240 



by copies : nor is the uncertainty of copies being accurately taken 

 greater in any case than in that of copied numbers. It is conse- 

 quently useful to contrive new and easy methods for computing new 

 tables, or for examining those we already have ; and it is particularly 

 useful to contrive methods by which any part of a table may be ve- 

 rified, independently of the rest ; for by examining parts taken at 

 random, we may, in some cases, acquire a moral certainty respecting 

 the accuracy of the whole. 



Among the various methods of computing logarithms, none, our 

 author says, possesses the advantage of forming them with tolerable 

 ease, independently of each other, by means of a few easy bases. 

 This desideratum, he trusts, the method described by him will supply ; 

 being very easy of application, as it requires no division, multiplica- 

 tion, or extraction of roots, and has its relative advantages highly in- 

 creased by increasing the number of decimal places to which the 

 computation is carried. 



The chief part of the work, according to the method laid down by 

 Mr. Manning, consists in merely setting down a number, under itself, 

 removed one or more places to the right, and subtracting ; then re- 

 peating this operation. This method, consequently, is very little 

 liable to error ; and may be performed, after a few minutes instruc- 

 tion, by any one who is able to subtract. Besides, from the com- 

 modious situation of the figures, the work may be revised with great 

 rapidity. It is as easy for large numbers as for small ones ; and, on 

 an average, about 27 subtractions will furnish a logarithm accurately 

 to ten places of decimals. 



A similar method, by addition only, may, Mr. Manning says, in 

 some cases, be used with advantage ; and various artifices may be 

 occasionally employed to shorten the computation, both in the me- 

 thod by subtraction and in that by addition : the two methods may 

 also be sometimes advantageously combined together. It must, how- 

 ever, be observed, that the method by subtraction has many advan- 

 tages over that by addition ; particularly as from its being more 

 simple, and more completely mechanical, it may be confided to the 

 most unskilful persons without much danger of error. 



Various examples of our author's mode of computation and rules 

 for conducting it are given, for which we must necessarily refer to 

 the paper itself. 



Description of the Mineral Basin in the Counties of Monmouth, Gla- 

 morgan, Brecon, Carmarthen, and Pembroke. By Mr. Edward 

 Martin. Communicated by the Right Hon. C. F. Greville, F.R.S. 

 Read May 22, 1806. [Phil. Trans. 1806, p. 342.] 



The basin, which is here described by Mr. Martin, is delineated 

 in a map annexed to the paper ; it is formed of limestone, and con- 

 tains all the strata of coal and iron ore in South Wales : it is up- 

 wards of 100 miles in length; and its average breadth in the coun- 

 ties of Monmouth, Glamorgan, Carmarthen, and part of Brecon, is 



