors in this department ; amongst the
number, by Mr. Arundell.f These gentlemen never seemed to have imagined
that the inscription was metrical ; much less was the true metre ascertained.
The consequence has been, that the learned public have been favoured with an
inscription, evidently in trimeters, with a spondee in the second seat of one of
the lines.

The following is a translation of this titulus :

" I hymn the god,

(The river) Meles,

My preserver;

Now that from pestilence of all kinds,

and distemper,

1 have been set free."

« See Vaillant. Numism. Imper. GroBC-Rom. pp, 266. ss.
•j^ Travels, &c. in Asia Minor, vol. ii. p. 406.

of the Grceco- Roman Era in certain ancient Sites of Asia Minor. 153

It was clearly a thanksgiving, after the cessation of some epidemic sickness,
from which the writer had been preserved, or if affected, had recovered,

I had contented myself at first with the transcription which I had made from
Mr. Arundell's volume. But I could not resist the curiosity which I experienced,
in consequence of the occurrence of the false quantity in the second line, to test
that gentleman's accuracy by an appeal to the original monument. It turned
out precisely as I had anticipated : the inaccuracy rests with the traveller. He
is, however, perfectly correct in his disposition of the lines, which to the un-
practised eye of the mere metrist appears quite extraordinary, the following in-
congruous assemblage having been formed : a monoraeter iambic, a hyperca-
talectic of the same, a species of hypercatalectic trochaic, but with a spondee in
the first seat, another iambic redundant by one syllable ; next follows a cretic,
and, last of all, a pure iambic monometer.

Horace says very truly, that in poetical compositions of a certain class, how-
ever you may break up their metrical arrangement,

" Invenias etiam disjecti membra poetae."

With regard to the poetical merits of the verses under consideration, I ven-
ture not to offer an opinion, but unquestionably the resolution has been very
complete, although not very happy in its sequence of metres.

The question naturally suggests itself, to whom are we to ascribe it? To
which I return for answer, doubtless to the laplcide, who had been employed by
this grateful votary of the health-restoring stream. I have been often quite
astonished at the unconcern which the ancient Greeks seemed to have felt about
the style in which their epigraphs were engraved. They seem to have left
almost every thing to their workmen ; and hence the capricious assemblages of
characters which occur in some, and the violations of the rules of the language
which we observe in others. Yet, on the whole, the persons of this class appear
to have been of a very superior order (I express myself, of course, comparatively),
and by no means unfit to be entrusted with the records which were, from time
to time, entrusted to their care.

One word more, suggested by the votive inscription which I have just now
noticed, and I shall dismiss it. The question has frequently been asked me, are

u2

154 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

the inscriptions which you have collected original ? Have they never been seen,
or copied, by any one else ? And the answer which I have uniformly returned
has been, that the circumstance of their having been so is perfectly unimportant
to me : this, for two reasons, which will, I trust, be deemed as satisfactory by my
learned auditory, as they are by myself. The first is, that I have reported no do-
cuments of this kind which have not been copied either by myself, or under my
immediate superintendence, from the original monuments ; and the second, that
I have as yet seen but few, extremely few indeed, into the copies of which
errors have not found their way, whether from haste, or inattention, or the ab-
sence of requisite accomplishments on the part of travellers. These oversights
are, as is manifest, best and most satisfactorily eliminated by a careful collation
with the monuments themselves, just in the same way as the mistakes of editors
would be remedied by authors' manuscripts, and many an ingenious reading,
many a conjectural emendation, over which vanity stands elated, prove but an
impotent conclusion. This I state, at the same time that I believe I can with
perfect confidence assure the Academy, that many of the inscriptions which I
hope to have the honour to submit to its notice, have never before been seen, or
at least considered by others, so as to have become the property of the public.

The greater number of the foregoing tituli is entitled to this distinction, as
also the remaining ones of the Smyrnjean series, which will be found arranged
from ftok in the copy, now before the President.

All these, with the exception of two of the Byzantine age, are mere frag-
ments, from tlie existing contents of which it is impossible to pronounce any
thing with certainty.

f. The first was copied from a piece of marble which has been built into the
wall of the Turkish barracks, adjacent to the Jewish cemetery, at the foot of
Mount Pagus. It contains the first and the last three letters of the Emperor
Trajan's name, and vestiges of the words ayaves and aycovoOiraiv. We may con-
clude, therefore, tliat the subject of it bore some reference to games instituted in
honour of that benefactor of his Asiatic provinces.

g. The next was taken from a piece of mosaic pavement which had been dis-
covered at Chalka-bunar, the name given by the Turks to that extent of low and
swampy ground where the temple of iEsculapius formerly stood. It is also

of the Grasco- Roman Era in certain ancient Sites of Asia Minor. 155

known by the name of Diana's Baths. The copy which I have given is a tran-
script of one I had from a gentleman resident in Smyrna, who accompanied it,
at the same time, with a facsimile of part of the mosaic which had come into his
possession. This I have subjoined.

The first part of this inscription was in so worn and illegible a state as
to preclude the possibility of extracting from it any consistent sense. The latter
half is, however, easily deciphered, with a few slight alterations. We read thus*:
rANYMHAOY2AIOIKHTOYnAKIAAH2AAMnPOTATH2: from which
the inference is obvious, that the tltulus was either commemorative of the virtues
of that officer, or that it had been inlaid at his expense for some other purpose ;
very probably to hand down to posterity a memorial of the most illustrious Pakiale,
his mistress.

h. The third of this series, which was copied from a marble in the wall of
a khan, or Turkish inn, opposite to the Armenian church, was evidently se-
pulchral ; but the fragment which remains of it contains no name to assist our
researches.

i. The next is, as I have stated, an inscription of the Byzantine age, and was
found engraved on a marble slab in one of those Greek churches which the
Turks have converted into mosques, at some distance from Smyrna. It was a
monumental tribute to the memory of an archbishop named ^Etherichus, and com-
mences accordingly with the stavros.

k. The last of this series was copied fi'om a cistern which has been imbedded
in the wall of the same khan where the last but one was found. I present it as
a curiosity, from its strange admixture of characters, without indulging in any
vague conjectures as to their precise import.

The entaphial inscriptions from Kutaieh, which have been subjoined to the
present fasciculus, may, I believe, with some degree of certainty, be reckoned
amongst the Inedlted ones which I have collected. They were copied from two
Armenian graves in the neighbourhood of the town, closed in, as usual, with
marbles abstracted from ancient soroi, and worked up so as to suit the tastes and
purposes of their more recent owners.

I have drawn sketches in outline of these interesting relics, the workmanship
of which sufficiently attests the rank and consideration of the family whose pro-
perty they were.

1 56 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments

The summits of both are surmounted with a circular arch, which in one is
repeated at an interval of about half a foot. The curves are marked by sculp-
ture in low relief.

The bodies of each are divided into compartments, which are, in the one I
have particularly referred to, rather more numerous, and more elaborately
worked. To three oblong rectangular spaces, of unequal breadths, which cross
the stone, succeeds a fourth of much ampler dimensions, divided into four square
compartments, with intermediate areas, on which the Armenians have sculptured
some characteristic devices, relating most probably to the occupations of the de-
ceased, but without altogether effacing the Greek ornaments. They have also
introduced here, as in most of their grave-stones which I saw at Ak-Hissar, in-
scriptions in their language, but have used some precaution, which I should con-
clude arose rather from the exigency of the case, than taste, in' selecting such
parts of the monuments for that purpose as had not been pre-occupied by the
Hellenic.

These last are, in consequence, almost perfect, and inform us of the following
particulars.

Firstly; that a lady named Nanas, erected this monument for the use of her
husband ApoUonius, and her own, which intention was subsequently carried into
effect by their sons, ApoUonius and Asalius.

Secondly; that a person of the name of Andromachus Latypus, I conclude of
the same family as the abovementioned, had been interred in the same soros.
This name occurs in the depressed space which intervenes between two of the
reliefs that run along the breadth of the stone, and immediately above the square
compartments, into which Its body is divided.

Thirdly ; that a person called Zelas Latypus, whose name was engraved as a
heading to the second stone, lay in the soros of which it formed a part ; thus
proving what I have stated above as to the ownership of these monuments. It
is then recorded, in an intermediate space, that Domna, the daughter of Proteas
and Tatias (individuals doubtless of the family of the Latypi), had done honour
to the memory of her parents, that is, had fulfilled their intentions in the erection
of the soros, by depositing their remains therein.

I have deemed the observation with respect to the names of the Latypi

of the GrcBco-Roman Era in certain ancient Sites of Asia Minor. 157

worthy of being inserted here, as it leads at once to the restoration of an inscrip-
tion which Mr. Fellows has copied from a grave in the same cemetery, but in a
form which, I must be pardoned for observing, it would be difficult for the
original engraver to recognize.*

I mention this also in illustration of the remarks on the subject of mechanical
copying with which I commenced this memoir. The particular comment I re-
serve for a more suitable place than the pages of an abstract like the present.

I have thus conducted the audience which I have the honour of addressing,
through those celebrated localities, the bare mention of the names of which
awakens emotions of the deepest kind in the Christian's heart. However
interesting their records — those I mean of their heathen state — may be in
themselves, as conducing to the illustration of their history, their social insti-
tutions, or their local characteristics, I must for one confess, that such are
not the sole causes which invest them in my eyes with their gorgeous and
attractive drapery. I may say, with truth, that I never passed an hour within
their mouldering palaces, their ruined halls, their prostrate shrines, their now
silent and forsaken agorae, their theatres, or their gymnasia, without the one
absorbing reflection being present to my mind, that over these the beloved
apostle of the blessed Jesus had exercised a spiritual rule, that here the apoca-
lyptic angels had preached, and that within these precincts they had received
those portentous warnings which but too truly, too faithfully, preluded the
fate of their communities. There is an air and a sense of indescribable
grandeur in those distant solitudes (for three of their number can be called by
no other name), a grandeur incomparably superior to all that civilization, art,
wealth, prosperity, could have bestowed on them. How is this ? We know how
difficult it is in the generality of cases to subject emotions to exact measures, or
to reason with a geometrical precision on their causes ; but here there is no
occasion for any refined disquisitions. The very causes which are every day

* Travels, &c., vol. i. pp. 127, 323.

158 Dr. Kennedy Bailie's Researches amongst the inscribed Monuments, Sfc.

rendering them more valueless as schools of taste and design, which are every
hour depriving them of their attractiveness in the eyes of the mere architect, or
the mere virtuoso, are, in those of the reader of and believer in the Bible, en-
hancing their interest. The gorgeous ruins of the city of Diana, the desolated
courts and shrines of Laodicea, the dethroned " Sardian Queen," address his
heart with eloquence immeasurably more touching and more sublime than they
could have done in the fulness of their beauty and magnificence. It is their
position on the threshold of those prophecies which announce the events and de-
velop the destinies of a better and higher than a mere political world : it is the
Spirit quenched, the Candlestick removed, the Hour of retribution, the utter
Rejection, which come home to his heart, imperishable monuments as they are of
the righteous dealing, the truth, the providence of God.

ADDENDA ET CORRIGENDA.

Page 123, line 18, for itpofivia readUpoiirjvia.

137, — 21, for legislature react legislation.

— 138, — 23, for makes read malte.

Note on Page 147, Line 19.

I have expressed the last of the Greek numerals, in this inscription, by 2, which is the letter
approaching nearest to the form in the original. But, accurately speaking, not 2, but 2T ((rrr),
is the representative of 6 in the Greek notation.

The engraver of the titulus had, I feel persuaded, the last of these in view : and the reader will
please to supply it in the note on the fifteenth line at mark f, or read the numerals thus, ^^fW.

le

7yjnf KM. V"OL.:XIK,

POLITB LIIEEArnEE PUU'E 1

/■/Mm. CA XXX .

'-^i:>77z/-ai'c^ ^fnxt^ a/i^itiMcA'e/Mu'^'Kliii«in-/n Sc^/t»^^m, VI, -Ca/^ CXKU

11

firvm ^<ni>i^-nt^ ^.'^u S^tB-na^X £/aZ. XiMWl.

S^c^i^/rf.'P^<r?7i.

■u/rt:pvm. iliccte^nj. ../ft'?! . J/u: IT ;>«.-'■ C»7Tt-'fe? 8

<^

Trxa^nj^. ^oi.jor.

POLrTE JJTEKATDEE PLATE 0

t-'^^Mt//^^ r^

■&>t,. Mv-.^L.-iaJr. cxvir. ? .

M-. ■3ir. .yz^,.,/f;sriu£cxir.L

r

L

^ae>

6o^iA?z.cm.'-7i. .^7t'/cd^ 'i^>09i- ^i^kAe^'y^A/^.^SS^?S.

*

ANTIQUITIES.

VOL. XIX.

ANTIQUITIES.

I. On the Irish Coins of Edward the Fourth. By Aquilla Smith, M.D.,

M.R.I.A.

Read 30th November, 1839.

1 HE study of the various coinages, which took place in Ireland, during the
reign of Edward the Fourth, is peculiarly attractive, from the number and
variety of his coins, which have reached our times ; and the difficulties which
have hitherto existed, in appropriating many of them to the exact period at which
they were struck, give additional interest to the investigation.

My object in tracing the history of the coins of this reign, is, to endeavour to
clear up some of the difficulties which have embarrassed our most skilful numis-
matists ; and although I cannot pretend to remove all the obstacles which have
been experienced, I trust I shall be able to bring forward some illustrations,
particularly of one of the most interesting coinages of this reign, which will
enable me to attain a greater degree of precision, in fixing the dates of some
coinages, than has been the case heretofore.

I propose to notice, as briefly as possible, the several mintages which are
described in the Acts of Parliament passed during this reign, of which we
possess more records than of any of the preceding or subsequent reigns, for a
long period. For this purpose, it will be convenient to divide the history of the
coins into four sections, each distinguished by its peculiar type ; and as there are
a few coins known, of which we possess no records, except such as we derive
fromjthe pieces themselves, these will be described in connexion with the types,
to which they bear the closest resemblance.

a2

4 Dr. Smith on the Irish Coins of Edward the Fourth.

THE FIRST SECTION

Includes those coins, the type of which was peculiar to Ireland.

1461. — In the first year of this reign, at a parliament held at Dublin, it was
enacted that a maille or halfpenny, and a quadrant or farthing of silver, be made
in the Castle of Dublin, according to the rate of the new penny made in the last
year of the reign of Henry the Sixth.* As none of these halfpence or farthings
have been discovered, it is unnecessary to take any further notice of them.

1462. — In the next year, a farthing of copper, mixed with silver, was ordered
to be made in the Castle of Dublin, having a crown on one side, with suns and
roses in the circumferance of the crown ; and on the other side, a cross, with the
name of the place of mintage.! I am not aware of any of these farthings being
in existence.

It appears that letters patent were granted to Germyn Lynch, of London,
on the sixth of August, in the first year of Edward's reign, by which he was
authorized to make coins within the Castles of Dublin and Trim, and in the
town of Gal way, to the tenor and effect of the statute or statutes, made by autho-
rity of a parliament held at Drogheda, in the last year of Henry the Sixth.
The coins specified in the letters patent are, a groat of silver, whereof ten shall
go to the ounce ; J half groats and pennies were also authorized to be made, and
a privy sign to be on every piece of silver money.§

Before I proceed to describe the coins made under the authority of the letters
patent, it is necessary to refer to the statute of Henry the Sixth, according to
the tenor and effect of which, Lynch was empowered to make coins.

In the year 1460, at a parliament held at Drogheda, it was enacted, that a
groat should be made of the weight of three pence sterling, (forty-five grains
Troy,) and to pass for four pence sterling, having on one side a crown, and on
the other a cross, with the name of the place of mintage. And at an adjourned
session of the same parliament, a penny of silver was ordered to be made, and to
have the same impression as the groat. ||

* Simon, Appendix, No. VI. t Simon, Appendix, No. VII.

X The Tower ounce = 430 grains troy. § Simon, Appendix, No. VIII.

II Simon, Appendix, No. V.

Dr. Smith on the Irish Coins of Edward the Fourth. 5

Simon has published a groatof this type, (PI. III. fig. 61,) its weight forty-two
grains, the crown is very shallow, and within a double tressure of twelve arches,
in both of which particulars, it differs from the undoubted coins of Edward the
Fourth, of a similar type ; the ornaments at the points of the tressure are also
different from those on Edward's coins. For these reasons, I appropriate this
groat to Henry the Sixth.

Snelling, in his Supplement to Simon's Essay, has published a penny, (PI. I.
fig. 16,) its weight nine grains and a half, the crown is shallow, within a double
tressure of twelve arches, and without ornaments at the points of the tressure.
This penny I also consider as belonging to Henry the Sixth.

All the other coins, of a similar type, I appropriate to Edward the Fourth,
for the following reasons. The crown on all of them is similar in form and
workmanship, and very different from that on the coins just described ; the
double tressure round the crown consists of eight or nine arches, instead of
twelve ; and at each point of the tressure there are three pellets, instead of a
trefoil with pointed leaves.

Of the groats there are four kinds. In the first, the crown, which is deep
and broad, is within a double tressure of nine arches, with three pellets at each
point of the tressure. On the reverse, a cross, with three pellets in each of its
quarters ; those in the first and third are connected by an annulet, (some pieces
have the annulets in the second and fourth quarters of the cross;) legend, civitas
DVBLiNiE, (PI. I. fig. 1.) This groat weighs forty-four grains and a half, which
is half a grain less than the standard : the deficiency may be accounted for by the
remedy which was allowed to the mint-master, of six pence in the pound, or half
a grain in each groat.*

* Simon, Appendix, No. VIII.

In every instance in which the habitat of the coin, if I may use the expression, is not men-
tioned, the reader will please to bear in mind, that the descriptions have been drawn up from coins
which have been submitted to my inspection. And I avail myself of this opportunity of acknow-
ledging my obligations, and expressing my grateful thanks, to the Very Reverend the Dean of
Saint Patrick's, for the most unrestricted access to his extensive and very valuable collection, to
which I am chiefly indebted for the illustrations of this paper. I am also under many obligations
to the Reverend Mr. Butler, of Trim ; Mr. Lindsay, and Mr. Sainthill, of Cork ; and Lieutenant-
Colonel Weld Hartstonge, of Dublin ; for the loan of some of the rarest and most interesting coins
of the Irish mints, and their permission to publish them.

6 Dr. Smith on the Irish Coins of Edward the Fourth.

The groat (PI. I. fig. 9) has a double tressure of ten arches round the crown ;
the legend on the reverse is blundered, the s in Civitas is reversed, i is substituted
for B, and an inverted l for n in Dublinie : it weighs only twenty-eight grains.
The deficiency of its weight, although it is nearly as broad as the other groats,
the blundered legend, the inferior workmanship, and the apparent impurity of
the metal, lead me to believe that this coin is an ancient forgery.

The second kind of groat, (PI. I. fig. 3,) differs only from the first in having
three small crosses above the crown, in the angles outside the tressure ; these
crosses were, perhaps, privy marks, which by the letters patent were ordered to
be placed on the silver coins ; it weighs forty-four grains. Some minor dis-
tinctions on their reverses prove that there are, at least, three varieties of this
kind.

The third kind of groat has the crown within a double tressure of eight
arches, and a small sun in each angle outside the tressure. Reverse similar to
the first kind. Weight, forty -four grains and a half. — (PL I. fig. 5.)*

The fourth kind differs only from the preceding one in having roses instead
of suns outside the tressure. Weight, forty-two grains and a half. — (PI. I. fig. 7.)

The suns and roses on these groats are sufficient evidence, as Mr. Lindsay
remarks, that they belong to Edward the Fourth ; they are the only coins of the
type under consideration which he appropriates to this reign, and supposes they
were coined in the first year.

Reluctant as I am to differ from so high an authority, I cannot help thinking
they were coined in 1462, or early in 1463 ; for I have already shewn, that in
1462, a farthing of copper, mixed with silver, was ordered to be made in the
Castle of Dublin, having suns and roses within (without?) the circumference of
the crown ; which enactment probably led to the alteration in the type of the
groat. And the difference in the number of arches in the tressure may, I think,
be accounted for, by supposing that the artist reduced them from nine to eight,
to leave more room for the suns and roses in the angles outside the tressure.
The groats of the first and second kind were probably coined in the first year of
this reign.

* In Mr. Lindsay's " View of the Coinage of Ireland," a groat is described (page 39,) and
engraved (PI, V. fig. 106) as having small roses in the angles outside the tressure.

Dr. Smith on the Irish Coins of Edward the Fourth. 7

No half groats of the type under consideration have been discovered. Simon
has pubUshed a coin, (PI. IV. fig. 71?) which the Rev. Mr. Butler has referred
to as a half groat of Henry the Sixth.* This coin is similar to the second kind
of the groat which I have described ; it is somewhat smaller, which has probably
led to the supposition of its being a half groat ; but its weight is thirty-seven
grains, whereas the half groat should weigh only twenty-two grains and a half.
I may also observe, that the diameter of the circle on the reverse corresponds
exactly with that of the groats, which I have occasionally found very deficient in
weight.

I think it is very probable that half groats of this type were never struck,
notwithstanding they are mentioned in the letters patent, for the half groat was
not ordered to be made by the statute of Henry the Sixth, according " to the
tenor and effect" of which statute, Lynch was authorized to make coins. This
opinion is supported by the fact of the half groat not appearing in either of the
subsequent coinages, or previous to the year 1467.

There are pennies corresponding with the groats of the first and second kinds,
(PI. I. figs. 2, 4.) There is another which has only eight arches in the tressure ;
this may, possibly, be a penny of 1462 ; the form of the crown differs a little
from the others, but it has not either the suns or roses outside the tressure. —
(PI. I. fig. 6.) The remarkable penny without the tressure, (PI. I. fig. 8,) is,
I believe, unique ; I do not know of any groat similar to it. The same remark
is applicable to the penny having a circle of small pellets instead of the tressure
round the crown.f These pennies weigh from nine to twelve grains.

Mr. Lindsay remarks, that " the pennies of this coinage, do not appear to
present any mode of distinguishing them from those of Henry the Sixth. "| But
if I am correct in my appropriation of the groats, the pennies I have noticed, all
certainly belong to Edward the Fourth.

There are no coins of this type from any mint, except Dublin ; and I am
inclined to think that none were struck at Trim or Galway, for in the enactments
of the first and second years of this reign, halfpence and farthings were ordered
to be made in the Castle of Dublin only. The earliest coin known from the

* Numismatic Journal, vol. ii. p. 73. f Editor's additional plate to Simon, fig. 15.

+ View of the Coinage of Ireland, page 40.

8 Dr. Smith on the Irish Coins of Edward the Fourth.

mint of Trim, as I shall hereafter shew, was struck in the year 1467, and it
does not appear that silver coins were made at any time in Galway.

It is evident that the coins I have described were minted before the year
1463, under the authority of the letters patent granted to Germyn Lynch, for
in this year they were confirmed at a parliament held at Wexford, which confir-
mation was rather an indemnity for the coins made under the authority of the
letters patent, than a renewal of the privilege for continuing a coinage of the
same type ; for by the same parliament, and in the same year, coins of a new type
were ordered to be made.*

I proceed now to describe the brass and copper coins made under the same
authority as the groats and pennies ; and here again it is necessary to refer to the
Act passed in the last year of Henry the Sixth.

At a parliament held at Drogheda, in 1460, it was enacted, that " a proper
coyne, separate from the coyne of England, was with more convenience agreed
to be had in Ireland, under two forms ; the one of the weight of half-quarter
of an ounce troy (Tower ?) weight, on which shall be imprinted, on one side a
lyon, and on the other side a crown, called an Irelandes d'argent, to pass for
the value of one penny sterling ; the other of vii. ob. (grains) of troy weight,
having imprinted on one part of it a crown, and on the other part a cross,
called a Patrick, of which eight shall pass for one denier." At an adjourned
sitting of the same parliament, the former coin was declared to " be utterly
void."t

The letters patent which authorized Germyn Lynch to make groats, half
groats, and pennies of silver, gave him power to make " also eight pieces of brass,
running at, and of the value of one penny of our said silver," and to " be
imprinted, and bear scripture, and be of the weight, allaie and fyness, as is speci-
fied in the said statute or statutes" of Henry the Sixth. He was also empowered
to make " four pieces of brass or copper, running at one penny of our said silver,
to be imprinted with the figure of a bishop's head, and a scripture of this word
PATRicivs about the same head, on the one side, and with a cross with this word
SALVATOR then (there|) about, on the other side," and "that the weight and

* Simon, Appendix, No. VIII. f Simon, Appendix, No. V.

:]: So it is in Harris's edition of Sir James Ware's worlss, p. 212.

Dr. Smith on the Irish Coins of Edward the Fourth. 9

quantity of the said moneys of brass or copper be devised and made continually
by the discretion of the master."*

These farthings and half-farthings were first published by the Rev. Mr.
Butler, of Trim.f

The farthing has on one side a bishop's head, full face, vsrith mitre richly
ornamented ; at the top, on the right side of the mitre, a sun of eight rays ; on
the left, a rose of six leaves ; legend, patricivs, divided below by the robed
bust, which extends to the margin of the coin. On the other side, a cross, a sun
in two of its quarters, and a rose in the alternate quarters ; legend, salvator,
divided into four parts by the arms of the cross ; suns and roses alternately
between the two letters in each division of the legend : it weighs nine grains. —
(PI. I. fig. io.)t

Another has, at the right side of the mitre, a small cross instead of a sun ;
and at the left, a sun in place of a rose. — (PI. I. fig. ll.)§

One variety of the half-farthing has, on one side, an open crown, within a
circle of pellets, outside which is the word patrik ; pa is separated from trik
by a branch, and a similar branch is interposed between the termination and
beginning of the word, and after the letter k there is a small annulet. On the
other side, a cross, within a circle of pellets : it weighs eleven grains. — (PI. I.
fig. 12.)

In another, the crown is close ; legend same as that just described ; it has the
letter p in one of the quarters of the cross on the reverse : it is corroded, and
weighs nine grains. — (PI. I. fig. 13.)

