Decline of Science in England [32]
Latitudes as True latitudes observed. computed by a mistake of Capt. Sabine's.
deg.min.sec. deg.min.sec. Alph.Lyrae, 28th Aug. . . . 2 31 22.0 2 31 42.4 Alph.Lyrae, 29th Aug. . . . 31.8 43.8 Alph.Pavonis, 29th Aug. . . 44,0 44.5 Alph.Lyrae, 31st Aug. . . . 42.6 44.6 Alph.Cygni, 31st Aug. . . . 39.2 42.0 Alph.Gruris, 2d Sept. . . . 27.4 42.2
what are the chances that, by one error all the latitudes in the first column should be brought so nearly to an agreement as they are in the second column? The circumstance of the number of divisions of the level being almost arbitrary within limits, might perhaps be alleged as diminishing this extraordinary improbability: but let any one consider, if he choose the error of each set, as independent of the others, still he will find the odds against it enormous.
When it is considered that an error, almost arbitrary in its law, has thus had the effect of bringing discordant observations into an almost unprecedented accordance, as at Maranham; and not merely so, but that at eight of the nine stations it has uniformly tended to diminish the differences between the partial results, and that at the ninth station it only increased it by a small fraction of a second, I cannot help feeling that it is more probable even that Captain Kater, with all his admitted skill, and that Captain Sabine himself, should have been both mistaken in their measures of the divisions of the level, than that so singular an effect should have been produced by one error; and I cannot bring myself to believe that such an anticipation is entirely without foundation.
Whatever may be the result of a re-examination, it was a singular oversight NOT TO MEASURE the divisions of a level intended to be used for determining so important a question; more particularly as, in the very work to which reference was made by Captain Sabine for the purpose of comparing the observations, it was the very first circumstance which occupied the French philosophers, and several pages [See pages 265 to 275 of the RECUEIL D'OBSERVATIONS GEODESIQUES, &c. PAR MM. BIOT ET ARAGO, which forms the fourth volume of the BASE DU SYSTEME METRIQUE.] are filled with the details relative to the determination of the value of the divisions of the level. It would also have been satisfactory, with such an important object in view, to have read off some of the sets after each pair of observations, in order to see how far the system of repetition made the results gradually converge to a limit, and in order to know how many repetitions were sufficient. Such a course would almost certainly have led to a knowledge of the true value of the divisions of the level; for the differences in the altitude of the same star, after a few minutes of time, must, in many instances, have been far too great to have arisen from the change of its altitude: and had these been noticed, they must have been referred to some error in the instrument, which could scarcely, in such circumstances, have escaped detection.
I have now mentioned a few of the difficulties which attend Captain Sabine's book on the pendulum, difficulties which I am far from saying are inexplicable. He would be bold indeed who, after so wonderful an instance of the effect of chance as I have been just discussing, should venture to pronounce another such accident impossible; but I think enough has been said to show, that the feeling which so generally prevails relative to it, is neither captious nor unreasonable.
Enough also has appeared to prove, that the conduct of the Admiralty in appointing that gentleman one of their scientific advisers, was, under the peculiar circumstances, at least, unadvised. They have thus lent, as far as they could, the weight of their authority to support observations which are now found to be erroneous. They have thus held up for imitation
deg.min.sec. deg.min.sec. Alph.Lyrae, 28th Aug. . . . 2 31 22.0 2 31 42.4 Alph.Lyrae, 29th Aug. . . . 31.8 43.8 Alph.Pavonis, 29th Aug. . . 44,0 44.5 Alph.Lyrae, 31st Aug. . . . 42.6 44.6 Alph.Cygni, 31st Aug. . . . 39.2 42.0 Alph.Gruris, 2d Sept. . . . 27.4 42.2
what are the chances that, by one error all the latitudes in the first column should be brought so nearly to an agreement as they are in the second column? The circumstance of the number of divisions of the level being almost arbitrary within limits, might perhaps be alleged as diminishing this extraordinary improbability: but let any one consider, if he choose the error of each set, as independent of the others, still he will find the odds against it enormous.
When it is considered that an error, almost arbitrary in its law, has thus had the effect of bringing discordant observations into an almost unprecedented accordance, as at Maranham; and not merely so, but that at eight of the nine stations it has uniformly tended to diminish the differences between the partial results, and that at the ninth station it only increased it by a small fraction of a second, I cannot help feeling that it is more probable even that Captain Kater, with all his admitted skill, and that Captain Sabine himself, should have been both mistaken in their measures of the divisions of the level, than that so singular an effect should have been produced by one error; and I cannot bring myself to believe that such an anticipation is entirely without foundation.
Whatever may be the result of a re-examination, it was a singular oversight NOT TO MEASURE the divisions of a level intended to be used for determining so important a question; more particularly as, in the very work to which reference was made by Captain Sabine for the purpose of comparing the observations, it was the very first circumstance which occupied the French philosophers, and several pages [See pages 265 to 275 of the RECUEIL D'OBSERVATIONS GEODESIQUES, &c. PAR MM. BIOT ET ARAGO, which forms the fourth volume of the BASE DU SYSTEME METRIQUE.] are filled with the details relative to the determination of the value of the divisions of the level. It would also have been satisfactory, with such an important object in view, to have read off some of the sets after each pair of observations, in order to see how far the system of repetition made the results gradually converge to a limit, and in order to know how many repetitions were sufficient. Such a course would almost certainly have led to a knowledge of the true value of the divisions of the level; for the differences in the altitude of the same star, after a few minutes of time, must, in many instances, have been far too great to have arisen from the change of its altitude: and had these been noticed, they must have been referred to some error in the instrument, which could scarcely, in such circumstances, have escaped detection.
I have now mentioned a few of the difficulties which attend Captain Sabine's book on the pendulum, difficulties which I am far from saying are inexplicable. He would be bold indeed who, after so wonderful an instance of the effect of chance as I have been just discussing, should venture to pronounce another such accident impossible; but I think enough has been said to show, that the feeling which so generally prevails relative to it, is neither captious nor unreasonable.
Enough also has appeared to prove, that the conduct of the Admiralty in appointing that gentleman one of their scientific advisers, was, under the peculiar circumstances, at least, unadvised. They have thus lent, as far as they could, the weight of their authority to support observations which are now found to be erroneous. They have thus held up for imitation