1883.] of Venus across the Sun. 317 



observation according to the rules given, with the following results ; 

 for the sake of clearness and certainty, I give the actual computa- 

 tions for the first contact, as well as the results for the other three 

 critical times. 



The Nautical Almanac gives as the time of first contact for any 

 place on the earth's surface, radius p, Geocentric North Latitude L, 

 and East Longitude X. : Dec. Gth, 



1 h. 55 m. 57 s. + [2*5471] p sin L - [2-4789] p cos (X - 87° 533'). 



The quantities in brackets being the logarithms of seconds of time. 



If cf> = Geographical, </>' = Geocentric latitude, <£ — cp' = c sin 2<f>. 

 Supposing 



c = ^k?tk l sin 2< A - 97703755 



29915 



$ = 18° 3 V 20 ,v 



log- c = -=- 6 46 



7-2944865 



2-4758890 



7-2944865 



= log -0019701 <*>-17o6 34 = Z. 



.'. <p-<p' =6' 46" 



p=l-csin 2 <£ = 94912763x2 



1-0000000 2-4758890 x _ »7° = - -y i V 



log -0003211 = 65066636 = 195°° 19' 21" =X' 



p= 99996789 



2-47890 G.M.T. for first contact. 

 2-54710 log p= 999986 *• ™- ■ p , , 



log p = 999986 J cos Z= 9*97835 °? aqi 



Z sin £ = 9-48865 I cos (X') = 9-98428 n. \ Jg 



2-03561 = 244139 n. 



= 108£ = 1'48£" =4'36i'(-) 2 2 22 



i?5t 



2 22 

 5 7 9 W.Long. 



8 55 13L.M.T. 



The Connaissance des Temps while giving a similar formula for 

 obtaining the equation of contact for any locality where the phase 

 is visible gives a special formula for finding the Geocentric 

 Latitude; which it says may be found by the relation tan</>' = 

 0-99666 tan <p : as this will make <p' = 17° 59' 57", I have ventured 

 to read 999666 for 09 &c, implying a logarithm instead of a real 

 number; which gives </>' = 17° 55' 34". 



The first contact will then be given approximately by 



P. M. T. = 2 h. 4 m. 21 s. + a, sin <j>' - b t cos <p' cos (X + c,) + &a 



23—2 



