ON MATHEMATICAL TABLES. 133 



At the cud of tlio preface Mrs. Taylor makes the following curious re- 

 mark : — " Some errors have crept into the calculations from the multiplicity 

 of entries &c. ; these, I trust, will claim the indulgence of the public ; for 

 the system on which I have worked being mathematically correct, and 

 founded on sound principles, any slight oversight in the figures can be of 

 but little moment, and very easily rectified." It is to be presumed that this 

 does not refer to the tables included in this Eeport, as they would not havo 

 been calculated afresh. 



Mrs. Taylor was also the author of a work on navigation, the tables in 

 which arc described below. 



Janet Taylor, IS-iS. T. 3. Log sines, tangents, and secants to every 

 quarter point, to 6 places. 



T. 4. Six-figure logarithms of numbers to 10,000. 



T. 5. Log sines and tangents for every 10" to 2° ; and log sines, tangents, 

 and secants for eveiy minute of the quadrant, to 6 places, with differences. 



T. 30. Log versed sines for every 5' to 8^ to 5 places. 



T. 32. Natural sines for every minute of the quadrant, to 6 places. 



T, 35. Proportional logarithms for every second to 3°, to 4 places ; same 

 as T. 74 of Rapee. 



Mrs. Taylor, as we learn from an advertisement, kept a nautical academy 

 in the Minorics. 



Michael Taylor, 1792. [T. I.] Logarithms of numbers to 1260, to 7 

 places. 



[T. II.] Logarithms of numbers from 10,000 to 101,000, to 7 places, with 

 differences and proportional parts. The change in the tliird figure, in the 

 middle of the line is not marked. 



[T. III.] Table of log sines and tangents to every second of the quadrant, 

 to 7 places (semiquadrantally arranged). The change in the leading figures, 

 when it occurs in the middle of the column, is not marked at all ; and it 

 requires very great care in using the table to prevent errors from this 

 cause. If any one is likely to have to make much use of the table, it will 

 be worth his while to go through the whole of it, and fiU in with ink the first 

 after the change (making it a black circle such as is used to denote full 

 moon in almanacs), and also to make some mark that will catch the eye at 

 the top of every column containing a change. This will be a work of con- 

 siderable labour, but is absolutely necessary to ensure accuracy. It is uo 

 doubt chiefly on account of the absence of any mark at a change that 

 Bagat has so completely superseded this table, though difference of size &c. 

 are also in favour of the former. 



[T. I.] and [T. II.] present no novelty ; but [T. III.] is an enormous table, 

 containing about 450 pages, with an average number of about 7750 figures 

 to a page, so that it contains nearly three milhons and a half of figures. 

 The left-hand pages contain sines and cosines, the right-hand tangents and 

 cotangents. This is unfortunate, as the sines and cosines (which are used 

 far more frequently than the tangents and cotangents) are thus separated 

 at least a foot from the computer's paper as he works with the table on his 

 left ; and it is well known that the number of errors of transcription is 

 * proportional to the distance the eye has to carry the numbers, [T. III.] was 

 calculated by interpolation from YLAca's ' Trigonometria Ai-tificiahs,' to 10 

 places, and then contracted to 7 ; so that the last figure should always^ be 

 correct. Taylor was a computer in the Nautical Almanac Office ; he unfor- 

 tunately died almost at the moment of the completion of his work, only five 

 pages remaining unfinished in the press at the time of his death. These 



