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SCIENCE 



[N. S. Vol. XLIV. No. 1127 



ture from this regular motion which is by 

 no means negligible in magnitude. So it 

 is, in the ease of the weather. There is 

 a fairly definite average of weather condi- 

 tions at a place from year to year, and a 

 fairly typical rhythmic variation, but there 

 is an erratic departure from average and 

 from type, and this erratic variation of the 

 weather can only be studied statistically. 



Turbulence is characteristic of those 

 physical and chemical changes which are 

 called irreversible or sweeping processes. 5 

 The most familiar example of such a proc- 

 ess is ordinary fire, and, as every one knows, 

 a fire is not dependent upon an external 

 driving cause, but when once started it goes 

 forward spontaneously and with a rush. 

 It is not, however, exactly correct to speak 

 of a fire as spontaneous, because this word 

 refers especially to the beginning of a proc- 

 ess, whereas we are here concerned with the 

 characteristics of a process already begun. 

 Therefore it is better to describe a phenom- 

 enon like fire as impetuous because it does 

 go forward of itself. Tyndall, in referring 

 to the impetuous character of fire, says that 

 it was one of the philosophical difficulties of 

 the eighteenth century. A spark is suffi- 

 cient to start a conflagration, and the effect 

 would seem to be out of all proportion 

 greater than the cause. Herein lay the 

 philosophical difficulty. This difficulty may 

 seem to be the same as that which the biol- 

 ogist faces in thinking of the small begin- 

 nings of such a tremendous thing as the 

 chestnut-tree blight in the United States. 

 The chance importation of a spore is in- 

 deed a small thing, but it is by no means an 

 infinitesimal, whereas, under conceivable 

 conditions a fire can be started by a cause 

 more minute and more nearly insignificant 

 than anything assignable. This possibility 



5 There is one type of irreversible process which 

 is steady and amenable to measurement while under 

 way, namely, the so-called steady sweep. 



of the growth of tremendous consequences 

 out of a cause which has the mathematical 

 character of an infinitesimal is the remark- 

 able thing; and this possibility is not only 

 characteristic of fire, but it is characteristic 

 of impetuous processes in general. 



STATIC AND DYNAMIC INSTABILITY 



Impetuous processes, such as storm 

 movements of the atmosphere, are inti- 

 mately connected with conditions of insta- 

 bility. Indeed, an impetuous process seems 

 always to be the collapse of an unstable 

 state. Let us consider, therefore, two ideal 

 eases where the condition of instability is 

 assumed to be completely established at the 

 start. 



(a) Imagine a warm layer of air near 

 the ground overlaid with cold air. Such a 

 condition of the atmosphere is unstable, 

 and any disturbance, however minute, may 

 conceivably start a general collapse. Thus 

 a grasshopper in Idaho might conceivably 

 initiate a storm movement which would 

 sweep across the continent and destroy New 

 York City, or a fly in Arizona might initi- 

 ate a storm movement which would sweep 

 out into the Gulf of Mexico ! These results 

 are different, surely, and the grasshopper 

 and the fly may be of entirely unheard-of 

 varieties, more minute and insignificant 

 than anything assignable. Infinitesimal 

 differences in the earlier stages of an im- 

 petuous process may, therefore, lead to 

 finite differences in the final trend of the 

 process. And yet it is quite generally be- 

 lieved that if we knew enough we could 

 predict the weather as we predict an 

 eclipse ! 



(&) Consider a smooth spherical ball 

 traveling through still air. There certainly 

 is no more reason to expect the ball to 

 jump to the right than to the left. There- 

 fore we may conclude that it will not jump 

 either way. Similarly, a sharp pointed 

 stick stands in a perfectly vertical position 



