For builders and bricklayers, all is for naught if one’s work is not level. After all, who wants to sleep in a bed that been placed on a sloping floor, and if your brick patio is laid at the wrong angle, the winter rains will saturate your home’s foundations rather than running off harmlessly into your flower beds or lawn.

There are two types of antique levels of interest to collectors of antique tools. The first is an inclinometer, which, as its name implies, measures a slope’s degree of incline, which is read via the tool’s circular protractor. Some 19th-century American inclinometer manufacturers only made the device, which customers would mount in rosewood, cherry, and other woods of varying lengths as they saw fit. Most, though, sold their inclinometers in cast-iron or wooden frames—hard woods with brass accents were the rule.

One of the companies most highly regarded for its inclinometers was Davis Level & Tool Co., whose pierced-and-japanned cast-iron housings resembled the trimwork on the Victorian Era homes they helped build. Inclinometers labeled Davis and Cook were often shaped like mantel clocks, although many manufacturers made inclinometers in this classic style...