358 Astronomical and Nautical Collections. 



reverse takes place in south latitude, or if the correction is 

 required for midnight, unless both these circumstances concur. 



The second part is additive when the sun's longitude is com- 

 prehended between 0» and 3», or between 6' and 0* ; otherwise 

 subtractive. But this application changes if the interval ex- 

 ceeds 12 hours. 



Example. On the afternoon of the 17th of September, 1810, 

 altitudes of the sun were observed at Marseilles ; and equal ones 

 on the forenoon of the 18th : the interval was 21'' 50"" ; the la- 

 titude of Marseilles 43° 17' 50" N. : the " Connaissance des 

 Tcms" gives the sun's declination for midnight of the 17th at 

 Marseilles as 2° 14' 23" N. ; the diurnal declinatory movement 

 dl> being — 23' 14" = - 1394". With these data the equa- 

 tion to equal altitudes is required. 



Log. A (Table) 9.0349 + 



Log. Tang. L 9.9742 + 



■ Log. 1394" 3.1443 — 



Log of 1st part 2.1534— 142",37 first part. 



Log. B (Table) 9 0172 — 

 Log. Tang. D 8.5923 + 

 Log. 1394" 3.1443 — 



Log. of 2d part 0.7538 + 5,"67 second part. 



Equation for midnight — 136",70 — 2"' 16",70. 



Former tables which give the equation for noon, and which 

 are to be found in Lalande's Astronomy, Mendoza's Collection, 

 and several of the Spanish Nautical Almanacs, have all of them 

 the following defects : — 1st, they are of double entry, and con- 

 sequently both complicated and troublesome in use, exacting 

 double, and even triple, proportional parts: 2d , they are con- 

 structed for short intervals, and consequently " in the majority 

 of cases" cannot give the correction for midnight: 3d, they 

 suppose the perihelium of the earth, and the obliquity of the 

 ecliptic, constant, and it is necessary if accuracy is required to 

 renew them from time to time : 4th, they are of no use for planets. 



Baron Zach, in 1812, published at jNlarseilles, at the end of 

 his particular tables of aberration and nutation, others for the 

 present object which we are engaged in ; they are free from the 

 1st and 2d objections, but the 3d and 4th still remain in his 



