VOL. LVIII.] PHILOSOPHICAL TRANSACTIONS. 50f 



Remarks. — 1. If it should be thought that the reasoning in art. 3 rests too 

 much on a metaphysical principle of Leibnitz, and requires, if not an apology, 

 at least a more formal proof: the ground of such reasoning, and its extensive 

 use, may be more particularly explained on some other occasion. Suffice it at 

 present to add to the note on that article, that as the given factors a and q^ in 

 p and X, may be joined with m", or with m' " " indifferently, the case is similar 

 to that of an equal chance at play, for the stakes n and 1 — m, where the just 

 expectation of each gamester is \, whatever be the value of n. The 5 th and 

 6th propositions of element ] , scarcely needed any other demonstration, than 

 that it is manifestly impossible to assign any reason of inequality, of the angles 

 in one of these theorems, and of the sides in the other. In the following pro- 

 position, where it is proved, that 2 lines being extended from the extremities of 

 a right line, ab, to a point c, there is no other point on the same side of ab, 

 to which lines from a and b equal to the former can be drawn; he who holds the 

 contrary is supposed to fix on that other point d ; but why d ? rather than d, d', 

 d", &c. he is silent; and therefore Dr. M. concludes, there is no such point 

 different from c. And the like may be said of some other simple theorems, 

 that are commonly demonstrated by showing the absurdity of asserting their 

 contraries. 



2. The title of this paper renders it almost needless to remind the reader, that 

 the moon's parallax is not here proposed as the properest medium for determining 

 that of the sun. Our data are still too uncertain for that purpose, scarcely one 

 of them having been determined to an unexceptionable precision; and the num- 

 bers in the table show how much a small difference in the moon's distance must 

 affect the several conclusions. It may be of use however, to know in what 

 manner those conclusions, as well as the quantities from which they derive,* 

 stand related to each other. For if hereafter the necessary data should be more 

 exactly known, the calculus may be repeated; and if the transit of Venus, which 

 is to happen in 1769, should confirm Mr. Short's calculations from that of 1761, 

 we may thence conclude the true mean distance of the moon, better than in any 

 other way. 



3. In the mean time, if any person should have the curiosity to examine the 

 numbers of the table, he will please to take notice: that as no two measure- 

 ments, nor any two lengths of a second-pendulum, hitherto observed, make the 

 earth of the same spheroid figure. Dr. M. has retained for the ratio of its greatest 

 and least diameters, that of 231 to 230; answering to the hypothesis of its uni- 



• The connections of r, s, q, are manifest ; and the relation of m to q' is easily deduced from 

 prop. 59, Princip. book 1 . — Orig. 



