42 Compendious Logarithmic Tables. [No. 121. 



Lalande's tables to 10,000 occupy no less than 110 pages, 18mo. and 

 part of the 1 1 1th page. Mr. Bailey has given, in his astronomical tables, a 

 table of Logarithms to 1000 contained on 3 pages, 4to. but only to 4 

 places of decimals ; and subsequently he has given, as being more con- 

 venient for ordinary use, an Antilogarithmic table, of the same size and 

 extent as the former, and besides these I am not aware of any smaller 

 hitherto published.* 



Having occasion some years ago to lay off the divisions on some 

 sliding rules, I felt it was desirable to have at one view a table of 

 Logarithms to 1000, that I might avoid the inconvenience of turning 

 leaves with a beam compass in hand : I therefore wrote out the body 

 of the first table nearly in its present form. It was immediately evident 

 that if furnished with differences and proportional parts, the table would 

 serve for most common purposes : accordingly the difference between the 

 numbers in columns 4 and 5 having been written, the decimal parts 

 were got by means of a sliding rule, with no more labour than writing 

 them off. 



The extension of the table beyond 1000 was partly to fill up the 

 blank space, and also to avoid partly the inconvenience of the unequal dif- 

 ferences at the beginning of the table. I found, however, that as it 

 stood, even when the differences were most unequal, by attending to the 

 actual difference between the columns, and allowing a proportional part 

 for the difference between that and the difference here given, (and still 

 more easily by allowing at sight for the difference between the proporti- 

 onal part on that and the next line according to the distance from the 

 middle of the line,) I could get a result true, generally, within one, and 

 always within two units in the last figure ; and the same more conveni- 

 ently by taking the proportional part of the actual difference by means 

 of a sliding rule, which when engaged in calculation, I like to have al- 

 ways within reach. 



The second table was made for the purpose of finding the number to 

 a given Logarithm more readily than can be done by the other table. 

 It has also the advantage of having more equal common differences. 

 The utility of it for all ordinary purposes has been experienced by others 

 besides myself. 



* Dr. Maclear, for the use of the Cape Observatory, has remodelled Mr. Bailey's 2d 

 Table, and printed it on two foolscap pages, with proportional parts, in a form not 

 unlike that here jjriven. 



