248 



Onjinding the Longitude 



By the term parallax, astronomers understand the angular di- 

 stance between the places of the centre of a celestial bodvj as 

 seen at the surface, and at the centre of the earth ; or, which 

 amounts to the same thing, the angle under which the earth's 

 semidiameter would appear when viewed from the centre of the 

 celestial object. This angular distance is the arch of a vertical 

 circle, and consequently, to an observer on the earth, parallax, 

 m changing the apparent places of oljects, operates only in a ver- 

 tical direction. 



The " common popular doctrine" to which Mr. M. alludes, is 

 therefore a true doctrine ; and little more is necessary to be said 

 on the subject when it is evident he misunderstands the term. 



But though in changing the apparent places of objects paral- 

 lax operates only in a vertical direction, its effects on the appa- 

 rent distances of objects from each other are estimated in every 

 direction. If Mr. M. were elevated as high above London bridge, 

 as in his own estimation he is elevated above the insignificant 

 crowd of writers on navigation, — though the effect ofthat eleva- 

 tion on his distance from surrounding objects would be apparent 

 in every direction, the elevation itself would be estimated in a 

 vertical one ; and it would be in that direction chiefly that he 

 would be solicitous to protect himself against the consequences of 

 a fall. 



When parallax is understood in the sense in which it has been 

 here explained, it obviously cannot, by operating only in a verti- 

 cal direction, have any such effect on the figure of the moon as 

 Mr. M. affirms it would have. And though he says it would be 

 very easy, he cannot show that the apparent figure of a spherical 

 body would be at all affected by parallax operating only in a ver- 

 tical direction. 



But even taking the meaning of the term in the unusual sense 

 in which he appears to understand it, it is not quite true, as he 

 says in the next sentence, that " the difference of the parallaxes 

 of any two diametrically opposite limbs constitutes what is called 

 the augmentation of the diameter." 



To prove this, conceive the earth and 

 moon to be cut by a plane through their 

 centres, B and C. Let A be a point in 

 the great circle which bounds the section 

 of the earth, and from A and B let the 

 tangents AD, A F, B G, B E, be drawn 

 to the circle which bounds the section of 

 the moon. G B E is the measure of the 

 moon's diameter at the centre of the 

 earth, and DA F its measure at the point 

 A J and D A F — G B E is the augmenta- 

 tion. 



