2 RELATIONS PERTAINING SIMPLY [BOOK I. 



IV. For different bodies moving about the sun, the squares of these quotients 

 are in the compound ratio of the parameters of their orbits, and of the sum of the 

 &quot;&amp;gt; jhjiftfgs of the sun and the moving bodies. 



, Denoting, therefore, the parameter of the orbit in which the body moves by 

 J %p, the mass of this body by p (the mass of the sun being put = = 1), the area it 



describes about the sun in the time t by kg, then ^wff+Tj! wil1 be a constant 

 for all heavenly bodies. Since then it is of no importance which body we use 

 for determining this number, we will derive it from the motion of the earth, the 

 mean distance of which from the sun we shall adopt for the unit of distance ; the 

 mean solar day will always be our unit of time. Denoting, moreover, by n the 

 ratio of the circumference of the circle to the diameter, the area of the entire 

 ellipse described by the earth will evidently be n &amp;lt;Jp, which must therefore be 

 put %y, if by t is understood the sidereal year; whence, our constant becomes 



In order to ascertain the numerical value of this constant, here- 

 ~ 



after to be denoted by k, we will put, according to the latest determination, the 



sidereal year or /= 365.2563835, the mass of the earth, or ^ = 354710 = 

 0.0000028192, whence results 



Iog2jt ........ 0.7981798684 



Compl. log t ...... 7.4374021852 



Compl. log. \/ (!+!&quot;*) 9.9999993878 



log k ......... 8.2355814414 



k= 0.01720209895. 



2. 



The laws above stated differ from those discovered by our own KEPLER 

 in no other respect than this, that they are given in a form applicable to all kinds 

 of conic sections, and that the action of the moving body on the sun, on which 

 depends the factor y/(l-j-(U-), is taken into account. If we regard these laws as 

 phenomena derived from innumerable and indubitable observations, geometry 

 shows what action ought in consequence to be exerted upon bodies moving about 



