TRANSACTIONS OF THE SECTIONS. 
Section A.—MATHEMATICAL AND PHYSICAL SCIENCE. 
PRESIDENT OF THE Section.—Proressor Horace Lamps, M.A., 
PED EBS. 
THURSDAY, AUGUST 18. 
The President delivered the following Address :— 
Tux losses sustained by mathematical science in the past twelvemonth have 
perhaps not been so numerous as in some years, but they include at least one name 
of world-wide import. Those of us who were students of Mathematics thirty or 
forty years ago will recall the delight which we felt in reading the geometrical 
treatises of George Salmon, and the brilliant contrast which they exhibited with 
most of the current text-books of that time. It was from him that many of us 
first learned that a great mathematical theory does not consist of a series of 
detached propositions carefully labelled and arranged like specimens on the shelves 
of a museum, but that it forms an organic whole, instinct with life, and with 
unlimited possibilities of future development. As systematic expositions of the 
actual state of the science, in which enthusiasm for what is new is tempered by a 
due respect for what is old, and in which new and old are brought into harmonious 
relation with each other, these treatises stand almost unrivalled. Whether in 
the originals, or in the guise of translations, they are accounted as classics in every 
university of the world. So far as British universities are concerned, they have 
formed the starting-point of a whole series of works conceived in a similar spirit, 
though naturally not always crowned by the same success. The necessity for this 
kind of work grows, indeed, continually; the modern fragmentary fashion of 
original publication and the numerous channels through which it takes place 
make it difficult for anyone to become initiated into a new scientific theory unless 
he takes it up at the very beginning and follows it diligently throughout its course, 
backwards and forwards, over rough ground and smooth. The classical style of 
memoir, after the manner of Lagrange, or Poisson, or Gauss, complete in itself and 
deliberately composed like a work of art, is continually becoming rarer. It is 
therefore more and more essential that from time to time some one should come 
forward to sort out and arrange the accumulated material, rejecting what has 
proved unimportant, and welding the rest into a connected system. There is 
perhaps a tendency to assume that such work is of secondary importance, and can 
be safely left to subordinate hands. But in reality it makes severe demands on 
even the highest powers; and when these have been available the result has often 
done more for the progress of science than the composition of a dozen monographs 
on isolated points. For proof one need only point to the treatises of Salmon 
himself, or recall (in another field) the debt which we owe to such books as the 
‘ Treatise on Natural Philosophy’ and the ‘Theory of Sound,’ whose authors are 
happily with us. 
A modest but most valuable worker has passed away in the person of Professor 
Allman. His treatise on the history of Greek Geometry, full of learning and 
