Astronomical and Nautical Collections. 359 



XlXth table. To deduce the equation of Altitudes from these 

 tables, the author finds two auxiliary arcs « and P, and two 

 numbers o and 6 ; and afterwards has to seek five logarithms to 

 seven places of figures, and even then in the preceding example 

 which he has computed in his introduction, he does not arrive at 

 the exactitude of the tenth of a second. In fact, he himself 

 says, that using his table XIX, he found " for the correction 

 — 2"'16%77." 



It is true he proposes another method accurate in its results, 

 and applies it himself to the same example ; but by this mode 

 the same two auxiliary arcs a and (3 must be found, and also 

 seven different logarithms to seven places of figures, " although 

 two of them are constant," to obtain the solution - 2"' 16%67, 

 which is the same we have found with so much greater facility 

 with merely the unimportant difFerence of 0%03. 



On this occasion we ought to notice some ambiguities which 

 Baron Zach has overlooked in the application of his tables to 

 the correction of the transit of a planet, determined by means of 

 equal altitudes. At Florence, he says. Mars was observed on 

 8th April, 1809; the interval being = 8" 20'"; djD = 

 + 6' 38" ; latitude = 43° 46' 40" N. ; declination = 5° 9' 40" S ; 

 required the correction for the planet's superior passage ? 

 By our method we shall have 

 ["Log. A (Table) 8.1155 - 

 Log. Tang. L 9.9815 + 

 <. Log. 398" 2.5999 + 



[Log. of 1st part 0.6969 — 4",98 first part. 



[Log. B (Table) 7.7799 + 



Log. Tang. D 8.9558 - 



< Log. 398' 2.5999 +_ 



[Log. of 2d part 9.3356 - 0",22 second part 



Equation - 5",20 

 Baron Zach finds, First part + 4",97 

 Second part - 0",22 



Equation . . . . + 4" ,75 



Re-examining his calculation (page 36 of the prefatory 



part of his little work already cited) and correcting the slight 



ovcrsiKlit in taking out the number corresponding to the Log. 



0.6908897, we find for the first part + 4",98, Correcting also 



