II] OF THIN FILMS 69 



the arithmetic of multipHcation. So passing up and down by easy- 

 steps, as Archimedes did when he numbered the sands of the sea, 

 we compare the magnitudes of the great beasts and the small, of 

 che atoms of which they are made, and of the world in which they 

 dwell*. 



While considerations based on the chemical composition of the 

 organism have taught us that there must be a definite lower hmit 

 to its magnitude, other considerations of a purely physical kind lead 

 us to the same conclusion. For our discussion of the principle of 

 similitude has already taught us that long before we reach these 

 all but infinitesimal magnitudes the dwindling organism will have 

 experienced great changes in all its physical relations, and must at 

 length arrive at conditions surely incompatible with life, or what we 

 understand as life, in its ordinary development and manifestation. 



We are told, for instance, that the powerful force of surface-tension, 

 or capillarity, begins to act within a range of about 1/500,000 of an 

 inch, or say 0-05 />t. A soap film, or a film of oil on water, may be 

 attenuated to far less magnitudes than this; the black spots on a 

 soap bubble are known, by various concordant methods of measure- 

 ment, to be only about 6x 10~' cm., or about 6m/x thick, and Lord 

 Rayleigh and M. Devaux have obtained films of oil of 2mjLt, or even 

 1 m/x in thickness. But while it is possible for a fluid film to exist 

 of these molecular dimensions, it is certain that long before we 

 reach these magnitudes there arise conditions of which we have 

 little knowledge, and which it is not easy to imagine. A bacillus 

 lives in a world, or on the borders of a world, far other than our 

 own, and preconceptions drawn from our experience are not valid 

 there. Even among inorganic, non-living bodies, there comes a 

 certain grade of minuteness at which the ordinary properties become 

 modified. For instance, while under ordinary circumstances crystal- 

 lisation starts in a solution about a minute sohd fragment or crystal 



* Observe that, following a common custom, we have only used a logarithmic 

 scale for the round numbers representing powers of ten, leaving the interspaces 

 between these to be filled up, if at all, by ordinary numbers. There is nothing 

 to prevent us from using fractional indices, if we please, throughout, and calling 

 a blood-corpuscle, for instance, 10~^"^ cm. in diameter, a man lO^'^^ cm. high, or 

 Sibbald's Rorqual lOi"*^ metres long. This method, implicit in that of Napier of 

 Merchiston, was first set forth by Wallis, in his Arithmetica infinitorum. 



