658 



Mr. J. R. Airey : Tables of 



ation, on the ground that it has served as a most useful clue 

 towards experiment and design of apparatus — stating it with 

 brevity, as explained in my paper. 



That paper was not concerned with discharge round a 

 closed contour in a self-contained completely-gaseous circuit, 

 which is a simpler matter : it is manifest that statements 

 about the behaviour of electrodes are not applicable when 

 there are no electrodes. 



The possibility that inconspicuous positive ions may after 

 all be the main carriers of current for the greater part of the 

 distance between, electrodes seems to me consistent with 

 Sir J. J. Thomson's old measurement of the speed at which 

 positive luminosity travels from the anode in a long tube, 

 which can be conveniently referred to in his Clarendon 

 Press 1893 volume, ' Recent Researches,' §§105, 106, 107, 

 p. 118; Proc. Roy. Soc. vol. xlix. p, 84. See also, as to the 

 influence of bounding surfaces or discontinuities like elec- 

 trodes, § 86, p. 103 of the same book. 



LXIII. Tables of Neumann Functions G n (x) and Y„(V). Bt/ 

 John R. Airey, M.A., B.Sc, late Scholar of St. Johns 

 College y Cambridge*. 



(A.) 



npHE values of the functions Gr (V) and Gri(#) have been 

 JL calculated by Aldisf to 21 decimal places from ^ = ()*1 

 to 6'0 by intervals of 0*1; In a paper by Michell on "The 

 Wave-resistance of a Ship," tables of these functions in the 

 form 



kJ (x)—Y (x) and fcJ^x) — Y^x), 



where /e = log 2 — y=-11593 . . . 



were given by Smith J from ^ = 0'00 to 1*00 and from 1*0 

 to 10"3. The calculations were carried out to four places of 

 decimals with an error of one in the last place and possibly 

 of two when the value of x is greater than 3 or 4. 



The following values of the G (x) and Gti(x) functions were 

 calculated from the semiconvergent series 



Go(-r) = - \/ ~ { P, sin ■(#- I) . + Qo cos (*- f ) } 



GiW= \/h{ p i° os (*- 1) -Qi sin (•'- j)} 



* Communicated by the Author. 



t Aldis, Proc. Rov. Soc. lxvi., 1899-1900. 



% Michell. Phil. Mag. [5] xlv., 1898. 



