These are photographic plate holders from the the Prime Focus Spectrograph of the 200 inch Hale Telescope at the Mt. Palomar Observatory operated by the California Institute of Technology. At the beginning of an observing run, the observer would cut small suares or rectangles of glass-backed spectroscopic emulsions and place them inside these holders, and within the box, for hand transport from the observatory darkroom to the prime focus cage. For each exposure, the observer then fitted the plate holder into one of the several solid Schmidt cameras so that when the camera was closed, the plate itself would press against a field flattener in the camera.
The Prime Focus Spectrograph was designed and manufactured at the California Institute of Technology in the late 1940's for installation on the then-new 200 inch Hale Telescope. It was in use almost continually from 1950 through 1973 providing a wealth of data on the redshift, on white dwarf stars, and on quasars. It was donated to NASM by the California Institute of Technology in 1998.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.