1882.] of transit of any star across the prime vertical. 247 



From these, with a value of c = 37° 47' 50", which corresponds 

 nearly to the place of the transit instrument at the New Museums, 

 all that part of the table (except the refractions) which corresponds 

 to polar distances ranging from 50° to 90° at intervals of 30 was 

 computed at my request by one of the sons of Mr Todd, the Junior 

 Assistant at the Observatory. 



The earlier part of the table, computed by myself, ranges from 



38° to 45° of polar distances at intervals of 15', and then from 45° 



to 50° at intervals of 20'. To obtain the desired quantities with 



sufficient accuracy a modification of the formulae was requisite. 



We find from those already given by introducing the expressions for 



1 — cos z . 1 — cos h ,, „ , 



z and t the formula? 



1 + cos Z 1 -f- COS II 



tan 8 a =tan — — .tan — — (3), 



tan gfe = sin(A ~ c) (4) 



2 sin (A + c) v ; ' 



When A is not greatly different from c, these formulae are ab- 

 solutely necessary, and in most cases they would be more exact for 

 logarithmic computation until A approaches the value 90°. The 

 original formulae are however sufficiently exact in the major part 

 of the table, as is evident from the steady progression of the 

 differences both of the hour-angle and of the zenith distances. 



The refractions are obtained in about the last half of the table 

 by successive approximations. This is necessary, inasmuch as the 

 tables of refraction ordinarily accessible, give the refraction corre- 

 sponding to an observed zenith distance, whereas an object is 

 to assign the refraction corresponding to a true zenith distance 

 in order to derive from it the apparent, or to-be-observed, 

 distance. 



I find since that de Zach has suggested the method of ap- 

 proximation which it occurred to me to employ. See his Intro- 

 duction to his Tables of Bessel's Mean Refractions printed in 

 the Correspondance Astronomique du Baron de Zach, vol. ix., 

 p. 116. Genes, 1823*. 



For the convenience of students of astronomy resident at 

 Cambridge, I have caused the following table for transits over 

 the prime vertical to be printed. A copy will be given to any 

 one who desires it. 



* Professor Adams has pointed out to mo that Bessel in his Essay Einflu*8 der 

 Strahlenbrechnung auf Mikrometer-beobachtunaen (Astronomische I rntersuchungen, 



Vol. i. p. 153) has given a method of determining the refract inns corresponding to 

 true zenith distances, and has also constructed a table of such refractions (p. P.IK). 



