Gordon reached a reassuring hand over to Leah. All memory of their quarrel was obliterated in the face of their present peril. He felt her slender fingers twine firmly with his. The warm contact gave them both new courage. "We of Xoran need your planet and intend to take possession of it," Arlok continued, "but the vast distance which separates Rigel from your solar system makes it impracticable to transport any considerable number of our people here in space-cars for, though our space-cars travel with practically the speed of light, it requires over five hundred and forty years for them to cross that great void. So I was sent as a lone pioneer to your Earth to do the work necessary here in order to open the Gate that will enable Xoran to cross the barrier in less than a minute of your time. * * * * * "That gate is the one through the fourth dimension, for Xoran and your planet in a four-dimensional universe are almost touching each other in spite of the great distance separating them in a three-dimensional universe. We of Xoran, being three-dimensional creatures like you Earthlings, can not even exist on a four-dimensional plane. But we can, by the use of apparatus to open a Gate, pass through a thin sector of the fourth dimension and emerge in a far distant part of our three-dimensional universe. "The situation of our two worlds," Arlok continued, "is somewhat like that of two dots on opposite ends of a long strip of paper that is curved almost into a circle. To two-dimensional beings capable only of realizing and traveling along the two dimensions of the paper itself those dots might be many feet apart, yet in the third dimension straight across free space they might be separated by only the thousandth part of an inch. In order to take that short cut across the third dimension the two-dimensional creatures of the paper would have only to transform a small strip of the intervening space into a two-dimensional surface like their paper. "They could, do this, of course, by the use of proper vibration-creating machinery, for all things in a material universe are merely a matter of vibration. We of Xoran plan to cross the barrier of the fourth dimension by creating a narrow strip of vibrations powerful enough to exactly match and nullify those of the fourth dimension itself. The result will be that this narrow strip will temporarily become an area of three dimensions only, an area over which we can safely pass from our world to yours." * * * * * Arlok indicated one of the pieces of apparatus along the opposite wall of the room. It was an intricate arrangement of finely wound coils with wires leading to scores of needle-like points which constantly shimmered and crackled with tiny blue-white flames. Thick cables ran to a bank of concave reflectors of some gleaming grayish metal.