A third variety has the crown open, but of a very different form from that
on the first variety ; the legend, which is defaced, is evidently somewhat different
from either of those described : it has not the letter p on the reverse, and weighs
only seven grains. — (PI. I. fig. 14.)

* Simon, Appendix, No. VIII. f Numismatic Journal, vol. ii. p. 70.

X The coin published by Mr. Butler is represented as having a three-quarter face, owing to the
imperfection of the coin from which the drawing was made. — Numismatic Journal, vol. ii. p. 75.

§ Fynes Moryson says, " there were lately found brass coins, by ploughing up the earth, whose
stamp shewed that the bishops of Ireland had of old the privilege of coining." — Itinerary, Part i.
Book iii. Chap. vi. vii. London, 1617.

VOL. XIX. b

10 Dr. Smith on the Irish Coins of Edward the Fourth.

A fourth variety has been recently discovered ; it bears on its reverse a cross
of a peculiar form ; its weight is only six grains. — (PI. I. fig. 15.)*

I have been particular in noting their weights, as on this ground I conclude
that some of them, at least, belong to Edward the Fourth ; and that all of them
are not to be assigned to Henry the Sixth, for by the letters patent granted to
Lynch, he was authorized to regulate their weights, at his discretion ; whereas,
by the Act of Henry the Sixth, the Patricks were ordered to be made of the
weight of seven grains troy.

I have now described the coins comprised in the first section, the type of
which was peculiar to Ireland ; and proceed to notice the coins next in succession
as to date, and which, from their type, may be denominated Hiberno-English.

THE SECOND SECTION,

Or Hiberno-English type, comprises those coins which bear devices peculiar
to the Irish mint on the obverse, and the motto of the English mint, " Posul
Deum Adjutorem Meum," on the reverse. They are of two kinds ; one with
the king's name and titles ; the other with the king's head, name, and titles.

1463. — By the Act of the third year of Edward, which confirmed the letters
patent to Germyn Lynch, a new coinage was ordered to be made, and the said
Lynch was empowered to act according to the said letters, within the cities of
Waterford and Limerick, during his life, in the same manner as is ordained to be
done within the castles of Dublin and Trim ; and that he shall make such scripture
on the said coin of silver as ensues, viz., on the side of the crown, " Edwardus
Dei Gratia, Dominus Hlbernle ;" and on the side of the cross, " Posul Deum
Adjutorem Meum," together with the name of the place of mlntage.f

The Dublin groat of this coinage has on the obverse a crown, within a
double tressure of nine arches, trefoils at the points of the tressure, and outside it,
a small annulet in each angle, all within a dotted circle ; mint mark, a cross ;
legend, edwardvs dei gra dns hybernie, with small crosses interposed
between the words. On the reverse, a cross, with three pellets in each quarter,

* From the small weight of this coin, and the remarkable form of the cross, it may possibly
belong to Henry the Sixth.

f Simon, Appendix, No. VIII.

Dr. Smith on the Irish Coins of Edward the Fourth. 11

the pellets in the second and fourth quarters connected by an annulet. In the
outer circle, posvi devm adivtorem mev ; in the inner circle, civitas dub-
LINIE. Weight, thirty-eight grains. — (PI. I. fig. 16.)

There is a variety which has not the annulets in the alternate quarters of the
cross, and the words on the obverse are separated by small annulets : it also
weighs thirty-eight grains. — (PI. I. fig. 18.)

The Waterford groat has on the obverse, small pellets, instead of annulets,
in the angles outside the tressure ; mint mark, a rose. On the reverse, it has
not annulets connecting the pellets in the quarters of the cross ; legend, posvi,
&c. ; in the inner circle, civitas waterford : it weighs forty grains. — (PI. I.
fig. 20.)

These groats should weigh forty-five grains.

No half groat of this type has been discovered, nor is it to be expected.

A very fine and unique penny, resembling this type, has on one side a crown
within a dotted circle ; legend, edward di o dns hyb ; mint mark, a kind of
lozenge, pierced in the centre. On the other side, a cross, with three pellets in
each quarter ; legend, civitas dvblin : weight, nine grains and a quarter. —
(PI. I. fig. 17.)*

A fragment of a Waterford penny, the only specimen known, has the crown
within a double tressure, with trefoils at its points ; on the reverse, civitas
w —(PL I. fig. 19.)

Although this coin does not bear the king's name, like the Dublin penny, it
certainly belongs to the coinage under consideration, for coins were not autho-
rized to be made at Waterford previous to the year 1463 ; and besides, the
trefoils, instead of pellets, at the points of the tressure, distinguish it from the
coins of 1461 and 1462.

Halfpence and farthings were also ordered to be made at Waterford, but
none of them have been discovered.

There are not any coins of this type known from the mints of Trim or
Limerick.

1465. — A few specimens of a coinage are known, of which no record exists,

* This coin is remarkable for the absence of the tressure round the crown, yet, from its type,
and bearing the king's name, it cannot be referred to any other period of this reign.

62

12 Dr. Smith on the Irish Coins of Edward the Fourth.

except such as the coins themselves afford, and according to the arrangement I
have adopted, they must be placed in this division of the second section.

The groat has, on the obverse, a large rose of five leaves, with a small cross
in its centre ; there is a pellet in each angle, outside the double tressure of five
arches, vphich surrounds the rose, all within a circle of pellets ; mint mark, a
cross ; legend, edwardvs dei gra dns hyber.* Reverse, a sun of sixteen
rays, having a large annulet in its centre ; mint mark, a rose ; in the outer circle,
posvi, &c. ; in the inner circle, civitas dublinie. Apiece of the coin is broken
ofP, and it weighs only twenty-seven grains. — (PL I. fig. 22.)

The penny resembles the groat, and has not the tressure round the rose : the
legend, as collected from the only two specimens which have come under my
observation, is edwar dns hyber. Reverse, a sun of sixteen rays, like the

groat ; legend, civitas dv "Weight, eight grains and a half. — (PI. I.

fig. 23.)

1465. — In the fifth year of this reign, at a parliament held at Trim, an Act
was passed, the roll of which is lost ; but a part of it, relating to the rise of the
value of the gold noble, from eight shillings and four pence to ten shillings, is
recited in the Act of the seventh year of this reign.f

Mr. Lindsay supposes that these coins were made in pursuance of the Act of
1465, an opinion which, in my mind, is strongly corroborated by the evidence
furnished by the coins themselves.

The legend on the groat corresponds with that of 1463 ; and it is evident
these coins must have been minted subsequent to that date, at which time the
king's name was introduced on his Irish coins ; and the absence of the king's
head proves that they were minted previous to the year 1467, for in that year a
new type, bearing the king's head, was ordered to be made. The rose on the
obverse, and the sun on the reverse, also indicate for these coins a place in the
series, between the years 1463 and 1467- In the latter year the king's head was
substituted for the rose, and the sun was retained, having in its centre a small
rose, instead of an annulet, as in the coins under consideration.

* The Inscription on this coin is somewhat defaced ; I have made up the deficiency by reference

to Snelling's engraving, which has a small rose instead of an annulet in the centre of the sun

Snelling's Supplement to Simon, PI. I. fig. 19.

f Simon, Appendix, No. IX.

Dr. Smith on the Irish Coins of Edward the Fmirth. 13

The weight of these pieces may also be adduced as evidence in favour of the
date to which they are referred. It may be presumed that in 1465, when the
value of the gold noble was raised one-fifth, that silver was raised in the same
proportion in Ireland. And in the same year, the weight of the groat in England
was reduced from sixty to forty-eight grains.*

The groat of 1463 weighed forty-five grains, and was afterwards probably
reduced to thirty-six grains. The penny which I have described is well pre-
served, and weighs eight grains and a half, which nearly corresponds in propor-
tion with the supposed weight of the groat ; and I have already shewn that in
the last year of Henry the Sixth the Irish groat was one-fourth less in weight
than the English, and that the same relative weights were continued during the
first three years of this reign. Hence the weight of the Irish groat of this year,
which I suppose to have been thirty-six grains, still bears the same proportion to
the English groat, and is exactly one-fourth less.f

It will presently appear that the value of silver was enormously raised in

* Ruding's Annals of the Coinage, vol. li. p. 358, 2nd edit. 8vo.

f The rose was the badge of the House of York, and the sun was first introduced by Edward
upon the coins. This impress he adopted in commemoration of an extraordinary appearance in the
heavens, immediately before the battle of Mortimer's Cross in Herefordshire, (1461,) where three
suns were seen, which shone for a time, and then were suddenly conjoined in one. As Edward
was then victorious, he took a sun for his impress, which afterwards stood him in good stead at the
battle of Barnet. — Ruding's Annals of the Coinage, vol. ii. p. 359, 2nd edit. Svo.

" And on Ester day in the mornynge, the xiiij day of Apryl, [1471,] ryght erly, eche of them
came uppone otbere ; and ther was suche a grete myste, that nether of them myght see othere
perfitely ; ther thei faughte, from iiij. of clokke in the mornynge unto x of clokke the fore-none.
And dyverse tymes the Erie of Warwyke party hade the victory, and supposede that thei hade
wonne the felde. But it hapenede so, that the Erie of Oxenfordes men hade uppon them ther
lordes lyvery, bothe before and behynde, which was a starre withe stremys, wiche (was) myche lyke
Kynge Edwardes lyvery, the sunne with stremys ; and the myste was so thycke, that a man myghte
not profytely juge one thynge from anothere ; so the Erie of Warwikes menne schott and faughte
ayens the Erie of Oxenfordes menne, wetynge and supposynge that thei hade been Kynge Edwardes
menne ; andanone the Erie of Oxenforde and his menne cryed 'treasoune ! treasoune !' and fledde
awaye from the felde withe viij. c. menne. — And so Kynge Edwarde gate the felde." — Wark-
worth's Chronicle, p. 16; edited by J. O'Halliwell, Esq.; printed for the Camden Society:
London, 1839.

14 Dr. Smith on the Irish Coins of Edward the Fourth.

Ireland in 1467 ; and it is probable that so great a change was not suddenly
adopted, but was rather preceded by the reduction I have supposed.

There is a small copper coin, of which only two or three specimens are
known, and it presents some difficulties in assigning it to its proper place in this
series. Obverse, a shield, bearing three crowns, two above, and one below ;

mint mark, a rose ; legend, edwardvs d Reverse, a cross, having a small

rose in its centre ; and in each quarter of the cross three rays, which, with the
four arms of the cross, present the appearance of a sun of sixteen rays, as on
the coins of 1465 ; legend, civitas dvblinie : it weighs nine grains. — (PI. I.
fig. 21.)

A coin of this type, in the cabinet of the Dean of St. Patrick's, has on the
reverse civitas dvblin ; it evidently is not from the same die as the coin just
described.

The value of this piece, concerning which no record has been discovered,
may be supposed to have been a farthing, for its weight corresponds with that of
the copper farthings minted in 1463.

Mr. Lindsay conjectures that this coin was struck about the latter end of
this reign,* but the analogies of its type induce me to fix its date about the year
1467j the only period at which the sun, with a small rose in its centre, appears
on the reverse of the coins of this reign. The three crowns on the shield will
be explained in the fourth section.

1467. The next coinage of which any record exists, took place in the seventh
year of this reign. Of this coinage, which comes within the second division of
the Hiberno-English type, only one specimen was known to Simon. — (PI. IV.
fig. 72.) Snelling, in his Supplement to Simon's Essay, published four more,
(PI. I. figs. 20, 21, 22, 25,) and remarked that we had no record of them, except
from the pieces themselves. Two pieces from the mint of Trim, and one of
Drogheda, have been recently discovered, and have added considerably to the
interest attached to this very remarkable coinage.

Mr. Lindsay is of opinion, that the coins published by Snelling were struck
in 1467, as their reverses correspond with the description in the Act ; and adds,

* View of the Coinage, p. 47.

Dr. Smith on the Irish Coins of Edward the Fourth. 15

that *Hhe obverse may have been changed by a subsequent proclamation."*
This conjecture is not consonant with the evidence which I shall presently
offer.

In the year 1467, at a parliament held in Dublin, it was enacted, as Ireland
was destitute of silver, that a piece of silver called a Double should be coined,
having on one side the print of a crown, with this inscription, " Edwardus Dei
Gratia, Dominus Hybernias ;" and on the other side a sun, with a rose, and the
name of the place of mintage, which coin shall pass in Ireland for eight pence,
and that ten such pieces shall make an ounce, according to the rightful standard
of the tower of London. Groats, half groats, pence, half pence, and farthings,
were also ordered ; and the said coins to be made in the castles of Dublin and
Trim, the cities of Waterford and Limerick, and the towns of Drogheda, Gal-
way, and Carlingford.f

Hence it appears, that silver was at this time raised to double its former value
in Ireland, for the Double was of the same weight as the groat of the last year of
Henry the Sixth, according to which standard, the coinages of the three first
years of this reign were regulated.

Some months ago, a coin, belonging to the Rev. Mr. Butler, of Trim, was
submitted to my inspection. It has on one side the king's head crowned, within
a double tressure of nine arches ; on the other side, a sun of twenty-four rays,
having a small rose in its centre : it weighs only ten grains.

The weight of this piece would lead one to suppose it was a penny, but it
occurred to me that I had never seen either an English or Irish penny with the
head within a tressure ; hence I concluded that it must be a half groat of the
year 1467 ; and as its type differed from every other coin described in the Acts
of this reign, I conjectured that Simon had committed an error in transcribing
the description of the Double in the Act of 1467.

Shortly after, I called on Sir William Betham, and mentioned to him my
conjecture ; he very kindly permitted me to inspect his manuscript notes from
the Irish records, and immediately produced the volume containing the extract
from the Act of the seventh year of Edward the Fourth. I was highly pleased
to find my conjecture confirmed, for the coin called a "double" was described

* View of the Coinage, p. 41. t Simon, Appendix, No. IX.

16 Dr. Smith on the Irish Coins of Edward the Fourth.

in Sir William's extract as "having an impression oi a face and crown on one
side," and on the other side, the device and inscription as given by Simon.*

I am also indebted to Sir William Betham for permission to publish a clause
which he has transcribed, relating to the penny, half penny, and farthing, of this
coinage. It states, that " in consequence of the smallness of the penny, it shall
be lawful to insert the weight of ten pennies of alloy above the silver, at the
king's cost, so that the eighty pennies shall weigh an ounce and a half, and
contain the impression of the groat ; and that the half pennies or farthings may
be alloyed at the discretion of the Lord Lieutenant or Lord Deputy."

By this clause, it appears that the penny should weigh nearly eight grains
and a half. The Act, as published by Simon, says, " Also that a piece be made,
called a denier, (penny,) containing the half of the piece of two deniers, eighty
of which shall go to the ounce, besides the alloy."f

Before I enter on the description of the coins, it is necessary to say a few
words respecting the standard weight, as the writers on Irish coins have occa-
sionally confounded the troy pound with that of the tower.

It should be recollected that the coinage of England and Ireland was regu-
lated by the standard of the tower pound, which continued in use until the
eighteenth year of the reign of Henry the Eighth, at which time it was abolished
by proclamation, and the troy pound established in its stead.J

The tower pound differed from the troy pound in weight only, being lighter
by three quarters of an ounce ; the denominations of their parts were the
same. The troy ounce consisted of 480 grains ; the tower, of only 450. It
appears from the Act, that the coins of 1467 were ordered to be made " according
to the rightful standard of the tower of London ;" and consequently, the double,
ten of which went to the ounce, should weigh forty- five grains.

A double groat was discovered in June, 1839, at Trim. Obverse, the
king's head crowned, within a double tressure of nine arches ; a trefoil, with

* This confirmation of my conjecture induced me to inquire into some other obscure points
respecting Edward's coins, and ultimately led to the investigation, the fruits of which I now
present.

•)■ Simon, Appendix, No. IX.

f Ruding's Annals of the Coinage, vol. i. p. 18, 2nd edit. 8vo.

Dr. Smith on the Irish Coins of Edward the Fourth. 17

pointed leaves at six points of the tressure ; mint mark defaced ; legend,

Dvs DEI GRA DNS HYBER. Reverse, a large sun of twenty-four rays, having
a small rose in its centre ; legend, . illa de drog .... divided into four
parts by suns and roses alternately : a portion of it has been broken off, and it
weighs only thirty-eight grains. This unique and interesting coin is the earliest
piece known from the mint of Drogheda. — (PI. I. fig. 24.)

The double groat of the Dublin mint has a rose mint mark ; legend,
edwardvs DEI GRA DNS HYBERN. Rcvcrse, civiTAs DVBLiNiE. This piecc is
in' fine preservation, and weighs forty-four grains. — (PI. II. fig. 25.)

A groat of the Dublin mint was the only coin of this type known to Simon,
as was before observed ; mint mark, a rose ; legend, edward di gra dns hyber ;
weight, twenty-two grains and a half.* The weight of this piece corresponds
exactly with the standard fixed by the Act, and Simon referred it to its proper
date ; yet it is evident he did not clearly understand this coinage, for he describes
a penny of a different type as belonging to it.t

A half groat of the Dublin mint was discovered at Trim, in 1834; type

same as the groat ; mint mark, a sun ; legend, edwa hybernie.

Reverse, civitas dublinie : weight, ten grains. — (PI. II. fig, 26.)

The half groat now appears, for the first time, in the Irish series.

The Trim groat is unique ; type similar to the others ; it has not trefoils at
the points of the tressure, as in the double groat. Reverse, ... la de trim ;
it weighs twenty-three grains and a half, and is the earliest coin on which the
name of this town appears. — (PI. II. fig. 27.)

An interesting addition to the very few pieces of this type which are known,
was discovered in August, 1839, near Castlecomer, county Kilkenny ; it is the
half groat of Trim, and is unique ; mint mark, a rose ; two small pellets over the
crown; legend, edwardvs di gra dns hybe. Reverse, a sun of twenty-four
rays ; legend, villa de trim ; after the word Trim, there is a trefoil with
pointed leaves, and pellets between them ; its weight is eleven grains and a
quarter, which accords exactly with the standard. — (PI. II. fig. 28.)

I must now make a few remarks on the three small coins engraved in Snel-
ling's Supplement to Simon.| They are described as "having a large sun of

* Simon, PI. IV. fig. 72. f Simon, p. 26, and PI. V. fig. 114. % PI. I. figs. 20, 21, 25.

VOL. XIX. C

18 Dr. Smith on the Irish Coins of Edward the Fourth.

fifteen rays" on their reverses ; yet in the engravings, figs. 20 and 21 have suns
of sixteen rays ; and fig. 25, a sun of only ten rays, although it is full as large
as fig. 21. Fig. 20, from its small size, and the absence of the tressure round
the head, I believe to be the penny of this coinage ; but its weight is said to be
eleven grains and a half, which must be a mistake, as I have already shewn that
the weight of the half groat ought to be eleven grains and a quarter ; besides,
according to the clause which I have given, on the authority of Sir William
Betham, the penny should weigh about eight grains and a half; and by the Act,
as published by Simon, it should weigh only about five grains and a half. — (See
p. 16.) Fig. 21 corresponds in size with the Dublin half groat which I have
published, but differs from it in having a rose for its mint mark ; and the legends
on the obverse and reverse are also different ; besides, the sun has only sixteen
rays, instead of twenty-four, the number on the five pieces in my plates. Its
weight is stated to be twenty-two grains, being only half a grain less than the
groat published by Simon. — (PI. IV. fig. 72.)

Fig. 25 is very remarkable ; its obverse is similar to an English penny of
Edward the First or Third ; yet from the sun on its reverse, it cannot be appro-
priated to any king but Edward the Fourth ; it has no rose in its centre, and
the legend, civitas dvblini, is not divided into four parts by suns and roses, as
in all the coins which I have published : its weight is said to be fourteen grains
and a half.

Mr. Lindsay conjectures that this piece may have been a pattern for a penny ;
it presents several anomalies in its type, concerning which I cannot oflFer any
explanation, as I have not seen the coin.

The Act of the seventh year of Edward authorized coins to be made in the
castles of Dublin and Trim, the cities of Limerick and Waterford, and the towns
of Drogheda, Galway, and Carlingford.

The coins from the Dublin mint are the most numerous, viz. : the double
groat, groat, half groat, and penny. Of Trim, there are the groat and half
groat, both unique. And of Drogheda, the double groat, which Is also unique.
None of Limerick or Waterford have been discovered ; and it does not appear
that silver coins were ever minted in Galway or Carlingford.

It Is a remarkable circumstance, that during the first seven years of this reign,
seven distinct coinages were issued from the Irish mints ; some of them present

Dr. Smith on the Irish Coins of Edward the Fourth. 19

several varieties of their types ; and I may add, that the coins of this period are
generally found to correspond in weight, very nearly, with that specified in the
several Acts. But the history of the period on which I am about to enter is
much embarrassed by the gross frauds which were practised in the authorized, as
well as the illegal Irish mints.

Before I proceed to the consideration of the coins of the English type, it is
necessary to notice a few from the mints of Drogheda and Dublin, which are
not described in any of the Acts of this reign which have been published.

They are distinguished from the coins of the English type by having a rose
in the centre of the reverse, instead of three pellets in each quarter of the cross,
and for this reason I place them in this section.

The groat has the king's head crowned, within a double tressure of nine
arches, a small sun at the right side of the crown, and left of the neck, and a
rose at the left of the crown, and right of the neck ; mint mark, a rose ;* legend,
EDWARDvs . . . GRA DNS HYBER. Reverse, a cross, with a rose in its centre ;
mint mark, a sun ; legend, posvi, &c., and in the inner circle, villa drogheda,
— (PI. II. fig. 29.) In another, the suns and roses at the sides of the crown
and neck are transposed ; legend, edwardvs di gra dns hyber. ; mint mark
on the reverse, a rose. — (PL II. fig. 30.) They weigh from twenty-seven to
twenty-nine grains.

No other coins of this type from the Drogheda mint have been discovered.

The groats of the Dublin mint present two varieties in the disposition of the
suns and roses, like those of Drogheda ; legend, edwardvs dii gra dms iber.
Reverse, posvi, &c., and civitas dublinie ; weight, thirty-two grains. — (PI. II.
fig. 31.)

The penny corresponding with the type of this groat weighs only six grains.
—(PI. II. fig. 32.)

The groat, PI. II. fig. 33, has a different legend, edwardvs frae d ;

weight, twenty-six grains.f

The penny of this variety weighs only six grains. — (PI. II. fig. 34.)

* Simon, PI. IV. fig. 82, has published one with a sun mint mark.

■j" The groats published by Simon, PI. IV. figs. 80, 81, are both different from those I have
described ; the mint marks are a crown, and a sun.

c2 .

20 Dr. Smith on the Irish Coins of Edward the Fourth.

Snelling, In his Supplement to Simon,* has published two halfpennies of this
coinage, but has omitted to state their weight.

The Act of the first year of Richard the Third, which Simon speaks of as
defaced by time and vermin, and which, as Mr. Lindsay remarks, " is evidently
composed of parts of two Acts, and relate to coins of a very different descrip-
tion,"! enables me to fix the date of these coins in the year 1470.

In the first year of Richard, the master of the mint was authorized to make
coins "in such manner and in such places, as is ordained by a Statute" of the
tenth year of Edward the Fourth.J Now there are groats of Richard which
correspond in every particular, except the king's name, with those of Edward ;
and my opinion as to their date, is supported by the fact of their deficiency in
weight, for in 1472, Germyn Lynch, master of the mints in Ireland, was indicted,
" for that when the Statute said, that every pound of bullion coined, should be
forty-four shillings in money, he coined out of every pound forty-eight shillings,
and that he coined at Drogheda one thousand groats, which being tried, it was
found that eleven weighed but three quarters of an ounce,"§ instead of an ounce;
so that the average weight of the groats was a little more than thirty grains,
which agrees nearly with the weight of those now in existence.

There are several Dublin pennies which were probably coined about this
time ; they rarely exhibit the legends entire, but may be readily recognized by
their reverses, which bear a cross, having a small rose in its centre, and the legend
civiTAs DUBLIN. In the quarters of the cross, there are alternately two roses and
a sun, and two suns and a rose, instead of pellets, as in the coins of the next
section. — (PI. II. figs. 35, 36.) The former weighs nine grains, the latter only
six.

The penny, fig. 37, is remarkable for the legend on its obverse, ed . . . di
GRA REX NGi F : it Weighs nine grains and a half.

THE THIRD SECTION.

The coins included in this section are similar in type to the English coins of
Edward.

»

Plate I. figs. 23, 24. f Lindsay, p. 47.

X Simon, Appendix, No. XVIII. § Simon, p. 27,

Dr. Smith on the Irish Coins of Edward the Fourth. 21

The value of silver in Ireland vpas raised enormously in 1467, the consequence
of which was, that the price of every thing increased in proportion ; to remedy
which evil, the next parliament held in Duhlin, in 1470, enacted " that the master
or masters of the coinage shall have power to make and strike within the castles of
Dublin and Trym, and the town of Drogheda, five sorts of silver coynes, according
to the fyness of the coynes struck in the Tower of London," viz. the groat, half
groat, penny, halfpenny, and farthing. The groat to have on one side the print of
a head crowned, with the writing, " Edwardus Dei Gratia, Rex Anglle Dominus
Hibernie ;" and on the other side the print of a cross, with the pellets according
to the groat made at Calais, and the motto, " Posui Deum Adjutorem Meum,"
with the name of the place of mintage ; of which groats, eleven shall make the
ounce, troy (tower?) weight ; and that the fifth part of every pound be struck
in small pieces. It was also enacted that the master might allay the halfpence
and farthings according to the Statute made in the fifth year of this reign, which
Statute cannot be found. By this Act, the coinage of 1467 was reduced to half
its original value, and forbidden to be taken for a coin after the feast of the
Purification next.*

1471.t — By an Act of this year, it appears that a great part of the coinage of
1470 was neither of full weight nor fine allay .J

1472. — The Act of this year states, that false coins were made in Cork,
Youghal, Kinsale, and Kilmallock.§

1473. — At a parliament held in Dublin, it was enacted, that the coins should
be struck, for the time to come, within the castle of Dublin only, and in no
other place in Ireland ; and that fourteen groats should make an ounce, accord-
ing to the just standard of the Tower of London ; and to be made according
to the fineness and alloy of the said tower ; and that Germyn Lynch be master
of the said mint during good behaviour.||

1475. — The groat made in England at this time was ordered to pass, if not
clipped, for five pence ; and all the moneys to be struck in Ireland, to be of the

* Simon, Appendix, No. X.

f In Simon's Appendix, this Act is dated 1472 ; and at page 27, he calls it the Act " of the
eleventh of this prince."

