Elements of Natural Philosophy, Volume 1 |
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Page 4
The mathematical condition to be expressed in any case of it is simply that the
distance measured along the line from any one point to any other , remains
constant , however the line be bent . 17. The use of a cord in mechanism
presents us ...
The mathematical condition to be expressed in any case of it is simply that the
distance measured along the line from any one point to any other , remains
constant , however the line be bent . 17. The use of a cord in mechanism
presents us ...
Page 20
The motion of the treadle in a spinning - wheel approximates to the same
condition when the wheel moves uniformly ; the approximation being the closer ,
the smaller is the angular motion of the treadle and of the connecting string . It is
also ...
The motion of the treadle in a spinning - wheel approximates to the same
condition when the wheel moves uniformly ; the approximation being the closer ,
the smaller is the angular motion of the treadle and of the connecting string . It is
also ...
Page 25
But the plane and position of the circle of which this projection is taken may
clearly be found so as to fulfil the condition of having the projections of the ranges
coincident with any two given mutually bisecting lines . Hence any two given
simple ...
But the plane and position of the circle of which this projection is taken may
clearly be found so as to fulfil the condition of having the projections of the ranges
coincident with any two given mutually bisecting lines . Hence any two given
simple ...
Page 28
... is to say , that no other complex harmonic function than the one we have found
can satisfy the conditions . ] 90. We now pass to the consideration of the
displacement of a rigid body or group of points whose relative positions are
unalterable .
... is to say , that no other complex harmonic function than the one we have found
can satisfy the conditions . ] 90. We now pass to the consideration of the
displacement of a rigid body or group of points whose relative positions are
unalterable .
Page 29
It is not necessary to suppose the figure to be a mere flat disc or plane - for the
preceding statements apply to any one of a set of parallel planes in a rigid body ,
moving in any way subject to the condition that the points of any one plane in it ...
It is not necessary to suppose the figure to be a mere flat disc or plane - for the
preceding statements apply to any one of a set of parallel planes in a rigid body ,
moving in any way subject to the condition that the points of any one plane in it ...
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acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain remarkable respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire