A new estimating procedure is suggested to estimate the population size in
a capture-recapture experiment. The capture intensities for first-capture a
nd recapture are allowed to be different and time dependent but they are as
sumed to be proportional. It is shown that the information on the proportio
nality constant is crucial to the estimation of the population size. Sensit
ivity analysis with a misspecification of the proportionality constant is c
onducted. The method has also been extended to the case with an unknown pro
portionality. A real example is given.