X Simon, Appendix, No. XI. § Simon, Appendix, No. XII.

II Simon, Appendix, No. XIII.

22 Dr. Smith on the Irish Coins of Edward the Fourth.

same value as they now are ; and that all the mints in Ireland shall cease, except
those of Dublin, Drogheda, and Waterford.*

1476. — The coin lately made in Cork, Youghall, Limerick, and other places
in Munster, except Waterford, being neither lawful in itself, nor of lawful
• weight and alky, was declared void, and forbidden to be taken in payment.t
I have now given the substance of the several Acts which were passed from
the year 1470 to 1476 ; and, from the number and variety of coins struck during
this period, which are in existence ; the obscurity and imperfections of the Acts
of parliament ; and the general deficiency of the coins in weight, the most con-
venient arrangement which can be adopted, is, to describe, first, the coins of the
several mints ; and afterwards endeavour to assign them to their proper dates.

CORK MINT.

Two varieties of the groat are known ; one has the king's head, within a
double tressure of nine arches ; trefoils at six of its points ; and at each side of
the neck, a quatrefoil ; legend, edwaRDvs dei era dns hibcENiE. Reverse, a
cross, with three pellets in each quarter ; motto, posi devm aivtore mevm ; in
the inner circle, civitas corcagie ; mint mark, a rose in three places ; weight,
thirty-eight grains. — (PL II. fig. 38.)

The other has a pellet at each side of the king's neck, and only a single
pointed leaf at the points of the tressure ; legend, edwardvs dei gra dns
iBERia. Reverse, posv . dev . adivtor mev ; in the inner circle, civitas
corcagie ; no mint mark on either side. This piece is well preserved, and
weighs only thirty grains. — (PI. II. fig. 39.)

DROGHEDA MINT.

The groat bears the king's head, within a double tressure of nine arches ;
legend, edwardvs dei gea dns hyber, or hyberni ; mint marks, a crown,
and a cross pierced in the centre. Revefse, posvi, &c. ; and in the inner circle,
VILLA DE drogheda. They weigh from thirty-three to thirty-four grains. —
(PL IL figs. 40, 41.)

* Simon, Appendix, No. XIV. f Simon, Appendix, No. XV.

Dr. Smith on the Irish Coins of Edward the Fourth. 23

The groats with the letter g on the king's bust are more numerous ; mint
mark, a cross pierced in the centre ; legend, edwardvs dei gra dns hybern.
Some have an annulet at each side of the king's neck. The average vf eight of
eight well preserved pieces is thirty-two grains. — (PI. II. figs. 42, 43.)

A half groat has been recently discovered, and is unique ; legend, edward
Di GRA DNS HYBER ; mint mark, a sun ; it has not trefoils at the points of the
tressure. Reverse, posvi, &c., and villa de droghe : weight, fifteen grains.
—(PI. II. fig. 44.)

Of the pennies, there are four varieties.

The first has a pellet at each side of the king's neck. Reverse, villa de
DROGHE : weight, eight grains. — (PI. II. fig. 45.)

The second has a small rose in the centre of the reverse, and weighs only
six grains. — (PI. II. fig. 46.)*

The third has an ornament, consisting of four loops united, so as to form a
kind of quatrefoil, in the centre of the reverse ;f legends, edward dns hyber,
and villa de drogheda : weight, seven grains. — (PI. II. fig. 47.)

The fourth variety has a small sun at each side of the king's neck ; and the
legend on the obverse is different from all the others, viz. edward rex ang .
FR ; mint mark, a cross.J I do not know of any Drogheda groat with a similar
legend.

DUBLIN MINT.

The legend on the groat is edwardvs di gra dns hybernie ; mint marks,
a rose, and a cross pierced in the centre. Reverse, posvi & ; and in the inner
circle, civitas dvblinie. They weigh from thirty-five and a half to forty-five
and a half grains. — (PI. III. fig. 48.) This is the heaviest piece of the English

* I should have placed this coin at the end of the second section, on account of the rose on its
reverse, were it not that the pellets in the quarters of the cross identify it more closely with the
coins described in this section. This piece, taken together with No. 36, exhibits the transition of
the type from the coins of the Hiberno-English series to that of the English type described in this
section.

f A similar ornament occurs on the York and Durham pennies of Edward the Fourth. — Ku-
ding, Suppl. PI. III. figs. 21, 28, 2nd edit.

% Simon, PI. IV. fig. 92.

24 Dr. Smith on the Irish Coins of Edward the Fourth.

type which I have met with ; it is more than four grains above the standard
weight fixed by the Act under the authority of which it was coined.

The groats with the letter g on the king's bust are more numerous ; the
legends are, edwardvs dei gra dns hyber, hybern, and hyberni ; mint
marks, a sun, a cross, and a cinquefoil. They present many varieties, which it
is unnecessary to particularize, and usually weigh about thirty-two grains each.
—(PI. III. figs. 49, 50.)

The legend on the half groat is, edward di gra dns hyber ; some have
small pellets between the words, others small crosses ; the latter is the most com-
mon on the coins of this type ; mint marks, a sun and a cross. Reverse, posvi,
&c., and civiTAS Dublin. They weigh seventeen grains. — (PL III. figs. 51,
52.)

The penny weighs seven grains and a half, and has a small cross at each
side of the king's neck; legends, edward di gra dns hyber, and civitas
dublinie. — (PL III. fig. 53.)

Another has small pellets, instead of crosses, at each side of the king's neck.

A third variety has a kind of quatrefoil in the centre of the reverse, and the
legend, civitas Dublin ; it weighs only six grains. — (PL III. fig. 54.)

limerick mint.

The groats present three varieties in the legends, edward di gra rex angl
et fr or FRANC, and edwakd di gra dns hvberni. They all have the letter l
on the king's bust, and have either a rose, a cross, or a cinquefoil, at each side of
the neck ; mint marks, on the obverse, a cross pierced in the centre, and a
cinque foil at the beginning of the legend on the reverse ; in the inner circle,
civitas limirici, and one of the pellets in the alternate quarters of the cross is
replaced by a cinquefoil. They weigh in general about thirty-one grains. —
(PL III. figs. 55, 56, 57.)

The only half groat which I have seen has the legends much defaced, yet it
weighs seventeen grains ; there is a quatrefoil at each side of the neck, and on
the reverse, civitas limirici, (PL III. fig. 58 ;) it has not the letter l on the
king's bust, nor the cinquefoil instead of the pellet in the alternate quarters of
the cross, like the groats, and the half groat published in the Editor's additional
plate to Simon, (fig. 16.)

Dr. Smith on the Irish Coins of Edward the Fourth. 25

The only penny of this type which has been discovered is represented in the
same plate, fig. 17.

Another penny has a kind of quatrefoil in the centre of the reverse, and
weighs nine grains and a half. — (PI. III. fig. 59.)

TRIM MINT.

The legend on the groat is edwakdus dei gra dns hyber, or hybern ;
mint marks, a rose, and a cross pierced in the centre. Reverse, posvi, &c. ; and
in the inner circle, villa de trim. One has a rose before the word posvi,
and another has a small cross in one of the quarters of the reverse. They weigh
from twenty-eight to thirty-four grains. — (PI. III. figs. 60, 61.)

The half groat of this type is unique ; it was found at Trim, and weighs
twenty-three grains. — (PI. III. fig. 62.)

A penny, of any coinage, from this mint would be an interesting discovery ;
there can be no doubt that such pieces were minted.

waterford mint.

Several varieties of the coins from this mint are known. One groat has a ^
on the king's bust, and a small plain cross at each side of the neck ; mint mark,
a rose ; weight, forty-three grains. — (PI. III. fig. 63.)

Another has a v on the king's bust, and weighs only twenty-eight grains. —
(PI. III. fig. 64.)*

Others have the letter o on the bust ; mint marks, a rose, cinquefoll, and a
cross pierced in the centre. They weigh from thirty-two to thirty-three grains.
—(PL III. figs. 68, 69.)

There is a fourth variety, without any letter on the bust ; mint marks, a
rose, trefoil, and a cross pierced in the centre. Some have a quatrefoil at each
side of the neck, others a plain cross, and some are without any mark in this
place. They weigh, in general, about thirty-one grains each. — (PI. III. figs. 65,

m, 67.)

* A trefoil is the mint marlt of this variety, as appears from the coin published by Simon, PI. IV.
fig. 84.

VOL. XIX. d

26 Dr. Smith on the Irish Coins of Edward the Fourth.

Mr. Lindsay mentions a sun, as a mint mark on the Waterford groats, but
does not say on which variety it occurs.

The legend on the obverse presents little variety ; and they all have on the
reverse, civitas waterford, many of them having a small cross in the alternate
quarters, with the pellets.

No half groat of any type, from this mint, has been discovered.

There are several varieties of the pennies ; one has a pellet at each side of
the king's crown, and two small crosses at each side of the neck ; legend, edward
Di GR DNS iBERNia ; mint mark, a cross. Reverse, civitas waterford ;
weight, ten grains. — (PI. IV. fig. 70.) A variety of this type has on the reverse,

civitas WATFORD.

Another has an annulet at each side of the king's neck; it weighs nine
grains and a half. — (PI. IV. fig. 71.)

A third variety has a pellet at each side of the neck ; mint mark, an annulet.
Reverse, civitas watford : weight, eight grains. — (PI. IV. fig. 72.)

The legend of the fourth variety is, edward dns hyber, and it has a small
cross at each side of the neck. Reverse, civitas watford ; it also has a kind
of quatrefoil in the centre, and weighs eight grains. — (PI. IV. fig. 73.)

WEXFORD mint.

The only kind of coin known from this mint is the groat, which was pub-
lished by Simon, PI. V. fig. 93, and represented as if in as good preservation,
and as equal in workmanship to any of the coins of this reign. I am inclined to
think the engraver has not given a correct delineation of the coin, as I have
recently had an opportunity of seeing one, belonging to the Rev. Mr. Butler, of
Trim, and it is remarkable for the rudeness of its execution ; it has the king's
head crowned, within a double tressure of ten arches. The legends are very
defective, and appear to have been greatly blundered. Reverse, villa weisfor ;
the s is reversed, and on the coin it looks very like an x, for which it may have
been intended ; the metal is apparently impure, and the coin weighs only twenty-
six grains. — (PI. IV. fig. 74.)

One small brass piece is known, which corresponds in tjrpe with the coins
described in this section. It exhibits on one side the king's head crowned, and

Dr. Smith on the Irish Coins of Edward the Fourth. 27

on the other, the cross and pellets ; small strokes, or lines, appear to have been
substituted for the legends : it weighs three grains and a half. — (PI. IV. fig. 86.)

This may possibly be a farthing, as at one period of this reign, the Lord
Lieutenant, or his Deputy, was empowered to allay the halfpence and farthings
according to his discretion,* a privilege very likely to be exercised to its utmost
extent.

Of the seven cities and towns in which the coins described in this section
were minted, only four, viz. Drogheda, Dublin, Trim, and Waterford, are recog-
nized as legal mints in the Acts which have been preserved.

I shall first dispose of the mints which were not legally qualified. The Cork
groats appear to have been made between the years 1470 and 1473, for the Act
of the year 1472 informs us of " there being divers coiners in the city of Cork,
and the towns of Youghal, Kinsale, and Kilmallock, who make false coins without
authority ;"f and in 1473, it was enacted that the coins should "be struck for the
time to come within the Castle of Dublin only, and in no other place in Ireland,"!
and by this Act the weight of the groat was reduced to about thirty-two grains ;
hence it is clear, that one at least of the Cork groats which weighs thirty-eight
grains was minted before 1473 ; and their blundered inscriptions, together with
the apparent impurity of the metal, plainly indicate that they were the work of
some fraudulent artist.

Wexford, as a place of mintage, is not mentioned in any of the Acts of this
reign ; and the only coin which I have seen from this mint is very deficient in
weight, and bears evident proof of the fraudulent design of the person by whom
it was executed. I am unable to assign any particular date to this piece.

The weight of the Limerick groats, which in no instance have I found to
exceed thirty-two grains, makes it probable that they were not minted previous
to the year 1473, at which period the standard weight of the groat was reduced
from forty-one to nearly thirty-two grains ; and as the privilege of making coins
was restricted to Dublin only from 1473 to 1475, it is likely that the coins of
this mint were issued during the latter year, for the Act of 1476 states, that
" the silver coin lately made in Cork, Youghal, Limerick, and other places in

• Page 16. t Simon, Appendix, No. XII.

X Simon, Appendix, No. XIII.

d2

28 Dr. Smith on the Irish Coins of Edward the Fourth.

Munster, except Waterford, being neither lawful in itself, nor of lawful weight
and allay," was declared void, and forbidden to be taken in payment.*

Although Limerick does not appear in the Acts as a legal mint, after the
year 1467, I am disposed to think that city enjoyed authority to coin money at
a subsequent period. The Limerick coins described in this section are as well
executed as any pieces from the authorized mints ; and besides the varieties of
the groats which are known, there are also two varieties of the half groat and
penny. — (PI. III. figs. 55, 56, 57, 58, 59 ; see also Editor's additional plate to
Simon, figs. 16, 17.) The number of coins issued from this mint distinguish it
from those of Cork and Wexford, of which only groats of rude execution are
known.

Of the coins from the authorized mints, those of Trim appear to have been
made between the years 1470 and 1473, for in the latter year the privilege of
striking money was withdrawn from this mint, and it does not appear to have been
restored at any subsequent period.

The groats of Drogheda, Dublin, and Waterford, without the letter g on
the king's bust, were all minted previous to the year 1473, as was also the Water-
ford groat with the letter ^ on the bust ; the latter weighs forty-three grains,
and is the heaviest piece of the English type which I have met with, except fig.
48, which weighs forty-five grains and a half.

The pieces with the letter g on the bust were all struck subsequent to the
year 1473 ; some of those of Dublin may have been minted in that year, but
the Drogheda and Waterford groats were probably issued in 1475, when the
authority for making money was restored to those places.

I do not know of any half groats or pennies with the letter g on the bust.

Mr. Lindsay has stated, that the letter g is " probably the initial of Germyn
Lynch,"f an opinion which I shall endeavour to corroborate.

Simon, on the authority of a manuscript in the Library of Trinity College,
Dublin, states that in 1472, Germyn Lynch was indicted for making light
groats at Drogheda. J But, independent of this authority, there is evidence in
the Act of 1471, that Lynch had been deprived of his office of Master of the

♦ Simon, Appendix, No. XV. f View of the Coinage, p. 43.

X Page 27.

Dr. Smith on the Irish Coins of Edward the Fourth. 29

Mint, for on the eighteenth of October, in the tenth year of this reign, (1470,)
William Crumpe and Thomas Barby, merchants, were by letters patent consti-
tuted masters of the coinage ;* and in 1473, it was ordered, that Germyn Lynch
be Master of the Mint during good behaviour.f

It is reasonable to suppose, that Lynch, being restored to his oflfice, would be
anxious to adhere more strictly to the provisions of the Statutes ; and as so many
frauds had been committed in the coinage, he probably adopted the letter g as
his privy mark ; and I find that the groats with this mark on them are remarkable
for the uniformity of their weight, and correspond pretty closely with the stan-
dard fixed in 1473. Lynch's coins are more numerous than the other varieties,
which, with few exceptions, do not appear to be regulated by any standard.

There are four pennies described in this section, which I am unable to refer
to any particular date, viz. Nos. 47, 54, 59, 73. No groats corresponding in
type with them are knovra, and it is only from the larger pieces that the types
described in the Acts can be satisfactorily determined.

There is one particular respecting the inscription on the coins of this period,
which requires some notice. The Act of 1470 orders that the groat shall have
the words rex anglie in the inscription on the obverse. Now I have observed
this title on only three coins, (figs. 37, 55, 56,) and on a Drogheda penny
engraved in Simon's Essay.J

Before I conclude my remarks on this section, I must say a few words
respecting the weight of these coins. In 1470, it was enacted that eleven groats
should make an ounce troy ; each groat should, therefore, weigh very nearly
forty-four grains, or 43^. I presume the troy ounce has been erroneously
substituted for that of the Tower, and consequently that the groat of this year
should weigh very nearly forty-one grains, or 40-1^. I only know of two coins
which exceed the standard as fixed in 1470.§

* Simon, Appendix, No. XI. f Simon, Appendix, No. XIII.

X Plate IV. fig. 92.

§ Figs. 48, 63. The occasional extra weight is explained by the Act of 1470, which states :
" And as the said money cannot always be made to agree according to the just standard, being, in
default of the Master, sometimes made too great, and sometimes too small in weight or allay, by
four deniers in every pound, which four deniers shall be a remedy for the said Master." — Simon,
Appendix, No. X.

30 Dr. Smith on the Irish Coins of Edward the Fourth.

That the Tower ounce was the standard used in Ireland, is evident from the
Act of 1467, which directs the coins to be made " according to the rightful
standard of the Tower of London ;" and from that of 1473, which enacts, that
fourteen groats should make an ounce, "according to the just standard of the
Tower of London ;" and again, in 1479, " according to the fineness and stan-
dard of the Tower of London r therefore, the groat of the year 1473 should
weigh a little more than thirty-two grains, and not " about thirty-four grains to
the groat," as stated by Mr. Lindsay.*

THE FOURTH SECTION

Comprises a class of coins of a very remarkable type, which were the last
issued during this reign, and may be denominated the Anglo-Irish type. They
have on the obverse a shield, bearing the arms of England and France quartered ;
and on the reverse, three crowns in pale, a device peculiar to the Irish coinage.

1478. — In the eighteenth year of this reign, at a parliament held at Trim,
before Henry Lord Grey,f Deputy to George Duke of Ckrence, it was enacted,
that for the time to come, the liberty of Meath be restored and exercised,
with all manner of liberties, in as ample a manner as was exercised and occupied
in the time of Richard, late Duke of York, or his noble progenitors, lords of
Meath ; and that Henry Lord Grey, Lord Deputy, shall enjoy and exercise,
by himself or his Deputy, the said liberty by the name of Seneschal and Trea-
surer of the said liberty of Meath, in as ample a manner and form as any Senes-
chal or Treasurer heretofore occupied and enjoyed the same. And further, this
Act confirms a grant made by the king of the office of Seneschal and Treasurer
of Meath to the said Henry, dated at Westminster the third day of March, in
the seventeenth year of his reign. And by this Act, the said Henry, by himself
or his officers, may for the future strike and coin all manner of coins of silver
within the Castle of Trim, according to such fineness and allay as in the Statute
for that purpose is provided.|

* View of the Coinage, p. 42. .

f Sir James Ware, in his Table of the Chief Governors of Ireland, does not mention Henry
Lord Grey, Lord Deputy to George Duke of Clarence.
:j: Simon, Appendix, No. XVL

Dr. Smith on the Irish Coins of Edward the Fourth. 31

The Statute here referred to is not to be found, but we learn from Sir James
Ware, " that in the eighteenth year of Edward the Fourth, an Act passed a
parliament held under Gerald Earl of Kildare, Lord Justice of Ireland, granting
liberty to the Mint Master of coining pieces of three pence, two pence, and a
penny ;" and he adds, that "it is, however, worth observing that the impress on
the coins of this time, on the reverse, was three crowns, denoting the three
kingdoms of England, France, and Ireland."*

1479. — At a parliament held at Dublin, before Gerald Earl of Kildare,
Deputy to Richard Duke of York, it was " enacted that Germjm Lynch, Master
of the MInters, have power to strike coin at four shillings and ten pence per
ounce, rendering to the merchant four shillings and four pence, and to the king
and workmen six deniers, according to the fineness and standard of the Tower
of London."!

1483. — " An indenture for Ireland was made with Thomas Galmole, Gent.,
Master and Worker of the Money of Silver, and Keeper of the Exchanges in
the cities of Devylyn (Dublin) and Waterford. He was to make two sorts of
monies ; one called a Peny, with the king's arms on one side, upon a cross
trefoyled on every end ; and with this inscription, rex anglie et fbancie : and
on the other side, the arms of Ireland, upon a cross, with this scripture, dns
HiBERNiE ; of such Penyes in the pound weight of the Towere, iiii. c. 1. pecs,
which is in nombre xxxvij s. vjd. The other money to be called the Halfpenny,
with the like impression and inscription, and in weight one-half of the first, all
of the old sterling."!

These are the only records which remain of the last five years of this reign.

There are two varieties of the type of the coin issued during this period.
One has on the obverse a shield, bearing the arms of England and France, quar-
tered by a cross, the extremities of which are terminated each by three pellets ;
the shield is within a circle of pellets. Reverse, three crowns in pale, on a
similar cross ; mint marks, a trefoil, rose, and fleur de lis.

The other variety has a shield, quartered by a cross, whose arms are termi-
nated each by three annulets ; at each side of the shield is a smaller one, bearing

* Harris's Ware, vol. ii. p. 215. f Simon, Appendix, No. XVII.

X Ruding's Annals, 2nd edit. vol. ii. p. 376.

3i

Dr. Smith on the Irish Coins of Edward the Fourth.

a saltire, The Arms of Fitzgerald Earl of Kildare and Lord Justice of Ireland
in 1479 ;* all within a plain circle. The crowns on the reverse are closer, and
of a more regular form, than those of the first variety, and are within a double
tressure of eight, or more generally, nine arches ; they invariably have a fleur de
lis, on one or both sides, in some part of the legend, which is rarely found on the
pieces of the first variety.

The following Table exhibits the most remarkable varieties of the legends
which occur on the coins of the Anglo-Irish type.

WITHOUT THE FITZGERALD ARMS.

EDWAR REX ANGLIE FRANCI.

EDWARDVS . . . ANGL

EDWARDVS RANC.

REX ANGLIE FRANCIE.
REX ANGLIE FRANCIE.
DOMINVS HYBERNIE.

EDWARD DOM HYBE.
REX ANGL FRANCIE.
REX ANGL FRANCIE.
REX ANGL FRANCIE.
REX ANGL FRANCIE.
REX ANE FRANCIE.
DOMIN . . . RERIE.

REX ANGL FRANCIE.
REX ANG FRANC.

GHOATS.

DOMINVS HYBERNIE.t

DEMINVS HYBERNIE.

PI. IV.

fig. 76.

ET : REX HYBERNIE.

>»

75.

ET REX HYBERNIE.

»

77.

DOMINVS HYBERNIE.

»

78.

DOMINVS HYBERNIE.

>>

80.

HALF GROATS.

CIVITAS DVBLINIE.t
CIVITAS . . . LIN.
DOM HYBERNIE. §

87.

DOMINVS HIBERNIE.

)>

88,

DOMINS VBE.

»>

89.

DOMINOS VRER.

»>

90.

DOMINOS V . .

»

91

NIES.

DOMNVS HYBENIE.II

DOMINVS HIBERN . .

»

93

* The small shield which Simon represented as a figure of 8, (PI. III. fig. 65,) and described as
a mint mark, (p. 22,) was first recognized by the Rev. Mr. Butler as the arms of the Fitzgeralds. —
Numismatic Journal, vol. ii. p. 73.

t Simon, PI. IV. fig. 87. ' % lb. PI. V. fig. 94,

§ lb. PL V. fig. 95. II lb. PI. IV, fig. 90.

Dr. Smith on the Irish Coins 0/ Edward the Fourth. 33>

WITH THE FITZGERALD ARMS.
GKOATS.
REX ANLIE FRA. DOMINOS VRERNI. PL IV. fig. 82.

REX ANLIE FRA.

DOMINOS VRERNIE.

»

83,

EEX ANCIE CIE.

DOMINS VRER.

)»

84,

REX ANIE FRANCI.

HALF

DOMINOS VRENIE.
GROAT.

55

85,

DOMINOS.

DOMINO - .

»

92

Mr. Lindsay has published a small coin of this type, which he supposes to
be a farthing,* and that " it may possibly belong to Henry the Seventh." This
little piece is in the cabinet of the Dean of St. Patrick's, is greatly corroded and
defaced, and weighs only two grains, which probably led to the supposition of its
being a farthing. It is, however, the remains of a penny, for the diameter of
the circle, and the size of the shield, correspond exactly with those of a well-
preserved penny ; and besides. Sir James Ware makes no mention of farthings of
this type.

Some have thought, that as the arms of England and France are impressed on
these coins, that they should be ascribed to Henry the Seventh, who was the first
monarch who had these arms stamped on the English silver coins. To refute
this opinion it is only necessary to refer to the coins of this type which bear the
name of Edward.— (PI. IV. figs. 75, 76.)

According to Simon, Henry the Eighth " having, in his thirty-third year,
assumed the title of King of Ireland, was so proclaimed the thirteenth of June,
1541, in St. Patrick's Church, near Dublin ;"f and Ruding informs us, that in
the same year the title et hybernie rex was first used on the Great Seal of
England.! Now the coins of PI. IV. figs. 75, 77, not only prove that the arms of
England and France appeared first on the Irish coins, but that the title of rex
hybernie was impressed on the coins of this country many years earlier than the
date usually assigned to the introduction of this title. These pieces are therefore

* View of the Coinage, PI. VI. fig. 128. f Simon, p. 33.

i Railing's Annals, toI. ii. p. 443, 2nd edit.

VOL. XIX. e

34 Dr. Smith on the Irish Coins of Edward the Fourth.

indubitable evidences of a fact, the account of which has been imperfectly re-
corded by historians. Figs. 79 and 81 are peculiar in having the border of the
shield formed of small pellets, instead of plain lines, and the former has a fleur
de lis before the v?ord rex ; the only instance in which I have found this mint-
mark on the groats without the Fitzgerald arms.

