WITH A FOURTEEN FEET REFLECTOR. 171 



of the larger stars are well settled by fixed instruments, there will be far less 

 room for error in estimations which spread, as from so many centres, over the 

 remaining intervals. It was extremely desirable, in the present case, to ensure 

 accuracy by such a course ; although it would have been preferable, had the 

 means existed, to have resorted to it in the first instance. The opportunity 

 was, however, fortunately aiforded at a late period of this research, by the un- 

 expected arrival of an excellent micrometer from England, belonging to Yale 

 College, and adaptable to the ten feet Clarke's telescope in the observatory of 

 the institution. I was enabled, by the kindness of Professor Olmsted, to avail 

 myself of this instrument, and, during the fall of 1839, took repeated measures 

 in right ascension and declination of so many stars in each nebula as would 

 serve to determine, within a very small quantity, the places of those which 

 were utterly too faint for any measurement. An abstract of these measures is 

 contained in this paper. By these means the places of all the stars were 

 brought to such a degree of exactness that it was thought expedient to throw 

 them into the form of catalogues, especially as a direct reference could thus be 

 made to any particular star, and, through it, to any portion of each nebula, 

 without the necessity of encumbering the map with multitudes of letters or 

 numbers. These catalogues, which are contained in Articles 37, 38 and 39, 

 will be referred to constantly in this paper, and from them the star correspond- 

 ing to any number in the catalogues will be easily found on the maps. 



9. There must be a very considerable, though partial dependence, after all, 

 upon the eye of the observer and the delicacy of its judgments. And as, in 

 the use of any instrument, we feel unsafe and distrustful until aware of its 

 errors and their probable amount, so in this kind of estimation by the eye, a 

 knowledge of its liability to error is necessary to command the confidence either 

 of the observer or of others in the results obtained by this means. To ascer- 

 tain the liability of these charts to error from this source, I frequently drew a 

 set of triangles upon paper, and after estimating their angles and the compara- 

 tive lengths of the sides, measured the same. From the mean of a great num- 

 ber of trials, I found my average error in such estimations to be less than two 

 degrees upon angles, and 2V o*^ to in comparative distances. A fairer allow- 

 ance may, perhaps, result from estimated angles of position and distances of 

 double stars. I have a record of a considerable number of such, observed on 

 the meridian during the summer of 1838, thirty -six of which are comparable 



