Decline of Science in England [30]
53.9 Arago
Mean of 1318 Observations, 38deg. 39min. 54.93sec.
*
Sets of Observations made with a six-inch repeating circle, at Maranham.
Star. Number of Latitude Observer. Observations. deduced.
deg. min. sec. alpha Lyrae 8 2 31 42.4 Capt. Sabine alpha Lyrae 12 43.8 Ditto alpha Pavonis 10 44.5 Ditto alpha Lyrae 12 44.6 Ditto alpha Cygni 12 42.1 Ditto alpha Gruris 12 42.2 Ditto
Mean latitude deduced from 66 observations 2deg. 31min 43.3sec.
In comparing these results, although the French observations were more than twenty times as numerous as the English, yet the deviations of the individual sets from the mean are greater. One second and three-tenths is the greatest deviation from the mean of the Maranham observations; whilst the greatest deviation of those of Formentera, is two seconds and two-tenths. If this mode of comparison should be thought unfair, on account of the greater number of the sets in the French observations, let any six, in succession, of those sets be taken, and compared with the six English sets; and it will be found that in no one instance is the greatest deviation from the mean of the whole of the observations less than in those of Maranham. It must also be borne in mind, that by the latitude deduced by the mean of 1250 superior culminations of Polaris by the same observers, the latitude of Formentera was found to be 38deg. 39min 57.07sec., a result differing by 2.14sec. from the mean of the 1318 inferior culminations given above. [This difference cannot be accounted for by any difference in the tables of refraction, as neither the employment of those of Bradley, of Piazzi, of the French, of Groombridge, of Young, of Ivory, of Bessel, or of Carlini, would make a difference of two-tenths of a second.]
These facts alone ought to have awakened the attention of Captain Sabine, and of those who examined and officially pronounced on the merits of his observations; for, supposing the skill of the observers equal, it seems a necessary consequence that "the performance of the six-inch circle is" not merely "fully equal to that of circles of larger dimensions," but that it is decidedly SUPERIOR to one of sixteen inches in diameter.
This opinion did indeed gain ground for a time; but, fortunately for astronomy, long after these observations were made, published, and rewarded, Captain Kater, having borrowed the same instrument, discovered that the divisions of its level, which Captain Sabine had considered to be equal to one second each, were, in fact, more nearly equal to eleven seconds, each one being 10.9sec. This circumstance rendered necessary a recalculation of all the observations made with that instrument: a re-calculation which I am not aware Captain Sabine has ever thought it necessary to publish. [Above two hundred sets of observations with this instrument are given in the work alluded to. It can never be esteemed satisfactory merely to state the mean results of the corrections arising from this error: for the confidence to be attached to that mean will depend on the nature of the deviations from it.]
This is the more to be regretted, as it bears upon a point of considerable importance to navigation; and if it should have caused any alteration in his opinion as to the comparative merits of great and small instruments, it might have been expected from a gentleman, who was expressly directed by the Board of Longitude, to try the question with an instrument constructed for that especial purpose.
Finding that this has not been done by the person best qualified for the task, perhaps a few remarks from one who has no pretensions to familiarity with the instrument, may tend towards elucidating this interesting question.
The following table gives the latitudes as corrected for
Mean of 1318 Observations, 38deg. 39min. 54.93sec.
*
Sets of Observations made with a six-inch repeating circle, at Maranham.
Star. Number of Latitude Observer. Observations. deduced.
deg. min. sec. alpha Lyrae 8 2 31 42.4 Capt. Sabine alpha Lyrae 12 43.8 Ditto alpha Pavonis 10 44.5 Ditto alpha Lyrae 12 44.6 Ditto alpha Cygni 12 42.1 Ditto alpha Gruris 12 42.2 Ditto
Mean latitude deduced from 66 observations 2deg. 31min 43.3sec.
In comparing these results, although the French observations were more than twenty times as numerous as the English, yet the deviations of the individual sets from the mean are greater. One second and three-tenths is the greatest deviation from the mean of the Maranham observations; whilst the greatest deviation of those of Formentera, is two seconds and two-tenths. If this mode of comparison should be thought unfair, on account of the greater number of the sets in the French observations, let any six, in succession, of those sets be taken, and compared with the six English sets; and it will be found that in no one instance is the greatest deviation from the mean of the whole of the observations less than in those of Maranham. It must also be borne in mind, that by the latitude deduced by the mean of 1250 superior culminations of Polaris by the same observers, the latitude of Formentera was found to be 38deg. 39min 57.07sec., a result differing by 2.14sec. from the mean of the 1318 inferior culminations given above. [This difference cannot be accounted for by any difference in the tables of refraction, as neither the employment of those of Bradley, of Piazzi, of the French, of Groombridge, of Young, of Ivory, of Bessel, or of Carlini, would make a difference of two-tenths of a second.]
These facts alone ought to have awakened the attention of Captain Sabine, and of those who examined and officially pronounced on the merits of his observations; for, supposing the skill of the observers equal, it seems a necessary consequence that "the performance of the six-inch circle is" not merely "fully equal to that of circles of larger dimensions," but that it is decidedly SUPERIOR to one of sixteen inches in diameter.
This opinion did indeed gain ground for a time; but, fortunately for astronomy, long after these observations were made, published, and rewarded, Captain Kater, having borrowed the same instrument, discovered that the divisions of its level, which Captain Sabine had considered to be equal to one second each, were, in fact, more nearly equal to eleven seconds, each one being 10.9sec. This circumstance rendered necessary a recalculation of all the observations made with that instrument: a re-calculation which I am not aware Captain Sabine has ever thought it necessary to publish. [Above two hundred sets of observations with this instrument are given in the work alluded to. It can never be esteemed satisfactory merely to state the mean results of the corrections arising from this error: for the confidence to be attached to that mean will depend on the nature of the deviations from it.]
This is the more to be regretted, as it bears upon a point of considerable importance to navigation; and if it should have caused any alteration in his opinion as to the comparative merits of great and small instruments, it might have been expected from a gentleman, who was expressly directed by the Board of Longitude, to try the question with an instrument constructed for that especial purpose.
Finding that this has not been done by the person best qualified for the task, perhaps a few remarks from one who has no pretensions to familiarity with the instrument, may tend towards elucidating this interesting question.
The following table gives the latitudes as corrected for