DECElVrBEE 20, 1895.] 



SCIENCE. 



827 



of these elementary controlling forces and 

 conditions (generally quite unknown as 

 such) is sufiBciently large there will be a 

 definite integral, which becomes more stable 

 in form and character as the number from 

 which it is derived' increases, and that it 

 may be depended upon and treated with as 

 much confidence as if it were an observed 

 and explained phenomenon. This is, of 

 course, the basis of all statistical studies of 

 natural phenomena. One or two simple 

 illustrations may be given. In the case of 

 tossing a coin it may be impossible to dis- 

 cover by any physical examination of the 

 coin itself, or of the conditions influencing 

 it when thrown in the air, any reason for 

 the appearance of one face rather than the 

 other. The a priori probability of the ap- 

 pearance of a given face may, therefore, be 

 properly put at one-half. But in ten thous- 

 and trials there might be shown a tendency 

 towards the appearance of heads, and if this 

 persisted with an increase of the number of 

 trials it would be legitimate to conclude that 

 the coin was not uniform or symmetrical in 

 structure or that the balance of forces and 

 condition in tossing was not good. The 

 universality of this principle has given rise 

 to the idea of the long run, or, as it is some- 

 times put, the Law of the Long Eun. In 

 simple language this means that however 

 obscure or relatively ineffective an influen- 

 cing condition may be, in the long run it will 

 make itself felt and may be evaluated in 

 quantity and character if the number of ex- 

 amples is sufficiently great. It will be ob- 

 served that this principle is different from, 

 although not necessarily inconsistent with, 

 the statement often made that minor de- 

 partures from a general law, due to minute 

 and continually varying influences, will, ' in 

 the long run,' cancel and destroy each other. 

 It is not necessary to quote examples of 

 the useful aplication of this principle of the 

 long run in bringing to light hitherto un- 

 suspected relations or unconsidered influ- 



ences, but I maj' be allowed to refer to one 

 simple and easily understood illustration, 

 an account of which was published about 

 ten years ago. It was founded on the fol- 

 lowing reasoning : An author with a gen- 

 erous vocabulary at his service must be 

 continually making a choice among words 

 that are nearly identical in meaning. The 

 influences which control the choice are 

 often numerous and doubtless generally 

 unrecognized, but in the long run a certain 

 set will prevail and the composition will be 

 marked by this characteristic. It might 

 not be impossible to discover the existence 

 of each separate influence by an extensive 

 analysis of the author's composition in 

 such a manner as to reveal the character- 

 istic of this influence to the exclusion of all 

 others, but the labor of doing this would in 

 many cases be enormous. In the paper re- 

 ferred to, the simple and easily reached 

 characteristic dependent on the number of 

 letters in the words used was proposed, 

 and it was shown that when properly an- 

 alyzed the composition of any author 

 could be made to produce what was called 

 a ' characteristic curve,' which, it was sug- 

 gested, might pi'ove to be peculiar to him 

 and which might thus afford a clue to his 

 identification. Some further applications 

 of the suggested method have been made 

 since the time of first publication which 

 have tended strongly to confirm the view 

 then held. 



The application of the calculus of prob- 

 abilities to the determination of life expec- 

 tation and other quantities of great impor- 

 tance to life insurance and annuity com- 

 panies has long been admitted, and statis- 

 tical methods based on the principle of the 

 long run have long been in vogue in the 

 study of the distribution and prevalence of 

 disease. There is good reason for believing 

 that what is ordinarily known as purely 

 accidental death and injury is governed in 

 distribution by the same inexorable laws, 



