
51 Cal.2d 314 (1958)
THE FLYING TIGER LINE, INC. (a Corporation), Respondent,
v.
THE COUNTY OF LOS ANGELES et al., Appellants.
L. A. No. 24532. 
Supreme Court of California. In Bank.  
Dec. 16, 1958.
 Harold W. Kennedy, County Counsel, Gordon Boller, Assistant County Counsel, and Alfred Charles DeFlon, Deputy County Counsel, for Appellants.
 Hill, Farrer & Burrill, Carl A. Stutsman, Jr., and Leon S. Angvire for Respondent.
 McCOMB, J.
 Defendants appeal from a judgment in favor of plaintiff in an action to recover 1953 taxes paid under protest to the Tax Collector of Los Angeles County upon the assessment of five airplanes.
 Facts: Plaintiff is a Delaware corporation, with its principal place of business in the county of Los Angeles. It is engaged in business as a common carrier of freight by air, operating in interstate and foreign commerce under a certificate issued by the Civil Aeronautics Board.
 On the assessment date in 1953, the first Monday in March, plaintiff owned and operated 37 aircraft of two different types. It had 27 C-46 planes, which were used only in its domestic commercial service. These planes did not have a sufficient range for overseas flying. They were assessed at a portion of their book value determined by computing the percentage of the total time, during a test period selected by the county assessor, that the planes were physically present in the county of Los Angeles. The tax on these planes is not disputed.
 Plaintiff also operated 10 DC-4 planes in flying the Pacific airlift under control of the military authorities and in support of the war in Korea. The route of this lift was from the United States to Tokyo, Japan. Five of these planes were leased by plaintiff and five were owned by it. Plaintiff's interest in the leased planes was assessed on the same formula applied to the C-46 planes. This tax is undisputed.
 The other five DC-4 planes that were operated on the Pacific airlift were removed from the remainder of plaintiff's fleet of 37 planes by the county assessor and were assessed at 100 per cent of their value without regard to the time they were physically present in the county. The difference between the amount of the tax paid on the full assessment of these five planes and the amount which would have been taxed if the assessor had assessed them on the same basis as all the other planes is the amount sought to be recovered.
 Plaintiff filed a petition for redetermination of the assessment before the Los Angeles County Board of Supervisors, *317 sitting as a board of equalization, for the year 1953-1954. After two hearings before the board, the application for relief was denied. The tax was subsequently paid under protest. Thereafter plaintiff filed this suit for recovery against the county of Los Angeles and the city of Burbank. The city was made a defendant as required by section 5138 of the Revenue and Taxation Code.  [fn. *]
 Questions: [1] First. Does defendant county have the power to assess an ad valorem property tax upon the full value of aircraft which are regularly flown in interstate and foreign commerce and physically present in the county only a part of the time during the period for which the tax is collected?
 No. The five planes involved were used chiefly in the performance of the Pacific airlift instituted in 1950 as a result of the Korean war, and operations during the period in question were scheduled by the military authorities and not by the Civil Aeronautics Board.
 A proper decision of this case rests upon the application of four United States Supreme Court decisions. In 1944 the Supreme Court of the United States decided, in Northwest Airlines, Inc. v. Minnesota, 322 U.S. 292 [64 S.Ct. 950, 88 L.Ed. 1283, 153 A.L.R. 245], that Minnesota, the home port state of the airline, could levy a property tax on the entire value of a fleet of planes in spite of the fact that the same planes were admittedly taxed on a portion of their value by six of the seven other states through which they operated.
 In 1949 the Supreme Court, in Ott v. Mississippi Valley Barge Line, 336 U.S. 169 [69 S.Ct. 432, 93 L.Ed. 585], modified the rule previously laid down in Northwest Airlines, Inc. v. Minnesota, supra. The Ott case involved barges and tugs operated up and down the Mississippi River and owned by a corporation domiciled in Ohio. These tugs and barges were taxed on an apportioned basis by the State of Louisiana, where *318 they made certain irregular stops. The court held that Louisiana could tax the vessels on a portion of their value. With reference to the question of the due process aspect of a tax of this type, the court stated at page 174: "So far as due process is concerned the only question is whether the tax in practical operation has relation to opportunities, benefits, or protection conferred or afforded by the taxing State. (Citation.) Those requirements are satisfied if the tax is fairly apportioned to the commerce carried on within the State."
