ox THE SQUARE BAR MICROMETER. 173 



which is the apparent value of the diagonal, as affected by the refraction. 

 The term in i? is inappreciable for small values of p. When it cannot be 

 neglected it can be determined by means of (32). 



The apparent value of (j found from (33) may be freed from refraction by 

 applying the correction 



l^(j ^= — g K (tan- 1, sin^ q — tan ^ cos q tan 8 + 1). (34) 



If the observations for determining the diagonal are made upon equatorial stars, 

 in the meridian, the refraction correction reduces to 



^(f = — (fK, (35) 



and can thus be allowed for in a very simple manner. The diagonal may also 

 be found by means of pairs of stars whose differences of declination are accu- 

 rately known, by means of the relation (3), or, for the highest precision, (28), 

 employing the apparent differences of declination. As this method possesses no 

 advantages over that above presented, and the procedure is obvious, it is not 

 worth while to give details. 



14. Deformation of ihe square. — In what has preceded it has been assumed 

 that the micrometer is a perfect square. It should be tested in this respect 

 either by measurement, or by observation of transits of equatorial stars near 

 the meridian. Thus any perceptible inequality of the diagonals can be ascer- 

 tained by the preceding article, while the equality of the sides may be certified 

 bj placing each in succession parallel to the diurnal motion, and observing 

 transits across the adjacent sides near its intersection with them. 



If the square has been carefully constructed the errors should be very small. 

 The effect of any tendency to rectangular or rhomboidal form will be eliminated 

 from observed differences of right ascensions and declination, if the comparisons 

 are taken with the square placed first with one, and then witli the other diag- 

 onal, parallel to the divirnal motion, an equal number of comparisons in each 

 position. 



15. Numerical illustrations. — In the following examples of the application of 

 the preceding formula?, some of the corrections are very small and, in practice, 

 wovdd be neglected, but are here computed for illustration. 



Example I. — Great comet 1881, III., observed at Harvard College observa- 

 tory ((^ = 42' 22'.8), June 29, 1881. Square assumed adjusted to true diurnal 

 motion. Diagonal, 889".8. Approximate 8 = 66° 10'.5, S' = 66° 1'.5. ^=67^42', 

 ? = + 29\2. Comet's motion in a second, -f 0'.0049, and + 0".101. 



