II] THE EFFECT OF SCALE 25 



and sub-atomic magnitudes, belong to other orders of things and 

 other principles of cognition. 



A common effect of scale is due to the fact that, of the physical 

 forces, some act either directly at the surface of a body, or otherwise 

 in proportion to its surface or area; while others, and above all 

 gravity, act on all particles, internal and external alike, and exert 

 a force which is proportional to the mass, and so usually to the 

 volume of the, body. 



A simple case is that of two similar weights hung by two similar 

 wires. The forces exerted by the weights are proportional to their 

 masses, and these to their volumes, and so to the cubes of the 

 several Hnear dimensions, including the diameters of the wires. 

 But the areas of cross-section of the wires are as the squares of the 

 said linear dimensions; therefore the stresses in the wires 'per unit 

 area are not identical, but increase in the ratio of the linear dimen- 

 sions, and the larger the structure the more severe the strain becomes : 



Force l^ 



A^ ^ r^ ^ ^' 



and the less the wires are capable of supporting it. 



In short, it often happens that of the forces in action in a system 

 some vary as one power and some as another, of the masses, distances 

 or other magnitudes involved; the "dimensions" remain the same 

 in our equations of equilibrium, but the relative values alter with 

 the scale. This is known as the "Principle of Similitude," or of 

 dynamical similarity, and it and its consequences are of great 

 importance. In a handful of matter cohesion, capillarity, chemical 

 affinity, electric charge are all potent; across the solar system 

 gravitation* rules supreme; in the mysterious region of the nebulae, 

 it may haply be that gravitation grows negligible again. 



To come back to homelier things, the strength of an iron girder 

 obviously varies with the cross-section of its members, and each 

 cross-section varies as the square of a linear dimension; but the 

 weight of the whole structure varies as the cube of its linear dimen- 



* In the early days of the theory of gravitation, it was deemed especially 

 remarkable that the action of gravity "is proportional to the quantity of solid 

 matter in bodies, and not to their surfaces as is usual in mechanical causes; this 

 power, therefore, seems to surpass mere mechanism" (Colin Maclaurin, on Sir 

 Isaac Newton's Philosophical Discoveries, iv, 9). 



