We model the observed size and brightness of the VLBA radio core of the jet in Cygnus X-1 to derive an expression for the jet power as a function of basic jet parameters .
We apply this expression to recent constraints on the jet power from observations of a large scale shocked shell around the source by Gallo et al .
2005 , which leads us to a set of alternative conclusions : either ( a ) the jet contains large amounts of protons : ( \geq 2000 protons per radio emitting electron ) , ( b ) it has a very low volume filling factor of f \lesssim 3 \times 10 ^ { -5 } , ( c ) the steady , radio emitting VLBA jet is not the source of the kinetic energy powering the ISM shell , or ( d ) its asymptotic behavior differs fundamentally from a broad set of plausible analytic jet models .