The article continues previous historical research by {\it H. W. Gould} [Util. Math. 61, 97--106 (2002;

Zbl 1004.26003)] and {\it W. P. Johnson} [Am. Math. Mon. 109, No. 3, 217--234 (2002;

Zbl 1024.01010)] on the predecessors of Italian mathematician and Catholic priest Francesco Faà di Bruno (1825--1888), in his discovery, between 1855 and 1857, of the generalized (for the $n$-th derivative) chain rule of differentiation for composite functions.
Craik investigates in particular the work by Alsatian mathematician Louis Arbogast (1759--1803) and the three British mathematicians, John West (1756--1817), Augustus de Morgan (1806--1871), and Thomas Knight. The latter is a rather shadowy figure. With the help of a genealogist, the author makes the living dates 1775--1853 probable. The author shows that none of the three British authors gave fully rigorous proofs of their results, while Faà di Bruno, who published later, gave no proof at all. Why nevertheless the formula has been traditionally connected to the latter, whether this is due to the Italians fame outside mathematics (he was declared a Saint in 1988), the author passes no judgment on.