CHAP. XIII.] OBSERVATIONS FOR ERROR 319 



In working the rigorous expression, an approximate value 

 for a is first obtained, disregarding the term Cos. a, and then 

 rework, using the vaUie of a thus found. 



Notes on the Computation. 



The constant logarithm 4-138339 is an abridgment of Chau- 

 venet's formula, by adopting it to circular measure, and is 

 correct so long as the equation of equal altitude is small ; 

 certainly up to four minutes no error is introduced by its use. 



The cosine of a with an equation of equal altitude under 

 four minutes changes so slowly that it is practically the same 

 for each set unless separated by a very long interval. 



The R. A. M. S. must be foimd for the Greenwich date 

 corresponding to the chronometer middle time. In cases of 

 a small equation of equal altitude and changing slowly, this 

 is the same for each set ; but where it is large, and therefore 

 changing rapidly, as in the second example, the R. A. M. S. 

 must be corrected for every set. But this merely involves 

 applying the acceleration due to the difference of the chrono- 

 meter middle time of each successive set to the R. A. M. S. 

 for the first set. 



A more or less accurate knoAvledge of the G. M. T. is there- 

 fore necessary, but this is inherent to the use of stars for time 

 under all circumstances, and a second approximation must 

 be made if the error on local time has been assumed more than 

 three or four seconds in error. 



It is worthy of remark that tan c^xtan 8x4-138339 and 

 tan ^xtan gx 4-138339 form absolutely constant logarithms 

 for the same stars, at the same place, for any night in the 

 year, and it is only necessary to add the logarithm of h E. T. 



Page 319, linen 32, 33, 34. — Cancel ami snhstitute. 



The equation of equal altitude is nearly always so large as to 

 exclude all possibility of doubt as to which way to apply it, 

 but the investigation gives the rule. If the declinations of the 

 two stars are nearly equal, it is necessary to pay close attention 

 to the signs of the expressions of the formula to avoid any 

 chance of making a mistake. 



