The principles of geometry and trigonometry are so continuously used by mining engineers for the purpose of accurately and intelligibly recording their measurements, that the writer is prompted to lay the following cursory remarks upon mine surveying before the members of this Institution in the hope of eliciting a free interchange of opinion upon details of this interesting branch of the profession. He proposes to deal with surveying only so far as it concerns the mining engineer, not to intrude upon the domain of the professional surveyor, and, in this instance, to discuss more especially that which may be termed the mechanical, rather than the mathematical side of surveying.In the latter part of the eighteenth century and the beginning of the present one, the usual underground surveying equipment in the English metalliferous mines, consisted of a magnetic needle in a fiat square wooden box of about 9-inch sides, a two-foot rule, a long cord, aud a stool, upon which to place the needle and box. The operator took his bearing by sending his assistant with the end of the cord as far in a straight line as the length of the cord would admit.On its being drawn that he held its end in one hand and placed the side of the compass-box against it with the other, and noted the bearing thus found either by a book entry, or by ticking it off with a piece of chalk on the board the compass lay in. He then measured the cord with a two-foot rule. It is needles to say that with these appliances the accuracy of the results were open to question, and mining surveying was not unduly popular.In the present day, engineers have the advantage of using instruments brought to such a state of perfection, and of employing such an exact system of underground surveying, that inaccurate work must usually be attributed either to lack of care, or lack of ability in the operator.