Transactions of the Cambridge Philosophical SocietyUniversity Press, 1849 - Science |
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Common terms and phrases
æther algebraical angle appears assume axes axis B₁ become infinite body centre co-ordinates coefficients condition consequently considered constant convergent convergent series corresponding cos² cosines curve definite integral denote determined direction displacement distance divergent divergent series dx dy elements equal equation equilibrium exact differential expansion expression fact finite fluid force formula function given glacial motion glacier gravity Greenwich Mean Hence hypothesis integral limit mass means motion negative observed obtained P₁ parallel parallelepiped particle perpendicular plane polarized positive pressure probability propagation proposition quantity radius remontoir respect result satisfied shew suppose surface syllogism symbol theorem theory true V₁ vanishes velocity velocity of propagation vibrations wave zero ηπα аф
Popular passages
Page 168 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 693 - ... on the hypothesis of original fluidity. The object of the author in the first part of this paper is to obtain the general connexion between the form of the surface and the variation of gravity along it, by an application of the doctrine of potentials, without making any hypothesis whatsoever respecting the distribution of matter in the interior of the earth. The latter part of the paper was devoted to the consideration of the irregularities produced in the variation of gravity by the irregular...
Page 448 - It is remarkable that this equation coincides with that of the prolate cycloid, if the latter equation be expanded according to ascending powers of the distance of the tracing point from the centre of the rolling circle, and the terms of the fourth order be omitted. The prolate cycloid is the form assigned by Mr Russell to waves of the kind here considered.
Page 676 - Gcf = mEa2, r= +<e-Jm)-(i-cos'0) ............ (16). Consider now the effect of the earth's attraction on the moon. The attraction of any particle of the earth on the moon, and therefore the resultant attraction of the whole earth, will be very nearly the same as if the moon were collected at her centre. Let therefore r be the distance of the centre of the moon from that of the earth...
Page 614 - He cannot see the force in either case ; he supplies it out of his own Ideas. And thus, a true Theory is a Fact; a Fact is a familiar Theory. That which is a Fact under one aspect, is a Theory under another. The most recondite Theories when firmly established are Facts : the simplest Facts involve something of the nature of Theory.
Page 172 - ... or italics or capitals can give. We see from what has been said, that when this is urged, before we can estimate the truth, or the value of the assertion, we must ask to whom is it a fact? what habits of thought, what previous information, what ideas does it imply, to conceive the fact as a fact ? Does not the apprehension of the fact imply assumptions which may with equal justice be called theory, and which are perhaps false theory ? in which case the fact is no fact.
Page 173 - If any one does not clearly comprehend this distinction of necessary and contingent truths, he will not be able to go along with us in our researches into the foundations of human knowledge; nor, indeed, to pursue with success any speculation on the subject."t In the following passage we are told what the distinction is, the non-recognition of which incurs this denunciation.
Page 692 - A'$r respectively, so as to get the part of Aw which is due to g by our knowledge of the height of the land and the depth of the sea, and the part which depends on A'</ by the result of pendulum-experiments. It may be observed that a constant error, or a slowly varying error, in the height of the land would be of no consequence, because it would enter with opposite signs into g
Page 171 - We have termed them ideas. It may be said they are relations of things, or of sensations. But granting this form of expression, still a relation is not a thing or a sensation; and therefore we must still have another and opposite element, along with our sensations. And yet, though we have thus these two elements in every act of perception, we cannot designate any portion of the act as absolutely and exclusively belonging to one of the elements. Perception involves sensation, along with ideas of time,...
Page 309 - The capability which solids possess of being put into a state of isochronous vibration shews that the pressures called into action by small displacements depend on homogeneous functions of those displacements of one dimension. I shall suppose moreover, according to the general principle of the superposition of small quantities, that the pressures due to different displacements are superimposed, and consequently that the pressures are linear functions of the displacements.