54 Tranmctions. 



will cause a change in the reading. I consider a six-minute 

 interval between stars the minimum during which a deliberate 

 reading (including reversal of level) for inclinations of the axis can 

 be made. How to treat the various level-readings for one position 

 of the instrument will depend upon circumstances. The readings 

 may show a decided and unquestionable gradual change of level ; 

 in such a case the readings may be plotted and the level-reading 

 for each star interpolated therefrom. If. on the other hand, the 

 level - readings are confined within the errors of reading and 

 .small fluctuations, we may then take the mean of the various 

 readings as the reading for that position of the instrument. 

 The angular value of the level - reading expresses the angle 

 between the vertical plane (in the case under consideration the 

 meridian) and that described by the " transit ; the two great 

 circles intersect each other in the horizon, where the level-correc- 

 tion is nil. The level factor, usually designated by B, is ex- 

 pressed by cos (<^ — S) sec 8. This factor computed for each 

 .star, multiplied by the inclination of the axis, expressed in time, 

 gives then the level -correction to be applied to the respective 

 transits. Errors of level are measured directly, while those of 

 azimuth and collimation with portable astronomic instruments 

 are not directly measured, as is the case with the large transits 

 in observatories. This leaves then the determination of three 

 unknowns — the azimuth, collimation, and clock corrections ; 

 the minimum number of stars to determine which is three. 

 With only three stars, however, there would be no measure of 

 the accuracy of the observations, for one, and only one, value 

 for each of the unknowns would satisfy the three observation 

 equations ; there would be no probable error. If the instrument 

 is not in the meridian it is evident that the times of transit of 

 stars north of the zenith will suffer a correction of opposite sign 

 from those to the south. If the telescope is pointing west of 

 north, north stars transit too late, and south stars too soon ; 

 and vice versa if pointing east of north. As polar stars move 

 slowly they are well adapted for obtaining the azimuth-correc- 

 tion, and hence one polar star is included in each time set for 

 each position of the instrument, and the general azimuth-factor 

 is sin (<^ — 8) sec 8. 



AVith the collimation-error, however, the correction for north 

 and south stars is of the same sign for one position of the instru- 

 ment ; but when the instrument is reversed, then the error is of 

 opposite sign, and the transits of stars are similarly affected. 

 The effect of the collimation - error becomes therefore more 

 apparent and is more accurately deduced when some stars are 

 observed in one position of the transit, and others with the 

 telescope or axis reversed. 