 In 1952 the Supreme Court, in Standard Oil Co. v. Peck, 342 U.S. 382 [72 S.Ct. 309, 96 L.Ed. 427, 26 A.L.R.2d 1371], involving vessels travelling on the Mississippi River, adopted the rule that a domiciliary state could not tax the full value of property located only part of the time within a state without constituting an unreasonable burden upon interstate commerce and thus violating the due process clause of the United States Constitution. The court said at page 384: "No one vessel may have been continuously in another state during the taxable year. But we do know that most, if not all, of them were operating in other waters and therefore under Ott v. Mississippi Barge Line Co., supra, could be taxed by the several states on an apportionment basis. The rule which permits taxation by two or more states on an apportionment basis precludes taxation of all of the property by the state of the domicile. (Citation.) Otherwise there would be multiple taxation of interstate operations and the tax would have no relation to the opportunities, benefits, or protection which the taxing state gives those operations."
 In 1954 the Supreme Court, in Braniff Airways, Inc. v. Nebraska State Board of Eq. & A., 347 U.S. 590 [74 S.Ct. 757, 98 L.Ed. 967], applied the rule previously laid down in Standard Oil Co. v. Peck, supra, to aircraft flying in interstate commerce. This case involved a fleet of planes which had its home port in the State of Minnesota, but which was used in and out of the taxing state, Nebraska. Nebraska imposed an apportioned ad valorem tax on the equipment, based upon the percentage of time in and out of the state. The court said at page 600: "We perceive no logical basis for distinguishing the constitutional power to impose a tax on such aircraft from the power to impose taxes on river boats."
 [2] It thus appears that the United States Supreme Court has now held that the rule which permits taxation by two or more states on an apportioned basis precludes taxation on all the property by the state of domicile. *319
 In Standard Oil Co. v. Peck, supra, at page 384, the court said: "Those cases, though exceptional on their facts, illustrate the reach of the taxing power of the state of the domicile as contrasted to that of the other states. But they have no application here since most, if not all, of the barges and boats which Ohio has taxed were almost continuously outside Ohio during the taxable year. ... The rule which permits taxation by two or more states on an apportionment basis precludes taxation of all of the property by the state of the domicile. (Citation.) Otherwise there would be multiple taxation of interstate operations and the tax would have no relation to the opportunities, benefits, or protection which the taxing state gives those operations."
 [3] A taxpayer resisting an ad valorem tax on personal property based on an unapportioned assessment does not have the burden of showing that other states have actually imposed a tax on such property. He is entitled to an assessment on an apportionment basis if the record shows that he was, during a tax year, receiving substantial benefits and protection in more than one state.
 In the present case, there was no apportionment with respect to the assessment of the five planes. Therefore, as a matter of law, the tax was not levied upon a proper basis.
 The holding in Slick Airways, Inc. v. County of Los Angeles, 140 Cal.App.2d 311 [295 P.2d 46], is in accord with the foregoing views. In that case, a fairly apportioned assessment on planes of this type was determined by the Los Angeles County Assessor. The company had its principal place of business in California in 1952 and 1953. The court, at page 312, had this to say with reference to the normal assessment procedure in Los Angeles County: "Plaintiff is engaged in flying a fleet of airplanes in interstate and foreign commerce. Such airplanes, under the practice of the county assessor of Los Angeles County, are assessed on the basis of a fair allocation of time, to wit, the ratio of the time spent in Los Angeles County as compared to total time."
 Thereafter, the court properly recognized that under the circumstances present, which were similar to those in the instant case, the county of Los Angeles had authority to tax only a portion of the value of the planes. In referring to the decision of the United States Supreme Court in Braniff Airways, Inc. v. Nebraska State Board of Eq. & A., supra, the court, at page 314, said: "The Supreme Court, in upholding the validity of the tax, said, at page 600: 'The limitation imposed *320 by the Due Process Clause upon state power to impose taxes upon such instrumentalities was succinctly stated in the Ott Case: "So far as due process is concerned the only question is whether the tax in practical operation has relation to opportunities, benefits, or protection conferred or afforded by the taxing State." ' "
 [4] Second. When relief from an improper assessment is sought from the board of supervisors sitting as a board of equalization, and denied in the belief that the only issue is one of law for the courts, is the applicant bound by this decision on an appeal to the superior court?
