Full text: Theoria combinationis observationum erroribus minimis obnoxiae

AT 
THEORIA COMBIN. OBSERV. ERRORIBUS MINIM. OBNOXIAE. 2 ? 
Ceterum hic valor minimus ipfe fequenli modo emitur. Ae 
quatio (V) docet eile 
cta ct a a" a" -j- etc. = x 
ab + ab' + a b" -f- etc. rr o 
a c -]■* a c -j~ ct c -j- etc. ~ o etc. 
Multiplicando has aequationes refp. per [aa], [a@], [ay] etc. 
et addendo, protinus habemus adiumento aequationum (IV) 
aa -f- a a -j” a a 4" e *- c * — £ ce ce ] 
21. 
Quum obreruationes fuppeditauerint aequationes (proxime 
veras) v = o, v — o, v'— o etc., ad valorem incognitae x inde 
eliciendum, combinatio illarum aequationum talis 
X V -\- K V x' *>" “b CtC. — ° 
adhibenda elt, quae ipii x coeiDcientem i conciliet, incognitas- 
que reliquas y, z etc. eliminet; cui determinationi per art. 13« 
pondus 
X X X X ~J~ X X “T e ^ c * 
tribuendum erit. Ex art. praec. itaque fequitur, determinationem 
maxime idoneam eam fore, vbi ftatualur x~a, x— ct, x" — a etc. 
Hoc pacto x obtinet valorem A, manifeiloque idem valor etiam 
(absque cognitione multiplicatorum a, ct, a" etc.) protinus per 
eliminationem ex aequationibus £ = 0, y — etc. elici poteit, 
i 
Pondus huic determinationi tribuendum erit = Icta] * ^ Uie error 
medius in ipfa metuendus 
— mV p [ a a ] = rn V p' [a a] = vn V p" [a ct] etc. 
Prorfus iimili modo determinatio maxime idonea incognita 
rum reliquarum y, z etc. eosdem valores ipiis conciliabit, qui 
D 2
	        
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