16 REPORT — 1878. 



tion of light and darkness must be dependent 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 exhausted column we have a vehicle for elec- 

 tricity 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 accompanying stratification form a magnified image 

 of phenomena belonging to disruptive discharges in general ; and that 

 consequently, so far from expecting among the known facts of the latter 

 any clue to an explanation of the former, we must hope ultimately to find 

 in the former an elucidation 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 actual measurements are the wave lengths of light ; 

 and that all others, excepting so far as they can be deduced from these, 

 await future determination. In the meantime, when unable to approach 

 these small quantities individually, the method to which we are obliged 

 to have recourse is, as indicated above, that of averages, whereby, disre- 

 garding the circumstances of each particular case, we calculate the average 

 size, the average velocity, the average direction, &c, of a large number of 

 instances. But although this method is based upon experience, and leads 

 to results which may be accepted as substantially true; although 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 evidence 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 uni- 

 formity there underlies a diversity whose depths we have not yet probed, 

 and whose secret places are still beyond our reach. 



The present is not an occasion for multiplying illustrations, but I can 

 hardly omit a passing allusion 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 super- 

 ficial manner. Without it we could never attain to any clear ideas of the 

 condition of the Poor, we could never hope for any solid amelioration of 

 their condition or prospects. Without its aid, sanitary measures, and even 

 medicine would be powerless. Without it, the politician and the philan- 

 thropist 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 itself, that I desire to speak. I wish from the latter 

 point of view to indicate connexions between Mathematics and other sub- 



