33 



which is gone and time which is to come. It is clear 

 that in actual experience there is no process to which 

 such measurements correspond. Time has no meaning 

 except as future or past; and the present is but the 

 meeting point of the two. Or, once more, suppose that 

 we are gravely told that all circles pass through the 

 same two imaginary points at an infinite distance, and 

 that every line drawn through one of these points is 

 perjJendicular to itself. On hearing the statement we 

 shall probably whisper, with a smile or a sigh, that we 

 hope it is not true, but that in any case it is a long way 

 off, and perhaps, after all, it does not very much signify. 

 If, however, we are not satisfied to dismiss the question 

 on these terms, the Mathematician himself must admit 

 that we have here reached a definite point of issue. 

 Our Science must either give a rational accoimt of the 

 dilemma, or yield the position as no longer tenable. 



Special modes of explaining this anomalous state of ExplaDation 

 things have occurred to Mathematicians. But, omit- ^ ^^^^^^* 

 ting details as un suited to the present occasion, it will, 

 I think, be sufficient to point out in general terms that 

 a solution of the difficulty is to be found in the fact 

 that the formulae which give rise to these results are 

 more comprehensive than the signification which has been 

 given to them ; and when we pass out of the condition 

 of things first contemplated they cannot (as it is obvious 

 they ought not) give us any results intelligible on 

 that basis. But it does not therefore by any means 

 follow that upon a more enlarged basis the formulas 

 are incapable of interpretation ; on the contrary, the 

 difficulty at which we have arrived indicates that there 

 must be some more comprehensive statement of the 

 problem which will include cases impossible in the more 

 limited, but possible in the wider view of the subject. 



c 



