The Quarterly Journal of Pure and Applied Mathematics, Volume 11J.W. Parker, 1871 - Mathematics |
From inside the book
Results 1-5 of 32
Page 6
... sign : thus , is the greatest value of and the greater of the two quantities A , A , is the least value of w " . Suppose that in the following investigations A , is not less than ,, which if equivalent to the hypothesis that g ' is not ...
... sign : thus , is the greatest value of and the greater of the two quantities A , A , is the least value of w " . Suppose that in the following investigations A , is not less than ,, which if equivalent to the hypothesis that g ' is not ...
Page 7
... sign : thus A , is the greatest value of w and the greater of the two quantities A , A , is the least value of w " . Suppose that in the following investigations A , is not less than A ,, which if equivalent to the hypothesis that g ...
... sign : thus A , is the greatest value of w and the greater of the two quantities A , A , is the least value of w " . Suppose that in the following investigations A , is not less than A ,, which if equivalent to the hypothesis that g ...
Page 11
... sign from + to , the expression within the brackets does not change sign : thus we see that when d ( w3 ) dt d ( w3 ) dt -- d ( 12 ) changes sign from + todt changes sign from - + to or from to + . Consequently the maximum value of a ...
... sign from + to , the expression within the brackets does not change sign : thus we see that when d ( w3 ) dt d ( w3 ) dt -- d ( 12 ) changes sign from + todt changes sign from - + to or from to + . Consequently the maximum value of a ...
Page 43
... sign , we will suppose that n and q are odd , and consequently , that p is even ; the same result will be arrived at on any other supposition rela- tive to this point . Also p , q are > 0. We have then ( apa ( − papaq + 1 + ... + a a P ...
... sign , we will suppose that n and q are odd , and consequently , that p is even ; the same result will be arrived at on any other supposition rela- tive to this point . Also p , q are > 0. We have then ( apa ( − papaq + 1 + ... + a a P ...
Page 46
... is a first evectant when k or n is even . When is odd and n is odd , the invariant ( I ) vanishes identically by virtue of opposite signs . The preceding result may be regarded as a generalisation of 46 Note on a Binary Erectant Form .
... is a first evectant when k or n is even . When is odd and n is odd , the invariant ( I ) vanishes identically by virtue of opposite signs . The preceding result may be regarded as a generalisation of 46 Note on a Binary Erectant Form .
Other editions - View all
Common terms and phrases
a+b+c action af-g angle angular velocities axes body Cayley centre circle coefficient columns common tangent concyclic cone confocal conic conicoids conjugate coordinates corresponding cubic curvature cusps denote differential dt dt elements ellipsoid envelope equal equation Euler's equations evectant evolute expression fixed point formulæ given curve greatest value Hence inflexion instantaneous axis integral intersection line IJ log mv magic square nodal normal obtain pairs parallel curve perpendicular points of contact pole quadric quartic surface radius reciprocal respectively shewn solenoid solution stationary tangent suppose tangent planes theorem torse triads unlike signs vertex w₁ whence WILLIAM WALTON zero square
Popular passages
Page 187 - On the small oscillations of a Rigid Body about a Fixed Point under the action of any Forces, and more particularly when gravity is the only force acting," Transactions of the Boyal Irish Academy, vol.
Page 59 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 188 - ... to these directions are at right angles. III. A Free Rigid Body. 4. A free rigid body may receive any displacement by being screwed along an axis in space, the distance it travels along the axis when turned through the unit of angle being termed the pitch of the screw.
Page 50 - Д0 be the area of the triangle formed by joining the points of contact of the...
Page 189 - ... of these axes, as about a fixed axis, and its motion is always compounded of vibrations about these axes. 15. The length of the simple pendulum isochronous with the vibration about each normal axis is proportional to the square of the ratio of the corresponding diameter in the ellipsoid of equal energy to that of the momental ellipsoid.
Page 6 - I)2 = 0 ; and by reason of this property it is very easy to find the equations of the reciprocal surfaces, or plane-equations of the quartic surfaces in question. And, in the same paper, it is noticed that the surfaces of the form in question include the reciprocals of several interesting surfaces of the orders 6, 8, 9, 10, and 12 ; viz., order 6, parabolic ring : order 8, elliptic ring : order 9, centrosurface of paraboloid : order 10, parallel surface of paraboloid ; envelope of planes through...
Page 189 - A body rotating about a fixed point has throe degrees of freedom; its motion is compounded of vibrations about three normal screws whose pitch is zero, and whose directions pass through the point. NB — The screws in this case may be conveniently called the normal axes. V.
Page 9 - General Solution and Extension of the Problem of the 15 School Girls,
Page 309 - On the summation by definite integrals of geometrical series of the second and higher orders.