QUEKETT MICROSCOPICAL CLUB. 47 



' apparent jumps,' the changes appearing as jumps only because 

 our senses are unable to perceive infinitely small variations in 

 infinitely small intervals of time. In fact the variations are 

 gradual and continuous, and there are, as a rule, and at least 

 between certain limits, no jumps in Nature : Natura non facit 

 saltum. This observation seems important because the notion 

 of ' Continuity ' in Nature brings natural phenomena, or varia- 

 tion in Nature, in close afiinity to what is understood as ' Con- 

 tinuity ' in mathematics : Continuity in mathematics means 

 infinitely small variations in infinitely small intervals of time. 

 " Continuity is the general rule both in mathematics and in 

 Nature ; we find gradual continuity in most events and in most 

 phenomena ; it obtains even in such series of changes as, say, 

 the study of some arts ; fencing, practising on the violin and 

 the like ; I am told that progress in these practices is actually 

 gradual and continuous, but realised both by pupil and master 

 only as apparent jumps. What actually happens is this ; for 

 days and days no progress is noticeable, and then all at once 

 a step forward is realised and the master can report progress. 

 Here there is also undoubtedly a case of an ' apparent jump.' 

 " Now although Continuity in mathematics and in Nature 

 is the general rule, yet it appears that there are exceptions to the 

 Law of Continuity, certainly in mathematics, and probably also 

 in Nature. Some mathematical quantities or elements are not 

 continuous but discontinuous ; discontinuous quantities being 

 those that in an infinitely small interval of time truly effect a 

 ' jump.' To state what such quantities are would lead me too 

 far, but I may mention that the study of discontinuous quan- 

 tities in mathematics has been recently taken up as a new 

 branch of mathematical investigation, this separate branch 

 having received the name of Arithmology. It is highly probable 

 that discontinuity is to be found also in Nature ; I am strongly 

 inclined to think, for instance, that the actual passage from 

 rest to motion, or from motion to rest, is a case of discontinuity 

 showing something like a ' true jump.' But I repeat that such 

 cases are probably only exceptional, the majority of natural 

 phenomena being subject to the vast and powerful Law of 

 Continuity." 



In reply to these remarks, Mr. Hilton writes : 



" The highly interesting comments made by Sir Nicholas Yer- 



