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. 



1 , „ „ , .... 1.1 1 



If we now suppose ^"— +__, we shall find m" 



10' 



this value of the mass we shall find, 



A[T^1=— 0".086n07, 

 A[TTT]=— .6630587, 

 AF^1= 0. 

 AG[3=— .1756449, 



Whence we get, 



^E\=g— 5".6564265; 

 JTTT1=<7— 11.9778269; 

 [aTi] =9—13 .0721730; 

 \s^]=g— 17.7285094; 



~368689~335172' 



And by using 



A[IT3=— 0".0008812, 

 A[EGD=— .0001004, 

 A[I3=— .0000086, 

 A[T77] = — .0000018, 



\*Z\=g— 7".5132566 

 riT^1=<7 — 18 .5963133 

 ri~51==<y — 2.7662608 

 \ry\=g— 0.6479587. 



These quantities will give the following equations, 



. [7T?irTTll=(7 2 — 17.6342534.(7+ 67.75169748957285 ; 

 \^Z\\^\ =c?— 18.7285995./7+ 73.94178576978450 ; 

 |T^ir^1 =^— 23.3849359,(7+100.28001037565910; 

 DHHM]^— 25.0499999.0+156.57622540085370; 

 [TTT1 ^l ^^ 2 — 29.7063363,g+212.34901678822286; 

 \*J\ \rz\=f— 30.8006824.0+231.75014190892620. 



(TTri[Tnr| =(y a — 26.1095699.<y+139.71887363689278; 



|4,4|| s, 6| =ff 2 — 10.2795174..g+ 20.78362721292128 ; 

 )4,4||7,7[ = (7 ii — 8.1612153.0+ 4.86827997930242; 

 rr»ir«T«1 =(7*— 21.3625741.0+ 51.44225250630864; 

 pm \T7f\=€J t — 19.2442720,(7+ 12.04964299066071 ; 

 [iT6ir777l= < 7«— 3.4142195.0+ 1.79242275182896. 



CEH lUD LH3 LHH =.9 4 — 48.4349358.0 3 +842.64887773.0 2 1 

 ~ —6173.539244345.0 +15701.465507779 J 



[7T71 [TTil RT^j [T7TI =g i — 29.5237894.fl 8 +23O.655O99Q78.0 ! ) 

 —523.830290018.0+250.4352879666 J 



(251) 



(252) 



(253) 



► (254) 



(255) 



(256) 



We shall therefore obtain the following 



Fundamental Equations for |[i"=+ I 1 - 5 -; or for m"= l-i-335 172. 

 A =f— 42.46419343.0 +208.5335061 ; 

 ^'=0 2 — 23.40766437.0 +100.5097899 ; 

 A"=f— 18.77149338.0 + 74.00017359; 

 4,=0 2 — 14.594665902.0+ 45.9827890 ; 

 A 2 =f— 10.00852823.0 + 6.35481085; 

 4 ? =0 2 _26,18393OO14.0+ 82.93563982 ; 



(257) 



