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To hurt anyone was atrocious; to hurt Hilary unforgivable. He would have done a great deal now to make amends. He stammered over it. "I did think, I'm afraid, that you and Cheriton were doing it to make him happy or something. I'm awfully sorry; I was an ass; I ought to have known. But it never occurred to me that you didn't kn that you had a different opinion of the things.

Here BL and KM are the sines of angles BKL, KBM; that is to say, of the angles PBA, QBC; and therefore they are to one another as the velocity of light in the medium A is to the velocity in the medium C. Then the time along LB is equal to the time along KM; and since the time along BC is equal to the time along MN, the time along LBC will be equal to the time along KMN. But the time along AK is longer than that along AL: hence the time along AKN is longer than that along ABC. And KC being longer than KN, the time along AKC will exceed, by as much more, the time along ABC. Hence it appears that the time along ABC is the shortest possible; which was to be proven.

Now let us assume that the ray has come from A to C along AK, KC; the point of refraction K being nearer to A than the point B is; and let CN be the perpendicular upon BC, KN parallel to BC: BM perpendicular upon KN, and KL upon BA.

"But it is always so in life," he continued, with a sigh, "we must not be discontented because the best we can get is not the best we can imagine. I am still young, but not too young to have kn Let us not talk about that. What did you think of the play last night?" I replied that it was a fine play. He agreed, saying it was "strepitosamente bello."

That was all; but the tone and the manner of the maid told that Jabez was a person of note with the messenger; every movement and glance were self-conscious. "That old ! He is a nuisance! What does he want now? Is his wife worse, or is he after a new one?" "I d' n' kn', m'm," said the maid, sheepishly, twisting her body and looking away, to appear unconcerned. "Would n' tell me. He ain' after me!