VOL LVIII.] PHILOSOPHICAL TRANSACTIONS. 5S5 



months happened on the 2d day of January in the morning; the quicksilver 

 then stood at 17.2 below the point of freezing. 



XXIII. Introduction to two Papers of Mr. John Smeaion, F. R. S., by the 



Rev. N. Mashelyne, B. D., F. R. S. p. 154. 



The two following papers Mr. M. received from Mr. Smeaton, with his desire 

 to communicate them to the Royal Society, if he thought they contained any 

 hints conducive to the improvement of astronomy. As the first paper points 

 out the time of observing the menstrual parallaxes of the planets in those 

 circumstances in which they will be greatest, and at the same time shows how 

 to obviate the error, which would otherwise arise from the inaccuracy of their 

 theories (which must necessarily be used in the calculation), by correcting them 

 from other observations, made on purpose, before and after the first-mentioned 

 observations; and the 2d paper gives a new and accurate method of observing the 

 places of the heavenly bodies out of the meridian, independent of refraction, 

 Mr. M. apprehends they would prove acceptable presents to astronomers. 



Mr. M. adds one other remark, that has been suggested by the perusal of 

 Mr. Smeaton's first paper; that, as it is there proposed to find the dimensions of 

 the orbit described by the revolution of the earth about its common centre of 

 gravity and the moon's, by means of the menstrual parallax of Mars, near his 

 opposition, or of Venus, near her conjunction with the sun; the same may also 

 be determined with advantage from the sum of the menstrual parallaxes of these 

 two planets, when they happen to be in the required positions at the same time, 

 which will indeed happen but seldom ; or even from the sum of the menstrual 

 parallaxes of Mars and the sun, which may be observed together at every 

 opposition of Mars to the sun ; the sum of* the menstrual parallaxes of Mars 

 and Venus in these circumstances, according to the numbers used by 

 Mr. Smeaton, will sometimes amount to 87", and the sum of those of Mars 

 and the sun to 52". 



XXIV. A Discourse concerning the Menstrual Parallax, arising from the 

 Mutual Gravitation of the Earth and Moon; its Influence on the Observations 

 of the Sun and Planets ; with a Method of observing it. By J. Smeaton, 

 F.R.S. p. 156. 



It is demonstrated by Sir Isaac Newton in the Principia, that it is not the 

 earth's centre, but the common centre of gravity of the earth and moon, that 

 describes the ecliptic; and that the earth and moon revolve in similar ellipses, 

 about their common centre of gravity. The same great author has also 

 investigated, from the different rise of the tides, when the moon is in conjunc- 

 tion or opposition to the sun, to those which happen when the moon is in her 

 quadratures; that the quantity of matter in the earth is to that in the moon, 



