This is an interesting question, because in medicine you can find a similar problem, that is how to measure the so-called residual volume of the lung (which is the remaining volume after maximun expiration). The problem is, that you can't measure such volume directly, because you can never pull it out of lung, or in your case, from the cylinder. In medicine one can use a sort of dilution method: if  you have a closed circuit, at which you can determine the volume of all external components (your pipes,  reservoir etc.), then you can determine the residual volume by adding a second gas into the circuit. With the known volume of the external components you get a concentration (the ratio of the added volume to the kown volume). Leaving it for some time in the "closed" circuit (or you do some strokes) the added portion will also interfuse with residual volume) and you get a new concentration (the ratio of the added volume to the total volume). Now you can calculate the residual volume from Vres = C1xV1/C2-V1. It's not an easy way because you need some equipment for measuring gas concntration, but hopefully this may help.

Mr. Michael Scharfschwerdt  Thank you very much to  your help.  but please tell me C1&C2 mean concentration of gas.thank you very much again

If you know the pressure before and after compression as well as the displaced volume you can estimate the dead volume (compression volume) using an isentropic (or polytropic) compression model. P1V1n=P2V2n, where 1 refers to the state before compression and 2 refers to the state after compression. If heat losses and leakage are negligible, n=1.4, otherwise somewhat lower.