^{page 1 note *} The results of this paper were communicated to Section A of the British Association at its meeting in Edinburgh on September 8, 1921.

^{page 7 note *} So far as I know, this remark was first made by Klein.

^{page 7 note †} The locus of points whose co-ordinates satisfy a linear equation ax + by + cz + dt + e = 0 is called a hyperplane. The intersection of two hyperplanes is in general a plane, and the intersection of three hyperplanes is in general a straight line.

^{page 12 note *} From κάλαμος, a reed-pipe.

^{page 16 note *} Palermo Rend., xii (1898) p. 163.

^{page 17 note *} This result is not new, and is inserted here only because it is necessary for what follows in § 12.

^{page 22 note *} This device was suggested to me by the recollection of the method published in 1876 by Hamburger for integrating systems of simultaneous partial differential equations.