218 
NATURE 
[ Yan. 4, 1883 
a cousin of Euclid, had given me no prejudice in favour 
of the family. But in the first glance at the book, when I 
came to ‘a line is length without breadth,’ I felt that I 
had gained expression for an idea which I distinctly 
possessed by image, but could not have put into words. 
And so, in a small way, I found that geometry dd exist 
as a science.” 
Before we leave these records of his school-days, we 
will cite some further remarks on the modes of instruction 
then in vogue—which, by his books, he more than any 
other writer helped to improve. When a boy arrives at 
school, “he is taught to say the table of numeration, and 
then proceeds through a number of rules . . . which, if 
he understand, it is well, but if not, nobody cares. ... 
As to the reasons for the rules, the pupil cannot trouble 
his head (to use a common term for that much-avoided 
operation, thinking) about them, not knowing whether 
there are any at all, or whether the rules themselves 
came from the moon, or are a constituent part of that 
wisdom of our ancestors about which he sometimes hears. 
Should there be any natural defect in his mind, owing to 
which he finds it difficult to produce a correct result, 
knowing neither what he is to do, nor how to do it, there 
are several approved methods of proceeding. The best 
of these, unfortunately now somewhat exploded, is a 
flogging ; which works on a principle recommended by 
physicians, of curing a disorder in a part which cannot 
be got at, by producing one in another which can, Next 
to this, comes the method of keeping the patient from all 
recreation until he has done what is required of him, it 
being considered the same thing in the end, whether he 
cannot work for want of means, or will not from want of 
application. It has been suggested to teach the principles 
involved in the rules, and thus to render the pupil their 
master instead of their slave; but to this plan, inde- 
pendently of its being an innovation, there are grave 
objections.”’? 
At the age of sixteen years and a half he entered at 
Trinity College, Cambridge, and in 1825 gained a Trinity 
Scholarship. Devoting much of his time to music and 
to a rather wide range of reading (he had always “an 
insatiable appetite for novel-reading . . . let it be good 
or bad in a literary point of view, almost any work of 
fiction was welcome, provided it had plenty of incident 
and dialogue, and was not over-sentimental”’ *) he failed 
to attain the highest place in the Tripos, but came out 
Fourth Wrangler in 1827. Mrs. De Morgan notes that this 
failure, in a possibly fallacious test, was his own early, 
but unintentional, protest against competitive examina- 
tions, for which he felt excessive disapprobation even 
before his experience as a teacher showed him not only 
their mischievous effect upon mind and health, but their 
insufficiency to determine the real worth of a candidate 
for Honours (pp. 18, 56, 169). In connection with this 
subject we may mention that he had a great objection to 
marks in looking over examination papers. He said he 
could judge of the merits of the competitor from the whole 
t “On Infinity; and on the Sign of Equality.” Camb. Phil. Soc. Trans., 
vo!. xi. Part 1. 
2 From a paper “On Mathematical Instruction,’’ which, with four other 
parers by De Morgan, is reprinted (from the Quarterly Fournal of Educa- 
n) in the Schoolmaster, vol. ii., 1836. The five papers amply repay 
perusal even at the present date. 
3 In reference to this period of his life, he writes (1869, p. 393), “ I read 
n enormous deal of fiction—all I could get hold of—so my amusement was 
ot all philosophical.’” 
work, but he could not reckon it up by marks, and he 
always refused to examine in this way. 
Having conscientious scruples about the doctrines of 
the Established Church, he was prevented from proceeding 
to his M.A. degree and from sitting for a Fellowship, to 
which he would doubtless have been elected. “A strong 
repugnance to any sectarian restraints upon the freedom 
of opinion was one of De Morgan’s characteristics 
throughout life.” A further career at the University 
being thus closed against him, and having abandoned 
the study of medicine, he turned his thoughts to law, and 
entered at Lincoln’s Inn. The establishment in 1828 of 
the London University—now University College—however 
gave him the opportunity of leaving the study of the Law, 
“‘ which he did not like,” for the teaching and pursuit of 
science. At the age of twenty-two, though much younger 
than any of the other thirty-one candidates? for the post, 
he was unanimously elected to the Chair of Mathematics. 
From this time, with the exception of an interval of five 
years,” he devoted himself with the greatest assiduity to 
the duties of the post until his final resignation in 1866. 
It has been frequently remarked that De Morgan was 
unrivalled as a teacher of mathematics, and certainly no 
teaching in our University experience ever approached 
his in the faintest degree. Mr. Sedley Taylor writes :— 
De Morgan regularly delivered four courses of lectures, 
each of three hours a week, and lasting throughout the 
whole academical year. He thus lectured two hours 
every day to his College classes, besides giving a course 
addressed to schoolmasters in the evening, during a 
portion of the year . . . De Morgan was far from thinking 
the duties of his chair adequately performed by lecturing 
only. At the close of every lecture in each course he 
gave out a number of problems and examples illustrative 
of the subject which was then engaging the attention of 
the class. His students were expected to bring these to 
him worked out. He then looked them over, and returned 
them revised before the next lecture. Each example, if 
rightly done, was carefully marked with a tick, or if a 
mere inaccuracy occurred in the working it was crossed 
out, and the proper correction inserted. If, however, a 
mistake of Jrincifle was committed, the words ‘show me’ 
appeared on the exercise.’ The student so summoned 
was expected to present himself on the platform at the 
close of the lecture, when De Morgan would carefully go 
over the point with him privately, and endeavour to clear 
up whatever difficulty he experienced. The amount of 
labour thus involved was very considerable, as the 
number of students in attendance frequently exceeded 
one hundred. The claims which University or 
College examinations might be supposed to have on the 
studies of his pupils were never allowed to influence his 
programme in the slightest degree. He laboured to form 
sound scientific mathematicians, and, if he succeeded in 
this, cared little whether his pupils could reproduce more 
or less of their knowledge on paper ina giventime... 
all cram he held in the most sovereign contempt. I 
remember, during the last week of his course which 
preceded an annual College examination, his abruptly 
addressing his class as follows: ‘I notice that many of 
you have left off working my examples this week. I know 
perfectly well what you are doing ; YOU ARE CRAMMING 
FOR THE EXAMINATION. But I will set you such a 
paper as shall make ALL YOUR CRAM of no use.’ .. . De 
« Ina letter to Sir J. Herschel, August 9, 1862 (p. 312), De Morgan says, 
“«T was picked out of fifty candidates.”’ 
2 In consequence of a disagreement with the Council he resigned his Pro- 
fessorship, July 24, 1831. On the death of his successor, in October, 1836, 
he was requested to resume his office, and did so. 
3 The exercises were placed in a case of pigeon-holes hung on the wall 
near the entrance to the Mathematical Theatre. 
