60 



SECULAR VARIATIONS OF THE ELEMENTS OF 



what extent the variation of the constants is proportional to the variation of the 

 masses ; and will also enable us to interpolate the constants for intermediate values 

 of the earth's mass. 



And by using 



If we now suppose ^"=+ we shall find m" i ^ 2: -^^= f 



this value of the mass we shall find, 



A[o7o]= 0".0861707, 

 A[T7J]= .6630587, 



Af87J]= .1756449, 



1 

 335172' 



T7T1 = =_0".0008812, 

 77]:= .0001004, 

 Tcj^O .0000086, 



777]= .0000018, 



Whence we get, 



[J7o]=ff 5".6564265; 

 JT7n=7 11.9778269; 

 [T7I1=ff 13.0721730; 

 [T7?1 =ff IT .7285094; 



=g 7".5 132566; 

 ]=flr 18.5963133 

 =ff 2.7662608 

 =ff 0.6479587. 



These quantities will give the following equations, 



[o7JJ[77T]=ff 2 17.6342534.ff+ 67.75169748957285 ; 

 [oTJJUTJ^ff 2 18.7285995.ff+ 73.94178576978450 ; 

 |77^|lT71=ff 2 23.3849359.ff+100.28001037565910; 

 [77iirm=.g > 25.0499999,9+156.57622540085370; 

 [177117771 =g a 29.7063363.ff+212.34901678822286; 

 fam|T73l=,ji' 30.8006824,^+231.75014190892620. 



}=<f 26.1095699.ff+139.71887363689278; 

 }=/ 10.2795174.7+ 20.78362721292128 ; 

 ]=ff 2 8.1612153.ff+ 4.86827997930242; 

 ]=ff a 21.3625741.ff+ 51.44225250630864 ; 

 }=g> 19.2442720^+ 12.04964299066071 ; 

 ]=g* 3.4142195.ff+ 1.79242275182896. 



|773]=ff* 48.4349358.ff+842.64887773.ff 2 1 

 6173.539244345.^ +15701.465507779 J 



r5. a ||6.6|r777|=ff 4 29.5237894.(7 3 +230.655099078.ff 8 ) 

 523.830290018.^+250.4352879666 J 



(251) 



(252) 



(253) 



(254) 



(255) 



(256) 



We shall therefore obtain the following 



Fundamental Equations for (i"=-\-^; or for 7n'=l-f-335172. 

 A =/ 42.46419343.*? +208.5335061 ; 

 A'=tf 23.40766437.ff +100.5097899 ; 

 A"=g* 18.77149338.ff + 74.00017359; 

 A\=f 14.594665902.ff+ 45.9827890; 

 A,=/ 10.00852823.ff + 6.35481085; 

 -4 3 =/ 26.183930014.ff+ 82.93563982 ; 



(257) 



