Royal Astronomical Society. 307 



N.P.D., and semidiameters of the sun and moon. The solution of 

 these equations, on the supposition that the place of the sun in the 

 Berlin Ephemeris is correct, shows that the true R.A. of the moon 

 at the time of the eclipse is less than that of the Berlin Ephemeris 

 by 19"-30, and less than that of the Nautical Almanac by 18"-55, 

 while the true north declination is less than that of the Berlin 

 Ephemeris by l''*26, and less than that of the Nautical Almanac 

 by 1"*21. These are the corrections which ought to be applied to 

 the tabular values of the moon's place in deducing longitudes, &c, 

 from observations of this eclipse. 



III. On the position of the ecliptic, as inferred from transit and 

 circle observations, made at Cambridge Observatory, in the year 

 1833. By Professor Airy. 



Those observations only were employed in which both limbs 

 were observed ; giving 140 transit, and 134 circle, observations, 

 six microscopes being read for each limb in the latter. The clock 

 errors were deduced from a catalogue differing from Pond's of 11 12 

 stars by a mean excess of S *11, and from Bessel's in the Tab. Reg. 

 by a mean excess of s * 18. 



In the circle observations, the first limb was observed by setting 

 the instrument approximately, reading the microscopes, and mea- 

 suring the distance of the limb from the fixed wire by a micrometer 

 wire. The other limb was observed in the usual way. The re- 

 fractions used were Bessel's, the parallaxes those of the Berliner 

 Jahrbuck, both applied separately to each limb. The latitude of 

 the place was derived from 917 observations, with six microscopes, 

 of 10 circumpolar stars. See Camb. Ofor., vol. vi. The method 

 adopted, that of Normal Places, is thus described : 



"In England, in deducing values of the obliquity, or places of 

 the equinox, from a set of observations, the usual method has been 

 to calculate from each observation by a trigonometrical operation 

 the place of the equinox, &c., and to take the mean of all the 



f)laces so found. The method of Normal Places consists in calcu- 

 ating trigonometrically no single observation whatever; but in com- 

 paring every observation with the place in the ephemeris, in taking 

 the difference or apparent error of the ephemeris, in taking the 

 mean of all those apparent errors over an extent of time in which 

 we have h priori reason to think that they ought not to vary much, 

 and then in considering that we have thus obtained, for the mean 

 of all those times of observations, an error of the ephemeris which 

 is very much more accurate than any one error. By applying this 

 error with changed sign to a place in the ephemeris for a time near 

 to the mean of the times of observation, we obtain a single corrected 

 place, which possesses all the accuracy derived from the mean of 

 numerous observations ; and this is a Normal Place. The only 

 requisites for the ephemeris to be used in these calculations are, — 

 that it be consistently and accurately calculated on some elements, 

 and that these elements be not extremely far from the truth (their 

 being very near to it is of no importance whatever). We may now, 

 if we please, use the Normal Places for trigonometrical calculation, 



2 It 2 



