delivered the opinion of the court.
*83The ultimate question presented for determination on this appeal is the validity of assessments levied to defray the cost of constructing what is known as the Fourteenth street viaduct, in the city of Denver. The city authorities created a viaduct district and assessed the cost of constructing the viaduct against the realty of the district. Appellees, owners of property in the district, brought an action the purpose of which was to annul these assessments. From a judgment in their favor the defendants appeal. The questions presented by the record require a discussion and determination of the following general propositions:
1.. The power of the city authorities to create the viaduct district, and is the viaduct a local improvement?
2. Was the apportionment according to benefits?
3. The constitutionality of certain charter provisions ; and
4. Were there such irregularities on the part of the city authorities as would render the assessment void?
These several propositions will be considered in their order in connection with the particular facts bearing upon each.
1. The charter of the city of Denver provides that the board of public works may order the construction of viaducts, and unless otherwise directed by the city authorities, the cost of construction shall be assessed against the district benefited thereby. Such district may be created by ordinance on recommendation of the board. — Sec. 181 (Sec. 24, Art. 7), Charter. Under this provision the Fourteenth street viaduct district was created, and the cost of the viaduct in question assessed against the real property included within its boundaries. In the *84.absence of constitutional restrictions municipal authorities have the right, when lawfully authorized, to direct that the expense of a public improvement shall be assessed against the real estate specially benefited thereby. — Palmer v. May, 6 Colo. 106; Wolf v. City of Denver, 20 Colo. App. 77 Pac. 364; Adams v. Shelbyville, 77 Am. St. Rep. 484, 154 Ind. 467.
The only limitation upon this authority,' or, perhaps, more accurately speaking, the rule which the municipal authorities must observe, is that the property assessed is specially benefited. Special assessments for a public improvement are upheld upon the theory that the burden thereby imposed is equivalent to the special benefits inuring to the property assessed to defray the expense of such improvement. — 25 Enc. Law, 2d ed.,. 1168. The essential element of a local improvement is, as. the term implies, that it shall benefit the property on which the cost thereof is assessed in a manner local in its nature, and which does not attach to other property of a like character. — Sperry v. Plygare (Minn.), 49 L. R. A. 757. The important question, then, is, Does the record justify the conclusion that the viaduct was not a local public improvement? Counsel for appellees contend that it does, because, they say, from its •very nature it could not be, for the reason that the benefits conferred, upon the real property within the viaduct district by the construction of the viaduct are no different from those inuring to the other real property within the limits of the city. To determine this matter,-it becomes necessary to refer briefly to the testimony and facts bearing on the question.
The viaduct extends over the Platte river and the railroad tracks on each side. It affords a convenient and direct means of travel between the territory north of the river embraced within the limits *85of the viadnet district and that on the sonth side included within its boundaries. The part of the district on the north side of the river lies substantially north, and west of the north terminal of the viaduct, and that on the south side in a line with Fourteenth street and embraces territory on each side in an irregular shape, extending out as far as the intersection of Broadway and Colfax avenue. In a northeasterly direction from the viaduct a bridge crosses the river at Fifteenth street, a viaduct at Sixteenth street, a bridge at Nineteenth street, and another viaduct at Twenty-third street. These several structures are conveniently located with respect to the territory outside of that embraced in the Fourteenth street district; in fact, are nearer than the. viaduct in question to such territory, but are not as safe or desirable because, in crossing the bridges, railroad tracks must be crossed on the surface, while the bridge at Fifteenth street and the Sixteenth street viaduct are burdened with street car tracks, and the Twenty-third street viaduct is old and very much out of repair. There is also a bridge at Seventh street, westerly from Fourteenth street, but in crossing this bridge numerous railroad tracks must also be crossed on the surface. - Generally speaking, it can be said that the most direct line of travel between the parts of the district on each side of the river is by way of the Fourteenth street viaduct, which is more conveniently located in this respect than either of the other structures mentioned, unless it should be the bridge at Seventh street.
