## Transactions of the Cambridge Philosophical Society, Volume 20 |

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angles approximation associated pair asymptotic expansion coefficients components compound condition consider constants contour convergent corresponding covariants deduced degree denote determinant diffuse to measure diurnal inequality double conic doubly-periodic functions elements equal expression faculae Falmouth follows formula frequency frequency-locus fundamental differential equation fundamental system Gamma-function given Hence integer integral equation irreducible law of error linear functions linearly independent locus log F(z mean powers method middle constituent monogenic function Morgan Crofton moved by calcite multiple negative notation obtain order 2n pair of roots period positive Q-series quadrics quantity quintic radius of convergence range remove respect satisfied shew sin2 singularities solution substitution sun-spot maximum suppose surface symbolic products syzygies theorem theory transformation triple point values vanish vibration weak and diffuse

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Page 252 - THE SOCIETY takes this opportunity of expressing its grateful acknowledgments to the SYNDICS of the University Press for their liberality in taking upon themselves the expense of printing this Number of the Transactions.

Page 322 - Also values of - for positive electrons, so far as known, are always much smaller iti than this. Hence it seems preferable to conclude that the vibrations are due to negative electrons in all cases, and to suppose that in the neighbourhood of the systems which give ' inverse ' displacements the magnetic field changes sign, ie that these inverse effects are diamagnetic in character.

Page 414 - It is true that our investigation is more cumbrous, but that is to be expected both from the nature of the case and from the fact that we have not had anything like the theory of equations and of elementary divisors on which to fall back.

Page 434 - After what has been said above it will be clear that the various...

Page 255 - And the integral is equal to the sum of the residues of the subject of integration inside the contour. But by Gauss...

Page 115 - ... Professor Morgan Crofton, in cases where the range is infinite we are met with a difficulty when we proceed to expand the expression for the frequency of the compound in terms of the mean powers of the elements*. Some of the constituents of these means now become infinite ; and accordingly we are employing Taylor's theorem for the expansion of f(x + h) in ascending powers of h, in cases where h is infinite. A similar difficulty is presented by Laplace's method when it is attempted to expand ^(a)...

Page 308 - ... will shade off very gradually from the point of maximum intensity. Thus, if the friction is large the band has much the same intensity throughout a large portion of its breadth, and so, when the crystal is acted on by a magnetic field, the components of the resulting doublet will run into one another, and the separation will not be observed. The band, however, on the whole, will increase in breadth. This explains how, in some cases, the bands are observed merely to broaden, without being doubled.

Page 295 - H] where v is the velocity of the electron and c the velocity of light in aether.

Page 258 - R(x)<0, and, however large | a and p \ ma} be, we may take this integral along a contour in the finite part of the plane parallel to the imaginary axis so that — a is to the left of the contour. If then k be any finite quantity, and...

Page 277 - For consider the integral round a contour which embraces the positive half of the real axis and encloses all the poles of the subject of integration. It is evidently...