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SCIENCE. 



[N. S. Vol. XXII. No. 5S6. 



notions as to the nature and properties of 

 analytic functionality; a discussion of the 

 hypotheses upon which a consistent system 

 of geometry can be framed could be made 

 as monumental as his ambition might 

 choose ; he could revel in an account of the 

 most recent philosophical analysis of the 

 foundations of mathematics, even of logic 

 itself, in which all axioms must either be 

 proved or be compounded of notions that 

 defy resolution by the human intellect at 

 the present day. Such discussions are 

 bound to be excessively technical unless 

 they are expressed in unmathematical phra- 

 seology; when they are so expressed, and 

 in so far as such expression is possible, they 

 become very long and they can be very thin. 

 Moreover, had I chosen any topic of this 

 character, it would have been the merest 

 natural justice to have given early utter- 

 ance of the sibyllic warning to the unini- 

 tiated; I must also have bidden the initi- 

 ated that, as they come, they should sum- 

 mon all the courage of their souls. So I 

 abstain from making such an experiment 

 upon an unwarned audience ; yet it is with 

 reluctance that I have avoided subjects 

 in the range which to me is of peculiar 

 interest. 



On the other hand, I must ask your in- 

 dulgence for not conforming to average 

 practice and expectation. My desire is to 

 mark the present occasion by an address of 

 Tinspecialized type which, while it is bound 

 to be mainly mathematical in tenor, and 

 while it will contain no new information, 

 may do little more than recall some facts 

 that are known, and will comment briefly 

 upon obvious tendencies. Let me beg you 

 to believe that it is no straining after 

 novelty which has dictated my choice ; such 

 an ambition has a hateful facility of being 

 fatal both to the performer and to the pur- 

 pose. It is the strangeness of our circum- 

 stances, in both place and time, that has 



suggested my subject. With an adven- 

 turous audacity that quite overcrows the 

 spirit of any of its past enterprises, the 

 British Association for the Advancement 

 of Science has traveled south of the Equa- 

 tor and, in accepting your hospitality, pro- 

 poses to traverse much of South Africa. 

 The prophet of old declared that ' many 

 shall run to and fro, and knowledge shall 

 be increased ' ; if the second part of the 

 prophecy is not fulfilled, it will not be for 

 the want of our efforts to fulfill the first 

 part. And if the place and the range of 

 this peripatetic demonstration of our an- 

 nual corporate activity are unusual, the 

 occasion chosen for this enterprise recalls 

 memories that are fundamental in relation 

 to our subject. It is a modern fashion to 

 observe centenaries. In this section we are 

 in the unusual position of being able to ob- 

 serve three scientific centenaries in one and 

 the same year. Accordingly I propose to 

 refer to these in turn, and to indicate a few 

 of the events filling the intervals between 

 them; but my outline can be of only the 

 most summary character, for the scientific 

 history is a history of three hundred years, 

 and, if searching enough, it could include 

 the tale of nearly all mathematical and 

 astronomical and physical science. 



It is exactly three hundred years since 

 Bacon published ' The Advancement of 

 Learning.' His discourse, alike in matter, 

 in thought, in outlook, was in advance of its 

 time, and it exercised no great influence for 

 the years that immediately followed its ap- 

 pearance ; yet that appearance is one of the 

 chief events in the Origins of modern 

 natural science. Taking all knowledge to 

 be his province, he surveys the whole of 

 learning: he deals with the discredits that 

 then could attach to it ; he expounds both 

 the dignity and the influence of its pur- 

 suit ; and he analyzes all learning, whether 

 of things divine or of things human, into 



