71 



single minutes. In this case, find the distance carefully between the transit and the 

 mark, and multiply this distance by the tangent of the azimuth. The result set off 



to the Pf^t i for western ( elongation, will point out the place of the true meridian. 



Meridian from Equal Altitudes of the Sun. 



If the direction of a star were observed with a transit when it had a certain altitude 

 on the easterly side of the meridian and the direction again observed when it had an 

 equal altitude on the westerly side, then the bisector of the angle would give the direc- 

 tion of the meridian. 



If these observations are made on the sun an allowance must be made for the slight 

 change in the sun's declination between the two observations. From about Decem- 

 ber 21 to about June 21 the sun is going north and from June 21 to December 21 it is 

 going south. The table given below shows the number of seconds the sun moves in 1 

 hour on different days in the year. 



To an observer in north latitude, when the sun is going north, the mean of the two 

 vernier readings would lie to the west of south ; if the sun is going south the mean 

 would lie east of south. The correction to the mean of the vernier readings is found 



by the formula ^ ; : In this formula D is the total increase or decrease in 



2 cos <p sin t. 



the sun's declination between the two observations ; <f> = the latitude ; t = the hour 

 angle, or very nearly | the elapsed time. 



Making the Observations. 



1. In the forenoon, set up the transit, with the vernier set at 0. Point at some ob- 

 ject for an azimuth mark, preferably at the left of the sun, using the lower clamp and 

 tangent screw. 



2. Loosen the upper clamp and point the telescope toward the sun and find the 

 sun's image in the field. Move the telescope slightly until the vertical and horizontal 

 wires are found. The beginner is cautioned against mistaking a stadia wire for the 

 middle wire. 



In the forenoon the sun is rising and moving to the right. If the telescope has an 

 inverting eye-piece these motions will of course appear to be reversed. If a prism is 

 used the vertical motion will be contrary to what it would be without the prism, while 

 the horizontal motion will not be affected. 



3. Set the telescope at an altitude a little above the sun. Set the vertical wire on the 

 left limb of the sun and follow it in azimuth, using the upper clamp and tangent screw, 

 until the lower limb of the sun just touches the horizontal wire. At this instant stop 

 following the motion in azimuth, note the time by a watch and then read the vernier. 

 It will be well also to read the altitude. 



4. In the afternoon turn the telescope toward the sun, the altitude being the same as at 

 the first observation. When it comes into the field set the vertical wire tangent to the 

 right limb of the sun. Follow it in azimuth until the lower edge of the sun again 

 touches the horizontal wire. Note the tune and read the vernier. 



Calculations. 



Take from the table the hourly change in declination for that day and multiply by 

 the number of hours and fraction of an hour between the observations. The result is 

 to be divided by twice the product of the cosine of the latitude by the sine of the hour 

 angle. This gives the correction to the mean of the vernier readings. The hour angle 

 is half the elapsed time and should be turned into degrees and minutes by multiplying 

 by 15. Take the mean of the vernier readings and then subtract the correction if the 

 sun is going north, add if it is going south. It is assumed that the circle reads from 

 to 360 in a clockwise direction. 



