55 



If the range of altitude is too great, or it is desirable to 

 compute A^^-A with the greatest precision possible, then this 

 value must be redncecl if z>Zo' or increased if ^<2(,, by the 

 amount 



cot^coszo [z — z^Y 



sin^ 1" (11) 



sin^ z^ 2 



The computation by means of (10) is somewhat facilitated 

 by making use of the same tables for circum-meridian calcula- 

 tions as have been shown to be suitable for the reduction by 

 the first method. For since z — z^ is a small angle, we have, 

 within the degree of accuracy to which the tables are 

 computed, 



{z-z,Y 2 sin^ 1 {z-z,) 



■■ — sin 1" = 



2 sinl" 



and consequently we can take the value of sin 1" 



2 

 straight from the tables. 



Then, writing 



cot p {z — z^Y 



B = , ill = sin 1" 



sin z, 



'0 



we get for each observation, just as in the previous method,, 



A, = A+B m 

 or, angle between R.M. and star at elongation, 



= observed angle between R.M. and star + B m. 

 Since B is a constant, we therefore get, on averaging the 

 whole set of observations: — 



Mean angle between R.M. and star at elongation 

 = mean observed angle between R.M. and star 

 + 5 X mean value of 771. 

 Whether the + or — sign is to be used depends upon 

 the position of the R.M. and upon which angle betw^een the 

 star and R.M. is measured. It will be obvious in any par- 

 ticular case which sign should be taken. 



If the tables for m are not available, then it is better 

 to write 



cot p sin 1 " 



B = , m = (z-z^Y 



sin z. 



'0 



and proceed as before, this time computing //? for each 

 observation. The use of the tables does not thus really make 

 very much difference. 



