340 PHILOSOPHICAL TRANSACTIONS. [aNNO I768. 



It is equally evident, that when the moon is in quartile with Mars, and 

 moving towards a conjunction, an observer at the earth's centre will see Mars 

 more backward in the ecliptic, than if seen from the common centre of gravity, 

 by 15'4-; and that when the moon is in her opposite quartile with Mars, and 

 moving from her conjunction, that then an observer at the earth's centre will see 

 Mars advanced in his orbit, more forward by 15"4^, than if seen from the com- 

 mon centre of gravity ; and the one observation checqued with the other, will, 

 according to a mean elliptic motion, differ by the quantity of 31* ; and such will 

 be the 2d and 4th observations above propounded. 



Now, from the 1st, 3d, and 5th, observations, 3 points of Mars's orbit will 

 be given ; which, by the help of the theory of Mars's motion in an elliptic orbit, 

 whose aphelion, eccentricity, and nodes, are known sufficiently near for this 

 purpose ; the intermediate places of Mars may be interred with the requisite 

 degree of accuracy : and particularly, as the two intermediate observations, viz. 

 the 2d and 4th, will be nearly at equal intervals of time between the 3 others : 

 hence it follows, that the difference between the inferred, or computed places, at 

 the quartiles, and the observed places at those times, will be the menstrual paral- 

 lax required. 



It is to be noted, that the times above specified are the most favourable for 

 the observation ; and could those be made uninterruptedly from weather, there 

 would be the less occasion for any other : but as much as possible to prevent 

 disappointments of this kind, it will be right to begin the observations, a month 

 preceding making the proper observations, at the conjunctions, quartiles, and 

 oppositions, of the moon with Mars, which will be the means of supplying such 

 observations as may happen to prove abortive before the opposition of Mars, and 

 also, in case any of the observations to be made after that opposition shall prove 

 deficient, the observations may be carried on for a month or competent time 

 afterwards. As a further security against disappointments, as well as cheque, it 

 will also be advisable to make the proper observations the night preceding and 

 subsequent to those in which the quartiles, conjunctions, &c. happen ; for, as 

 the quantities will not differ considerably from those obtained on the days speci- 

 fied, with proper allowances they may be brought in support and confirmation of 

 the former. 



In like manner, when Venus is moving towards her inferior conjunction with 

 the sun, as will happen next year, the same observations may be made with 

 respect to her : and continued for a necessary time, to get observations of the 

 place of Venus ; viz. the first, when the moon is in conjunction or opposition 

 with Venus : a 2d, when the moon is in her quartile with Venus ; a 3d, in con- 

 junction or opposition : a 4th, when the moon is in her opposite quartile to the 

 former : and a 3th, again in conjunction or opposition : the same opportunity 



