Giffard's injector appeared more than thirty years ago. The first serious attempt to explain its action on dynamical principles was made by the late William Froude at the Oxford Meeting of the British Association in 1860. The history of mechanical science is almost everywhere deeply marked by Rankine; and it seems, just as it ought to be, that he should be found to have contributed not a little to the literature of this particular subject in a paper presented to the Royal Society of London in 1870. As serving to show how far the problem is still interesting, even from a high standpoint, attention may be directed to the exceedingly curious procedure of Professor Greenhill, where he deals cursorily with the matter at the page numbered 448 of his article on Hydromechanics in the Encyclopædia Britannica.