With its 354 square miles, the town of Chesapeake in Tidewater Virginia is so large and sparsely populated that there is enough room and woods to hunt bear.

With its 45 square miles, next-door neighbor Portsmouth is so small and heavily developed there is scarcely room for a small factory needing five acres.

For all their obvious differences, Chesapeake and Portsmouth share a common identity. They are both cities.

In Northern Virginia, Alexandria and Arlington would seem to be similar urban creatures. They are geographically small and largely developed. Their populations are getting older and more likely to be living alone.

But for all their obvious similarities, Alexandria and Arlington do not share a common identity -- at least not legally. Alexandria is a city, Arlington is a county.

Do such puzzling differences matter?

They do indeed, and del. gerald l. Baliles (D-Richmond/Henrico) thinks it's time the state started looking at those differences.

In one important area, state moneys, the differences can be crucial. State aid, for instance, is allocated differently to cities and counties. Two localities may have common needs, but if they have different legal identities, such as Alexandria and Arlington, they will get state aid under different formulas.

On the other hand, two localities may have needs that are considerably different, but if they share legal identities, such as Chesapeake and Portsmouth, they will get state aid under the same formula.

What a local government can or can't do depends on whether it is a city or county.

There are yet other differences, involving taxation and whether a locality can annex land or itself be annexed.

Baliles, in what turned out to be one of the most provocative addresses at the 75th annual meeting of the Virginia Municiple League last week in Arlington, contended that the state needs to reconsider its definitions for city and county.

"We live with the terms city and county," Baliles told league members, "yet I submit that we do so without comprehending that time and events have blurred the definitions that city and county once had.

"How is it," he asked, "that in many areas of Virginia an urban city and an urban county adjoin each other, each one providing essentially the same level of services, yet one operates with a charter (as a city) and the other does not?"

Baliles acknowledged that there have been attempts to grapple with such paradoxes before: "We tinker almost annually, it seems, with state aid formulas for cities and counties. We adjust here for core city problems, alter there for suburban areas and change again for rural needs."

But Baliles contended the tinkering was not enough.

"The question should be asked," he said, "whether the time hasn't come to reexamine the nomenclature of local governments? Cities and counties: What are they now? What do we want them to be . . . If we are to succeed in finding solutions to problems that are linked to one's status as a city or county, can we afford to wait?"

Baliles proposed that the Municipal League and the Virginia Association of Counties create a joint study commission to examine, evaluate and propose "definitions of cities and counties in Virginia."

He suggested that the commission be staffed by the Institute of Government at the University of Virginia and that it make recommendations that would go to localities and, ultimately, to the General Assembly.

Mayor Vincent J. Thomas of Norfolk has a keen interest in wheter Baliles' proposal gains any currency. Norfolk is a lot like its neighbor, Portsmouth: It includes only 64 square miles and only 5 percent of its land is vacant.

With so little land that can be developed, Norfolk has been unable to compete for new industry with another neighbor, Virginia Beach, which has a lot of vacant land. Virginia Beach has even been able to lure away some Norfolk industries, which had wanted to expan but had no room at their Norfolk sites.

A redefinition of cities and counties, Mayor Thomas hopes, might lead to a "different tax mix" among disparate cities (such as Norfolk and Virginia Beach). The state already acknowledges the problem by providing some innercity tax aid. But Thomas thinks much more needs to be done.

He points out that Virginia Beach, because its tax base has been able to grow twice as fast as Norfolk's, is able to keep its tax rate at half of Norfolk's. Mayor Thomas asks: "How can we expect to depend on the real estate tax for increased spending when te tax base is not growing?"

That's a touch question. It may take an effort as formidable as the basic study of cities and counties proposed by Baliles to provide an answer.