252 On a neio Calculation of the 



in reference to the latitudes obtained by these stars admits of 

 no hesitation ; the results below the pole should be rejected, 

 and those above the pole preserved. 



To deduce, in the most advantageous manner, from the 

 results thus preserved, and from the results of all the series with 

 the other stars in which no remarkable difference from the mean 

 is observed, we must adopt a mode of combination essentially 

 different from that employed in the ' Base du Systeme Md- 

 trique,' and of which experience subsequent to that period has 

 established the preference. It is now known, that however 

 skilful the artist by whom a repeating circle has been made, 

 and notwithstanding the utmost attention which an observer 

 can bestow on the adjustments, the zenith distances observed 

 with it are still liable to be affected by certain errors which have 

 obtained the name of '* constant errors," but which are never- 

 theless constant only in a certain sense ; since the transporta- 

 tion of the instrument from one station to another, or the mere 

 laying it by, and putting it together again at the same station, 

 may cause an alteration in the bearing of the parts relatively to 

 each other, and thus a change in the amount of error. It is 

 now therefore admitted, that, whatever may be the nature and 

 sources of such errors, the best mode of obtaining latitudes 

 free from their influence is, to observe several series of well- 

 known stars both north and south of the zenith, and, as far as 

 may be possible, at equal distances from it ; then if the mean 

 result of those observed to the north gives the latitude in excess 

 or in defect, the mean result of those observed to the south will 

 give it erroneous to an equal amount but in an opposite direc- 

 tion, and the mean of the two will be the correct latitude. 



In applying this method to the observations of M. Mechain, 

 we shall at once perceive that it affords an explanation of 

 the supposed difference between the latitudes of Montjouy 

 and Barcelona : hardly, indeed, had the method been esta- 

 blished, before this was inferred by those who were engaged in 

 similar operations: at a meeting of the Bureau des Longi- 

 tudes in November, I8I8, M. Arago, whilst reading an account 

 of the mode in which M. Biot and himself had proceeded in 

 determining the latitude of Dunkirk, remarked, that the lati- 

 tude of Barcelona, deduced in a similar manner from the 



