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XLVI. Notices respect 'mg New Books. 



^n Analytical Calculationof the Solar Eclipse for the 7 th Day 

 of September KS20, J??/ D.MacGrkgor. Svo. pp.46. 35. 



X HERE is scarcely anv circumstance so well adapted to excite in 

 the minds of tlic unscientific an exalted opinion ot Astronomy, 

 as the power which its professors enjoy, of predicting to the 

 greatest nicety the various phaenomena of an echpse. And even 

 among tliose who have in some degree studied this subhme 

 science, there is no doubt a considerable number, whose attain- 

 ments will not enable them to so through the various calcula- 

 tions which are required upon such an occasion. 



We have been led to this remark, by the examination of a 

 pamphlet recently published, entitled " An Analytical Calcula- 

 tion of the Solar Eclipse for the Jth of September 1820. By D. 

 MacGregor." Svo. pp. 46. The Author professes to have 

 printed this work " not with the view of instructing mathema- 

 ticians or astronomers ; but of assisting thxise who are not vet 

 sufficiently conversant in. these subjects, and who are desirous 

 of being better acquainted with them." And certainly we Ijave 

 not observed in aiiy elementary work, or Cyclopaedia, .a more 

 clear elucidation of the calculus of a Solar Eclipse than is hsre 

 presented to the reader. 



The first step taken, is, to ascerLain, nearly, the time of New 

 Moon, which is done by Burckhardt's formula given at the end 

 of his Luiunr Tables ; and consisting of twelve terms. For the 

 epoch thus found, are calculated (from the last-mentioned ta- 

 bles) tiic nioon'.s true longitude, latitude, horary motion, hori- 

 zontal parallax, and semi-diameter ; and from Delambre's solar 

 tables, the sun's longitude, horary motion, horizontal parallax, 

 and semi-diameter. The conqjuted longitudes of the two lumi- 

 naries being then couqiared together, the difference is no more 

 than 2''; and the correction of the time of conjunction found by 

 the formula, only +44 seconds of time. 



The rie.st step is to conqjute, by spherical trigonometry, the 

 Right Ascensions and N. Pol ir distances of the two luminaries; 

 and the first poition of the processes concluded by the formation 

 of a " Table, of data for the general eclipse," in which the prin- 

 cipal quantities already eniunerated are set down for every 30 

 minutes of the duration of that ])hjenomcnon. 



The Author proceeds, in the second part, to give formulae for 

 tlie solution of eight problems relating to the eclipse, as affect- 

 ing the eailh generally, but without numerical examples ; and 

 then passes to the third ])ortion, which occupies 25 pages, and 

 contains five general analytical solutions, which have for their ob- 

 ject 



