On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function |
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On a General Method of Expressing the Paths of Light, & of the Planets, by ... William Rowan Hamilton No preview available - 2018 |
On a General Method of Expressing the Paths of Light, & of the Planets, by ... William Rowan Hamilton No preview available - 2022 |
On a General Method of Expressing the Paths of Light, & of the Planets, by ... William Rowan Hamilton No preview available - 2018 |
Common terms and phrases
7th portion analogous astronomical characteristic function chord circular arch components of normal const cosines cosmological principle curve deductive optics dium ds(r dz dv equa expressed Fermat formulæ given point Huygens induction infinitesimal changes initial co-ordinates initial element integral law of least law of stationary law of varying least action linear paths luminous or visual luminous path mathematical method mirror motion name of action Natural Philosophy neral normal slowness ordinary or extraordinary partial differential equations paths of light perpendicular point of incidence positive semiaxes principle propagation of light Ptolemy ratio reflecting or refracting reflexion or refraction refracting surface Royal Irish Academy Sd'V Sd'x semiaxes of co-ordinates Snellius stationary action stationary length straight line straight ray SV dz SV SV SV SV tangent theorem theory tion vanish variable varying action visible objects visual communication waves δε δι бу
Popular passages
Page 8 - And if Natural Philosophy in all its parts, by pursuing this method, shall at length be perfected; the bounds of Moral Philosophy will be also enlarged.
Page 8 - As in mathematics, so in natural philosophy, the investigation of difficult things by the method of analysis, ought ever to precede the method of composition. This analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments, or other certain truths. For hypotheses are not to be regarded in experimental philosophy.
Page 8 - Phenomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shall occur from Experiments, it may then begin to be pronounced with such Exceptions as occur. By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general. This is the Method of Analysis: And the Synthesis consists...
Page 8 - And if natural Philosophy in all its parts, by pursuing this Method, shall at length be perfected, the Bounds of Moral Philosophy will be also enlarged. For so far as we can know by natural Philosophy what is the first Cause, what Power he has over us, and what Benefits we receive from him, so far our Duty towards him, as well as that towards one another, will appear to us by the Light of Nature.
Page 8 - And although the arguing from Experiments and Observations by Induction be no Demonstration of general Conclusions; yet it is the best way of arguing which the Nature of the Thing admits of, and may be looked upon as so much the stronger, by how much the Induction is more general.
Page 8 - ... may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if, at any time afterwards,, any exception shall occur from experiments ; it may then begin to be pronounced, with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients ; and from motions to the forces producing them ; and, in general...
Page 13 - We cannot, therefore, suppose the economy of this quantity to have been designed in the divine idea of the universe : though a simplicity of some high kind may be believed to be included in that idea.
Page 13 - ... at a curved mirror this economy is often violated. If an eye be placed in the interior but not at the centre of a reflecting hollow sphere, it may see itself reflected in two opposite points, of which one indeed is the nearest to it, but the other on the contrary is the furthest ; so that of the two different paths of light, corresponding to these two opposite points, the one indeed is the shortest, but the other is the longest of any.
Page 8 - ... must rededuce variety, and force the discovered law to utter its revelations of the future.
Page 9 - Those who have meditated on the beauty and utility, in theoretical mechanics, of the general method of Lagrange — who have felt the power and dignity of that central dynamical theorem which he deduced, in the...