Some of these pieces are what are termed mules in numismatic language, e. g.
the obverses of 78 and 80 are different, while their reverses are from the same
die, as is evident from the blundered b in Hybernie.*

The many varieties, both in type and legends, which occur on the half-
groats, require some notice. Of the six I have published, only one agrees in
type with the groats of the first variety, and it is remarkable for having i instead
of Y in Hibernie (fig. 88). The same peculiarity occurs on the penny, (fig. 93,)
and I have seen a groat which corresponds in this particular with these two
pieces.

Only one half-groat, bearing the Fitzgerald arms, is known, and it has the
word DOMiNOs on each side (fig. 92.)

The obverse of 87 and 89 corresponds with the groats of the first variety,
while the reverse of each of them bears the cross with the annulets, and the plain
circle, which, with the legend domins vbe on the latter, identify them with the
Fitzgerald type.

The former was struck at Dublin, and I do not know of any groat of this
type from the same mint.

Figs. 90 and 91, although they have not the Fitzgerald arms on them, do, I
presume, properly belong to the second variety of this coinage. The former
bears a very close resemblance, in some particulars, to the groat, fig. 84.

Mr. Lindsay remarks, that "the half-groat has sometimes the initial of

* A curious fact may be learned from these two pieces, respecting the manner in which the
letters were made on the die. They were formed with punches, or steel types, as is practised at the
present time, for the artist manifestly put in the letter E by mistake, and to cover his blunder, he
afterwards punched over it the letter B. Other instances in support of this opinion may be adduced,
when, for instance, the artist substituted the reversed b for E, (PI. IV. fig. 70,) and occasionally
the letter l is represented in an ingenious manner by a double i, as in figs. 82 and 83. Such blun-
ders, especially the latter, could scarcely happen had the artist used a graver, or cutting tool of
any kind, in forming the letters.

Dr. Smith on the Irish Coins of Edward the Fourth. 35

the king's name before the word Rex."* I have not met with any such
variety.

Sir James Ware says, that liberty to coin " pieces of three-^&ace, two-pence,
and a penny," with three crowns on the reverse, was granted to the Mint
Master in the eighteenth year (1478) of this reign. I conceive he has com-
mitted some error on this subject, for Moryson, who wrote many years before
him, speaks of "cross-keale groats, with the Pope's triple crown."

Simon, relying on the correctness of Sir James "Ware's account, endeavours
to reconcile it with the standard fixed by the Act of 1479- He observes, " the
standard of the Tower of London must be understood here only as to the allay,
and not as to the weight of the Tower," and concludes that "the groat must have
weighed forty grains, and ten (twelve ?) of them to have been cut out of the
ounce Troy, in which case silver was again reduced to near its former value ;"t
and in the next page informs us that "the pieces with three crowns" weigh
from twenty-eight and a half to thirty grains, " the half piece fourteen to fifteen
grains," and the penny "with the crowns seven grains."

It is difficult, if not impossible, to reconcile his opinions with the following
facts :

In 1473 the weight of the Irish groat was reduced to nearly thirty-two grains,
and in 1479 Germyn Lynch was empowered " to strike coyne at four shillings
and ten pence per ounce, according to the fineness and standard of the Tower of
London,"! which reduced the weight of the groat to thirty one grains.§

Sir James Ware represents these pieces in the proportion of three, two, and
one, while Simon speaks of them as "pieces," and "half-pieces." I have
weighed many of them, and in general they correspond with the weights, as stated
by Simon ; they also agree with the standard fixed in 1479,11 and are in the pro-

* View of the Coinage, p. 46. -I" Simon, p. 29.

X Simon, Appendix, No. XVII.

§ Simon evidently did not take a correct view of this coinage, for he understood the standard as
applying to the allay, and not to the weight, whereas the Act expressly provides for both, in the
words, " according to the fineness (allay) and standard (weight) of the Tower of London." He was
in error in calculating the weight of the pieces according to the Troy ounce.

II Those of the Fitzgerald type are usually somewhat lighter than the others.

e 2

36 Dr. Smith on the Irish Coins of Edward the Fourth.

portions of four, two, and one, or in other words, groats, half-groats, and
pennies.

The groat of this tjrpe rarely exceeds thirty, and never, I believe, thirty-two
grains, a circumstance which cannot be reconciled with the Act of 1483, by
which the penny was ordered to be made of the weight of twelve grains, or in
the proportion of 450 to the pound Tower. Groats are not mentioned in this
Act.

The coins without the Fitzgerald arms, were probably minted in the Castle
of Trim, during the administration of Henry Lord Grey, in 1478; and those
with the Fitzgerald arms were coined at the same place in the following years,
under the authority of Gerald Earl of Kildare. The half-groat of Dublin, fig.
87, was probably minted by Germyn Lynch, in 1479.

It now only remains to offer some explanation of the meaning of the device
of the three crowns, which has given rise to various conjectures.

Fynes Moryson, when enumerating the old coins which circulated in Ireland,
says, "Also they had silver groats, called Cross- Keale groats,* stamped with

• As the meaning of this word, in its application to the groats, has not, I believe, been hitherto
accounted for, I venture to offer an explanation of it. Reflecting on the subject, it occurred to me
that the term was applied by the native Irish to the coin in reference to some peculiarity in the
device, as several instances are well known in which coins obtained popular names, having a relation
to their type, e. g. Rial or Royal, Angel, Harpers, &c.

As soon as I had made this conjecture, I expected to find its explanation in the Irish language ;
and on asking an Irish scholar the meaning of Cross- Keale, (cpoc caol,) he without hesitation
informed me it was " slender cross." The fitness of this name will be evident, on contrasting the
cross on one of the three-crown groats with any of the coins of the English type, or those described
in the first and second sections.

About this time, my attention was directed to a paper published in volume xv. of the Trans-
actions of the Royal Irish Academy, by Mr. Hardiman, in which I found that the term " Cross-
Keale money" was used in Ireland so early as 1419, in the reign of Henry the Fifth : " 18 marks
Cross- Keale money, with a penny addition in every groat," being mentioned as part of the payment
of a mortage. — Hardiman, p. 50.

This circumstance at first appeared to set aside the reasonableness of my conjecture, but when
I compared several groats belonging to the Henrys, I found those of Calais, with the " cross-cross-
let" mint mark, were remarkable for the slender cross on the reverse, which served well to distin-
guish them from others as well as those of Edward the Third, which have a much broader cross,
and they are all found in abundance in Ireland. The accompanying outlines of the reverses of two

Dr. Smith on the Irish Coins of Edward the Fourth.

37>

the Pope's triple crown ; and these groats were either sent hither of old by the
Popes, or for the honour of them, had their stamp set upon them."*

Sir James Ware considered the three crowns "as denoting the three king-
doms of England, France, and Ireland," an opinion in which Simon concurred.

Neither of these opinions is correct ; and it is a very remarkable circum-
stance, that this device, the meaning of which the learned research of Sir James
Ware failed to discover, has, after the lapse of nearly four centuries since its
introduction on the coins, been proved to be the arras of Ireland.

This highly interesting discovery was made by the Rev. Mr. Butler, of Trim ;
and I am much indebted to that learned gentleman for the following summary
of the evidence which he has collected.

" Mr. Butler is of opinion, that the three crowns were the arms of Ireland,
from the time of Richard the Second to the time of Henry the Seventh, for the
following reasons.

" 1. Richard the Second granted to Robert de Vere, permission to bear as
his arms, so long as he should be Lord of Ireland, three crowns within a
bordure.f

groats of Henry, in my possession, present a good illustration of the difference between the crosses,
and tend to support my conjecture.

CALAIS.

LONDON.

* Moryson's Itinerary, Part i. Book iii. p. 284, folio : London, 1617. '

■)■ Among the minor correspondence in the Gentleman's Magazine for June, 1840, the following
note occurs :

" I take this opportunity of appropriating the arms on a pavement tile, engraved in the Gentle-
man's Magazine for October, 1818, which appears to have been found in Essex. The arms are
described as three crowns quartering mullets. They are the arms of Robert de Vere, Earl of
Oxford, who was the favourite of Richard II., and by him created Marquis of Dublin, and Duke of
Ireland, on which occasion the king gave him for his arms, ' Azure, three crowns or, within a border

38 Dr. Smith on the Irish Coins of Edward the Fourth.

" 2. At Henry the Fifth's funeral, on the first car were emblazoned the
ancient arms of England ; on the second, those of France and England, quar-
terly ; on the third, those of France ; and on the fourth, three crowns on a
field azure, which, although erroneously ascribed by Monstrelet, who gives this
description, to King Arthur, were more probably the arms of Henry's great
Lordship of Ireland.

" 3. The crown first appears, on the first distinct and separate coinage for
Ireland, issued according to an Act of parliament in 1460, declaring the inde-
pendence of Ireland, and enacting that it should have a proper coin, separate
from the coin of England.*

" 4. The three crowns appear on the Irish coins of Edward the Fourth,
Richard the Third, and Henry the Seventh ; they are unknown to the English
coinage ; and when Henry the Eighth assumed the harp as the arms of Ireland,
they appear no more.

" 5. On the only silver coins on which the three crowns occur, they appear,
as the harp does afterwards, on the reverse ; the obverse bearing the arms of
England ; and when the legend, dominvs hybernie is on the coin, it is on the
same side with the three crowns, as it is afterwards on the same side with the
harp.

" 6. That these crowns are borne, not in a shield, but ' upon a cross,' is no
objection to their being armorial bearings, as the harp was never borne on a
shield, except on some coins of Queen Elizabeth, who instead of one harp, bore
three in her coinage of 1561 ; as Edward the Fourth bore sometimes one, and
sometimes three crowns. But that the three crowns were sometimes enclosed
within a shield, is a fact which is incontestibly proved by a small copper coin,f
two specimens of which were found at Trim, and another had been previously
discovered at Claremont, near Dublin ; the latter is in the cabinet of the Dean
of St. Patrick's.

argent,' quartered with his own coat of De Vera, ' Quarterly/ gules and or, in ihejirst quarter a
mullet argent.' He died without issue 16th Richard II., and was the only member of his family
who bore this quartering of the three crowns. His arms are so remaining now, on the porch of the
church at Lavenham, in Suffolk."

* Simon, Appendix, No. V. f Plate I. fig. 21.

Dr. Smith on the Irish Coins of Edward the Fourth. 39

" T. In 1483, Thomas Galmole, Gentleman, Master and Worker of the
Money of Silver, and Keeper of the Exchanges in the cities of Devylyn (Dublin)
and Waterford, was bound by indenture to make two sorts of monies ; one called
a penny, with the king's arms on one side, upon a cross trefoyled on every end,
and with this inscription, eex anglie et francie ; and on the other side, the
arms 0/ Ireland, upon a cross, with this scripture, dns hibeenie.*

" Some device must, therefore, have been as fully established as the arms of
Ireland, as the fleur de lis and the lions were established as the king's arms.
What were these arms, if they were not the three crowns ?

" If we admit that the three crowns were the arms of Ireland, we have no
difficulty about this indenture, and this coinage. If we deny it, the frequent
appearance of the crowns on the Irish coins is still to be accounted for ; we have
to seek for the arms of Ireland, and to wonder at the total loss of all coins, in a
rich and singularly varied coinage, which bear the stamp of the national heraldic
bearings.

" The three crowns were relinquished as the arms of Ireland by Henry the
Eighth, probably because they were mistaken for the Papal arms ; and supported
the vulgar notion, that the Pope was the sovereign of Ireland, and the king of
England merely the lord under him. That such an opinion prevailed, appears
from a letter of the Lord Deputy and Council of Ireland to Henry the Eighth,
in 1540 : ' And we thinke that they that be of the Irisherie wolde more gladder
obey your Highnes by the name of King of this your lande, than by the name
of Lorde thereof ; having had heretofore a folisshe opinyon amonges them, that
the Bisshope of Rome should he King of the same, for extirpating whereof we
think it write under your Highness pardon, that by authority of Parliament, it
shulde be ordeyned that your Majisty, your heirs, and successors, shulde be
named Kings of this lande.' "f

• Ruding's Annals, vol. ii. p. 376, 2nd edit.

•j" State Papers, Ireland, No. cccxxxi. vol. iii. part iii. page 278.

Mr. Butler's original remarks on this interesting subject were first published in 1837, in the
Numismatic Journal, vol. ii. p. 70, and additional evidence was given by him in Mr. Lindsay's " View
of the Coinage, p. 46. His opinions appear to derive some support from Sir James Ware's account
of the three crowns, as denoting the three kingdoms of England, France, and Ireland ; for if we
take into consideration the devices on both sides of the coins, we find the arms of England and

40 Dr. Smith on the Irish Coins of Edward the Fourth.

Simon was of opinion, " that the first pieces with the three crowns were
struck in the reign of Henry the Sixth," during his brief restoration, in 1470.
But it is very questionable whether Henry caused any money to be made in Ire-
land during that brief Interval ; and when we consider the weight of the pieces
appropriated to him, and compare them with those of Edward, ordered to be
made in 1470, in which year the standard of the Irish groat was fixed at nearly
forty-one grains, it cannot be admitted that any money of the three-crown type,
the groats of which rarely exceed thirty, and never, I believe, thirty-two grains,
was coined previous to the year 1478 ; and from the Act of the latter year, it
may be inferred, that the liberties of Meath had been in abeyance during the
first eighteen years of Edward's reign, and that when they were restored, the
new type was Introduced, and that the privilege of striking money, granted to
Lord Grey, the Lord Deputy, was indicated by placing on the coins the arms of
the Lord of Ireland.

I have now concluded my remarks, which have extended to a far greater
length than I anticipated, when I entered on this investigation ; and I trust that
when the opinions I have advanced, and the evidence I have adduced, shall be
duly considered, it will be admitted that I have in some degree succeeded in
clearing up several of the obscurities in which the history of the coins of this
reign have been so long involved.

France quartered on the obverse ; and on the reverse, the arms of Ireland. Now it is probable Sir
James Ware knew Ireland had been represented by arms of some kind, but that he committed the
mistake of supposing that the device on the reverse alone represented three kingdoms instead of
one.

Dr. Smith on the Irish Coins of Edward the Fourth. 41

APPENDIX.

While these sheets were passing through the press, I received a communica-
tion from the Rev. Mr. Butler, expressing his desire to make known a conjecture
which he had made respecting some of the three-crown groats, and offering at the
same time to permit me to publish it as an Appendix to my paper, I gladly availed
myself of the kind offer, and I trust that the originality of the conjecture, and
the ability with which my learned friend has supported his views, will render it
acceptable to my readers.

"Trim, 1840.
" My dear Sir,

" In Mr. Lindsay's very valuable * View of the Coinage of Ireland,'

he notices some newly discovered varieties of the money, commonly called the

three-crown money, from its bearing on the reverse the ancient arms of Ireland.

" One of these varieties, he observes, bears the ' remarkable legend. Rex
Anglie Francie et Rex Hibemie, the latter title being hitherto supposed to have
been first adopted by Henry the Eighth.'

" Mr. Lindsay is of opinion that these coins, of which he engraves two
specimens, (Nos. 126, 127,)* belong to Edward IV., and I believe that this
appropriation of these coins has met with your concurrence. It is hazardous to
oppose the judgment of two such numismatists, nor should I attempt to do so in
a case which had been fully examined and decided ; but it is probable that it
did not occur, either to Mr. Lindsay or to you, to investigate the obscure claim
which I shall now endeavour to urge upon you.

" The case we have to consider is this : We have coins bearing the title of
Rex Hybemie. To what king are these coins to be assigned ? From their
pattern, their execution, and their weight, it is plain that they are of the time
from Edward the Fourth to Henry the Seventh, inclusive ; but the public title of
all the recognized kings in that period, was Dominus Hybemie, which title
appears upon the coins of Edward the Fourth, Richard the Third, and Henry

* See also PI. IV. fig. 77, of this Essay.
VOL. XIX. f

42 Dr. Smith on the Irish Coins 0/ Edward the Fourth.

the Seventh ; and it is not to be supposed that Edward the Fifth coined money
in Ireland with a new die, and a new title, who, if he coined any money,
used in England his father's dies.

" If, therefore, we attribute these coins to any of these kings, we must sup-
pose, either that one of them, at some uncertain time, for some reason, which we
cannot conjecture, assumed this regal title, and afterwards as capriciously relin-
quished it ; or that some Mint Master chose to give his sovereign a title which
did not belong to him, and to impress it on his coins ; a most improbable act in a
Royal Mint Master, and one which a counterfeiter would carefully avoid.

" But there was another king to whom none of these reasonings apply, who,
we have reason to think, coined money in Ireland, and who had a motive for as-
suming the title of King of Ireland ; and (in the absence of direct evidence) to
suppose that he did take that title, and coined money bearing it, is a less violent
supposition than either of those which I have considered.

" In 1486, Lambert Simnel was received in Dublin with open arms by the
Geraldines and the other Irish lords, as the representative of the House of
York, which was always popular in Ireland, and ' as the son and lawful inheritor
of the good Duke of Clarence, their countryman and protector during his life,'*
and was proclaimed king, by the title of Edward the Sixth. Early in May,
1487, he was crowned in Christ Church, and 'the Parliament, Courts of Jus-
tice, Processes, Statutes, and Acts of the Council, came all out in his name.'f

" At that time there was a mint in Dublin, J and from the various patterns of

* Campion's History of Ireland, p. 103, Dub. 1633.

•j- Ware's Annals of Ireland, pp. 4 — 6, folio, 1705.

J If Thomas Galmole, alias Thomas Archibold, was Master and Worker of the Money of Silver,
in Dublin, in the reigns of Richard the Third and Henry the Seventh, {and it is probable that he
was so, for we find him so styled in 1483, (Ruding, vol. ii. p. 376,) and again, in 1506, (Rot. Can.
Hib.) it is likely that some of the coins usually given to Henry the Seventh do not belong to the Royal
Mint. The artist who could design and execute the Dominus Groat of Richard the Third, could
not have perpetrated such barbarisms of spelling as Sivitas and Duxlin, or the barbarities of execution
which disgraced these coins. If they belong to this reign they are probably some of the counterfeit
money against which Henry the Seventh issued a proclamation in 1492, (Ware.) I may observe, that
although more hastily executed, the Rex Groats, in the letters and whole style, appear to my not
much-practised eye strongly to resemble the Dominus Groats of Richard the Third. Were they
both the workmanship of Thomas Galmole ?

Dr. Smith on the Irish Coins 0/ Edward the Fourth. 43

Henry the Seventh's money, which are still extant, and from the fact that In 1483,
'the profits of the mint' were ' granted to the Earl of Klldare, in consideration
of the charges he is at in the government, during the time he continues in
it.'* It is to be inferred that there was, at that time, almost a constant coinage
in Dublin, and if any money was coined in Dublin in the latter part of 1486,
or in the beginning of 1487, it was Lambert Simnel's money, and bore his titles.

" It is extremely probable that he did coin money, for from his arrival in Ire-
land, he had at his command all the usual resources of the Irish Mint, and after
the landing of the Earl of Lincoln, if from the first he was not supplied with
money from Flanders, it was an obvious and easy method of multiplying his
Flemish Groats, to melt them down and debase them to the Irish standard ; a
method not strange to the Irish Mint Master ; and although Martin Swartz and
his Almaines, would probably require to be paid in the pure grosses of Charles
the Bold, some of which are still picked up in this country, and in the north of
England, his Irish followers would be satisfied with money of the alloy, to which
they were accustomed.

" Now, as it appears from the joy manifested by the Irish, at the passing of
the Act proclaiming Henry the Eighth King of Ireland,! from the jibe of
Henry the Seventh to the Irish lords at Greenwich, 'that if he did not come
over soon they would crown apes,' and from other notices, that the Irish of that
day were animated by an instinctive love of royalty, is it not probable that, too
wise not to know the power of names and titles, the crafty counsellors of this
mock king, the only English king ever crowned in Ireland, would not neglect
to flatter the vanity of the Irish, on whose enthusiasm in his behalf they chiefly
depended, by the cheap expedient of giving on Simnel's money, which was to
circulate amongst them, in addition to his other imperial titles, the title of King
of Ireland, thereby gratifying the national pride by nominally restoring Ireland
to its ancient dignity as a kingdom, and obliterating a mark of vassalage, and
of foreign domination.

" It is then probable that Lambert Simnel coined money in Dublin, and that
on it he bore the title of King of Ireland, and it is not probable that that title

* Simon, Appendix, No. XVIII.

t State Papers, Ireland, vol. iii. part. iii. No, CCCXL. p. 304.

. /2

44 Dr. Smith on the Irish Coins of Edward the Fourth.

was borne by any other king to whom we can assign these groats ; we shall there-
fore be justified in attributing them to Lambert Simnel, until some reason
is shown to the contrary.

" It is true that the claim here put forward rests entirely upon conjecture, and
that you and Mr. Lindsay, and other fully informed and experienced numisma-
tists, may be aware of facts, which render it untenable ; but the only evidence*
which I know of at all inconsistent with it, is the legend of a half groat in the
cabinet of the Rev. Mr. Martin, given by Mr. Lindsay in his Coins of Henry the
Seventh, which reads, henric di gear hibernie ; but what inference can be
drawn from so obscure a legend on a coin so blundered, that on the reverse it
has civiTAs DuxBLiN. Your beautiful engraving, which you were kind enough
to send me, of one of these groats, from the private collection of the Dean of
St. Patrick's, so truly called by Mr. Lindsay a public benefit, which has a legend
hitherto unknown, and reads, edwardvs on the obverse, and on the reverse,
ET REX HYBERNiE, (PI. IV. fig. 75,) Strengthens my position, that these coins
were struck by the mock Edward the Sixth.

" Apologizing to you for the length of this letter, which has much exceeded
my expectations,

" I am, my dear Sir,

" Yours most sincerely,

" R. Butler.
" Dr. A. Smith"

TABLE OF THE WEIGHT OF THE GROAT AT DIFFERENT PERIODS DURING THIS

REIGN.

1461 to 1465, the groat weighed 45 grains.
1465 „ 1467, „ 36 ? „
1467 „ 1470, „ ■ 22^ „
1470 „ 1473, „ 401^ „
1473 „ 1479, „ 32| „
1479 „ 1483, „ 31 „

* It is probable that decisive evidence on this subject is to be found in the unpublished Acts of
Poynyng's Parliament.

Dr. Smith on the Irish Coins of Edward the Fourth.

45

NAMES OF CITIES AND TOWNS WHICH APPEAR ON THE lEISH COINS OF EDWARD

THE FOURTH.

CORK. CIVITAS CORCAGIE.

DROGHEDA. VILLA DE DROGHE.

DROGHEDA.

CIVITAS DVBLIN.

.... DVBLINI.

.... DVBLINIE.

.... LIMIRICI.

VILLA DE TRIM.
WATERFORD. CIVITAS WATFORD.

.... WATERFORD. PI. III. fig. 63.
WEXFORD. VILLA WEISFOR. PI. IV. fig. 74.

DVBLIN.

LIMERICK
TRIM.

PI.

II. fig. 38.

„ 44.

29.

PL

I. fig. 17.

8.

1.

PI.

III. fig. 55.

„ 60.

PI.

IV. fig. 72.

TABLE SHEWING THE NUMBER AND DENOMINATIONS OF THE COINS ENGRAVED.

PLATE.

DOUBLE GROATS.

GROATS.

HALP-GROATS.

PENNIES.

COPPER AND BRASS.

TOTAL.

1

1

9

• •

7

7

24

. 2

1

11

3

8

, ,

23

3

, ,

15

4

3

, ,

22

4

••

12

6

5

1

24

2

47

13

23

8

93

^^

46^

Dr. Smith on the Irish Coins of Edward the Fourth.

EXPLANATION OF THE PLATES.

The numbers marked with an asterisk (*) have not been engraved before ; several of them are only
varieties of coins which have been published in other work^.

Plate I.

NO.

DENOMINATION.

MINT.

DATE.

WEIGHT.

PAGE.

REFERENCE.

1

Groat.

Dublin.

1461

44Jgrs.

5

D". of St. Patrick's.

2

Penny.

55

55

9

7

55

*3

Groat.

55

55

44

6

55

*4

Penny.

55

55

12

7

55

*5

Groat.

55

1462

44i

6

55

*6

Penny.

55

35

11

7

55

7

Groat.

55

59

424

6

55

*8

Penny.

55

?

10

7

55

*9

Groat.

55

?

28

6

55

10

Farthing, copper.

?

55

9

9

|Lieut.-Col. Weld
I Hartstonge.

*11

»5 5>

p

55

9

55

D". of St. Patrick's.

*12

Half-farthing, „

?

55

11

55

95

13

jj »>

P

55

9

99

Rev. Mr. Butler.

*14

5> 55

?

J5

7

99

99

*15

» 55

?

55

6

10

D».of St. Patrick's.

16

Groat.

Dublin. .

1463

38

11

,,

17

Penny.

55

55

H

95

55

*18

Groat.

55

55

38

95

55

19

Penny.

Waterford.

55

(Broken.)

95

Mr. Lindsay.

*20

Groat.

55

55

40

91

D". of St, Patrick's.

21

Farthing ?

DubHn.

?

9

14

Rev. Mr. Butler.

22

Groat.

5>

1465

27

12

D». of St. Patrick's.

23

Penny.

55

55

H

55

55

*24

Double Groat.

Drogheda.

1467

38

17

Rev. Mr. Butler.

Trans. KIA. VOL, TXT..

.^itlTIQUITma PLATE 1.

l^A,/^ ;^.p ,'V/'

m

Trans. iL£/f . VOL. XK.

jysrnQDTTiES plate e.

Dr. Smith on the Irish Coins of Edward the Fourth.

47

Plate II.

NO.

DENOMINATION.

MINT.

DATE.

WEIGHT.

PAGE. REFERENCE.

25

Double Groat.

Dublin.

1467

44 grs.

17

D". of St. Patrick's.

*26

Half-groat.

99

99

10

99

Rev. Mr. Butler.

27

Groat.

Trim.

99

231

99

(Lieut.-Col. Weld
l Hartstonge.

*28

Half-groat.

35

99

Hi

99

D". of St. Patrick's.

♦29

Groat.

Dfogheda.

1470

29

19

99

*30

j>

95

99

27

99

99

31

j>

Dublin.

59

32

95

99

*32

Penny.

>9

59

6

55

95

*33

Groat.

99

99

26

59

55

•34

Penny.

