Examinations Papers1898 |
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Page 58
... centre of mass from the outside angle of the square is √ a * + a'1 + 2 ( a + a ' ) ( aa ' — b2 ) b — ( a2 + a'2 ) b2 + 2b1 2 ( a + a ' - b ) 8. Prove that a system of forces in one plane on a rigid body can always be reduced to a ...
... centre of mass from the outside angle of the square is √ a * + a'1 + 2 ( a + a ' ) ( aa ' — b2 ) b — ( a2 + a'2 ) b2 + 2b1 2 ( a + a ' - b ) 8. Prove that a system of forces in one plane on a rigid body can always be reduced to a ...
Page 62
... centre of the circle . 5. Obtain the formula for the velocity and accelera- tion of a particle in plane polar coordinates . If the position of a particle in space is defined by the radius vector in the direction ( l , m , n ) , shew ...
... centre of the circle . 5. Obtain the formula for the velocity and accelera- tion of a particle in plane polar coordinates . If the position of a particle in space is defined by the radius vector in the direction ( l , m , n ) , shew ...
Page 63
... centre . Find the centre of mass of the top and its principal moments of inertia at the vertex . 10. Prove the property of the convertibility of the centres of oscillation and suspension of a rigid pendulum . Two pendulums of masses M ...
... centre . Find the centre of mass of the top and its principal moments of inertia at the vertex . 10. Prove the property of the convertibility of the centres of oscillation and suspension of a rigid pendulum . Two pendulums of masses M ...
Page 64
... centre , rolls down a rough plane of inclination a . Shew that the angular velocity is given by Ó2 ( k2 + a2 + c2 2ac cos 0 ) - = 2g { a0 sin a + c cos ( a + 0 ) } + C , where k is the spin - radius about the c.m. and ✪ is the ...
... centre , rolls down a rough plane of inclination a . Shew that the angular velocity is given by Ó2 ( k2 + a2 + c2 2ac cos 0 ) - = 2g { a0 sin a + c cos ( a + 0 ) } + C , where k is the spin - radius about the c.m. and ✪ is the ...
Page 76
... centre of gravity a short distance from the axis of suspension in the line joining its ends . How does this affect the accuracy of ( a ) the meridian , ( b ) the dip , deter- mined by its means ? How can any such inaccuracy be ...
... centre of gravity a short distance from the axis of suspension in the line joining its ends . How does this affect the accuracy of ( a ) the meridian , ( b ) the dip , deter- mined by its means ? How can any such inaccuracy be ...
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Page 20 - Du führst die Reihe der Lebendigen Vor mir vorbei, und lehrst mich meine Brüder Im stillen Busch, in Luft und Wasser kennen.
Page 290 - Adfirmabant autem hanc fuisse summam vel culpae suae vel erroris, quod essent soliti stato die ante lucem convenire carmenque Christo quasi deo dicere secum invicem seque sacramento non in scelus aliquod obstringere, sed ne furta, ne latrocinia, ne adulteria committerent, ne fidem fallerent, ne depositum appellati abnegarent.
Page 72 - Man may be excused for feeling some pride at having risen, though not through his own exertions, to the very summit of the organic scale; and the fact of his having thus risen, instead of having been aboriginally placed there, may give him hope for a still higher destiny in the distant future.
Page 199 - The sea of Fortune doth not ever flow ; She draws her favours to the lowest ebb : Her tides have equal times to come and go ; Her loom doth weave the fine and coarsest web; No joy so great but runneth to an end, No hap so hard but may in fine amend.
Page 205 - Far in a wild, unknown to public view, From youth to age a reverend hermit grew ; The moss his bed, the cave his humble cell, His food the fruits, his drink the crystal well: Remote from man, with God he pass'd the Prayer all his business, all his pleasure praise.
Page 210 - O daß dem Menschen nichts Vollkommnes wird, Empfind ich nun! Du gabst zu dieser Wonne, Die mich den Göttern nah und näher bringt, Mir den Gefährten, den ich schon nicht mehr Entbehren kann, wenn er gleich, kalt und frech, Mich vor mir selbst erniedrigt und zu nichts, Mit einem Worthauch, deine Gaben wandelt. Er facht in meiner Brust ein wildes Feuer Nach jenem schönen Bild geschäftig an. So tauml ich von Begierde zu Genuß, Und im Genuß verschmacht ich nach Begierde.
Page 73 - Till I the prince of love beheld, Who in the sunny beams did glide! He shew'd me lilies for my hair, And blushing roses for my brow; He led me through his gardens fair, Where all his golden pleasures grow.
Page 287 - Nee tibi diva parens, generis nee Dardanus auctor, Perfide ; sed duris genuit te cautibus horrens Caucasus, Hyrcanaeque admorunt ubera tigres.
Page 439 - To strew fresh laurels let the task be mine, A frequent pilgrim at thy sacred shrine ; Mine with true sighs thy absence to bemoan, And grave with faithful epitaphs thy stone.
Page 198 - ... the proper ingredients for qualifying a legislator ; that laws are best explained, interpreted, and applied, by those whose interest and abilities lie in perverting, confounding, and eluding them. I observe among you some lines of an institution which, in its original, might have been tolerable ; but these half erased, and the rest wholly blurred and blotted by corruptions.