United States or North Korea ? Vote for the TOP Country of the Week !
Similarly these curved lines can be found in all the cases which can be proposed, as will be sufficiently shown by one or two examples which I will add. Let there be given the surface of the glass AK, made by the revolution about the axis BA of the line AK, which may be straight or curved.
And the Master Mariner of the World did likewise, after which Ak, with sparkling eyes and smiling face, cried out: "I thank you, fellow immortals! For all have voted 'yes, and so to our dear Claus shall fall the one Mantle of Immortality that it is in our power to bestow!" "Let us fetch it at once," said the Fay King; "I'm in a hurry."
"Nevertheless," said the fair Queen, nodding her golden head at the Master Woodsman, "it would not be a vain guess that Ak has often assisted these hapless mortals." Ak smiled. "Sometimes," he replied, "when they are very young 'children, the mortals call them I have stopped to rescue them from misery.
Now if about the centres A, B, one describes the circles DK, EL, which represent the spreading of the waves which originate from these two points, and if one draws the straight line KL which touches these two circles, it is easy to see that this same line will be the common tangent to all the other circles drawn about the centres F, H, etc.; and that all the points of contact will fall within that part of this line which is comprised between the perpendiculars AK, BL. Then it will be the line KL which will terminate the movement of the particular waves originating from the points of the wave AB; and this movement will be stronger between the points KL, than anywhere else at the same instant, since an infinitude of circumferences concur to form this straight line; and consequently KL will be the propagation of the portion of wave AB, as has been said in explaining reflexion and ordinary refraction.
Therefore the whole line AH will represent the time along AD, DB. Similarly the line AC or AF will represent the time along AC; and FH being by construction equal to 3/2 of CB, it will represent the time along CB in the medium; and in consequence the whole line AH will represent also the time along AC, CB. Whence it appears that the time along AC, CB, is equal to the time along AD, DB. And similarly it can be shown if L and K are other points in the curve CDE, that the times along AL, LB, and along AK, KB, are always represented by the line AH, and therefore equal to the said time along AD, DB.
Finally the King of the Wind Demons, who had been whistling softly to himself, cried out: "What is your desire, O Ak?" "To bestow upon Claus the Mantle of Immortality!" said Ak, boldly. That this demand was wholly unexpected was proved by the immortals springing to their feet and looking into each other's face with dismay and then upon Ak with wonder.
He, who had supposed himself created differently from all others, now found the earth swarming with creatures of his own kind. "Indeed," said Ak, "the immortals are few; but the mortals are many." Claus looked earnestly upon his fellows. There were sad faces, gay and reckless faces, pleasant faces, anxious faces and kindly faces, all mingled in puzzling disorder.
The first such form which will occur to one's mind is the mere combination of the initial letters of the name as, for example, AB, or AK, which are the actual monograms of Andrew Both, the celebrated Flemish landscape painter, and of Antony Kölbel, a distinguished Austrian artist of more modern times.
And at last they returned to the grand old Forest of Burzee, where the Master set Claus down within the circle of nymphs, among whom the pretty Necile anxiously awaited him. The brow of the great Ak was now calm and peaceful; but the brow of Claus had become lined with deep thought.
"You have spoken well," returned Ak, and rising to his feet he continued: "Yet one thing must not be forgotten. Having been adopted as the child of the Forest, and the playfellow of the nymphs, you have gained a distinction which forever separates you from your kind.
Word Of The Day