An Introduction to Natural Philosophy: Designed as a Text- Book for the Use of Students in College

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Collins & Brother, 1860 - 456 Seiten
 

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Seite 27 - The sides of a triangle are proportional to the sines of the opposite angles.
Seite 47 - A weighted arithmetic mean is obtained by multiplying each value by some non-negative weight before summation and then dividing the sum of the products by the sum of the weights.
Seite 99 - For since the time of vibration is to the time of descent through half the length of the pendulum, as the circumference of a circle to its diameter, that is, as 3.14159 to 1?
Seite 136 - A man in a boat pulling a rope attached to a large ship, seems only to move the boat: but he really moves the ship a little, for...
Seite 186 - The cutting tool, shaped according to the pattern to be executed, is attached to the end of a screw; and the metal being held in a proper position beneath it, the Fly is made to urge the tool downwards with such force as to stamp out pieces of the required figure. When the pattern is complicated, and it is necessary to preserve with exactness the relative situation of its different parts...
Seite 186 - ... immense force against the substance destined to receive the impression. Some engines used in coining have flies with arms four feet long, bearing one hundred weight at each of their extremities. By turning such an arm at the rate of one entire circumference in a second, the die will be driven against the metal with the same force as that with which 7500 pounds weight would fall from the height of 16 feet ; an enormous power, if the simplicity and compactness of the machine be considered.
Seite 118 - Two equal circular disks with smooth edges, placed on their flat sides in the corner between two smooth vertical planes inclined at a given angle, touch each other in the line bisecting the angle. Find the radius of the least disk which may be pressed between them without causing them to separate. LXXIV. If two scales, one containing a weight P and the other a weight Q, be suspended by a string over a rough sphere, Q2...
Seite 396 - It is a general fact, to which there are only a few exceptions, that a ray of light in passing out of a rarer into a denser medium is refracted toward the perpendicular to the surface ; and in passing out of a denser into a rarer medium, it is refracted from the perpendicular. But the chemical constitution of bodies, as well as their density, sometimes affects their refracting power. Thus, inflammable bodies, as sulphur, amber, and...
Seite 163 - To investigate the proportion of the power to the weight in this case, let fig. 97. represent a section of the apparatus at right angles to the axis. The weight is equally suspended by the two parts of the rope, S and S', and therefore each part is stretched by a force equal to half the weight. The...
Seite 307 - ... to vibrate. That its motion may be free, the air contained within the drum has free communication with the external air by the open passage, f, called the eustachian tube, leading to the back of the mouth.

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