A Treatise on Practical Astronomy: As Applied to Geodesy and Navigation |
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Page 5
... follows that the curve will be symmetrical with respect to the axis of y ; and as small errors are more probable than large ones , it follows that the values of 4 near zero will correspond to large values of y , while as 4 becomes very ...
... follows that the curve will be symmetrical with respect to the axis of y ; and as small errors are more probable than large ones , it follows that the values of 4 near zero will correspond to large values of y , while as 4 becomes very ...
Page 15
... follows : Let 4 ' , Δ ' , 4 " " , etc. = the different errors which occur ; p ( 4 ' ) , p ( 4 ' ' ) , p ( 4 ' ' ) , etc. their respective probabilities . - - Then m being the whole number of errors , $ 12 . 15 THE MEAN ERROR . The mean ...
... follows : Let 4 ' , Δ ' , 4 " " , etc. = the different errors which occur ; p ( 4 ' ) , p ( 4 ' ' ) , p ( 4 ' ' ) , etc. their respective probabilities . - - Then m being the whole number of errors , $ 12 . 15 THE MEAN ERROR . The mean ...
Page 37
... follows : Let . the sum of all the coefficients entering into each equation be formed in succession , and represent them by s with the proper subscript . Thus : a1 + b1 + c1 + d a , + b1 + c2 + d2 - - n1 = s1 — n2 = S2 . ( 43 ) * Dr ...
... follows : Let . the sum of all the coefficients entering into each equation be formed in succession , and represent them by s with the proper subscript . Thus : a1 + b1 + c1 + d a , + b1 + c2 + d2 - - n1 = s1 — n2 = S2 . ( 43 ) * Dr ...
Page 57
... follows : 34. In the solution of equations ( 41 ) by successive substitu- tions we found for the final equations in w - see ( 56 ) — [ dd 3 ] w = [ dn 3 ] . We shall now show that the coefficient [ dd 3 ] I = and Q ' " " " is therefore ...
... follows : 34. In the solution of equations ( 41 ) by successive substitu- tions we found for the final equations in w - see ( 56 ) — [ dd 3 ] w = [ dn 3 ] . We shall now show that the coefficient [ dd 3 ] I = and Q ' " " " is therefore ...
Page 59
... follows : Let w be determined , as above , by substitution in the order x , y , z . We then have w with its weight from [ dd 3 ] w = [ dn 3 ] . Equations ( 56 ) then give successively z , y , and x . Let now the elimination be performed ...
... follows : Let w be determined , as above , by substitution in the order x , y , z . We then have w with its weight from [ dd 3 ] w = [ dn 3 ] . Equations ( 56 ) then give successively z , y , and x . Let now the elimination be performed ...
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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 formulæ 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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