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angle answered applied axis base becomes called centre circle circumference Coll College comet common cone constant construction contain corresponding curve demonstration denote derivatives described determine diameter direction distance divided draw drawn earth envelope equal equation event evidently expression figure fluid force four function Geometry given gives height Hence inscribed Journal length less light Mass Mathematics means method miles Monthly motion nucleus observations obtain opposite origin parallel pass perpendicular plane position possible present Prize probability problem Prof proposition prove questions radius ratio reasoning reciprocal reference represented respectively result right angles roots sides solid solution sphere square straight line Student suppose surface taken tangent theorem third tion triangle vertical volume whole
Page 293 - In whatever direction a body moves on the surface of the earth there is a force arising from the earth's rotation which deflects it to the right in the northern hemisphere, but to the left in the southern.
Page 177 - Swift of foot was Hiawatha; He could shoot an arrow from him, And run forward with such fleetness, That the arrow fell behind him! Strong of arm was Hiawatha; He could shoot ten arrows upward, Shoot them with such strength and swiftness, That the tenth had left the bow-string Ere the first to earth had fallen!
Page 301 - We conclude, therefore, that the rings must consist of disconnected particles ; these may be either solid or liquid, but they must be independent. The entire system of rings must therefore consist either of a series of many concentric rings, each moving with its own velocity, and having its own system of waves, or else of a confused multitude of revolving particles, not arranged in rings, and continually coming into collision with each other.
Page 5 - Multiply each payment by its term of credit, and divide the sum of the products by the sum of the payments ; the quotient will be the average term of credit.
Page 192 - The Latitude of the Cambridge Observatory, in Massachusetts, determined from Transits of Stars over the Prime Vertical, observed during the months of December, 1844, and January, 1845, by William C.
Page 10 - The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 94 - ... to that event. This perhaps is the first instance where an envelope has been seen in embryo at the surface of the nucleus, and has been traced through successive stages to a full development. The same phenomenon was subsequently illustrated in the case of the present comet by several exhibitions of a similar nature ; their history has a peculiar value, because it affords an insight into the mysterious processes by which the train is thrown out from the nucleus, under the stimulating influence...
Page 149 - A Treatise on the Application of Analysis to Solid Geometry. Commenced by DF GREGORY, MA, late Fellow and Assistant Tutor of Trinity College, Cambridge ; Concluded by W. WALTON, MA, Trinity College, Cambridge. Second Edition, revised and corrected. 8vo. 12s.. Gregory and Walton. — Examples of the Processes of the Differential and Integral Calculus.
Page 390 - the cause of the atmosphere being so very much less in the southern than in the northern hemisphere remains to be determined." This is very satisfactorily accounted for by the preceding principle ; for as there is much more land, with high mountain ranges, in the northern hemisphere, than in the southern, the resistances are greater, and consequently the eastern motions, upon which the deflecting force depends, is much less ; and the consequence is, that the more rapid motions of the southern hemisphere...