360 Astronomical and Nautical Collections. 



for having given the sign + to the Tang, of the declination in 

 the calculation of the second part when it ought to bear the 

 sign — in consequence of the declination being South, we find 

 or the second part + 0",22, and the total equation + 5",20, 

 the same that we have deduced above, but with the contrary 

 sign ; it thus appears that independently of the oversight pecu- 

 liar to this example, Baron Zach has changed the sign of the 

 whole equation. 



To make this more perceptible, let us calculate the other ex- 

 ample proposed in the same page. At Pisa equal altitudes of 

 Venus were taken on the 23d of March, 1809; the interval 

 being = 8'' 50"'; latitude 43° 43' 11" N., declination == 

 20° 42' 40" N. ; and dD = + 20' 5", or 1205". 



[Log. A (Table) 8.1272 — 



Log. Tang. L 9.9806 + 



JLog. 1205' 3.0810 + 



!_Log. 1st part 1.1888 - 15",45 First part. 



[Log. B (Table) 7.7322 + 

 I Log. Tang. D 9.5776 + 

 ^Log. 1205" 3.0810 4- 



[Log. 2dpait 0.3908 + 2",46 Second part. 



Equation ... — 12",99 

 According to Zach + 12",98 



It is thus seen that using Zach's rules the sign is equivocal 



for the passage of planets ; this, in my opinion, arises from that 



celebrated Astronomer's having changed (without doubt from 



inattention) the fundamental formula for the correction of the 



superior passage. In effect that formula is as we have already seen. 



Equation of altitudes =r — Li- . _L. AD Tung. L 



c- r^ CO ^^ 360 

 Sine (15" — 1 



2 / 

 + 1— L. d D Tang. D 



Tang.(15°-I.) 



360 



Zach exhibits this m his work before mentioned (page 30,) 

 with the signs reversed. 



Mr. Delambre has also mistaken the signs of the analytical ex- 

 pression of the equation for midnight, or the inferior passage, in 



