Doctors Crisp and Henkle are the best two medicos (i.e., medical doctors) in the Queen's Society. The Society's leader Lord Bunstable assigns them both to examine the recovered remains of murder victim Tobias Homlomium (also spelled "Homnomium"). He does this because of their known antipathy towards one another, hoping to prevent any possible collusion.
Whether or not this gambit is successful is unknown; in the process of the investigation, they are both murdered in turn by Trogulus, who also tampers with the remains; he has no involvement in the original murder, but is trying to prevent the summoning of Red (extradimensional being) by giving the impression that Homnomium is still covertly alive. We also don't know for sure Crisp and Henkle were supporting that ultimately-successful summoning, but evidently pretty much everyone else in the Society dome is.
Queen's Spark Trelawney Thorpe later tries to about this whole series of events, but — except to excuse himself by referring to them all as evil cultists — no time! Oh well! Bye!