# Surveying Problems and Solutions

This book is an attempt to deal with the basic athematical aspects of 'Engineering Surveying', i.e. surveying applied to construction and ining engineering projects, and to give guidance on practical methods of solving the typical problems posed in practice and, in theory, by the various examining bodies.
The general approach adopted is to give a theoretical analysis of each topic, followed by worked examples and, finally, selected exer- cises for private study. Little claim is made to new ideas, as the ground covered is elementary and generally well accepted. It is hopedthat the mathematics of surveying, which so often causes trouble to beginners, is presented in as clear and readily understood a manner as possible. The main part of the work of the engineering surveyor, civil and mining engineer, and all workers in the construction industry is confined to plane surveying, and this book is similarly restricted. It is hoped that the order of the chapters provides a natural sequence, viz.:

#### Fundamental measurement

• Linear measurement in the horizontal plane,
• Angular measurement and its relationship to linear values, i.e. trigonometry,
• Co-ordinates as a graphical and mathematical tool.

#### Fundamental surveying techniques

• Instrumentation.
• Linear measurement in the vertical plane, i.e. levelling,
• Traversing as a control system,
• Tacheometry as a detail and control system.

#### Industrial applications

• Three-dimensional aspects involving inclined planes,
• Mensuration,
• Curve surveying.

Basic trigonometry is included, to provide a fundamental mathematical tool for the surveyor. It is generally found that there is a deficiency in the student's ability to apply numerical values to trigonometrical problems, particularly in the solution of triangles, and it is hoped that the chapter in question shows that more is required than the sine and cosine formulae. Many aspects of surveying, e.g. errors in surveying, curve ranging, etc. require the use of small angles, and the application of radians is suggested. Few numerical problems are posed relating to instrumentation, but it is felt that a knowledge of basic physical properties affords a more complete understanding of the construction and use of instruments. To facilitate a real grasp of the subject, the effects of errors are analysed in all sections. This may appear too advanced for students who are not familiar with the elementary calculus, but it is hoped that the conclusions derived will be beneficial to all.

With the introduction of the Metric System in the British Isles and elsewhere, its effect on all aspects of surveying is pin-pointed and conversion factors are given. Some examples are duplicated in the proposed units based on the International System (S.I.) and in order to give a 'feel' for the new system, during the difficult transition period, equivalent S.I. values are given in brackets for a few selected examples.
The book is suitable for all students in Universities and Technical Colleges, as well as for supplementary postal tuition, in such courses as Higher National Certificates, Diplomas and Degrees in Surveying, Construction, Architecture, Planning, Estate Management, Civil and Mining Engineering, as well as for professional qualification for the Royal Institution of Chartered Surveyors, the Institution of Civil Engineers, the Incorporated Association of Architects and Surveyors, the Institute of Quantity Surveyors, and the Institute of Building.