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APPLICATION OF THE PARALLELOGRAM LAW IN KINE- 
MATICS. By THOMAS PRESTON, M.A., F.R.U.I. 
[Read Decempsr 16 ; Received for Publication Decemperr 18, 1896; 
Published Aprin 3, 1897.] 
Own a Fundamental Method in Kinematics.—In this note I wish to 
attract attention to a method of determining the accelerations of 
a moving point in terms of any system of coordinates, and the 
advantages which the method appears to possess lie not only in 
the ease and uniformity of its application to all systems of coordi- 
nates but also, and what is probably most important, in the direct- 
ness with which what we might term the fundamental or physical 
condition of motion is employed and kept in view. 
By way of a preliminary remark we may mention, that since 
acceleration is defined as rate of change of velocity, and since 
velocity possesses both magnitude and direction, it follows that an 
acceleration exists when the velocity changes either in magnitude 
or directions. For example, when a moving point describes a curve 
with constant speed its direction of motion changes from point to 
point, while its speed remains the same, and this is produced by an 
acceleration directed towards the concave side of the curve. This 
is mentioned, because beginners sometimes find a difficulty in 
understanding how it is that an acceleration exists when the speed 
of a moving point remains uniform 
3 ; R R 
(for example, in the case of a point 
describing a circle with uniform 
speed), and to such I think the 
difficulty will be at once removed 0 Q 
if they keep in view the fact that Bigg 
any quantity, such as a velocity, or acceleration, or a force, 
which can be compounded or resolved according to the parallelo- 
gram law, may be changed in direction or magnitude, or both 
magnitude and direction, by simply compounding it with another 
quantity of the same sort. For example, a force, P (fig. 1), if 
combined with another force, Q of properly chosen magnitude, will 
