One of the greatest among these was Jan de Witt, Grand Pensionary of Holland and West Friesland, a disciple of Descartes, and author of a mathematical work of note.
About contemporary with him, the eminent French thinker, Pascal, had laid down the first principles of the doctrine of chances. The celebrated Christian Huygens enlarged upon these inquiries in a treatise written in Dutch. When, in 1671, the States-General applied to De Witt to elaborate the best plan for raising a loan, he was the first to apply the principles of the science to a practical subject. In a memorable report he states that, for reasons given, it is better to negotiate funds by life-annuities, which by their nature are terminable, than to resort to either perpetual or terminable annuities. He shows that it had long been the practice in Holland to grant life-annuities at double the rate of interest current. That is to say, if four per cent, was customary, a loan of one hundred florins would bring four florins per annum, while one hundred florins applied to the purchase of a life-annuity would yield an income of eight florins. He goes on to prove that the practice of making no distinction between the ages, the selling a life-annuity on the same terms to the young and the old, was based on a fallacy. He then applies the doctrine of chances to data, most likely deduced from former annuity experiences, and proceeds to construct a mortality-table. This table, though erroneous in many respects, is still the first application of mathematical principles to questions of this kind, and, as such, deserves the highest consideration.
The report was never acted upon, and was lost before De Witt's contemporaries had become acquainted with it.
Toward the end of the seventeenth century, the subject of calculating a table of mortality began to create interest in scientific circles in England; but the difficulty was, to obtain reliable statistics. A few registers had been kept since 1538, and by 1600 they had been introduced into probably one half the parishes of England. Unfortunately, only births or baptisms had been entered. During the plague, the government was induced to publish mortality bills, showing the number of deaths; but here, also, the ages were not stated. The Royal Society, finding no data at home, turned to the Continent of Europe.
The city of Breslau, in Silesia, had kept an exact register of births and deaths for some time, and reliable copies for the five years from 1687 to 1691 were obtained. These were intrusted to the Astronomer Royal, the celebrated Dr. Halley, renowned for having calculated the orbit of a comet, which has been named after him. He published a treatise, which appeared in the "Philosophical Transactions" in 1693, giving the following mortality-table, the first that had ever been constructed on exact scientific principles:
