Some contractors, whose workmen are required to perform especially skilful labor, figure 15 per cent on all labor and 10 per cent on materials.

Extent of Duplication of Parts. The matter of duplication is an important factor in estimating, as a considerable saving is often made if large quantities of material, either worked or unworked, are required; this is especially true of manufactured parts, such as doors and windows, columns, balustrades, etc. Modern machines are capable of duplication with astonishing rapidity, and workmen can put together similar parts more quickly and cheaply than they can variable members.

Transportation. The distance of the work from the shop of the contractor, or from centers of manufacture, will affect the cost to a marked degree, as much time is consumed in teaming and especially in handling the material a number of times.

If communication between the works and the building site can be established by water, it will usually save considerable expense in freight and handling, with perhaps less risk of damage, and, consequently, less expense for crating and boxing. A careful study should be made of the means of transportation to each different building site from the shop, the office, and the mill, and the data kept for future reference, subject to varying rates and conditions, to change of seasons, and amounts to be transported.

Special Conditions of Each Job. These are some of the more important matters which require preliminary consideration as affecting all estimates, but they are only a small part of the real question involved, as different localities and customs require different treatment, and numerous questions will arise to confront the contractor, all of which may be successfully met by the exercise of care and judgment.

METHODS OF ESTIMATING

Estimates are formed by many and varying methods, depending upon the degree of accuracy required, the capability of the contractor, and the character of the building. A broad division may be made between approximate estimates and accurate detailed estimates, only the latter of which should be considered when it is the intention actually to carry out the work under a definite contract.

Approximate Methods. Estimating by Cubing. Approximate estimates are obtained with varying degrees of accuracy by several methods, the most convenient and reliable of which is the system of cubing, i.e., the cubical content of the proposed building is ascertained and multiplied by a given price per cubic foot. This rate is obtained by careful comparison of the plans and requirements with similar buildings which have been erected under conditions as nearly as possible like the conditions under which the proposed building can be erected.

Several methods are used to determine the cubical units, depending upon the size and shape of the proposed building. One method is to multiply the square feet in the plan of the building by the distance from half the depth of foundations to half the height of the walls; another system uses the distance from the bottom of the foundation, and another obtains the actual cubical contents. Any of these may be used if the data for comparison is obtained in the same way, but all are subject to important variations which experience and judgment alone will determine. For instance, if the contour of the building is very uneven, with low portions, such as porches and sheds, and high portions, such as towers and cupolas, these must either be omitted from the whole and compared separately, or a lump sum added or subtracted according to the size and elaboration of these members.

Another variation arises in the size of rooms, giving a ratio of partitions and division walls which is not constant; then, too, a large building with many duplicated parts will, of course, require a different rating from a smaller one. The method of estimating by cubing is, therefore, at best approximate, and its degree of accuracy depends largely upon the experience and judgment of the contractor. Even long experience will afford no safeguard against unusual elaboration of interior or exterior, so that cube rates can be applied only to buildings of ordinary character, and comparisons are reliable only between buildings of like description and uses, as the treatment of even the same materials will vary largely in buildings of varying uses.

The height of the building will not increase the cube rate proportionately, unless the internal voids are alike, although it is certain that the higher the building is from the ground, the more time and

expense it requires to put the material in place, to say nothing of thicker walls and necessarily heavier construction.

Estimating by the Square. A convenient method of estimating is by the square of one hundred surface feet. This is especially applicable to office buildings, schools, mills, stables, and all buildings where the floors are few in number or similar in plan. For one-story buildings the price per square is taken to include the roof, walls, floor, and foundations, but for buildings of two or more stories the price per square should be taken separately for each floor, the lower floor being priced to include the foundations and the top floor to include the roof.

This method of estimating by the square is not so accurate as estimating by cubical contents, but the results are often more convenient and adaptable, because the tabulation of the square area of the various floors may be easily reduced to terms of accommodation for public buildings or shops. For instance, a given floor area in a school house means accommodation for a certain number of pupils; in a church, a certain number of sittings; in factories for the manufacture ofstaple goods, a certain number of machines and operatives.

