Empirical Formulas
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0002, Aa+. IAb+. OiAc= —. 0013, Aa+. 2Ab-\-. 04Ac= . 0008, Aa+. :^Ab+. OgAc= . 0027, Aa-\-. 4Ab-\-. I6Ac= . 0024, Aa-\-. SAb-\-. 2sAc= . 0034, Aa-^. 6Ab-^. $6Ac= —. 0045, Aa+. JAb+. 4gAc= —. 0038, Aa+. 8A6+. 64Ac= — . 0010, Aa + . GAb+. SiAc= . 0007.
From these are obtained the three normal equations ioAa+4. 5 A& + 2. 85 Ac=— . 0004, 4. 5Aa+2. 85 A6+2. 025 Ac=— . 00203, 2. 85Aa+2. 025A6+i. 5333A6:= -. 002059. Solving Aa= +. 00033, A6= +. 00254, Ac =-. 00531, which added to the values of ao, bo,... and co, give a= 3-19513, b= . 44254, ^=-•76531- the same as just found.
The above process may be applied to linear equations con- taining more than three constants. But as the method of pro- cedure is quite evident from the above the general statement of the process will be made with reference to equations con- taining only three constants.
DEDUCED BY THE METHOD OF LEAST SQUARES 97 Let the observation equations be represented by . Aix-\rbiy-\rciz = ni pi, a2X+b2y-\rC2Z = n2 p2, asx+b3y-{-C3Z=n3 p3, amX-\-hmy-\-CmZ = nTn pm- The normal equations will then be Upa^ ' X + i:pah • y + i:pac ■ z = Zpan, i:pab'X+i:pb^-y+i:pbc'Z = i:pbn, Xpac-x+Upbc-y-h^pc^ 'Z^llpcn, where a, b, c, and n are observed quantities, and x, y, and z are to be determined, pi, p2, p3 - - • pmSire the weights assigned to the observation equations.
What to read after Empirical Formulas?
You can find similar books in the "Read Also" column, or choose other free books by Theodore R Theodore Rudolph Running to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
0002, Aa+. IAb+. OiAc= —. 0013, Aa+. 2Ab-\-. 04Ac= . 0008, Aa+. :^Ab+. OgAc= . 0027, Aa-\-. 4Ab-\-. I6Ac= . 0024, Aa-\-. SAb-\-. 2sAc= . 0034, Aa-^. 6Ab-^. $6Ac= —. 0045, Aa+. JAb+. 4gAc= —. 0038, Aa+. 8A6+. 64Ac= — . 0010, Aa + . GAb+. SiAc= . 0007.
From these are obtained the three normal equations ioAa+4. 5 A& + 2. 85 Ac=— . 0004, 4. 5Aa+2. 85 A6+2. 025 Ac=— . 00203, 2. 85Aa+2. 025A6+i. 5333A6:= -. 002059. Solving Aa= +. 00033, A6= +. 00254, Ac =-. 00531, which added to the values of ao, bo,... and co, give a= 3-19513, b= . 44254, ^=-•76531- the same as just found.
The above process may be applied to linear equations con- taining more than three constants. But as the method of pro- cedure is quite evident from the above the general statement of the process will be made with reference to equations con- taining only three constants.
DEDUCED BY THE METHOD OF LEAST SQUARES 97 Let the observation equations be represented by . Aix-\rbiy-\rciz = ni pi, a2X+b2y-\rC2Z = n2 p2, asx+b3y-{-C3Z=n3 p3, amX-\-hmy-\-CmZ = nTn pm- The normal equations will then be Upa^ ' X + i:pah • y + i:pac ■ z = Zpan, i:pab'X+i:pb^-y+i:pbc'Z = i:pbn, Xpac-x+Upbc-y-h^pc^ 'Z^llpcn, where a, b, c, and n are observed quantities, and x, y, and z are to be determined, pi, p2, p3 - - • pmSire the weights assigned to the observation equations.
What to read after Empirical Formulas?
You can find similar books in the "Read Also" column, or choose other free books by Theodore R Theodore Rudolph Running to read onlineMoreLess
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