There was testimony pro and con on the subject of the benefits conferred on the property embraced within the .district by the construction of the viaduct. The city extends for several miles along the' river, .and the other portions not embraced -within the district are separated thereby. It is not charged that *86the action of the city authorities in creating the viaduct district was fraudulent, but contended that the viaduct is so manifestly an improvement of like benefit to practically all property within the limits of the city, that the determination by the municipal authorities that it was a local improvement should be set aside. On this question there was doubtless room for discussion before the city authorities when the matter of creating the district was under consideration; hut that does not by any means serve as a criterion in determining whether their action in creating the district and assessing the cost of the viaduct to the property therein may he questioned in the courts. Specific power was delegated by the legislature to the city authorities to construct the viaduct. They were specially empowered to determine whether the expense of its construction should he assessed against the district or paid for by the city. In determining this question it was within their province to determine whether or not special benefits were conferred upon the property embraced within the boundaries of the district equal to the expense of construction. The viaduct furnishes a safe and direct means of travel between the portions of the district which it connects. None of the other structures mentioned are as desirable as a means of travel because of the necessity of crossing numerous railroad tracks, the presence of tracks over which street cars frequently pass, or the roundabout way in which persons living in the. district would he compelled to travel in order to cross the river. This last observation applies particularly to the viaduct at Twenty-third street. As the city grows, the necessity for better facilities for communication between the portions separated by the river will increase; so that from time to time in the future other viaducts must be constructed. Residents of that portion of the city *87west of thé river and south of the north terminal of the viaduct are certainly not afforded as direct means of reaching the part of the district south of the river by way of the Fourteenth street viaduct as they would be if one should be constructed a half a mile further up the stream. Neither would the construction of a viaduct at the point last indicated afford the residents of the district'on the north side of the river as ready access to the business portion of the city as the present viaduct does. -It is true this viaduct may be, and is, used by persons living outside of the district, and is convenient of access by them. This does not, however, necessarily establish that the viaduct does not specially benefit the real property in the district. A paved street is utilized by the public because of the improvement; but for this reason alone it. cannot be held that the expense of paving should be borne by the city rather than by the abutting property. Just where the lines should be drawn in creating the district, or whether other property in the near vicinity is also specially benefited by the construction of the viaduct, are matters upon which different minds might well disagree; but they serve to illustrate the necessity for the rule so often declared, that the exercise of the discretion vested in municipal authorities in the lawful discharge of the duties conferred upon them by law cannot be interfered with by the courts. The law has designated the city authorities as the proper body to determine what property was and what was not specially benefited by the construction of the viaduct; clothed them with a discretion in the matter; authorized them to act upon their own judgment, and not upon the judgment of some one else. It must be presumed that their action was legal and regular. No facts are called to our attention from which it could be reasonably inferred that they were not justified *88in creating the district. On the contrary, it appears from the record that there are ample grounds upon which they could base the conclusion that this district was specially benefited to the extent of the cost of the viaduct. The exercise of the discretionary power and judgment of municipal officers, when acting within the scope of their authority, is conclusive, unless it clearly appears that their action was fraudulent or unreasonable. — Cooley on Taxation, 3d ed., 1180; Cooley on Taxation, 1st ed., 428; Burckhardt v. City of Atlanta, 30 S. E. 32; Beck v. Holland (Mont.), 74 Pac. 410; Hewes v. Glos, 170 Ill. 436; Preston v. Budd, 84 Ky. 150.
2. The city authorities divided the viaduct district into seventeen sub-districts, and in each sub-district assessed the several lots and parcels of land of the same size a uniform rate. The law provides no specific rule which shall be observed by the city authorities in apportioning the cost of the construction of a viaduct on the property included in the viaduct district, but directs that such cost shall be assessed upon the real property in such district in proportion to the benefits to each piece or parcel. The members of the board of public works testified that they endeavored to apportion the cost of the viaduct to .the different parcels of real estate in the district in proportion as they were benefited; that in fixing the assessments they took into consideration the relative position of the property to the viaduct, the line of travel which would be followed in reaching the respective terminals, and in all respects exercised their best judgment, after careful examination of the property in the district with a view to determine what the apportionment of the cost of construction thereon should be; that in considering this matter they examined plats, and interviewed citizens, and grouped the property into sub-districts which, *89in their judgment, was affected alike. It appears from an examination of the plat that the property nearest the terminals is assessed at a higher rate than that located some distance from, such terminals. The assessment ordinance recites, in substance, that the apportionment made upon the several pieces of real estate in the district represents, in the opinion of the board of public works and the city council, upon consideration of the proximity of the several lots to, and the accessibility from, the viaduct,' the area and valuation of such lots, and any and all matters relating to the subject of benefits, by reason of the construction of the viaduct, the comparative benefits to the several parcels of real estate in each of the sub-districts. It thus appears from the record that the city authorities, in apportioning the cost of the viaduct to the several pieces of real estate in the district, were guided by the law, which requires that such cost shall be apportioned to each piece of real estate in proportion to the benefits thereto. In making such an apportionment, absolute equality is not to be expected. A reasonable approximation thereto is all that can be required, and when proper city authorities have, in good faith, endeavored to apportion to each tract and parcel of land in the,district its share of the expense of construction, as measured by the special benefits accruing by reason of the erection of the viaduct, their action will not be annulled unless it is affirmatively shown that the result of the apportionment was not according to benefits. The burden was upon the plaintiffs to make this showing. It will, be presumed that the city authorities, in making special assessments, did so with reference alone to the special benefits accruing to the property assessed. — Medland v. Linton (Neb.), 82 N. W. 866. The main fact or circumstance relied upon to establish a failure on the part of the city *90authorities to apportion the cost as the law provides, is, that the district was divided into sub-districts, and each lot or parcel in each sub-district assessed at a uniform rate. Standing alone, this method might be objectionable. It affirmatively appears, however, that in apportioning the cost to each parcel of real estate the city authorities had in mind that such apportionment must be made' according to special benefits, took into consideration the various matters which it would be proper to consider, for the purpose of determining what such benefits would be as to each parcel, and then grouped the property into sub-districts which, in their judgment, would be affected alike, and made the assessments accordingly.
3. We shall next consider the questions raised below concerning the constitutionality of the charter provisions under which the district was created, and the proceedings adopted which finally culminated in the levy of the assessments of which plaintiffs complain. The charter provides that the cost of construction of viaducts shall, unless otherwise ordered,be assessed upon all the real estate in the.districts benefited. This means against the district specially benefited — 25 Enc.' Law, 2d ed., 1184 — and there is, therefore, no merit in the contention of counsel for appellees, that the law gives the city authorities unlimited power to assess the expense of a viaduct to particular property without regard to special benefits. The charter further provides that after the completion of the improvement, the city clerk, by advertisement for a time specified, shall notify the owners of real estate to be assessed that the improvement has been, or is about to be, completed and accepted, therein specifying the whole cost of the improvements, and the share apportioned to each lot or tract of land, and that any complaints or objections that may be properly made by the owners to *91the city council and filed with the city clerk within the time provided, will be heard and determined by the proper city authorities before the passage of any ordinance assessing the cost of the improvement. After the period specified in this notice, the city council is directed to sit as a board of equalization, and hear and determine all such complaints and objections as may be made in pursuance of the notice above required, and that on consideration thereof, it may recommend any modification of the apportionments made by the board of public works as may seem equitable and just. — Sees. 30-31, Art. 7 (Secs. 187-188), Charter. These provisions afford the owners of real estate in the district full opportunity to be heard upon any and all questions affecting their rights. The constitutional provision relative to “due process of law” is fully complied with when the property owner is afforded an opportunity to be heard and test the validity of a special assessment and the proportion of the general cost of the improvements which shall be assessed against his property. — 25 Enc. Law, 2d ed., 1173; Brown v. City of Denver, 7 Colo. 305; Fallbrook Irr. Dist. v. Bradley, 164 U. S. 112; Pittsburgh Ry. v. Board, 172 U. S. 32 (45); Bauman v. Ross, 167 U. S. 548 (590). Other constitutional questions raised are determined in City of Denver v. Dumars, post, p. 94, and City of Denver v. Londoner, post, p. 104.
4. After some steps had been taken to construct the viaduct, it was found that the original estimate of the expense was not sufficient to complete the work. Thereupon a new estimate was made by the city engineer, and such proceedings had that notice was again given the owners of property in the district of the estimated cost, the boundaries of the district, and other details, as required by the charter provisions on the subject of notice. By these pro*92ceedings the cost as originally determined was materially increased.. The charter provisions prohibit an increase in the cost of construction above the estimate of the original, but under the proceedings adopted by the city authorities this inhibition does not apply. The effect of the further proceedings with respect to the expense and estimated cost of the construction of the viaduct were, in effect, original, so far as that question was concerned. All parties had a full opportunity to be heard under this second notice on any question which they might have raised, the same as though such notice had been the first.
It was contended in the court below that the cost of construction, as assessed against the property of the district, was increased by the addition of interest and cost of collection. Counsel for the city contend that there is, in fact, no excess, because the items referred to were properly taxable as part of the cost and expense which could be assessed against the property of the district. It is not necessary to undertake to determine the questions thus presented by the respective claims of counsel. If, as a fact, there has been assessed against the property of the district a sum in excess of that which was properly taxable, and which, according to the claim of counsel for appellees, is susceptible of exact mathematical calculation,' the entire assessment could not be voided, but only that which was excessive. Plaintiffs, however, in order to take advantage of this condition, if it, in fact, exists, must first pay or tender the amount which would represent the correct assessment against their property after deducting that which is alleged to be excessive. They have made no such offer or tender, nor do they plead an offer on their part to do equity. For these reasons the question of the alleged excess of the assessment over and above the *93amount of the estimated cost is immaterial. — State Railroad Tax Cases, 92 U. S. 575 (616); Meggett v. City of Eau Claire, 51 N. W. 566; 1 High on Injunctions, 3d ed., sec. 497.
It is apparent, from the questions discussed and determined, that on the record the plaintiffs wholly failed to make a case entitling them to any relief. The judgment of the district court is reversed, and the cause remanded, with directions to enter judgment that plaintiffs take nothing by their action, and dismissing the same at their cost.
Reversed and remanded..