Estimating by Units of Accommodation. This unit of accommodation is sometimes carried further, and, by the reverse process, made the basis of another method of estimating the approximate cost of such buildings as the above mentioned, i.e., schools, churches, factories, hospitals, etc. This is also a method by comparison, the known data being supplied by previous experience or calculation, and it is often valuable as a means of determining the approximate cost of buildings necessary to accommodate a given number of individuals or machines, before any definite plans have been drawn.

All of these methods are approximate, with varying degrees of accuracy, and should never be advanced as accurate, or used as the basis of a contract, unless the contractor has had a long and varied experience and feels absolutely certain of his judgment, or unless a proper margin is added for possible variations.

Accurate Method. Estimating by Quantities. The only sure and correct method of estimating is by taking off the actual quantities in detail and carrying out the prices accurately, with the cost of labor, the percentage for profit, and contingencies added.

For this, accurate and complete drawings and specifications are necessary to give the absolute quantity and quality of materials and

labor. The various items are then taken off, similar portions grouped, the amount of labor estimated, and a complete and classified schedule prepared and priced at current rates; the cost of transportation, board of men, and any other contingencies noted, a percentage of profit added, and a sum total reached which should be correct if faithfully done.

This, of course, takes considerable time, but is well worth the expense and trouble if a definite contract is to be made.

Preliminary Investigations. In order to estimate to a sufficient degree of accuracy, some things other than the possession of plans and specifications are necessary. A visit to the site should be made, to ascertain the nature of the soil, the levels of the lot, the distance from railroad or wharf, the condition of the roads, and the preparation of the site necessary to receive and dispose of materials. Some knowledge should be obtained of the nature of the subsoil, the presence of ledges or water below the surface which will require especial or costly treatment, etc. Often a deposit of sand will be found upon the site which will not only save carting away the material excavated, but, if of proper quality, may be used for the work. There are many such incidental factors involved, so that a knowledge of existing conditions will be of great advantage to the estimator.

Regarding underground conditions, there is always an element of chance, as the most thorough examination will not always reveal hidden perils. The author knows of a case where a mason had contracted for the building of a sewer, and was in a fair way to make a good profit, when a narrow vein of quicksand was uncovered, to overcome which not only took away all the anticipated profit but caused a severe loss besides.

Ground water is another source of loss and it will be well for the contractor to examine his contract closely, to see to what extent, he is to furnish protection from this danger, as a vein of water which may have been temporarily stopped or diverted by the operation of building, will sometimes unexpectedly make its presence known during or after the completion of the work, when it may become a source of great annoyance and expense to the contractor if he has agreed to insure a waterproof job. Numerous illustrations could be given of the danger from unforeseen causes which can at best be only partially obviated by the most careful examination.

IMPORTANT ARITHMETICAL PRINCIPLES

In order to take off a building accurately, either by quantities, square, or cube, a good knowledge of arithmetic is necessary; and, while we may assume that the reader already possesses this, it may be well to include some of the essential rules of that branch of arithmetic which is known as mensuration. This consists primarily in the science of obtaining such definite data regarding given figures or surfaces, as area, solidity, capacity, linear dimensions, and comparison with other bodies.

Definitions of Arithmetical Terms. The area, or superficial dimension of any figure is the measure of its surface, without regard to its thickness or any other third dimension.

The cubical content of any figure is the measure of its solidity, or whole capacity, and has reference to the three dimensions, length, breadth, and thickness.

If the figure is considered as hollow, then the cubical content becomes its capacity or capability of containing matter.

The linear dimension of a figure is expressed by its length in a direct line in any direction and has no regard to breadth or thickness.

Units of Measurement. The application of these dimensions is made by fixing a unit by which the figure may be compared and the required dimension obtained: thus, for calculating the area of a figure the unit is usually a square, one side of which is the unit of length; and the area becomes the square measure of the figure.

This is expressed in common terms by square inch, square foot, square yard, or any other given unit, and the measure of the surface is computed by obtaining the number of these square units which are contained in the figure, the process being called squaring.

In a similar manner the cubical contents or solidity of a figure is obtained by computing the number of cubical units which it contains, which is called cubing it.

Rules for Determination of Unknown Dimensions. Numerous rules have been framed for obtaining unknown dimensions from given dimensions. There are given below the formulas and data which should enable the student to solve most of the ordinary problems which will arise in common practice.