^{page 1060 note *} What is denoted by x in this and following expressions, is the (x - vt) of §§ 36 …. 40; the origin of co-ordinates being now fixed relatively to the travelling forcive.

^{page 1062 note *} However sudden and great the commotion is, the motion of the liquid is, and continues to be, irrotational throughout.

^{page 1073 note *} Proc. L.M.S., 1883: republished in Rayleigh's Scientific Papers, vol. ii. art. 109.

^{page 1074 note *} This is opposite to the direction of the motion of the forcive in fig. 26.

^{page 1079 note *} Of this kind of co-ordinates in a plane, we have a well-known case in the elliptic co-ordinates consisting of confocal ellipses and hyperbolas.

^{page 1082 note *} In the case of even the highest speed attained by a duckling, this angle is perhaps perceptibly greater than 19° 28′, because of the dynamic effect of the capillary surface tension of water. See Baltimore Lectures, p. 593 (letter to Professor Tait, of date 23rd Aug. 1871) and pp. 600, 601 (letter to William Froude, reprinted from Nature of 26th Oct. 1871).

^{page 1084 note *} Proc. Lond. Math. Soc., xv. pp. 69–78, 1883; reprinted in Lord Rayleigh's Scientific Papers, vol. ii. pp. 258–267.