 No. Defendants argue that plaintiff is entitled to a trial "of factual matter which should have been but was not presented to said Board for determination." This question is not presented to this court, because the trial court rendered its decision without consideration of any evidence offered before the trial court, basing it upon a question of law.
 Security-First National Bank v. County of Los Angeles, 35 Cal.2d 319 [217 P.2d 946], relied on by defendants, is not applicable to the facts of the present case, for in that case no application for relief was filed with the board of supervisors.
 The duties of a board of supervisors sitting as a board of tax equalization are prescribed in article XIII, section 9, of the California Constitution, which reads, in part: "The boards of supervisors of the several counties of the State shall constitute boards of equalization for their respective counties, whose duty it shall be to equalize the valuation of the taxable property in the county for the purpose of taxation. ..."
 [5, 6] The duties of the board are fully set forth by this court in Universal Consolidated Oil Co. v. Byram, 25 Cal.2d 353, 356-357 [153 P.2d 746]: "It must be conceded, of course, that it is well settled in this state that to the authorized county board of equalization has been confided the duty of determining 'the value of the property under consideration for assessment purposes upon such basis as is used in regard to other property, so as to make all the assessments as equal and fair as is practicable'; that in discharging this duty, 'the board is exercising judicial functions, and its decision as to the value of the property and the fairness of the assessment so far as amount is concerned constitutes an independent and conclusive judgment of the tribunal created by law for the determination of that question,' adjudicating necessarily that 'the property is assessed at the same value proportionately as all the other property in the county'; that such adjudication *321 'cannot be avoided unless the board has proceeded arbitrarily and in willful disregard of the law intended for their guidance and control, with the evident purpose of imposing unequal burdens upon certain of the taxpayers ... or unless there be something equivalent to fraud in the action of the board'; and that 'Mere errors in honest judgment as to the value of the property will not obviate the binding effect of the conclusion of the board.' (Citations.) While not classifiable with any aspect of fraud or bad faith, the lack of due process distinguishing the procedural phase of these equalization matters as submitted to the board furnishes an equally appropriate basis for the court's intervention in protection of the plaintiffs' constitutional rights." (Emphasis added.)
 [7] The court said, at page 360 [3] et seq.: "The fundamental premise of the plaintiffs recourse to the court for relief rests upon the proposition that, as with any ad valorem tax, their constitutional right to an equalization hearing comprehends a decision in the light of the evidence there introduced before any determination becomes final as to them. (Citations.) [8] As any tax proceeding is in invitum in nature, each step must be taken in compliance with law or the proceeding is void. The equalization stage is no exception to this rule. [9] Compliance with the constitutional requirement for an equalization hearing is not met unless the substance as well as the form of the hearing is granted to the complaining taxpayer. (Citation.) Typical illustrations of the denial of procedural due process which have been held to invalidate purported equalization determinations are: One man hearings (citation); the taking of evidence without the presence of the taxpayer or his representative (citations); the refusal to allow reasonable opportunity for cross-examination (citation); the refusal to permit reasonable argument (citation); reliance in the concluding steps upon the advice of the assessor or the assessor's attorney, particularly if done secretly (citation); and the attempted determination of a case by members of the board who did not hear the evidence, if their vote be necessary to the determination (citation)."
 "In line with these instances of the denial of procedural due process are the present cases. The concluding steps of the equalization proceeding are many times the most essential to the preservation of the taxpayer's rights."
 [10] Again the court said, at page 362 [6]: "As appears from the numerous authorities cited in the forepart of this opinion, the respective county board of equalization is the fact-finding *322 body designated by law to remedy excessive assessments (Cal. Const., art. XIII,  9), and when that tribunal, after due hearing and within the limits of reasonable discretion, makes its findings on the facts, such decision is final and conclusive."
 [11] It is evident from the foregoing authority that when a board of equalization purports to decide a question of law, or refuses to hear a case on the ground that it involves only a question of law to be decided by the courts, a taxpayer has the right to resort to the courts for determination of such question.
 In the present case, there was no dispute as to the facts, a question of law alone being presented to the board of equalization, as appears from the following excerpt from the transcript:
 "Mr. Jessup [Member of the Board]: Mr. West, there is no chance of you and this gentleman sitting down and working this thing out?"
