The Mathematical Miscellany, Volumes 1-2W. E. Dean, printer, 1836 |
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Termos e frases comuns
a₁ algebraic angle angular ARTICLE astronomer axes axis b₁ becomes Catlin centre of gravity chord Clinton Liberal Institute co-ordinates cone constant cos² cosec cubes curve denote diameter difference distance divide drawn ellipse equal equation formula fraction give given circles given point Hamilton College Harvard University Hence integral intersection locus logarithms Macully mathematical motion multiplied negative observations odd number parabola Paul's College Peirce perpendicular plane positive Prof Professor quantities QUESTION r₁ radii radius real roots SECOND SOLUTION sides sin² sphere spherical square Sturm's Theorem substituting suppose surface tangent theory THIRD SOLUTION tion triangle values velocity vertex vertical whence whole number x₁ y₁
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Página 179 - Thy waters wasted them while they were free, And many a tyrant since; their shores obey The stranger, slave, or savage ; their decay Has dried up realms to deserts : not so thou; Unchangeable save to thy wild waves' play, Time writes no wrinkle on thine azure brow: Such as creation's dawn beheld, thou rollest now.
Página 50 - ... else respecting them is involved in profound mystery. From the whole of the facts M. Wartmann thinks that the most rational conclusion we can adopt is, that the meteors probably owe their origin to the disengagement of electricity, or of some analogous matter, which takes place in the celestial regions on every occasion in which the conditions necessary for the production of the phenomena are renewed.
Página 136 - ... on the surface of the earth, with the same instruments, and by the same methods which he had employed from Berlin to the mouth of the Obi, and thence to the Sea of Okhotsh. M. de Humboldt remarks that our epoch, marked by great discoveries in optics, electricity, and magnetism, is characterized by the possibility of connecting phenomena by the generalization of empirical laws, and by the mutual assistance rendered by sciences which had long remained isolated. Now, he observes, simple observations...
Página 136 - ... (as had been hitherto imagined) to the larger and extraordinary changes ; but that even the minutest deviation at one place of observation had its counterpart at the other. Gauss was thus led to organize a plan of simultaneous observations, not at intervals of an hour, but at the short intervals of five minutes. These were carried on through twenty-four hours six* times in the year ; and magnetic stations taking part in the system were established at Altona, Augsburg, Berlin, Bonn, Brunswick,...
Página 87 - Herschel it was who by night acted as his amanuensis; she it was whose pen conveyed to paper his observations as they issued from his lips; she it was...
Página 190 - ... as that betrayed by the Newtonian school in deciding on all that had been done in earlier times and all that was done around it. With disgust and indignation we find Priestley, in his History of Optics, like many before and after him, dating the success of all researches into the world of colours from the epoch of a decomposed ray of light, or what pretended to be so ; looking down with a supercilious air on the ancient and less modern inquirers, who, after all, had proceeded quietly in the right...
Página 40 - It is a singular result of the simplicity of the laws of nature, which admit only of the observation and comparison of ratios, that the gravitation and theory of the motions of the celestial bodies are independent of their absolute magnitudes and distances ; consequently, if all the bodies of the solar system, their mutual distances, and their velocities, were to diminish proportionally, they would describe curves in all respects similar to those in which they now move ; and the system might be successively...
Página 187 - ... collected and an idea of the character will be presented to us. The colours are acts of light ; its active and passive m.odifications : thus considered we may expect from them some explanation respecting light itself. Colours and light, it is true, stand in the most intimate relation to each other, but b we should think of both as belonging to nature as a whole, for it is nature as a whole which manifests itself by their means in an especial manner to the sense of sight. The completeness of nature...
Página 29 - The observer, who withdraws from all society, in order to devote his nights to watching the stars, is enervated by his loss of sleep, and unfitted for the labors of the day. He cannot live two lives ; and if he works while others sleep, he must sleep while others work. While he sustains science, science must sustain him.
Página 33 - Something has assuredly been discovered, and if that something be not parallax, we are altogether at fault, and know not what other cause to ascribe it to. The instrument with which Bessel made these most remarkable observations is a heliometer of large dimensions, and with an exquisite object'glass by Fraunhofer. I well remember to have seen this object'glass at Munich before it was cut, and to have been not a little amazed at the boldness of the maker who would devote a glass, which at that time...