You have an object that is curved and you want to know how round it is. How would you measure it? This may seem like a rather strange question, but it is an important part of our evermore technological day. We rely on lenses in our smart phones, back-up cameras in our cars, and eye glasses. Perfectly-shaped lenses help us avoid blurry images, but how do you make and measure one?
Lenses date back to ancient times, with artifacts and references to magnifying lenses being found in the Middle East dating to the third millennium BCE, Egypt in the first millennium BCE, and in ancient Rome. Eye glasses, or "reading stones," were used starting roughly in the twelfth century by monks who needed to read and write manuscripts for hours on end, by candle light no less. By the late thirteenth century, spectacles were starting to be used across Europe.
During the Renaissance, lenses found their way into spy glasses (usually credited to Hans Lippershey of Holland in 1608), telescopes (Galileo Galilei in 1609) and microscopes (usually credited to Lippershey or Galileo at about the same time as the telescope). So naturally, the precision grinding of these glass lenses became an important consideration. If the surface of the lens was not a perfect portion of a sphere or parabola, the light would not all focus at the focal point, and the image would be blurry or have other problems.
To make sure the curvature of his lenses were just right, French optician Robert-Aglaé Cauchoix is believed to have invented the first spherometer in 1810.
A spherometer does exactly what its name suggests: it is a device that measures a sphere. In particular, it measures the radius of curvature (the radius of a sphere that fits just perfectly against the curved surface).
It is a handy little device that was also used by astronomers to grind their lenses and mirrors. Though modern computer-guided laser methods have made the spherometer obsolete for professional use, many amateur astronomers still grind their own lenses and use spherometers in the process. They are also used to measure the thickness of items such as pipes and metal plates. In particular, they are used in the oil industry even today to check for variations in the thickness of pipes to search for possible weak points.
The Smithsonian has a collection of spherometers that were built during the nineteenth century. Some were used by practitioners and others were used in the classroom to exhibit properties of light. My favorite spherometer in the collection is this Clark spherometer given to the museum by the U.S. Naval Observatory. It was part of the inventory of devices acquired for the 1874 U.S. expedition to observe the transit of Venus.
It is only a few inches tall and comes in a handy home-made box, presumably made so it would travel safely on the expedition. All the Smithsonian spherometers in this object group, along with some details about how they work and the mathematics behind them can be explored online.
Dr. Amy Shell-Gellasch is an historian of mathematics who volunteers in the Division of Mathematics and Computer Science. She has also blogged about kinematic models and ellipsographs.
