ON MATHEMATICAL TABLES. 133 



places. T. YII. (which occupies six closely printed pages). Modified Gaus- 

 sian logarithms. B (=log 1+j) and C ( =log ^rrU ^^^ tabulated for argu- 

 ment A (=log a-), to 5 places, from A=5 to 3 at intervals of -1 ; from A = 3 

 to 2-7 at intervals of -01; from A = 2-7 to 1-3 at intervals of -001 ; and 

 from A=l-3 to 3-0 at intervals of -01, and thence to A=5 at intervals of -1. 

 T. Yin. Log (1.2.3. .x) from x=l to .r=1000, to 5 and (for the argu- 

 ments ending in 0) to 8 places. 



Then follow 2 or 3 pp. of barometric &c. tables, and a page of constants 



(including a small table of log —, and the same for the tangent). 



The second volume contains T. III. of the 1844 edition, followed by some 

 spherical-trigonometry formulae, and the same page of constants as in vol. i. 



In the advertisement to the second (1849) edition, Shortrede says "a 

 small edition of this work was published in 1844, before I had an opportu- 

 nity of seeing it complete, which in several respects was such as I did not 

 like. In the present edition many alterations have been made to conform it 

 more to my views ; and for the convenience of purchasers it is now published 

 in two separate volumes." The prices of the two volumes are, Vol. 1. 12s., and 

 Vol. II. 30s. ; it is worth noting this, as we have seen it stated that the price 

 of Shortrede's logarithms (by which some might understand the whole work) 

 is 125. De Morgan says, " They [Shortrede's tables] first appeared in 

 1844; but some defects and errors having been found, the edition of 1844 

 was cancelled, and a new edition from corrected plates issued in 1849." 

 This may be true ; but although "we have seen four copies of the 1844 edi- 

 tion in difi'erent libraries, we were not able to obtain a sight of the 1849 

 edition anywhere till we bought it. Our copy of Vol. i. is dated 1849,- and of 

 Vol. ii. 1858. There are few tables in which, relatively to the number of 

 fgures, the pages are so clear, and the logarithmic canon to seconds is much 

 the most complete we have seen. Every one must agree with De_ Morgan 

 that the work shows extraordinary energy and public spirit. This is the 

 most complete second canon in existence, and is the most accessible. Only 

 two others have been published :— Michael Taylor, 1792, which has several 

 defects attending its use ; and Bagay, 1829, which is scarce. 



A list of twenty-six errors (nearly all in the antilogarithms) is given by 

 Shortrede himself in the 'Monthly Notices of the Eoyal Astronomical 

 Society' for January 1864; and a supplemental list is added in the same 

 publication for May 1867, where he says that "the unauthorized issue in 

 1844 contains several others." One erratum is also given in the 'Monthly 

 Notice ' for April 1867. Shortrede adds that the great majority of the 

 errata were communicated to him bj' Mr. Peter Gray. 



In the ' Insurance Eecord ' Mr. Fxlipowski charged Shortrede with having 

 corrected his table by the aid of his (Filipowski's). That the charge was 

 utterly unfounded is proved by the letter of Mr. Peter Gray (' Insurance 

 Record,' June 9, 1871), who states that the errata in Dodsox were given tv 

 Shortrede by himself (Mr. Gray) ; and we have seen reason to impute un- 

 fairness to Mr. Fihpowski in another matter with regard to Dodson (su 

 FiLiPOWsKi, 1849, § 4). Mr. Gray has kindly placed at our disposal his 

 copious list of errors in Dodson, of which we hope to make use in a sub- 

 sequent Heport. 



Shortrede did not pay sufficient attention to the examination of the errata- 

 lists of previous works ; and, in consequence, his tables contain a much greater 

 number of the hereditary errors that had descended from Vlacq than do the 



