The Theorem of Mutual Confirmation (specifically referring to the stock market) states that the movements of the Dow Jones Railroad Average and the Dow Jones Industrial Average must be considered simultaneously. Reliable conclusions cannot be drawn until the movements of both indices confirm each other. Observing the movement of one index alone without verification from the other is highly prone to misleading interpretations.

Many analysts overlook the profound implications contained in Dow's Tenth Theorem. The true meaning of Dow's Tenth Theorem does not lie in simply observing the correlation between two sets of data, but rather in the deep theoretical question Dow raised: a truly healthy and promising stock market must exhibit a consistently positive trend in both the production sector (represented by the Dow Jones Industrial Average) and the transportation sector (represented by the Dow Jones Railroad Average, later renamed the Transportation Average). Any negative trend in either sector signals serious problems ahead for the stock market.