OF ARTS AND SCIENCES. 



409 



they differed by one grade, and in one case only by two grades. The 

 rehition between the grades and the scale of magnitude of the Bond 

 Catalogue was next found by grouping the stars by half-magnitudes. 

 The middle points of each group are given in the first column of Table 

 IT., the number of stars in the group in the second column, and the 

 mean of the corresponding values in grades in the third. Points were 

 then constructed with the first and third columns as ordinates, and a 

 smooth curve drawn through them. The comparative values of the 



TABLE II. 



grades and magnitudes derived from this curve are given in Table 

 III. Applying the results of this table to the last column of Table I. 

 gives the fourth column of that table. The results for all the stars in 

 the Bond Catalogue differing less than 1000" in right ascension and 

 declination from 6' Ononis, the brightest star in the nebula, are given 



TABLE III. 



in Table IV. The first four columns give the number, difference in 

 right ascension and declination from 6' Orionis, and magnitude accord- 

 ing to the Bond Catalogue. The fifth column gives the magnitude 

 found as described above from F, the photograph of Mr. Common- 



