Recently I have been doing a lot of pinhole photography, and due to that I have had to explain to a number of people (unfamiliar with the more technical parts of photography) what reciprocity failure is.
Reciprocity is the relationship between shutter speeds and apertures, which means that as you reduce exposure with a change in, lets say the shutter speed by one stop, then increase the exposure by one stop with the aperture, you will have exactly the same exposure. Each one-stop adjustment of the shutter speed, is equivalent to a one-stop adjustment of the aperture. This holds true throughout the normal use of the camera in most lighting situations.
This linked relationship begins to slip away with exposures longer than one second, and the longer the indicated exposure, the more of a difference there is between the indicated exposure and what is actually needed. Many years ago I included in my book on night photography, a chart for working out the amount of exposure correction you might need in situations where exposures were between 1 second and 17 minutes. I have been referring to this chart for my extended pinhole exposures, and I include a link to a word document here which shows the full chart: