CHAPTER I. 



INTRODUCTORY. 



723. THE often-used illustration of rapid growth fur 

 nished by a rolling snowball, exemplifies what may be named 

 compound accumulation. The snowball does not gain in size 

 by like increments but by increments of larger and larger 

 amounts. At every roll over, its augmented weight gives it 

 additional power of licking up the snow; and, further, at 

 every roll over, the increase of its bulk increases the surface 

 for the adhesion of more snow. So that the increments 

 stand in what may be roughly called triplicate ratios. In 

 the spread of a great fire we see a kindred instance. Observe 

 the stages : A spark falling on drying linen, a slow smoul 

 dering combustion, a small flame, a large flame from ad 

 jacent light fabrics that take fire, a volume of flame greatly 

 augmented by the setting alight of furniture, a roaring 

 flame from the burning framework of the partitions and the 

 floor-joists. There results a conflagration of the house, then 

 perhaps of adjacent houses, and then possibly of a whole 

 quarter of the town : successive additions to the fire enabling 

 it to spread not only by contact but by radiant heat, which 

 inflames objects at a distance. 



While serving to suggest the course of human progress, 

 and more especially industrial progress, under one of its 

 aspects, these instances serve but incompletely ; for not only 

 does industrial progress exhibit a compound acceleration 

 resulting from increase of the operative forces, but it exhibits 

 a further acceleration resulting from decrease of resistances. 

 .While the power of the evolving influences augments in a 

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