Spencer Heath Archive

Item 90

Original includes ten pages of pencil formulaics preceding this text and two following. These could not readily be transcribed and should be photocopied before they are lost, since the notepad paper is disintegrating.

     The formula E = Mv²/2 is based upon a unit mass taking a unit of acceleration during a unit of time. Since M stands for the inertial and not the gravitational mass, and there are the same number of grams as of dynes and there is no numerical error in the employment of grams although the units of inertial mass are in actuality grams. /Not a sentence but conforms with original/

     Similarly, with respect to v². This in reality represents not velocity times velocity as indicated but velocity times the time elapsed during the acceleration. However, since each unit of acceleration occupies just a single unit of time, the velocity multiplied by the elapsed time is numerically the same as the velocity squared. V² therefore represents in actuality the rate of motion at the end of a unit of time. Since the mean velocity under uniform acceleration is only one half the final velocity, it is necessary to divide by 2 the length or distance represented by v² in order to obtain the actual space or distance covered under the influence of the inertial mass as dynes during the unit or units of time required to impart the given unit or units of velocity. The formula thus turns out to be merely the statement of a force times a length, the same as the older formula for work or energy, except that it is related to /a/ particular period of time.

     Now, the single event of one dyne acting through ½ centimeter to impart (from zero) a velocity of one centi­meter per second can be set up as a wave in which the mass or particle element is 2 grams, the wave length 1 centimeter, the wave period or duration one second, the frequency n = 1, the velocity ln/t and the energy content one erg-second. And this unit of energy being unity, is of the same magnitude as Planck’s constant h multiplied by that number which is the reciprocal of 6.55 x 10^-27.

     Taking this metric unit of energy as the first of a series and as having the composition aforesaid, it forms the number one horizontal Column in the series set up in tabular form in Figure 1.