Astronomical and 'Nautical Collections. 361 



his Compendium of Astronoimj , (page 223,) and in his Astronomy, 

 (vol. 1st, page 560.) This may easily be seen by comparing 

 the said expression as found in the two Treatises just cited, with 

 what we have above deduced, or with that which the author 

 himself has stated to be correct in the prefatory part of his Solar 

 tables, published by the (French) Board of Longitude in 1806. 



Such mistakes, and made by such respectable authors, have 

 obliged me, at the beginning of this memoir, to occupy myself in 

 giving demonstrations of both formulas, in order to show, be- 

 yond a doubt, which are the correct expressions. 



The same Mr. Delambre, in the first volume of his Astronomy, 

 has given tables for the equation of altitudes ; by which five 

 logarithms are to be found, as in our method, with only this 

 difference that four of them are found in his tables ; it is how- 

 ever necessary to have recourse to the ordinary logarithmic 

 tables for the tangent of the latitude ; and to find the two parts 

 of the equation by means of his logarithms : besides, four pro- 

 portional parts are almost always required for the four loga- 

 rithms which his tables furnish, while by our method no pro- 

 portionals are required ; " except, perhaps, for the logarithms 

 A and B :" and in finding the log. tangents of the latitude and 

 declination, the nearest minute may be used, without danger of 

 any sensible error in the result, from neglecting the odd seconds. 

 I believe, therefore, that if no disadvantage attends Delambre's 

 mode, it at least has no advantage over our method in point of 

 brevity. In regard to accuracy, the 1st table has the 3d and 

 4th defects of the general ones of double entry which have 

 hitherto been in use, defects common to all the class of which 

 the sun's longitude is the argument. In the case of the first 

 example we have given, with the said longitude for midnight of 

 the 17th, at Marseilles, (174° 22') the tables we speak of give 

 2" 16',9 for the equation of equal altitudes, differing from that 

 found above by Zach's accurate method, and by our own, by 

 0',2 ; a quantity which Astronomers will not disregard v?ithout 

 some reluctance ; to this may be added that the differences in 

 the said 1st table are considerable in some cases, and the inter- 

 polation is consequently very troublesome. 



Those who, nevertheless, prefer Delambre's table, ought to 



