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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。
To what extent this doctrine is correct； may perhaps yet admit of doubt。 It cannot； however； admit of a doubt； that it is unwise to crown it with official authority； and thus expose the officers of their service to depend on means which may be quite insufficient for their purpose。
How the Board of Longitude； after EXPRESSLY DIRECTING THIS INSTRUMENT TO BE MADE AND TRIED； could come to the decision at which they arrived； appears inexplicable。 The known difference of opinion amongst the best observers respecting the repeating principle； ought to have rendered them peculiarly cautious； nor ought the opinion of a Troughton； that instruments of less than one foot in diameter may be considered； 〃FOR ASTRONOMY； AS LITTLE BETTER THAN PLAYTHINGS；〃 ＇Memoirs of the Astronomical Society； Vol。I。 p。53。＇ to have been rejected without the most carefully detailed experiments。 There were amongst that body； persons who must have examined minutely the work on the Pendulum。 Captain