Prof. Tait on Listing's Topologie. 31 



of very great importance, and has been recognized as such by- 

 many of the greatest investigators, including Gauss and others; 

 but each, before and after Listing's time, has made his sepa- 

 rate contributions to it without any attempt at establishing a 

 connected account of it as an independent branch of science. 



It is time that a distinctive and unobjectionable name were 

 found for it; and once that is secured, there will soon be a 

 crop of Treatises. What is wanted is an erudite, not neces- 

 sarily a very original, mathematician. The materials already 

 to hand are very numerous. But it is not easy (in English at 

 all events) to find a name for it without coining some alto- 

 gether new word from Latin or Greek roots. Topology has a 

 perfectly definite meaning of its own, altogether unconnected 

 with our subject. Position, with our mathematicians at least, 

 has come to imply measure. Situation is not as yet so defi- 

 nitely associated with measure; for we can speak of a situa- 

 tion to right or left of an object without inquiring how far off. 

 So that till a better term is devised, we may call our subject, 

 in our own language, the Science (not the Geometry, for that 

 implies measure) of Situation. 



Listing, to whom we owe the first rapid and elementary, 

 though highly suggestive, sketch of this science, as well as a 

 developed investigation of one important branch of it, was in 

 many respects a remarkable man. It is to be hoped that 

 much may be recovered from his posthumous papers; for there 

 can be little doubt that in consequence of his disinclination to 

 publish (a disinclination so strong that his best-known dis- 

 covery was actually published for him by another), what we 

 know of his work is a mere fragment of the results of his long 

 and active life. 



In what follows I shall not confine my illustrations to those 

 given by Listing, though I shall use them freely ; but I shall 

 also introduce such as have more prominently forced them- 

 selves on my own mind in connexion mainly with pure phy- 

 sical subjects. It is nearly a quarter of a century since I 

 ceased to be a Professor of Mathematics; and the branches of 

 that great science which I have since cultivated are especially 

 those which have immediate bearing on Physics. But the 

 subject before us is so extensive that, even with this restric- 

 tion, there would be ample material, in my own reading, for a 

 whole series of strictly elementary lectures. 



I ought not to omit to say, before proceeding to our busi- 

 ness, that it is by no means creditable to British science to 

 find that Listing's papers on this subject — the Vorstudien zur 

 Topologie (Gottinger Studien, 1847), and Der Census raum- 

 licher Complete {Gottinger Abhandlungen } 1861) — have not 



