Rome de l'Isle authorized two of his pupils, Arnould Carangeot (1742-1806) and Claude Lermina (1749-1806), to construct an instrument for the measurement and reproduction of crystal angles; Carangeot, accordingly, designed the prototype of a contact goniometer. Nicolas Vincard was entrusted with constructing the actual instrument.
He stated that he had precisely determined different angles of several quartz crystals with his contact goniometer, had recognized the constancy of the angles between comparable crystal faces, and had related these observations to Rome de l'Isle.
The prototype of the contact goniometer invented by Carangeot consists of a graduated semicircular arc whose diameter also serves as the stationary measuring limb.
Carangeot then invented the
contact goniometer in order to pursue such measurements on all of the minerals available, providing a massive amount of data that gave Rome de l'Isle's new work a solid mathematical base.