Me. Justice Caedozo
delivered the opinion of the Court.
The question is whether a statute of North Carolina laying a tax upon the net income of interstate railway companies has been so .applied to the appellant as to violate the prohibitions of the Constitution of the United States.
The Norfolk & Western Railway Company, a Virginia corporation, has lines of railway in North Carolina, Virginia, Maryland,"West Virginia, Kentucky and Ohio. Its lines in North Carolina aré branches,'connecting with the main line at Roanoke, Lynchburg and Abingdon, and running'from .those points of junction to Winston-Salem, Durham and- Elkland. For the years 1927,1928, and 1929, •it made réturn .to-thé. Commissioner of. Revenue of North Carolina that it had no taxable income. The Commissioner notified the company that the returns were erroneous, and made reassessments as follows: for 1927, $29,727.04; for 1928, $27,481.57; and for 1929, $29,213.10, in all $86,421.71. The amount so fixed was paid, and this suit was brought in accordance with, an applicable statute to recover back the payment. The Superior Court of Wake County, refusing to confirm the report of a referee in favor of the taxpayer, gave judgment for the state. The Supreme Court of North Carolina affirmed, 208 N. C. 397; 181 S. E. 248, and the case is here upon appeal. Judicial Code, § 237, 28 IT. S. C., § 344.
The net income of interstate railways doing business in North Carolina is taxed in accordance with the following formula (Public Laws of 1927, chapter 80, § 312; Public Laws of 1929, chapter ,345, § 312): "And when their business is in part within and in part without the State, their net income within this State shall be ascertained by taking their gross 'operating revenues' within the State, including in their gross 'operating revenues' within this State the equal mileage proportion within this State of their interstate business, and deducting from their gross 'operating revenues' the proportionate average of 'operating expenses' or 'operating ratio' for their whole business, as shown -by the Interstate Commerce Commission standard classification of accounts." The formula thus adopted is not void upon its face. Pittsburgh, C., C. & St. Louis R. Co. v. Backus, 154 U. S. 421, 430, 431; State Railroad Tax Cases, 92 U. S. 575, 608, 611; Louisville Board of Trade v. Indianapolis, C. & S. Traction Co., 34 I. C. C. 640, 642; Low Moor Iron Co. v. Chesapeake & Ohio Ry. Co., 42 I. C. C. 221, 227; cf. Atlantic Coast Line R. Co. v. Doughton, 262 U. S. 413. A division of revenues and costs in accordance with state lines can never be made for a unitary business with more than approximate correctness. There is a tendency, none the less, for rates to be so adjusted to expenses over different portions of a system as to produce, when averages are considered, a uniformity of net return, or a fair approach thereto. Thus mileage may have at times a relation to a tax upon net income which it may not bear to a property tax or even to one upon the' value of a franchise. Cf. Rowley v. Chicago & N. W. Ry. Co., 293 U. S. 102, 111; Wallace v. Hines, 253 U. S. 66, 69. Taxpayer and state would be swamped with administrative difficulties if left to struggle through every case without the aid of a formula of ready application. In the perplexities besetting the process of' assessment the statute is the outcome of a reasonable endeavor to arrive at. a proportion of general validity. Pittsburgh, C., C. & St. L. Ry. Co. v. Backus, supra. No contention to the contrary is made by the appellant.
This is not to say that the tax is valid as imposed. A formula not arbitrary on its face or in its general operation may be unworkable or unfair when applied to a particular railway in particular conditions. Cf. Hans Rees' Sons v. North Carolina, 283 U. S. 123, 129, 132; Southern Ry. Co. v. Kentucky, 274 U. S. 76, 83, 88. A segment of the line may operate under handicaps resulting from the nature of the traffic, the topography of the country, the maladjustment or inadequacy of passenger or freight tariffs in one district or another. As applied to such a segment the average mileage prorate of the entire railway system may be an arbitrary test of the relation between revenue and expenses. Cf. Northern Pacific Ry. Co. v. Department of Public Works, 268 U. S. 39, 44; Low Moor Iron Co. v. Chesapeake & Ohio Ry. Co., supra. If this is made to appear with an ensuing burden on the taxpayer grossly in excess of the results of a more accurate apportionment, the statute to that extent is an unconstitutional endeavor to tax the income of a business in another jurisdiction. Hans Rees' Sons v. North Carolina, supra.
Appellant now insists, as it insisted in. the courts below, that the operating expenses for its North Carolina branches were far in excess of those allowed by the Commissioner, who refused to depart from the statutory, formula. There is evidence in the record giving support to that position, though its weight, is contested by counsél for the state. If the evidence be accepted, the higher cost may be attributed to the mountainous terrain and the low density of traffic as well as to other causes which it is needless to develop. Up to that point the Railway took upon itself the burden of making out a case for the rejection of the formula. There, however, it stopped, declining to go farther. From the- testimony of its witnesses we learn that actual expenses were greater in North Carolina than the average expenses apportioned to that state on the basis of the ratio between state and system mileage. We learn nothing from these witnesses as to the ratio between revenues, average and actual. For all that appears in the case developed by the Railway, actual gross revenues in North Carolina may have been so far in excess' of average gross revenues computed under the statute as to neutralize the discrepancy between actual and average costs of operation. If such a counterbalance exists, appellant has not been injured through the application of the formula.
