of Edinburgh, Session 1883 - 84 . 571 
true chronometry should have been previously attained to, in idea 
at least, and approximately in fact. 
Sometimes it is found convenient to apply, temporarily at least, 
the name velocity (for want of any other name) to the rate of travel 
of a point along a line as referred to the progress of something else 
moving relatively to a frame or to a dial. Thus, for a point moving 
along a line, the motion at any point of the path may sometimes be 
said to have a velocity of so many feet per unit of angular space 
turned by the crank shaft of a steam engine relatively to the 
framing of the steam engine. What is thus specified might be 
called a quasi-velocity, not a true velocity, as it is customary to 
regard true velocity as being referred not to the revolution of a 
steam engine shaft, nor to the revolution of a hand of a badly-going 
clock, but to the progress of absolutely true time when once the idea 
of progress of true time has been arrived at. 
Before arriving at any principle of absolute chronometry, how- 
ever, we cannot deal with true velocity at all. We cannot specify a 
rate of progress of any moving point relatively to progress of true 
time, or relatively to progress of a clock hand on its dial advancing 
proportionally to progress of true time. But, without assuming or 
presupposing any principle of absolute chronometry, we can refer 
motions of points to an assumed reference frame, jointly with an 
assumed dial-traveller. The dial-traveller may conveniently be 
imagined as a clock hand or index travelling continuously along a 
graduated dial, such as the face of a clock, but without the adapta- 
tion of any pendulum or balance wheel, or other chronometric 
arrangement for regulating the motion of the hand. The traveller, for 
instance, might be kept moving round its dial by a winch handle, 
such as that of a grindstone, or of a barrel organ, turned by hand. Or 
it might be an index projecting out radially from the crank shaft of a 
steam engine, and revolving round a dial fixed to the adjacent frame- 
work of the engine, so as to surround the shaft. Or the traveller might 
be an index kept revolving by the shaft of a water wheel, with a 
motion depending on variable conditions of rain-fall and stream-flow. 
For purely kinematic considerations as to relative motions of 
points or bodies we have no essential concern with true time, nor 
with true velocities, understood as velocities of motions relative to a 
frame, and specified quantitatively as true time rates. 
