Still more expeditious is the use of a **planimeter**, such as Captain Prytz's " Hatchet **Planimeter**," which yields fairly accurate results, or G.

Coradi's " Polar **Planimeter**," one of the most trustworthy instruments of the kind.'

Tennant, " The **Planimeter** " (Engineering, xlv.

These theorems may prove useful in preliminary calculations where the pressure-curve is nearly straight; but, in the absence of any observable law, the area of the pressure-curve must be read off by a **planimeter**, or calculated by Simpson's rule, as an indicator diagram.

The construction of a second funicular may be dispensed with by the employment of a **planimeter**, as follows.