This action is for a balance claimed to be due under a contract to finish a levee at Cairo, Illinois. The contract sued on is to wit:
“St. Louis, July 14,1890.
“This agreement made and entered into between the firm of Dean, Berry & McKinney and J. F. Roth-well & Bro., by which the firm of Dean, Berry & McKinney, now holding subcontract from the 'firm of Greenlee & Little, general contractors on Cache Levee in Alexander county, Illinois, and with their consent, do hereby sublet to J. F. Rothwell & Bro. "all unfinished work on said Cache Levee between station numbers 83 and 117 and between station numbers 123 and and 129 of said levee. It is further agreed between the firm of Dean, Berry & McKinney and J. F. Roth-well & Bro. that the said J. F. Rothwell & Bro. shall complete the said work in accordance with the plans and specifications of the Cairo Board of Drainage Commissioners, and to their approval and acceptance of the said work, and, further, that the said firm of Dean, *430Berry & McKinney shall pay to the said J. E. Rothwell & Brother fourteen cents per yard for embankment, which shall be payable after each monthly estimate, and be paid between the fifteenth and twentieth of each month, except, however, ten per cent. (10 per cent.) of all estimates, which is retained by said Cairo Board of Drainage Commissioners until the completion of said levee; and, further, the said J. E. Rothwell & Bro. shall prosecute the-work continuously until it is completed, and shall have all the work completed to the satisfaction of the said Cairo Board of Drainage Commissioners before October 1, 1890.
“Now, if the said J. E. Rothwell & Bro. shall have completed the said work to the satisfaction of the said Cairo Board of Drainage Commissioners, then the said firm of Dean, Berry & McKinney agree to pay to the said J. E. Rothwell & Bro. the sum of three hundred dollars ($300) extra, above all estimates.
“J. E. Rothwell,
“Dean, Berry & McKinney.”
The answer was a general denial, and contained a plea of payment. The case was tried before a jury, who found a verdict for the plaintiffs in the sum of $1,311, stating in their verdict that they allowed plaintiffs nothing for the work done by the Hakes force gang, hereinafter referred to. From a judgment entered upon this verdict the defendants prosecute the present appeal, and assign for error that the court in its instructions to the jury misconstrued the contract between themselves and the plaintiffs, and admitted illegal evidence against defendants’ objections, and that the verdict is excessive under the evidence.
In order to understand the substantial controversy between the parties, the following facts developed by the evidence become material. The levee work sublet to the plaintiffs consisted of several detached sections. *431One of these sections lay east of the railroad embankment of the Illinois Central Railroad, and comprised stations from 83 to 108, each station being one hundred feet in length, the whole aggregating a length of two thousand, five hundred feet. It is in regard to this section that the controversy in the main arises. As this station was nearest the Ohio River, and near the confluence of the Ohio and Cashe Rivers, it was that part of the work which was most subject to overflow by a sudden rise of these rivers. The bulk of the work, which the defendants did prior to subletting the work to the plaintiffs, was done on this section. Besides this section, the defendants sublet to the plaintiffs work on sections west of the embankment of the Illinois Central Railroad, touching which, however, there is no substantial controversy.
Charles Throop, a witness for the plaintiffs, testified that he was the chief engineer of the Levee Company engaged in doing this work. According to his uncontradicted evidence he had been a civil engineer for a period of near forty years, and as such engaged in the supervision of large enterprises. Touching his thorough qualifications as an expert there can be no doubt. He testified that he made an estimate of the work done by the defendants prior to the time that they quit work, and found that the work done by them amounted to twenty-nine thousand and eighty-nine cubic yards of earth, east of the embankment of the Illinois Central Railroad. The defendants did some work after this measurement was made, but all the testimony seems to concede that this work was done on the four stations next to- the embankment of the Illinois Central Railroad.
In the early part of the year 1890, the waters rose to a great height in the Ohio and Cashe rivers, and flooded part of the work that had been done by the *432defendants. The work at that time was in the following shape: There were about seven hundred feet of it between stations 92 and 99 raised to the established grade. This portion was above high water mark, and was not affected by the rise of the ■ waters. On both sides of this high fill, but mainly on the western side thereof, the bank was left by defendants much below grade, and was overflowed by the waters. The soil of which the embankment was made was in part sandy, and washed and floated off easily. After the waters had subsided, the chief engineer examined this bank, and he testified upon the trial that, in his opinion, from three thousand five hundred to five thousand yards had been thus washed off. What the loss thus caused amounted to, how it affected the final estimates, and whether it should fall upon plaintiffs or the defendants, were the main points controverted at the trial.
When the engineer, testified as to the amount of the loss caused by the overflow, the defendants objected to the testimony on two grounds: first, because, according to théir contention losses of that character had to be borne by the plaintiffs under the terms of their contract, and, next, because the evidence was vague and indefinite touching a subject which was capable of being ascertained by exact measurement. The first of these contentions is based on the theory that plaintiffs were bound by the terms of their contract to make good any injury to the work done before the subletting to them by floods or casualties of all kinds. This contention has for its only support section 9 of the plans and specifications referred to in the contract in suit. By this section the contractor was required to take all risks from floods and other sources which might occur before the final completion of the work. The section in question, however, does not by its terms, nor any sound principle of interpretation, operate *433retrospectively. It only undertook to make provision, as between the parties to this suit, for losses or damages occasioned by the excepted causes after the beginning of the work. It was not intended to impose any liability on plaintiffs for losses or damages, which had fallen on defendants in their previous construction of the levee. There is, therefore, no merit in that assignment. The plaintiffs’ contract with the defendants bears date July 14, 1890, and there is no pretense that any losses were caused by the floods subsequent to said date.
