Spencer Heath Archive

Item 355

Penciled by Heath on long, narrow sheets. Relates to Item 347.

About 1949?

     There is anomaly in the fact that both formulas, when the same numerical values are substituted give identical results and that although neither actually employs any unit of time as a factor, a rate of time seems implicit in distance or length just as motion is implicit in mass if the formula is to be of any effect.

     However, the anomaly is more apparent than real for we shall find, upon examination that in neither formula does E represent energy as a quantity but only as a ratio — the number denoting what relationship will be found in the given conditions between energy and time. It does not represent any energy units as a quantity but energy rate — the number of energy units per second. Hence the numbers that are equated with E must also be ratios, and not quantities at all. And this we find to be the case

     A quantity is not multiplied unless the number of its units is increased. The multiplier stands only for times — the number of times that a quantity is taken in addition. A number of force units cannot be multiplied (increased) by a number of length units any more than a number of horses can be multiplied (increased) by a number of apples.

     But two ratios can be combined into a third. Let us take as example, in the formula:

E (Pounds-Feet per Minute) = F (6 pounds per 1 foot) x D (4 feet per l/3 minute)

 

     However if the constant ratio of pounds to feet is fixed at (say) 6 to 1 and pounds and feet are coming and going in quantities of 4 feet then it is important to know how often (at what rate or ratio) we have 4 feet. Say we have our 4 feet three times in each minute. Then we have 6 x 4 x 3 = 72 pounds feet each minute or at the rate of 72 pounds feet per minute. To get this ratio, we have multiplied the static ratio of pound to feet 6/1. by the moving ratio of feet to minutes (4 x 3)/1. Although in practice we disregard the denominators /?/ of our two ratios, what we actually do is to compound (multiply) together the two ratios — the ratio of pounds to feet (6/1) and the ratio of feet to minutes (4 x 3)/1 to obtain a third ratio which is the ratio of the compound quantity, pounds-feet, to minutes — the rate of energy in action per unit of time.

     It is noteworthy that our first ratio F = 6/1, being the number of pounds associated with each foot, is really an energy or work ratio — a pounds-feet ratio, and that our second ratio D = 4/3 feet per minute is a velocity ratio; while our third and derived ratio is the rate of energy in action per unit of time. Actually we have compounded the two ratios, energy and velocity, and thereby obtained the rate of energy in action or, more simply action per unit of time.

     In the formula E = F x D if the force is 30 pounds and the motion or distance it moves (or is able to move) is 20 feet then the ratio of force to motion — the number of pounds per each foot of motion is thirty to one 30/1. The frequency of the thirty pounds per foot, as the number of times it is repeated in the twenty feet of motion or distance is twenty to one 20/1. Multiplying the rate of pounds, pounds to feet 30/1, by its frequency of motion (number of times contained in 20 feet) 20/1 we have E = FxD = 30/1 x 20/1  = 600/1 pounds feet of work
Now the E in this case stands for

 

/See very similar thinking in Item 347/