92 OUTLINES OF NATURAL PHILOSOPHY. 



seasons of the year, d and d' his apparent diameters 



!! - d l 



v' ~~ d' 



v d* 

 at the same times, v i i/ : i d* : d' z 9 or ~, = 



94. As the apparent diameters of the sun must 

 be inversely as his rectilineal distances from the 

 earth ; therefore the apparent velocities of the 

 sun are inversely as the squares of his distances 



from the earth, 

 -sft 



If D and D' be the real distances of the sun from the 

 earth, at the two instants, when the angular velo- 

 cities are v and r/, v : v' : : D' 3 : D a ; so that v D* 

 is a constant quantity ; that is, the product of the 

 diurnal motion into the sun's distance from the 

 earth remains always the same. 



95. As it is easy to prove that v D* is double 

 of the sector which the line drawn from the sun 

 to the earth describes, while it moves through 

 the angle v ; therefore the areas described by 

 the line drawn from the sun to the earth, in 

 equal increments of time, are equal, and, in any 

 times whatever, are proportional to the times. 



This is the First Law of KEPLER, in as far as relates 



to the motion of the sun. 



. 



96. On 



