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Such are that the rays of light are propagated in straight lines; that the angles of reflexion and of incidence are equal; and that in refraction the ray is bent according to the law of sines, now so well known, and which is no less certain than the preceding laws. The majority of those who have written touching the various parts of Optics have contented themselves with presuming these truths.
If the medium or the substance of the thin plate is water, as in the case of the soap-bubble, which produces beautiful colours according to its different degrees of thinness, the thicknesses at which the most luminous parts of the ring appear are produced at 1/1.336 the thickness at which they are produced in air, and, in the case of glass or mica, at 1/1.525 at thickness, the numbers 1.336, 1.525 expressing the ratio of the sines of the angles of incidence and refraction which produce the colours.
It will be clear to the reader familiar with trigonometry that this ratio of the two sines is nothing else but the ratio of the two distances which served us as a measure for the respective apertures of the cone. It is now clear that the concept of the ray, as it figures in the usual picture of refraction, is in reality the boundary between the luminous space and its surroundings.
"No, I don't think there's any question as to his identity." "Have you worked it out by mathematics, dad?" Cub inquired. "Yes, by sines and cosines." "What are sines and cosines?" asked Hal. "You'll find out when you go to college and study trigonometry," Mr. Perry replied.
They have only to apply sines and co-sines, tangents and logarithms to a stock exchange quotation for me to grovel before their superior wisdom and consult them at every turn in life. Honoria had resolved to turn her great acquirements in Algebra and the Higher Mathematics to practical purposes. Moreover Honoria's purpose was two-fold.
To do him justice, he studied for two or three hours everyday, and it was not his fault if he did not advance but his head was confused with technical terms; he mixed all up together, and disparts, sines and cosines, parabolas, tangents, windage, seconds, lines of sight, logarithms, projectiles and traverse sailing, quadrature and Gunter's scales, were all crowded together, in a brain which had not capacity to receive the rule of three.
But "Pat", the engineer, oiler of the domestic machinery of the establishment, and keeper of this menagerie, seems overcome with fatigue; the Astronomer is eclipsed in a corner; the professors are absorbed in sines and co-sines; the Fisherman nods over his paper; Grandma knits her brows and the stocking; Elsie is deep in a book; and no one displays any special interest in the matter until pencils and paper are distributed for the game of Crambo.
In such a tide of charging and chasing, on that Right Wing and round all the Field in the Prussian rear; in such wide bickering and boiling of Horse-currents, which fling out, round all the Prussian rear quarters, such a spray of Austrian Hussars for one element, Maupertuis, I have no doubt, wishes much he were at home, doing his sines and tangents.
I ain't no spishus nigger myse'f, but I 'spizes fer ter year dogs a howlin' an' squinch- owls havin' de agur out in de woods, an' w'en a bull goes a bellerin' by de house den my bones git col' an' my flesh commences fer ter creep; but w'en it comes ter deze yer sines in de a'r an' deze yer sperrits in de woods, den I'm out den I'm done. I is, fer a fack.
The other arm of the lever describes also a triangle; and the corresponding sides of those two triangles, calculated scientifically, or measured geometrically, and also the sines, tangents, and secants generated from the angles, and geometrically measured, have the same proportions to each other as the different weights have that will balance each other on the lever, leaving the weight of the lever out of the case.
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