Clarence H. Swick, 96, a mathematician who retired from the U.S. Coast and Geodetic Survey in 1948 after 38 years of service, died Tuesday at the Carriage Hill nursing home in Arlington. He had cancer.

Mr. Swick was born on a farm in Niagara county, N.Y. He earned a bachelor's degree in field engineering from Cornell University and joined the Survey in 1908.

For the first three years of his government service, Mr. Swick traveled in the United States, conducting hydrographic surveys and similar work. In 1911, he was stationed at the agency's headquarters in Washington and spent the rest of his career there.

Mr. Swick's field was geodesy, which is the branch of applied mathematics concerned with measuring the earth, determining its shape, and locating exact points on its surface. Mr. Swick's special interest was the study of gravity.

In 1921, he published a book called "Modern Methods of Measuring the Intensity of Gravity." He also wrote many papers on gravity and other aspects of geodesy.

Mr. Swick established his home in Capital Heights in 1911 and lived there until a year ago, when he moved to the Carriage Hill nursing home. He was an early civic leader in Capital Heights and was active in its Congressional Church, now part of the United Christian Church in Seat Pleasant.

His wife, the former Hattie Haight, died in 1957.

Survivors include four daughters, Helen Perry of Cambridge, Mass., Eunice Tertell of Hyattsville, Alice Davis of Avon, N.C., and Eloise evans of Los Cruces, N.M.; a son, Edgar H. Swick of Arlington; a brother, Louis Swick of Lockport, N.Y.; a sister, Gladys Clark of Cleveland, Ohio; 13 grandchildren, and 10 great-grandchildren.

The family suggests that expressions of sympathy be in the form of contributions to the United Christian Church Seat Pleasant, Md.