 "Mr. Anson [Deputy County Counsel]: There is a very definite legal issue other than the facts; I don't think there is too much of a quarrel as regards the facts."
 "Mr. Hahn [Member of the Board]: There's no quarrel with the facts, but a legal question?"
 "Mr. Anson: Primarily a legal question; that is, as far as the five aircraft covered under this second item are concerned."
 (See also Mahoney v. City of San Diego, 198 Cal. 388, 403 [9] [245 P. 189], where an arbitrary method of property valuation adopted by the assessor and approved by the board of supervisors was held a proper subject for court review.)
 [12] Applying the foregoing rule to the present case, it appears that plaintiff sought relief before the board of equalization. This relief was denied solely because the board, on the advice of its counsel, applied an improper principle of constitutional law. Therefore, plaintiff properly applied to the superior court for relief.
 In light of the foregoing, the trial court was correct in holding that defendant county had exceeded its power to tax the airplanes here involved and in entering judgment in favor of plaintiff.
 The judgment is affirmed.
 Shenk, J., and Schauer, J., concurred. *323
 CARTER, J.
 I concur in the judgment of affirmance.
 The issue presented by this case is: To what extent can the domicile state of an interstate and foreign air carrier impose an ad valorem tax on its property when one or more nondomiciliary states have acquired the power to impose an ad valorem tax on an apportioned basis. While the decided cases seem to hold that under the circumstances the domicile state cannot tax on the basis of the full assessed valuation of all the property, the precise extent of its power to tax has not yet been decided by the Supreme Court of the United States.
 The principles bearing on this issue are contained in several recent cases. In Northwest Airlines, Inc. v. Minnesota, 322 U.S. 292 [64 S.Ct. 950, 88 L.Ed. 1283, 153 A.L.R. 245], the court held that Minnesota, the domicile of the airline, had constitutional power to tax the airline's entire fleet of aircraft at its full value even though all the planes were continuously engaged in interstate flights. In this case Chief Justice Stone wrote a vigorous dissent in which he held that Minnesota could only impose an apportioned tax. In 1949 the Supreme Court held in Ott v. Mississippi Valley Barge Line Co., 336 U.S. 169 [69 S.Ct. 432, 93 L.Ed. 585], that Louisiana, a nondomiciliary state, could tax barges and tugs, moving in and out of the state, on an apportioned basis according to the commerce carried on within the state. In Standard Oil Co. v. Peck (1952), 342 U.S. 382 [72 S.Ct. 309, 96 L.Ed. 427, 26 A.L.R.2d 1371], involving vessels traveling on the Mississippi River, the Supreme Court adopted the rule that a domiciliary state could not tax the full value of property located only part of the time within its borders, and which must have acquired a tax situs elsewhere, without constituting an unreasonable burden on interstate commerce. The court said, at page 384: "The rule which permits taxation by two or more states on an apportioned basis precludes taxation of all of the property by the state of the domicile." Northwest Airlines was distinguished on the ground that in that case it had not been shown that "a defined part of the domiciliary corpus" had acquired a taxable situs elsewhere. The court did not spell out, however, the extent of the domicile's taxing power under the circumstances. Finally, in 1954, in Braniff Airways, Inc. v. Nebraska State Board of Equalization and Assessment, 347 U.S. 590 [74 S.Ct. 757, 98 L.Ed. 967], the court, applying the reasoning of the Ott case, upheld the *324 power of a nondomiciliary state to impose an apportioned tax on planes and flight equipment used by the taxpayer in operating a purely interstate line.
 In the present case Los Angeles County, the domicile for tax purposes, seeks to impose an ad valorem property tax on the full value of five aircraft belonging to Flying Tiger Line, used chiefly in the Korean Airlift, but also used in other foreign and interstate commerce. The tax was paid under protest, and in the suit for refund the trial court gave judgment for plaintiff in an amount equal to the difference between the tax paid on the full value and the tax that should have been paid on a value apportioned according to the time the planes were physically present in the county during a certain test period.
 I agree with the views expressed in the opinion prepared by Mr. Justice McComb which holds, in effect, that where a nondomiciliary state has acquired the power to impose an apportioned tax, the domicile must also impose an apportioned tax. There is no express authority to support this proposition, but it appears to be in harmony with sound principles of constitutional law.
