First of three volumes on a 'greater' Adams; Both Sides of the Ocean: A Biography of Henry Adams, His First Life, 1838-1862, by Edward Chalfant. Hamden, Conn.: Archon Books (Box 4327, 06514). 550 pp. $32 .50.

The United States has no Gothic cathedrals or imperial monasteries filled with medieval art, as do the French and Japanese. Our ''national treasures'' are more apt to be families, which over successive generations have made important contributions to American culture and government. The Peales and the Wyeths come to mind as painting families.

Henry Adams, the subject of Edward Chalfant's important new biography, was the grandson and great-grandson of presidents; the son of Charles Francis Adams, Massachusetts congressman and antislavery crusader. Later, Henry's father served as Lincoln's minister to Great Britain and is often credited with restraining the British from recognizing the Confederacy, thereby in his own small way saving the Union.

Mr. Chalfant speaks from time to time of the ''greater'' and the ''lesser Adamses.'' Henry's father, despite his political prominence, is ranked with the ''lesser,'' while Henry, who never fought his way up the American political ladder, stands with the Adams presidents among the ''greater.''

His monumental ''History of the United States'' has earned him a place among the great American historians, and ''The Education of Henry Adams'' is perhaps the most elegant autobiography any American has written. Yet if his achievements stopped there, this lesser-known Adams would scarcely deserve all the painstaking scholarship Mr. Chalfant has devoted to his first 24 years.

There are perhaps in each historical period a few people who have digested an age, and live with one foot in an older world and the other foot in the new. The Henry Adams who much later in life would write ''Mont Saint-Michel and Chartres'' was one of these, and what Mr. Chalfant is writing is the early history of an intellect.

There are scenes that are familiar to readers of the ''Education,'' such as the famous story of the small Henry adamantly refusing to go to school, being quietly taken by the hand of ''The President,'' his ancient grandfather, John Quincy, and led off to his lessons.

Mr. Chalfant retells this story because it marks the beginning of a lifelong hatred of school, and a lifelong process of self-education more rigorous than any formal schooling could offer. For two years after Harvard, Henry traveled around Europe mastering German, French, and Italian, achievements his family cared little for. (In the 1850s, Adams sons were expected to be clerking in prestigious Boston law firms and to be equipped with ''good characters, good wives, and growing families.'')

His skill at languages, and the taste for spectacular political milieux acquired on a junket through the Italian War of Liberation, served young Adams well when called to be his father's closest aide in Congress during the ''secession winter'' of 1860-61 and later in London as second in command of the American mission.

Henry Adams's double life in the American ministry, mailing weekly secret reports to the New York Times, reports that surely influenced the final British decision not to open a second front for the Confederacy against the North, is told with the day-by-day excitement of a good detective story. ''Both Sides of the Ocean'' is at times amusing, suspenseful, and engrossing. Mr. Chalfant's style shows just how much good history benefits from good writing.