Peirsol may be the spelling of the last name.

1880 census North Sewickley, Beaver, Pennsylvania, p 322:
Benj'n. PIERSAUL Self M Male W 44 PA Farmer PA PA
Emaline PIERSAUL Wife M Female W 33 PA Keeping House PA PA
Mary PIERSAUL Dau S Female W 18 PA At School PA PA
Louiza PIERSAUL Dau S Female W 14 PA At School PA PA
George PIERSAUL Son S Male W 10 PA At School PA PA
Charles PIERSAUL Son S Male W 5 PA PA PA
Henry PIERSAUL Son S Male W 2 PA PA PA

1. Mary PIERSOL b. CAL 1862, Pennsylvania, probably North Sewickley, Beaver, Pennsylvania.
2. Rebecca PIERSOL b. EST 1864, Of North Sewickley, Beaver, Pennsylvania.
3. Louiza PIERSOL b. CAL 1866, Pennsylvania, probably North Sewickley, Beaver, Pennsylvania.
4. George PIERSOL b. CAL 1870, Pennsylvania, probably North Sewickley, Beaver, Pennsylvania.
5. Jane PIERSOL b. EST 1872, Of North Sewickley, Beaver, Pennsylvania.
6. Charles PIERSOL b. CAL 1875, Pennsylvania, probably North Sewickley, Beaver, Pennsylvania.
7. Henry PIERSOL b. CAL 1878, Pennsylvania, probably North Sewickley, Beaver, Pennsylvania.
8. Edna PIERSOL b. EST 1881, Of North Sewickley, Beaver, Pennsylvania.