Narch 
23) 
i8; 1] 

on artisans.” The Department desires to call the serious 
attention of the Committees of Schools to this instruction 
where fees are not imposed. They fiud that in some 
places not only is there an entire abscnce of fees, but that 
there has even been an unseemly competition on the part 
of teachers to get students by any means to join their 
classcs with a view of earning the payments on results, 
They therefore give notice to the Committees of Schools 
that unless they themselves take steps to remedy the pre- 
sent evils by imposing at least some small fees, which 
should Le paid to the Committee direct, it will be neces- 
sary to reduce the amount of the payments on results. 
They have no wish to reduce the payiments on results at 
present, and they would avoid as long as possible the im- 
position of new conditions which necessarily complicate the 
system of aid, and 1ender the rules burdensome and diffi- 
cult to work under, but the want of proper vigilance on 
the part of the Committees may render this step neces- 
sar). 

AUGUSTUS DE MORGAN 
HOSE readers of NATURE who are in the habit of 
examining the obituary column of the Ziwes, will 
have regretted to see, on Monday morning last, the 
announcement of the death of the eminent mathematician, 
Augustus De Morgan. He had been seriously ill for the 
past two years. A disease of the kidneys, complicated 
with other disorders, had reduced him to a shadow of his 
former self, and rendered him incapable of any protracted 
exertion. This was the more trying as his mind retained 
all its former energy, and the doctors forbade his reading 
more than an hour or two in the day. He was, however, 
allowed to see his friends, and often amused and instructed 
them by the hour together from the stores of his extra- 
ordinary memory. During the last few weeks he had 
become considerably weaker, and on Saturday the 18th, 
at one o'clock in the afternoon, his spirit was released 
from the body which for so many months had been only 
a burden to it. 
Augustus De Morgan was the son of a Colonel in the 
Madras army. He could trace his descent from the 
mathematician, James Dodson, author of the “ Anti-Loga- 
rithmic Canon.” He was born in the summer of 1806, in 
Southe:n India. While yet a school-boy, he showed his 
taste for mathematics by filling thick notebooks with “ in- 
finite series,” which he interspersed with grotesque figures 
and quaint faces. In 1823 he went to Cambridge, where 
he entered at Trinity College; his rooms were in the 
south-east corner of the great court, then called “ Mutton 
Hole Corner,” which he affirmed was a contraction from 
Merton Hall Corner, 
in the tripos of 1827 he was Fourth Wrangler, but he 
never proceeded to the degree of M.A., owing to his 
objection to subscribe to the tests, and it is sad to think 
that the same conscientious scruples debarred this illus- 
trious man from a Fellowship. On leaving Cambridge 
he entered at Lincoln’s Inn, and would have forsaken 
Mathematics for the study of the Law, but that in 1828, 
the London University, now University College, was 
founded, and he was offered the Professorship of Mathe- 
matics there, which he accepted, and rémained a firm 
supporter of the College and its principle of no tests till 
the year 1866, when the Council, in making an appoint- 
ment to the chair of Logic and Mental Philosophy, 
refused, as the Professor believed, one of the candidates on 
account of his religious opinions. Prof. De Morgan remon- 
strated, but his remonstrances weie disregarded. He 
then thought it his duty to inform them that he must 
forsake the College if the College forsook its principles. 
But the Council turned a deaf ear ; and Prof. de Morgan, 
who had for nearly forty years been the chief honour and 
ornament of their institution, left them, and, we are in- 
formed, never afterwards entered their gates. 
NATURE 
409 




To estimate the energy of the Professor we must 
look at him not only as a teacher of mathematics, but 
as a mathematician, an actuary, a logician, an_his- 
tonan, a biographer, and a bibliophile. First, then, as a 
teacher of mathematics perhaps no man has been more 
Successful in training distinguished mathematicians. 
Amongst the latter we may mention the names of Prof. 
Clifton. Judge Hargreave, Mr. Routh, and Mr. Todhunter, 
Prof. Sylvester also attended his leciures, though the rc- 
lationship of professor and pupil did not in this case last 
very long. Hehada method of interesting his hearers in 
| the subjects on which he lectured, and of making them love 
mathematics forits own sake, which few other men have ever 
attained to. He expended a great deal of work upon his 
classes. The subject-matter of every lecture which he 
delivered was entered in a note-book and sent into the 
library of the college for the benefit of his pupils while 
writing out and expanding their own notes. 
_As a mathematician, his work was so various that it is 
difficult for any one man to review it, and it would be out 
of place to attempt anything of the kind here ; but we 
may allude in passing to his double algebra, which was 
ce1tainly the forerunner of Quarternions, and contained the 
geometrical interpretation of the symbol ,/—1. Sir W. 
1X. Hamilton, in the preface to his Lectures on Quaternions, 
p- 41, says, “ But I wish to mention that among the 
circumstances which assisted to prevent me from losing 
sight of the general subjects, and from wholly abandoning 
the attempt to turn to some useful account those early 
speculations of mine, on triplets and on sets, was probably 
tLe publication of Prof. De Morgan’s first paper on the 
‘Foundation of Algebra,’ of which hesent mea copy in 1841.” 
As a writer of mathematical text books, he took the 
highest rank, his books being more suitable, Lowever, for 
teachers than for pupils. They were characterised by 
extreme clearness, exhaustiveness, and suggestiveness. 
Perhaps those best known are his ‘‘ Elements of Arith- 
metic,” published 1830 ; his “ Elements of Algebra,” pub- 
lished 1835 ; and his “ Differential and Integral Calculus, 
with elementary illustrations,” which is a perfect mine of 
original thought, and in which some of the most important 
extensions which the subject has since received, are dis- 
tinctly indicated, and it was published by the Society for 
the Diffusion of Useful Knowledge. 
As an actuary he occupied the first place, though he 
was not directly associated with any particular office, but 
his opinion was sought for on all sides, by actuaries, on 
questions connected with the theory of probabilities as 
applied to life contingencies. In 1838 he wrote his “ Essay 
on Probabilities,” which still retains a high place among 
the literature of insurance offices. 
As a logician he was well known, and his “ Formal 
Logic,” together with the Treatise of Mr. Boole, may be 
said to have created a new era in logical science. His 
controversy with Sir William Hamilton will long be re- 
membered, 
As an historian and biographer, the English Evcyc/o- 
pedia says of him that “he had a great affection for, and 
an extensive and minute erudition in, all kinds of literary 
history, biography, and antiquities.” He was one of the 
most extensive contributors to the Penny Cyclopedia, 
many of the articles of scientific biography having been 
written by him, as well as most of the mathematical and 
astronomical articles. The lives of Newton and Halley 
in Knight’s “ British Worthies,” were also from his pen. 
As a bibliophile, his “ Arithmetical Books from the 
Invention of Printing to the Present Time, 1847,” and his 
“ Budget of Paradoxes” will long remain celebrated. He 
was the possessor of a very large collection of old mathe- 
matical works, ‘ 
In addition to this the Professor contributed largely to 
the Philosophical Magazine, the North British Review, 
the A/hen@um, and the Transactions of the Cambridge 
Philosophical Society, in which he published most of his 
