The observed modulation of galactic cosmic ray ( GCR) intensity, on time and spatial scales, contains information regarding their transport in the heliosphere. One way to extract crucial information from the data is to study the rigidity dependence of modulation. A methodology is described to study the rigidity dependence of the short-term variations in galactic cosmic ray intensity Earth, in terms of the median rigidity of detector response ( R-m) to cosmic ray spectrum. We define R-m as the rigidity below which lies 50% of detector counting rate. For neutron monitors ( NMs), it is easily calculated from the latitude survey obtained at sea level and higher elevations. We compute R-m values for some NM sites; solar cycle dependence for them is shown to be small. Their practical utility is demonstrated in a study of transient cosmic ray solar modulation ( Forbush decreases ( FDs)), using data published in the literature. We plot the rigidity dependence of the amplitudes of three large Forbush decreases that occurred during the declining phase of three solar cycles ( 19, 20, and 21). We show that the Forbush decrease amplitude varies inversely with Rm over a large range ( 1 to 300 GV) of GCR rigidities. Thereby, we rule out the existence of a "transition rigidity'' suggested by Jokipii even for a short-term modulation ( large Forbush decreases). We speculate that the force field model may be applicable to large Forbush decreases.