Nonagesimal degree of the ecliptic. 301 
the table gives the log. tangent of the arch G. This log. added to 
the log. B of the table, rejecting 10 in the index, will be the log. tan- 
gent of the arch F ; these arches being less than 90° when T is found 
in the column A. M. otherwise greater: This rule is general except 
in places situated within the polar circles, which is a case that very 
rarely occurs. Within the north polar circle the supplement of F to 
360° is to be taken instead of F ; within the south polar circle, the sup- 
plement of G to 180° is to be taken instead of G; the other terms re- 
maining unaltered. Then the longitude of the nonagesimal is equal 
to the sum of the arches F, G, and 90°, rejecting as usual 360° when 
the sum exceeds that quantity. 
To the log. C add the log. cosine of the arch G, and the log. se- 
cant of the arch F, the sum, rejecting 20 in the index, will be the log. 
tangent of half the altitude of the nonagesimal. 
Example. 
Required the altitude and longitude of the Nonagesimal at Sa- 
lem, September 17, 1811, at OA. 55’ 14’3, the observed apparent 
time of the beginning of the eclipse of the sun; the obliquity of the 
ecliptic being 23° 27’ 41”*9, the reduced latitude 42° 22 04” N, and 
the sun’s right ascension 11A. 37’ 33’"°9. 
11h. 37’ 33-9 ©’s right ascension. 
O 55 14 3 App. time. 
6 AO 079834 
Tis 3248-2 Cotang0O 062375=log. cotang of 1T turned into a 
G 54 13.03 Tan. 0 142209 Cosine 9 766940 
90 B 9 476623 C 9 854020 
F22 3430 Tan. 9 618832 ““Setant=  ~ 34621" 
‘Sum 166 47 33=Long. Niniesex: 24 20 412 Tan. 9 655581 
LA Pr, 4 44 23 Alitude Nonages... 
“hours it must be called 2 H. A. M. the corresponding log. tangent is equal to 
the log. tangent of {T turned into degrees and minutes in the usual way. 
: 38} 
