VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. l65 



The identity of each nebula in this catalogue has been well ascertained by a 

 projection on a proper map, made on purpose, which pointed out all other 

 nebulae near its place, and thus afforded the means of a rigorous examination. 

 When therefore several nebulae are found within the limits of the accuracy with 

 which my telescope can discriminate them, in different nights, it may be con- 

 cluded, that they were seen either at once in the same field of view, or otherwise 

 in immediate succession during the same sweep. In the same manner these 

 nebulae have been compared with those that are contained in the 2 volumes of 

 the Connoissance des Temps, for the years 1783 and 1784, of which none have 

 been inserted in this catalogue. It was indeed easy enough to distinguish the 

 nebulae of that excellent collection from those of mine which in several places 

 are very near them: the quantity of good light in my telescope having enabled 

 me, even in bright moon-light nights, to see occasionally some of the most feeble 

 of the former, when the latter could not by any means be perceived. 



Dr. H. adds the catalogue of the 1000 new nebulae and clusters of stars, with 

 an explanation of the marks and columns in which they are disposed; all which 

 it is unnecessary to repeat in this place. 



XXVI 11. Investigation of the Came of that Indistinctness of Vision which has 

 been ascribed to the Smallness of the Optic Pencil. By William Herschel, 

 LL. D., F. R. S. p. 500. 



Soon after my first essays of using high powers with the Newtonian telescope, 

 I began to doubt whether an opinion, which has been entertained by several emi- 

 nent authors, " that vision will grow indistinct, when the optic pencils are less 

 than the 40th or 50th part of an inch," would hold good in all cases. To judge 

 according to so rigid a criterion, I perceived that I was not entitled to see dis- 

 tinctly with a power much more than about 320, in a 7-feet telescope which bore 

 an aperture of 6.4 inches ; whereas in many experiments on double stars I found 

 myself very well pleased with magnifiers that far exceeded such narrow limits. 

 This induced me, as it were, by way of apology to myseF, for seeing well where 

 I ought to have seen less distinctly, to make a few experiments on the subject of 

 the diameter of optic pencils. It occurred to me, that an opinion which limits 

 them to any given size cannot be supported by theory, which does not determine 

 on subjects of this nature, but must be decided, like many other physical ques- 

 tions relating to matters of fact, by careful experiments made on the subject. 

 The way therefore to come at truth, in a case which seemed of considerable im- 

 portance, lay still open to me, as it had done to former observers ; and I thought 

 myself authorized, according to a Cartesian maxim, Dubia etiam pro falsis ha- 

 benda, to suppose, for a while, the size of optic pencils, requisite for distinct 

 vision, entirely undecided. 



