Marwick writes:
The phrase is ... borrowed from the distinguished American historian of science, Henry Guerlac ... `Witting' means deliberate or intentional; `unwitting' means unaware or unintentional. `Testimony' means evidence. ... it is the writer, creator, or creators of the document or source, who is, or are, intentional or unintentional, not the testimony itself ... Witting testimony is the information or impression that the person or persons who originally compiled the document or source intended to convey ... or record. ... Unwitting testimony is evidence which historians find very useful, but which the originator of the document is not conscious might be conveyed to later historians, for it would be known anyway, or taken for granted, by contemporaries. (Marwick, The Nature of History, p 216 and 218.)