98 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
There will be two similar equations in X"and X'". Put and substitute the value 
found above, and this becomes, after reduction, 
0=a+0-0005739 — 0•0008179^^— l-3880i/a. 
In a similar manner we obtain the following equations : 
0=a+0-0003548 — 0-00023 17^?—l•6095^/^, 
0=a+0-0004284 — 0-0005076 m;— 1 '5055ds. 
Eliminating a from the 1st and 2nd, the 1st and 3rd, and the 2nd and 3rd, we have 
the three following equations in ds : — 
0=z0-0002191— 0•0008179M+0•0002317^^ + 0•2215^/£, 
0 = 0-0001455 — 0-0008179m+0-0005076m; + 0-1175^/£, 
and 0 = 0-0000736+0-00023 17^^ — 0•0005076^^; + 0-1040^/£. 
These are the sai!ie as 
f/s=— 0-000989+0-003693%— 0-001046t;, 
ds= — 0-001238 + 0-00696U/— 0-004320W, 
= —0-001238 + 0-003685% — 0-001043%, substituting for %; by art. 62, 
and de= -0-000708 - 0-002228%+0-004881%;, 
= — 0-000708+0-003702% — 0-00 1 049%. 
The method of least squares shows that the arithmetic mean of these is the near- 
est value ; 
^/2=^(- 0-002935+0-01 1080% — 0-003138%) 
= -0-000978 + 0-003693% — 0-001046%. 
It is worthy of remark, that the terms depending upon the calculated deflection, 
viz. those in which % and % enter, are very nearly exactly the same in the mean value 
and the three separate values of dz. Adding the mean value of dz to s or (which 
equals 0-003324), we have 
corrected ellipticity =0-002346+0-003693%— 0-001046% ; 
and by adding the three equations in a together, substituting for dz its mean value, 
and dividing by 3, we have 
«=- 0-0039737 — 0-0051426%+0-0016881% ; 
.-. corrrected semi-axis major =%(!+«) 
= a{0-9960263-0-0051426%+0-0016881%}. 
66. With regard to these results, I will first observe, that if mountain attraetion be 
neglected altogether, or %=1 and %=1, 
ellipticity =0-002346 + 0-003693 — 0-001046 
1 
l96-3‘ 
= 0-005093 = 