99

99

6

59

J»

*35

>>

99

?

9

20

95

*36

»>

99

?

6

99

99

*37

35

99

?

H

95

59

*38

Groat.

Cork.

1470-2

38

22

99

*39

99

99

99

30

55

99

*40

>9

Drogheda.

99

33

5>

>9

*41

99

99

99

34

J»

>>

*42

99

99

1473-8

321

23

39

*43

99

99

55

33

55

55

*44

Half-groat.

99

99

15

55

99

*45

Penny.

99

99

8

55

Mr. Lindsay.

*46

99

99

99

6

59

D".of St. Patrick's.

47

99

99

99

7

99

99

48

Dr. Smith on the Irish Coins of Edward the Fourth.

Plate III.

NO.

DENOMINATION.

MINT.

DATE.

WEIGHT.

PAGE.

REFERENCE.

•48

Groat.

Dublin.

1470-2

45igrs.

23

Mr. Lindsay.

*49

j>

»5

1473-8

32

24

D". of St. Patrick's.

*50

j»

55

55

32

33

51

Half-groat.

35

55

17

55

*52

5J

»

55

17

Mr. Sainthill.

•53

Penny.

55

55

7i

D», of St. Patrick's.

54

5?

55

55

6

Mr. Lindsay.

•55

Groat.

Limerick.

1473-6

3H

D". of St. Patrick's.

•56

)5

55

35

31

55

•57

5)

55

55

31

55

•58

Half-groat.

55

35

17

55

59

Penny.

55

55

9*

25

Mr. Lindsay.

•60

Groat.

Trim.

1470-2

28

D". of St. Patrick's.

•61

5>

55

8 5

34

55

•62

Half-groat.

55

55

23

Rev. Mr. Butler.

63

Groat.

Waterford.

55

43

Mr. Sainthill.

64

5>

55

55

28

D'-.of St. Patrick's.

•65

5?

55

55

31

33

66

>»

55

55

31

55

•67

55

55

55

30i

35

*68

)5

55

1473-8

33

35

•69

55

55

55

32

55

Tranj. RXA. VDL.3IX.

■ANTIQnmES PLAIE 3

J. i'rrut/iMIJ.Drl*

^JCj An^od Sc

^^

,!»''*;'?;

t^^-3

'v^l

•*^ »

-^^

/yansRU. VOL. 3JX.

ANTIQUrriES PLATE 4

J.Sm,&Vl>M'

J.SriewoadJ^

Dr. Smith on the Irish Coins of Edward the Fourth.

49

Plate IV.

NO.

DENOMINATION.

MINT.

DATE.

WEIGHT.

PAGE

REFERENCE.

*70

Penny.

Waterford.

1473-8

10 grs.

26

D". of St. Patrick's.

*71

5»

»j

5J

H

?J

55

72

5»

5»

J>

8

9)

Mr. Sainthill.

73

5)

»)

J9

8

3J

5)

•74

Groat.

Wexford.

?)

26

55

Rev. Mr. Butler.

*75

35

Trim. ?

1478

23i

32

D".ofSt. Patrick's.

76

>>

»

59

29

99

Mr. Lindsay.

77

55

j>

99

27

99

D".ofSt. Patrick's.

*78

"

95

95

30

59

55

79

J>

55

55

28

34

Mr. Lindsay.

*80

3J

59

59

30

32

D".of St. Patrick's.

*81

5>

95

95

30

34

Mr. Lindsay.

*82

>)

55

1479

26

33

D". of St. Patrick's.

*83

))

55

99

26

95

99

*84

»>

55

99

28

59

19

*85

))

55

99

29

99

9}

86

Farthing. ? Brass.

?

?

3i

27

99

*87

Half-groat.

Dublin.

1478-9

11

32

99

*88

5>

Trim.?

99

13

99

99

*89

3J

55

99

12

99

>9

*90

5)

5>

99

13i

95

99

*91

5>

>>

59

14^

55

Rev. Mr. Butler.

*92

)»

59

99

11

34

Dn.ofSt. Patrick's.

*93

Penny.

59

99

5

32

55

VOL. XIX.

S

50

11. — On the Irish Coins of Henry the Seventh. By Aquilla Smith, M.D.,

M.R.LA.

Read 14th June, 1841.

INTRODUCTION.
As the coins which I am about to describe, belong to some of the Henrys, it
appears to me that the best course which can be adopted, is, in the first place to
inquire, whether any of them can be assigned to the predecessors of Henry the
Seventh, who bore the same name ; for by proceeding in this manner, the period,
to which the coins can be appropriated, will be reduced to the smallest possible
limit, and the inquiries which follow in the subsequent pages will be greatly
facilitated.

Simon has pointed out the mistake committed by Bishop Nicholson, who
says that " Henry the Fourth, in the year 1404, ordered the noble of his five
immediate predecessors to pass in Ireland for ten shillings ; and, from that time,
all sorts of coin went at a higher value here than in England."*

The words referred to by the learned Prelate, who quoted from Sir John
Davis's Reports, are these, " Mes le primer difference et inequalitie enter les
standards del English moneys et Irish moneys est trove en 5 Edw. 4. Car
donques fuit declare en parliament icy, que le noble fait en temps Edw. 3. R. 2.
Hen. 4. Hen. 5. et Hen. 6. serroit de cest temps en avant currant en cest realm
pur 10s. et issint le demy noble, et touts auters coines solonque mesme le rate.
Vide Rot. Parliament, 5 Edw. 4. cap. 40. et 11 Edw. 4. cap. 6. et 15 Edw. 4.
cap. 5. in le office del RoUes in Castro Dublin."f

The error of Bishop Nicholson in writing Henry IV., instead of Edward IV.,
is so palpable from his reference to Davis, that it would not require any notice

* Irish Historical Library, 8vo. 1724, p. 162. f Davis's Reports, fol. 1674, p. 22.

Dr. Smith on the Irish Coins of Henry the Seventh. 51

here, had not Simon remarked, that "this last Act (15 Edw. IV.) seems to hint,
that some kind of money was coined here In this reign, (Henry IV.,) as well as
in that of Henry V."* He also conjectures that the great scarcity of money in
England seems to have been a reason for coining the more money in Ireland,
and therefore believes that the groats, figs. 56, 57, 58, 59, 60 in his 3rd Plate,
belong to Henry the Fifth.

The Act of 1475, from which Simon drew his Inference, ordains " that the
coin called the gross, made in the reigns of Edward the Third, &c., not clipped,
shall be of the value of six denlers. The gross made in England in the time of
the present king, not clipped, shall pass for five denlers, and all the moneys struck
in Ireland to be of the same value as they now are^-f

The latter part of this extract Is the only passage in the Act which could
give any support to his opinion ; but it appears to me to have reference only to
the numerous coins of various types, " struck in Ireland" in the first fifteen
years of Edward's reign, during which period his Irish money was considerably
less in value than his English.J

In 1421, the ninth year of Henry the Fifth, in a parliament held at Dublin,
before James Earl of Ormond, the Lords and Commons agreed to send a peti-
tion to the king, praying for the redress of several grievances. The petition
contains nineteen articles, the third of which prays, " that certain money be
struck in Dublin as in England, and that the necessary officers, moneyers, &c.,
be appolnted."§

From this evidence it is probable, that no legal money was coined in Ireland
for some time previous to the date of the petition, and it leaves no grounds what-
ever for Simon's appropriation of any Irish coins to Henry the Fifth, who died

* Essay on Irish Coins, p. 19. f Simon, Appendix, No. XIV.

J I am indebted to my learned friend, the Rev. Richard Butler, of Trim, for directing my atten-
tion to several important records of the reigns of Henry the Fifth and Sixth, which have hitherto
been unknown to writers on Irish coins, and which may be found in the " Rotulorum Patentium et
Clausorum Cancellariae Hibernise Calendarium," vol. i. pars I.

§ " Art. 3. Petunt quod certe monete cudantur in Dublinia sicut in Anglia, cum omnibus
officiariis, monetariis, &c., necessariis." — Rot. Pat. 9, Hen. V. cap. 111.

In the extracts from the Calendar, the words in full have been substituted for the contractions,
which it would be useless and inconvenient to retain.

g2

52 Dr. Smith on the Irish Coins of Henry the Seventh.

in 1422 ; but this subject may be more conveniently discussed hereafter, when
I shall endeavour to support Mr. Lindsay's appropriation of the coins in question,
to Henry the Seventh.

A writ, directed to the Sheriff of Dublin, in the first year of the reign
of Henry the Sixth, recites, " that the king had learned that many merchants
brought into Ireland large sums of counterfeit, washed, and clipped gold, and
that they carried away the king's silver money."* And a roll of the same year,
after reciting, " that Henry the Fifth had been informed, that there were coun-
terfeiters of gold and silver, and washers, clippers, and weighers of the same in
Ireland, and that he had caused proclamation to be made against such practices,
under the penalty of loss of life and limbs, and that no person should presume to
weigh or refuse gold (except such as was counterfeit or washed) ; appoints Janico
Dartas, Nicholas Daly, and Richard Talloun, jointly and separately, to inquire
after those who presumed to weigh the king's gold, and also of those who dared
to carry clipped, washed, or counterfeit gold from England into Ireland, for the
purpose of accumulating the king's silver money, and further gives the aforesaid
officers power to arrest such offenders, together with their money, and commit
them to prison." f

* " Breve vicecomiti Dublinie directum, in quo recitatur regem, ex gravi querela ligeorum
Hibernie, accepisse quod quamplures mercatores ad Hibernian) venientes hue portant secum, causa
vendendi et emendi, maximas summas auri Regis controfecti, loti, et tonsi, ad dictum populum de-
cipiendum, et pecunias Regis argenteas bine, ad opus suum, subdole extorquendum de die in die non
desistunt." — Rot. Claus, 1 Hen. VI. cap. 40.

f " Rex (recitatur qualiter H. V., cum, ex gravi el clamosa inslnuacione dominorum spiritu-
alium et temporalium ac communium Hibernie in parliamento existentium, accepisset quod
nonnuUe persone extiterint controfectores cune monete auri et argenti, ac lotores, tonsores, et pon-
deratores ejusdem monete infra Hiberniara, per brevia sua fecerit proclamari quod ne quis, sub
pena vite et membrorum, foret controfector, lotor, tonsor, vel ponderator dicte monete, et quod ne quis
aurum in recepcionibus, &c., (auroloto et controfecto excepto) ponderare seu denegare presumeret,)
assignavit Janico Dartas armigerum, Nicholaum Daly, et Ricardum Talloun, conjunctim et divisim,
ad inquirendum de eis qui cum belanciis aurum Regis in vendicionibus &c., ponderare presumpse-
rint, ac de illis qui aurum Regis tonsum, [aut lotum,] seu controfectum, extra Angliam in Hiber-
niam cariare presumpserint, ad monetam Regis argenti pro hujusmodi auro, vel alio modo accumu-
landum ; et culpabiles, una cum mone [ta] Regis argenti sic accumulata, in quotumcumque manibus
existat, capiendum, et ipsos prisone committendum. Dub, 10 Julii." — Rot. Pat. 1 Hen. VI. Durso,
cup. 109, b.

Dr. Smith on the Irish Coins of Henry the Seventh. 53

In the second year of this king, in a great council, held on the morrow of AH
Souls, before Edward Bishop of Meath, deputy of Edmund Earl of March, it was
ordained, that the noble, half, and quarter noble (except counterfeit gold) should
be universally received by weight, and that a standard weight should be depo-
sited in the Irish Exchequer, and that all the sheriffs, mayors, &c., throughout
the land, should have weights agreeing with the said standard, and that every
liege subject should have access to the standard weight as often as he pleased,
and that no person should refuse gold contrary to the aforesaid ordinance, under
a penalty of ten shiUings, to be paid to the king, and that any offender might be
committed to gaol, and kept there until he made redemption and fine."*

It does not appear that the petition for the establishment of a mint in Dublin,
in the ninth year of Henry the Fifth, was granted before the third year of Henry
the Sixth, for on the 6th of February in that year, a grant of the office of
master of the coinage in the Castle of Dublin, was made to John Cobbham,
during the king's pleasure, provided that the money be made of the same weight,
allay, and assay, as the silver money which is made in London, and that the said
John may receive for the making of one lb. of money, to be made in the aforesaid
Castle, only as much, and that he shall pay to the king as much, as the master of
the coinage in London receives and pays for one lb. of the same sort, and he shall

* " In magno consilio, coram Edwardo episcopo Midie, deputato Edmundi comitis Marchie
locum tenentis, in Crastino Animarum tento, ordinatum est, ad supplieacionem communium ad dic-
tum consilium per brevia Regis electorum, quod nobilis, obelus, et quadrans auri (auro controfecto
excepto) secundum pondus et valorem per ligeos ac alias gentes ad Hiberniam confluentes recipi-
antur per pondus universaliter : et quod unum standardum ponderis dicti auri standardo Anglie
concordans sit, et in thesauro in custodia thesaurarii et camerariorum saccarii Hibernie, de cetero
remaneret: et quod quilibet vicecomes, major, ballivus, senescallus, superior, et propositus, pertotam
terram, ad eorum prosecucionem habeant pondera dicto standardo recte concordancia : et insuper,
quod quilibet ligeus terre predicte habeat cursum ad dicta standarda in quolibet loco ubi assistunt,
ad pondera standardi quociens sibi placuerit faciendum : et eciam, quod ligei, et indigene, et ali-
enigene ad Hiberniam confluentes hujusmodi aurum, licet tonsum seu lotum, per pondus, secundum
valorem et pondus ejusdem percipiant in futuro : et quod nullus hujusmodi aurum contra ordina-
cionem predictam refutet sul) pena 10' ad opus Regis solvendum : et quod corpus ejusdem delin-
quentis gaole committatur in ea moraturura quousque redempcionem et finem inde faciat &.c." —
Rot. Claits. 2 Hen. VI. prima pars. cap. 27. '

64 Dr. Smith on the Irish Coins of Henry the Seventh.

be bound by indenture to perform the premises, in the same manner and form as
the master in London is bound.*

In the third and fourth years of Henry, a grant of one hundred shillings a
year, during the king's pleasure, was made to William Goldesmyth, the striker
of the money in the Castle of Dublin.f

At a parliament held at Trim, in 1447, an Act was passed against clipping
and counterfeiting the king's coin, and it was ordained " that no money so
clipped be received in any place of said land, from the first day of May next to
come, nor the money called the O'Reyly's money, or any other unlawful money,
so that one coyner be ready at the said day to make the coyn."t

In 1456, a parliament was held at Naas, and it was enacted, at the request of
the Commons, that " whereas no mean could be found to keep the king's coin
within the land of Ireland," all foreign merchants " shall pay for every pound
of silver that they shall carry out of Ireland, forty-pence of custom to the king's
customer, to the use of the king ; and if any man shall do the contrary in con-
cealing of the said custom, he shall pay for every penny, twenty shillings to the
said customers, to the king's use,"§ and from the twelfth chapter of the same Act
it appears that Ireland was greatly impoverished by the daily exportation of silver,
and the great clipping of the coin, and that " the Irish money, called the O'Rey-
ley's," daily increased ; it was therefore enacted, that any person carrying silver
out of Ireland shall pay for custom to the king twelve-pence for every ounce ;
"except lords and messengers going to England upon business of the public, who
may carry plate with them, according to their degrees."||

* " Rex concessit Johanni Cobbham officium magistfi cunagii in castro Dublinie faciendi,
durante beneplacito, proviso quod moneta operata sit ejusdem ponderis, allaie, et assaie, sicut mo-
neta argenti que in Londonio operata est, et quod dictus Johannes tantum pro factura 1 libre monete
in castro predicto operate percipiat, et Regi tantutn reddat, quantum magister monete in terra pre-
dicta pro hujusmodi libra percipit et reddit, et quod idem Johannes ad premissa facienda per in-
denturam obligetur, eisdem modo et forma quibus magister cunagii in terra predicta pro tempore
obligatus existit. Trym, 6 Feb."— i?o<. Pat. 3 Hen. VI. cap. 21.

•J- " Rex eisdem mandat quod Willelmo Goldesmy[th ?], percussori monete in castro Dub-
linie, 100» per annum ei per Regem concessos durante beneplacito annuatim solvant. [ ] Julii,
anni predicti." — Rot. Claus. 3 & 4 Hen. VI. cap. 35.

J Simon, Appendix, No. III. § Ruding, 2nd edit. vol. ii. p. 341.

II Simon, Appendix, No. IV.

Dr. Smith on the Irish Coins of Henry the Seventh. 55

The next and last Act of this reign relating to the coinage contains much
that is important.

At a parliament held at Drogheda, in the year 1460, It was enacted, that the
value of English gold coins should be raised one-fourth in Ireland, and that the gross
of London, York, and Calais, not clipped within the extreme circle, should pass
for five-pence in Ireland, and the smaller pieces in the same proportion. " And
as not only the Dutchy of Normandy, but also the Dutchy of Guienne, when
they were under the obedience of the realm of England, yet were no less
separate from the laws and Statutes of England, and had also coynes for
themselves different from the coyne of England ; so Ireland, though it be under
the obedience of the same realm, is nevertheless separate from it, and from all
the laws and Statutes of it, only such as are there by the lords spiritual and tem-
poral freely admitted and accepted of in parliament or great council, by which a
proper coyne separate from the coyne of England, was with more convenience
agreed to be had in Ireland under two forms ; the one of the weight of half a
quarter of an ounce troy weight, on which shall be imprinted on one side a lyon,
and on the other side a crown, called an Irelandes d' argent, to pass for the value of
one penny sterling ; the other of vii. ob. of troy weight, having imprinted on one
part of it a crown, and on the other part a cross, called a Patrick, of which eight
shall pass for one denier. That a gross be made of the weight of three deniers
sterling, and to pass for four deniers sterling, which shall have imprinted on it
on one side a crown, and on the other side a cross like the coyne of Calais, bear-
ing about the cross in writing, the name of the place where the coin is made ; and
that every person, who brings bullion to the mint, ought to receive and have for
every ounce of silver, troy weight, nine of the said grosses of the value of three
deniers. That the coyne called the Jack,* be hereafter of no value and void, and
that the above coynes be made in the Castles of Dublin and Trymme ;" and at an
adjourned sitting of the same parliament It was enacted, " that the denier with
the cross called Irelandes be utterly void, and that in lieu of it a penny be

* Having lately seen some copper pieces of Jacohus the Second of Scotland, which were found
in Ireland, it occurred to me that the " Jacks " mentioned in the Act, might be these coins of James,
who was contemporary with Henry the Sixth.

Since this note was written I find that the same term was applied to the brass shillings of James
the Second. See " The Jacks put to their trumps," p. 123, in the Historical Songs of Ireland,
printed for the Percy Society, 1841.

56 Dr. Smith on the Irish Coins of Henry ike Seventh.

struck in silver, having the weight of the fourth part of the new gross of Ireland,
to be imprinted and inscribed as the new gross."*

From the grant to Cobbham, in the year 1425, which provides that the money
to be made in Dublin shall be of the same weight, allay, and assay, as the silver
money made in London, and the appointment in the following year of a moneyer,
with an annual salary of one hundred shillings, it is more than probable that some
money was coined in Dublin about that time.

I know of only one coin which I can venture to assign to Henry the Sixth,
during the early part of his reign. It has on the obverse, the king's head with
an open crown fleury, within a circle of pellets, a star of six rays at the left side
of the neck, mint mark a cross, legend henricvs dns hibnie, an annulet at the
end of the legend ; reverse, a plain cross with three pellets in each quarter, legend
civiTAs DVBLiNiE ; there is an annulet after civi. It weighs twelve grains and a
quarter.

This interesting coin, which is of the highest rarity, and in fine preservation,
is in the cabinet of the Rev. J. W. Martin, of Keston, to whom I am indebted
for the loan of it and several other Irish coins of great rarity.

That this coin, which on account of the absence of the tressure on the ob-
verse, I believe to be a penny, was struck in the early part of the reign of Henry
the Sixth, is very probable ; evidence is now, for the first time, adduced, which
proves that in 1425 Irish money was ordered to be made of the same standard
as the English money, and the weight of this piece, which is equal to many of the
English pennies of Henry the Sixth, and considerably more than the fourth part
of any of the Irish groats of Henry the Seventh, which Ibelieve never exceed thirty-
two grains, and rarely weigh so much, shows clearly that it must have been
coined during the reign of Henry the Sixth. The mint mark is similar to that
which occurs on some of the English coins usually assigned to Henry, the annulets
also, and the star, are marks which connect it with the same reign. The

• Simon, Appendix, No. V.

Da. Smith on the Irish Coins of Henry the Seventh. 57

occurrence of the Roman n in three places in the legends of this coin, is very
remarkable, I have not seen any other Irish coin from the time of Edward the
Third, to that of Henry the Eighth, which has the Roman n in its legend, ex-
cept a Dublin groat of the third year of Edward the Fourth.*

It is very doubtful, whether any money was coined under the authority of
the Act of ] 447, in which the provision for a new coinage depended on the
coiner being ready against a certain day; and the great scarcity of silver, together
with the daily increase of " the Irish money, called the O'Reyley's," mentioned
in the Act of 1 4.57, could scarcely have happened, had any legal money been
coined in the meantime.

The Act of 1460 appears to warrant the inference, that if any money was
coined in Ireland previous to that time, it must have been similar in type and
standard to the penny already described ; for by the same Act, " a proper coyne
separate from the coin of England, was with more convenience agreed to be had
in Ireland."

The type and weight of the coins ordered to be made in 1460, are so fully
described in the Act, that it would appear there could be little difficulty, in de-
termining which coins should be assigned to this date.

The penny called the " Irelandes d'argent," has not hitherto been dis-
covered. The Act which ordered it to be made, came into operation on the
17th of March, and on the Monday after Trinity Sunday (8th June), the penny
called " Irelandes" was declared to " be utterly void."

A few copper coins, of the type ascribed in the Act to the half-farthings called
" Patricks," have been found, but most of them exceed, by several grains, the
weight fixed by the Act. There is onef which I am inclined to appropriate to
Henry the Sixth, because it weighs only six grains, and the form of the cross
on the reverse is different from that on the heavier coins, which 1 believe were
minted early in the reign of Edward the Fourth.

The type of the groat as described in this Act, agrees so far with some of
the coins of Edward the Fourth, that it is still doubtful which of them are to be
considered as belonging to Henry.

Taking for granted that the groat published by Simon (PL III. fig. 61) is

* See Irish Coins of Edw. IV. PI. I. fig. 18, Trans. R. I. Academy, vol. xix.
flbid. PI. I. fig. 15.

VOL. XIX. h

58 Dr. Smith on the Irish Coins of Henry the Seventh.

accurately represented, as having a tressure of twelve arches round the crown,
which is very shallow, and a trefoil at each point of the tressure, I assign it to
Henry the Sixth. It is much to be regretted that this coin cannot now be found
in the numerous and extensive collections to which I have had access ; but that
such a piece was in Simon's possession can hardly be doubted, as the penny sub-
sequently published by Snelling in his supplement (PI. I. fig. 16) agrees with it
in the number of arches in the tressure, and in the form of the crown, and such a
coincidence can hardly be attributed to a mistake of the artist ; this penny I also
appropriate to Henry the Sixth.

I am aware that a distinguished collector in England does not believe that a
groat with twelve arches in the tressure ever was in existence, on the grounds
that no such piece is at present known ; but a short time since, the same argu-
ment might have been applied to a coin of James the Second,* as no specimen
of it was then known ; two however have been lately discovered ; one in pewter,
which was found in a sewer in Dublin, is in the cabinet of the late Dean of St.
Patrick's, and another in brass, in a good state of preservation, is in the possession
of the author.

I shall now proceed to the investigation of the coins, which I conceive be-
long to Henry the Seventh, a task which I enter on with much diffidence, as it
presents difficulties at almost every step of the inquiry.

There are many coins which may, without any doubt, be appropriated to
Henry the Seventh, although very few documents relating to his Irish coins have
been discovered, nor is it likely that any others have been preserved, from which
direct evidence can be obtained.

The almost total absence of records connected with the coinage of this reign,
is the more remarkable, as the greater part of the numerous Acts, relating to
money coined during the reigns of Henry's immediate predecessors, Edward the
Fourth, and Richard the Third, are still preserved among the State Papers in
Ireland.

Ruding, on the authority of Snelling, states, that in the first year of Henry
the Seventh " Robert Bowley" was " Malster of the Cunage and Mynt within
the Cities of Dyvelln (Dublin) and Waterford."t

• Simon, PI. VIII. fig. 177. f Annals, vol. i. p. 90.

Dr. Smith on the Irish Coins of Henry the Seventh. 59

On the 9th of March, 1491, Nicholas Flint* was by the king's appointment
" made overseer of the mints of Dublin and Waterford ;" and on the 15th of
April following, a proclamation was issued by the king at Greenwich, authorizing
Gerald Earl of Kildare "to cause and prescribe certain laws for the prevention
of false or mixt silver in coin within that his Lordship of Ireland."f

The English Act of his nineteenth year, 1504, states that " The coins, es-
pecially of silver, were so impaired as well by clipping as counterfeiting the same,
and by bringing into the realm the coin of Ireland, that great rumour and va-
riance daily increased among his subjects, for taking and refusing the same;" and
in the same year it was enacted, that no person should bring into England " of
the coin of Ireland, above the sum of three shillings and four pence, on pain of
forfeiture and imprisonment, and fine and ransom, at the king's pleasure."!

In 1506, the king granted to Thomas Galmole, alias Archibold, of Dublin,
Goldsmith, the office of Master of the Coinage and Monies, made within the
Castle of Dublin, and to hold the said office himself, or by his deputy, durino- the
king's pleasure. §

These scanty records and the coins themselves, are the only sources from
which evidence can be derived respecting the numerous coins of Henry which
have been preserved ; and before I enter on the description of them it will be
convenient to inquii-e, whether it be possible to determine the standard by which
the coinage was regulated. The want of any direct evidence on this subject
compels me to revert to such facts as may be collected from the history of the
preceding reigns.

