a tendency to form habits. These habits produce statistical uniformities. When the number of instances entering into the statistics are small compared with the degree of their variation, the law will be extremely rough, but when the number runs up into the trillions, that is to say cubes of millions, or much higher, as in the case of molecules, there are no departures from the law that our senses can take cognizance of. You will find one such rough uniformity illustrated in two maps in ‘Studies in Logic by Members of the Johns Hopkins University’'. Here is another that I have dug out
of our last Census on purpose for this lecture. The comparison is of the number of deaths per thousand of the population in the years 1890 and 1899 respectively, in over a dozen countries the comparison being made with numbers calculated from the law
r = R (1. 000157954)(T- t)2 where t is the date of the year A.D. r is the number of deaths in that year per thousand of the population in a given country T is the date when in that country the death rate will be lowest R is the lowest death rate, the same in all countries
The rates for the United States are separated from the others becasue they are separated by ten years instead of nine, like the others, and moreover they do not refer to any Calender year but to years of 365 day ending May 30. I have taken no pains to get the best values of the constants. So it would be a good exercise in Least Squares to work these out. Of course, the uniformity is only rough. It was quite violated by Holland or Switzerland, countries that I mark as bad because they diminished their death rate in that novennium in a manner wholly unauthorized by my rule.
The best way of settling the meaning of a word is to take it in such a sense as shall
render the word most useful. Now chance is the foundation of the great business of Insurance; and the Doctrine of Chances has been without much exaggeration called the logic of the exact sciences. But when chance is said to consist in our ignorance, it certainly can be of no use except to those who desire to prey upon us. The Insurance business is not run on ignorance in any further sense than that if a man knew when he was going to die he would not insure his life. That which renders chance so importanct is that there is immense diversity thoughout the universe. Diversity in many respects with uniformity