 The commerce clause is violated when a tax subjects interstate commerce to an undue burden or creates a risk of such a burden. However, it has been recognized that interstate commerce should "pay its way" in the states where it receives substantial benefits and protection, with the result that reasonable state taxation is permitted. To avoid a violation of the due process clause, the tax must bear a reasonable relation to the benefits and protection conferred by the taxing state. These rules were recognized in the Standard Oil case where the court said: "The rule which permits taxation by two or more states on an apportionment basis precludes taxation of all of the property by the state of the domicile. Otherwise there would be multiple taxation of interstate operations and the tax would have no relation to the opportunities, benefits, or protection which the taxing state gives those operations."
 The rule stated in the opinion prepared by Mr. Justice McComb presents no real risk of multiple taxation. A cumulative burden could result from the use in different states of different apportionment formulae, but this is not very likely. Apart from this slight possibility, apportionment of the tax base is generally acknowledged to be the best way to avoid multiple taxation. It was stipulated at the trial that the aircraft in question were physically present in Los Angeles *325 County only 36.37 per cent of the time during a test period. This percentage was used to apportion the value of the planes by the trial court and is reasonably related to the benefits and protection conferred by the county. Therefore, there does not appear to be a violation of due process.
 I can see no basis for holding that the case be remanded to the board of equalization for a hearing to determine whether any other state has acquired the power to impose an apportioned tax under the rule of the Braniff case. The trial court was apparently satisfied that such a showing had been made. If no state has such power, then Los Angeles County may tax on the full value of the aircraft under the holding of the Northwest Airlines case. On the other hand, if one or more states have such power, then the Standard Oil case applies, and the full value cannot be taxed.
 I have found no authority holding that the board of equalization should determine to what extent the property has acquired a taxable situs elsewhere, and then should order a reassessment of the tax accordingly. Under this basis of taxation an undue burden on interstate commerce is likely to result in two different ways. The board of equalization is required to determine whether any portion of the Flying Tiger Line's property has acquired a taxable situs elsewhere and what that portion is. Although tests framed by the Supreme Court are available to aid the board in this determination, there are no iron-clad rules describing what contacts are sufficient to give a state jurisdiction to tax. Thus it may be that while the board will find that certain property has not acquired a taxable situs in another state and so is taxable in full by Los Angeles County, the taxing authorities in that state may reach a contrary determination and impose a tax under that state's apportionment formula. The cumulative burden that would result is apparent.
 An undue burden may also arise because of the various formulae for apportionment used among the states. These formulae are computed on the basis of the presence of the aircraft in and out of the state, mileage in and out of the state, arrivals and departures in and out of the state, revenue earned in and out of the state, as well as many combinations of these factors. With a 100 per cent tax base being applied in the domicile state, different formulae applied by other states are very apt to lead to excessive taxation.
 That personal property has its situs at the owner's domicile, *326 has long been recognized as a fiction employed to prevent migratory property from avoiding taxation completely. (Pullman's Palace Car Co. v. Pennsylvania, 141 U.S. 18, 29 [11 S.Ct. 876, 35 L.Ed. 613].) This fiction was primarily used in cases involving ocean-going vessels which acquired no actual situs elsewhere. It was thought that if they were not taxable at the domicile they might not be taxable at all. (Ott v. Mississippi Valley Barge Line, supra, p. 173.) As Chief Justice Stone said in his dissenting opinion in the Northwest Airlines case: "And our decisions establish that, except in the case of tangibles which have nowhere acquired a tax situs based on physical presence, and for that reason remain taxable at the domicile even if never present there, the state's power to tax chattels depends on their physical presence and is neither added to nor subtracted from because the taxing state may or may not happen to be the state of the owner's domicile." But where it appears that the carrier will not avoid taxation on a considerable portion of its property, there should be no reason to employ the fiction in whole or in part. It is obvious that to permit Los Angeles County to tax the full value of the property here involved, would impose a tax beyond that justified by its physical contacts with the county, a tax that the county has no power to impose, and thus violate due process. Moreover the tax is not reasonably related to the benefits and protection conferred by the county. "So far as due process is concerned the only question is whether the tax in practical application has relation to opportunities, benefits, or protection conferred or afforded by the taxing state." (Ott v. Mississippi Valley Barge Line, supra, p. 174.)