* This person held several offices connected with the English mint, in the early part of this reign
1485 — 1487, he was, " Cont'. Monete et Cunagii infra Turrim Lond." " Assaiator Monete et
Cunagii" — " Sculptor de et pro ferris," " Campsor Monete et Cunagii infra Tur. London" — and on

the 17th of May, 1486, he was appointed Keeper of the King's Exchange Ruding, vol. i. pp. 98,

106, 119, 161, and vol. iv. p. 194.

t Ware's Annals of Ireland, A.D. 1491. % Ruding, vol. ii. pp. 397 and 399.

§" 18. Rex concessit Thomae Galmole de Dublinia, goldsmyth, alias Thomae Archibold, magis-
terium cunagii et numismatum infra castrum Dublinie fiendorum, habendum officium predictum per
se vel deputatum, durante beneplacito. 6 Julii." Rot. Pat. 21 Hen. VII. cap. ) 8.

This Thomas Galmole was probably the same person who was "master and worker of the money
of silver, and keeper of the exchanges in the cities of Devylyn and Waterford," in 1483. Ruding,
vol. ii. p. 376.

A 2

60 Dr. Smith on the Irish Coins of Henri/ the Seventh.

I have already shewn, that in the third year of Henry the Sixth (1425),
the master of the coinage in Dublin was bound, by indenture, to make the coins
of the same weight, allay, and assay, as the silver money, which leas made in
London, from which time until the thirty-eighth year of the same reign (1460),
it does not appear, nor is it probable, that any change in the standard took place ;
but in the latter year the Irish groat was ordered to be made " of the weight of
three deniers sterling." The penny, or " denier sterling" of that time, weighed
fifteen grains, consequently the Irish groat of 1460 should weigh only forty-five
grains, and was a fourth less in weight and value than the English groat. And
from this time " the first difference and inequality betwixt the standard of the
English and Irish monies"* is to be dated, and not, as Sir John Davis supposed,
from the fifth year of Edward the Fourth, at which time, however, the standard
in Ireland was again changed, while its proportion to the English groat was pre-
served, which had been reduced in 1464 from sixty to forty-eight grains. During
the subsequent years of Edward's reign, the standard of his Irish money was fre-
quently altered, according to the exigencies of the times, and in the first year
of Richard the Third, 1483, his Irish money was ordered to be made according
to the standard of the twelfth year of Edward the Fourth, at which time the
weight of the Irish groat was about thirty-two grains, or a third less than the
English.

It has been just stated, that Edward reduced the English groat to forty-eight
grains, which standard was adhered to in England, until the eighteenth year of
Henry the Eighth. The Irish groat, during the latter part of Edward's reign
and that of Richard, was about a third less than the English, and that the same
proportion was observed in the early part of the reign of Henry the Seventh, is
evident, from a passage in a letter, written by Octavian, Archbishop of Armagh,
to the king in 1487, "recommending Arthur Magennis to that prince, for the
bishopric of Dromore, wherein he says, that the revenue of that diocese is not
worth above forty pounds, of the coin of Ireland, which is less hy the third part
than the coin sterling."^ From this evidence and also from the fact, that some of
Henry's groats, when in good preservation, weigh thirty-two grains, which I be-
lieve they never exceed, I conclude that the standard in Ireland was not altered
during the reign of Henry, and that his Irish groat was always a third less than
the English of the same period.

* See p. 50. f Simon, p. 31.

Dr. Smith on the Irish Coins of Henri/ the Seventh. 61

Some arrangement is necessary, for the purpose of attempting to determine
the order in which the several coins were issued from the mints. In the absence
of documents by which the dates might be fixed, the only safe guide which
remains are the coins themselves, and from deliberate consideration of the types
and numerous varieties which have come under my observation, I have se-
lected the cross on the reverse, as the character which best distinguishes the
three sections into which I propose to divide them.

THE FIRST SECTION.

The coins included in this section have on the obverse a shield, bearing the
arms of England and France, quartered by a cross, the extremities of which are
generally terminated by three annulets ; and on the reverse, three crowns in pale
(the arms of Ireland),* with a similar cross : all the groats which I have seen
have (with one exception) the letter h under the crowns ; they usually weigh
about twenty-eight grains, and never I believe exceed thirty.

The description of the numerous varieties of this type will be facilitated by
dividing them into three classes : 1st, coins minted at Dublin ; 2nd, those which
bear the name of Waterford ; 3rd, coins without the name of the place of
mintage.

Of the Dublin mint there are groats, half-groats, and pennies.

The groat (PI. V. Fig. 1) has the legends henric di gracia, and civitas
DVBLiNiE. The lions on the shield have their tails doubled back in a manner
which distinguishes this coin from the three crown money of Edward the Fourth
and Richard the Third. The upper crown on the reverse has a double arch,
surmounted by a ball and cross. It is evident that the artist at first Inserted the
letter e in the name of the city, and afterwards attempted to conceal his blunder
by punching over it the letter v.

A groat has been lately found at Trim, the obverse of which is from the
same die as fig. 1, the reverse has the cross and arches over the upper crown,
but the legend is divided as follows : civit-asdv-blin-iee, with a fleur-de-lis
after the last letter. The coin is in the cabinet of the Rev. R. Butler, a small
portion is broken off, and it weighs twenty-seven grains.

* See Irish Coins of Edward IV., p. 37.

62 Dr. Smith on the Irish Coins of Henry the Seventh.

It is not unlikely that the coin which Simon published (PL III. fig. 63) was
partly defaced, and that in the attempt to restore the legend, rex was substituted
for ACiA ; the fleurs-de-lis in the legends are also omitted, and at the ends of the
cross there are pellets instead of annulets.

All the half-groats have annulets at the ends of the cross on each side, but
have not the letter h under the crowns ; they weigh from twelve to thirteen
grains.

Fig. 2 has the legends henricvs di orai, and civitas dvbbl-. The letter
o has been substituted for g, as is also very evident on the obverse of fig. 3, which
is undoubtedly from the same die ; the legend on the reverse of the latter coin
is civ-iTA DEB-lin. On fig. 4, the legends are henricvs d, and civitas deblin,
and fig. 5 reads henricvs dig, and civitas debli.

The half-groat published by Simon (PI. III. fig. 67), with the remarkable
legend henric dom obar, if correctly represented, should perhaps be dom vber,
an abbreviation of dominos vbernie, the legend on several of the groats pre-
sently to be described.

The penny (Fig. 6) has a circle of pellets on each side, and pellets at the
ends of the cross, the legends are he-NRicvs rex an, and civitas dvblin -, it
weighs seven grains.

Groats are the only coins which are known from the mint at Waterford.
The shield on the obverse is within a tressure of four single arches, outside
which is a circle, sometimes formed of pellets, but more generally a plain line.
The legend, in its most complete form, is, henricvs di gkacia rex, and on the
reverse, civitas waterforde, one or more letters are generally omitted. The
crowns on the reverse are within a tressure of double arches, the number of
which is generally nine ; the marks which occur in the legends are, a trefoil, a
star of five rays, and a small cross.

Fig. 7 has the legends henricvs graia rex, and civitas WA-terfor-DE, the
arms of the cross are terminated by pellets, as on some of the three crown groats
of Edward the Fourth, the tressure on the reverse has only eight arches, there
are small trefoils at its points, and in the angles outside it, and a fleur-de-lis at
each side of the middle crown ; another of similar type has the legend henricvs

DI GRACIA RX.

Fig. 8 has the circle on each side formed of pellets, the legends are henricvs
D GRACIA REX, and civitas waterford.

Dr. Smith on the Irish Coins of Henry the Seventh. 63

Fig. 9 has a circle of pellets on the obverse, and a plain circle on the reverse ;
the legends are henricvs di graci rex, and civtas waterfor.

The circle on each side of all the other varieties is formed by a plain line ;
the legends on fig. 10 are henricvs di gracia r, and civitas waterforde, in
two of the angles outside the tressure on the obverse there is a star of five rays.

On fig. 11 the legends are henricvs di grab, and civ-iTAS waterford.

Fig. 12 has a star of five rays at each side of the lovrer crovrn, and the
legends are henricvs di gracia, and civitas waterfor.

Figs. 13 and 14 are of ruder workmanship, and have a cross in the lower
angles outside the tressure on the obverse ; on the reverse of one, the legend be-
gins below, and on the other, at the left of the crowns, while on a third specimen
the legend commences in the usual place ; these rude coins weigh from twenty-
five to twenty-six grains. Fig. 14 is the only groat which I have seen without
the letter h under the crowns.

There are other varieties which differ only from those described, in the
arrangement of the letters in the quarters of the cross.

Of the coins without the name of the place of mintage, there are groats, half-
groats, and pennies.

There are several varieties of the groats. Fig. 15 is a remarkably fine coin,
it weighs thirty grains ; a fleur-de-lis occurs in three places in the legends —
henricvs di gracia, and dominos vbernie.* Fig. 16 reads rex anlie franc,
and dominos vbeunie. Fig. 17 is remarkable for having dominos vbernie on
both sides, and the mint mark on the obverse is a cross formed by five small pel-
lets. The next variety, fig. 18, has the borders of the shield, and the circles
formed of pellets; the legends are rex anglie F-rancie, and dominos vbernie ;
and fig. 19, which is of a similar type, has on the reverse dominvs hibern. ; it
weighs only twenty-two grains.

These four last groats have the tails of the lions doubled back in the same
manner as on the Dublin groat.

Fig. 20 (PL VI.) has the Fitzgerald arms at each side of the shield, the legends
are rex anlie fra, and dominos vrernie. The letter h under the crowns
distinguishes it from similar coins minted in the reign of Edward the Fourth.

* The king's name is invariably found on the groats of Dublin and Waterford, while on those
without the place of mintage it occurs only on this groat.

64 Dr. Smith on the Irish Coins of Henry the Seventh.

Every groat of this type which I have seen, either of Edward the Fourth or
Henry the Seventh, has vrernie on the reverse, but Simon gives one, PI. III.
fig. 65, which has hybernie, and fig. 66 of the same plate has a tressure on
each side like the Waterford groats, and the legends the same as his fig. 64.

Very few half-groats are known ; fig. 21 has on the obverse a cross terminated
by pellets, and a rose before the legend rex angl francie ; reverse domnos

NIE, the letter h under the crowns, and over them a cross patee, instead of

three annulets as at the other ends of the cross ; it weighs thirteen grains. The
cx'oss patee on the reverse seems to identify this coin with the Dublin groat, fig. 1,
while the obverse corresponds exactly with some of the half-groats of Edward
the Fourth.*

Simon's half-groat, fig. 68, appears to have the same obverse as the coin just
described, but the legend on the reverse is dom hibernie.

Pennies are also very rare ; fig. 22 has a circle of pellets on each side, the cross
on the obverse is without either pellets or annulets at its extremities, the legend
probably was Rex angl-iE. On the reverse, which is not quartered by a cross, is
the word vrerni, divided equally by a small cross ; it weighs six grains, and were
it not for the h under the crowns, it would be difficult to assign this coin to its
proper place in the Irish series.

Mr. Lindsay has published a penny, with h under the crowns, the legends
are rex anglie and dom .f

Simon did not hesitate to appropriate all the preceding coins to Henry tlie
Sixth, for his words are, " Whether these coins were struck before the year
1460, or after the year 1470, during the short time this prince had reassumed
the crown, is hard to ascertain ; but by the letter h, which is on all the pieces
with the three crowns, one might be tempted to believe, that they were coined
during that short period, as it seems to be a distinguishing mark from those of
Edward IV. struck before that time."J

* See Irish Coins of Edward the Fourth, figs. 88, 89. The practice of using the dies of deceased
Dionarchs was not unusual ; it is well known that Henry the Eighth, in his first coinage, used his
father's dies ; and I have lately seen a coin in the cabinet of Mr. Cuff, which affords a more inte-
resting illustration of the fact of old dies being altered. Mr. Cuff's coin is a Drogheda groat of
Richard the Third, struck from a die used by Edward the Fourth, which was altered by punching
the letters Ric, over edw, the remains of which are very evident.

t PI. VI. fig. 135. J Page 22.

Dr. Smith on the Irish Coins of Henry the Seventh. 65

That the letter h was placed under the crowns as a distinctive mark, is very
probable, but there is not any evidence whatever to support the appropriation of
these coins to Henry the Sixth, who died eight years previous to the introduction
of the three crown type into the Irish coinage.*

Simon's conjecture that these coins " were probably intended for three penny
and three-halfpenny pieces, "f appears to have been grounded on Sir James
Ware's statement, that, in 1478, liberty was granted to the master of the mint
to coin " pieces of three pence, two pence, and a penny,"| that is, in the propor-
tion of 3, 2, and 1, while the weights of the coins are as 4, 2, and 1, or groats,
half-groats, and pennies, as they are denominated in 1 Ric. III. cap. 8, in which
the type is particul^ly described.§

The appropriation of these coins to Henry the Sixth, was not questioned
until Mr. Lindsay, in his " View of the Coinage of Ireland," transferred them
to Henry the Seventh, and that they were struck early in his reign is probable,
— from the style of workmanship and correspondence in weight between them
and the coins of Edward the Fourth and Richard the Third of the same type, —
from the fact of one of Edward's dies having been used for the obverse of the
half-groat, fig. 21, — at i the appointment in the first year of Henry the Seventh
of a master of the coina ^e in the cities of Dublin and "Waterford.

This is the most coi, venient place to notice a small coin, whose type is very
different from any othei' known coin of any of the Henrys. The mint mark is
a cross pierced in the centre, and the legend HE-nri-cvs dns hib, the words se-
parated by small crosses ; reverse, a plain cross with a rose on its centre, civit is
all that remains of the legend, it weighs five grains. — (Fig. 23.)

This coin is much defaced, but from the size of the circle and its weight, it
appears to have been Intended for a penny ; it is difficult to assign it to any par-
ticular date, the rose proves that it was not struck previous to the time of Edward
the Fourth, and as Richard the Third coined pennies with a rose on the reverse, ||
and three crown groats, it is not unlikely that his successor coined money of
different types. The rose pennies of Edward and Richard have suns and roses

* Ware's Antiq. by Harris, p. 215. f Page 22.

% Ibid. p. 215. § Simon, Appendix, No. XVIII.

II Snelling's Suppl. to Simon, PI. I. fig. 27.

VOL. XIX. »

66 Dr. Smith on the Irish Coins of Henry the Seventh.

alternately on the field of the obverse, while on this coin of Henry neither of these
badges appear.

On the other hand, it is now believed that Henry the Sixth coined money at
London, Bristol, and York, during his brief restoration in 1470,* and although
no documentary evidence exists to prove that Henry exercised his prerogatives in
Ireland in 1470, it is not impossible that this penny may have been minted in
that year. Without presuming to decide this difficult question, I may remark
that the Dublin pennies coined by Edward, in 1470, have a rose on the centre of
the reverse.

THE SECOND SECTION.

The cross patee extending to the edge of the reverse, with three pellets in
each quarter, is the character common to all the coins in this section, which com-
prises two types ; one having the king's head with an open crown — the other a
crown with a double arch.

The Dublin groats with the open crown present several varieties, they weigh
from twenty-six to thirty-one grains. Fig. 24 has the legend henbicvs di gra
DNS HYBEBNiE, ouc or two pellcts between the words, no trefoils at the points of
the tressure ; reverse, two pellets before the motto posvi devm adivtore' mevm,
in the inner circle, crviTAS dvblinie. Fig. 25 has a mint mark of four pellets,
and DEI in the legend ; reverse, a pellet after civitas, in which e has been sub-
stituted for c. The legend of fig. 26 is, henricvs dei gra dns hybeb, there
are trefoils at some of the points of the tressure ; mint mark on the reverse, a
cross pierced in the centre, and in the inner circle civitas dvblnnie.

The four following groats have a small cross at the beginning of the legend,
which is henbicvs or henricvs dei gra dns hiber, small crosses between the
words, and trefoils at the points of the tressure. The mint mark on the reverse
of fig. 27, is a small cross patee ; on fig. 28, a trefoil ; fig. 29, has two small
crosses, before the motto posvi dev adivtore mev. Fig. 30 has civitas
dvblin, and is without a mint mark on the reverse.

The name of the city on fig. 30 has been read dvblym, but it appears to
me to have been blundered by punching the letters in twice on the die ; the
letter taken for y, is only the i doubled ; and that taken for m, is a double N, as
is evident from the projection at the top of the letter on the left, whereas the m

• Hawkins' Silver Coins of England, p. 108.

Dr. Smith on the Irish Coins of Henry the Seventh. 67

is always rounded at the top ; the coin is evidently blundered, and does not war-
rant the adoption of a reading for which there is no other authority.

Simon assigns to Henry the Sixth a groat of the same type as those now
described, and conjectures that it was struck " before this unfortunate prince was
dethroned by Edward the Fourth."* Mr. Lindsay assents to the appropriation,
but thinks the coin was struck " after his restoration in 1470," as well as another
groat which he has published.f

Although it cannot be proved that the coins already described in this section,
belong to Henry the Seventh, there are many objections against assigning them
to Henry the Sixth.

There is no evidence that any coins were minted in Ireland during Henry's
brief restoration, nor even that his temporary authority was recognized in this
country, and if coins had been struck at that time, it is not likely that he would
have ventured to reduce the weight of the groat which in 1470 was nearly forty-
one grains, to thirty-one, the greatest weight of any of these coins I have met
with.

Until very lately it was universally believed, that Henry the Seventh did
not coin any money with an open crown, but this opinion is now known to be
erroneous, and to quote the words of Mr. Hawkins, it may be considered " as
established beyond controversy, that Henry the Seventh did strike coins with an
open crown."J

The coin which led Mr. Cuff to this important discovery, is a York penny
of Thomas Rotherham, who was archbishop of that see from 1480 to 1504.
Mr. Hawkins, in his able and valuable work, describes a penny with the king's
name on the obverse, and as having the archbishop's initial, " a t at one side of
the neck and a (fleur-de-) lis at the other, with an h in the centre of the re-
verse ;"§ but as the representation of the coin (fig. 367) is defective, inasmuch as
it has not the " t at one side of the neck," I subjoin the figure of one which
has lately come into my possession.

* P. 22, and PI. III. fig. 70. t P- 37, and PI. V. fig. 104.

t Silver Coins of England, p. 120. § P. 120.

i2

68 Dr. Smith on the Irish Coins of Henry the Seventh.

This little coin differs from the three varieties described by Mr. Hawkins, in
having a small cross at one side of the neck ; and it possesses additional interest
in relation to some other Irish coins of Henry, as will appear hereafter.

It may not be amiss to notice a few particulars of the coins themselves. The
small crosses on figs. 27» 28, 29, 30, as mint marks, are similar to those on coins to
be described hereafter. The letter b is frequently substituted for r, a blunder
which I have not observed on any of the coins of Edward the Fourth, struck in
or about 1470, from which these coins are also distinguished by the absence of
the hair on the king's forehead, a peculiarity common to the undoubted English
and Irish coins of Henry the Seventh. The word hiber in the legend is also
remarkable, and I may add, it is not probable that such a variety of mint marks
would have been adopted, during the very short period, within which these coins
could have been struck by Henry the Sixth.

One groat of the Waterford mint is known ; the letters which are preserved
on the obverse are just sufficient to identify it as belonging to one of the Henrys.
The legend appears to have been henric dei gra rex angli franc ; reverse,
posvi, &c., and civitas waterford ; it weighs thirty-two grains. — (Fig. 31.)

The last coin in this division has a large cross, mint mark, and the legend
HENRIC DEI gra BEX ANGL FR, with small ciuque-foils between the words ; re-
verse, posvi, &c., and civitas dvblinie. The c is represented by e, and the d
by an e reversed; it weighs twenty-nine grains. — (Fig. 32.)

This groat appears to be the link, as to type, between the preceding coins,
and those with the double-arched crown in the next division.

The coins in the second division of this section, are distinguished by the
double-arched crown, surmounted by a ball and cross. The number of arches in
the tressure varies, and some have a pellet at each point of the tressure.

The legend on the groats is henric dei gra rex angl fr. The c in the
king's name is in most instances reversed, and the words are divided either by a
small cross or two cinque-foils ; reverse, posvi devm aivtore mevm, and in the
inner circle, civitas dvbiinie ; when in good preservation they weigh from thirty
to thirty-two grains. — (Figs. 33, 34.)

Simon says he had some groats " with a single, and others with a double-
arched crown."* I do not know of any such variety, and I have little doubt but
his fig. 97 is incorrectly represented. The legend is henricvs di gra rex agl

• P. 32.

Dr. Smith on the Irish Coins of Henry the Seventh. 69

& FR, and at each point of the tressure there is a small cross ; now in all the
arched crown groats of Henry which I have seen, they have only henric, nor
have any of them crosses at the points of the tressure ; in the next place, his coin
has the motto posvi devm aivtorivm, which I have observed only on coins with
a cross Jburchee on the reverse.

All these differences can, perhaps, be accounted for, by supposing that Simon
had before him a groat similar to my fig. 40, and it is very remarkable that the
relative position of the letters on the reverses of his coin and mine are the same ;
thus POSVI and inie are in the same quarter of the cross, instead of posvi and
CI VI as on most other coins. It is probable, that the legend on the obverse was
imperfect, and that the deficiency was supplied by copying from a groat with
the arched crown, and the arches of the tressure may have been mistaken for
those of the crown.

The half-groat has the crown apparently with a single arch, surmounted with
a ball and cross, the hair in long flowing curls, trefoils at the points of the tres-
sure, and on the breast the letter v inverted. The legend is henric di gra
REX ANLiE ; reverse, posvi devm adivtor, and civitas dvlin, with a cross
after dv. It weighs twenty-one grains and a half. — (Fig. 35.)

The arches of the crown, which are plain, the arrangement of the hair, the v
on the breast,* the meaning of which I cannot explain, the legends, and the
trefoils at the points of the tressure, distinguish this coin from the groats. The
small cross in the inner circle has been taken for an x, but a similar cross occurs
at the end of the motto, and also on the reverse of the penny, fig. 22, on which it
certainly does not represent a letter. The weight of this piece is considerably
more than half of the groat ; another specimen which I have seen weighs only
fourteen grains and a half.

Henry the Seventh, in his fifth year, introduced the type of the arched
crown on the English coins,f and shortly after (1491) Nicholas Flint, who held
several offices in connexion with the English mint, in the early part of Henry's
reign, was appointed master of the mint in Dublin and Waterford.

From these data I infer that the arched-crown groats were minted by Flint,

* Mr. Hawkins mentions a Durham penny of Edward the Fourth, with a v on the breast. — Silver
Coins of England, p. 115.
+ Hawkins, p. 107. .

70 Dr. Smith on the Irish Coins of Heny the Seventh.

and this conjecture is supported by the very close resemblance between the
English and Irish coins, in type and workmanship.

The half-groat, notwithstanding all its peculiarities, appears to be contem-
porary with the groats.

Mr. Lindsay supposes the Waterford groat (fig. 31) to have been struck by
Henry the Sixth " after his restoration in 1470." The legend of the coin, how-
ever, is not in favour of this appropriation, and the form of the letters have some
resemblance to those on the coins which I conceive were struck while Flint was
master of the mints of Dublin and Waterford. This coin is remarkable for
having the hair on the king's forehead.

I also consider fig. 32 to be the work of an English artist, it resembles some
of the arched-crown groats in almost every particular except the crown, and even
in this there is some resemblance, for if the cross was resting on a ball, the
arches of the tressure might readily be taken for those of the crown.

THE THIRD SECTION.

All the coins in this section (with one exception) have the king's head on
the obverse, and a cross fourchee with three pellets in each quarter, on the re-
verse. They may be divided into two classes ; first, those having a double-arched
crown ; second, those with an open crown.

The coins in the first class have the arched crown, surmounted by a ball and
cross ; the arches are usually formed of pellets, but in some specimens they are
plain lines ; the number of arches in the tressure round the head varies, and there
are generally three pellets at each point of the tressure, some have annulets
within the tressure, and also between the words of the legend ; the hair is always
in long hanging curls, resembling in this respect the English groats of Henry.
All the specimens which I have seen have the letter h* in the centre of the re-
verse, they are rudely executed and the legends are more or less defective ; they
appear to have been clipped, and weigh from twenty-six to twenty-eight grains.

* A boar's head is very neatly represented as occupying the centre of the reverse of a groat,
pubhshed by Simon, PI. V. fig. 99. In this instance, I suspect that he mistook the h for a boar's
head, and the engraving seems to represent the coin in greater perfection than the original ; my sus-
picion is supported, if not confirmed, by his ovf n description ; he says, " the last of these (arched-
crown groats) has on the reverse, in the centre of the cross, a boar's head, mint mark ; and though
much clipped and worn, they weigh from twenty -seven, to thirty-one grains.'' — p. 32.

Dr. Smith on the Irish Coins of Henry the Seventh. 71

Fig. 36 has the legend henric dei gra rex anlie fr, and on the reverse
civiTAs dvbline; the motto appears to have been intended for posvi devm

ADIVTORIVM.

The legend on fig. 37 is henries dei gra ries anli, and on the reverse

CIVITAS DVBILINI.

On fig. 38 the legends are henries di gr — rex a e, and civitas

DVBLINIE.

I do not know of any half-groats of this type.

The penny, fig. 39, has on the obverse a double-arched crown, and the letter

H under it, the legend is henr ; reverse, a cross pierced at each extremity,

and the legend civitvs , it weighs five grains and a half.

The pierced cross on this curious little piece, connects it with the coins in
this section, but it is more particularly identified with them, by the form of the
H in the king's name, which seems to be identical with the first letter in the
legend on the obverse of fig. 38.

It is difficult to account for the peculiarities of this penny. The artist per-
haps did not possess sufficient skill to execute a head on so small a scale, and as a
substitute for it, transferred the initial of the king's name from the reverse to
the obverse, the crovra on which, resembles that on the coins in the first section,
while the arches are the same as on the groat, fig. 34.

