Gray and Co., the largest Washington-based lobbying and public relations firm, has acquired The Strayton Corp., a Wellesley, Mass., public relations and advertising firm that specializes in high-tech clients.

"Through Strayton, we will substantially expand our market, propelling our growth as one of the largest public communications companies in the world, with combined revenues expected to exceed $20 million in this fiscal year," said Robert Keith Gray, Gray & Co.'s chairman.

This $20 million figure, however, includes nearly $10 million in advertising billings and out-of-pocket reimbursed expenses and production costs, which are not normally counted by public relations firms in calculating fee incomes, said Jack O'Dwyer, who publishes a newsletter on the public relations business.

According to the Gray's 1984 annual report, its "revenue" for the latest year includes $2.6 million in ad billings for the Kennedy Center for the Performing Arts and $3.5 million in out-of-pocket reimbursed expenses. Strayton, which provides marketing, public relations and advertising services for more than 250 clients, many in high-tech industries, reported $3.1 million in fees for 1983. But, Gray & Co. described Strayton's revenue as approaching $8 million.

Strayton's actual fee income to July 31 was $4.5 million and that included $500,000 in ad commissions, O'Dwyer argued. "Apparently Gray is reporting the gross ad billings of Strayton, mixing them in with PR fee income," O'Dwyer wrote in his newsletter. "It would be more logical for Gray to 'capitalize' its PR fees (multiply them by 6.67) and report as an ad agency." But by doing so, O'Dwyer added, Gray could no longer claim to be one of the largest.

"This is an industry bicker over a minor thing," said Chuck Crawford, Gray & Co. spokesman. "O'Dwyer is measuring us against the public relations industry, but we are more than just a public relations company. We are a total communications company that does advertising as well. O'Dwyer is not recognizing any other areas we are involved in."

"This is an argument that O'Dwyer has been having with his readers for a long time," added Frank F. Mankiewicz, executive vice president of Gray. "Some firms include billings and some do not. Earnings is a word of art in some connections and is generic in others."

"O'Dwyer has a legitimate argument, but his is not the only way to calculate earnings," Mankiewicz added.

O'Dwyer acknowledges that Gray has every right as a public company to come up with the largest income figures possible, lumping in gross ad billings and production and other reimbursed client expenses with its hourly time charges for PR service. "But, it cannot then compare this figure with those reported by other PR operations, which it does," O'Dwyer said.

"O'Dwyer is right in the sense that one shouldn't compare firms that do add billings to revenues and those that don't," Mankiewicz said. "But, I don't think we do that."

Gray's merger announcement, however, referred to Gray as "the only independent public relations agency with publicly traded stock," and public relations agencies don't normally include billings and reimbursed expenses in their calculations of fee incomes, O'Dwyer pointed out.

Gray's new subsidiary, Gray Strayton International, will remain in Wellesley with no expected changes of management.