IX AUG URAL ADDRESS BEFORE THE BRITISH ASSOC! ATI OX. 503 



others, to be of microscopic size. The micro- 

 phone affords another instance ' of the unexpect- 

 ed value of minute variations — in this case of 

 electric currents — and it is remarkable that the 

 gist of the instrument seems to lie in obtaining 

 and perfecting that which electricians have hith- 

 erto most scrupulously avoided, viz., loose con- 

 tact. 



Once more, Mr. De La Rue has brought for- 

 ward, as one of the results 8 derived from his stu- 

 pendous battery of 10,000 cells, strong evidence 

 for supposing that a voltaic discharge, even when 

 apparently continuous, may still be an intermit- 

 tent phenomenon ; but all that is known of the 

 period of such intermittence is, that it must recur 

 at exceedingly short intervals. And, in connec- 

 tion with this subject, it may be added that, what- 

 ever be the ultimate explanation of the strange 

 stratification which the voltaic discharge under- 

 goes in rarefied gases, it is clear that the alternate 

 disposition of light and darkness must be de- 

 pendent on some periodic distribution in space or 

 sequence in time, which can at present be dealt 

 with only in a very general way. In the ex- 

 hausted column we have a vehicle for electricity 

 not constant like an ordinary conductor, but itself 

 modified by the passage of the discharge, and 

 perhaps subject to laws differing materially from 

 those which it obeys at atmospheric pressure. 

 It may also be that some of the features accom- 

 panying stratification form a magnified image of 

 phenomena belonging to disruptive discharges in 

 general ; and that consequently so far from ex- 

 pecting among the known facts of the latter any 

 clew to an explanation of the former, we must 

 hope ultimately to find in the former an elucida- 

 tion of what is at present obscure in the latter. 

 A prudent philosopher usually avoids hazarding 

 any forecast of the practical application of a 

 purely scientific research. But it would seem 

 that the configuration of these striae might some 

 day prove a very delicate means of estimating 

 low pressures, and perhaps also for effecting some 

 electrical measurements. 



Now, it is a curious fact that almost the only 

 small quantities of which we have as yet any act- 

 ual measurements are the wave-lengths of light ; 

 and that all others, excepting so far as they can 

 be deduced from these, await future determina- 

 tion. In the mean time, when unable to approach 

 these small quantities individually, the method 



1 Royal Society's " Proceedings," May 9, 1878. 



8 " Philosophical Transactions," vol. clxix., pp. 55, 

 155, and other papers catalogued in the Appendix to 

 Part II. of the "Memoir." 



to which we are obliged to have recourse is, as 

 indicated above, that of averages, whereby, dis- 

 regarding the circumstances of each particular 

 case, we calculate the average size, the average 

 velocity, the average direction, etc., of a large 

 number of instances. 1 But although this method 

 is based upon experience, and leads to results 

 which may be accepted as substantially true ; al- 

 though it may be applicable to any finite interval 

 of time, or over any finite area of space (that is, 

 for all practical purposes of life), there is no evi- 

 dence to show that it is so when the dimensions 

 of interval or of area are indefinitely diminished. 

 The truth is, that the simplicity of Nature which 

 we at present grasp is really the result of infinite 

 complexity ; and that below the uniformity there 

 underlies a diversity whose depths we have not 

 yet probed, and whose secret places are still be- 

 yond our reach. 



The present is not an occasion for multiplying 

 illustrations, but I can hardly omit a passing allu- 

 sion to one all-important instance of the appli- 

 cation of the statistical method. Without its aid 

 social life, or the history of life and death, could 

 not be conceived at all, or only in the most su- 

 perficial manner. Without it we could never at- 

 tain to any clear ideas of the condition of the 

 poor, we could never hope for any solid ameliora- 

 tion of their condition or prospects. Without its 

 aid, sanitary measures, and even medicine, would 

 be powerless. Without it, the politician and the 

 philanthropist would alike be wandering over a 

 trackless desert. 



It is, however, not so much from the side of 

 science at large as from that of mathematics it- 

 self that I desire to speak. I wish from the latter 

 point of view to indicate connections between 

 mathematics and other subjects, to prove that 

 hers is not after all such a far-off region, nor so 

 undecipherable an alphabet, and to show that 

 even at unlikely spots we may trace under-cur- 

 rents of thought which, having issued from a com- 

 mon source, fertilize alike the mathematical and 

 the non-mathematical world. 



Having this in view, I propose to make the 

 subject of special remark some processes pecul- 

 iar to modern mathematics ; and, partly with the 

 object of incidentally removing some current mis- 

 apprehensions, I have selected for examination 

 three methods in respect of which mathemati- 

 cians are often thought to have exceeded all rea- 

 sonable limits of speculation, and to have adopted 

 for unknown purposes an unknown tongue. 



And it will be my endeavor to show not only 

 1 See Maxwell " On Heat," chapter xxii. 



