Scanlan v. San Francisco & San Joaquin Valley Railway Co.

VAN FLEET, J. This is an action, brought by a contractor for the construction of a railway embankment to recover the contract price for the alleged cubic contents of the embankment. The defendant had paid to the plaintiff what it claimed to be the whole amount earned, except about $20, which it brought into court. The plaintiff had judgment for the balance claimed by him, and the defendant appeals.

The contract, among other things, contained the following provisions: “On embankments a percentage for shrinkage must be added to the fill, and said percentage will be as specified and marked out by the engineer [of the company], but will in no case exceed ten per cent of height of bank.” “Material will be measured in embankment, but no measure- , ment will be made of the material added for shrinkage, nor payment made for same.” Under this contract it was incumbent upon the plaintiff to prove the cubic contents of the material placed by him in the embankment, measured in the embankment, excluding the material added for shrinkage. The plaintiff produced as a witness an engineer, who testified that he had measured the embankment after its completion, and had found it to contain a certain number of cubic yards, which he stated; but he did not give the data upon which his computations (for he testified to two) were based. In his measurements and computations he made no allowance for any material added for shrinkage; nor did plaintiff in any way prove how much had been so added, though it was admitted that such additions had been made. The witness testified that his computations were made by measuring a certain number of cross-sections, finding the average area of these cross-sections, and multiplying this average area by the length of the embankment. One of the computations submitted by him was based entirely upon his own measurements, and the other, which was much less, upon the measurements of the defendant’s engineer, except as to the heights, as to which the witness used his own measurements. The court, in its findings', adopted neither of these computations, but fixed the amount at an intermediate figure, for which we are unable to find [212]any basis in the evidence. We think that there was no evidence before the court by which the contents of the embankment could be ascertained. The finding depends entirely upon the accuracy of the computations made by plaintiff’s engineer, since the measurements themselves were not before the court, and it is evident that these computations were inaccurate.

1. The court takes judicial notice of the laws of nature (Code Civ. Proc., see. 1875, subd. 8), among which are the principles of mathematics. The science of mensuration, which must control in this case, is a branch of pure mathematics, with which the court is presumed to be acquainted. By the rules of mensuration, the contents of an irregular prismoidal body, such as a railway embankment, is ascertained by dividing it by vertical planes at every change of contour of the underlying ground into a series of prismoids, and computing the contents of each of these prismoids by adding together its two end areas and four times its middle area, dividing this sum by six, and multiplying the quotient by the length of the prismoid. The product will be the actual contents of the prismoid: See Enc. Brit., 9th ed., art. “Mensuration.” This method was not employed by the witness. His method was an approximation, which assumes that the middle area of a prismoid is equal to half the sum of its end areas. This is true only in the ease of a prism, or in a prismoid consisting of the frustum of a regular pyramid. This approximation, it is true, will give results correct enough for practical purposes in very uniform embankments, where there is but little difference in height. But in other cases its results are always too large, and it would be easy to suppose cases in which the excess would be greater than the difference between the estimates of the respective parties in this case.