is all decimal, the franc being the standard of which the other coins, whether gold, silver, or copper, are multiples or measures; they knew, too, that the caliber or diameter of each piece of money is rigorously determined by law, and that the diameters of the silver coins representing five francs, two francs, and fifty centimes measure thirty-seven, twenty-seven, and eighteen millimeters respectively; and they accordingly guessed that Professor Rosette had conceived the plan of placing such a number of these coins in juxtaposition that the length of their united diameters should measure exactly the thousand millimeters that make up the terrestrial meter.
The measurement thus obtained was made by means of a pair of compasses divided accurately into ten equal portions, or decimeters, each of course 3.93 inches long. A rod was then cut of this exact length and given to the engineer of the Dobryna, who was directed to cut out of the solid rock the cubic decimeter required by the professor.
The next business was to obtain the precise weight of a kilogram. This was by no means a difficult matter. Not only the diameters, but also the weights, of the French coins are rigidly determined by law, and as the silver five-franc pieces always weigh exactly twenty-five grams, the united weight of forty of these coins is known to amount to one kilogram.
"Oh!" cried Ben Zoof: "to be able to do all this, I see you must be rich as well as learned."
With a good-natured laugh at the orderly's remark, the meeting adjourned for a few hours. By the appointed time the engineer had finished his task, and with all due care had prepared a cubic decimeter of the material of the comet.
"Now, gentlemen," said Professor Rosette, "we are in a position to complete our calculation; we can now arrive at Gallia's attraction, density, and mass."
Everyone gave him complete attention.
"Before I proceed," he resumed, "I must recall to your minds Newton's general law, 'that the attraction of two bodies is directly proportional to the product of their masses, and inversely proportional to the square of their distances."
"Yes," said Servadac; "we remember that."
"Well, then," continued the professor, "keep it in mind for a few minutes now. Look here! In this bag are forty five-franc pieces—altogether they weigh exactly a kilogram; by which I mean if we were on the earth, and if I were to hang the bag on the hook of the steelyard, the indicator on the dial would register one kilogram. This is clear enough, I suppose?"
As he spoke the professor designedly kept his eyes fixed upon Ben Zoof. He was avowedly following the example of Arago, who was accustomed always in lecturing to watch the countenance of the least intelligent of his audience, and when he felt that he had made his meaning clear to him, he concluded that he must have succeeded with all the rest. In this case, however, it was technical ignorance, rather than any lack of intelligence, that justified the selection of the orderly for this special attention.
Satisfied with his scrutiny of Ben Zoof's face, the professor went on. "And now, gentlemen, we have to see what these coins weigh here upon Gallia."
He suspended the money bag to the hook; the needle oscillated, and stopped. "Read it off!" he said.
The weight registered was one hundred and thirty-three grams. "There, gentlemen, one hundred and thirty-three grams! Less than one-seventh of a kilogram! You see, consequently, that the force of gravity here on Gallia is not one-seventh of what it is upon the earth!"
"Interesting!" cried Servadac, "most interesting! But let us go and compute the mass."
"No, captain, the density first," said Rosette.
"Certainly," said the lieutenant; "for as we already know the volume, we can determine the mass as soon as we have ascertained the density."
The professor took up the cube of rock. "You know what this is," he went on to say. "You know, gentlemen, that this block is a cube hewn from the substance of which everywhere, all throughout your voyage of circumnavigation, you found Gallia to be composed—a substance to which your geological attainments did not suffice to assign a name."
"Our curiosity will be gratified," said Servadac, "if you will enlighten our ignorance."
But Rosette did not take the slightest notice of the interruption.
"A substance it is which no doubt constitutes the sole material of the comet, extending from its surface to its innermost depths. The probability is that it would be so; your experience confirms that probability: you have found no trace of any other substance. Of this rock here is a solid decimeter; let us get at its weight, and we shall have the key which will unlock the problem of the whole weight of Gallia. We have demonstrated that the force of attraction here is only one-seventh of what it is upon the earth, and shall consequently have to multiply the apparent weight of our cube by seven, in order to ascertain its proper weight. Do you understand me, goggle-eyes?"
This was addressed to Ben Zoof, who was staring hard at him. "No!" said Ben Zoof.
"I thought not; it is of no use waiting for your puzzle-brains to make it out. I must talk to those who can understand."
The professor took the cube, and, on attaching it to the hook of the steelyard, found that its apparent weight was one kilogram and four hundred and thirty grams.
"Here it is, gentlemen; one kilogram, four hundred and thirty grams. Multiply that by seven; the product is, as nearly as possible, ten kilograms. What, therefore, is our conclusion? Why, that the density of Gallia is just about double the density of the earth, which we know is only five kilograms to a cubic decimeter. Had it not been for this greater density, the attraction of Gallia would only have been one-fifteenth instead of one-seventh of the terrestrial attraction."
The professor could not refrain from exhibiting his gratification that, however inferior in volume, in density, at least, his comet had the advantage over the earth.
Nothing further now remained than to apply the investigations thus finished to the determining of the mass or weight. This was a matter of little labor.
"Let me see," said the captain; "what is the force of gravity upon the various planets?"