The arched crown, the long hanging curls, and the cross fourchee on the
reverse, all concur in establishing the appropriation of these groats to Henry. It
is now admitted, that the plain cross was not abandoned on the English coins
until some time after the accession of Henry the Seventh ; and in the Scotch
series it does not appear, that the cross fourchee was adopted prior to the reign
of James the Fourth, who was contemporary with Henry ; nor does any instance
of it occur on the numerous coins struck in Ireland during the reigns of Edward
the Fourth and Richard the Third, while it invariably occurs, more or less
modified, on all the Irish coins of Henry the Eighth; hence I conclude that these
coins were struck subsequent to the arched-crown groats described in the second
section, and the idea of placing the initial of the king's name on the reverse may
have been derived from Rotherham's penny.* The rude manner in which they
are executed makes it probable that they were not the work of an English artist,

* See p. 67.

72 Dr. Smith on the Irish Coins of Henry the Seventh.

while the occurrence of the words henries and ries, imply that they were exe-
cuted by a Frenchman.

The coins in the second class have an open crown, and may be divided into
those having a tressure round the head, and those without a tressure. The
varieties of the first kind are numerous.

Fig. 40 (PI. VII.) has the legend henricvs dei gracia kex alie ; reverse,
posvi devm aivtorivm, and in the inner circle civitas dvblinie. Fig. 41,
reads henri-cvs dei gratia eex anlie ; the motto is blundered, and in the inner
circle it has sivitas dvbline, the d being represented by an inverted g. Fig.
42 is engraved to show the degree to which it is blundered on the reverse.

The number of arches in the tressure on these coins varies from eight to
eleven, and at each point there is a small cross, the hair is in long hanging curls,
just as it appears on the English groats of Henry with the arched crown ; they
weigh from twenty-seven to twenty-eight grains and a half.

The groat which Simon published (PI. III. fig. 69) as belonging to Kenry
the Sixth, is evidently of the same type as my fig. 40.

Fig. 43 has a cross mint mark, the legend is henric D-ei gra-ciA rex agl,
with small crosses between the words, there are three crosses within the tressure,
and the hair is in long hanging curls; the motto is posvi dvm adivtoriv mevm,
and in the inner circle civitas dvblinie. The c is represented by e, and an
inverted e is substituted for d ; it weighs thirty grains.

Fig. 44 has the hair in short close curls ; the legend is henri-c de-i gracia
rex angle, with annulets between the words ; the letter l is represented by a
double I, as on some of three-crown groats ;t reverse, posvi, &c., and civitas
dvblinie ; it has the letter h in the centre of the reverse, and weighs twenty-nine

grains.

The mint mark on fig. 45 is a small cross, the tressure has only six arches,
the crown is very flat, and there is a cross at each side of the neck. The legend
is henric dei gr-ACiA rex alie fr ; reverse, posvi devm adivtorivm, and
civitas dvblini ; it weighs only twenty-three grains.

Of the groats without the tressure round the head the varieties are very nu-
merous.

Fig. 46 has a cross at each side of the crown, and the hair in long hanging

* See figs. 16, 18, 19, PI.V.

Dr. Smith on the Irish Coins of Henri/ the Seventh. 73

curls ; the legend is henricvs di gracia rex ani ; reverse, sivitas dvblinie ;
the motto is blundered ; it weighs twenty-nine grains. Fig. 47 is of the same type,
but the legends on both sides are unintelligible ; it weighs twenty-seven grains.

Simon's coin (PI. III. fig. 59) is identified with this type, by wanting the
tressure, and having the cross at each side of the crown ; but if the details of his
engraving are correct, the coin is very different from any I have seen.

Fig. 48 is a very remarkable coin, it has a rose or cinquefoil at each side of
the crown, and also as a mint mark, the hair is in long full curls, and the bust is
concealed by drapery, resembling a cloak, henbic is all that remains of the legend ;
the reverse is altogether unintelligible, and it weighs only twenty-four grains.

.The coin in Simon's third Plate (fig. 60) is of this type, and is represented
as being perfect in every respect ; it is much to be regretted that many of the
most curious coins which he possessed cannot now be discovered.

The remaining coins in this division are chiefly distinguished by the absence
of the tressure round the head. The crown is open and very shallow — the hair
is in short, close curls, which stand out from the face — the shoulders are more
displayed than on any of the preceding coins, and are without drapery — and the
mint mark is a cross. The legend on the obverse, in its most perfect form, is,
henricvs di gracia rex aglie fr ; reverse, posvi devm adivtorivm, and in
the inner circle civitas dvblinie ; a few have sivitas ; the name of the city is
generally abridged, and several are blundered to an extreme degree; they weigh
from twenty-four to twenty-nine grains and a-half.

No half-groats or pennies of this type are known, and Dublin is the only place
of mintage.

The following list exhibits the legends of the most remarkable varieties :

Fig. 49, HENKCVS DI GEACIA BEX AGLIE FR. POSVI-DEVM -ADIVT-OBIVM. CIVI-TAS -DVBL-INIE.
50, HENKCVS DI GRACIA REX AGLIE FE. POSVI-DEVMA-DIVTO-BIVM. CIVI-TAS -DVB -LINI.
51,HENRCVS DI GEACIA BEX AGNIE. POSVI-DEVM -ADIVT-OBIVM. CIVI-TAS -DVB -LIN.

52, HENBCVS DI GBACIA BEX AGNIE. POSV -IDEV -MADI -VTOB. CIV -ITA -SDV -BL.

53, HENEICVS DI GBACIA BEX AGNI. POSV -IDEV -MADI -VTOB. CIV -ITA -SDV -BLI.

54, HENEICVS DI GBACIA BEX AGNI. POSV -IDEV -MDEV -TOEIV. CIV -ITA -SD -VB.

55, HENEICVS DI GBACIA BEX AGN. POSVI-DEVMI -ADIVT-OBIVM. SIVI-TASD-DVB -LINE.

56, HENEICVS DI GBACIA REX AGN. lEMA -MIVI -TASD -VELA. CIVI-TAS -DVB -LIE.

57, Blundered. Blundered. civ -itas-dvb -iaii.

VOL. XIX. fe

74 Dr. Smith on the Irish Coins of Henry the Seventh.

I have had occasion, in more than one instance, to doubt the accuracy of
Simon's engravings ; and it is plain that he sometimes erred in attempting to
restore the legend of a defaced coin. His fig. 56, has gra, but my fig. 55 has
GRACiA, and is identified with Simon's, by having the letters ne in the name of
the city united exactly as he has represented them ; and my friend, the Rev.
J. W. Martin, has a groat which certainly has been struck from the same die as
mine, but defective in the legend exactly in the place where Simon's differs
from fig. 55. Mr. Martin's coin has been traced to Simon's possession.

Of the many coins without the tressure which I have seen, I have not met
with any so perfect as those engraved in Simon's Essay. The errors, for such I
must consider them, which appear in the legends, &c., of figs. 56, 57, 58, may be
accounted for by his attempting to restore partially defaced coins, while the letters
in the inner circle correspond with pieces known at present.

In making these observations, I by no means intend to insinuate that Simon
intentionally misrepresented the legends on any of his coins, on the contrary, I
am satisfied that his errors are to be attributed to the want of opportunities en-
joyed by his successors, and his work, which he " modestly styled an Essay only,"
has received a well merited eulogium from the able and impartial author of the
" Annals of the Coinage of Britain."

Mr. Lindsay was the first writer who questioned the correctness of Simon's
appropriation of the groats without the tressure to Henry the Fifth; and as several
distinguished numismatists are still of opinion, that these groats are the earliest
in the Irish series, it is necessary to enter at some length into the discussion of
this question.

I shall first lay before my readers, an abstract of Mr. Lindsay's opinions,
and then proceed to investigate the objections which have been urged against
them.

" It must in the first place be observed," says Mr. Lindsay, " that no records
have hitherto been discovered, which direct, or even refer to, an Irish coinage
from the reign of Edward III., until the 38th Henry VI., 1459-1460."*

In the Introduction to this essay, I have quoted a roll of the 9 Henry V.,
and another of the 3 Henry VI., which, although unknown to Mr. Lindsay

* View of the Coinage of Ireland, p. 31. .

Dr. Smith on the Irish Coins of Henry the Seventh. 75

when he wrote, tend to support his opinion that Henry the Fifth did not coin
money in Ireland.

He next observes, " this Act (38 Henry VI.) would seem to imply that a
separate coinage for Ireland, of a type and standard different from that of Eng-
land, was then for the first time adopted ; if so, the coins assigned to Henry V.,
viz., Nos. 56, 7, 8, 9, 60, of Simon, could not have been struck before that
period, as they differ in type, and still more in weight from any English coins
hitherto struck."

I have already shown, that if any money was coined in Ireland during the
early part of the reign of Henry the Sixth, it ought to be of the same weight,
allay, and assay, as the silver money made in London.* The difference in type
will be noticed hereafter.

At an adjourned sitting of the parliament of the 38 Henry VI., it was ordered
that the groat " shall pass for five-pence," and on these words, Mr. Lindsay
remarks, "it is nearly certain that these coins must have been of the English
standard, then sixty grains to the groat, otherwise they would not have been
ordered to pass at the rate of a penny more than the new (Irish) groat of forty-
five grains, and could not possibly have meant or Included the groats given by
Simon to Henry V.," and adds, "let us now consider the coins themselves, and
compare them with the English coins of the Henrys. The first peculiarity which
presents itself, is the want of the double tressure round the king's head" — the
next, " is the cross fourchy on the reverse," then, " the king's title," and lastly,
" their weight."

Mr. Lindsay, with the candour of an enlightened and impartial writer, con
eludes by saying, "having thus given to the coins an appropriation very different
from that of Simon, or indeed I will admit of any other writer who has noticed
them, I think it fair to lay before ray readers, the opinion of a learned friend on
whose judgment in matters relating to the English and Irish coinage, I have the
greatest reliance."

With the arguments of Mr. Lindsay, in support of his appropriation, I fully
concur, and therefore I feel imperatively called upon to institute a rigid Inquiry
into the objections of his learned friend, whose opinions are deservedly entitled
to the highest respect.

* See p. 53.

k2

76 Dr. Smith on the Irish Coins of Henry the Seventh.

The first objection is to the workmanship, of which he says, "comparing
those groats assigned by Simon to Henry V., with the undoubted coinages of
Edward IV. and Henry VH., I should say that the design and workmanship of
the former is so very poor, imperfect, and barbarous, that coming from the same
mint of Dublin, I cannot conceive them subsequent to Edward IV., and still less
suppose them contemporaneous with those of the arched crown of Henry VII.
To me they are evidently the first groats in the Irish series, the workmanship of
very rude, ignorant artists, who had very imperfect command of the graver, could
design little, and execute less."*

The appearance of the bust — the form of the letters — the blundered legends
— the flat crown — the circle round the head, are all noticed ; and he adds, " I
cannot but repeat, that their appearance and fabric appear to me to exclude them
altogether from the coinage of Henry VII."

The appearance of the bust and the workmanship on these coins is certainly
very rude ; yet the difference between the coins, " coming from the same mint
of Dublin," may, in some measure, be accounted for, by the fact, that Nicholas
Flint, who was " sculptor de et pro ferris," in the mint of London, in I486, was
made " overseer of the mints of Dublin and Waterford" in 1491j and was suc-
ceeded in his office in Dublin, in 1506, by Thomas Galmole alias Archibold, a
goldsmith in Dublin.

" The letters are thin and uncertain" yet when they are compared with those
on the rude coins of Henry the Seventh, with the arched crown (see figs. 36,
37, 38), it will be admitted, that if they are not identical, they bear a very close
resemblance to them.

" The erroneous legends," are not more remarkable than the blunders which
occur on some of the Irish groats of Henry the Eighth,f and are very similar
to the legends on figs. 42 and 47, which, in my opinion, are identified with the
time of Henry the Seventh, by having the hair in long hanging curls.

" The crown is quite level," but it is identical with that on the tressured
groat (fig. 45), and bears a close resemblance to the crowns on some of the groats
described in the first division of the second section.

" The head is encircled by a mere line, ana not a dotted circle," such, no
doubt, appears to be the case on a few of these coins, but on most of them which

• Lindsay, p. 34. f Ibid. PI. VII. figs. 147, 148.

Dr. Smith on the Irish Coins of Henry the Seventh. 77

I have met with, the circle is more or less indented ; on fig. 53 it is even roped,
and several others have a circle of pellets very distinctly marked.

Mr. Lindsay's correspondent, relying on the objections which I have endea-
voured to refute, says, " this is what may be termed the internal evidence fur-
nished by the coin itself, and to me completely decides the question."

" The array of Acts of Parliament, weight of coins," &c., are not allowed to
be of much importance ; but I cannot consent to give up the evidence derived
from such authorities, for the Irish coins of Edward the Fourth are generally
found to be in strict accordance with the standard fixed by the Acts ; and while
it is admitted, that " the groat of Henry V. should weigh sixty grains," it
appears to me incredible that any groats should be issued by him at so low a
weight as "twenty-eight" grains.

It is also asserted, that no coinage took place in Ireland " from the death of
Edward II. to the accession of Henry V.," and that "after such a lapse of time
(nearly a hundred years), the attempt at a coinage may be expected to be very
wretched, and so it is. Supposing, as is natural, that the Irish engraver would
make the current English groat his copy, as near as his want of ability would
allow him, the copy, such as we see it, is more Edward the Third's and
Richard the Second's, than Edward the Fourth's, — in the former, a larger space
was left unoccupied by the bust than on the latter ; and where the artist could
scarcely attempt the plain circle surrounding the head, it is no wonder that he
abandoned the tressure."

Here again, the authority of authentic records is disregarded, for in 1336
(10 Edward HI.) " a proclamation was then issued by the king and council, for
the coining of pennies, halfpennies, and farthings in Ireland ;"* and in 1339, a
writ, entitled, "De cunels in Hiberniam mittendis," was issued ;f and if it be
admitted that the English coins which have the name *' Edwardus" belong to
Edward the Third, this question is settled respecting the Irish coins ; for in Fe-
bruary, 1841, a farthing was found at Trim, on the obverse of which is a head
within a triangle, and the legend edw-ardv-srex ; reverse, cross and pellets,
with civiTAs DVBLiNiE. This coin is in the cabinet of the Rev. Richard Butler,
of Trim. And if " nearly a hundred years" elapsed without any coinage taking
place in Ireland, it does not follow that the first attempt should necessarily be

* Simon, p. 16. | Ibid. Appendix, No. II.

78 Dr. Smith on the Irish Coins of Henri/ the Seventh.

" very wretched," for the earliest groats minted in Ireland, of which we have
any authentic records, were as well executed as the English coins of the same
period ; nor can I perceive that the coins in question are more like " the cur-
rent English groat" than the Irish coins of Edward the Fourtli ; for on all the
London groats of Richard the Second, and Edward the Third, which I have seen,
the Roman n is used in the name of the city, while on these Irish coins of Henry
it never occurs. The form of the letter i is also different ; on Henry's coins it
is always more or less forked, and never square at the ends, as is invariably the
case on the supposed models. The objection of the plain circle roimd the head,
has been already answered, and the striking resemblance in almost every respect
(except the tressure and crosses at each side of neck), between fig. 45, and the
untressured groats, induces me to believe that the artist " abandoned the tres-
sure," rather from choice than inability to execute such a trifling ornament.

It also strikes me as very extraordinary, that an artist so ignorant as has been
supposed, should invent a cross fourchee for the reverse of his rude coin ; and how
did the illiterate artist (who it is conjectured *' could not spell") learn that the
GRA on the supposed models, was only an abbreviation for gracia, which is found
without exception on the untressured groats, as well as on some others of which
little, if any doubt can exist, that they belong to Henry the Seventh, as the half-
groat, fig. 35, and the tressured gi-oats figs. 40 and 45 ; and why did not the
copyist adopt the usual motto, but instead of it engrave on his die, posvi devm

ADIVTORIVM. ?

Several authorities are cited to show " that rex agl mai/ have been also used
in Ireland before the reign of Henry VII. ;" but the Act of 10 Edward IV.,
which ordered that rex anglie should form part of the legend on the coins, has
not been noticed, and there is not any Irish coin known with this title, which can
be referred to an earlier date. The penny of Henry the Sixth has the legend

HENRICVS DNS HIBNIE.*

In bringing these observations to a conclusion, I feel bound to acknowledge,
that, if I have been at all successful in establishing opinions different from those
of preceding writers, it has been chiefly owing to the advantage I enjoyed of
having so large a number of coins of the different types before me at one view.
It now only remains for me to assign such reasons as appear to warrant the
appropriation of the coins in the last plate to Henry the Seventh.

* See p. 56.

Dr. Smith on the Irish Coins of Henry the Seventh. 79

Assuming that it will be admitted that the groat with the arched crown, and
the H in the centre of the reverse (fig. 36) belongs to Henry the Seventh, it can
scarcely be doubted that figs. 40, 41, 42, are nearly contemporary with it —
GRAciA in the legend — the arrangement of the hair — and the cross fourchee on
the reverse are common to both. The cross on fig. 43 over the crown, which
seems to have single arches, and the words rex agl in the legend, connect this
coin with the double-arched groats figs. 33, 34, while the crosses within the
tressure, the word gracia, and the long curls, show how closely allied it is to
figs. 40 and 44, the latter of which is remarkable for the h in the centre of
the reverse. The cross at each side of the neck and the tressure on fig. 45,
connect it with fig. 43, and in every other particular it is almost identical with
fig. 50.

Notwithstanding all the objections which Mr. Lindsay's correspondent has
made against the appropriation to Henry the Seventh, of the " groats assigned
by Simon to Henry V.," he admits, " the curious groat in (Mr. Lindsay's) col-
lection, without a tressure,* to be an early groat of Henry VII." To me this
admission is important, yet I must in some measure dissent from it, in expressing
my belief, that the coin was struck in the latter part of Henry's reign ; the hair,
and the cross at each side of the crown connect it with fig. 41, the absence of the
tressure with fig. 55, and the word sivitas occurs on the three coins ; fig. 47 is
only a blundered variety of fig. 46, and fig. 48 is a very remarkable coin.

Of the remaining coins little need be said ; the blundered legends on fig. 57
are not more remarkable than those on figs. 42, 47, and 48, and the want of the
tressure is the chief distinction between them and fig. 45 ; the word gracia
on the obverse — sivitas on three varieties, and the cross fourchee on the
reverse — and the form of the letters, concur in making it probable, that all the
coins in the last Plate were minted about the same time ; and from the many
varieties of type, and the bad style of workmanship of these coins, it is evident
that the mint of Dublin was in a very unsettled state ; under these circumstances
it is not surprising to find the arched crown abandoned, and the open crown re-
sumed in place of it.

I feel little hesitation now in appropriating these coins to the latter part of
the reign of Henry the Seventh. It is not improbable that many of them were

* See fig. 46.

80 Dr. Smith on the Irish Coins of Henry the Seventh.

struck by Galmole, who was appointed master of the mint of Dublin on the 6th
of July, 1506, and that he abandoned the tressure in imitation of Henry's latest
English coinage.

I cannot conclude without acknowledging my obligations, and expressing my
gratitude to those who have so kindly favoured me with the means of illustrating
this very obscure period of the History of the Irish coinage.

^.^X^.VOL.XDC.

ANTIQXnTIES PLATE 5.

Dr. Smith on the Irish Coins of Henry the Seventh.

81

EXPLANATION OF THE PLATES.

Plate L

NO.

DENOMINATION.

MINT.

WEIGHT. PAGE.

REFERENCE.

1

Groat.

Dublin.

27 grs.

14

Mr. CuflF.

2

Half-groat.

99

12i

15

9?

3

)»

99

13

Dr. A. Smith.

4

»>

99

12

99

5

99

99

12

Dean of St, Patrick's.

6

Penny.

)9

. 7

99

7

Groat.

Waterford.

26

Mr. Sainthill.

8

99

99

28

Dean of St. Patrick's.

9

9

99

28

16

99

10

9

99

30

99

11

9

99

28

Dr. A. Smith.

12

9!

99

28

Dean of St. Patrick's.

13

9

99

26

Mr. Sainthill.

14

9

99

25

Mr. Lindsay.

15

9

99

30

Dean of St. Patrick's.

16

9)

?

30

Dr. A. Smith.

17

9

?

27

99

18

9!

?

28

Rev. R. Butler.

19

9J

?

22

Dean of St. Patrick's.

VOL. XIX.

W

82

Dr. Smith on the Irish Coins of Henry the Seventh.

Plate II.

NO.

DENOMINATION.

MINT.

WEIGHT.

PAGE.

REFERENCE.

20

Groat.

?

26 grs.

16

Dean of St. Patrick's.

21

Half-groat.

?

13

17

Rev. J. W. Martin.

22
23

Penny.

>>

?

Dublin ?

6
5

99

18

Rev. R. Butler.

95

24

Groat.

Dublin.

26

19

Dean of St. Patrick's.

25

9>

J5

30

95

Dr. A. Smith.

26

?5

J5

28

99

Dean of St. Patrick's.

27
28
29

5?
35

55
55

30
30
31

55

"
55

59

Mr. Sainthill.

30
31

55
55

55

Waterford.

31
32

5»

21

99

55

32

55

Dublin.

29

53

Dean of St. Patrick's.

33

55

59

32

35

Mr. Sainthill.

34
35

53

Half-groat.

99

95

30
2H

33

22

,9 9

Rev. J. W. Martin.

36

Groat.

95

27

24

Dean of St. Patrick's.

37

38

33
J3

55
59

26
28

55

99

Mr. Sainthill.

39

Penny.

55

H

99

Rev. R. Butler.

if«ow.i2:Zj4.VOL . XDC.

ANTIQUITIES PLATE 6.

Tr^s. R.IA . VOL.XIX .

AJrTIQTJITIES PLATE 7.

Db. Smith on the Irish Coins of Henry the Seventh.

83

Plate III.

NO.

DENOMINATION.

M

INT.

WEIGHT.

PAGE.

REFERENCE.

40

Groat.

Dubl

in.

27 grs.

25

Dean of St. Patrick's.

41

28

)5

42

27i

»J

43

30

Rev. R. Butler.

44

29

Dean of St. Patrick's.

45

23

5J

46

29

Mr. Lindsay.

47

27

26

Dean of St. Patrick's.

48

24

»>

49

26

55

50

24

55

51

28

Dr. A. Smith.

52

25

Dean of St. Patrick's.

53

28

Mr. Sainthill.

54

25i

Mr. Lindsay.

55

29i

Dr. A. Smith.

56

28

Dean of St. Patrick's.

57

29

Dr. A. Smith.

12

84

III. — On the Norse Geography of Ancient Ireland* By George Downes,
M.A.; M.R.I. A.; M. R. S. N. A., Copenhagen ; F. H.M. M.S., Jena.

Read April 26th, 1841.

IN the First Series of the Annals and Memoirs of the Royal Society of Northern
Antiquaries, published in Copenhagen in 1837, there is a small Map of this country,
annexed to an Essay on the Earliest Expeditions from the North to Ireland.
This Essay is nearly identical with an English one, already published in the same
.city in 1836, and incorporated in the Address of the Society to its British and
American Members. The Map in the latter publication exhibits some improve-
ments on that in the former. A new locality is introduced, and an old error
corrected, namely, the location of Clontarf to the north-west of Tara. The cor-
rection of this error is due to a distinguished member of the Academy, the late
Dr. William West, by whose premature decease the progress of northern litera-
ture in this country has been greatly retarded.

The Norse Map of Ireland, though but a modem compilation, is so far in-
teresting as it exhibits the scanty amount of the Irish localities, noticed in such
of the Icelandic Sagas as were published previously to 1837. On these localities,
which are mostly given both in Norse and English, I shall submit to the Aca-
demy a few observations, after which I shall undertake a slight extension of what
may be termed the Norse Geography of Ancient Ireland. By Norse I mean Old
Danish, which was originally denominated the Danish Tongue, afterwards Nor-
raene, or Norse, but which has been long better known as Icelandic — the remote
island, though but a colony, having imposed its name on the language of its un-

* A considerable time having elapsed since the reading of this paper, I have profited by the cir-
cumstance to introduce into it several corrections and improvements, in which I have received much
assistance from a gentleman, acknowledged to be the best living authority on the subject of ancient
Irish topography.

Mr. DowNES on the Norse Geography of Ancient Irleand. 85

lettered founders, by virtue of its literary celebrity. The term Runic, so fre-
quently applied to this language, even by such scholars as Parkhurst, is a mis-
nomer, being applicable only to a peculiar form of its characters, like the term
Ogham in Irish. In tracing to a foreign origin a few of our local names, I shall
unavoidably startle vernacular prejudices, researches such as the present being but
too frequently marked by a national bias. Local investigations recall local
associations, and there is a charm about ancient things, by which the judgment
becomes warped : a chastened imagination will indeed rather aid than obstruct
inquiry into the topography of an imaginative people, but patriotism is a bad
etymologist.

Of the four provinces of Ireland, which are all given in English on the Map,
but two are given in Norse — Ulaztir and Kunnaktir ; Leinster and Munster
are, however, mentioned in the Essay, and two portions of the former are laid
down on the Map — Dyflinar-skiri, or Dublinshire, and Kunnjdttaborg, which
occupies much of the present county of Meath. The Danish writer asserts, after
Chalmers, that 5^er, the termination of the names of three provinces, is a cor-
ruption of the Norse sta'^r, " place," not adverting to its occurrence without an s
in Kunnaktir, where, however, it may have been omitted for euphony. It cer-
tainly has no connexion with the Irish cfp, which was invariably the leading word
in local designations wherein it occurred, as in Tir-Anlave, or Tirawley — a name
apparently Norse, but which is found, as Tir-Amhalgaidh, in the Book of Ar-
magh, written about 680, a period anterior to the earliest northern invasion of
Ireland on record, and which is misinterpreted in the Essay as Olafs Hdj, or
" Olave's Height." To the apparently idle tradition that Ulster owes its name
to one Ullagh, a Norwegian, the Essay naakes no allusion.