The state took up the case where the railway put it down. Witnesses for the state maintain that through the application of the formula the gross revenues of operation are underestimated to a greater extent than operating costs. They tell us' that the effect of the rejection of the formula will be to allocate to the state 159% of the revenues produced by applying it. . In support of that conclusion they make elaborate studies and analyses, which are exhibits in the case. From their testimony it appears that the general level of rates in territory classified as Southern is higher than that in territory classified as Northern or "Official." Cf. Sloss-Sheffield Steel & Iron Co. v. Louisville & N. R. Co., 35 I. C. C. 460, 467; Corporation Commission v. Norfolk & Western R. Co., 19 I. C. C. 303, 311; Southern Class Rate Investigation, 100 I. C. C. 513, 520, 645, 671; 109 I. C. C. 300, 324; 113 I. C. C. 200; 128 I. C. C. 567, 580. There is emphasis besides on a concession by the railway that the average system revenue per mile of line is only five times greater than that for the North Carolina branches] though the traffic density for the system is seven and a half times greater. Accountants for the railway criticize the studies and analyses with the accompanying computations as defective and misleading. They also take the position that there is no method of allocating revenues with any greater approach to certainty than by means of a mileage prorate. Whether for that reason or some other, they have not made an attempt to ascertain receipts, no matter how approximately, by any other method, as assuredly they would have tried to do if the statutory formula had been abolished altogether. By implication, if not expressly, the trial judge refused to yield assent to their position. Without finding the exact figures either for revenue or for expenses, he approved, at least in its main outline, the position of the state. "The evidence seems persuasive that if the actual gross operating revenues should be determined, the amount returned by the defendant [i. e., the railway] would be increased by a much greater proportion than the operating expenses in North Carolina are increased over the operating expenses determined by the use of the statutory formula." Upon appeal to the Supreme Court of the state, this finrli-np; was approved.
We are unable to accept the argument for the appellant that its burden was discharged when it gave evidence of the ratio between actual and average expenses while keeping silent as to the ratio between actual and average receipts. The statutory formula is not framed on an assumption that gross operating revenues are uniform actually for every mile throughout the system. It is not framed on an assumption that for every mile of the system there is uniformity of expense. Such assumptions, if made, would be contrary to notorious facts. What the formula does assume is this, that barring exceptional conditions there will be throughout the system such an average relation between revenues and expenses as'will cause the net income of a part to vary, in proportion to the mileage, with the net income of the whole. The implications of the formula being what they are, a taxpayer does not escape the application of the statute by evidence directed to only one of the related terms. Its evidence to be effective must be directed to each of them alike, for only thus can the assumed relation between them be proved to be unreal. This taxpayer disclaims the duty and even the endeavor to respond to such a test. It varies the numerator of the fraction while accepting the denominator.
A finding that the statute, though fair upon its face, is oppressive toward the railway in its practical operation cannot rest upon so fragmentary and partial a showing of facts. We must bear in mind steadily that the burden is on the taxpayer to make oppression manifest >by clear and cogent evidence. Underwood Typewriter Co. v. Chamberlain, 254 U. S. 113, 121; Maxwell v. Kent-Coffey Mfg. Co., 204 N. C. 365, 372, 374, 168 S. E. 397; 291 U. S. 642; Bass, Ratcliff & Gretton, Ltd. v. State Tax Comm'n, 266 U. S. 271, 280, 283. For 1927; it has had to pay a certain tax, for 1928 another, for 1929, another, a total of $86,421.71. Would it have had to pay less if- net income had been ascertained without reference. to mileage? Would the difference have been so great as to overpass the bounds of reason? In the evidence for the-railway, there is no answer' to those questions. On the other hand, the judge, who was the appointed trier of the facts, found the evidence for the state persuasive that the tax would have been as heavy and even heavier if the test of a mileage prorate had been excluded from the reckoning. The railway does not help its case greatly by its criticism of this evidence in one feature or another. The computations for the state may have been charged here and there with errors and omissions. They were not. shattered so completely that the trier of the facts could not build on them at all. The criticisms too were not invulnerable, but were subject to the possibility of explanation or rejoinder. Indeed, apart from the computations, there was significance,' if not compulsion, in facts admitted by the railway, though with the addition of many a gloss supposed to minimize their force. What weight should be ascribed to the whole composite mass was thus an inference of fact for the judge appointed to the task, and may not be disposed of here as an inference of law. All this becomes the plainer when we recall that the state in presenting computations did not lift the burden from the railway of satisfying the court, after all the evidence was in, that it was a victim of oppression. If different or supplementary computations were needful to that end, the railway, not the state, was under a duty to submit them.
In what has been written we have assumed that revé°nue can be apportioned between one state and another by a method more accurate than by .that of a mileage prorate, however useful such a formula may be in expressing a relation between revenue and.expenses. The appellant denies, though, it seems, rather guardedly, that the possibility exists. Even so, the trier of the facts was at liberty to. discredit the denial. There was impeachment of the denial in the evidence for the state. There was impeachment as effective in the failure of appellant to lay before the court such studies as its accountants could supply, figuring out a fair apportionment to the best of its ability and then appraising the results. Something more was to b'e expected in the way of genuine endeavor before a sweeping non possumus could be accepted as conclusive. We do not now determine how incapacity, if made out, would affect the application of the statutory formula. For present purposes it suffices that there is no such showing now.
The judgment is
Affirmed.
See Huang, State Taxation of Railways in the United States, Columbia University Press, 1928, pp. 97, 98, 100, 188, 189; cf. Seligman, Essays in Taxation, 9th ed., p. 283; Census Bureau Bulletin 21, Commercial Valuation of Railway Operating Property in the U. S. 1904, pp. 45, 50.
"In cases of the class examined, including the present case, the. statutory formula is not invalid on its face without regard to the particular circumstances of the taxpayer." Appellant's brief, p. 40. "Clearly enough the Bailway case must be proved specifically." p. 41.