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known in any plane triangle, the sum of the known sides is to their difference as the tangent of the half sum of angles at base is to the tangent of half their difference. In triangle CDE, therefore, CD + DE or 651.7 : CD-DE or 188.3 :: tan. 108.12 • 2 or tan. 54° 06' : tan. 54° 06' X 188.3 · 651.7 .399 = tan. 21° 45', half the difference of the angles at the base.

Log. 188.3. .
Tan. 54° 06'

2.274850 0.140334 2.415184 2.814048

Log. 651.7
Tan. 21° 45'. Diff..



The angle at C, being evidently the lesser of the two angles at the base, is equal to the half sum of these angles decreased by their half difference, : 54° 06' 21° 45' 32° 21'.

Set the transit, then, at C, foresight to D, deflect 32° 21' left, and fix in that range two points F and G, between which a cord may be stretched, and as nearly as can be judged on opposite sides of E. Move to D, foresight to C, deflect 71° 48' right, and establish a point E at intersection with FG. Cross to E, BS to D, and deflect the angle z= 64° 10 into the line of the tangent A B prolonged.







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i. THE CHIEF ENGINEER, after conference with his employers in regard to the character of the work contemplated, and its general route, should, before organizing field-corps, go over the ground in both directions, and, aided by the best attainable maps, qualify himself by actual observation to instruct his assistants as to the conduct of the survey. Equipped with hand-level, pocket-compass, and in rough regions with the aneroid, he can often not only prescribe lines for examination, but indicate the gradients to be tried, thus saving a vast. amount of random labor and needless expense. Such thorough preliminary exploration is due both to himself and his principals: it is too often omitted, or done with a perfunctory rush. In broken topography, no maps, notes, or information derived from others can supply the want of personal acquaintance with the ground itself. He must indispensably make that acquaintance, in order to project an intelligent location, - a work which should rarely be delegated; being capital service, it comes within the special function of the chief engineer, and only the necessary distribution of labor attending a great charge should relieve him from its direct performance.

2. A FIELD-CORPs in settled regions generally consists of mr me senior assistant or chief of corps, one transitman, one

leveller, one rodman, two chainmen, one slopeman, and two

or more axemen.

The following notes in regard to the allotment of duties and the conduct of work may be acceptable. They are copied from the 'writer's memoranda for the guidance of his fieldparties, with the addition of some detail, and practical hints

3. THE SENIOR ASSISTANT will receive instructions from the principal assistant in charge, or the chief engineer, and will act exclusively under his direction.

He will be held responsible for the good conduct of the corps, and for the rapid, exact, and economical performance of the work. Indecent or blasphemous outcries in the field should be prohibited. The writer's various travel by land and sea has brought him acquainted with many cultivated, estimable, energetic, profane fellows, but not one in whom swearing was a grace; nor has he ever seen an instance where it forwarded work. Those considerate of others' pride and self-respect will generally find that a good leader makes good followers.

The senior assistant is empowered to appoint and dismiss employes below the rank of rodman, and will report any inefficiency or neglect of duty in the ranks above to his chief.

He will pay the authorized expenses of the corps for supplies, repairs, transportation, and subsistence, taking duplicate vouchers. Accommodations should be sought near the work. When not thus obtainable, transportation to and from the field is to be regarded as a measure of economy for the company, compensating the expense incurred by saving time and labor.

He will superintend field operations in person, keeping in advance of the transit to direct and expedite the work, and establish the turning-points. On preliminary surveys, the axe should-be little used; and on alternative locations, or such as may be subject to revision, trees over four inches in diameter need rarely be felled.

He should be patient with sensitive landholders. He will find exercise for that amiable virtue, also, with the field visitors who so often spare time from useful toil to tell him he is on the wrong line, and to show him where the right one is.

Note for record the kind and quality of material to be moved, observing quarries, wells, or other indications for the purpose; the timber and rock in the country traversed, with a view to their use in construction, and the widths of passage to be provided for streams, together with the character of their banks and beds.

Note the names of residents in the immediate vicinity of the work on survey; and, on location; cause the property-lines to be observed and recorded also when convenient.


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