Some Investigations in the Theory of Map Projections
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In our eReader you can find the full English version of the book. Read Some Investigations in the Theory of Map Projections Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Some Investigations in the Theory of Map Projections
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This leads in our notation to the two equations ^ (« + X — ^) ~ sin (x — 8) = sin X - « (« + x) = '^ ('^ + X + ^) ~ sin (x + 8), whence n = cos x sin 8/8 = cos x ( i ~ t + ■ • • ) i a + X = tanxiScot|8 = tanx(i " i^"-^---)- The map extends from co-latitude 20° to co-latitude 50° and Euler finds by a calculation not so direct as ours « =0-8098, « = o'o853 = 4° 53' 22".
As this value of a is so nearly 5° = o'o873 Euler adopts the latter value and so fails to reproduce one of his conditions, viz.,... that of equality of errors at middle and extremes. The following Tables give the particulars of this map calculated from the Minimum Error formula, from Euler's own con- stants, and from the correct values of Euler's constants.
3—2 36 MINIMUM ERROR Minimum Error Formulae.
« = cos X ( I + — =o' 30/ 82156, a = tan x ( ,.--^x= : 0-07927.
e 6 in cm. and r sin 9 nrjsm 6 nrjsm 8-1 V= Squares VAnB 20° 25° 30° 0^34907 ■42834 ■43633 •51560 •52360 •60287 •61086 •69013 .
What to read after Some Investigations in the Theory of Map Projections?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Ernest Young to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This leads in our notation to the two equations ^ (« + X — ^) ~ sin (x — 8) = sin X - « (« + x) = '^ ('^ + X + ^) ~ sin (x + 8), whence n = cos x sin 8/8 = cos x ( i ~ t + ■ • • ) i a + X = tanxiScot|8 = tanx(i " i^"-^---)- The map extends from co-latitude 20° to co-latitude 50° and Euler finds by a calculation not so direct as ours « =0-8098, « = o'o853 = 4° 53' 22".
As this value of a is so nearly 5° = o'o873 Euler adopts the latter value and so fails to reproduce one of his conditions, viz.,... that of equality of errors at middle and extremes. The following Tables give the particulars of this map calculated from the Minimum Error formula, from Euler's own con- stants, and from the correct values of Euler's constants.
3—2 36 MINIMUM ERROR Minimum Error Formulae.
« = cos X ( I + — =o' 30/ 82156, a = tan x ( ,.--^x= : 0-07927.
e 6 in cm. and r sin 9 nrjsm 6 nrjsm 8-1 V= Squares VAnB 20° 25° 30° 0^34907 ■42834 ■43633 •51560 •52360 •60287 •61086 •69013 .
What to read after Some Investigations in the Theory of Map Projections?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Ernest Young to read onlineMoreLess
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