Among all these various occupations which took up Van Swinden's time at Franeker, he applied himself with assiduity to various branches of ma thematics, as political arithmetic, the doctrine of chances, mortality, tontines, Etc. In the works of the Haarlem Society, he gave a new demonstration of Newton's formula of the binomial theorem.
In 1785, he accepted the situation of professor of philosophy at Amsterdam. Amongst the new duties imposed upon him were mathematical lec tures. He explained the elements of geometry, and indeed of mathematics in general, in an excel lent work, which would have established his fame as a geometer, if it had been written in a language more generally known. In this book, the strict ness of demonstration of the ancients is united with practical illustrations, the use of mathematical in struments, and the history of the science. In the last edition of his work, published in 1816, it is striking to find how the venerable author, then far advanced in years, knew and had studied even the most recent publications.
Another work, which he began to publish after he was removed to Amsterdam, is more generally known. The Positeones Physicae, as far as they are published, are allowed to rank amongst the best elements of natural philosophy.
Some time after he came to Amsterdam, he was elected one of the directors of the school for the education of seamen. With equal ardour he managed the concerns of the school for the blind; and the interests of the Walloon Church, to which he belonged, found in him a ready and zealous promoter.
As early as 1787, the present minister of marine of the Netherlands had instituted a commission for correcting charts, introducing improvements in navigation, and publishing useful books on nautical subjects. Van Swinden was its chairman. In that capacity he caused the first accurate nautical almanack published in Holland to be printed. He wrote an excellent and extensive work on the theory and practice of finding the longitude by lunar ob servations, and another un the use of nautical in struments.
In 1793, Van Swind.•n was one of the two depu ties sent from Holland to the Scientific Congress at Paris respecting the new system of weights and measures.
After his return from that capital, he published an elaborate and learned work on the subject of weights and measures, and he greatly contributed to make the new system adopted in the Nether lands.
It was about that period that he was called from his studies to the most eminent functions. Van Swinden himself was soon convinced that politics were not for him, nor he for politics. In that pe riod he had the satisfaction of making government resolve to order a general accurate trigonometri cal and astronomical survey of the country; which has since been ably executed by General Krayen hoff. In less than a year, one of those political discussions then so frequent on the continent, drove our author from office, and he cheerfully returned to his studies and resumed his wonted occupations. But when Napoleon gave the management of our affairs to his brother Louis, the new king treated Van Swinden with particular favour, and pressed him eagerly to enter again into political life. This, however, he constantly and firmly declined. At Louis's desire, he framed the plan of the present Royal Institute of the Netherlands. He was at first president, and took a most active part in all its proceedings.
When Holland became a part of Napoleon's im mense empire, Van Swinden retired as much from the public eye as was practicable. The king of the Netherlands honoured him with his confidence on many occasions, and, as a Councillor of State, he faithfully discharged his duty. Respected and be loved by his countrymen, full of activity and life, he was suddenly seized with an illness, which he soon felt to be fatal. With that strength of mind which sustained him through life, he foretold and awaited its close: and in his last moments he dis played the calmness, serenity, and resignation, which become a man and a Christian. lie expired on the 9th March 182S.