68 ON MAGNITUDE [ch. 



gravitational axis its radiate symmetry remains, undisturbed by 

 directional polarity, save for the sun. Among animals, radiate 

 symmetry is confined to creatures of no great size ; and some form 

 or degree of spherical symmetry becomes the rule in the small world 

 of the protozoon — unless gravity resume its sway through the added 

 burden of a shell. The creatures which swim, walk or run, fly, 

 creep or float are, so to speak, inhabitants and natural proprietors 

 of as many distinct and all but separate worlds. Humming-bird 

 and hawkmoth may, once in a way, be co-tenants of the same 

 world; but for the most part the mammal, the bird, the fish, the 

 insect and the small life of the sea, not only have their zoological 

 distinctions, but each has a physical universe of its own. The 

 world of bacteria is yet another world again, and so is the world of 

 colloids ; but through these small Lilliputs we pass outside the range 

 of hving things. 



What we call mechanical principles apply to the magnitudes 

 among which we are at home; but lesser worlds are governed by 

 other and appropriate physical laws, of capillarity, adsorption and 

 electric charge. There are other worlds at the far other end of the 

 scale, in the uttermost depths of space, whose vast magnitudes lie 

 within a narrow range. When the globular star-clusters are plotted 

 on a curve, apparent diameter against estimated distance, the 

 curve is a fair approximation to a rectangular hyperbola; which 

 means that, to the same rough approximation, the actual diameter 

 is identical in them all*. 



It is a remarkable thing, worth pausing to reflect on, that we can 

 pass so easily and in a dozen fines from molecular magnitudes f to 

 the dimensions of a Sequoia or a whale. Addition and subtraction, 

 the old arithmetic of the Egyptians, are not powerful enough for 

 such an operation; but the story of the grains of wheat upon the 

 chessboard shewed the way, and Archimedes and Napier elaborated 



* See Harlow Shapley and A. B. Sayer, The angular diameters of globular 

 clusters, Proc. Nat. Acad, of Sci. xxi, pp. 593-597, 1935. The same is approxi- 

 mately true of the spiral nebulae also. 



t We may call (after Siedentopf and Zsigmondi) the smallest visible particles 

 microns, such for instance as small bacteria, or the fine particles of gum-mastich 

 in suspension, measuring 0-5 to 1-0/x; sub-microns are those revealed by the ultra- 

 microscope, such as particles of colloid gold (2-15m/Lt), or starch-moleculea (5m/x); 

 amicrons, under Im^, are not perceptible by either method. A water-molecule 

 measures, probably, about 0-1 m/i. 