 It is of some significance to note that recommendations made by the Civil Aeronautics Board in 1945, as a result of the confusion engendered by the Northwest Airlines case indicate disapproval of the domicile basis for taxation and support for some system of apportionment of the tax base. (See Multiple Taxation of Air Commerce, H.R. Doc. No. 141, 79th Cong., 1st Sess.)
 It has been suggested that Flying Tiger Line will probably avoid taxation of a large portion of its property because the greater part of Flying Tiger's Flights are overseas. This suggestion is probably well-founded. Another quotation from the dissenting opinion of Chief Justice Stone in the Northwest Airlines case, however, adequately disposes of this point: "It is no answer to suggest that the states other than Minnesota have not asserted their constitutional power to tax or that we *327 do not know how or to what extent they have exercised it. The extent to which one state may constitutionally tax the instruments of interstate transportation does not depend on what other states may happen to do, but on what the taxing state has constitutional power to do."
 The logic of the foregoing is inescapable.
 TRAYNOR, J.
 I dissent. Migratory property not subject to taxation elsewhere remains taxable at the owner's domicile, for otherwise it would escape taxation altogether. (New York Central & H. R. Co. v. Miller, 202 U.S. 584, 597 [26 S.Ct. 714, 50 L.Ed. 1155]; Southern Pac. Co. v. Kentucky, 222 U.S. 63, 69, 73 [32 S.Ct. 13, 56 L.Ed. 96]; Northwest Airlines, Inc. v. Minnesota, 322 U.S. 292, 294 [64 S.Ct. 950, 88 L.Ed. 1283, 153 A.L.R. 245]; Braniff Airways, Inc. v. Nebraska State Board of Eq. &A., 347 U.S. 590, 602 [74 S.Ct. 757, 98 L.Ed. 967]; Olson v. City & County of San Francisco, 148 Cal. 80, 83, 84 [82 P. 850, 113 Am.St.Rep. 191, 7 Ann.Cas. 443, 2 L.R.A. 197]; California Shipping Co. v. City & County of San Francisco, 150 Cal. 145, 146 [88 P. 704].) To the extent that the property is taxable elsewhere it cannot be taxed by the domiciliary state, for otherwise it would be subject to multiple burdens in violation of the commerce clause. (Standard Oil Co. v. Peck, 342 U.S 382, 385 [72 S.Ct. 309, 96 L.Ed. 427, 26 A.L.R.2d 1371]; Western Live Stock v. Bureau of Revenue, 303 U.S. 250, 255-256 [58 S.Ct. 546, 82 L.Ed. 823, 115 A.L.R. 944].) Random excursions of migratory property into a state do not render the property taxable there, but if there is habitual use of such property in a state, the average amount thus habitually used is taxable there, even though the specific items are not continuously the same. (American Refrigerator Transit Co. v. Hall, 174 U.S. 70, 82 [19 S.Ct. 599, 43 L.Ed. 899]; Johnson Oil Ref. Co. v. Oklahoma, 290 U.S. 158, 162 [54 S.Ct. 152, 78 L.Ed. 238].)
 Under the foregoing rules defendants are not precluded from taxing the aircraft in question except to the extent that they are taxable elsewhere. The majority opinion, however, is at odds with these rules in holding that the county must limit the tax on the aircraft according to the time they are physically present in the county, even if they are not taxable elsewhere.
 The county board of equalization was likewise at odds with these rules in deciding that the aircraft were taxable on *328 their full value at the commercial domicile  [fn. 1] on the ground that apportionment of the tax was not required as a matter of law since the aircraft were not flown on a schedule. The board's failure to determine whether or not any part of the property had acquired a taxable situs elsewhere was error, for defendants' power to tax is diminished accordingly if the property has acquired a taxable situs elsewhere (Standard Oil Co. v. Peck, supra, 342 U.S. 382, 384), whether or not other jurisdictions elect to assert their taxing power. (Johnson Oil Ref. Co. v. Oklahoma, 290 U.S. 158, 162 [54 S.Ct. 152, 78 L.Ed. 238].) Even migratory property that does not travel on a schedule may become subject to taxation in other jurisdictions.
