Decline of Science in England by Charles Babbage (ebook reader with android os .TXT) 📕

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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