^{page 407 note *} If we continue the argument-curve to the side of the origin for x-negative, we must include large negative values of i in (146): but for simplicity we have confined the argument-curve to positive values of x.

^{page 416 note *} Nature, August 1877, and Brit. Ass. Report, 1877

^{page 427 note *} Remember that downward ordinates in all the curves of figs. 36, 37, 38, 39, correspond to positive values of the quantities represented.

^{page 428 note *} The scale of ordinates of the third, fourth, and fifth curves of fig. 38 is double that of the first and second, indicated on the figure.

^{page 431 note *} Mémoires de l'Institut, 1810. See Gregory's, Examples, p. 480.Google Scholar

^{page 433 note *} The beautiful mathematical discovery, seems to have been made by Euler about 1730.

^{page 433 note †} Phil. Mag., October 1871.

^{page 433 note ‡} See Glaisher, , “On a Class of Definite Integrals,” Phil. Mag., October 1871Google Scholar; and Burgess, , “On the Definite Integral ” Tram. Roy. Soc. Edin., 1898.Google Scholar