Though Leinster is not included among the Norse localities on the Map,
Johnstone, in his edition of the Lodbrokar-Quida, or Death-Song of Lodbroc
(otherwise called the Krakumdl), printed in 1782, gives " Leinster" as the
translation of " Lindis-Eyri" in a description of a sea-fight between the North-
men and the Irish : in the notes, however, he suggests that Lindisfarne may
be intended, that is. Holy Island, off the coast of Northumberland (or now of
Durham), and adds, that some suppose the Lindesnes, commonly called the
Naze, in Norway, to be the locality in question. In Rafn's edition of the same
poem, published in 1826, various opinions are cited. If eyn, "strand" (the

86 Mr. DowNES on the Norse Geography/ of Ancient Ireland.

Danish ore, as in Elsinore), be the correct reading, Lindis might be found in
Lindsay, the northern part of Lincolnshire, did not the context almost directly
point to Ireland. Olaus Wormius assigns as the scene of conflict an island
on the Irish coast, and the presumption of the insular nature of the district in-
tended is favoured by a different reading, eyju, suggested by Arni Magnusson,
the founder of the Arna-Magnaean Commission, and perhaps the most consum-
mate Icelandic scholar that has ever existed. If the opinion of these distin-
guished authorities be well-grounded, the locality in question may be the island
of Lamhay, laid down on Ptolemy's map as Limnos and Limpnos, forms not
unlike the Norse Lindis, to which another form, Linos, bears a still stronger
resemblance. This etymological conjecture seems also to admit of geographical
support. In this part of the poem there appears to be a local progression. The
naval battle-fields, mentioned in immediate connexion with Lindis-Eyri, are off
the Scottish islands of Sky and Isla, and the Welsh island of Anglesey : it is,
therefore, more natural to seek for Lindis-Eyri on the east coast of Ireland than
on the east coast of England. Indeed, the achievements of Lodbroc on the
coasts of Northumberland and Norway are alluded to in an earlier part of the
poem ; and the distinguished editor, Professor Rafn, himself is in favour of the
Irish hypothesis.

Of our estuaries, but three are named on the Map. On the north-west coast
appears Jolduhlaup [Jollduhlaup'], which is variously stated to be three, four,
five, or eight days' sail from Iceland. "The name," says the English Essay,
" signifies the run or breaking of waves, a designation applicable to no other
place within the limits specified than Lough Swilly." I have elsewhere met
with the assertion, that JoUduhlaup is a translation of the Irish name of the
lough, which, however, is not adduced. It may be reasonably doubted that the
locality here assigned to JoUduhlaup is the real one ; and it is certain that Lough
Swilly possesses no Irish name, which would admit of the above interpretation.
In Olave Tryggvason's Saga this locality is expressly stated to be in Ireland,
and distant five days' sail from Reykjanes, in the south of Iceland.

The site of Ulfreksjjor^r or XJlfkelsfjoY^r, Ulfrek's or Ulf kel's Firth, as the
Danish writer admits, cannot be ascertained, nor even with certainty referred to
Ireland. The Sagas mention a battle fought, in 1018, between an Irish king,
named Konofogr, supposed by Suhm to be Conochar O'Melachlin, king of

Mr. DowNEs on the Norse Geography of Ancient Ireland. 87

Meath, and the Orkneyan earl Einar, in this firth, which Schoning locates in
the north of Ireland. However, as the eastern coast, in the neighbourhood of
Dundalk, was equally the resort of the Scandinavian rovers, the matter has been
compromised on the Map, where Lough Foyle figures as Ulfreksfjbr^r, and Car-
lingford Bay as tJIfkelsfjor^r, with a note of interrogation added to each word,
though Lough Foyle appears to have the stronger claim, the name Carlingford
being itself evidently Norse.

Were the name alone of this firth taken into consideration, its locality might
be reasonably sought in England. Ulfkell, surnamed Smiling, or Excellent,
was a son-in-law of Ethelred IL, from whom a great part, if not the whole, of East
Anglia was named Ulfkell Snilling's Land. The estuary called the Wash, or
Boston Deep, is adjacent to this territory ; but the countries of the belligerents,
Ireland and Orkney, render it unlikely that their place of encounter would be
there. However, as Ulfkell appears to have at one period exercised a kind of
vice-regal authority over the north of England, the firth in question may be one
of those on its north-western shore. The Danish writer finds a similarity be-
tween the name Ulfkel and the Irish O' Kelly, in which Kelly is the Norse
Kjallak : however, O' Kelly does not occur in Ireland as a topographical name
so early as the time of Ethelred II. The name Ulfkel is of rare occurrence :
one Thollak Ulfgelson, or Thorlak Ulfgestson, is, however, mentioned in Inge
Bardson's Saga. The other reading, UlfreksQor^r, seems to point to that branch
of Morecambe Bay, in Lancashire, which runs up to Ulverstone.

The principal towns specified on the Map are Dyflin, Hlimrek, and Ve'Sra-
fjiir^r. Dyflin is a slightly modified adaptation of Ouib-linn, the Irish name of
Dublin. The opinion that the metropolis of Ireland was founded by the Danes
can be easily confuted from its want of an original Norse name, and more satisfacto-
rily from the consideration that it was a bishop's see before the arrival of the North-
men, and contained within its precincts a round tower, and a place of worship
sacred to St. Michan (which is still perpetuated in the church of that name), as
mentioned in the Calendar of Aengus, which dates so early as the eighth cen-
tury. Hlimrek, in like manner, appears to be an adaptation of Luimneac, the
Irish name of Limerick, for which various derivations have been proposed,
and which was certainly an ancient appellation of the Lower Shannon. VeSra-
Qor^r, on the contrary, or Waterford, is pure Norse ; and its etymology is

88 Mr. DowNES on the Norse Geography of Ancient Ireland.

given in the notes to the Death-Song of Lodbroc, already mentioned, from
vedr, " tempestas" andjiordr, " sinus ;" instead of vedr, fadr, or " father," has
been suggested, meaning Odin ; and the reading Vatsjiord, equivalent to
Vatnsfj6r'(,r — the name of tvpo localities in Iceland — is given in the Antiquitates
Celto- Scandicce : of this reading Waterford is an exact translation; hov?ever,
it would appear that Johnstone's derivation is to be preferred. A townland, de-
signated BaUyvedra alias Weatherstown, exists in the neighbourhood of Wa-
terford ; but it seems not unlikely that it owes its name to the family of Madray,
long settled in that part of the country. However this be, there is, perhaps, no
district in Ireland more essentially Danish than the vicinity of Waterford. Hence
it is the opinion of a high authority, that even the Irish name of that city, Port-
largy, is derivable from the name of some northern warrior, perhaps the Larac,
mentioned in the Annals of the Four Masters at the year 951, as having wasted
Tigh Moling, on the Barrow, now St. MuUin's. There appears, however, to
be a connexion between the name of the adjacent locality Portlaw, derived from
laim, "hand," and Portlargy, derived from laipje, "thigh," to the shape of
which member of the body the harbour is supposed to bear some resemblance.

Kunnjdttaborg, though laid down as an extensive district, would, from its
termination, seem rather to have been a town, or castle. The nuptials of Brian
Boru with Gormllath, whose Norse name is Kormlod, are recorded to have
been solemnized at Kunnjattaborg ; but in the Niala — a Saga of great authority,
called after the distinguished Nlal, by whom, about the year 1000, a kind of
law-school was established in Iceland — the name is given asKantaraborg, which,
as Brian was king of Munster, Schonlng identifies with Carbury, in the county
of Cork. The Danish writer, however, infers from the context, that, notwith-
standing its final syllable, the word is rather applicable to a tract of country; and
this tract he, rightly and much to his credit, finds in Kiennachtabregh, or Bregia,
in the county of Meath, which was within the range of Brian's conquests. In
Johnstone's Antiquitates Celto- Scandicce the reading Kunnaktirborg is given,
and rendered ^'urbi Connacice." It seems strange that this reading Is not no-
ticed by the Danish writer : it must, however, be remembered, that both the
text and version, in the work wherein it occurs, should be always consulted with
suspicion. I say this by no means in disparagement of an industrious pioneer,
who published sixty years ago, when the Arna-Magnaean Commission had but

Mr. Down Es on the Norse Geography of Ancient Ireland. 89

lately begun their severe labour of deciphering and collating the Icelandic ma-
nuscripts. Kantaraborgar is also given by Johnstone, and rendered similarly
" urbem Connacice"

Iniskillen is laid down, and described by the Danish writer, after the Royal
Mirror, as a small island in Logherne, called in some manuscripts Misdredan —
an ocular misconception of Inisdredan — in which a certain holy man, named
Diermicius, possessed a church. The variations of orthography in the name con-
cluded to be Iniskillen, as given in the Antiquitates Celto- Scandicce, are so ex-
traordinary as to render identification almost hopeless. Among the readings is
Inhiskladran, perhaps Inkclothran in Lough Ree — cited as Inis-Cloghran by
the Danish writer — where an abbot, named Dermit, resided. The site of the
island may have been assigned to a wrong lake, or to the right one with some
distortion of the name : Ree is convertible into Erne by a much less violent
alteration than the name of the island has itself undergone.

Tara \^Teamuir'\ and Glendaloch are likewise laid down after the Royal
Mirror, in their Norse form, as Themar and Glendelaga, but the latter place
is in the Essay located in Ulster.

There remains but one more Norse locality on the earlier Map, namely,
Smjorvik, now Smerwick, on the coast of Kerry. The name is to all appearance
Norse, but respecting its origin the Danish writer offers no opinion. The ter-
mination wick or ivich (the Norse vik), so frequent in these countries, both in
Scandinavian and Saxon localities, whether maritime or inland, is supposed to
derive its applicability to either a bay or town, from the idea o{ protection im-
plied in both. Although, as I shall hereafter show, there is room for doubting
that the first syllable was originally Smjor, there are plausible grounds for this
supposition. The word smjor, "butter," was in the North a frequent and some-
times absurd element both in local and personal names, as in those of Butter-
waterheath in Iceland, Bjarn Caskbutter, Einar Butterback, Archbishop John
Butterbelt, and Thorolf, who earned a nickname for life, by asserting that but-
ter dripped from every blade of grass in Iceland. But the name Smerwick may
have originated in a more important circumstance. That the Northmen carried
on some kind of traffic with the south-west of Ireland would appear even from
the surname of Hlymreksfari, or " Limerick trader," which was given to one
Hrafn, who is supposed to have fought under the banner of Sigurd, earl of Orkney,
VOL. XIX. m

90 Mr. DowNES on the Norse Geography of Ancient Ireland.

at the battle of Clontarf. One article of this traffic may have been butter ; and it is
possible that Smerwick Harbour may have been in some way connected with a trade
in this commodity.* The following curious tradition, to the sequel of which I shall
have occasion to advert hereafter, shows at least, that on one of their homeward
voyages from Ireland the Northmen had butter on board, either as an article of
traffic, or diet. The sea-rover Leif, son of Hrodmar (who must not be con-
founded with the more celebrated Leif, son to Erick the Red), while ravaging
the shores of Ireland, came to a large subterraneous house, lighted only by the
gleaming of a sword, held by a man who had taken refuge within, but was slain
by the Northman, who was thenceforward called Hjbrleif, or " Sword-Leif,"
from the weapon, which was of great value. After continuing his devastations
along a great extent of coast, Leif at length sailed for Norway, conveying, with
other booty, ten or twelve Irish slaves, among whom one, named Duvthak, had
the pre-eminence. In the following spring Leif sailed for Iceland with his slaves,
accompanied by his foster-brother Ingolf, each in his own ship. The latter, on ap-
proaching the shore, flung overboard, according to usage, the columnar posts of
the chief seat in his paternal mansion (which usually ended atop in the sculptured
head of some deity, generally that of Thor) ; and at the spot where they were

• In an interesting paper on the Antiquities of the Church of Kilmelchedor, read before the
Academy on the 11th of April, 1842, my derivation of Smerwick, from a word signifying butter,
was treated as an absurdity, and the commission of it imputed to the Danish antiquaries, who, as I
have stated in the text, are quite silent on the subject. The charge was grounded on the state of Smer-
wick Harbour, which was asserted to be so dangerous that no vessel could safely ride in it for many
hours, even in the calmest weather. That this is a correct representation of its present state I en-
tertain no doubt ; but what says Dr. Smith, who wrote many centuries after the district was visited
by the Northmen ? " Beyond these is the haven of Smerewick, which lies up from N. to S., and is
exposed to N. and W. winds. The whole is deep and good holding ground, the bottom being
actually a turf bog, which vessels have pulled up with their anchors, which shews that it was once
dry land: there is no danger in sailing into this place." — The Antient and Present State of
the Counlxj of Kerry, p. 360.

In the same paper another derivation of the name Smerwick was proposed, from the Irish pin-up
(which is cognate both with the Icelandic smjor and the English smear), the inlet in question hav-
ing a tendency to spread its waters over the adjacent shores. But, conceding for the sake of ar-
gument that the first syllable of the name is the Irish pmdup, I would ask, whether the poverty
of the ancient language of Ireland was such, as to render it necessary to send to Iceland for the se-
cond syllable, expressive of so familiar an idea as harbour, or bay ?

Mr. DowNES on the Norse Geography of Ancient Ireland. 91

drifted ashore he founded the colony of Ingolfshbf^i, or " Cape Ingolf." Leif,
meanwhile, was driven so far westward, that the fresh water on board became
at length exhausted, upon which one of the Irish slaves kneaded meal and butter
together, asserting that this mixture would allay thirst. Rain falling soon after,
what remained of the mynn]>ak, as the mixture was called by the slaves — and the
first syllable of which word appears to be the Irish mm, " meal" — was thrown
overboard ; and the place on the southern coast of Iceland, where it was drifted
ashore, was thence named Mynn\pakseyri, " Cape," or rather " Strand — Mynn-
>ak."

But the word Smerwick admits of a more dignified etymology. By Fynes
Moryson this locality is designated " St. Mary Wic, vulgarly called Smerwick,"
and on Mercator's map as " Smerwik als S* Mary wyk." Of these names,
the one would appear to be a contraction of the other : nor will this contraction
seem forced when it is recollected, that Marie-la-Bonne has been degraded into
Marrowbone, as the name of a lane in this city, — and seems also to have become,
in a translated form, the parent of another word, very different both in sound and
associations, namely, gossamer, good St. Mary — in French, y?/ de la bonne vierge —
or, perhaps, gauze o' Mary (which is substantially a translation of the French
expression), though the last syllable has been otherwise derived, from the French
mere {mere de Dieu). Had the Danish writer been aware of the above expla-
nation of Smerwick, he would doubtless have adverted to it in connexion with
the Map, especially as a passage in Olave Tryggvason's Saga appears to throw a
little twilight on the obscure subject. It is recorded of this celebrated wanderer,
that in the year 993, when about twenty years of age, he was baptized in the largest
of the Scilly Islands, at a monastery, situated in a place called in Norse, Mariuhbfn,
and still St. Mary's Haven, and that he proceeded thence to England and
Ireland, from which latter country he returned to Norway, two years after his
baptism. Now, as Saxon localities are hardly found in Kerry, the termination wick
seems to ascertain the Norse origin of the word ; and no Northman was more likely
to confer the honour of local perpetuation on the name of Mary than the indi-
vidual, who, in addition to receiving the solemn rite of baptism at a seaport under
her special protection, had been on the same occasion elated by a prediction,
confirmatory of several preceding ones, that he would one day become king of
Norway, which was uttered by the abbot who baptized him. Nay, the very pre-

to2

<)2 Mr. DowNES on the Norse Geography/ 0/ Ancient Ireland.

f'erence of wick to haven, which has nearly the same meaning, would imply the wish
to prevent confusion between two places, separated by only a short navigation.

In addition to the localities already noticed, Kaupmannaey appears on the
more recent Map, at the entrance of Belfast Lough : the English name is not
added, nor is the place mentioned in the Essay. This local name occurs, under an
incorrect plural form, in the Anecdotes of Olave the Black, published by Johnstone,
who translates it " Merchant Isles," but adds, " I know not what isles were so
called." Yet it requires but a slight acquaintance with the northern languages
to recognize Kaupmannaey as Copeland Island, — especially as it may be inferred
from the narrative, that the place was in the vicinity of Cantire and the Isle of
Man : besides, Johnstone was a resident of Copenhagen, and must have been aware
that its name meant " Merchants' Haven." In English, kaup becomes chap in
" chapman," and Chip, as the first syllable of " Chipping" (in such local names
as Chipping Barnet, Chipping Norton, &c.), which is pronounced almost exactly
as the Swedish Raping, however different in orthography, and, like it, signifies
" market." The plural form in Johnstone's publication may have arisen from
grouping the adjacent Light-House Island, and Mew Island, with Copeland : in-
deed the group is called on the spot the Copeland Islands.

To the preceding observations, suggested by the inspection of the Norse Map
of Ireland, I would subjoin a brief consideration of some other localities, which,
though not mentioned in any of the Sagas published antecedently to the Map,
seem equally Norse in their origin with any of its meagre details.

There are three countries, in particular, where the Northmen have left topo-
graphical traces of their invasions, namely, Normandy, Eastland, and the British
Islands. In Normandy, where they achieved a permanent conquest of the entire
land, several classes of local names exist, originally Norse, and unknown in the
rest of France : such are those ending in Jleur, beuf, tot, and others, indicative
of peaceful possession — the final settling-down of the invader, " utfons, ut cam-
pus, ut nemus placuit." In Eastland — called also Eastway, in contradistinction
from Norway — which extended from Mecklenburgh to the White Sea, and included
Vindland, or Northern Sclavonia, they founded a few settlements, which were
exclusively maritime, such as Rostock, and Dantzick (Danes' Wick); (or Stargard,
or " Old Town," the name of two inland localities, is Sclavonian, notwithstanding

Mr. DowNEs on the Norse Geography of Ancient Ireland. 93

its Norse aspect — star being cognate with the word starost, meaning "magistrate,"
or, literally, " elder" (which has been adopted into English by British travellers
in Russia), and gard being equivalent to the Russian gorod, or " town," as in the
name of the celebrated city of Novogorod, the Holmgard of the Northmen. In
Ireland (to omit the other British Islands,) the Northmen never obtained a footing
in the interior ; but as, in addition to planting a few commercial establishments
on its shores, they also, during a long period, carried the trade of war to the very
centre of the country, it seems likely that they would leave some topographical traces
of their presence, and that such would be in some way commemorative of military
enterprise, such, for example, as the fording of a river in the face of the enemy :
and here it may be well to observe, that the meaning of the ievmfwd — a fre-
quent termination of Irish local names — is ambiguous, being equivalent to the
Norse vfoxAfjbr^r, " firth," when applied to a maritime locality, and to the Norse
word y^r^a, or " ford," when applied to an inland one. Examples of the former
application of the term are found in Carlingford and Strangford, names of
undoubted Northern origin, — of the latter, in Odin's Ford, the name of a
locality on the Barrow, near Carlow, which (like Odin's Fields, in the county of
Dublin) appears to owe its name to the great deity of the North, and, perhaps, in
Urlingford, a town in the county of Kilkenny.

While the generality of our local names, terminating mford, are either trans-
lations from the Irish, or originally English, the vernacular name of Urlingford
— Qc Uplann, or "Urlann'sFord" — seems to be an exception. Respecting the
existence of any Irish individual of this name both history and tradition are silent;
but, on turning to the records of the North, the name is found to bear a strong
affinity to one of very frequent occurrence in the annals of Scandinavian warfare.
To what Frling the town in question may be indebted for its name there
are no means of ascertaining, but it may be allowable to offer a conjecture. The
name Urlingford may date from the celebrated expedition of the Norwegian
king, Magnus Barefoot, to Ireland, who, confederated with the Irish king Myr-
jartak, or Murkertach, subjugated in 1103 the greater part of Ulster, and also
Dublin, and Dublinshire already mentioned, from which they may have extended
their conquests into the northern part of the present county of Kilkenny.
Among the chieftains in Magnus's army was a son of Erlend, earl of Orkney,
named Erling, who was slain with the Norwegian king on his second visit to

94 Mr. DowNES on the Norse Geography of Ancient Ireland.

Ulster, and must therefore have been living when the allied monarchs ravaged
Leinster ; and, even if the conjecture that he gave name to Urlingford be
groundless, it may have been called after some other Erling, a participator in one
of the numerous expeditions, undertaken by the Danes from their settlements on
the coast, during which they penetrated even to Clonmacnoise, in the very heart
of the island : as Urling this name appears to be still extant in these countries, in
connexion with a branch of manufacture. It is true that Urlingford is aspi-
rated by the peasantry ; but, as no tradition appears to exist, which would connect
the name with a popular pastime, I would rather suppose the aspirated pronun-
ciation to have originated in the circumstance, that the word hurling expresses
an idea familiar to the mind, which Urling does not, in the same way as Regi-
nald's Tower, on the quay of Waterford, has been converted into Ring Tower,
to which corrupt denomination its round form gave a shade of plausibility.

Wexford, otherwise written Weisford, has a Saxon aspect: it may, how-
ever, mean West j^or^r, or "firth," as the Irish were denominated Westmen
by the Northmen, in contradistinction from the name Eastmen, which they
assumed themselves. Thus Vestmannseyiar, off the south of Iceland, means
" Irishman's Islands ;" and they owe their name to the following circumstance,
which forms the sequel of the tradition respecting Leif, the sea-rover. Hav-
ing at length effected a landing in Iceland, at a place called after him Hjiir-
leifsli6f'6i, or " Cape Hjorleif," where he built two houses, he in the following
spring set about preparing the ground for sowing ; and, although possessed of an
ox, commanded his Irish slaves to yoke themselves to the plough. Duvthak,
thereupon, concerted with his countrymen to destroy the ox, and say that a bear
had killed it ; and, when Leif and some of his followers went in quest of the bear,
the Irish surprised and slew him, after which they fled in boats to the islands just
mentioned, taking with them Leif's wives, and some of his effects. Meanwhile,
two slaves, belonging to his foster-brother Ingolf, while in quest of the columnar
seat-posts which had been flung into the sea, and on which the site of his future
habitation was to depend, discovered the body of Leif, and informed their master
of the circumstance. Ingolf, thereupon, having ascended a promontory to view
the country, and ascertain, if possible, whither the homicides might have fled,
descried the islands, and, rightly conjecturing that they had taken refuge there,
pursued them, and slew them in a place thence called the Slave's Isthmus. As to

Mr. DowNEs on the Norse Geography of Ancient Ireland. 95

the presumed change of st into the x in Wexford, it is borne out by that of Ost-
mentown into Oxmantown, a local name in this city.

Wicklow appears to have been at least partially a northern settlement, its
Ostmen inhabitants being mentioned in history. Its present name is, however,
Saxon, and a modification of Winchiligillo, or Gwykingelo, as Cambrensis writes
it : as an actual Norse locality, the name would terminate in wick (vik).

I shall briefly advert to another class of names, likewise of Norse origin, which
are scattered about all the coasts of the British Islands — I mean those terminating
in ey, " island" (or one of its orthographical variations), which is found in the
Irish aoi, and i, and even in the Hebrew >N, but perhaps in its most extensive
sense of a maritime district. Two examples of this class have been already no-
ticed, namely, the Copeland Islands, and Lambay, or " Lamb Island" — a proba-
ble modification of its earlier Norse name, with ey annexed, and which occurs in
a plural form among the islands of Greenland {Lambeyjar) : to these may be
added the Saltees. The names Dalkey and Dursey are doubtful, being likewise
found far inland. That of a maritime parish, in the northern part of the county of
Dublin, is derived from another Norse word for " island" — I mean Holmpatrick,
a translation of the name of the neighbouring island of Inispatrick. The word
holm implies covering, or concealment, and is usually applied to small uninhabited
islands, as being best suited to such purposes. It is considered cognate with
hialmr, "helmet," and is derived from the verb hylia, "conceal." The consist-
ent first-fruits of the introduction of Christianity into Iceland, in the year 1000,
was the legislative abolition of duelling ; and some desert island was thencefor-
ward chosen as the scene of conflict by individuals, who were too feebly imbued
with the spirit of the mild religion to eschew sanguinary encounters : hence
holmgangr, literally " island-going," became tantamount to "single combat."
In the parish of Holmpatrick is a town, to which a neighbouring cluster of islets
has given the name of Skerries, which in Norse means rocks in the sea, espe-
cially covered ones, and is probably found in the first syllable of the Norman lo-
cality Cherbourg, but which is equally derivable from the Irish f ceip, " sharp
sea rock." Kalfr, "calf," in modern Danish kalv, is a third Norse word for
" island." It is applied to a small object in juxtaposition with a comparatively
large one — for instance, to a hill beside a mountain, or an islet beside an island.
Off the coast of Kerry are three islets — the Bull, the Cow, and the Calf. The

96 Mr. DowNES on the Norse Geography of Ancient Ireland.

last of these is close to Dursey Island, which, though small, is of much greater
extent than the others, and the name Calf is perhaps of Norse origin : those of
Bull and Cow may have been subsequently added, to make out the group, by
persons unacquainted with the local meaning o^calf. However this be, the
Calf of Man is an undoubted example. In Normandy this word is supposed to
be represented by cauf. The investigation of certain ruins, adjacent to one of
the Greenland firths, was impeded by what are in Danish called kalvisen, by a
number of which the firth was blocked up ; this word, doubtless, means " ice-
calves," or small masses of ice in the neighbourhood of large ones. The word
sound, applied to some of our narrow straits, may be likewise of Norse origin.

In conclusion, I would with deference recommend to the attention of the
Irish antiquary, and especially of the topographical and historical investigator,
the hitherto neglected literature of the North. Although the most important
works of the Scandinavian antiquaries are accessible through Latin versions,
their minor publications teem with interesting and rapidly accumulating matter,
locked up in languages which are in this country almost utterly unknown. Yet
the comparative anatomy of antiquities cannot be too extensively cultivated. A
fragment of an ancient object, found in one country, may be elucidated by com-
paring it with a corresponding fragment found in another ; and, what is of still
greater importance, long-established errors may be thus removed. " The short
sword or dagger," with which King, in his account of Richborough, has equipped
a Roman bagpiper, would still maintain its belligerent masquerade, had not the
discovery of a more perfect specimen in Scandinavia proved it to be the more
appropriate appendage of a pipe ; and certain objects, deified in Sweden, the
figures of which have been published by Pennant, might have long maintained
their sanctity, had not the subsequent discovery of more perfect specimens in
Denmark desecrated them into — knife-handles.

END OF VOLUME XIX.

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