282 



I)R J AS. BURGESS ON 



tallies the values of this factor are given for every value of t, and, at larger intervals, 

 from t=l'25 to t = 6'0 (on p. 295). The following values were also computed with 

 extreme accuracy : — 



X. 



€ •'■ 



2 _,. 





 | 



1 

 2 

 3 

 4 

 5 

 G 

 7 

 8 

 9 

 10 



1-000 

 •606 530 G59 712 633 423 603 799 534 990 

 •367 879 441 171 442 321 595 523 770 161 

 •135 335 283 236 612 691 893 999 494 972 

 •049 787 068 367 863 942 979 342 415 650 

 •018 315 638 888 734 180 293 718 021 273 

 006 737 946 999 085 467 096 636 048 423 

 •002478 752 176 666 358 423 045 167 431 

 •000 911 881 965 554 516 208 003 136 084 

 •000 335 462 627 902 511 838 821 389 126 

 •000 123 409 804 086 679 549 497 636 691 

 •000 045 399 929 762 484 851 535 591 516 



1128 379 167 095 512 573 896 158 903 

 0684 396 560 624 433 066 358 502 37 

 0-415 107 497 420 594 703 340 268 249 

 0-152 709 514 177 164 314 421 873 367 

 0-056 178 690 737 057 656 594 924 613 

 0020 666 985 354 092 053 857 068 941 

 0-007 602 959 022 761 767 784 966 646 

 0002 796 972 316 542 974 354 763 250 

 0-001 028 948 612 781 823 885 494 178 

 0-000 378 529 040 664 308 164 933 856 

 0-000 139 253 051 946 747 853 890 418 

 0000 051 228 334 931 587 428 772 169 



25. The first part of the table contains the values of H from £ = to £=r250, 

 at intervals of *001 to nine places of decimals, together with the first and second 



differences, and the corresponding values of-^e~ .* These values were computed in 

 1862, by using the general series for intervals of *02, and interpolating for the inter- 

 mediate values with six or more orders of differences. The second part contains tbe 

 values from t= 100 to t = 3"00. computed recently, to fifteen decimal figures, — (l) from 

 t = 1-000 to £ = 1-500 at intervals of '001, and (2) from t=V5 to t=3Q at intervals of 

 •002, with four orders of differences. In the last column of this portion of the table 



are given the corresponding values of log r^e - ' +10, to sixteen decimal places. And 

 (3) lastly, values of H and G from 3"0 to 6"0 are appended,! computed by means of 

 Laplace's fraction (§ 9), — the values of L (16) being preserved. These would enable us 

 to extend the general table still farther if required. 



* The differences of these values have been omitted from want of room on the page. The differences given through- 

 out the tables are stated to the nearest figure in the last place, being taken from the computations. 



t Mr J. W. L. Glaisher's table (referred to above, § 4) of the values of G from < = 3-00 to 4-50 (Phil. Mag., 4th 

 Ber., 1871, vol. xlii. p. 436) is computed for differences of O'Ol and to seven significant figures, that is from eleven to 

 fourteen decimal places ; the appended table gives the values computed to fifteen places. But the values of L wouhl 

 enable us to carry them to a much larger number of figures. 



