Souris, J.

This case, like Palmer Park Theatre Co. v. City of Highland Park, 362 Mich 326, decided by us after entry of the decree here appealed, presents for decision the validity of a municipality’s imposition of an annual charge upon users of air-conditioning equipment which does not recirculate water, in addition to the charge made for water actually used. In the Palmer Park Theatre Case a city ordinance required annual purchase of a license at the cost of $20 per ton of capacity for each unit exceeding 5 tons. In the case at bar, the Detroit board of water commissioners on May 7, 1956, imposed an annual “demand charge”, beginning at $1.50 per ton of capacity in the first year to $7.50 per ton for 1961, upon all such equipment used for human or animal comfort. The license fee in the Palmer Park Theatre Case and the demand charge in the case at bar were in addition to the regular-charges for water actually consumed.

We held, in the Palmer Park Theatre Case, that *435 the license fee there imposed was unreasonable and arbitrary, and therefore invalid, because no longer necessary to its original purpose of conserving water, additions, improvements, and repairs to the city’s water system having increased its capacity to meet all foreseeable demands. A majority of this Court also held the license fee invalid because exemption of the users of such equipment with less than 5 tons of capacity was arbitrary and discriminatory as against those users of such equipment with capacity in excess of 5 tons who were required to pay the license fee, thereby denying the latter equal protection of the laws.

Differences between the 2 cases appear from the foregoing. In the first we dealt with a city ordinance requiring purchase annually of a license for a fee; in the case at bar the hoard of water commissioners imposed annually an additional charge computed on the basis of the tonnage capacity of the equipment used. Another difference is that in the first case all water-cooled air-conditioning equipment of the nonrecirculating type for whatever purpose used, except equipment less than 5 tons in capacity, was required to he licensed; in the case at bar the additional charge was imposed only upon such equipment if used for human or animal comfort, but without regard to its tonnage capacity. Another significant difference in the 2 cases is that defendants made no effort to justify the annual demand charge as an emergency water conservation measure, as was the situation in the Palmer Park Theatre Case. Although, as we shall see, the board of water commissioners in announcing the imposition of the additional demand charge indicated its concern over the current and future impact of air-conditioning equipment upon the water system’s capacity, it was stipulated below that the system’s capacity was sufficient to meet all demands of its *436 customers for the next several years except for “spot inadequacies” and assuming lawn sprinkling could be banned if necessary.

Plaintiffs’ bill of complaint was for a declaratory decree and for recovery of the additional charges already paid. After a lengthy hearing, the chancellor rendered a carefully prepared opinion in defendants’ favor dismissing the bill. Our review, of course, is de novo.

In the city of Detroit the board of water commissioners establishes water rates, pursuant to authority expressly granted by title 4, ch 12, § 9, of the charter of the city to fix such rates “upon such basis as shall be equitable.” First, a monthly charge is imposed for water actually consumed by each customer of the system at a specified rate for the first 10,000 cubic feet, at a lower rate for the next 90,000 cubic feet and at a still lower rate for all water consumed in excess of 100,000 cubic feet. Second, a monthly service charge is imposed, which charge is a demand charge based upon the size of meter used, the charge increasing from 24^5 for a 5/8-inch meter to $53.28 for a 24-inch meter. Finally, since 1957, the annual demand charge has been imposed only upon customers owning water-cooled air-conditioning equipment for human or animal comfort which does not recirculate water. This last annual demand charge was announced by the board of water commissioners in May of 1956 by adoption of a new rule and issuance of an accompanying statement of explanation. The explanatory statement, substantially in its entirety, follows:

“The impracticability of supplying water for water-wasting air-conditioning equipment is becoming generally recognized by the water-works industry throughout the country—and steps are being *437 taken to control the situation. The 2 principal methods in use are:

“(1) Prohibit by ordinance the use of water-wasting air-conditioning equipment.

“(2) Give users of air-conditioning equipment the choice of converting to the water-conserving type of equipment, or of paying the full cost of ’delivering water for the water-wasting air-conditioning load. This is usually done by imposition of a demand charge.

