Spencer Heath Archives

Item 95

Pencil by Heath on lined notepad paper. Original begins with a page of diagrammatics requiring photocopying.

No date

 

White envelope contains original of item 153.

 

 

     A dyne is that magnitude or dimension of force which acting uniformly on a gram of mass during any one second would be sufficient to increase its velocity by one centi­meter per second during that second. This increase in velocity varies during one second from zero at the beginning to one centimeter per second at the end of that second. Therefore the average or equivalent uniform velocity imparted to the gram of mass would be one-half centimeter per second. Hence the distance through which the dyne of force must act during that second is one-half centimeter.

 

     It follows that any gram mass having attained a velocity or increase of velocity of one centimeter must have acquired the amount of energy represented by one dyne of force acting through one-half centimeter of space, distance or motion interval. Such an amount, magnitude or dimension of energy is called the erg and is the standard unit employed to take the dimension of energy of any mass having motion with respect or relative to the motion of the earth which for this purpose is taken as zero motion. Any body, therefore, moving with respect to the earth at any number of centimeters per second taken as acceleration therefrom possesses that dimen­sion of energy, that number of ergs, represented by its mass in grams multiplied by the space or distance it must have moved with respect to the earth to acquire that change of velocity with respect to it.

 

     This distance is ascertained by taking one half this change or increase of velocity, which is the equivalent average velocity, and multiplying this average velocity by the number of seconds elapsed in acquiring the given change or increase of velocity. This gives the number of centimeters through which the number of dynes corresponding to the number of grams must have acted at uniform and average velocity to bring about the observed or final velocity.

     Now, in the stated conditions under which the dyne of force is defined — as bringing about a change or increase of velocity — the change or increase of velocity at the end of any one second is one centimeter per second. Hence the number of seconds elapsed is always the same as the number of units of velocity attained.

 

     Therefore the distance of motion ascertained by multiplying one half the attained velocity (the average velocity) by the number of seconds elapsed is the same thing as taking the square of the attained velocity and dividing by two. V²/2 thus represents the number of centimeters through which the number of dynes, corresponding with the number of grams must have acted, hence the number of ergs of energy possessed by any given mass at its acquired velocity as observed. Thus the general formula for ascertaining the dimension of energy possessed by any mass moving at any velocity relative to any point on the earth is E = Mv²/2 in which E is the energy in ergs; M is the mass in grams, representing the equivalent number of dynes; and v²/2 is the distance in centimeters through which the number of dynes must have acted upon the same number of grams to impart to that mass the velocity observed.