570 
Proceedings of the Boyal Society 
throe rectangular co-ordinate planes — to which the situations, in- 
stantaneous or successive, of points may be referred. 
Any arrangement whatever of points, lines, or planes, changeless 
in mutual configuration, will, for present purposes, be named as a 
reference frame, or briefly as a frame. 
The word motion, in ordinary usages, has several varied signi- 
ficances. 
1 . Thus it is often said that a body, or rather some specified point 
of it, has performed a motion from a point A to a point B, along a 
straight or curved line of motion AMB. It may be often said 
that this same motion has been effected slowly on one occasion 
and quickly on another, speed or velocity of the moving point not 
being treated as any essential quality or condition of the motion. 
2. Again, it is often said that a point, moving along a curve 
GABH, has a certain motion at the instant of its passing A, and 
that its motion undergoes change during the passage from A to B, 
and that at B it has a motion changed from that which it had at A. 
In this sense the motion at A is regarded as determined by the line 
of motion specified as being the tangent to the curve at A, and the 
ward, or way, of the motion along its line at the point of contact A, 
and the velocity of the motion at that point. The velocity of the 
motion is usually understood as meaning a true time rate of motion 
— a rate which may be specified, for instance, as being that of so 
many feet per second, or the like. For this ordinary *mode of 
specifying that which is to be called velocity, it is necessary that 
