^{page 384 note *} Henceforth T, instead of ½ Q, is used to denote the “mechanical value,” or, as it is now called, the “kinetic energy” of the motion.

^{page 385 note *} These equations will be very conveniently called the Eulerian equations of the motion. They correspond precisely to Euler's equations for the rotation of a rigid body, and include them as a particular case. As Euler seems to have been the first to give equations of motion in terms of coordinate components of velocity and force referred to lines fixed relatively to the moving body, it will be not only convenient, but just, to designate as “Eulerian equations” any equations of motion in which the lines of reference, whether for position, or velocity, or moment of momentum, or force, or couple, move with the body. or the bodies whose motion is the subject.

^{page 386 note *} See “Vortex Motion,” §6, Trans. Roy. Soc. Edin. (1868).