A Treatise on Practical Astronomy: As Applied to Geodesy and Navigation |
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Page 4
... respectively 2 , 3 , etc. Then the probability of drawing any given number from the wheel will be a function of the number itself — viz .: Suppose I ticket in every 55 numbered 1 ; 2 tickets in every 55 numbered 2 ; 3 tickets in every ...
... respectively 2 , 3 , etc. Then the probability of drawing any given number from the wheel will be a function of the number itself — viz .: Suppose I ticket in every 55 numbered 1 ; 2 tickets in every 55 numbered 2 ; 3 tickets in every ...
Page 9
... respectively equal to the same constant , k . We have therefore dlog p ( M1— x ) - = ( M , — x ) d ( M , x ) - - dlog p ( M , - x ) ( M , - x ) d ( M , - x ) = dlog p ( Mm - x ) ( Mm - x ) d Mm Writing for ( M — x ) in general 4 , we ...
... respectively equal to the same constant , k . We have therefore dlog p ( M1— x ) - = ( M , — x ) d ( M , x ) - - dlog p ( M , - x ) ( M , - x ) d ( M , - x ) = dlog p ( Mm - x ) ( Mm - x ) d Mm Writing for ( M — x ) in general 4 , we ...
Page 12
... respective probabilities are equal we shall have Sta e h22 hd s ta ' = e a ' h2s3h'ds , which equation will be satisfied by making ha = h'a ' , or h : h ' = a ' : a . ( 16 ) We see from this equation that in two different series of ...
... respective probabilities are equal we shall have Sta e h22 hd s ta ' = e a ' h2s3h'ds , which equation will be satisfied by making ha = h'a ' , or h : h ' = a ' : a . ( 16 ) We see from this equation that in two different series of ...
Page 13
... respective probable errors , which will now be considered . The Probable Error . 10. The probable error of any observation of a given series is a quantity such that if the errors committed be arranged according to their magnitude ...
... respective probable errors , which will now be considered . The Probable Error . 10. The probable error of any observation of a given series is a quantity such that if the errors committed be arranged according to their magnitude ...
Page 15
... , 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 error.
... , 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 error.
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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 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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