Symbols and things: mathematics in the age of steam

simple algebra based on the laws of probability, under certain assumptions. For example, he assumes that if A and B die in the same year, the probability that A dies first is the same as the probability that B dies first. In this paper Morgan does not use anything that might be called ‘higher’ mathematics: his main concern is to extract useful information from the tables of life expectancy. He recommends the table culled from the records of the town of Northampton. Morgan wrote several more papers on actuarial matters for the Philosophical Transactions and was elected a Fellow of the Royal Society in 1790. He also wrote some highly controversial pamphlets about the government’s economic policies, and he became involved in radical activities. This led to his being summoned to appear as a witness in the trial of Horne Tooke for High Treason in 1793, although he did not, in fact, have to give evidence. His statements on the affairs of the Equitable Assurance Company were increasingly attracting adverse comments from influential and knowledgeable people. It was clear that the tables from Northampton were not a good basis for insurance valuations, particularly in the case of the people who actually had the means to invest in life policies. In 1819, the young Charles Babbage became interested in the subject and drew up a scheme of his own, which he sent to Morgan, asking for his opinion. Morgan’s reply was phrased in the elaborate language of the time, but in effect it was a curt refusal to engage in debate. The controversy came to a head in 1826, with the publication of Babbage’s Comparative View of the Various Institutions for the Assurance of Lives. In the same year, Francis Baily, who was later to become famous for his astronomical discoveries but had already published books on actuarial matters, wrote a letter critical of Morgan to the Times, to which Morgan responded in his typically assertive way. A couple of years later, an anonymous letter addressed to Morgan appeared in the Philosophical Magazine, with the opening ‘Dear Sir, Having unfortunately failed on some former occasions, of fully comprehending the meaning of your expressions... ’. The author was in fact Thomas Young, the eminent polymath, and the letter is printed in his MiscellaneousWorks, edited by Peacock. The need for improved data and amore sophisticated basis for the calculation of premiums was generally recognized. When William Morgan died in 1833, he had been overtaken in his position as the leader of the actuarial profession, but he is rightly remembered as one of the pioneers in the field.