An Elementary Treatise on Mechanics: Comprehending the Doctrine of Equilibrium and Motion, as Applied to Solids and Fluids, Chiefly Compiled, and Designed for the Use of the Students of the University at Cambridge, New EnglandHillard and Metcalf, at the University Press; sold by W. Hilliard, 1825 - 440 σελίδες |
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Σελίδα 28
... radius AC , we describe an arc of a circle HCG , meeting in G and H the directions of the forces p , q , and let fall from the point C upon AD , AB , the perpendiculars CF , CI , and from the point H upon AD the perpendicular HL , it ...
... radius AC , we describe an arc of a circle HCG , meeting in G and H the directions of the forces p , q , and let fall from the point C upon AD , AB , the perpendiculars CF , CI , and from the point H upon AD the perpendicular HL , it ...
Σελίδα 47
... radius being supposed equal to 1 , 1 : AI :: sin AIA " : AA " " :: cos DGL : AA " = AI x cos DGL ; that is , substituting for AI its value above found , AA " = AA ' cos DGL — AA ' × sin DGL ; hence , if we multiply by the mass m to ...
... radius being supposed equal to 1 , 1 : AI :: sin AIA " : AA " " :: cos DGL : AA " = AI x cos DGL ; that is , substituting for AI its value above found , AA " = AA ' cos DGL — AA ' × sin DGL ; hence , if we multiply by the mass m to ...
Σελίδα 59
... radius . These formulas may be applied to any other curve . We pass now to the consideration of the centre of gravity of plane surfaces bounded by curved lines . 104. Let it be required to find the centre of gravity of the Fig . 42 ...
... radius . These formulas may be applied to any other curve . We pass now to the consideration of the centre of gravity of plane surfaces bounded by curved lines . 104. Let it be required to find the centre of gravity of the Fig . 42 ...
Σελίδα 61
... radius CA , which bi- Fig . 45 . sects the arc , and that it must be at the same distance from NN " as the centre of gravity of each of the two semi - segments APM , APM , we shall have 2 × 8 × PM3 ᎯᏢᎷ CE = PM3 24 = = ᎯᏢᎷ MM APM 3 ...
... radius CA , which bi- Fig . 45 . sects the arc , and that it must be at the same distance from NN " as the centre of gravity of each of the two semi - segments APM , APM , we shall have 2 × 8 × PM3 ᎯᏢᎷ CE = PM3 24 = = ᎯᏢᎷ MM APM 3 ...
Σελίδα 62
... radius , and two thirds of the chord of the arc . The formulas above found may be applied to any other curve , as the parabola , & c . 108. We now proceed to the consideration of curved surfa- ces , confining ourselves to those of ...
... radius , and two thirds of the chord of the arc . The formulas above found may be applied to any other curve , as the parabola , & c . 108. We now proceed to the consideration of curved surfa- ces , confining ourselves to those of ...
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Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Mechanics: Comprehending the Doctrine of ... John Farrar Πλήρης προβολή - 1825 |
An Elementary Treatise on Mechanics: Comprehending the Doctrine of ... John Farrar Πλήρης προβολή - 1825 |
Συχνά εμφανιζόμενοι όροι και φράσεις
according accordingly action angle angle of friction applied atmosphere axis bulk centre of buoyancy centre of gravity collision column consequently considered cord curve cylinder decomposed density described determine diameter direction distance effect elastic equal equation equilibrium exerted feet fluid force q friction fulcrum Geom gravity G heavy body hence horizontal inches inclined inclined plane infinitely small instant length Let us suppose lever machine mass Mech mercury moment of inertia move moveable multiplied parabola parallel parallelogram parallelopiped particles pass pendulum perpendicular piston point F power q pressure proportion pulley pump quantity of motion radius ratio represented resistance respect resultant rotation sides space specific gravity steam straight line stratum surface temperature tion triangle tube valve velocity vertical vessel weight wheel whence zero
Δημοφιλή αποσπάσματα
Σελίδα ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα ii - An Elementary Treatise on Mechanics, comprehending the Doctrine of Equilibrium and Motion, as applied to Solids and Fluids, chiefly compiled, and designed for the use of the Students of the University at Cambridge, New England. By John Farrar, Professor of Mathematics and Natural Philosophy.
Σελίδα 34 - ... the sum of the moments of the forces which tend to turn the body in one direction must be equal to the sum of the moments of those which tend to turn it in the opposite direction about the same axis.
Σελίδα ii - CLERK'S OFFIcE. BE it remembered, that on the eleventh day of November, AD 1830, in the fiftyfifth year of the Independence of the United States of America, Gray & Bowen, of the said district, have deposited in this office the title of a book, the right whereof they...
Σελίδα ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Σελίδα 354 - ... have, in the short branch, a quantity of air separated from the external air, and at the same pressure. Mercury is then poured into the long branch, so as to reduce the volume of this inclosed air by one-half; it will then be found that the difference of level of the mercury in the two branches is equal to the height of the barometer at the time of the experiment; the compressed air therefore exerts a pressure equal to that of two atmospheres. If more mercury be poured in so as to reduce the...
Σελίδα 416 - Here, too, we drop the consideration of friction and the weight of the piston. 536. The velocity of the water flowing from the sucking pipe into the barrel should be equal to the velocity with which the piston moves. For if it be greater, less work will be done than the pump is competent to effect; and if it be less, a vacuum will be produced below the piston, which will therefore be moved upwards with great difficulty. If v be the velocity of the water in the sucking pipe, d the diameter of that...
Σελίδα 388 - ... water. A body in motion appears to be resisted by a stagnant fluid, because it is a law of mechanical nature that force must be employed in order to put any body in motion. Now, the body cannot move forward without putting the contiguous fluid in motion, and force must be employed for producing this motion.
Σελίδα 359 - If this is so it is seen that air is being depleted from that part of the pattern between the ridge line AB and the trough line CD while it is accumulating between CD and EF. There is consequently divergence to the...
Σελίδα 415 - Hence the total pressure upon the side of a vessel containing water will be equal to the weight of a column of water whose base is equal to the area of...