“The cost of meeting the water-wasting air-conditioning load in Detroit is over $7.50 per annum per ton of refrigeration, in excess of the charge for water consumption at current rates.

“The air-conditioning demand has practically no diversity factor. Under maximum conditions 95% or more of air-conditioning equipment will be in simultaneous operation. By comparison even the lawn sprinkling load shows less than 20% of potential in use at maximum.

“While the present air-conditioning load is something to be reckoned with, it is the future load that causes great concern. It is expected that there will be a tremendous increase in the use of air-conditioning equipment, both commercially and domestically, within the next few years. Air-conditioning tonnage in Detroit increased 9.6% during 1955. Pligher rates of increase are expected.

“During 1955, over 20% of maximum hour demand was chargeable to the air-conditioning load. This means that over 20% of plant facilities are used to meet the air-conditioning load. Twenty per cent of present plant capacity is enough to meet the maximum domestic demand of an additional population of approximately 800,000 people.

“It is obvious that either water-wasting air-conditioning must be prohibited in Detroit, or the plant expanded to meet the present and potential air-conditioning load.

“The Detroit board of water commissioners favors the addition of a demand charge to the water rate, *438 in the belief that it will in effect prohibit new installations of water-wasting equipment, and will : result in conversion of all or nearly all the water-wasting equipment now in use, and cause those, if any, who continue to use water-wasting equipment, to pay for the service rendered.”

Stated simply, the principal question is whether defendants may impose an additional annual demand charge only upon users of nonrecirculating air-conditioning equipment used for human or animal comfort without violating constitutional rights of due process and equal protection of the laws. * Plaintiffs argue forcefully that exemption of water-wasting- refrig-eration equipment used for commercial or industrial processing, and failure to impose the additional annual demand charge upon other seasonal users of water, renders the attempted classification discriminatory and, therefore, denies them equal protection of the laws. † In our disposition of this case, however, we need not consider this issue, for it is our conclusion that the additional annual demand charge was unreasonable and arbitrary and, therefore, deprived plaintiffs of property without due process of law.

The chancellor ruled that the demand charge was valid. He found that because such equipment is used only during the summer months and that then virtually all of such equipment operates simultaneously, particularly on the day and at the hour of peak demand upon the system, great demand is thereby placed uj)on the water-producing eapaeityy of the city’s system, necessitating- it to maintain substantial capacity in excess of its customers’ normal needs. He concluded that the cost of providing water for such use was greater than for other uses, thereby justifying the additional demand charge.

*439 Plaintiffs contend that the chancellor erred in his finding’s that virtually all of such equipment is in use simultaneously and that such simultaneous use occurs at the peak hour of demand. Prom these factual errors, plaintiffs claim the chancellor was led to his erroneous conclusion that the water system’s excess capacity was required to meet the peak demands of such equipment, the users of which should, therefore, bear the cost of maintaining such excess capacity.

There were offered by defendants statistical tables and charts prepared by their expert witnesses and the ivater system’s staff which support the chancellor’s findings and conclusions. One such group of tallies purports to allocate the system’s costs and revenues to various customer classifications: domestic, commercial, industrial, United States government, semicharitable, construction, suburban, and' nonrecirculating air-conditioning equipment used for human or animal comfort. A very great use of test data and estimates was required to accomplish the allocation. The technique used for determining Avater consumption by nonrecirculating air-conditioning equipment used for human or animal comfort, preliminary to the allocation of costs and revenues thereto, is found in the direct examination of William Patterson, defendants’ expert witness, who at this point was testifying from a previously prepared report:

“A. In developing the cost of service to nonconserved [nonconserving?] air-conditioning equipment it is first necessary to develop the water-use characteristics of this type of equipment. Prom the department of water supply files, test data are available on water-usage characteristics of customers using air-conditioning equipment of the nonconserving type.

*440 “This data includes maximum hourly rates of water use and average daily use, for the days of test readings. Tonnage installed, monthly water consumption, and revenues received were also available. With this data we were able to estimate the maximum and average annual rates of water used by, and the annual revenue received from, the average ton of nonconserving type air conditioning.

