"My dear, I wouldn't put anything past the two of us together. But let me show you how it works."
He spread out the drawings he had made from the construction-records while she searched the Pilot. He expounded their meaning enthusiastically and she listened and made admiring comments, but it is rather doubtful if she really understood. She was too much occupied with the happy knowledge that he was again confident and hopeful.
But the idea was not particularly complicated. Every fact was familiar enough. Space-ships, in the old days, and the Starshine, in this, were able to exceed the speed of light by enclosing themselves in an overdrive field, which was space so stressed that in it the velocity of light was enormously increased. Therefore the inertia of matter, its resistance to acceleration, or its mass, was reduced by the same factor, y.
The kinetic energy of a moving space-ship, of course, had to remain the same when an overdrive field was formed about it. Thus when its inertia was decreased by the field, its velocity had to increase. Mathematically, the relationship of mass to velocity with a given quantity of kinetic energy is, for normal space, MV=E. In an overdrive field, where the factor y enters, the equation is M/y, yV=E. The value of y is such that speeds up to two hundred times that of light result from a space-ship at normal interplanetary speed going into an overdrive field.
A matter-transmitter field, as everyone knows now, simply raises the value of y to infinity. The formula then becomes M/infinity, infinity V=E. The mass is divided by infinity and the velocity multiplied by infinity. The velocity, in a planet-to-planet transmitter, is always directly toward the receiver to which the transmitter is tuned.
In theory, then, a man who enters such a transmitter passes through empty space unprotected, but his exposure is so exceedingly brief—across the whole First Galaxy transit was estimated to require .0001 second—that not one molecule of the air surrounding him has time to escape into emptiness.
Thus the one device is simply an extension of the principle of the other. A matter-transmitter is merely an enormously developed overdrive-field generator with a tuning device attached. But until this moment, apparently it had not happened that a matter-transmitter technician was in a predicament where the only way out was to put those facts together. Kim was such a technician, and on the Starshine he had probably the only overdrive field generator of space-ship pattern still in working order in the Universe.
"All I've got to do is to add two stages of coupling and rewind the exciter-secondary," he told her zestfully. "Doing it by hand may take a week. Then the Starshine will be a matter-transmitter which will transmit itself! The toughest part of the whole job will be the distance-gauge. And I've got that."
Worshipfully, Dona looked up at him. She probably hoped that he would kiss her again, but he mistook it for interest.
He explained at length. There could be, of course, no measure of distance traveled in emptiness. Astrogation has always been a matter of dead reckoning plus direct observation. But at such immeasurably high speeds there could be no direct observation. At matter-transmitter speeds, no manual control could stop a ship in motion within any given galaxy!