ON MATHEMATICAL TAIJLES. 13 



all niatbcmaties, as tliey arc iti reality merely tables for the solution of right- 

 angled triangles ; we have noticed one such table (MASS.VLOur, § 3, art. 10), 

 •which was constructed for mining- (not nautical) purposes. 



AVo hope to repair the omission by Jippending a separate list of traverse 

 tables to a future Keport. 



Art. 13. A very important incidental gain that it was hoped would be 

 afforded by the present lleport, was the opportunity of correcting errors in loga- 

 rithmic and other tables by giving references to the places in which errata-lists 

 had been published. In the introductions or prefaces to works containing 

 tables, it is usual to give a list of the errors that have been found during 

 their preparation in previous tables ; and as few possessors of a work can be 

 acquainted with the publications that have appeared subsequently, it was 

 thought that by referring, under each title, to the works or periodicals in 

 which lists of errata in it had appeared, an important service would be rendered. 

 It was soon evident, however, that it was impossible to deal adequately with the 

 subject of errors in this manner. Many of the important collections have 

 been through very numerous editions ; and it was not always stated in which 

 editions the errors M'crc found ; and when the edition was stated, it was 

 doubtful (without examination) whether the errata-list in question had come 

 under the eye of the editor, and the errors been corrected in subsequent 

 editions, or not. In the case of stereotyped tables, successive tirages are more 

 and more accurate ; and in regard to collections of such tables published long- 

 ago, as, for example, Callct (first published in 1783, though since reset), it seems 

 useless to waste space by giving references to the numerous errata-lists that 

 have been published, some of which must necessarily relate only to the earlier 

 tirages, and must have been corrected long ago. This is the case with all the 

 chief tables, and only in particular instances, when circumstances rendered it 

 probable that the errata-lists would be of use, have references been given to 

 them. As, however, this state of affairs is very unsatisfactory, it is hoped 

 that in a subsequent Report a complete list of errors in later editions of the 

 most-used mathematical tables, still unsuperseded, may be given ; but it is ne- 

 cessary first to be satisfied that the errata given are not erroneous themselves. 

 Many of the chief modern lists of errata arc noticed in this lleport, and also 

 others that it seemed desirable to give references to at once ; but we have 

 made no effort to deal with the matter in a complete manner. It is much to 

 to be regretted that it is not iisual for editors of a new edition of a table to 

 give a list of the errors that occurred in former editions, and have been corrected 

 in that edition. It is only fair for the purchaser of a new edition of a work 

 to be informed wherein it difters from its predecessors ; but imfortunately the 

 object of the editor and publisher is to sell as many copies of the new edition, 

 not to render the old as valuable as the new. It is proper to add, however, 

 that usually, when tables are published by a mathematician for the advance- 

 ment of science, and not by a bookseller and editor for the sake of profit, an 

 exception is made to this rule, and errata are freely acknowledged. A renuirk 

 made by De Moi'gan with reference to mathematical books in general, viz. 

 that the absence of a list of errata means, not that there are no errors, but 

 merely that they have not been found out, is more applicable to tables than 

 to any other class of work, in spite of the care usually bestowed on them ; 

 and an error in a table is far more fatal than an error in any other class of 

 work, as there is no context (as far as the user is concerned) to show imme- 

 diately that the result taken from the table is erroneous. The subject of 

 errors will particularly occupy the attention of the Committee in a future 

 lleport. 



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