98 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



The southern star, and occasionally the polar star, will 

 be observed on several threads, and from the several ob- 

 served times the time of transit over the middle thread 

 may be found by Bessel's method," or as follows: The re- 

 duction of any thread to the middle thread is given by the 

 equation 



^' - -^^^ dz ^ 2 dz- ^ •■■■ 



= T -\- 1 see (p cosec A^ -\- -^ c..„ -, /..." ^ ' 0-^) 



i' sec <p coRec A^ cot A^ 



sin z tan q 



where q is the parallactic angle of the star when on the 

 middle thread. 



When the star is observed at its transit over the almu- 

 cantar passing through the pole, we have rigorously 



q = t z = m" - (p 



and since the last term of (15) is very small we may in 

 most cases substitute these approximate values in it. 

 From the observations on the first and last threads we ob- 

 tain, approximately, 



f = sec (p cosec A^ = {T" - T) -i- {i" - i') (16) 



Applying (15) to each observed thread and taking the 

 mean of the resulting equations, we obtain 



T^ = —\2T+f2i\ +/5 cos A cott—:2 ^ ^"^' ; ^ (17) 

 ^ n { ' -^ ) ' '' n sin 1 



The last term rarely amounts to more than a few hun- 

 dredths of a second, and if the star observed is near the 

 prime vertical, or near elongation, it may be neglected. It 

 should be noted that owing to the factor cosec An, f is posi- 

 tive for stars west of the meridian and negative for stars 

 east of the meridian. 



Effect of Diurnal Aberration. — The effect of the diurnal ab- 

 erration is to displace every star toward the east point of 

 the horizon by the amount 



s. 

 D = 0.021 cos q> sin A 



1 Chauvenet, Table VIII. 



