To measure frequencies of eosinophils and neutrophils in airways
The original tests where done with blood and then:


  An eosinophillc index was calculated by multiplying the percentage of
  eosinophiles found in the routine white blood count by the total white
  blood count. An index of greater than 250 was considered positive.


See table 8 in this paper: "Field evaluation of a respiratory syncytial virus vaccine and a trivalent parainfluenza virus vaccine in a pediatric population." So they measure the eosinophils in the periphery not in the airways.

This article used histologic techniques: "Respiratory syncytial virus disease in infants despite prior administration of antigenic inactivated vaccine." Both articles are from 1969.

Newer studies used micropical techniques and FACS analysis, but these experiments were done with mice: "Respiratory synctial virus infection in BALB/c mice previously immunized with formalin-inactivated virus induces enhanced pulmonary inflammatory response with a predominant Th2-like cytokine pattern."