A Treatise on Statics: With Applications to Physics, Volume 2Clarendon Press, 1889 |
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Page 52
... element on which it acts . One very simple method of proof consists in imagining a surface precisely equal and similar to that of the given body to be traced out in a weightless fluid which is subject to any pressure . 5. If a curved ...
... element on which it acts . One very simple method of proof consists in imagining a surface precisely equal and similar to that of the given body to be traced out in a weightless fluid which is subject to any pressure . 5. If a curved ...
Page 64
... element of length at Q , 0 = angle between PQ and ds . If each element ds is acted upon by a force k sino.ds 2.2 perpendicular to the plane of PQ and ds , k being a constant , find the resultant force and couple of this force system ...
... element of length at Q , 0 = angle between PQ and ds . If each element ds is acted upon by a force k sino.ds 2.2 perpendicular to the plane of PQ and ds , k being a constant , find the resultant force and couple of this force system ...
Page 95
... element pole at the extremity of μ , we have by definition μdm = Idx dy dz , where dx dydz is the volume of the element of the body at the point considered . If f is the tensor of y , or the Earth's resultant magnetic force per unit ...
... element pole at the extremity of μ , we have by definition μdm = Idx dy dz , where dx dydz is the volume of the element of the body at the point considered . If f is the tensor of y , or the Earth's resultant magnetic force per unit ...
Page 115
... elements of work done during the passage ) is Px projection of AB along the direction of P. As an instance , take the ... element of work is expressed by ( 1 ) , and the total work done between A and B is S ^ ( Xda + Yay + Zdz ) , ( 2 ) ...
... elements of work done during the passage ) is Px projection of AB along the direction of P. As an instance , take the ... element of work is expressed by ( 1 ) , and the total work done between A and B is S ^ ( Xda + Yay + Zdz ) , ( 2 ) ...
Page 116
... elements , QR , of arc along the corresponding directions of 7 between A and Q. We may , of course , choose the small arcs QR , ... of such lengths that the elements , MN , ... are all equal , i . e . dp may be taken as a constant element ...
... elements , QR , of arc along the corresponding directions of 7 between A and Q. We may , of course , choose the small arcs QR , ... of such lengths that the elements , MN , ... are all equal , i . e . dp may be taken as a constant element ...
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Common terms and phrases
A₁ attraction axes axis catenoid centre of gravity charge co-ordinates coefficients components conductor cone constant couple curvature curve cylinder cylindroid denote density direction direction-cosines displacement distance ds ds dx dy dz element element plane ellipse ellipsoid elongation equal equation equilibrium equipotential surface expression external forces fixed force-intensity function Hence infinite integral intensity intersect inverse law of attraction length M₁ magnitude mass N₁ normal osculating plane P₁ P₂ parallel parallelopiped particle perpendicular pitch plane position Potential principal produced quadric radius rectangular resultant right line rigid body rotation round shear shearing stress shell Solid Harmonic sphere spherical Spherical Harmonics strain stress string suppose surface surface-density T₁ T₂ tangent tension term Theorem twist vector vertical wire wrench zero µ² аф
Popular passages
Page 234 - And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.
Page 97 - Supposing that an axis exists for all displacements round which the equilibrium is astatic, prove that if each force is resolved into two components, one parallel and the other perpendicular to the axis, each of these component sets is astatic for displacements round the axis. 13. In a non-equilibrating system of forces, if each force is resolved into two components, one...
Page 444 - P be any point in the beam, at which we shall calculate the Bending Moment, ie the sum of the moments of all the forces acting on the beam between P and A ; let the horizontal...
Page 374 - K and E are the complete elliptic integrals of the first and second kinds with modulus...
Page 234 - But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses: for whatever is not deduced from the phenomena is to be called an hypothesis ; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
Page 4 - ... draw the axis of the couple through the face or through the back of the watch. (y) Two couples result in a single couple whose axis is found from the axes of the component couples by the parallelogram law. Let the planes of the couples intersect in the line AS (Fig.
Page 31 - ... within the limits of the course in a reliable manner; (2) for the mark AB the candidate must be familiar with the subject matter in (1), with discussion of statics of a flexible string, with more extended development of rigid dynamics, including Lagrange's equations of motion and the elements of the theory of the motion of a rigid body about a fixed point, with hydrostatics, with differential equations of hydrodynamics and Bernoulli's theorem, with the theory of small vibrations applied to organ...
Page 275 - Surface, is such that the attraction is everywhere in the direction of its normal. For in no direction along the surface does the potential change in value, and therefore there is no force in any such direction. Hence if the attracted particle be placed...