Introduction to Part II.

The prize-essay topics proposed by the Royal Academy of Sciences in Paris for the years 1724 and 1726 were concerned with the collision of bodies: in the competition of 172424 the bodies were to be perfectly hard and the prize was won by MacLaurin for his essay [66], with which this article is concerned; elastic bodies were to be considered for 1726, when the winning essay was that of Père Maziere, described as Prêtre de l'Oratoire [76]. In a Notice prefixed to the published version of MacLaurin's essay (see Appendix II.1, p. 79) it was stated on behalf of the Academy that many of the submissions, while excellent in themselves, had not dealt with the topic as proposed. Amongst these was an extensive work by Jean Bernoulli, which had apparently been submitted in both 1724 and 1726 and had been praised on both occasions. Bernoulli's essay [13] was also published in the volumes containing the prize essays [1]; one reason for this may have been the desire to present both sides of an on-going controversy concerning the force of a moving body (see below). In fact, MacLaurin had also transgressed the limits of the proposed question, dealing not only with the collision of perfectly hard bodies but also with cases of elastic collisions. [ABSTRACT FROM AUTHOR]