Decline of Science in England - Charles Babbage (reading well .txt) 📗
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having been entertained respecting the value of the principle of
repetition.
The following series of observations were made with the two
instruments. [I have chosen the inferior meridian altitude of
Polaris, merely because the number of sets of observations are
rather fewer. The difference between the extremes of the
altitude of Polaris, deduced from sets taken above the pole by
the same observers, amounts to seven seconds and a half.]
Latitude deduced from Polaris, with a repeating circle, 16 inches
diameter.—BASE DU SYSTEME METRIQUE, tom. iv. p. 376. 1807.
Number of Latitude Names of Observers.
Observations. of Formentera.
deg. min. sec.
64 38 39 55.3 Biot
100 54.7 Arago
10 56.2 Biot
88 56.9 Biot
120 56.7 Arago
84 54.9 Biot
100 56.5 Arago
102 57.1 Arago
80 54.5 Biot
88 53.3 Arago
90 53.6 Arago
88 53.8 Arago
92 53.7 Arago
42 55.6 Chaix
90 54.1 Chaix
80 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 recalculation 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 the
error of level:
Station. Star Latitude Latitude Diffe-by Capt. corrected for rence
Sabine error of level.
deg.min.sec. deg.min.sec. sec.
Sierra Leone Sirius 8 29 27.9 8 29 34.7 6.8
Ascension Alph.Centuri 7 55 46.7 7 55 40.1 6.6
Bahia Alph.Lyrae 12 59 19.4 12 59 21.4 2.0
Alph.Lyrae 21.2 58 49.8 31.4
Alph.Pavonis 22.4 59 5.1 17.3
Maranham Alph.Lyrae 2 31 42.4 2 31 22 20.4
Alph.Lyrae 43.8 31.8 12.0
Alph.Pavonis 44.5 44 .5
Alph.Lyrae 44.6 42.6 2.0
Alph.Cygni 42.1 39.2 2.9
Alph.Gruris 42.2 27.4 14.8
Trinidad Achernar 10 38 56.1 10 38 58.2 2.1
Alph.Gruris 52.2 50.8 1.4
Achernar 59.3 56.6 2.7
Jamaica Polaris 17 56 8.6 17 56 4.6 4.0
6.6 3.3 3.3
New York Sun 40 42 40.1 40 42 44.6 4.5
Polaris 48.9 38.2 10.7
Sun 41.4 47.2 5.8
Beta Urs.Min. 42.3 58.4 16.1
Hammerfest Sun 70 40 5.3 70 40 7.2 1.9
Spitzbergen Sun 79 49 56.1 79 49 58.6 2.5
Sun 55.9 44.8 11.1
Sun 58.6 52.7 5.9
Sun 59.3 51.6 7.7
Sun 55.8 51.6 4.2
Sun 50 1.5 57.0 4.5
Greenland Sun 74 32 19.9 74 32 32.4 12.4
Sun 17.9 18.7 0.8
Drontheim Sun 63 25 51.3 63 26 6.1 14.8
Alph.Urs.Min. 57.2 49.4 7.8
This presents a very different view of the latitudes as
determined by the small repeating circle, from that in Captain
Sabine’s book; and confining ourselves still to Maranham, where
the latitudes “WERE OBTAINED, WITH ESPECIAL REGARD TO EVERY
CIRCUMSTANCE BY WHICH THEIR ACCURACY MIGHT BE AFFECTED,” and
where “A MORE THAN USUAL ATTENTION WAS BESTOWED,” it appears,
that if we take Captain Sabine’s own test, namely, “the
differences of the partial results from the mean at each
station,” the deviations become nearly ten times as large as they
were before; a circumstance which might be expected to have some
influence in the decision of the question.
There is, however, another light in which it is impossible to
avoid looking at this singular oversight. The second column of
the table of latitudes must now be considered the true one, as
that which really resulted from the observations. Now, on
examining the column of true latitudes, the differences between
the different sets of observations is so considerable as
naturally to excite some fear of latent error, more especially as
nearly the greatest discordance arises from the same star,
Alph.Lyrae, observed after an interval of only three days. It
becomes interesting to every person engaged in making
astronomical observations, to know what is the probability of his
being exposed to an error so little to be guarded against, and so
calculated to lull the suspicions of the unfortunate astronomer
to whom it may happen.
In fact, the question resolves itself into this: the true
latitude of a place being determined by sets of observations as
in the first of the following columns—
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 observations
which may induce hundreds of meritorious officers to throw aside
their instruments, in the despair of ever approaching a standard
which is since admitted to be imaginary; and they have ratified
the doctrine, for I am not aware their official adviser has ever
even modified it, that diminutive instruments are equal almost to
the largest.
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