Ladd, J.
A bayou three and eight-tenths miles long curved to the southeast, and then back to the southwest, flowing through a narrow channel into the Missouri River. This channel was crossed by a wagon bridge six hundred feet from the river and the hayou by the railroad bridge about a mile further north. Into the north end of the bayou emptied an old county ditch, which extended to the north seven thousand four hundred feet, and beyond it was “Mule” slough. By appropriate proceedings the board of supervisors of Fremont County established a drainage district and ordered the construction of a bulkhead across the channel, with flood gates, to prevent the water backing from the river into the bayou, the widening of the channel to the width of eighteen feet for a distance of about one thousand feet from the river, the excavation of a ditch six feet wide and two and one-half feet deep for a distance of about one thousand three hundred feet long, through a bench of land north of the railroad bridge and across an arm of the hayou, extending east and north, and which held the water back when medium or low. It also directed that the county ditch be widened to twenty feet and deepened from one to three feet, and that a ditch he excavated through Mule slough varying in width from twenty to four feet. This order was in pursuance of a report of the engineer, appointed by the board of supervisors, filed with the county auditor and accompanied with plat and profile of the proposed improvements, together with estimates of their probable cost. There were several laterals concerning which there is no controversy. The work was completed in 1907, and the disparity between the preliminary estimates of the engineer and his final report of the actual cost was such as to lead to the investigation involved in this 'action. On the part of plaintiff it is contended that the main ditch [122]*122extending from the north end of the bayou was exc'avated deeper and wider than the specifications called for, and that no charge should be made for the excess, and that much of the work in the bayou was not included in the contract, and that, if directed or approved by the engineer, this was the result of collusion and fraud between him and the contractors. In response to these charges the contractors assert that, even though the main ditch may have been excavated wider and deeper than indicated in the specifications, the engineer- rejected any excess over that called for in making the measurements, so that the main 'ditch cost no more according to the final report than it would have had it been no wider and the bottom no lower than .the line estimated in their preliminary survey. They further assert that the® preliminary report was uncertain and indefinite as to the amount of excavation in the bayou, and that they performed the work under the direction of the engineer, and should be compensated therefor.
1. Drainage: liability for work of construction. I. The dispute as to the main ditch first may be disposed of. In the final report the engineer certified that about one-third more earth was removed than had been estimated in the preliminary report on which the hoard of supervisors acted in ordering ^ improvement. This is a large discrepancy, and indicates either that the work of the preliminary survey was not performed as carefully as it should have been, or that the final report is incorrect. It appears that the elevations were taken at points one thousand feet apart in making the preliminary survey, and, of course, those of the ground intervening were merely inferred. The preliminary report was but of estimates, while that finally made was, if properly prepared, a statement of accurate measurements of what had been done. Some differences between the two- were to be anticipated, and that these are large will not alone justify the inference that there was fraudulent collusion between the engineer and contractors. [123]*123If tbe number of cubic yards reported as excavated in tbe engineer’s final report was actually removed, and in measuring the same be included therein nothing below tbe grade line established in tbe preliminary report as the bottom of tbe ditch nor any of tbe excess in width, then tbe plaintiffs are not entitled to relief. In tbe practical work of excavating ditches tbe depth and width often vary, and all that is required is that tbe ditch be constructed in substantial conformity with the specifications. Tbe complaint here is not that the work was improperly done, but that tbe contractors have'been allowed by the engineer for ■ excavating deeper or wider than was contemplated by tbe original report and profile. Tbe engineer testified that in tbe final report nothing of the excavation below the grade line established by the preliminary survey nor of any excess in width was included. The evidence was undisputed, ' and therefore we necessarily reach tbe conclusion that tbe plaintiffs are not entitled to relief with respect to any work done on the main ditch.
