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PRESIDENTIAL ADDRESS TO THE 
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contributed to the Association reports on Magnetic Forces in 1836-7-8, and about 
forty papers to the Philosophical Transactions; originated the system of Magnetic 
Observatories, and otherwise signally promoted the science of Terrestrial Magnetism. 
There is yet a very great loss: another late President and trustee of 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 promoted 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 you, recalling the Presidential Addresses at former meetings—for instance, the 
resume and survey which we had at York of the progress, during the half century 
of the lifetime of the Association, of a whole circle of sciences—Biology, Palaeontology, 
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 Southampton, the discourse 
of my friend who has in such kind terms introduced 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 I 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 President 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 for 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 connexion (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 do it—in such manner as in the Republic Socrates 
was required to defend justice, quite irrespectively of the worldly advantages which