The isochronism of a pendulum is only true to a first approximation. If we make the arc large, the period increases, reaching infinity just before the pendulum makes complete circuits. Assuming the full value of the Circular Error, the actual calculation is given in No. 2 of this series (Proc. Roy. Soc. Edin., vol. xxxviii, 1918, p. 169) for the first few degrees, where it is seen that even with variations that may occur in practice, the change of daily rate may easily amount to several seconds. The defect was recognized before regulation of pressure and temperature were considered feasible, as early, for instance, as in 1673, when Huygens published his Horologium Oscillatorium. In fact Huygens invented the cycloid to prevent it, and gave an ingenious device to make the pendulum describe true cycloids—a device that has been given up for various reasons, among others, that it involves disturbance of the pendulum which it is very desirable to avoid.