VOL. liXI.] PHILOSOPHICAL TRANSACTIONS. 181 



struments, to ascertain the rate of the clock, his true time, and the latitude and 

 longitude of his observatory, which were, viz. 6° 10 south latitude, and 104° 

 30' longitude, east of Paris observatory. The cloudy sky however prevented any 

 observations of the planet's passage over the solar disk ; so that the exits only 

 could be distinctly observed, which were as follow: viz. 1769. 



June 4, Venus'sexit, before noon, true time. 



Interior contact, or beginning of the exit 8*' 30"" 13' 



Exterior contact, or the total exit 8 48 31 



Nov. 10, Mercury's exit, before noon. 



Interior contact, or beginning of the exit 7 33 32 



Exterior contact, or the total exit 7 35 11 



XLVI. Kepler s Method of Computing the Moons Parallaxes in Solar Eclipses, 

 Demonstrated and Extended to all Degrees of the Moon's Latitude, as also to 

 the Assigning the Moons Correspondent apparent Diameter, with a Concise 

 Application of this Form of Calculation to those Eclipses. By the late H. 

 P ember ton, M.D., F.R.S. Communicated by M. Raper, Esq., F.R.S. 

 p. 437. 



The calculation of solar eclipses having been generally reputed a very operose 

 process, from the repeated computations required of the moon's parallaxes by 

 their continually varying during the progress of the eclipse. Dr. P. was once in- 

 duced to consider Kepler's compendium for perfonning this, delivered in his 

 Rudolphine tables, of which he had given a demonstration in his treatise en- 

 titled Astronomiae Pars Optica. But this demonstration is perplexed, and the 

 method itself wants correction to render it perfect. Both these defects he 

 endeavoured to supply by the following propositions, by which may be deter- 

 mined with sufficient exactness the moon's apparent latitude, not only in eclipses, 

 but in all distances of the moon from the ecliptic. And to these propositions 

 Dr. P. premises the method he generally used for computing the nonagesime 

 degree, and its distance from the zenith; this form of calculation not being en- 

 cumbered with any diversity from the difference of cases. 



Lemma. To find the nonagesime, or 90th degree of the ecliptic from the 

 horizon, and its distance from the zenith; the latitude of the place, and the 

 point of the equinoctial on the meridian being given. In pi. 5, fig. 1 , 2, 3, 4, 

 let AB be the ecjuinoctial, AC the ecliptic, d the zenith, de the meridian, and dp 

 perpendicular to the ecliptic; whence f is the nonagesime degree, and dp the 

 distance of that point from the zenith. Then from de, the latitude of the 

 place, and ae the distance of the meridian from Aries, the arch of the ecliptic 

 AF, and the perpendicular df may be thus found. Let i be the pole of the 

 equinoctial, and H the pole of the ecliptic. Then ae augmented by 90° is the 



