45] ROYAL ASTRONOMICAL SOCIETY TO PROF. H. D' ARREST. 345 



and parallel to our own. If a large number of instances, however, were 

 taken, it might be asserted with a high degree of probability that those 

 bodies which had a large proper motion were on an average nearer to us 

 than those whose proper motion was small. 



Now we know, at least approximately, the proper motions of many of 

 the fixed stars, and materials are gradually accumulating which will give 

 us a much more accurate and extensive knowledge respecting them ; but 

 of the proper motions of the nebulae we know little or nothing. 



Unfortunately for this object, the instruments of Sir William Herschel 

 were not well adapted for the very accurate determination of the places 

 of nebulse. He himself estimates that after 1785 the uncertainty of his 

 places might amount to 1^- minute of space in R. A., and from ! to 2 

 minutes in Declination, and that his earlier observations were liable to 

 much greater errors. Hence these observations can scarcely be employed 

 in such a delicate research as that of the determination of proper motions. 



The degree of accuracy attained in Sir John Hei'schel's two catalogues 

 is much greater. The author considers the probable error of a single obser- 

 vation in his northern catalogue not to exceed 1^- seconds of time in R. A., 

 and 30" in Declination. In his Cape Observations he estimates that the 

 error of a single observation will seldom exceed 30" of space in the direction 

 of the parallel, or 45" in that of the meridian. 



Both of these catalogues give the results of the separate determinations 

 of the place of a nebula, and therefore afford the means of calculating the 

 probable errors of the observed places. 



Professor D' Arrest has thus found that the probable error of a single 

 position is nearly 15" in R. A. and 19"'5 in Declination. 



Considering the comparatively recent date of these observations, however, 

 it is plain that a considerable time must elapse before the comparison of 

 Sir John Herschel's observations with later ones of a similar degree of 

 accuracy can be expected to yield trustworthy results respecting the proper 

 motions of the nebula?. 



M. Laugier was the first who attempted to determine the places of 

 certain selected nebulse with much greater precision than is attained in 

 Sir John Herschel's catalogues, in order that they might furnish a secure 

 foundation to future investigations respecting proper motion. In the Comptes 



A. 44 



