In the meantime Nicholl and Barbicane awoke. "Was that a cock?" said Nicholl. "No, my friends," answered Michel quickly. "I wished to awake you with that rural sound." So saying he gave vent to a cock-a-doodle-do which would have done honour to the proudest of gallinaceans. The two Americans could not help laughing. "A fine accomplishment that," said Nicholl, looking suspiciously at his companion. "Yes," answered Michel, "a joke common in my country. It is very Gallic. We perpetrate it in the best society." Then turning the conversation-- "Barbicane, do you know what I have been thinking about all night?" "No," answered the president. "About our friends at Cambridge. You have already remarked how admirably ignorant I am of mathematics. I find it, therefore, impossible to guess how our _savants_ of the observatory could calculate what initial velocity the projectile ought to be endowed with on leaving the Columbiad in order to reach the moon." "You mean," replied Barbicane, "in order to reach that neutral point where the terrestrial and lunar attractions are equal; for beyond this point, situated at about 0.9 of the distance, the projectile will fall upon the moon by virtue of its own weight merely." "Very well," answered Michel; "but once more; how did they calculate the initial velocity?" "Nothing is easier," said Barbicane. "And could you have made the calculation yourself?" asked Michel Ardan. "Certainly; Nicholl and I could have determined it if the notice from the observatory had not saved us the trouble." "Well, old fellow," answered Michel, "they might sooner cut off my head, beginning with my feet, than have made me solve that problem!" "Because you do not know algebra," replied Barbicane tranquilly. "Ah, that's just like you dealers in _x_! You think you have explained everything when you have said 'algebra.'" "Michel," replied Barbicane, "do you think it possible to forge without a hammer, or to plough without a ploughshare?" "It would be difficult." "Well, then, algebra is a tool like a plough or a hammer, and a good tool for any one who knows how to use it." "Seriously?" "Quite." "Could you use that tool before me?" "If it would interest you." "And could you show me how they calculated the initial speed of our vehicle?" "Yes, my worthy friend. By taking into account all the elements of the problem, the distance from the centre of the earth to the centre of the moon, of the radius of the earth, the volume of the earth and the volume of the moon, I can determine exactly what the initial speed of the projectile ought to be, and that by a very simple formula." "Show me the formula." "You shall see it. Only I will not give you the curve really traced by the bullet between the earth and the moon, by taking into account their movement of translation round the sun. No. I will consider both bodies to be motionless, and that will be sufficient for us." "Why?"