A Treatise on Mechanics; Intended as an Introduction to the Study of Natural Philosophy

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1814 edition. Excerpt: ...separately what part of it arises from the action of the spirals of the screw upon each other, and what from the action of the lever. As the machine turns round, each point of the external screw acts upon the corresponding one of the internal screw with a force analogous to that by which a body is sustained upon an inclined plane when the power acts parallel to the base of the plane; the whole force therefore of the screw will be of the same kind, and (by Art. 1.) will bear to the weight which it could support, the ratio of " the distance between two spirals: circumference of the cylinder." This would be the case, supposing the force to act close to the surface of the cylinder; when it acts therefore at the extremity of the lever BC, it will be increased in the proportion of the radius of the lever: radius of the cylinder. 5. Let rf= the distance between two spirals of the screw, a = length of the lever (CB), / = 3.1415 &c. then the circumference (BDE) of the circle described by i--.. the extremity of the lever / = ipa. Let/1 = the power acting at the extremity of the lever, p = the power acting at the surface of the cylinder, fF=the weight which is kept in equi-'--E-" librio by P, then, by Art. 4, p. IV:: d: circumference AFG, P: p:: CA: CB:: circumf. AFG: circumf. BDE; ipaP ipaP jp, and a-j; hence, if any three of the four quantities IV, P, a, d be given, the fourth may be found. 6. We () AFG represents a section of the cylinder upon which the screw is cut. (b) From this proportion it appears that the relation of P W depends entirely upon the distance between the spirals and the circumference which the power describes, whatever be the thickness of the cylinder upon which the screw is cut; and since P ( Wd Wd, d =2paJ X a ' en s...show more

Product details

• Paperback | 96 pages
• 189 x 246 x 5mm | 186g
• Miami Fl, United States
• English
• black & white illustrations
• 1236558375
• 9781236558374