Royal Astronomical Society. 147 



kinds (except that of the moon's semidiameter) upon the computed 

 distance between the moon's centre and the point on her limb, were 

 calculated and expressed symbolically; and finally, the computed 

 distance, with the addition of these symbolical terms, was made ab- 

 solutely equal to the tabular diameter, with the addition of a sym- 

 bolical term : thus the final equation contains one numerical term 

 derived from the observation, and seven symbolical terms. This is 

 essentially the simplest and most complete result which can be de- 

 rived from the observation of an occultation ; and if the numerical 

 values of any one of the symbols shall become known, such symbols 

 may, by numerical substitution, be removed from the equation. 



The equations, in the form just described, are published in the 

 various volumes of the Cambridge Observations from 1830 to 1835. 

 The form can now be simplified for the following reasons : — 

 1st. The stars have been carefully determined, hence the symbols 

 for their errors in R.A. and N.P.D. can be got rid of in all cases. 

 The same may be said, with few exceptions, of the places of the 

 occulted planets. 



2nd. Mr. Henderson's investigation of the value of the horizontal 

 parallax of the moon (Mem. Roy. Ast. Soc, vol. x.) enables us to 

 remove the corresponding symbol. 



3rd. An error had been committed in the computation of the sym- 

 bolical factor respecting the correction to be made to the time of 

 observation. The change in the place of the moon's centre had been 

 correctly computed ; but the change in the correction for parallax, 

 consequent on a change in the hour angle depending on a correction 

 for time, had been omitted. The equations are now cleared of this fault. 

 To facilitate the application of the results to lunar theories, the 

 form of the equations has been changed ; and they now depend on 

 errors of longitude and ecliptic north polar distance, and not on 

 errors of R.A. and N.P.D. 



It was not thought advisable to introduce into the equations the 

 numerical correction of the moon's semidiameter, as deduced from 

 transit and circle observations, as it would be hazardous to assume 

 that this semidiameter is necessarily the same as the semidiameter of 

 the opake body behind which the occultations occur. 



To the year 1833 inclusive, the lunar elements are computed from 

 the Berliner Jahrbuch: for 1834 and 1835, they are derived from 

 the Nautical Almanac. The computations have been partly made 

 by Mr. Glaisher, partly by Mr. H. Breen, Jun. ; and the Astronomer 

 Royal places great reliance on the accuracy of the results. 

 'rhe memoir is divided into three sections. 

 Sect. I. Places of the occulted stars adopted for computation. 

 Sect. II. Correction of the assumed value of horizontal parallax, 

 and correction of the factor of the error of time, depending on the 

 change of parallax during the error of time. 



Sect. III. Transformation of the final equations, from the form 

 depending on errors of the moon's place in R.A. and N.P.D. to a 

 form depending on errors of the moon's place in longitude and eclip- 

 tic north polar distance ; and exhil)ition of the final results. 



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