The Martians, however, multiply this by another factor:
[( c-v ) / (c2 -2cv+v2 )].
Thus, the entire equation becomes:
Tv = To[1-(v2 !c2 )] . [(c-v)/(c2 -2cv+v2 ) ].
As you can clearly see, as long as the velocity of the moving body remains below the velocity of light [443,778 haads per tal), the first factor is a positive number, and the second factor has a value of +1. This, I believe, is why it has never been discovered by Earth scientists; multiplying a number by +1 has no effect whatever, and is not noticeable.
When v is exactly equal to c, both factors become zero; in other words, the moving body experiences zero time. Its clock stops, so to speak.
However, when v exceeds c, the equation a.s.sumes the form:
Tv=To(xi)(i)
where i is the square root of minus one, and x is a function of v.
If the second, or Martian, factor is neglected, it is obvious that the experienced time of the moving body would become imaginary, which is unimaginable in our universe.
However:
(xi) (i)=xi
2.
=-X.
In other words, if the body is moving at greater than the velocity of light, the elapsed time becomes negative. The body is moving backwards in time!
According to the most learned savants in Helium, this is exactly what happened to me. Indeed, so great was my velocity that I traveled an estimated 50,000 years into the past!
Thus, the Mars that I am used to has, in Earth terms, been dead for fifty millenia. This explanation seemed perfectly sound when Menz Klausa first elucidated it, but suddenly a thought occurred to me.
Why did I always go forward in time when I returned to Earth?
For surely that must be so, else I could not be here today. If that formula I quoted were true, when I returned the first time, I should have found myself a hundred thousand years in the past, in about the year 98,000 B.C. Considering the number of trips I have made, I should, by now, be somewhere back in the Miocene.
However, that, too, is explained by our Martian theorists. Another factor comes into play at ultralight velocities, that of gravitation field strength. At light velocity, this factor accounts for the gravitational red-shift of light when it is attempting to escape from a strong gravitational field, and the violet-shift when the light is falling toward the gravity source.
At velocities greater than that of light, the factor becomes +1 when the direction of travel is from a greater gravitation field force to a lesser one, and -1 when the direction is from a lesser to a greater.
Thus, when I return to Earth, the negative time factor becomes positive, and I go into the "future" of Mars, which is your "present."
I trust that is all very clear.
Unfortunately, there is no way I can translate the gravity factor into Earth"s mathematical symbolism. I can handle simple algebra, but tensor calculus is a bit much. I am a fighting man, not a scientist.
By the way, it becomes obvious from this that the Gridley Wave is an ultralight and trans-time communicator.
Another puzzle that the photos brought out was that they show no trace of the ca.n.a.ls of Mars. And yet, Giovanni Schiaparelli saw them. Percival Lowell not only saw them, but drew fairly accurate maps of them. I can testify to that, myself. And yet they do not show on the photographs taken from a thousand miles away. Why?
The answer is simple. As you know, certain markings that are quite unnoticeable from the ground are easily seen from the air. An aerial photograph can show the San Andreas Fault in California quite clearly, even in places where it is invisible from the ground. The same is true of ancient meteor craters which have long since weathered smooth, but have nonetheless left their mark on the Earth"s surface.
From an orbiting satellite, more markings become visible when there is a break in the cloud cover.
Many modern paintings must be viewed from a distance to understand the effect the artist wished to give. Viewed under a powerful magnifying gla.s.s, a newspaper photo becomes nothing but a cl.u.s.ter of meaningless dots. One is too close to get the proper perspective.
Thus it is with the ca.n.a.ls of Mars, long since eroded away, from your viewpoint in time. In order to see those ancient markings properly, you have to stand back forty or fifty million miles.
But what is going to happen to the Mars I love? Or, from Earth"s viewpoint, what did happen to it?
According to Menz Klausa, that is explained by one significant feature on the photos you sent.
Remember, even "today" (from the Martian viewpoint), Mars is a dying planet. Our seas have long since vanished; our atmosphere is kept breatheable only by our highly complex atmosphere plant.
Martians have long since learned to face death stoically, even the death of the planet. We can face the catastrophe that will eventually overtake us.
From Earth"s viewpoint in time, it happened some forty thousand years ago. A great mountain of rock from the Asteroid Belt-or perhaps from beyond the Solar System itself-came crashing into Mars at some 24 haads per tal [10 miles per second]. So great was its momentum that it smashed through the planetary crust to the magma beneath.
The resulting explosion wrought unimaginable havoc upon the planet-superheated winds of great velocity raced around the globe; great quakes shook the very bedrock; more of the atmosphere was literally blown into s.p.a.ce, irretrievably lost.
But it left no impact crater like those of the Moon. The magma, hot and fluid, rushed up to form the mightiest volcano in the Solar System: Mons Olympus. And the d.a.m.ned thing landed directly on our atmosphere plant!
However, we won"t have to worry about that for another ten thousand years yet. Perhaps I won"t live that long.
Give my best regards to Greystoke. Your Aunt Dejah sends her love,
All my best, Uncle Jack
REFERENCE TABLE.
MARTIAN/ENGLISH AND MARTIAN/METRIC.
DlSTANCE: Martian English - Metric
Circ.u.mference: 360 karads - 13,392.6 miles - 21,551.38 km
1 karad: 100 haads - 37.20167 miles - 59.86494 km
1 haad: 200 ads - 1964.248 feet - 59,864.94 cm
1 ad: 10 sofads - 9.82129 feet - 299.3247 cm
1 sofad: [n/a] - 11.78555 inches - 29.93247 cm
TIME UNITS: Martian - Terran 1 day: 10 zodes - 24 hours, 37 minutes, 22.58 seconds
1 zode: 50 xats - 2 hours, 27 minutes, 44.26 seconds
1 xat : 200 tals - 2 minutes, 57.26 seconds
1 tal: [n/a] - .886291 seconds
VELOCITY OF LIGHT:.
ENGLISH: 186,282 miles per second METRIC: 2.99793 x 1010 centimeters per second MARTIAN: 443,778 haads per tal
SURFACE GRAVITY OF MARS:.
ENGLISH: 12.9 feet/second2
METRIC: 392 centimeters/second2
MARTIAN: 1.27 ads/tal
2.
PREHISTORIC NOTE.
By Randall Garrett
Sprague, in his more serious moments, writes historical works. Since I don"t want to make this introduction longer than the piece itself, I will merely say that it is a touch of Robert E. Howard as by L. Sprague de Camp with a soupcon of Ferdinand Feghoot.
Of all the antedeluvian empires. perhaps the most stable and longest-lived was the Double Kingdom of Mekh-Pyget.
The two kingdoms were forcibly combined (c. 1250 BD) through the able generalship of Prince Ahlmos, eldest son of the then King of Mekh. The Prince presented the King with the crown of Pyget.
thus making his father the first ruler of the Double Kingdom.
Within the year. the old King died, and his son then reigned as the first King Ahlmos. (There were fourteen of that name.) The father"s name. unfortunately, has not come down to us, for his grandson.
Vekos I, hated the old man and had his name excised from the histories and effaced from all monuments.
The sixty-one kings following Vekos I. including their names and genealogies. are well doc.u.mented.