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XXXV. Places of Saturn computed by Hansen's Formula. 

 By S. M. Drach, Esq., F.R.J.S. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 TPHE new analytical methods proposed by M. Hansen having 

 -*- of late attracted much attention, I have for some time 

 employed myself in computing several places of Saturn rigor- 

 ously from his formula; selecting for the dates those speci- 

 fied in the Greenwich Observations for 1837-4-0, as the mean 

 day of the monthly observations. M. Hansen having as- 

 sumed the same elements as M. Bouvard (whose tables of 

 Saturn are now used for the Nautical Almanac), we derive the 

 great advantage of exactly testing the value of both methods 

 by reference to observation. I have therefore made the com- 

 putations for the London mean noons = Paris ones + 9 m 21 s, 5 

 for the 21 dates of the annexed table, in the following man- 

 ner: — 



The mean anomalies of Jupiter and Saturn gave the argu- 

 ments for all M. Hansen's perturbations in longitude, to which 

 adding M. Bouvard's Georgian part of the great equation, viz. 



— 34"'58 (sex.) sin {3n"t + 3e" —nt — e — 95S r '08} 



and applying the sum tog' = Saturn's mean anomaly, there re- 

 sulted the corrected anomaly, wherewith the equation of the 

 centre and elliptical value of the radius vector was computed. 

 M. Bouvard's tables furnished the perturbations produced by 

 ]$, and adding the constant perih. long. 89° 8' 20", the sum 

 gave the true perturbed longitude in the orbit from the mean 

 equinox of 1800 = r;. After allowing for the reduction to the 

 ecliptic, M. Bouvard's value of the precession = 0& r, 01 5463 = 

 50"* 1001 (sex.) and the ephemeridal equation of the equinoxes 

 (p. 266) were applied, whence the true longitude from the true 

 equinox was ascertained, and its comparison with the Nautical 

 Almanac value exhibited in column 3. The other two coor- 

 dinates are exhibited in columns 6 and 9 in the same manner. 

 The errors in Hel. lat. are immediately extracted from 

 the Greenwich Observations, and likewise those in Hel. 

 long, for 1837-39. The volume for 1840 being deficient 

 in these, they were approximatively supplied as follows. The 

 planet never being as far as l h 4 m in Geo. R.A. from the 

 solstitial colure, the variation in declination has little influence 

 on the R.A. ; hence the effect of the small monthly average 

 error in the latter on the Hel. long, could be found nearly 

 by simple proportion: thus in No. 16, March 9 —March 8 

 = + 9 s -40 in Geo. R.A. and + 108"'6 in Hel. long. 



