Among those who have contributed to the development of Infinitesimal Geometry, Sophus Lie is distinguished by several important discoveries which place him in the first rank. He was not one of those who showed from childhood a very marked aptitude, and when he was leaving the University of Christiania in 1865, he was still hesitating between Philology and Mathematics. It was Plücker’s works which made him fully conscious for the first time of his vocation. He published, in 1869, his first paper on the interpretation of imaginaries in Geometry, and by 1970 he was in possession of the ideas which guided the whole of his career.

The Mean Rate of Increase which was investigated by Prof. Bryan in No. 48 of the Mathematical Gazette may evidently be thought of as the inclination of a straight line to an axis. The object of the following note is to point out an example in which this inclination naturally occurs.