II. Tbe following extract from tbe report of the engineer clearly indicates tbe work which was to be done in the bayou:
The outlet from the bayou is a small channel under the above-mentioned highway bridge. During the time of high water in tbe river the water is held back in the bayou; in fact, tbe bayou fills up with backwater from tbe river. Tbe water level in tbe bayou will vary several feet according to tbe stage of the river. Tbe backwater from tbe river can be kept out of tbe bayou by a bulkhead across tbe channel fitted with gates, which, when closed, will close tbe channel and when open will allow the water to drain from tbe bayou, tbe bottom of tbe gates to be set so as to lower tbe water in tbe bayou from elevation of one hundred and one and thirty-five-one-hundredths, its present stage, at elevation ninety-nine. A design for a bulkhead with an estimate of cost accompanies this report. To put in tbe bulkhead will necessitate tbe removal of tbe highway bridge and replace that with an embankment, and [124]*124build a twenty-foot bridge across the channel leading to the bulkhead. This channel should be eighteen feet wide and about one thousand feet long. It is nineteen thousand and eighty-three feet or three and eight-tenths miles from the mouth of the bayou to its northern end, where the county ditch empties into it. It has a fall of four and six-tenths feet in the distance. From the river to the crossing under the C. B. & Q. bridge No. 5, a distance of one mile, the channel is several hundred feet wide. From the railroad bridge an arm of the bayou bears east and north close to the highway. There is a bench of land across this arm extending from the railroad bridge north about one thousand three hundred feet, which bench holds water above it, during medium and low stages of water in bayou below. A channel six feet wide and two and one-half feet deep should be cut through this bar. The building of the bulkhead and the cutting through the bar will, in my opinion, preclude the possibility of flooding any of the land to the west of the bayou during flood periods and will afford good drainage to the land at all times.
In the same report are the estimates of cost: “Excavating outlet channel (3000 cu. yd. at 30c.) $900. . . . Excavating channel in bayou above railroad bridge (725 cu. yds. at 40c.) $290.” And summarizing, under the heading “Bayou and Outlet”: “Length of outlet channel, one thousand feet. Length of channel above railroad, one thousand three hundred feet. . . . Excavation above bridge seven hundred and twenty-five cu. yds.
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Ladd, J.
A bayou three and eight-tenths miles long curved to the southeast, and then back to the southwest, flowing through a narrow channel into the Missouri River. This channel was crossed by a wagon bridge six hundred feet from the river and the hayou by the railroad bridge about a mile further north. Into the north end of the bayou emptied an old county ditch, which extended to the north seven thousand four hundred feet, and beyond it was “Mule” slough. By appropriate proceedings the board of supervisors of Fremont County established a drainage district and ordered the construction of a bulkhead across the channel, with flood gates, to prevent the water backing from the river into the bayou, the widening of the channel to the width of eighteen feet for a distance of about one thousand feet from the river, the excavation of a ditch six feet wide and two and one-half feet deep for a distance of about one thousand three hundred feet long, through a bench of land north of the railroad bridge and across an arm of the hayou, extending east and north, and which held the water back when medium or low. It also directed that the county ditch be widened to twenty feet and deepened from one to three feet, and that a ditch he excavated through Mule slough varying in width from twenty to four feet. This order was in pursuance of a report of the engineer, appointed by the board of supervisors, filed with the county auditor and accompanied with plat and profile of the proposed improvements, together with estimates of their probable cost. There were several laterals concerning which there is no controversy. The work was completed in 1907, and the disparity between the preliminary estimates of the engineer and his final report of the actual cost was such as to lead to the investigation involved in this 'action. On the part of plaintiff it is contended that the main ditch [122]*122extending from the north end of the bayou was exc'avated deeper and wider than the specifications called for, and that no charge should be made for the excess, and that much of the work in the bayou was not included in the contract, and that, if directed or approved by the engineer, this was the result of collusion and fraud between him and the contractors. In response to these charges the contractors assert that, even though the main ditch may have been excavated wider and deeper than indicated in the specifications, the engineer- rejected any excess over that called for in making the measurements, so that the main 'ditch cost no more according to the final report than it would have had it been no wider and the bottom no lower than .the line estimated in their preliminary survey. They further assert that the® preliminary report was uncertain and indefinite as to the amount of excavation in the bayou, and that they performed the work under the direction of the engineer, and should be compensated therefor.
