or that the President had called for the porter to remove her. They said that she had worn white muslin and a turban, or had been dressed like a Quaker. One gentleman, who had certainly not been there, told the story at White's for a fortnight with a different number of minutes in it every time.
What she actually did took a little under four minutes, and she did not write very much at all.
She did not touch his worked example. She went to the clean right-hand side of the board and wrote, small and neat, in the hand she used for the computing sheets she sent every month to the comparer in Kennington:
cot 60° = + 0.577 cot 90° = 0 cot 116° = − 0.488
"The cotangent," she said, without turning round, "falls to nothing at a right angle and passes below the line beyond it. That is in every book of trigonometry. Now, sir, the common tables of logarithms give us the log cotangent of one hundred and sixteen degrees by giving us the log cotangent of its supplement, sixty-four degrees, which is the same number. They do not tell us it is negative. The computer must remember that for himself."
She wrote: log cot 116° = log cot 64° = 9.6882, and beside it, very firmly, (negative).
"Your third correction is the square of the moon's correction, multiplied by this cotangent, and reduced. If the cotangent is negative, so is the correction. I believe whoever computed the table for you looked out these logarithms in the common way and forgot to carry the sign across. It would be the easiest thing in the world to do. I have done it myself." That brought a sound from the gallery that was not quite a laugh. "So the value in your table, fifteen seconds, ought to stand with a minus. You have made the distance fifteen seconds too great, where it ought to have been fifteen seconds too little. The error is thirty seconds."
She wrote, beneath his underlined true distance, his own figures with one sign altered, and carried them down: a new true distance, half a minute less.
"There are some who will say thirty seconds of arc does not signify," she said. Now she did turn round. The faces were very far away, and very blurred, and she was glad of it. "But the moon goes about half a minute of arc against the stars in a minute of time. Thirty seconds in the distance is a minute of Greenwich time. A minute of time is fifteen minutes of longitude. And at the Line, fifteen minutes of longitude is fifteen miles."