Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 4
... develope these functions in series ascending according to integral powers of y , by Taylor's Theorem , which can always be done as long as the origin is arbitrary , we get a series which I shall write for shortness , d U = 2 cos ( y ) F ...
... develope these functions in series ascending according to integral powers of y , by Taylor's Theorem , which can always be done as long as the origin is arbitrary , we get a series which I shall write for shortness , d U = 2 cos ( y ) F ...
Page 5
... develope each term , such as ax " , in F ( x ) or f ( x ) , in a series , and then sum the series by the formula cos no +1 sin n✪ = cos " ( 1 + n 0 ( 1 + 2/2 √ = 1 tan 10 —... ) , 1 we find that the general value of U takes the form U ...
... develope each term , such as ax " , in F ( x ) or f ( x ) , in a series , and then sum the series by the formula cos no +1 sin n✪ = cos " ( 1 + n 0 ( 1 + 2/2 √ = 1 tan 10 —... ) , 1 we find that the general value of U takes the form U ...
Page 236
... developements has since become an important branch of pure mathematics . Among the various series by which an arbitrary function f ( x ) can be expressed within certain limits , as 0 and a , of the variable x , may particularly be ...
... developements has since become an important branch of pure mathematics . Among the various series by which an arbitrary function f ( x ) can be expressed within certain limits , as 0 and a , of the variable x , may particularly be ...
Page 238
... the method of this paper is an infinite series which may be summed , to a sufficient degree of approximation , without much trouble . The series for the developement of an arbitrary function con- 238 ON THE CRITICAL VALUES OF.
... the method of this paper is an infinite series which may be summed , to a sufficient degree of approximation , without much trouble . The series for the developement of an arbitrary function con- 238 ON THE CRITICAL VALUES OF.
Page 239
George Gabriel Stokes. The series for the developement of an arbitrary function con- sidered in this paper are two ... developements of the derived functions . 1. By the term function I understand in this paper a quantity whose value ...
George Gabriel Stokes. The series for the developement of an arbitrary function con- sidered in this paper are two ... developements of the derived functions . 1. By the term function I understand in this paper a quantity whose value ...
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according angle apply approximation arbitrary axes axis become infinite Cambridge Philosophical Society canal centre co-ordinates condition Consequently considered constant convergent series corresponding cosines cylinder Demy Octavo denote depth determined direction discontinuous divergent series dx dy elastic equal equation essentially convergent ether exact differential expansion expression finite force formula friction function given h vanishes Hence homogeneous function horizontal increases inertia integral length limit molecules moment of inertia observed obtained Octavo order of approximation oscillation oscillatory waves paper parallel parallelepiped particles perpendicular plane Poisson positive pressure quantities ratio rectangular refracting respect result satisfied shew shewn sines solid solitary wave sphere St John's College suppose surface tangential theorem theory tion variables velocity of propagation wave motion whence zero ηπα аф
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