28 REPORTS ON THE STATE OF SCIENCE. — 19l5. 



April 1909; and Eussell's 'Alternating Currents,' 2nd Edn., vol. 1, 

 chap. VII.). 



For the convenience of those who frequently require such Tables, 

 the following summary of some other important Tables of Bessel func- 

 tions and Zonal Harmonics may be useful : 



(1) Jo(a;) and Ji(a;) ; range a? = to 15-5, interval O'Ol, to 12 places 

 (Gray and Mathews' Treatise). 



(2) J„(.r) from n = upwards (integral) to from 16 to 60, according 

 to X ; for integral values of x between 1 and 24, to 18 places (ibid.). 



(3) J/cc) = ; first 50 roots, to 16 places (ibid.). 



(4) -Further Tables of roots of Bessel functions (Airey, ' Proc. Phys. 

 Soc.,' vol. 23 (1911), p. 219). 



(5) i„{x) ; Tables for calculating phase and amplitude (A. Lodee, 

 ' Brit. Ass. Rep.,' 1907, pp. 94, 95 ; 1909, p. 33). 



(6) ^i{x) : range x = to 5'1, interval 0001, to ninth decimal figure, 

 with first difference (Lodge, ' Brit. Ass. Rep.,' 1893, p. 229). 



(7) Io(a;) ; range, &c., as in (6) {iUd. 1896, p. 99). 



(8) I„(a;) ; range a? = to 6, interval 02, n = to 11 (integral) (' Brit. 

 Ass. Rep.,' 1889, p. 29). 



(9) Yo(x), Yi(x), Go(2;), Gi(a;) ; range x = to 16, interval OL to 

 7 figures approximately (Airey, ' Brit. Ass. Rep.,' 1913, p. 116). 



(10) Ko^a;) and Ki(a;) ; range a; = to 12, interval 01, to many figures 

 (Aldis, ' Roy. Soc. Proc' (1898), vol. Ixiv., p. 203). 



(11) K„(j'); range .c = to 5, interval 02, to 5 figures (Isherwood, 

 'Manc'i. Mem.,' vol. 48 (1904), No. 19. 



(12) ber x, bei x, ber'x, bei' x ; range a; = to 10, interval 0-1, with 

 first seven dift'erences (Webster, ' Brit. Ass. Rep.,' 1912, p. 57). 



(13) Definition, properties, and tables of ber x, kcr x, &c., and allied 

 functions (Russell and Savidge, ' Phil. Mag.,' April 1909 and Jan. 1910). 



(14) Exact Tables of P„(ju,) from n = 1 to w = 7, yu, = to /* = 1, 

 interval 001 (Glaiaher, ' Brit. Ass. Rep.,' 1879, p. 49). 



(15) Po(At) to P7(/x) ; four-figure Tables at 1° interval (Perry, ' Phil. 

 Mag.,' Dec. 1891, p. 512). 



(16) Pi(cos«)toP.a,(cos(9)., ^ = 0°to90°, interval 5°, 7 figures ^Lodge, 

 ' Phil. Trans.,' vol. 203 (1904), p. 100). 



The Committee has in course of preparation some sine and cosine 

 Tables proceeding by fractions of radians instead of degrees. A large 

 demand for these Tables has always existed, and, in particular, they will 

 be of very great value for the rapid calculation of large classes of im- 

 portant transcendental functions from their asymptotic series. Those 

 in hand at present are the sine and cosine of angles from 001 to 1'60 

 radians by intervals of 001, and from 00001 to 00100 by intervals of 

 0*0001 , These Tables will be comparatively short, and the calculations 

 are proceeding to 10 significant figures. 



Table I. 

 The Bessel Functions, J„(a;). 

 These functions have been tabulated by Meissel to eighteen places 

 of decimals for integral values of x from 1 to 24. From the values of 

 Jo(x) and Ji(x), the following supplementary tables have been calculated 

 to six places of decimals from x = 0-2 to 6-0 by intervals of 0-2, the actual 

 computation being carried to ten places, and from 6'0 to ]6"0 by intervals 

 of 0-5 to ten places from results obtained to twelve places. 



