1911-12.] Obituary Notices. 493 
a paper on Minding’s theorem, which Tait had shortly before discussed 
by quaternion methods. Chrystal developed the subject in illustration of 
Pliicker’s complexes and congruences. 
After a few years Chrystal found himself compelled to give up experi- 
mental work, in large measure, no doubt, on account of increasing demands 
on his time. The tercentenary celebrations of 1884 were followed by an 
awakened interest in University reform : the mathematics department was 
being rapidly developed, and much of Chrystal’s leisure must have been 
spent in preparing his text-book on Algebra. Also, as he himself once 
said, he found that he was monopolising all the best pieces of apparatus 
in the Physical Laboratory, so that the senior students were seriously 
handicapped. 
The publication of the first volume of ChrystaTi Algebra marked an 
epoch in the teaching of mathematics in our schools and colleges. Already 
in 1885, as President of Section A of the British Association at its meeting 
in Aberdeen, Chrystal had pointed out in clear, unequivocal terms the need 
of a revolution in the presentment of algebraic theory. The following 
quotations are not altogether inapplicable even in these days : — 
“ In the higher teaching, which interests me most, I have to complain 
of the utter neglect of the all-important notion of algebraic form. I found, 
when I first tried to teach University students co-ordinate geometry, that 
I had to go back and teach them algebra over again. ... I found that their 
notion of higher algebra was the solution of harder and harder equations. . . . 
Many examination candidates, who show great facility in reducing 
exceptional equations to quadratics, appear not to have the remotest idea 
before hand of the number of solutions to be expected. . . . The whole 
training consists in example grinding. What should be merely the help to 
attain the end has become the end itself. The result is that algebra, as we 
teach it, is neither an art nor a science, but an ill-digested farrago of rules 
whose object is the solution of examination problems. . . . The end of all 
education nowadays is to fit the student to be examined ; the end of every 
examination not to be an educational instrument, but to be an examination 
which a creditable number of men, however badly taught, shall pass. We 
reap, but we omit to sow. Consequently our examinations, to be what is 
called fair — that is, beyond criticism in the newspapers — must contain 
nothing that is not to be found in the most miserable text-book that any- 
one can cite bearing on the subject. One of my students, for example, who 
was plucked in his M.A. examination — and justly so, if ever man was — 
by the unanimous verdict of three examiners, wrote me an indignant 
letter because he believed, or was assured, that the paper set could not 
