Prime Minister Pierre Trudeau, quickly following up on his promise of a "brand new constitution," has summoned the leaders of Canada's 10 provinces to his summer residence June 9 for private talks on the new charter.

Trudeau's pledge played a crucial role in the outcome of the May 20 referendum in Quebec, when that predominantly French-speaking province voted down a proposal to seek political independence from Canada. But even those who voted for Canadian unity did not necessarily agree that all was well with the federation.

Ironically, the fulfillment of Trudeau's promise to Quebecers may now be thwarted by other Canadian provinces, which also seek a diminished federal role, but in a different way and for different reasons.

Newfoundland Premier Brian Packford said last week that a new constitution should make 'the federal government an agent of the provinces," and not the other way around. But the nine provinces of English-speaking Canada cannot agree on what kind of federal system they want.

Packford and Premier Peter Lougheed of Alberta believe the provinces must decide what powers should be reserved for the federal government. Ontario, the most populous province and Canada's industrial heartland, believes that the federal government must retain the approximate amount of power it now wields. Trudeau agrees with Ontario Premier Bill Davis. Otherwise, they argue, Canada would become unmanageable.

Other provinces have taken positions between these two extremes. All favor devolution of power to them but not necessarily through wholesale decentralization. British Columbia, for instance, wants devolution to take place through reform of federal institutions.

Moreover, English-speaking Canada does not support French-speaking Canada's basic objectives -- constitutional recognition if its "special status" as one of the two founding nations and the protection of French speakers' legal rights.

The threat of a secessionist victory had obscured English-speaking Canada's differences before the referendum, and all the provinces rallied behind the drive to save the federation. But after the May 20 referendum, these differences have become more pronounced and are likely to severely strain the already fragile Canadian institution in the course of constitutional talks.

A crucial test will be in the wealthy western provinces, where the drive for greater provincial rights has been particularly intensive.

Unlike Quebec, which is preoccupied with its unique cultural and linguistic heritage, the oil-producing province of Alberta is driven by its enormous surplus revenue to seek a curtailment of federal power. It does not want Ottawa to take is cash away.

As a result, constitutional bargaining must involve painful compromises between the federal government and provinces on their respective rights and interests.

Today's Canadian crisis in many ways resembles the period in the United States before the 1787 Philadelphia convention that produced the U.S. Constitution, which gave the federal government more powers than it had had under the Articles of Confederation.

However, the 113-year-old Canadian confederation now appears to be moving in the opposite direction with the provinces virtually certain to receive greater authority when the new charter is produced.

Underlying the complex arguments is the struggle over taxation authority and provincial demands to have "sovereign" control over social services, mineral resources and communications.

The current Canadian constitution, which is an act of British Parliament adopted in 1867, grants mineral rights to provinces. In its conflict with Ottawa, the Albertan government has used this provision to insist on control over its own energy prices while the federal government in Ottawa has fought to keep Alberta's oil prices well below the world levels.

The Albertans also have a law on their provincial books giving them the authority to control oil production levels. They could use this law to cut off oil supplies if Ottawa fails to accomodate their aspirations.

It is this conflict between Alberta and Ottawa as well as strong insistence by other provinces on their right to pursue their own interests that threatens Trudeau's drive for a new constitution.

Although there are reports that a constitutional convention may convene as soon as July, there are no indications that compromises will be made quickly enough to resolve the differences between the federal government and the provinces. English-speaking Canadian politicians talk about three to five years of negotiations before the new charter is adopted.

Trudeau has warned that protracted haggling over a new constitution would frustrate Quebec residents and provide ammunication for Quebec Premier Rene Levesque to hold another referendum on sovereignty.

About one-half of French-speaking Quebecers, who comprise 80 percent of Quebec's population of 6.3 million are so unhappy with their role in the Canadian federation that they voted for its destruction in the referendum. The other half voted for Canada, with some apparent reluctance.

On the day of the referendum, a correspondent for the Paris weekly, Vendredi Samedi Dimanche, and this correspondent had a conversation with one of the top aides to Claude Ryan, the leader of Quebec federalists. The official confided to us that he was a closet separatist. He really wanted to vote for Levesque's proposal, he said, but he worried about economic consequences and voted no "with a heavy heart."