ATOM. 481 



difficulty about the equality of the mass of all atoms by laying it down as 

 a doctrine which cannot be disproved by experiment, that mass is not a 

 quantity capable of continuous increase or diminution, but that it is in its 

 own nature discontinuous, like number, the atom being the unit, and all masses 

 being multiples of that unit. We have no evidence that it is possible for the 

 ratio of two masses to be an incommensurable quantity, for the incommen- 

 surable quantities in geometry are supposed to be traced out in a continuous 

 medium. If matter is atomic, and therefore discontinuous, it is unfitted for 

 the construction of perfect geometrical models, but in other respects it may 

 fulfil its functions. 



But even if we adopt a theory which makes the equality of the mass of 

 different atoms a result depending on the nature of mass rather than on any 

 quantitative adjustment, the correspondence of the periods of vibration of actual 

 molecules is a fact of a different order. 



We know that radiations exist having periods of vibration of every value 

 between those corresponding to the limits of the visible spectrum, and probably 

 far beyond these limits on both sides. The most powerful spectroscope can 

 detect no gap or discontinuity in the spectrum of the light emitted by incan- 

 descent lime. 



The period of vibration of a luminous particle is therefore a quantity which 

 in itself is capable of assuming any one of a series of values, which, if not 

 mathematically continuous, is such that consecutive observed values differ from 

 each other by less than the ten thousandth part of either. There is, therefore, 

 nothing in the nature of time itself to prevent the period of vibration of a 

 molecule from assuming any one of many thousand different observable values. 

 That which determines the period of any particular kind of vibration is the 

 relation which subsists between the corresponding type of displacement and the 

 force of restitution thereby called into play, a relation involving constants of 

 space and time as well as of mass. 



It is the equality of these space- and time-constants for all molecules of 

 the same kind which we have next to consider. We have seen that the very 

 different circumstances in which different molecules of the same kind have been 

 placed have not, even in the course of many ages, produced any appreciable 

 difference in the values of these constants. If, then, the various processes of 

 nature to which these molecules have been subjected since the world began 

 have not been able in all that time to produce any appreciable difference 



VOL. II. 61 



