The determination of the proper clearance to allow between the bottom of the shaft and the inside of the timber or reinforced-concrete shell is an economic problem of importance. If it be made unnecessarily large, the volume of the base will be too great and the construction too costly. On the other hand, if it be made too small and an error in location should occur because of unanticipated trouble in sinking, it would be difficult to shift the shaft the right amount on top of the crib in order to get it into correct position; and this would involve delay, than which there is nothing more expensive in substructure construction. It is evident that one must endeavor to strike a happy mean in designing his cribs and caissons—but what is that mean? The author's practice is to allow as a minimum a foot clear all around the base of the shaft for easy conditions of sinking, and to increase this gradually as the said conditions become more and more unfavorable, up to a limit of about twice that amount. It would certainly be a case of either gross carelessness or extremely hard luck which would prevent the correct location of a pier-shaft when the larger allowance-limit for shifting was provided. With due care in sinking, the error of position of a crib-top should seldom exceed a few inches; consequently, when a bridge engineer, in order to be surely on the safe side, makes an abnormally-great allowance for error of crib position, he does so at the expense of the work, and therefore imperils his reputation as a true economist.

Whether to use the pneumatic process instead of either open-dredging or cofferdam excavation is fundamentally an economic problem based upon the theory of probabilities. Comparing the open-dredging and the pneumatic methods of sinking, while the former generally figures out to be the cheaper, its cost is rather uncertain, because of the possibility of encountering large logs or boulders; and, while the cost of installation of a pneumatic plant adds some two or three dollars to the cost per cubic yard of the bases, one can count almost with certainty upon the total expense involved in the sinking. If bed rock be within reach by the pneumatic process, that method of sinking should always be adopted, unless it be decided not to go that far down for a foundation, in which case the open-dredging process is likely to be the more economic. One should never sink a caisson to bed rock by open-dredging for fear that it will rest on one edge or one corner only and thus provide an unequal bearing. It would be far better to stop short of it a small distance and rest on sand, gravel, or boulders overlying the rock.

Comparing the cofferdam method with that of open-dredging into a clay or other fairly-hard foundation-material, unless the depth below the working stage of water be less than eighteen (18) or twenty (20) feet, the latter usually is preferable, because the former is likely to give trouble and nearly always involves a greater expenditure of money than that allowed in the preliminary estimate.

The economics of steel sheet piling for cofferdams is still an unsettled question among bridge engineers. Some of the old-time substructure con-