At the time when the calculation and publication of Taylor's Logarithms were undertaken, it so happened that a similar work was in progress in France; and it was not until the calculation of the French work was completed, that its author was informed of the publication of the English work. This circumstance caused the French calculator to relinquish the publication of his tables. The manuscript subsequently passed into the library of Delambre, and, after his death, was purchased at the sale of his books, by Mr Babbage, in whose possession it now is. Some years ago it was thought advisable to compare these manuscript tables with Taylor's Logarithms, with a view to ascertain the errors in each, but especially in Taylor. The two works were peculiarly well suited for the attainment of this end; as the circumstances under which they were produced, rendered it quite certain that they were computed independently of each other. The comparison was conducted under the direction of the late Dr Young, and the result was the detection of the following nineteen errors in Taylor's Logarithms. To enable those who used Taylor's Logarithms to make the necessary corrections in them, the corrections of the detected errors appeared as follows in the Nautical Almanac for 1832.
ERRATA, detected in Taylor's Logarithms. London: 4to, 1792.
| ° ' " | |||||
|---|---|---|---|---|---|
| 1 | E | Co-tangent of | 1.35.35 | for 43671 | read 42671 |
| 2 | M | Co-tangent of | 4. 4.49 | — 66976 | —— 66979 |
| 3 | Sine of | 4.23.38 | — 43107 | —— 43007 | |
| 4 | Sine of | 4.23.39 | — 43381 | —— 43281 | |
| 5 | S | Sine of | 6.45.52 | — 10001 | —— 11001 |
| 6 | Kk | Co-sine of | 14.18. 3 | — 3398 | —— 3298 |
| 7 | Ss | Tangent of | 18. 1.56 | — 5064 | —— 6064 |
| 8 | Aaa | Co-tangent of | 21.11.14 | — 6062 | —— 5962 |
| 9 | Ggg | Tangent of | 23.48.19 | — 6087 | —— 5987 |
| 10 | Co-tangent of | 23.48.19 | — 3913 | —— 4013 | |
| 11 | Iii | Sine of | 25. 5. 4 | — 3173 | —— 3183 |
| 12 | Sine of | 25. 5. 5 | — 3218 | —— 3228 | |
| 13 | Sine of | 25. 5. 6 | — 3263 | —— 3273 | |
| 14 | Sine of | 25. 5. 7 | — 3308 | —— 3318 | |
| 15 | Sine of | 25. 5. 8 | — 3353 | —— 3363 | |
| 16 | Sine of | 25. 5. 9 | — 3398 | —— 3408 | |
| 17 | Qqq | Tangent of | 28.19.39 | — 6302 | —— 6402 |
| 18 | 4H | Tangent of | 35.55.51 | — 1681 | —— 1581 |
| 19 | 4K | Co-sine of | 37.29. 2 | — 5503 | —— 5603 |
An error being detected in this list of ERRATA, we find, in the Nautical Almanac for the year 1833, the following ERRATUM of the ERRATA of Taylor's Logarithms:—
'In the list of ERRATA detected in Taylor's Logarithms, for cos. 4° 18' 3", read cos. 14° 18' 2".'
Here, however, confusion is worse confounded; for a new error, not before existing, and of much greater magnitude, is introduced! It will be necessary, in the Nautical Almanac for 1836, (that for 1835 is already published,) to introduce the following:
ERRATUM of the ERRATUM of the ERRATA of TAYLOR's Logarithms. For cos. 4° 18' 3", read cos. 14° 18' 3".
If proof were wanted to establish incontrovertibly the utter impracticability of precluding numerical errors in works of this nature, we should find it in this succession of error upon error, produced, in spite of the universally acknowledged accuracy and assiduity of the persons at present employed in the construction and management of the Nautical Almanac. It is only by the mechanical fabrication of tables that such errors can be rendered impossible.
On examining this list with attention, we have been particularly struck with the circumstances in which these errors appear to have originated. It is a remarkable fact, that of the above nineteen errors, eighteen have arisen from mistakes in carrying. Errors 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 19, have arisen from a carriage being neglected; and errors 1, 3, 4, 6, 8, 9, and 18, from a carriage being made where none should take place. In four cases, namely, errors 8, 9, 10, and 16, this has caused two figures to be wrong. The only error of the nineteen which appears to have been a press error is the second; which has evidently arisen from the type 9 being accidentally inverted, and thus becoming a 6. This may have originated with the compositor, but more probably it took place in the press-work; the type 9 being accidentally drawn out of the form by the inking-ball, as mentioned in a former case, and on being restored to its place, inverted by the pressman.
There are two cases among the above errata, in which an error, committed in the calculation of one number, has evidently been the cause of other errors. In the third erratum, a wrong carriage was made, in computing the sine of 4° 23' 38". The next number of the table was vitiated by this error; for we find the next erratum to be in the sine of 4° 23' 39", in which the figure similarly placed is 1 in excess. A still more extensive effect of this kind appears in errata 11, 12, 13, 14, 15, 16. A carriage was neglected in computing the sine of 25° 5' 4", and this produced a corresponding error in the five following numbers of the table, which are those corrected in the five following errata.