620 
NATURE 
[ Oct. 29, 1885 
“ Take your head from the stars or from transcendental 
mathematics and come and enjoy Folly and Friendship.” 
There are also copious letters to and from Aubrey De 
Vere, Lord Dunraven, the Marquis of Northampton, and 
many others, including not a few to his intimate friend 
the author of the present work; one of these we would 
specially mention (p. 357), in which Hamilton sketches 
the obligations of true friendship. The scientific corre- 
spondence of Hamilton with many of the leading philo- 
sophers of the last generation occupies, as might have 
been expected, a large proportion of the volume. 
At successive meetings of the British Association 
Hamilton was a well-known and a conspicuous figure. 
When the Association visited Dublin in 1835 he was but 
thirty years old, yet he had already attained a scientific 
renown which made him perhaps the most eminent man 
at that meeting. It was on this occasion that the Board 
of Trinity College entertained the distinguished visitors at 
a banquet. The guests had assembled in the venerable 
library of the University. The Earl of Mulgrave, then 
Lord Lieutenant of Ireland, called Hamilton to the centre 
of a little circle, and, after conferring upon him the honour 
of knighthood, said :— 
“T but set the Royal, and, therefore, the national mark 
on a distinction already acquired by your genius and 
labours” (p. 158). 
In speaking at the banquet subsequently, Whewell said, 
in language which the enthusiasm of the moment might 
perhaps excuse :— 
“Tt was now one hundred and thirty years since a 
great man in another Trinity College knelt down before 
his Sovereign and rose up Sir Isaac Newton ” (p. 159). 
In the year 1842 Sir R. Murchison, then general secre- 
tary of the Association, writes to Hamilton as follows 
(p. 387) :— 
“Your letter of the 16th having crossed mine, 7 am 77 
despair at your resolution not to visit Manchester ; and in 
order to shake it if possible, even at the eleventh hour, I 
enclose you a letter from Herschel, whose resolutions were 
quite as firm as yours, and who yet has made them fly 
before Bessel. Think of this philosopher coming on 
purpose to see such men as Herschel, yourself, and two 
or three others, and finding Airy and Baily flown to Italy 
and Sir William Hamilton /ecturzng in Dublin!! Pray 
put off your class for a week. Make a noble effort and 
lay it all on Bessel’s shoulders, and you will add to your 
glory.” 
On this occasion Hamilton had also the gratification of 
meeting the great mathematician Jacobi, who, after 
referring to Hamilton as the “ Lagrange of your country,” 
said (p. 388) :— 
“Provided that we give to the dynamical equations 
that remarkable form under which they have been pre- 
sented for the first time by the illustrious Astronomer 
Royal of Dublin, and in which they ought to be presented 
hereafter, in all the general researches of analytical 
mechanics.” 
We also read how Hamilton was received at the Oxford 
meeting in 1847, in which, to quote his own words from a 
letter to the author, he says (p. 585) :— 
“Tt has several times happened to me to sit between 
Struve and Le Verrier (both of whom, somewhat to my 
surprise, and certainly beyond my deserts, assigned to 
me a high place among British astronomers in their 
speeches at the concluding meeting). And when I rose to 
give an account of the application of the calculus of 
quaternions to the theory of the moon on the Thursday 
of last week, and saw before me not only those two 
eminent foreign astronomers, but also Herschel, and Airy, 
and Adams, and Challis, besides Peacock and Whewell, 
and others scarcely less distinguished, I could not refrain 
from acknowledging it to be an alarming and almost an 
awful thing to speak on any subject of physical astronomy 
in the presence of such an audience.” 
Hamilton also records in an unsent letter the following, 
which refers to the same meeting (p. 585) :— 
“My friend Struve, of Russia, at Oxford, 1847, said; 
that, though I held the title of Royal Astronomer of Ire- 
land, my astronomical brethren on the Continent would 
decidedly prefer my never looking through the telescope 
to my giving up or less ardently pursuing mathematics. 
‘You are,’ he was pleased to say, ‘our teacher.’” 
Hamilton was for many years not only the most dis- 
tinguished member of the Royal Irish Academy but also 
its president. Many interesting letters will be found in 
the volume relating to his election to this distinguished 
post. His rival, if so he can be called in what Hamilton 
describes as a “contest of generosity,” was the late 
Provost Lloyd. Lloyd retired in favour of his friend, and 
Hamilton writes many letters, the character of which is 
fairly represented by one to Lloyd (p. 218), in which he 
disclaims 
“ Entertaining even a thought which could be construed 
into ¢veason to our long and unclouded friendship, and 
that the part yow have taken (while in some respects it 
adds to my pain) furnishes a new proof of the justice of 
the high opinion that I have ever entertained of you.” 
Hamilton discharged in the most exemplary manner 
the laborious duties of President for several years, until, 
as he writes (p. 510) :— 
“The day has at length arrived when I am to accom- 
plish my desire of retiring from the chair of the R.I.A. 
How joyously, though not without a feeling of solemnity, I 
received the news of my being elected to the chair; how 
gladly now I resign it, yet not without a shade of that 
sadness which belongs to a farewell!” 
The chief interest in this volume will be found in the 
account of the great invention of quaternions, with which 
the name of Hamilton will be for ever associated. His 
own appreciation of the importance of this achievement 
is shown in an extract from a letter to Prof. Lloyd in 
December, 1851 (p. 445) :— 
“In general, although in one sense I hope that I am 
actually growing modest about the quaternions, from my 
seeing so many peeps and vistas into future expansions 
of their principles, I still must assert that this discovery 
appears to me to be as important for the middle of the 
nineteenth century as the discovery of Fluxions was for 
the close of the seventeenth.” 
The account of the discovery which, after fifteen years 
of studious meditation, seems suddenly to have flashed 
upon Hamilton is told in an interesting letter written from 
his deathbed many years later to his son Archibald 
(August 5, 1865), p. 434 :— 
“On the 16th day of October, 1843, which happened to 
be Monday, and a council day of the Academy, I was 
walking in to attend and preside, and your mother was 
walking with me along the Royal Canal, to which she 
had perhaps driven ; and although she talked with me 
now and then, yet an wsdercurrent of thought was going 
on in my mind which gave at last a vesw/t, whereof it is 
