In 1767 he sailed near Rockall, or Rokol. Although he may not have approached within sight of it, or even within 150 miles, he appears to have had good information regarding it. His charted position for it was only 16 miles North of its actual position and he accurately described its appearance and the nearby Helen's Reef, "East of Rokol, ¼ league away, there is a submerged rock over which the water breaks".1 Afterwards he published a map of the area in 1771.
In his report to King Louis XV, he greatly overestimated the value of the Kerguelen Islands; consequently, he was sent off on a second expedition, again reaching Kerguelen. By now, it had become clear that these islands were desolate and quite useless, and certainly not the Terra Australis. On his return, Kerguelen-Trémarec was sent to prison.