“Q. Will yon tell us your studies concerning the characteristics of water use by this equipment.

“A. From the test readings collected on 39 customers, representing a total of 7,767 tons, during the days of July 6, 7, 8, 21, 22, 23, 26, and 27, 1955, we have tabulated the maximum hourly rate of usage for each of these customers during those specific days.

“Q. Is this the maximum rate of water which you estimated was used for the air-conditioning equipment?

“A. No, this rate of usage included all water used on the premises at the time of test readings, and it is necessary to reduce the actual observed peak hourly rate in order to obtain the maximum hourly rate of use by the air-conditioning equipment proper.

“Q. Then will you explain how you determined the maximum hourly rate of use by the air-conditioning equipment ?

“A. We estimated the water use for purposes other than air conditioning by use of comparative consumption statistics on water use of similar customers without air-conditioning equipment. Basically, variation in winter to summer use of similar classes of customers varies as a group on a comparable basis, disregarding use for air conditioning.

“We found that non-air-conditioning commercial customers showed a maximum hourly use of approximately 3 times the average winter use. The average maximum usage of the air-conditioning customers, for purposes other than air conditioning, was estimated by applying this relationship of usage to the winter consumption.

*441 “The peak hourly rate of water consumption, as recorded by test readings for the group of air-conditioning customers, was reduced by the amount of the estimate hourly rate for the customer group for uses other than air conditioning, to obtain a peak hourly rate representing the water usage by the non-conserving air-conditioning equipment. By relating this total peak hourly rate to the tonnage of equipment in operation by these customers, we have determined a maximum hourly rate of water used per ton of nonconserved [nonconserving?] air-conditioning equipment.

“Q. What was this rate?

“A. The maximum hourly rate, average for the group, was 1.346 gallons per minute per ton.

“Q. How does this rate of usage per ton compare with general engineering theory concerning maximum rates of usage for this type equipment?

“A. Due to varied conditions that may govern for specific installations, the maximum rate could vary from 1 to 2 gallons per minute, but generally it can be said that air conditioning of the nonconserving type in this area will use about 1.5 gallons per minute when operating under full design load.

“Q. Why did you not use the higher maximum rate of 1.5 gallons per minute?

“A. If this rate were considered to be the maximum rate of usage and was applied to the total tonnage in the system, it would be necessary to apply a diversity factor to allow for units not in operation for 1 reason or another, or for units not operating at full capacity. Any diversity in air-conditioning use would be small as the heat of the day lasts for several hours and those with air conditioning would tend to be using it at the same time, with the result that on days of high temperatures practically all units would be operating at full capacity.

“If we were to assume as much as a 90% factor for diversity, the maximum rate of usage for the' groups would be 90% times 1.5 gallons per minute or 1.35 gallons per minute, or nearly the same rate *442 ■which, we found by analysis of the data collected on the 39 test customers.

“The Court: May I interpolate a question. When you use the 90% factor for diversity, do you mean as a method of computation you are assuming that 10% of those who had such equipment were not using it at that time; is that what you mean by 90% diversity Í

“A. Yes, that is what I mean and that would be under maximum conditions of use.

“Q. (By Mr. Reese): Did you complete your last answer ?

“The Court: I stopped him.

“Q. Will you continue?

“A. We believe that the derivation of the maximum hourly rate of use by this type of equipment which is based on the test data collected for the selected days of reading, provides a reasonable accurate basis for preparing our cost-of-service study.

“Q. What water-use characteristics, other than the maximum hourly rate, must be determined ?

“A. The total annual consumption by this type of equipment must also be determined. This consumption was determined by use [of?] the 39 test customers’ total annual consumption, less 6 months at the average winter-use rate and 6 months at the average summer-use rate, exclusive of air-conditioning use computing the summer rate as 1.20 times the winter-rate average.

“Air-conditioning consumption for the 1958 fiscal year, the most recent year of record, was estimated to average 42,400 gallons per ton for the 7,852 tons installed, and this average usage per ton was used as representative for the total tonnage installed in the system.”

