The" level is now reversed end for end, and the two ends again read off:— East end . 5"24 West end 5"34 Mean, East 51.00 West . which is the reading which the level would show in both positions it were in adjustment. Hence the west end is higher than the east to) half + the difference, or The level should be applied in reversed positions several times, and a mein taken.
Now let the telescope itself be reversed, and suppose the following entries of observations to he made : Illuminated end East. Telescope North. Altitude 45°. Observer North.
East West 546 5 .42 5 19 Mean East 5 Mean West 5 • The rotation of the earth requires the apparent place of a star to b Increased by 0.0206. cos. latitude x see. of loa declination. This comes to thy same thing as subtracting 0.0206 x cos. latitude from the collimation cor reetlon. In lat. 30' thls=0"013. The eorreettooa for collimation become +0.101 x sec. dee. • 111. end West. —0.127 x see. dcc. a Ill. end East.
t If the unit were or, the west end would be higher by the whole difference The difference is now and the west end is consequently too sigh by half the difference, or by 0925, a result which differs from he former (Illuminated end West) by 097. If the partial observa ions have been pretty accordant (we suppose 0'17 to be the mean .esult of a considerable number of observations), this difference between he values of the inclination, according to the position of the illumi ]ated end, must be supposed to be owing to a difference in the pivots ; 'lid if so, a little consideration will show that to obtain the true incli mtion of the axis in the two positions, of 0.17 must be subtracted the level error Ill. end West, and must be added to the error Ill. tnd East. The true level errors therefore are— Ill. West, +0'295-0'042, or +0'253; Ill. East, +0'125+0'042, or +0'•167.
By the mean of a great many careful observations made when the temperature is steady * and the sky overcast, the difference of the pivots, if it exists, is to be ascertained, and the correction due to that muse is to be applied to the indication of the level.
The error of inclination in the axis being measured, the corresponding nrrection which is to be applied to the observations is thus computed: If the west end of the transit axis be raised, it is clear that the circle perpendicular to that axis will continue to cut the,horizon at the north and south points, but will pass to the east of the zenith, from which it will be removed by an arc equal to the inclination of the transit axis. All the stars above the pole will therefore appear to pass too early, and those below the pole will pass too late ; and if the inclination be 15", the effect in time upon any star will be cos zenith distance cos declination x 1..
Now the level graduated as we have described gives the inclination in parts of which 15" is the unity; hence the corrections to be addeo to the observed times of passage of stars will be, using the preview example— cos. zen. dist.
Ill. end West + 0'253* x cos. declin. of cos. zen. dist.
Ill. end East +0167' x of star.
cos. deelin.
The above corrections, for errors of collimation and inclinatiou, an purely instrumental, and, as the reader will perceive do not requirt any celestial observation. Before proceeding to the third adjustment that by which the great vertical circle now described by the telescope is made to pass through the pole, it will be proper to mention hem transit observations are actually made, and then describe how this error is corrected or computed. The instrument is in or very near the meridian ; a star on entering the field Is placed between the two hori zontal wires. It will then gradually travel through the field, describin a parallel to the horizontal wires, and passing over the vertical wires it succession. The observer looks at his clock a little before the atm comes to the first vertical wire, and counting the beats steadily forwarc by ear, determines as well as he can the second and decimal of a second at which the star is immediately under the wire. He writes this down counting all the time, and goes through the same process at each of the seven wires with which his instrument is furnished. When the stet has passed all the wires, he looks again at the clock to see that hi count is right, and then sets down the hour and minute correspondim to the last wire. The habit of mentally counting on to sixty whip writing down the observation is easily acquired. The estimation o tho decimal of a second at which the star is covered by the wire is, matter of more difficulty, and, with some persons, requires considerabli practice.f. The observer is to attempt to fix in his mind the places o the star with respect to the wire at the preceding and succeeding beat and to divide the second in proportion to the two spaces. Thus if a 16' the star is rather nearer the wire, before passing, than it is at 17' after passing, ho sets down 16"4 : if he judges the proportion to is less than one to two, he sets down 161'3 ; and so on. Finally, th, mean of the observations over the seven wires is to be taken, which to be used as the actual time of transit. It would be desirable that ai observer should begin by learning to note the observation with con siderable exactness, and if it may be, under the care of a practise( guide; but the observation is so simple, that every acquires till power who has the will to try ; and we believe that, with a litt1 experience, one observer is nearly as good as another.