230 METHOD OF DETERMINING THE LATITUDE BY 



been induced to give it, in order that those who are desirous 

 may avail themselves, to the full extent, of the correction, 

 which for the Pole Star may become requisite, when the ob- 

 servations are extended from 15' to 20' or longer after its pas- 

 sage over the meridian. The product of these quantities give 

 a logarithm termed /, which, added to the logarithm of 



— in . e , ? — taken from the Table, corresponding to the horary 



angle, gives the logarithm of the correction to be added to the 

 altitude, or subtracted from the zenith distance ;. from whence 

 their apparent ones are to be determined. 



The accompanying Table, valuable for many purposes of 



astronomy, viz. — in * * is extended to 11' from noon, which 



is generally sufficient ; but those who are desirous of ob- 

 serving further from noon, may continue it agreeably to the 

 above formulae. This Table, with Lalande's small volume 

 of Logarithms *, are all that is required for the determina- 

 tion of the latitude by this method. The above correction, 

 or Log./, is equally applicable to the repeating circle as to 

 the sextant, with this difference only, that the number of re- 

 petitions must be multiplied by that number, or in other 

 words, the logarithm of the number must be added, in or- 

 der to obtain the reduction to noon for their sum. I have 

 been induced to compute for my own observatory logarithm/ 



for 



* No astronomer should be without this little work, or Callet's tables, both 

 of which, from their value, and universal use in calculations, have been stereoty- 

 ped in France, and abridge, in a most wonderful degree, the proportions required 

 in all astronomical computations. As the one term is invariaby constant, viz. 24 

 hours, the change that takes place in declination, the sun's longitude, or IR, serves 

 for all the calculations of one day ; so that in fact there are but two logarithms 

 to look out, in the most complicated proportion. 



