Rm^al Astronomical Society. 1 39 



into coincidence with the angular point by the clock's rate is noted. 

 In other respects the operation is the same as that just described. 

 The chronometer is compared with the transit-clock at the end of 

 the series (sometimes, also, before its commencement), and finally 

 the barometer and thermometer are read off. 



" With respect to the reduction of the observations, the chief 

 things to remark upon are the corrections for the clock's rate, and 

 for refraction. The differences of the hour-circle sector-readings for 

 the star are entirely due to these two causes, if the instrument be 

 supposed to be in good adjustment. The star being known, and the 

 times of bisection known, the effects of refraction on the hour-angles 

 are calculated for each observation of the star, by a process which 

 will be presently stated. Corrections for refraction being applied to 

 the hour-circle sector-readings for the star, the remaining differences 

 are due to the clock's rate, and by comparison with the times of bi- 

 section, determine the rate. The correction for rate of hour-circle 

 is a part of the loss or gain in the interval between consecutive bisec- 

 tions of the star, which bears the same ratio to the whole, as the 

 interval from either bisection of the star to the bisection of the planet 

 or comet bears to the interval between the two bisections of the star. 

 ITie following is the formula for this correction, the sidereal times 

 of the three bisections, in the order of their occurrence, being s,, tr, 

 5,2 ; H being the excess of the hour-circle sector-reading for the star 

 at 5, above the reading at s^ converted into time, and R the excess 

 of the correction for refraction in hour-angle for the star at s, above 

 that at Sjj : — 



Correction for rate of hour-circle = ^ (H-f-R). 



Sg — Sx 



This formula gives the quantity to be added to the algebraic excess 

 of the sector-reading for the comet or planet, above that sector-read- 

 ing for the star which was taken at the time s,, and is sufficient for 

 all cases. 



" It is to be remarked, that if the difference of the sector-readings 

 be affected by any other source of error acting proportionally to the 

 time, as, for instance, want of adjustment of the instrument, such 

 error is eliminated by the above calculation. For this reason, to 

 ensure greater accuracy, the excess of the reading of the declination 

 sector for the compared object, above that for the star at the time Sj, 

 is also corrected by the process just indicated, although that excess 

 is unaffected by the clock's rate. The formula for this purpose is 

 precisely the same as that given above ; H, in this case, representing 

 the excess of the declination sector- reading for the star at s^ above 

 the reading at 5.^, converted into arc ; and R the excess of the correc- 

 tion for refraction in north polar distance for the star at s^ above 

 that at ^2. 



" After applying the corrections now considered, it is presumed 

 that the instrumental measures of differences of apparent right ascen- 

 sion and north polar distance are affected only by refraction. The 

 total refractions for the star in R.A. and N.P.D. have been already 

 required, and therefore the obvious course is to calculate also the 



