209 
as the general expression for acceleration when derived from the yelocity- 
time curve. As before, this expression denotes tangent values so that the 
acceleration curve may be obtained from the velocity curve in the same 
manner as the velocity curve was obtained from the distance curve. It is. 
interesting to note that the acceleration curve reaches the X-axis at the 
same time the yelocity curve becomes horizontal and at the same time 
the distance curve becomes straight. This is shown mathematically as 
follows: 
uvdd - MWY) pu, ad 
Sanaa Oe Ot jew dae 
or the value of “v’ can be variable only so long as the distance time 
Vv =) for v= a constant. 
curve is not straight, and unless “vy” is a variable the second derivative of 
the distance cure will be zero. 
Physicists learned early that weight could not be taken as a standard 
of force on account of the variation of gravity with location on the earth’s 
surface. Knowing however that force was required to change the velocity 
of a body it developed that when the amount of substance—mass—in a 
. Ww s : a A 
given body was known (m=-~—)_ the force needed to give it a definite 
change in velocity in a given time was a definite function of these two 
quantities. The familiar expression for this is, Force = mass x accelera- 
tion. 
The equation is valuable to scientists and engineers alike. Using 
unit mass and unit acceleration, the scientist finds thereby a unit force 
which is constant. (The equation of the pendulum gives him the acceler- 
ation due to gravity at any point so that mass may be easily determined. ) 
Knowing the masses involved in a given car or machine, the engineer is 
able to predetermine the torque necessary at the motor shaft to bring the 
same up to speed in a given time. This information is valuable for pur- 
poses of design. 
After the apparatus has been assembled it is sometimes necessary to 
determine their performance. The mass being known it remains to meas- 
ure the acceleration to see if the motors meet the requirements. 
This measurement of acceleration has been attempted in many ways. 
A few of the more important schemes will now be considered. Accelerom- 
eters employing a freely moving mass of some sort have been most used. 
Dr. Sheldon’s device is of this type, using a suspended weight carrying 
pointer at the bottom (fastened thereto by rods) which plays over a scale. 
[ 14—23003 ] 