Prom the foregoing it is evident that defendants’ witness used 1955 test data taken from only 39 customers (all located in downtown Detroit) whose nonrecirculating air-conditioning equpiment totaled 7,767 tons as a basis for estimating all other data. *443 relating to all such equipment subjected to the annual demand charge. At the time of hearing below, early 1959, there were approximately 6,000 such units having a total rated tonnage of 75,000. * Furthermore, as a basis for estimating theoretical maximum potential demand for water by such equipment (based upon which estimate other computations were made) it was assumed that 90% of all units would be operated simultaneously at the peak hour of demand by such equipment. No basis other than the witness’ judgment and the estimated use of such equipment by the test customers was suggested for this assumption. Other judgment figures were relied upon, some of which were frankly stated to have been generally based upon past experience in other cities under different circumstances of climate. The foregoing suffices to demonstrate the tenuous nature of the statistical data supporting the expert witness’ opinion testimony defendants rely upon to uphold the chancellor’s findings and conclusions.

Included in the 6,000 units of equipment subject to the annual demand charge is equipment operated by theaters, department and specialty stores, drug stores, office buildings, banks, restaurants, supermarkets, public and private halls, churches and the like, located in all parts of the city. A sampling of 0.65% of the number affected, but involving over 10% of the tonnage affected, suggests to us a high probability that conclusions therefrom will not be representative of the entire group. Particularly is this so when all 39 samples are located in the heart' of the city and most operate only during the daylight hours of a commercial center’s normal busi *444 ness day, as contrasted with other users of such equipment, — for example, the neighborhood theaters owned by some of the plaintiffs. What we are concerned with here is the demand for water placed upon the system at its peak hour of demand during any particular year, for the additional demand charge is sought to be justified on the basis that the cost of maintaining the system’s excess capacity, claimed to be made necessary by the nonreeirculating air-conditioning equipment used for human or animal comfort, should be borne by users of such equipment. The evidence shows that this peak hour for the entire system occurred between the hours of 6 and 8 in the evening, but the peak hour for the 39 downtown customers occurs earlier in the afternoon. The percentage of equipment in use at any 1 time for such select customers was not demonstrated to have any relationship to the percentage of all such equipment in use at the system’s peak hour of demand. The data from the sampling was crucial to defendants’ contention, and the chancellor’s conclusion, that the water system’s excess capacity was required to meet the peak demands of such equipment and that, therefore, the owners of such equipment should bear the cost of maintaining such excess capacity. It is our conclusion that plaintiffs carried their burden of proving- there was no reasonable basis for the addition of a demand charge upon nonrecirculating air-conditioning equipment used for human or animal comfort.

Furthermore, the record amply supports plaintiffs’ claim that lawn sprinkling and other household uses occurring- on the water system’s peak day and at its peak hour of demand impose a substantially greater strain upon the system’s capacity than does the use of equipment singled out by defendants to hear the cost of maintaining the system’s excess capacity.

*445 Having concluded there was no reasonable basis for the additional demand charge here sought to be imposed, it necessarily follows that such charge was unreasonable and arbitrary and, therefore, invalid because it deprived plaintiffs of property without due process of law.

Reversed and remanded for further proceedings in accordance with this opinion. No costs, a public question being involved.

Dethmers, C. J., and Carr, Kelly, Black, and Kavanagh, JJ., concurred. Otis M. Smith and Adams, JJ., took no part in the decision of this case.

Mich Const 1908, art 2, §§ 1 and 16; US Const, am 14, § 1.

†

See the majority opinion in Palmer Park Theatre Co. v. City of Highland Park, 362 Mich 326.

There were 17,000 refrigeration units of all types licensed by the city at the end of 1958, the total tonnage of which was 171,000. In. addition to the 6,000 units subject to the annual demand charge, with, a total rated tonnage of 75,000, there were 11,000 units totaling 96,000' tons, equipment which recirculated water or nonreeireulating equipment used for commercial or industrial processing.