. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 3I( THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. [October. only to be contimietl at a future day, whilst the river Stour carried througli Rainsgate would form a third great shingle trap in Pegwell Bay, and scour that highly valuable harbour eli'ectivelv. PRACTICAL PROBLEMS IMPORTANT IN PLANE TRIGONOMETRICAL SURVEYING^ By Professor Oliver Byrne, Mathematician. Tlie common phrase, "Things that are really useful are always simple," IS far from being generally t
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 3I( THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. [October. only to be contimietl at a future day, whilst the river Stour carried througli Rainsgate would form a third great shingle trap in Pegwell Bay, and scour that highly valuable harbour eli'ectivelv. PRACTICAL PROBLEMS IMPORTANT IN PLANE TRIGONOMETRICAL SURVEYING^ By Professor Oliver Byrne, Mathematician. Tlie common phrase, "Things that are really useful are always simple," IS far from being generally true; people do not like to give themselves the trouble to understand a subject that may appear a little compound, in fact, that which appears difficult, whatever may be its usefulness or excellence, often falls into disuse, especially if one of those simple, clumsy substitutes be convenient. The truth of the foregoing observations will be readily admitted by the mathematician, and a more striking illustration conld not be given than that afforded by the class of problems which is here arranged under the title " Plane Trigotwmttrical Siirrtying" and will be found of great use to the practical surveyor, if only in the way of tests; the principles upon which they are based are simple, and may be explained as follows:— Proposition I.—If any number of lines A, B, C, D, &c., be drawn, the ratio compounded of the ratios of A : B, B : C, C : D, &c., continued in order to A, is a ratio of equality: or which is thesame thing, when each becomes an antecedent and a consequent, taken in the above-mentioned order, the continued product of the antecedents is equal to the continued product of the consequents. Proposition II.—If triangles be formed by j'dning in succession _. , the extremities of the lines of any contour and any point O, fig. 1, the continued product of the sines of the angles opposite the antecedents is equal to the continued product of the sines of the
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