A convergence of evidence is the same as a consilience of inductions -- where two or more separate and distinct sets of facts mutually reinforce each other. Such convergence allows the student of history to more confidently defend a particular version of an historical event as likelier to have occurred this way rather than that; its absence means having to fall back to some extent on speculative reasoning, on conjecture, to decide what might have happened -- and why. It's a sound, but hardly failproof, method of getting near the real version of events. For example:
As "proof" of the homicidal gassings said to have occurred at Dachau, in the trials of accused Nazi war criminals Nuremberg prosecutors were able to point to the "gas chamber" itself, refer to an official American congressional report of an on-site investigation, and to cite the "eyewitness" testimony of the onetime camp doctor, Franz Blaha. Yet, claims of death by gassings at Dachau are now largely dismissed as false, and so reams of what was once touted as damning evidence have become worthless. Many such Holocaust extermination claims, once widely accepted, have likewise been quietly discarded.
Take the stories of the Treblinka "steam chambers," a set of bizarre allegations now part of the Nuremberg record. At Nuremberg, American prosecutors submitted a report (exhibit USA-293) charging that Jews had been killed in Treblinka "by suffocating them in steam-filled chambers." 
One of the American prosecutors referred to it in an address to the Nuremberg court on December 14, 1945. The report, later added to the official Nuremberg trial record as document PS-3311, bolstered a November 1942 "eyewitness" account sent to London via the Warsaw ghetto underground organization that described masses of Jews being exterminated by the "steam pouring out of ... pipes." 
Today, despite this so-called convergence of evidence, no reputable historian still claims the stories of death-by-steaming
at Treblinka are factually true.
Although, the allegations were revived in 1979 and 1985 by the Anti-Defamation League of B'nai B'rith and included in a publication entitled The Record: The Holocaust in History. Among the several documents the ADL reproduced was an August 8, 1943 article from the New York Times claiming the Germans had murdered two million Jews in Treblinka by steaming them to death. This despite the fact no one at Nuremberg was ever convicted of the killing of masses of Jews by employing the grisly steaming method.
What could have motivated the ADL to revive this false, rather lurid old tale, I wonder? Was it simply “too good" to abandon?
1. IMT, Trial of the Major War Criminals ("blue series"), vol 3, p. 567-568.
2. "Likwidacja zydowskiej Warszawy, Treblinka," Biuletyn Zydowskiego Instytutu Historycznego (Warsaw), January-June 1951, pp. 93 -100.
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