KiRSTiNE Smith 
265 
and then putting 
N 
1 (a;, -m)^ 
V2n 
and xja = hs. 
we have on substituting the differentials in (2 a): 
+ Am {S ||J [K,,z,^, - hA]^ + 2NS 11^' [^.,,, - ZsY 
+ 
+ ^a(sH [{h\^,z,^,-KH,) - 2{h,^,z,,,- h,zd + 2NS h,zA) ^ 
the differential coefficients of being 
and 
dm 
N 
a 
N 
a 
2 V^s+l 
.(4). 
Illustration I. Fit of Normal Curve to Unilateral Data. 
Our first illustration treats a series of measurements by Bradley discussed 
by Bessel*. The mean of the observations is fixed, for in dealing with the observa- 
tions Bessel has added positive and negative variations together. 
TABLE I. Measurements of Right Ascension. 
Limits 
Observed 
Gaussian curve 
by moments 
Gaussian curve 
improved by 
minimum x' 
0"-0— 0" 
•1 
114 
101-Gl 
98-63 
0"-l— 0" 
•2 
84 
84-12 
82-59 
0"-2— 0" 
•3 
53 
57-65 
57-91 
0"-3— 0" 
•4 
24 
32-71 
34-00 
0"-4— 0" 
■5 
14 
15-36 
16-72 
0"-5— 0' 
•6 
6 
5-974 
6-881 
0"-6— 0" 
•7 
3 
1-923 
2-372 
0"-7-~0' 
•8 
1 
•5122 
-6843 
0"-8— 0' 
•9 
1 
-1370 
-2053 
* Emanuel Czuber, Theorie der BeobacMungsfehler, p. 192. Search has been made in vain in tlie 
Fundamenta Astmiomiae for the original data in order to remove the unilateral limitation. 
