an apparent distance; he must clear it, as the phrase is, and find the true one; and this clearing, by the rigorous methods of spherical trigonometry, has cost many a good officer half an hour of hard figuring with cold hands by a bad lamp, and has cost some of them their ships."
He let that sit. Somewhere in the front row a man in a blue coat, with his arm along the back of the bench, shifted his weight.
"I have spent eleven years," said Sir Augustus, "upon a set of tables that shall make the clearing of a lunar distance a matter of three lookings-out and two additions. You shall see it done."
He took up the chalk.
* * *
Judith knew the rigorous methods. She knew Borda's and she knew Dunthorne's and she knew the method in Dr. Maskelyne's Requisite Tables, which she could have worked in her sleep and had, on two occasions that she remembered and probably others that she did not, worked very nearly in her sleep, at three in the morning, with her father dictating the logarithms from memory because his eyes had gone. She knew too the family of short methods that had been coming out of Cambridge and Paris and Edinburgh for thirty years, every one of them promising what Sir Augustus was now promising, every one of them a series of corrections to be added to the apparent distance until it became the true.
Sir Augustus's method was of that family, and it was handsome. He wrote upon the board, in a large and beautiful hand, a worked example: a lunar distance of the moon from Aldebaran, observed at sea, of one hundred and sixteen degrees, fourteen minutes; the moon's apparent altitude so much, the star's so much. He showed how the first correction was taken from his first table by the moon's altitude, and the second by the star's; he wrote each one beneath the observed distance with a firm little plus or minus before it. The audience followed him as a congregation follows a psalm, half a line behind.
"And now," he said, "the third correction, which is the refinement of the method, and the part of it of which I am, I confess, a little vain. The great reductions are made; but the triangle in the sky is a curved triangle, and a curved triangle will not be hurried. There remains a small term, depending upon the square of the moon's correction, and upon the cotangent of the distance itself. In the rigorous method it is concealed in the general computation. In mine it is laid out in a table of its own, by distance and by altitude, already reduced to minutes and seconds, so that the sailor need only look it out, and add it."