 Now, according to Art. 11, the most probable system of values of x, y, z.... (and, consequently, the most probable system of errors) is that which makes the sum of the squares of the errors a minimum: thus, we are to reduce to a minimum the function [vv~]...  Elements of Physical Manipulation - Page 3by Edward Charles Pickering - 1873Full view - About this book
 | Abendaño - 1852 - 722 pages
...errors, and we wish to find what value A is most likely to be correct. If A was the true value, A^ — A, A.2 — A, &c., would be the errors of each observation,...Hence, when we have n such observations, we take A = (At -f- A2 -f- As -f- <fec.) -iw, or divide their sum by n. Thus the mean of 32, 33, 31, 30, 34,... | |
 | William Chauvenet - 1863 - 684 pages
...the most probable system of values of x, y, z (and, consequently, the most probable system of errors) is that which makes the sum of the squares of the errors a minimum : thus, we are to reduce to a minimum the function [CD] = i/i/ + v"v" + v'"v'" + . . . . Regarding... | |
 | William Chauvenet - 1864 - 684 pages
...probable system of values of x, y, z . . . . (and, consequently, the most probable system of errors) is that which makes the sum of the squares of the errors a minimum : thus, we are to reduce to a minimum the function [vv] = v'v' + v"v" + v'"v'" + .... Regarding [vv]... | |
 | William Chauvenet - 1864 - 680 pages
...most probable system of values of x, y, z.... (and, consequently, the most probable system of errors) is that which makes the sum of the squares of the errors a minimum: thus, we are to reduce to a minimum the function [vv~] = v'v' + v"v" + v'"v'" + .... Regarding [rr]... | |
 | William Chauvenet - 1868 - 122 pages
...probable system of values of x, y, z . . . . (and, consequently, the most probable system of errors) is that which makes the sum of the squares of the errors a minimum : thus, we are to reduce to a minimum the function \vv\ = v'v' + v"v" + v'"v'" + .... Regarding [OT]... | |
 | Mansfield Merriman - 1877 - 220 pages
...to the truth. The most probable system of values is, by the fundamental principle of Art. 14, that1 which makes the sum of the squares of the errors a minimum, that is which makes xl + X3 + ..• + xn a minimum. By the use of this principle we have in Part I.... | |
 | Louis Winslow Austin, Charles Burton Thwing - 1895 - 222 pages
...from these observations to determine the value of the constant a. The method of least squares states that the most probable value of (a) is that which makes the sum of the squares of the errors, or — (1) (yt - axtf + (yz - aa-2)2 + (y, - axs)2 + etc. ; or, 2 (y — ax)2 = a minimum.... | |
 | Norman Robert Campbell - 1920 - 590 pages
...according to Gauss' Law; for if that law is not assumed there is no reason for believing that the solution which makes the sum of the squares of the errors a minimum is the most probable solution and gives the true values. I have already given reasons for believing... | |
 | Richard Glazebrook - 1922 - 1090 pages
...naturally admits of solution in various ways. It is of interest to note that Fourier's method is the one which makes the sum of the squares of the errors a minimum. Taking for brevity the sine-series (13), and limiting ourselves, in the first instance, to a finite... | |
 | C. Suryanarayana, M. Grant Norton - 1998 - 302 pages
...using the least-squares method, which states that the most probable value of the measured quantity is that which makes the sum of the squares of the errors a minimum. Note that the random errors involved in measuring the peak positions are responsible for the deviation... | |
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