[bowman] fundamental PROCESSES IN HISTORICAL SCIENCE 555 



A comprehensive illustration of the same difference in the values 

 attached to pure and formal probabilities is afforded by the prevailing 

 attitude towards the dangers of lightning and railroads, respectively. 

 In a "census of fears" taken by Clark University, the dread of light- 

 ning stood in the foremost place. A severe thunderstorm is a positive 

 terror to many persons who fear nothing else; and yet the number of 

 persons struck by lightning is only 1 -5 per 100,000 of population in the 

 United States, and of these, one out of three recover, leaving a ratio 

 of but 1 death per 100,000 of population. The railroads of the United 

 States in 1909 (Nelson's Encyclopœdia, x, 184, 185) killed 7,807 

 persons and injured 91,076. Of these numbers, employees of the 

 roads represented 2,610 killed, and 75,006 injured; passengers, 253 

 killed, and 10,311 injured; other persons 4,944 killed (by far the largest 

 proportion of these being trespassers), and 5,759 injured. On this 

 basis, the ratio of passengers killed per 100,000 of population (total 

 population, census of 1910: 91,972,266) is only -27, or about one- 

 quarter of the proportion killed by lightning. Where a sudden casualty, 

 however, may end erratically either in a fatality or only in injuries, 

 men do not distinguish sharply between the two alternatives, but fear 

 both as a joint, inseparable danger; and the total casualties (killed 

 and injured, 10,564) among railway passengers constitute a ratio of 

 11-48 per 100,000 of population, or 765 per cent, of the ratio of total 

 casualties (persons struck) by lightning. In every other respect, 

 moreover, the dangers of the railroads are, as compared with lightning, 

 the greater. In 1909, 1 out of every 20 railway employees in the United 

 States^ was injured; of trainmen, such as enginemen, firemen, and con- 

 ductors, 1 out of every 205 was killed, and 1 out of 9 injured. The 

 number killed in the third of the above groups alone (4,944), chiefly 

 trespassers, constitutes a ratio of 5-3 per 100,000 of population, or 

 530 per cent, of the proportion killed by lightning; and the total 

 deaths (7807) and total casualties (98,883) in the above three groups 

 together constitute ratios respectively of 8-48 and 107-5 per 100,000 

 of population, or 848 per cent, and 7,166 per cent, of the corresponding 

 proportions for lightning. The probable security against casualties 

 by lightning, as compared with the probable security against railway 

 casualties, is, therefore, not only greater, but much the greater. In 

 the case of lightning, however, this security is a matter of pure chance 

 or pure probability, because there is no correct process, which, apart 

 from error in its application, will necessarily exclude the danger, but 

 the security depends on the blind action of a great number of favorable 

 chances upon a few unfavorable. The security against railway 

 casualties, on the contrary, is formal probability because the railroads 

 themselves apply correct processes with set effort, which, apart from 



