172 OBSERVATIONS ON NEBULAE 



with standard catalogues. The mean error of these estimations in position is 

 4", in distance .09 of the whole. As these estimations were of absolute dis- 

 tance, and included stars ranging from ^ Libras and ;i Ophinchi to such as 

 were several minutes asunder, it may be inferred that the errors of merely 

 relative distance in the drawings will be considerably less. 



A still better test is afforded by the comparison of the star-charts as first 

 copied from the heavens by simple estimation, with the projections afforded by 

 later micrometrical measurement. The latter were laid over the former, and 

 the discordances between the two are given in numbers in Article 34. By 

 taking from that table the mean of the errors of estimation on each star, we find 

 that, where they were made in the most careful manner, their average error in 

 right ascension is about 0.'4, and in declination about 6^". These were in a 

 space of 20' diameter; the spaces included between the settled, or standard 

 stars, are generally much smaller than this, and, of course, diminish the lia- 

 bility to error. Although the mean errors named above show that careful esti- 

 mations need not, in small spaces, be in error to so great an amount as 5" or 6', 

 (an accuracy not very far from that of actual measurement,) yet it may be well 

 to add, that some portions of the larger nebulae were more hurriedly and less 

 accurately observed, as explained in Article 34. From all these sources a 

 tolerably correct idea of the probable error of judgment, so to speak, may be 

 deduced. 



10. I will here speak of a method that I hit upon for the exact representation 

 of nebulae, which has essentially contributed to the accuracy of the accompa- 

 nying delineations; the one referred to in Article 2. It was first suggested by 

 the method usually adopted for the representation of heights above the sea- 

 level on geographical maps, by drawing curves which represent horizontal sec- 

 tions of hill and valley at successive elevations above the level of the sea, that 

 is, by lines of equal height; and it is the same in its principle. It is obvious, 

 that if lines be imagined in the field of view winding around through all those 

 portions of a nebula which have exactly equal brightness, these lines, trans- 

 ferred to our chart of stars, will give a faithful representation of the nebula and 

 its minutiae, and of the suddenness as well as of the amount of transition from 

 one degree of shade to another. I cannot better illustrate my idea than by a 

 reference to Plate II., the lines of which were transferred directly from the 

 field of view to the paper in this way, and will be immediately recognised as 



