The title of my address is “Mathematics for the Study of Frequency Statistics.”

By frequency statistics I mean statistics which give the result of counting. A statement as to the number of teachers receiving annual salaries in excess of a certain amount would come under the head of frequency statistics : a statement as to the total amount paid annually to these teachers would not. The sort of thing that I have mainly in mind is a table giving the numbers of boys of specified heights, the heights being taken to the nearest inch, or the numbers of girls who, having worked a paper with full marks 100, get under 5 marks, 5 and under 10, and so on. I may mention that the word “frequency” is usually applied to the actual number in a specified category; the proportion of this number to the total is called the “relative frequency.”

The first table of logarithms was published by John Napier in 1614 under the title of Mirifici Logarithmorum Canonis Descriptio…, at Edinburgh, but the explanation of the construction was not then given. The author, however, promised to publish this later, when he had been assured that the leading mathematicians of the day approved of his work. Any doubt on this point was very soon removed for, within a short time, Edward Wright, who, after studying at Cambridge, had devoted himself to navigation, was engaged in translating the Descriptio into English. Henry Briggs, Gresham Professor in London since 1596, lectured to his students on the work of Napier as soon as he had grasped its significance, and he took it up with great enthusiasm. Soon he was in communication with the inventor and even travelled twice to Scotland in the summers of 1615 and 1616, before Napier’s death, which took place in 1617. The Descriptio seems to have taken some time to reach the Continent, for it was not till 1617 that Kepler first saw a copy. He apparently did not realise its importance at that time, but in the following year he became so enthusiastic that he wrote a letter to Napier (i.e. after the latter’s death) expressing his admiration and hoping for the publication of the method of construction of the Canon. In 1619 the posthumous work of Napier appeared with the title, Mirifici Logarithmorum Canonis Constructio. The construction of the table of logarithms is fully given and the exposition of the procedure, step by step, is exceedingly simple and beautiful. This work was admirably translated by W. R. Macdonald in 1889.