"I beg your pardon," she said. Her voice came out clearer than she had meant. "I should like to put a question, if I may."
There was a pause of absolute astonishment. Then someone in the gallery tittered, and someone else said, quite audibly, "Good God," and the President of the Institution looked at Sir Augustus as a host looks at a guest whose dog has got upon the table.
Sir Augustus smiled. It was a kind smile, which was worse than an unkind one would have been.
"By all means, madam," he said. "We are honoured. Though I fear, if it is the cost of the volume that concerns you, that it has been answered already; and if it is the becoming colour of the moon on a summer evening, I must refer you to the poets."
The laughter came then, warm and easy and general. It was not cruel. That was the thing she would remember. Nobody in the room meant her any harm; they had merely been given, at the end of a long and serious evening, something charming to laugh at, and they were grateful for it.
Mrs. Gage had gone the colour of the ribbon on Judith's bonnet. In the front row, the man in the blue coat had turned all the way round upon the bench, and was looking at her with a frown of the most intense concentration, as if she were a light he had not expected to raise.
Judith waited for the laughter to finish. It took some time. When it had finished, she said, "It is not the cost of the volume, sir. It is the third correction in your example. You have added it."
"I have," Sir Augustus agreed pleasantly. "That is the method."
"The distance in your example is above ninety degrees. The cotangent of an angle above ninety degrees is negative. The third correction, in that case, must be subtracted. Your table gives it with the plus sign. I believe the table has been computed by logarithms, and the sign of the cotangent has been lost; so that every value in every column above ninety degrees is not merely wrong, but wrong by twice its amount. In your example you have made the true distance too great by thirty seconds of arc." She drew a breath. "It is quite an error, sir. It is fifteen miles of longitude at the Line in this one example, and more in the far columns." And then, because the board was there, and the example was on it, and she could not bear to stand any longer explaining in words what could be shown in figures: "If I might have the chalk, I can show you." * * *