1. Drainage: liability for work of construction. I. The dispute as to the main ditch first may be disposed of. In the final report the engineer certified that about one-third more earth was removed than had been estimated in the preliminary report on which the hoard of supervisors acted in ordering ^ improvement. This is a large discrepancy, and indicates either that the work of the preliminary survey was not performed as carefully as it should have been, or that the final report is incorrect. It appears that the elevations were taken at points one thousand feet apart in making the preliminary survey, and, of course, those of the ground intervening were merely inferred. The preliminary report was but of estimates, while that finally made was, if properly prepared, a statement of accurate measurements of what had been done. Some differences between the two- were to be anticipated, and that these are large will not alone justify the inference that there was fraudulent collusion between the engineer and contractors. [123]*123If tbe number of cubic yards reported as excavated in tbe engineer’s final report was actually removed, and in measuring the same be included therein nothing below tbe grade line established in tbe preliminary report as the bottom of tbe ditch nor any of tbe excess in width, then tbe plaintiffs are not entitled to relief. In tbe practical work of excavating ditches tbe depth and width often vary, and all that is required is that tbe ditch be constructed in substantial conformity with the specifications. Tbe complaint here is not that the work was improperly done, but that tbe contractors have'been allowed by the engineer for ■ excavating deeper or wider than was contemplated by tbe original report and profile. Tbe engineer testified that in tbe final report nothing of the excavation below the grade line established by the preliminary survey nor of any excess in width was included. The evidence was undisputed, ' and therefore we necessarily reach tbe conclusion that tbe plaintiffs are not entitled to relief with respect to any work done on the main ditch.
II. Tbe following extract from tbe report of the engineer clearly indicates tbe work which was to be done in the bayou:
The outlet from the bayou is a small channel under the above-mentioned highway bridge. During the time of high water in tbe river the water is held back in the bayou; in fact, tbe bayou fills up with backwater from tbe river. Tbe water level in tbe bayou will vary several feet according to tbe stage of the river. Tbe backwater from tbe river can be kept out of tbe bayou by a bulkhead across tbe channel fitted with gates, which, when closed, will close tbe channel and when open will allow the water to drain from tbe bayou, tbe bottom of tbe gates to be set so as to lower tbe water in tbe bayou from elevation of one hundred and one and thirty-five-one-hundredths, its present stage, at elevation ninety-nine. A design for a bulkhead with an estimate of cost accompanies this report. To put in tbe bulkhead will necessitate tbe removal of tbe highway bridge and replace that with an embankment, and [124]*124build a twenty-foot bridge across the channel leading to the bulkhead. This channel should be eighteen feet wide and about one thousand feet long. It is nineteen thousand and eighty-three feet or three and eight-tenths miles from the mouth of the bayou to its northern end, where the county ditch empties into it. It has a fall of four and six-tenths feet in the distance. From the river to the crossing under the C. B. & Q. bridge No. 5, a distance of one mile, the channel is several hundred feet wide. From the railroad bridge an arm of the bayou bears east and north close to the highway. There is a bench of land across this arm extending from the railroad bridge north about one thousand three hundred feet, which bench holds water above it, during medium and low stages of water in bayou below. A channel six feet wide and two and one-half feet deep should be cut through this bar. The building of the bulkhead and the cutting through the bar will, in my opinion, preclude the possibility of flooding any of the land to the west of the bayou during flood periods and will afford good drainage to the land at all times.