 It cannot be assumed, however, that the aircraft had acquired a taxable situs elsewhere merely because they were absent from Los Angeles County a large part of the time. No such assumption is supported by Standard Oil Co. v. Peck, supra, 342 U.S. 382, invoked by the majority opinion. The court there struck down an unapportioned tax imposed by the domiciliary state on oil barges that traveled the inland waters of the Mississippi and Ohio Rivers. It reasoned that river craft almost continuously within other states were subject to the taxing jurisdiction of those states, and a tax by the domiciliary state on their full value would result in "multiple taxation of interstate operations and the tax would have no relation to the opportunities, benefits, or protection which the taxing state gives those operations." Barges that navigate interstate waterways ordinarily acquire more than one taxable situs along their course. In contrast, aircraft navigating the sky ordinarily do not acquire any other taxable situs along their course. (See concurring opinion of Jackson, J. in Northwest Airlines, Inc. v. Minnesota, supra, 322 U.S. *329 292, 304.) The domicile is therefore free to tax all such aircraft so long as there is no showing that they have maintained sufficiently regular, recurrent physical and business contacts with other jurisdictions that would accordingly subject them to taxation there. (Braniff Airways, Inc. v. Nebraska State Board of Eq. & A., 347 U.S. 590, 600-602 [74 S.Ct. 757, 98 L.Ed. 967]; New York Central & H. R. Co. v. Miller, supra, 202 U.S. 584, 597 [26 S.Ct. 714, 50 L.Ed. 1155].)
 Since the board erroneously failed to determine whether any part of the property had acquired a taxable situs elsewhere, the case should be remanded to it for a redetermination of the tax on the basis of the evidence submitted at hearings before it.  [fn. 2] (Universal Consolidated Oil Co. v. Byram, 25 Cal.2d 353, 362 [153 P.2d 746].)
 If the evidence then showed that the aircraft were not subject to taxation elsewhere, the county would be free to tax them on the basis of their full value. (Southern Pac. Co. v. Kentucky, supra, 222 U.S. 63; New York Central & H. R. Co. v. Miller, supra, 202 U.S. 584; Northwest Airlines, Inc. v. Minnesota, supra, 322 U.S. 292, 298; Braniff Airways, Inc. v. Nebraska State Board of Eq. & A., supra, 347 U.S. at 602.) If, however, the evidence showed that the property had acquired a taxable situs elsewhere, the county would have to forego taxation to the extent that other jurisdictions had acquired the power to impose an apportioned tax. "The rule which permits taxation by two or more states on an apportionment basis precludes taxation of all of the property by the state of domicile." (Standard Oil Co. v. Peck, supra, 342 U.S. at 384.) The board would then be compelled to apportion the tax on a basis realistic enough to preclude due process and commerce clause objections. The formula upheld in the Braniff case, supra, exemplifies what can be done in this regard. It encompassed such realistic factors as arrivals and *330 departures, revenue tons handled by the carrier, and originating revenue.  [fn. 3] While not exhaustive, these solid contacts with the state reflect the "opportunities, benefits or protection conferred or afforded by the taxing state" (Ott v. Mississippi Valley Barge Line, 336 U.S. 169, 174 [69 S.Ct. 432, 93 L.Ed. 585]), and the factors that contribute to the value of the property. Moreover, such a combination is apt to insure a fairness to both taxpayer and taxing authority that a single factor not counterbalanced by others does not afford. Indeed a single factor formula, such as that of physical presence compelled by the majority opinion, may be highly arbitrary. Suppose that Airline "A" flies nonstop between New York and Los Angeles, that the aircraft are physically present in New York 10 per cent of the time and in Los Angeles 30 per cent of the time, and in the air the rest of the time. Under the majority view, the aircraft would be subject to tax on 10 per cent of their value in New York and on 30 per cent in California; 60 per cent of their value would escape taxation altogether. Yet an Airline "B," flying exclusively between Los Angeles and San Francisco would be subject to full taxation in California. Such a single factor formula leads to still more capricious results in a case like the present one of aircraft that travel over the high seas where they have no taxable contacts with any other jurisdiction. The arbitrariness of such a formula arises from the inclusion therein of "bridge time," i.e. the time the aircraft are in the air and afford no state jurisdiction to tax, and the time they are in jurisdictions on random excursions that do not render them taxable there. If physical presence is used as the formula of *331 apportionment or as one of the factors in the formula, certainly "bridge time" and the time spent in such random excursions should be excluded entirely from the formula, and the total time used should be only the time spent in jurisdictions where the property is taxable.
