I know that expensive instruments can be used to determine the color of an object, but is there a poor man's way to determine color using filters? By "determine color" I mean know the relative proportions of primary colors. In other words, using filters to know that the proportions of red, blue and green are 5, 3, and 1, for example, or maybe something using the natural color system.
One of the earliest forms of colorimetry involved a light sensor (or film) with a known sensitivity curve over the visible spectrum and, if film was involved, a densitometer to measure the resulting density.
You'd arrange constant lighting and measure the light level received (or density above bas+fog with a standardized development process) for each of three or more filters (also of known absorption characteristics, of course).
As you can probably see by now, this isn't exactly a "poor man's method", because of all the science needed behind the instrument(s). Still, it probably cost less to do it this way with a panchromatic film, in the 1950s, than to buy and use an actual colorimeter.
An alternative that was available at various times was color chips. This had limits, but the idea was that you'd hold a sample of known color against the object, and in the same light, and then move to a sample that was, say, a little more green, a little less blue, etc. until you had an exact match. This was time consuming, but if the fineness of your measurement needn't be too high, it was very likely to be less so than the film and filter method.
What you need is a color densitometer, likely you can find a used one on ebay. You can buy red, green and blue separation filters from many sources. Red 25, Green 58 and Blue 47. Try close focusing a through-the-lens metering camera on a uniform color patch you wish to analyze. Have the camera display the exposure as metered. Note the shutter speed, aperture, and ISO associated with this reading. Now mount one of separation filters and take a reading. When finished, you will have data from the four readings. Noting the differences you can figure out the differences. This method crudely replicates how a densitometer works.