42] ROYAL ASTRONOMICAL SOCIETY TO M. PETERS. 317 



It would be impossible for me to convey an adequate idea to any 

 one, unacquainted with M. Peters' paper, of the numerous precautions used 

 by him for this purpose. For instance,, the observations are made by 

 placing the wire very near the star, and then waiting for the time when 

 the star is exactly bisected by it. The large motions of the instrument 

 are always made without touching either the telescope or the divided 

 circle, or the pieces carrying the microscopes. In making the double 

 observation (face East and face West) the micrometer-screw is always 

 turned finally in the same direction, the reading of the levels is always 

 commenced at the same end of the scale (though they are protected from 

 heat by glasses). The effect of flexure of the telescope-tube is eliminated 

 by an important arrangement, by which the eye-piece and object-glass are 

 capable of being fixed at pleasure at either end of the tube. This trans- 

 position was made after every eight complete observations of the Sun. 



At every observation the readings of the microscopes are taken for 

 coincidence with both the preceding and succeeding divisions on the limb, 

 and the utmost pains are employed to correct for any inequality in the 

 micrometer-screw and for errors of division. 



Again, in the reduction of the observations and the elimination of the 

 unknown quantities, the same attention to minute accuracy is observable. 

 Thus, small terms are introduced into the expressions for aberration and 

 nutation which had hitherto been neglected, and an elaborate investigation 

 is entered into respecting the proper motions of the stars observed. The 

 unknown quantities to be determined are the correction to the assumed 

 latitude, the flexure of the telescope-tube, the correction of the thermo- 

 metrical coefficient of refraction, the correction of the assumed mean decli- 

 nation, the annual parallax, and the correction of the coefficient of aberration. 

 Of these, the first three are found by means of the observations of the 

 pole-star. All the equations are solved by the method of least squares, 

 and the greatest care is used in estimating the probable errors of all the 

 results, whether arising from probable errors of observation or uncertainty 

 in the elements employed in the calculation. 



There are also discussions on some curious points, such as the effect 

 of clouds on refraction, the possible variability of latitude, &c. The resulting 

 values for parallax are all positive, with the exception of that of a Cygni, 

 which comes out a minute negative quantity ; this, of course, only indicates 

 that the real parallax of that star is probably extremely small. 



