Elements of Plane And Spherical Trigonometry With Their Applications to Mensur

Cover Elements of Plane And Spherical Trigonometry With Their Applications to Mensur
Elements of Plane And Spherical Trigonometry With Their Applications to Mensur
Elias Loomis
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This table may be computed in the fol lowing manner : According to Art. 197, cosine of latitude is to radius, as the departure is to the difference of longitude ; that is, as a part of a parallel of latitude is to a like part of the equator, of any meridian.
But by Art. 28, cosine : R : : R : secant ; hence 1' of a parallel : V of a meridian : : R : sec. Latitude. But on Mercator's chart the distance between the meridians is the same in all latitudes ; that is, a minute on a parallel of latitud
...e is equal to a minute at the equator, or a geographical mile. Hence the length of one minute, on any part of a me- ridian, is equal to the secant of the latitude. Thus, The first minute of the meridian = the secant of 1' ; second " " = " 2', third " " = " 3', &c. , &c.
The table of meridional parts is formed by adding together the minutes thus found. Thus, Mer. Parts of 1' sec. 1' ; Mer. Parts of 2'= sec. I'+sec. 2' ; Mer. Parts of 3'=sec. I'+sec. 2'+sec. 3'; Mer. Parts of 4' sec. I'+sec. 2'+sec.


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