ON THE SQUARE BAR MICROMETER. 159 



at disappearance and reappearance. An additional injurious effect of this cause 

 proceeds, in the case of the ring, from the varying angle which the paths make 

 with its edge. 



A second advantage of the square is, that differences of right ascension and 

 declination are observed with equal accuracy, irrespective of the difference of 

 declination of the comet and the star, and of the parts of the micrometer which 

 they traverse. In the ring micrometer, on the contrary, a ' considerable portion 

 of its circumference cannot be used for declination determinations, and the diffi- 

 culties which often arise from the inconvenient position of the comet relative to 

 its comparison star, are such as require considerable skill and judgment to over- 

 come, and render it a dangerous tool in the hands of an inexperienced observer. 



In a third particular, of the least importance, the square recommends itself 

 by the greater simplicity of the reductions. This advantage obtains fully, how- 

 ever, only when the equatorial is provided with a position-circle, and is in good 

 adjustment; so that the same zero of position, once detex'mined, will serve for 

 observations in all parts of the sky. When the zero has to be determined at 

 each observation, the labor involved fairly offsets this advantage. 



From what experience I have had with both instruments I believe that the 

 square bar micrometer may be advantageously substituted for the ring micrometer. 

 As a means to bring it into wider employment, I have thought it would be 

 useful to describe the processes of observation, and to develop the various 

 formulae of reduction, and this I proceed to do. 



2. Orieiilaiion of the square. — The square is to be adjusted so that one diago- 

 nal is parallel either to the real, or to the apparent, diurnal motion. Which of 

 these modes of orientation is adopted by the observer will depend upon his cir- 

 cumstances and instrument. The processes involved in this adjustment, and in 

 the reduction of the observations, differ m the two cases in some important 

 particulars. Their description is deferred for convenience to articles 9 and 10. 



3. Mode of observation, and notaiion of transits. — The instants of transit to be 

 noted are those of disappearance of the star or comet behind the edge of each 

 bar. These transits will ordinarily be over those portions of the bars forming 

 the sides of the square ; but when the difference of declination is greater than the 

 diagonal, it will be necessary to observe one or both objects over the prolongations 

 of the bars beyond the square, north or south. 



In order to deduce general formuloe, applicable without special modification to 

 all observations, inside or outside the square, the following notation is adopted. 



