986 PHILOSOPHICAL TRANSACTIONS. [aNNO 1768^ 



as 39.78 to 1 ; whence, and the known distance of the earth and moon, it would 

 follow that the common centre of gravity of the two bodies falls without the 

 surface of the earth, by one half of its semidiameter: that is, that the centre 

 of the earth describes an epicycle round the common centre of gravity once a 

 month whose diameter is 3 semidiameters of the earth. 



Dr. Gregory, in his astronomy, has laid hold of this circumstance, in order 

 to prove the relative gravity of the earth and moon, by observation; which is 

 the subject of his 6oth proposition of the 4th book; in which he has demon- 

 strated, that if an observer on the earth makes a correct observation on the 

 sun's place, when the moon is in one quadrature, it will differ from a like 

 observation, taken in the opposite quadrature (according to a mean elliptic 

 motion) by an angle which the diameter of this epicycle will subtend at the sun. 

 The same learned author has also showed, in the scholium to the same propo- 

 sition, that this quantity, or parallax, will be twice greater to Mars in opposition, 

 and 3 times greater to Venus, in her inferior conjunction with the sun. The 

 difference thus produced in the apparent place of the sun, and of all the primary 

 planets, being governed by the moon, and having its period the same, may 

 perhaps be not unaptly called the menstrual parallax. 



Now if, with Sir Isaac Newton, the relative gravities of the earth and moon 

 be taken between the proportion of 3Q and 40 to 1 ; the menstrual parallax of 

 the sun will come out IS* oh the radius of the earth's epicycle, and will affect 

 the solar observations at the opposite quadratures, by double that quantity, 

 viz. 26": in like manner, the mean distance from the earth of Mars in 

 opposition, being to the sun's mean distance, as 1 to 2.1 ; and the least distance 

 of Mars from the earth, to the sun's mean distance as 1 to 2-5-, the menstrual 

 parallax of Mars will affect the observation on him in that situation, by 56" and 

 73"4-, respectively. " J,'. " 



The mean distance of Venus from the earth, in her inferior conjunction, 

 being to that of the sun as 3-i- to 1 nearly, and not very variable, on account of 

 the orbit of Venus being almost circular; the menstrual parallax would affect 

 the place of Venus, in that situation, by a quantity not less than Q2"; 

 and in all other situations in proportion to her distance; which also holds 

 with respect to all the rest of the planets. 



These disturbing quantities are by no means to be dispensed with, in the nice 

 and critical state that astronomical observations and calculations have arrived at, 

 in consequence of the discoveries of Dr. Bradley, who may be said to have given 

 a basis to astronomy ; however, could we rely on the data, on which Sir Isaac's 

 investigation of the relative gravity of the earth and moon is founded, we should 

 have nothing to do but to apply an equation to the particular cases, according 

 to the diameter of the epicycle, as deduced from the relative gra\'ity; but 



