45] ROYAL ASTRONOMICAL SOCIETY TO PROF. H. D' ARREST. 347 



Sir John Herschel and in the small catalogue of Laugier are likewise reduced 

 to the same epoch (1850) for the sake of comparison. 



We are so much accustomed to think of the observations of nebulae in 

 connection with the most powerful instruments, that it will be no doubt a 

 matter of surprise that a refractor of scarcely 4|- inches aperture should have 

 been found suitable for such work. Professor D'Arrest, however, from his 

 experience with such an instrument, estimates that it is capable of shewing 

 nearly a thousand nebulae, that is about a third part of all that have been 

 observed in our latitudes with the most powerful telescopes. He remarks 

 also that the small nebula? of Herschel, mostly round or elliptical in form, 

 can have their places determined more accurately than the majority of tele- 

 scopic comets. Besides, in observing nebula?, there is the immense advantage 

 of being able to repeat the observation of one and the same place on 

 different nights. The prevailing central condensation in nebulae, which some- 

 times attains a degree of concentration almost stellar, and which very 

 frequently offers a well-defined nucleus, gives a great degree of definiteness 

 to the observation. Those nebula? which, for various reasons, cannot be 

 observed accurately are, according to Professor D'Arrest, comparatively less 

 numerous. Of the 53 nebula? observed by Laugier, 31 have been re-observed 

 by Professor D'Arrest. Excluding one of Laugier's right ascensions, which 

 is evidently affected with a large error, and three of the declinations, which 

 appear to be about 1' in error, perhaps through mistakes in copying, and 

 assuming the probable error of one of Laugier's positions to be equal to that 

 of the mean of three of his own single positions, Professor D'Arrest finds 

 each of these probable errors to be about 6" both in right ascension and 

 declination. By a provisional calculation of the probable error of his obser- 

 vations, founded on a comparison of the several determinations with their 

 mean, Professor D'Arrest finds that the probable error of a definitive position, 

 that is of the mean of the observations of three nights, generally depending 

 on 9 transits, does not exceed 4 or 5 seconds of space in each coordinate. 



Professor D'Arrest makes an interesting use of his comparisons of his 

 own places with those of Sir John Herschel. The mean epoch of Sir John 

 Herschel's observations is nearly 25 years earlier than that of his own. 

 Hence the difference between the places of a nebula as given by the two 

 authorities, and reduced to the same epoch, will include not merely the 

 errors of the observations, but also the proper motion for 25 years and the 

 difference of the star-places used in the reductions. Now, from the probable 

 errors of Sir John Herschel's and Professor D'Arrest's places which have been 



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