4 REPORT— 1883. 
the Association, one who has done for it so much, and has so often 
attended the meetings, whose presence among us at this meeting we 
might have hoped for—the President of the Royal Society, William 
Spottiswoode. It is unnecessary to say anything of his various merits : 
the place of his burial, the crowd of sorrowing friends who were present 
in the Abbey, bear witness to the esteem in which he was held. 
I take the opportunity of mentioning the completion of a work pro- 
moted by the Association: the determination by Mr. James Glaisher of — 
the least factors of the missing three out of the first nine million numbers : 
the volume containing the sixth million is now published. 
I wish to speak to you to-night upon Mathematics. I am quite aware 
of the difficulty arising from the abstract nature of my subject; and if, 
as I fear, many or some of yon, recalling the Presidential Addresses at 
former meetings—for instance, the réswmé and survey which we had at 
York of the progress, during the half-century of the lifetime of the Asso- 
ciation, of a whole circle of sciences—Biology, Paleontology, Geology, 
Astronomy, Chemistry—so much more familiar to you, and in which 
there was so much to tell of the fairy-tales of science; or at South- 
ampton, the discourse of my friend who has in such kind terms intro- 
duced me to you, on the wondrous practical applications of science to 
electric lighting, telegraphy, the St. Gothard Tunnel and the Suez ~ 
Canal, gun-cotton, and a host of other purposes, and with the grand 
concluding speculation on the conservation of solar energy: if, I say, 
recalling these or any earlier Addresses, you should wish that you were 
now about to have, from a different President, a discourse on a different — 
subject, I can very well sympathise with you in the feeling. 
But, be this as it may, I think it is more respectful to you that ie 
should speak to you upon and do my best to interest you in the subject 
which has occupied me, and in which I am myself most interested. And_ 
in another point of view, I think it is right that the Address of a Presi- 
dent should be on his own subject, and that different subjects should be 
thus brought in turn before the meetings. So much the worse, it may 
be, for a particular meeting; but the meeting is the individual, which 
on evolution principles must be sacrificed fae the development of the 
race. 
Mathematics connect themselves on the one side with common life 
and the physical sciences; on the other side with philosophy, in regard 
to our notions of space and time, and in the questions which have arisen 
as to the universality and necessity of the truths of mathematics, and the 
foundation of our knowledge of them. I would remark here that the 
connection (if it exists) of arithmetic and algebra with the notion of time 
is far less obvious than that of geometry with the notion of space. 
As to the former side, I am not making before you a defence of 
mathematics, but if I were I should desire to te it—in such manner as in 
the ‘Republic’ Socrates was required to defend justice—quite irrespectively 
of the worldly advantages which may accompany a life of virtue and 