Nor is, in our opinion, the second of these contentions tenable. It is not satisfactorily shown that the losses thus caused were ever measured by the engineer in any other manner, except by the estimate which he thus placed upon them. He had nothing to do with questions arising between contractors and subcontractors. As between the company and the contractors, the loss was to be borne by the contractors, and it was immaterial what parts of the bank washed away before its final completion, as the loss of such washing had to be borne by the contractors in any event. The evidence disclosed that the plaintiffs requested the engineer to measure this loss, and that he declined to do so, it being a matter which did not concern his corporation. We hold that, in the absence of better evidence, the estimate of an engineer of nearly forty years experience in this class of work, who saw the bank both before and after the flood, and who presumably had all the data in his recollection which would enable him to form a measurably accurate approximar tion, was admissible evidence.
The plaintiffs, upon taking charge of the work in July, 1890, seeing that portions of it had been washed off, tried to obtain a measurement of the loss by the *434engineer, in which they failed as above stated. They thereupon went out with a tape line and a stick, measured the embankment between stations 83 and 108, at points one hundred feet apart, for the purpose of ascertaining the actual dirt then in the embankment. This embankment in places was twelve feet high. There was no pretense that the plaintiffs knew anything of the original topography of the ground, nor that they used any cross-section spirit level, and graduated rod in making this measurement. It thus necessarily appeared that the plaintiffs’ estimate of the elevation of various parts of the bank above the natural soil was a mere guess. They could not possibly ascertain it, as they were not in possession of the original profiles; nor, if they had been, is there any pretense that they ran profiles over any portions the bank already constructed. When the measurement thus made was offered in evidence, the defendants’ counsel objected to it on the ground that the estimate of the engineer in charge wras the only competent evidence, and on the further ground that the estimate was a mere guess.
Courts must take judicial notice of elementary mathematical propositions. It is an elementary proposition that to estimate the cubic contents of any body, its superficial outlines must be known. As it conclusively appeared from the plaintiffs’ evidence that they did not know the superficial outlines of the bodies of earth they pretended to measure, this estimate should have been rejected, and its reception was prejudicial error. According to this estimate there was at that time in the bank, between stations 83 and 108, about twenty-three thousand or twenty-four thousand cubic yards of earth. As the engineer’s estimate shows at that time twenty-nine thousand, eight hundred and eighty-nine yards, it is evident that, even giving credit for three thousand, five hundred yards washed away, *435there still should be twenty-six thousand, three hundred and eighty-nine remaining, conceding even that the defendants had done no work on that part of the levee between stations 83 and 108 after the engineer’s estimate in January, 1890, touching which there is some conflict in the evidence.
The following facts all the evidence concedes. The total amount of earth in that part of the levee covered by defendant’s and plaintiffs’ contract, when completed, was sixty-two thousand, two-hundred and eighty-six cubic yards. Of this the defendants, according to the engineer’s measurement, did in any event thirty-nine thousand, five hundred and thirty-seven yards, less such portions as were washed away by the water and had to be replaced, for which a liberal estimate under all the testimony 'legally admitted should not exceed three thousand, five hundred yards. This left twenty-six thousand, two hundred and forty-nine yards to be completed by the plaintiffs, which work there is legal evidence tending to show they performed. At fourteen cents per cubic yard, this would entitle the plainiffs to an aggregate compensation of $3,674.86. Of this the plaintiffs concede they received from defendants $2,723.13. One Hake was also paid on account of this work $645.52, with which under the findings of the jury the plaintiffs are chargeable, leaving a balance due plaintiffs of $306.21, to which the premium of $300 under the contract is to be added, — making an aggregate of $606.21. To this amount with interest at the rate of six per centum per annum from the date of the institution of the suit (July 27, 1891) to the date of trial- (December 18, 1893) plaintiffs have shown themselves entitled by legal evidence offered. This, however, would aggregate $693.17 only, instead of $1,311, as shown by the verdict of the jury. That verdict, therefore, is grossly excessive in any view of the *436evidence, and the judgment based thereon must be reversed.
In order to avoid a new trial, the respondents should be permitted, if they so elect, to remit in this court, of their recovery, all above the sum of $693.17. If they will do so within ten .days after the filing of this opinion, the judgment will be affirmed for the residue. In the contrary event, it will be reversed and the cause remanded. Should a new trial become necessary, the cause should be sent to a referee to take an account on the basis of the views hereinabove expressed.
In the foregoing opinion all the members of the court concur, taking the view of the evidence therein presented. My own opinion is that the testimony of the plaintiffs as to the method of measurement made by them should have been rejected not only on account of its intrinsic infirmity, but because it was not the method by which the parties were bound according to the contract. By that instrument plaintiffs were .restricted to a recovery for the number of cubic yards which they added to the levee according to the estimates thereof made by the engineer’s measurement. I also hold that even the testimony of the engineer as to the number of vards he thought had washed away was incompetent, and nothing outside of his official measurement should-have been received.