J^ SCIENTIFIC NFWS. 



Lunar tablas. iearcheft U to leave in uu indeterminate form, in the for- 

 mula of the longitude or latitude of the Moon, all the un- 

 known coefficients, multiplying them by the fraction which 

 €xpr€sises the aioe or cobine of the argument, on which the 

 inequality depends. All the equations in which the 

 same coefficient has the highest pobitive multipliers are 

 brought together; another 8um is made of those in which 

 this coefficient has the highest negative cofactors ; and from 

 their comparison resulis the Uiost probable value of the 

 unknown coefficient, that which agrees the best with the 

 observations. This method, which must have been followed 

 by Mayer, has since by JVIasson and Buerg, and all who 

 have calculated tables withn these twenty years. This 

 method i« easy, and has no inconvenience but the length of 

 the calculations when observations are taken by thousands; 

 as must be done if we would determine the coefficients of 

 those inequalities, which from their smallner-s have been ne- 

 l^lected in the theory of the Moon : and Mr. B. now offers 

 Wft a very simple method of abridging these calculations, 

 since it dispenses with the calculating and summing up of 

 all the sines of the argument. 



Conceive a series of sines of arcs, forming a decreasing 

 arithmetical progression from 90° to 90° minus a given 

 limit y : Mr. B. has found, that we shall obtain with suf- 

 ficient precision the value of the coefficient sought, by em- 

 ploying, instead of the mean arithmetical sine, the sine ofy 

 divided by the arc i/. According to this idea he gives the 

 fules to be followed in these researches, where we are liable 

 to the vexation of finding after long calculations, that the 

 inequality sought is null, or altogether imperceptible. As 

 a trial of his method, Mr, B. has made a selection out of 

 1300 observations by Dr. Maskelyne, and proposed to de- 

 termine an inequality, which should have for its argument 

 the mean anomaly of the Moon, increased by the argument 

 that regulates the inequality, the period of which is 180 

 years. Nine hundred observations gave him 4*7 " for the 

 coefficient. He is desirous, that farther examination should 

 be made of the goodness of an equation, which so well de- 

 serves to enter into the tables. 



Mr, Burckhardt proposes some other calculations for the 

 iJi^-'? i improveraept 



