Memoirs Presented to the Cambridge Philosophical Society on the Occasion of the Jubilee of Sir George Gabriel Stokes, Bart., Hon. LL. D., Hon. SC. D., Lucasian ProfessorThe University Press, 1900 - 447 من الصفحات |
من داخل الكتاب
النتائج 1-5 من 61
الصفحة iii
... Integers . By Major P. A. MACMAHON , R.A. , D.Sc. , F.R.S. , Hon . Mem . C.P.S. 12 III . On the Integrals of Systems of Differential Equations . By A. R. FORSYTH , Sc.D. , F.R.S. , Sadlerian Professor of Pure Mathematics 35 IV . Ueber ...
... Integers . By Major P. A. MACMAHON , R.A. , D.Sc. , F.R.S. , Hon . Mem . C.P.S. 12 III . On the Integrals of Systems of Differential Equations . By A. R. FORSYTH , Sc.D. , F.R.S. , Sadlerian Professor of Pure Mathematics 35 IV . Ueber ...
الصفحة 4
... integer ñ such that the modulus of the difference between FA ( x ) and the polynomial In ( x ) = Σc ! n ) Fv ( a ) ( x − a ) o ν for values of n greater than ñ , is less than σ for all the values of x belonging to X. The coefficients c ...
... integer ñ such that the modulus of the difference between FA ( x ) and the polynomial In ( x ) = Σc ! n ) Fv ( a ) ( x − a ) o ν for values of n greater than ñ , is less than σ for all the values of x belonging to X. The coefficients c ...
الصفحة 9
... integer λ exists such that ( λ ) | h ̧a2 ) ( 8 ) F11 ) ( a ) ( 1 + e ) ( x − a ) + h22 ) ( 8 ) F ′ ( 2 ) ( a ) { ( 1 + e ) ( x − a ) } 2 + ... + h§ ) ( a ) F ^ ( a ) { ( 1 + e ) ( x − a ) } ^ | < o , provided + xx . If on the ...
... integer λ exists such that ( λ ) | h ̧a2 ) ( 8 ) F11 ) ( a ) ( 1 + e ) ( x − a ) + h22 ) ( 8 ) F ′ ( 2 ) ( a ) { ( 1 + e ) ( x − a ) } 2 + ... + h§ ) ( a ) F ^ ( a ) { ( 1 + e ) ( x − a ) } ^ | < o , provided + xx . If on the ...
الصفحة 12
... integer , every coefficient is an integer . This fact depends analytically upon the circumstance that the product of any m consecutive integers is divisible by factorial m ; we have ( n + 1 ) 1 ' n + 2 2 ) ( ' n + 3 3 - 3 ) ... ( n + m ) ...
... integer , every coefficient is an integer . This fact depends analytically upon the circumstance that the product of any m consecutive integers is divisible by factorial m ; we have ( n + 1 ) 1 ' n + 2 2 ) ( ' n + 3 3 - 3 ) ... ( n + m ) ...
الصفحة 13
... integer n . There are other forms as well , e.g. the product X1X2X ̧2X1X5 , 51 which are not expressible in the rectangular lattice form , the theory of which is not yet complete . We see therefore that the product of N's contained in ...
... integer n . There are other forms as well , e.g. the product X1X2X ̧2X1X5 , 51 which are not expressible in the rectangular lattice form , the theory of which is not yet complete . We see therefore that the product of N's contained in ...
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
absorption acid aether amplitude axis B₁ bands centim chaîne chloride circle coefficients coil condenser conic constant contact transformations convergence coordinates corresponding cosh critical quadratic curve deflexion denote determined deux didymium diffuse dilution disc effect electric electrons equal équations erbium expression finite formula given Hence integer integrals vanishing Kimn linéaires lines lumière m₁ magnetic field minimal surface molecule monômes N₁ nitrate non-regular obtained opérateurs P₁ parallel period Periodogram peut plane plate polynôme régulier positive integer produits quantity quartic surfaces refrangible regular functions regular integrals rotation S₁ satisfied self-induction shews somme spark spectra spectrum subgroup substitution suppose surface t₁ t₂ tacnode tangent theorem theory thick u₁ U₂ V₁ variables velocity vibrations waves wire x₁ XVIII zero α₂ وو
مقاطع مشهورة
الصفحة 296 - A circular spindle is a solid generated by the revolution of a segment of a circle about its chord, which remains fixed.
الصفحة 218 - I found the proposition that by a centrifugal force reciprocally as the square of the distance a planet must revolve in an ellipsis about the centre of the force placed in the lower umbilicus of the ellipsis and with a radius drawn to that centre describe areas proportional to the times.
الصفحة xii - Talia propter merita non rnodo in insulis nostris doctrinae sedes septem te doctorem honoris causa nominaverunt, sed etiam exterae gentes honoribus eximiis certatim cumulaverunt. Hodie eodem doctoris titulo studiorum tuorum socios nonnullos exteris e gentibus ad nos advectos, et ipsorum et tuum in honorem, velut exempli causa, libenter ornamus. In perpetu.um denique observantiae nostrae et reverentiae testimonium, in honorem alumni diu a nobis dilecti et ab aliis nomismate honorifico non uno donati,...
الصفحة 57 - When the real part of X is positive, these integrals vanish with t] and there is a double infinitude of them. When the real part of X is negative, then it is necessary that A and B both vanish : that is, the integrals do not exist if they are to vanish with t. When B is zero, then the integrals become of the form where p2 is an arbitrary finite quantity, and pl is zero when t = 0.
الصفحة 42 - ... 0, t = 0. The equations are, in form, the same as before, except that the coefficients of the first power of the dependent variables on the right-hand side have been reduced by unity ; and the relation between the two sets of dependent variables is It is manifest that the equations in...
الصفحة 349 - For every free period of vibration (with a wave-length sufficiently large in comparison with the diameter of a molecule), there is a corresponding period (almost exactly, but not quite, coincident with it) of maximum dissipation for the incident waves.
الصفحة 68 - It has been proved that there are no rpgular integrals of the equation vanishing with t unless a is zero : and that, if a = 0, 'there exists a simple infinitude of regular integrals satisfying the equations. We proceed, not in the first place to the complete theorem but only to a partial theorem, by shewing that when a is not zero, there exists a simple infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t and t log t : and when a is zero, these non-regular...
الصفحة 53 - The equations in 77, and ^ possess regular integrals vanishing with t, and their expression involves A, the arbitrary constant; and therefore the original equations in u and v possess no regular integrals vanishing with t, unless the condition represented by a = 0 be satisfied ; but if that condition be satisfied, they possess a simple infinitude of regular integrals vanishing with t. The conditions represented by a = 0 and...
الصفحة 145 - A piece of brass wire 6'6 centims. long, with a screw thread cut on it, was fixed to this stirrup at right angles to the plane of the mirror, projecting equally on either side of the mirror. Two small brass cylinders could be screwed along this brass wire, and by means of them the moment of inertia and time of swing of the needle could be adjusted as required. The stirrup and mirror weighed 6'6 grms. The galvanometer has a solid...
الصفحة 292 - ... the angle 2-y at the summit of the cone, which is now directed outwards, being very small, n will be given...