His first practical employment was in the preliminary surveys of the Bear Mountain railroad, then a new enterprise, hut his mental activity in a higher sphere soon manifested itself in a communication to Mr. Bache, made in January, 1844, in which he called attention to errors in the formulas used in the Coast Survey in the computation of geographical positions, and gave his own development of correct formulas. In reply Mr. Bache wrote to the young man of nineteen: "You have overridden two of our most experienced computers and have shown that they are seriously in error." The incident was soon followed up by Bache with an offer of subordinate position in the Coast Survey, in accepting which young Hilgard remarked that he would rather "do high work at low pay than low work at high pay." He entered at once upon the work assigned him in the computing division, but his official appointment bears the date of December 28, 1846. In the year 1845-'46, however, we already find him engaged in the secondary triangulation of the Chesapeake, below Kent island, the illness of the chief of the party, Captain (since General, C. S. A.) Joseph E. Johnston, left Hilgard in charge of the work. Concerning this first trial of his strength the superintendent's report of that year says: