148 OUTLINES OF NATURAL PHILOSOPHY. 



red with one another, may belong to circles of the 

 same radius. 



r >mr 



150. The penumbra in a solar eclipse, if view- 

 ed from the moon, would subtend an angle e- 

 qual to the sum of the diameters of the sun and 

 moon, as seen from the earth. 



When the penumbra just touches the disk of the 

 earth, the distance of their centres is equal to half 

 the angle subtended by the section of the penum- 

 bra, plus the moon's horizontal parallax ; that is, 

 = semidiam. D -f- semid. Q + Hor. Par. D . 



If the least distance of the centre of the sun and 

 moon, (the same with the least distance of the 

 centres of the earth and of the penumbra), is less 

 than this, there can be no eclipse. 



The greatest value of the above angle is about ! 

 34?' 27". Supposing this to be the distance at the 

 time of the ecliptic conjunction, we get the dis- 

 tance from the node 17 21' 27". If the con- 

 junction happens nearer to the node than this, 

 there may be an eclipse. If it be more distant 

 there can be none. 



The limits of solar eclipses being greater than of lu- 

 nar, there are more eclipses of the sun than of the 



moon, 



