Local Attraction on Geodetic Operations, 269^ 

 ... ^3+A=20891032 + 9r09-2T3, 



VrA3 = _1_ {21 2981 06 + 2492183 T3} = 35497 +4 153'6 T3 ; 

 .-. a3=20926529 + 13862-8T3, $3 = 20855535 + 5555-6 T3, 



e,= — i-ri+o-iiroTg). 



' 294-8^ 



13. I have now, if possible, to find values of T3 which will make 



these three ellipses, which measure the Anglo-Gallic, the Russian, and the 

 Indian arcs, the same; that is, a-^^=a^=:^a^, b^=b^=b^. These give the 

 four following equations : — 



1577-7Ti- 345-2X2+ 956 = 0n r(3-1980244)Ti-(2-5380708)T2 + (2-9804579) = 0, 

 5885-9Ti+ 2832-4X2+14420 = 0, [^^j (3-7698129)Xi + (3-4521546)X2 + (4-1589653) = o[ 

 1577-7X1-13862-8X3+ 1661 = 0, [ I (3-1980244)X,-(4-1418509)X3 + (3-2203696)=^0, 

 5885-9 Xi+ 5555-6X3+ 8335 = 0,^ H3-7698129)Xi + (3-7447310)X3+(3-9209056) = 0, 



The most likely solutions of these four equations connecting the three 

 quantities T^ T^, T3 which we are seeking are found by the method of least 

 squares. This leads to the three following equations ;■ — 



2(6-3960488)1 Xi-(5-7360952)lX2- (7-3398753) lX3 + (6-1784823) + (6-4183940) 

 +2(7-5396258)/ +(7-2219675) i +(7-5145439) i +(7-9287782)+(7-6907185) = 0. 



(5-7360952) 1 Xi-(5-0761416) 1 X2+(5-5185287) 

 + (7-2219675) J +(6-9043092) J +(7-6111199) = 0, 



(7-3398753) I Xi-(8-2837018) lX3 + (7-3622205) 

 + (7-5145439) J +(7-4894620) J +(7-6656366) = 0, 



or 



2X 2489 - 545 -21871 + 1508 + 2621 



+2x34644 +16671 +32700 +84875 +49059 



74266 Xi +16126 X2 +IO829X3 +138063 =0 



(4-8707900) (4-2075267) (4-0345884) (5-1400773) 

 545 - 119 + 330 21871 -192177 +23026 



+16671 +8022 +40843 +32700 + 30865 +46306 



1721 6X1 +7903X2 +41173 = 0, 54571X1 - I6I312X3 +69832 = 

 (4-2359323) (3-8977920) (4-6146125) (4-7369619) (5-2076667) (4-8409337); 



X2=-(0-3381403)Xi-(0-7l68205), X3 = (r5292952)Xi+(l-6332670) ; 



.-. 16126X2= -(4-5456670)Xi- (4-9243472), 10829X3= (3-5638836 )Xi+ (3-6678554)- 

 = -35129X^-84013, =3663X[+4654 ; 



.♦. { 74266 - 35129+3663}Xi+ 138063 - 84013+4654 = 0, 

 42800Xi+58704 = 0, T^ = -l"'37, 

 X2=- - 2-18Xi -5-21 = +2-99 - 5-21 = - 2"-22, 

 X3 = 0-338Xi+0-430= -0-463+0-430= -0"-033. 



