This method of calculating logarithms by the resolution of numbers into factors of the form 1 - .1^(r)n is generally known as Weddle's method, having been published by him in _The Mathematician_ for November 1845, and the corresponding method for antilogarithms by means of factors of the form 1 + (.1)^(r)n is known by the name of Hearn, who published it in the same journal for 1847. In 1846 Peter Gray constructed a new table to 12 places, in which the factors were of the form 1-(.01)^(r)n, so that n had the values 1, 2, ... 99; and subsequently he constructed a similar table for factors of the form 1 + (.01)^(r)n. He also devised a method of applying a table of Hearn's form (i.e. of factors of the form 1 +.1^(r)n) to the construction of logarithms, and calculated a table of logarithms of factors of the form 1 + (.001)^(r)n to 24 places. This was published in 1876 under the title _Tables for the formation of logarithms and antilogarithms to twenty-four or any less number of places_, and contains the most complete and useful application of the method, with many improvements in points of detail. Taking as an example the calculation of the Briggian logarithm of the number 43,867, whose hyperbolic logarithm has been calculated above, we multiply it by 3, giving 131,601, and find by Gray's process that the factors of 1.31601 are (1) 1.316 (5) 1.(001)^(4)002 (2) 1.000007 (6) 1.(001)^(5)602 (3) 1.(001)²598 (7) 1.(001)^(6)412 (4) 1.(001)³780 (8) 1.(001)^(7)340 Taking the logarithms from Gray's tables we obtain the required logarithm by addition as follows:-- 522 878 745 280 337 562 704 972 = colog 3 119 255 889 277 936 685 553 913 = log (1) 3 040 050 733 157 610 239 = log (2) 259 708 022 525 453 597 = log (3) 338 749 695 752 424 = log (4) 868 588 964 = log (5) 261 445 278 = log (6) 178 929 = log (7) 148 = log (8) -------------------------------------------------------- 4.642 137 934 655 780 757 288 464 = log(10)43,867 In Shortrede's _Tables_ there are tables of logarithms and factors of the form 1 ± (.01)^(r)n to 16 places and of the form 1 ± (.1)^(r)n to 25 places; and in his _Tables de Logarithmes à 27 Décimales_ (Paris, 1867) Fédor Thoman gives tables of logarithms of factors of the form 1 ± .1^(r)n. In the _Messenger of Mathematics_, vol. iii. pp. 66-92, 1873, Henry Wace gave a simple and clear account of both the logarithmic and antilogarithmic processes, with tables of both Briggian and hyperbolic logarithms of factors of the form 1 ± .1^(r)n to 20 places.