298 Mr. Bowditch on the altitude and longitude of the 
On the Altitude and Longitude of the Nonagesimal degree of the 
PET, tp tic. 
The altitude and longitude of the nonagesimal degree of the eclip. 
tic, necessary in the calculation of the parallaxes in the preceding ob. 
servations, were found by the method I published in the third edition 
of the Practical Navigator, and as this is shorter and not liable to so 
many cases as that given in the first volume of the Memoirs of the 
A\cademy, I have thought that an explanation and demonstration of | 
the method would not be unacceptable. 
The method is considerably abridged by means of a table con- 
taining the logarithms marked A, B, C, which occur twice in calcu- 
lating a partial eclipse of the sun or occultation, and four times in a ae 
total or annular eclipse or transit. _ These logarithms are calculated — 
for the obliquity of the ecliptic 23°27' 40", by the following rule. 
In north latitudes subtract the reduced latitude from 90°, in south 
inatuardes spdd. the reduced latitude to 90°, the sum or difference 
will be the polar distance ; take half this and half of the obliquity of the — 
ecliptic (11° 43'50"), and find the sum Sand the difference D. Then 
Log. A= Log, Cos, D +Log. SpSe8 == 20. 
Log. C= Log. Tang. S. 
_ Log. B= Log. Tang. D— Log. C +10. pe 
‘Thus. foi Salem in the reduced latitude 42° 29' 4”, the half polaris 
tance is 23° 48’ 58”, the half obliquity 11°43’ 50”, the difference D=_ 
12°5'8”, the sum $= 95° 32’ 48”, 7 
Difference D 12° 5! 8” Cosine 9:9902660 Tang. + 10= 193306527 
Sum. | 8 35 3248  Secant 10-0895665 Tang. =C = 98540160 ¢ 
ewe. ae 
Sum A= 0°07 98325 Diff. B = 24706907 fe 
ai. 
In this way the logarithms may be found for places not ot inctodel ; 
inthe table. The changes for an increase of 100” in the latitude or 
