Ralph sprang into action. He immediately began taking observations. These told him that it would take him at least thirty days to reach Mars, even though he forced his machine to the utmost. He could not travel over 90,000 miles an hour, but, on the other hand, he felt sure that Llysanorh's machine was incapable of making more than 85,000 miles an hour. But the Martian had a handicap of probably 600,000 miles, and if Ralph gained on him at the rate of only 5,000 miles an hour, it would take 120 hours, or five terrestrial days to overtake him.

Ralph turned his machine towards the point in space where Mars would be at the end of thirty days, and now set himself to the task of making a search for the other flyer with the polarized wave apparatus.

For four wearisome and anxious hours he sought through space perseveringly, and was at last rewarded by locating another machine which he was certain was that of the Martian, as he had reasoned, heading for Mars.

At the same time the results of his calculations dismayed him greatly, for they revealed that Llysanorh's machine was making no less than 88,000 miles an hour. At this rate, Ralph was gaining only 2,000 miles an hour, and it would take thirteen or fourteen days to overhaul the other flyer. But as the Martian could not hope to reach Mars under twenty-nine days himself, Ralph figured that he, barring some unforeseen accident, would overtake him long before he landed there.

It was absolutely imperative that he do so, for once the Martian left Mars and headed for the Asteroids further pursuit would be useless. There were over 4,000 of these little planets already known[10] and it would be the work of a lifetime to search on each one for the fugitive and his victim. Speedy action on Ralph's part was urgent.

These little Asteroids, revolving in an orbit between Mars and Jupiter were practically uninhabited, although most of the larger ones had a good atmosphere, and a fair climate, considering their distance from the sun.

Some of them were only a few miles in diameter, and the largest measured but 485 miles. An electromobile, running at the slow rate of 60 miles an hour could circle such a tiny planet in 24 hours!

The larger planetoids had a superb vegetation, and as the gravity on these bodies was only a fraction of that on the Earth, the trees and shrubs were gigantic, while colossal fruits and vegetables grew in abundance. These plants helped to create a dense atmosphere, in spite of the small gravity, and life, on one of these little planets, was, in many respects, far more comfortable and pleasant than on Earth or Mars.

Now began the hardest part of the chase for Ralph. There was nothing more to do than he had already done. From now on he must wait with what patience he could summon to his aid, until such time as his machine should catch up with that of the Martian. He could force his own no further, and he was very sure that Llysanorh' was also flying at his utmost speed.