544 
Proceedings of the Royal Society 
abroad, were at once estimated at their true value, and pursued 
with zeal and genius.* 
“ Little by little, first by translating Lacroix’s elementary treatise 
on the differential and integral calculus, and by thus introducing, 
in face of determined opposition, the notation of differential co- 
efficients into Cambridge, so as for the first time to enable her 
mathematicians to understand a foreign treatise ; secondly, by 
publishing an excellent collection of examples; and thirdly, by 
their separate original treatises on different special parts of analysis, 
they put this country on a level with France and G-ermany, so far 
at least as opportunities of progress are concerned. It is to them 
mainly that we owe, not merely our modern British school of 
mathematicians, which is now certainly second to none in the 
world, but even the very possibility of the existence in this country 
of such great departed masters as Boole and Hamilton. 
“ Herschel’s 1 Treatise on Finite Differences,’ which appeared 
as a supplement to the translation of Lacroix, is one of the most 
charming mathematical works ever written, everywhere showing 
* Professor Tait has urged me to make known a reminiscence of my youth 
that at the time here referred to there were in Edinburgh, and in this Society, 
no fewer than three mathematical amateurs, who, though they never made 
themselves publicly felt as such, in some measure saved this corner of the 
land from the censure dealt in the text. These were Sir William Miller, 
Baronet, of Glenlee, better known as Lord Glenlee of the Scottish bench ; 
William Archibald Cadell, of the family of Cadell of Grange, who finished 
his earthly career but a few years ago ; and my own father, Professor of 
Latin in our University. Lord Glenlee, a man of very retiring habits 
and disposition, was usually called the first amateur mathematician in 
Scotland. Mr Cadell, also a man of great reserve and shyness, neverthe- 
less, in order to carry out his admiration of the modern continental mathe- 
matics, contrived to obtain, during the very hottest of our struggles with 
France, from that generally unyielding potentate, the First Napoleon, per- 
mission, through the influence of one of the great mathematicians of Paris, 
to repair to the French capital, to dwell there for seven years, and to return 
unhindered to Scotland, at a period when no other Briton was known to have 
put his foot on French soil without being made a detenu. My father, during 
the last ten years of his life, which ended in 1820, betook himself, as his idea 
of relaxation from routine professional life, to the differential calculus, and 
to Newton, Bernoulli, Euler, Lagrange, Laplace, Lacroix, &c., whose works 
were always at hand when not in his hands. As he made a vigorous attempt 
to indoctrinate me at a very early age in his favourite pursuits, I know well 
what these were, and what he knew of the kindred spirits Glenlee and 
Cadell. 
