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Thomson's lunar tables were first published in 1825. They were an instant commercial success, and they were re-printed annually and sometimes more frequently (these printings were called "editions" but that broke the normal definition used in publishing used in that era). There are a number of myths that developed about the tables soon after, but I thought it might be interesting to some of you to read a letter he wrote himself defending them against a bad review. Thomson died just a few years later in 1834 in Mauritius.

"A Letter to the Editor, from Mr. David Thomson, respecting his Lunar Tables.

Sir,

Having lately arrived from a voyage to India, I find that, during my absence, an attack has been made, in your 38th Number, on a set of Lunar and Horary Tables published by me ; and as I think that your correspondent has made several unfair comparisons of my Tables with some others, I trust you will insert the following answer to his remarks.

The person who has examined my book, has evidently done so with a determination to notice what he chooses to call its imperfections, without saying a single word in its favour ; and for that purpose, he has assumed a few examples of clearing the lunar distances from the effects of parallax and refraction, with the view of showing that the method given in my work is in some cases liable to error.

That such examples as those chosen by your correspondent could seldom or never occur in practice, must be obvious to every person conversant with the subject; and that my tables are not liable to any error of the least consequence, in any example that is likely to happen in practice, the following comparisons of the true distances, as found by my method, and those obtained by the usual modes of calculation, will, I trust, satisfy every unprejudiced person.

Examples taken from the second edition of Dr. Mackay's work on. the Longitude, being the first six given in that work.

[table: see original]

Four Examples taken from the seventh edition of Norie's Epitome of Navigation, in the order in which they stand in that work.

[table: see original]

Twenty-two Examples from Margett's Longitude Tables, calculated by Taylor's Logarithms, to the nearest tenth of a second.

[table: see original]

From these examples it may be seen how very unfairly your correspondent has examined my tables. For in none of them does the true distance, as computed by my method, differ so much as three seconds from the truth; and there are only four examples, out of the thirty-eight given, where the difference amounts to two seconds. In the last example given by your correspondent, to show the error to which my method is liable, he makes the error sixteen seconds, when it is only seven and a half seconds.

Your correspondent next gives an example, worked at full length by my method, with the view of showing that it is not shorter than the method given in the Appendix to the requisite tables, nor that given in Mr. Lax's tables. He, in fact, makes the latter method appear shorter than mine. This he has effected by introducing three proportions, wrought out in the most tedious manner, even to the tenth of a second, in order to find the third correction from my tables. I have worked many hundreds of examples by the method given in my book, and have never once had occasion to employ the Rule of Three in finding the third correction; nor did I ever hear of any one that had ; and, certainly, a man must be very unfit to determine the longitude of a ship at sea, by the lunar method, who is incapable of making such proportions at a glance. In fact, the number of figures required in correcting a lunar distance by my tables, is only about me third of the number your correspondent wishes to make appear necessary.

I shall not enter into an examination of all the strange cavilling remarks that your correspondent makes on my tables, as I feel confident the object he had for making them must be obvious to most of your readers; and even if his objections were well founded,—which they are not,—they would be of little or no consequence to the practical navigator, for whose use my book is intended. I may, however, notice his concluding remark, which is as follows:—" When the parallax is very great, or very small, the correction, by Capt. Thomson's method, must confessedly be defective." Now it will be seen, by several of the foregoing examples, that even when the moon's horizontal parallax is greater than 61', or less than 53', there is not the least error in the true distance deduced by my tables; and I have no doubt but your correspondent knows very well that it is only when the distance is very small, both altitudes low, and at the same time nearly equal, that the parallax makes the least difference in my method. That such a combination of circumstances could seldom happen is perfectly evident; but, in fact, such distances and altitudes are never observed at sea, for the purpose of determining the longitude.

22, Birchin-lane, August 26, 1826. David Thomson.

[Note.—The "concluding remark" was added by the Editor.] "

...from the Quarterly Journal of Science, Literature, and the Arts, 1827. You can find the rest including the specific cases which he has tried for comparison in the original article.

More later...

-FER

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