29 



This is the final correction which must be added to the nieasured coordinate 

 along line 2, if the star be situatcd at the intersection of liues 2 and 31. 

 The corresponding coiTections have been computed in the same way for all 

 the points of intersection on the reseau. The results are set down in the 

 final table printed at the end of this paper. The last decimal has been 

 dropped, and the unit of the quantities in the table is the micron. 



It is very difficult to form a reliable estimate as to the accuracy of these 

 numbers. They are the result of the successive summation of so large a num- 

 ber of quantities independently observed, that they must necessarily contain a 

 considérable accumulation of error. Nor can the Repsokl measuring machine 

 be considered very well suited for the investigation of these réseaux, since 

 it M^as designed more especially for the measurement of plates. The uuraber of 

 comparisons between the scale and réseau for any one line is very great. The 

 proximity of the observer's body is almost certain to produce sensible and 

 irregulär changes of température. These changes will be différent for the 

 scale and réseau, nor is it possible even by the greatcst care to eliminate 

 the injurions effects from the results. If a glass scale could be substituted 

 for the metal one, this difficulty would probably disappear. 



Another objectionable feature of this machine is the difficulty of doing 

 away with the projection error discovered by Donner. It is very douptful if 

 this error is constant, and in any case its présence adds greatly to the num- 

 ber of quantities whose summation goes to make up our final corrections. 

 The projection error could doubtless be removed by changing somewhat the 

 design of the machine. The precision of the results could also be greatly in- 

 creased, even with the present machine, if in all the operations Avhere 

 bisections of the nine principal points occur, these points were bisected, several 

 times instead of once, This improvement of our methods did not occur to us 

 until the work was finished. 



