A Treatise on Practical Astronomy: As Applied to Geodesy and Navigation |
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Page 1
... resulting from observation shall be combined so as to give the best possible value of the quantity sought . The theory of probabilities furnishes the basis for such an investigation ... result INTRODUCTION TO THE METHOD OF LEAST SQUARES.
... resulting from observation shall be combined so as to give the best possible value of the quantity sought . The theory of probabilities furnishes the basis for such an investigation ... result INTRODUCTION TO THE METHOD OF LEAST SQUARES.
Page 2
... result from a variety of causes , such as errors in the instruments used , personal error of the observer , errors in the constants of re- fraction , parallax , etc. , used in the reduction of observations . A proper investigation will ...
... result from a variety of causes , such as errors in the instruments used , personal error of the observer , errors in the constants of re- fraction , parallax , etc. , used in the reduction of observations . A proper investigation will ...
Page 8
... result will be applicable to all cases . We have assumed as an axiom that in the case of direct measurement of the quantity sought the most probable value will be the arithmetical mean of the individual measurements . This principle ...
... result will be applicable to all cases . We have assumed as an axiom that in the case of direct measurement of the quantity sought the most probable value will be the arithmetical mean of the individual measurements . This principle ...
Page 19
... and probable errors of the arithmetical mean , we have , from formulę ( 19 ) , ( 21 ) , ( 25 ) , and ( 25 ) ,, € : € = r ̧ : r = h : h1 = 1 : √ m . ( 26 ) That is , the precision of a result obtained by $ 14 . 19 THE ARITHMETICAL MEAN .
... and probable errors of the arithmetical mean , we have , from formulę ( 19 ) , ( 21 ) , ( 25 ) , and ( 25 ) ,, € : € = r ̧ : r = h : h1 = 1 : √ m . ( 26 ) That is , the precision of a result obtained by $ 14 . 19 THE ARITHMETICAL MEAN .
Page 20
... result obtained by direct measurement is directly as the square root of the number of measurements . Determination of the Probable Error . 15. From the foregoing principles we can now compute from the observations themselves the ...
... result obtained by direct measurement is directly as the square root of the number of measurements . Determination of the Probable Error . 15. From the foregoing principles we can now compute from the observations themselves the ...
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Common terms and phrases
accuracy altitude angle applied approximation arithmetical mean ascension and declination axis azimuth Bessel catalogue celestial sphere centre chronograph chronometer circle circumpolar stars clamp co-ordinates coefficients collimation computation constant convenient culmination determined difference differential dt dt earth east ecliptic elongation emersion ephemeris equal example follows formulę geocentric given gives Greenwich horizon hour-angle instant latitude limb logarithms longitude mean solar measured meridian method micrometer middle thread moon moon's right ascension multiplied Nautical Almanac obtained occultation parallax plane position prime vertical probable error proper motion reading reduced refraction right ascension screw semidiameter sextant sidereal sin² star's stars observed Substituting subtract telescope tion transit instrument unknown quantities values vernier weight write zenith distance ΙΟ
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