24 ON MAGNITUDE [ch. 



We are accustomed to think of magnitude as a purely relative 

 matter. We call a thing big or little with reference to what it is 

 wont to be, as when we speak of a small elephant or a large rat ; and 

 we are apt accordingly to suppose that size makes no other or more 

 essential difference, and that Lilliput and Brobdingnag* are all 

 alike, according as we look at them through one end of the glass 

 or the other. Gulliver himself declared, in Brobdingnag, that 

 "undoubtedly philosophers are in the right when they tell us that 

 nothing is great and little otherwise than by comparison": and 

 Oliver Heaviside used to say, in like manner, that there is no 

 absolute scale of size in the Universe, for it is boundless towards 

 the great and also boundless towards the small. It is of the very 

 essence of the Newtonian philosophy that we should be able to 

 extend our concepts and deductions from the one extreme of magni- 

 tude to the other; and Sir John Herschel said that "the student 

 must lay his account to finding the distinction of great and little 

 altogether annihilated in nature." 



All this is true of number, and of relative magnitude. The Universe 

 has its endless gamut of great and small, of near and far, of many 

 and few. Nevertheless, in physical science the scale of absolute 

 magnitude becomes a very real and important thing; and a new 

 and deeper interest arises out of the changing ratio of dimensions 

 when we come to consider the inevitable changes of physical rela- 

 tions with which it is bound up. The effect of scale depends not on 

 a thing in itself, but in relation to its whole environment or milieu ; 

 it is in conformity with the thing's "place in Nature," its field of 

 action and reaction in the Universe. Everywhere Nature works 

 true to scale, and everything has its proper size accordingly. Men 

 and trees, birds and fishes, stars and star-systems, have their 

 appropriate dimensions, and their more or less narrow range of 

 absolute magnitudes. The scale of human observation and ex- 

 perience lies within the narrow bounds of inches, feet or miles, all 

 measured in terms drawn from our own selves or our own doings. 

 Scales which include light-years, parsecs. Angstrom units, or atomic 



* Swift paid close attention to the arithmetic of magnitude, but none to its 

 physical aspect. See De Morgan, on Lilliput, in N. and Q. (2), vi, pp. 123-125, 

 1858. On relative magnitude see also Berkeley, in his Essay towards a New Theory 

 of Visio7i, 1709. 