In the same report are the estimates of cost: “Excavating outlet channel (3000 cu. yd. at 30c.) $900. . . . Excavating channel in bayou above railroad bridge (725 cu. yds. at 40c.) $290.” And summarizing, under the heading “Bayou and Outlet”: “Length of outlet channel, one thousand feet. Length of channel above railroad, one thousand three hundred feet. . . . Excavation above bridge seven hundred and twenty-five cu. yds. Excavation at outlet, two thousand seven hundred yds.” In addition to the above, the profile filed with the county auditor indicates the extent of the above excavations to be as stated. The report also represented that a portion of the work in the outlet channel and all of that through the bench of land would have to be done by the use of the spade. But the contractors made use of a dredge, and, instead of excavating 'in accordance with the preliminary survey, made the ditches in the bayou eight thousand five hundred and ninety-five feet in length and twenty feet in [125]*125width, instead of the two small channels as recommended in the original report. This was done by the contractors at the instance and under the direction of the engineer; so that, although the contractors constructed the main ditch with a dredge at seventeen cents per cubic yard, they claim, and the engineer ,in his final report allowed, for excavation in the same manner in the bayou twenty-eight and thirty-eight bents per cubic yard, and, instead of widening one channel one thousand feet long and excavating a small channel one thousand three hundred feet long, removing in so doing three thousand seven hundred and twenty-five cubic yards of earth, they dug channels eight thousand five hundred and ninety-five feet long .and removed twenty thousand one hundred and sixty-two cubic yards of earth. According to the testimony of the engineer, the amount removed in the bayou south of the railroad bridge was ten thousand four hundred and sixty-eight and eight-tenths cubic yards and was computed at twenty-eight cents per cubic yard. This work was not limited to widening the channel outlet as contemplated in the contract, bud, after doing this, it was extended along the right bank of the hayou, so that, instead of merely widening the channel from the bayou to the Missouri River, an attempt was made to create a new channel along the bottom of the bayou. Instead of a narrow channel six feet wide through the bench, separating the waters of the bayou, north of the railroad bridge, a channel twenty feet wide was excavated, and it extended along the bottom of the bayou by the removal of nine thousand six hundred and ninety-five cubic yards of earth, and this was computed at thirty-eight cents per cubic yard. Not a paper on file gave any intimation of this work or its character, and clearly it was not contemplated in the original report or the contract as entered into by the board of supervisors.
2. Same. Butit is said that the preliminary surveys and estimates of the work to be done in the bayou were uncertain [126]*126and indefinite, and that there, has been a substantial compliance with them. The estimates are not required to be definite. The length of the channel to be widened was reported about one thousand feet long and of that to be excavated “about one thousand three hundred feet.” The adverb “about” as here employed means “nearly, approximately, almost,” and indicates that the distances were not intended to be accurately stated, but estimated and otherwise ascertainable. Thus the first, the small channel to be widened, was described as extending from the bayou under the wagon bridge to the river. As the lower part of the bayou was several hundred yards wide, no difficulty could be experienced in understanding precisely what was intended. Nor could any doubt arise regarding the excavation of a ditch six feet wide through the bench of land north of the railroad bridge. It was through this, whether somewhat more or less than one thousand three hundred feet wide or long, that the ditch was to be dug. This was as apparent to the contractors as to any one else who chose to examine the engineer’s report and profile. If, then, the statement of the distances named be regarded as uncertain, the character of the improvements to be made was not left in doubt, and neither the contractors nor the engineer were authorized to change them nor add others without an order of the board of supervisors.
3. Same: enlargement of drain: compensation. The statute of which both had notice points out precisely how changes of this kind may be effected. “If, after said contract shall have been let and the work begun, it shall become apparent to the engineer in charge that the dimensions of the levee, ¿i(-ch, or drain should be enlarged, deepened or otherwise changed for. the better service thereof of the lands benefited, then the engineer shall report such fact .to the supervisors, explaining to them the necessity for such change in the dimensions of said improvement as the [127]*127engineer shall recommend, provided that, before such action shall be taken, like notices shall be given and like proceedings had as hereinbefore provided for the establishment of the levee or drainag’e district.” No report such as contemplated was ever made nor action of the board of supervisors taken. No price for excavating the channel in the bottom of the bayou was agreed to, and the computation by the engineer in his final report was arbitrary and unwarranted. Possibly the action of the waters carried the debris into the bayou, and, owing to changed conditions, the engineer might have supposed he was endowed with authority to change the plans to meet the new conditions. The statute, however, covers such a contingency, and directs the course to be pursued. While the engineer appointed by the board of supervisors “has charge of the work of construction” (section 1989a7, Code Supp. 1907), he is not authorized to modify the plans adopted by the board without its approval by widening the drainage ditch or unduly extending it. He is a creature of the law which prescribes the course to be pursued in order that either may be done, and in the case at bar, in directing the contractors to make the change in question and in reporting that they were entitled to the increased compensation, he was acting in excess of his authority as the contractors, whose familiarity with the law is to be assumed, must have known, and in fraud of the rights of the taxpayer. His final report being so tainted furnishes no obstacle to ascertaining the “balance due” the contractors by the county auditor.