 The perennial contention arises that there is always danger of multiple taxation latent in the possibility that different states would evolve different formulas of apportionment. It bears noting therefore that no court has found such a danger serious enough to invalidate an apportionment that reasonably reflects the opportunities, benefits and protection afforded by the taxing state.
 Gibson, C.J., and Spence, J., concurred.
 "If all or any portion of the taxes paid under protest and sought to be recovered were collected by officers of the county for a city, an action must be brought against the city for the recovery of such taxes and judgment must be sought against the city. Where actions are brought against both a county and a city such actions may be joined in one complaint."
 "Any city for which county officers collect taxes may provide for the defense by counsel for the county of actions brought against the city under this article, in which event it shall be the duty of such counsel to defend such actions, or the city may provide that such actions shall be defended by its own counsel."
NOTES
[fn. *]  *. Section 5138 of the Revenue and Taxation Code reads: "Within six months after the payment, an action may be brought against a county or a city in the superior court to recover the taxes paid under protest.
[fn. 1]  1. Although the state of incorporation is regarded as the legal domicile of a corporation, its domicile for tax purposes is its principal place of business or headquarters. Thus, the "commercial domicile" rather than the state of incorporation is given the power to tax intangible property of the corporation on the ground that "it is there that the owner in every practical sense realizes the economic advantages of his ownership." (First Bank Stock Corp. v. Minnesota, 301 U.S. 234, 241 [57 S.Ct. 677, 81 L.Ed. 1061, 113 A.L.R. 228]; see Wheeling Steel Corp. v. Fox, 298 U.S. 193 [56 S.Ct. 773, 80 L.Ed. 1143]; Southern Pac. Co. v. McColgan, 68 Cal.App.2d 48 [156 P.2d 81]; Pacific Western Oil Corp. v. Franchise Tax Board, 136 Cal.App.2d 794 [289 P.2d 287].) Although plaintiff is incorporated in the state of Delaware, its principal place of business, the home port of its planes, and its repair terminal are all located in the County of Los Angeles. Its aircraft habitually return to their California headquarters.
[fn. 2]  2. "[T]he proper procedure upon the failure of an administrative board to give a hearing under appropriate circumstances is to remand the case to the board for proper proceedings. (Citations.) The policy underlying such a rule is that the determination of the issues should first be made by the administrative agency. It is given jurisdiction for that purpose, and interference with that jurisdiction should not be permitted until it has been pursued to the point of exhaustion." (Steen v. City of Los Angeles, 31 Cal.2d 542, 546 [190 P.2d 937].) Although the term of a board of equalization is limited by statute (Rev. & Tax. Code,  1603), "that provision is directory only and does not deflect from the statutory scheme that the authorized tribunal pass upon matters properly within its jurisdiction though in the completion of its work it must act at a time beyond the prescribed period." (Universal Consolidated Oil Co. v. Byram, 25 Cal.2d 353, 362-363 [153 P.2d 746].)
[fn. 3]  3. " 'The proportion of flight equipment allocated to this state for purposes of taxation shall be the arithmetical average of the following three ratios: (1) The ratio which the aircraft arrivals and departures within this state scheduled by such air carrier during the preceding calendar year bears to the total aircraft arrivals and departures within and without this state scheduled by such carrier during the same period; Provided, that in the case of nonscheduled operations all arrivals and departures shall be substituted for scheduled arrivals and departures; (2) the ratio which the revenue tons handled by such air carrier at airports within this state during the preceding calendar year bears to the total revenue tons and handled by such carrier at airports within and without this state during the same period; and (3) the ratio which such air carrier's originating revenue within this state for the preceding calendar year bears to the total originating revenue of such carrier within and without this state for the same period.' " (Braniff Airways, Inc. v. Nebraska State Board of Eq. & A., supra, 347 U.S. at 593.) This is the formula of the " 'proposed uniform statute to provide for an equitable method of state taxation of air carriers' adopted by The Council of State Governments upon the recommendation of the National Association of Tax Administrators in 1947." (Ibid)
