Transactions and proceedings of the Royal Society of Victoria Volume 12-14

9781130485189: Transactions and proceedings of the Royal Society of Victoria Volume 12-14

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 Excerpt: ...then, it is obvious that by putting D,, D2, D,, for the angles of this spherical triangle which correspond to the angles K,, K2, K,, of the chordal triangle, we should have--cos D, 008 k («., + 008 £ («.! + "n)--tan J (a,, + a21)-tan (o„ + a,J)j By comparing the values of the angles D,, D2, D, of the imaginary spherical triangle as given in the formulae (133), with the correct values of the corresponding angles C,, C, C,, of the spheroidal triangle as given in formulae (132), it Is evident that, with due respect to the utmost accuracy required in practice, we have--cosC,--cosD, = tan£(a1,+ a,)tan (o2+ a21) their logs being the same to at least 8 or 9 places of decimals. From these it is evident that cases may occur in geodetic surveying in which one of the angles of the spherical triangle is greater than the corresponding angle of the spheroidal triangle, and that another angle of the spherical triangle is less than its corresponding angle of the spheroidal triangle. However the differences are very small indeed. As an instance we may consider the large spheroidal triangle of article 7, page 234, of the "Account of the Principal Triangulation of Great Britain and Ireland." Here we find that at the station whose latitude is 53, 30', the spheroidal angle exceeds the corresponding angle of the Legendre spherical triangle by about Tg0 of a second; and, although such may be disregarded in actual practice, it is nevertheless obvious that the usual method of manipulating the measured angles of a spheroidal triangle (by means of Legendre's theorem, so as to have their sum give the desired spherical excess) is erroneous in principle. NOTES. It is easy to perceive that the principal theorems arrived at apply to any surface wha...

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