4. Same: payment of cost: engineer’s estimates: determination of balance due. Appellants argue that as the engineer has made estimates in pursuance of statute, and these have keen approved by the board of supervisors, such estimates should be treated as conclusive, Section 1989a9, Code Supp. “The engineer in charge of the construction shall furnish the contractor monthly estimates of the amount of work done on each [128]*128section, and upon filing the same with the auditor he shall draw a warrant in favor of such contractor, or deliver to him improvement certificates, as the case may be, for eighty per centum of the value of the work done according to estimate, and when said improvement is completed. to the satisfaction of the engineer in charge thereof and so certified by him to the board and approved by it, the auditor shall draw- a warrant in favor of said contractor upon the levee or drainage fund or deliver to him improvement certificates, as the case may be, for the balance due.” No authority is thereby conferred on the board of supervisors to pass on the estimates preceding the final report of the engineer. Nor did the board assume such duty. An approval with date was indorsed on each of the estimates by the chairman of the hoard, describing himself as such, but, as this was not in discharge of an official duty, it was of no significance. It is only when the work is completed that the board of supervisors is called upon to approve or disapprove it, and, if approved, the auditor to issue warrant or certificate for the “balance due.” The main purpose of withholding from the estimates the twenty percent reserve is to insure the completion of the improvement. But another purpose also is served by obviating overpayment, through mistake or design, to the contractor. The statute does not direct payment of the twenty per centum reserved, but .of the “balance due,” and this can only be ascertained from a careful computation of the work performed under the contract at the prices agreed upon and the deduction of the sums paid under the engineer’s estimates. This computation is to be made by the county auditor, based on estimates and reports of the engineer of the improvement ordered by *the board of supervisors. How far his action may be determined by the board need not be considered farther than to say that its approval might well indicate the portions of the work within the contract. Here neither the' board nor the auditor have [129]*129acted, and all now necessary is to indicate what must be excluded by the auditor as not within the contract in computing the amount for which a warrant shall issue upon the approval of the improvement by the board. That it has been completed in substantial conformity with the contract is not questioned. The only issues are with respect to the compensation to which the contractors are entitled. Shall they be paid for excavations along the bottom of the bayou, which have proven of no benefit, and are not included in the contract, and for widening one channel two feet and excavating another fourteen feet more than called for? There should be little difficulty in responding to this inquiry, especially in view ' of the statute quoted. But it is urged that the engineer was the agent of plaintiffs who petitioned for the improvement. If so, the extent of his agency was defined by law, and in the respects mentioned he did not act within the scope of his authority.
5. Same: estoppel. Equally without support is the plea of estoppel. Plaintiffs are not shown to have been aware of the lowering of the bottom of the bayou, or that the channels were being made wider than called for in the specifications.. They had the right to assume, in the absence of knowledge to the contrary, that the work was being performed in compliance with the contract. Racer v. Wingate, 138 Ind. 114 (36 N. E. 540); Steckert v. City of East Saginaw, 22 Mich. 104. The contractors do not pretend to have been misled by their conduct or acquiescence. Complaint was promptly made, and no reason has been suggested for not affording them a hearing by any of the 'numerous authorities cited by appellant. See Wood v. Hall, 138 Iowa, 308; Thompson v. Mitchell, 133 Iowa, 527; McCoy v. Able, 131 Ind. 417 (30 N. E. 528, 31 N. E. 453); Ricketts v. Hyde Park, 85 Ill. 110. The remedy sought is not to enjoin an assessment or the collection of compensation approved by those authorized to determine the amount, but [130]*130to enjoin the county board and auditor from including payments for work not included in the improvement as ordered or provided for in the contract in computing the “balance due” the contractors. The work in the bayou if done according to the original report and profile would have cost $1,415.50. The final report recommended the payment of $6,915.36, or an excess of $5,499.86. Deducting this from the balance as reported by the engineer, $6,335.19, and we have as the amount for which no warrant has been issued the sum of $835.93. The decree of the district court will be so modified as to direct the auditor to issue a warrant for this amount, and the cause remanded for proceeding not inconsistent with this opinion. One-half of the costs in this court will be taxed to each party. — Modified and affirmed. ■.