ofJVaiurid Fkilosoijliy. 147 



Prop. 13. To make the demonstration from fig. 10, con- 

 sistent, EPLH ought to be regarded as a circle in the heav- 

 ens ; it is therefore improper to place the spectator at P. 

 The diagram should have been constructed hke fig. 2, with 

 a small concentric circle to denote the earth. 



Prop. 35. Cor. " Hence it appears that the earth, at the 

 winter solstice or Capricorn, is in its perihelion." The stu- 

 dent will be apt to infer, from this mode of expression, that 

 the two points mentioned have some necessary connexion. 

 But so far is this from being true, that the time when the 

 earth is in its perihelion is about ten days later than that of 

 the winter solstice. The angular motion of the earth in the 

 interval (for 1820) is about 9^ 50'. 



Prop. 35. Prob. 6. The method of finding the bearing 

 of two places on the earth's surface, here described, is 

 manifestly erroneous, except when the places are very near 

 each other. This part of the problem does not appear ca- 

 pable of a solution on the artificial globe. 



Chapter iii. on Twilight, has undergone several material 

 improvements in the last edition. The Cor. to prop. 37, is 

 however out of place, and should have been expunged. 

 The demonstration of prop. 39, is freed from several theo- 

 retical errors ; although we think the attempt to distinguish 

 between the sun's centre and upper limb, in an angle liable 

 to so much uncertainty as the sun's depression at the com- 

 mencement of twilight, attended with no advantage sufficient 

 to compensate for the additional complexness it gives the 



* In calculating (his distance, 57' IT' was retained as the mean equatorial 

 parallax : this being the result obtained by Delambre and Lalande, and be- 

 ng employed in Burg's Lunar Tables. 



t Delambre, Astronomie IH. 142. Philos. Trans. 1S18. Although Mr. 

 Pond fixes the greatest possible limit at 0",5, he supposes that in all proba- 

 bility the double parallax does not equal 0",25, even for Arcturus and Lyra. 



It is scarcely necessary to remark (hat when either of the foregoing num- 

 bers are employed in calculations, in different parts of the Astronomy, 

 corresponding alteration? must be made in the results deduced from them. 



