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Webster 1913 Edition

adv.

In an irrational manner.

Boyle.

adv.

Without reason; in a manner contrary to reason; absurdly.

irrationally ‎(comparative more irrationally, superlative most irrationally)

In an irrational manner; without reason; in a manner contrary to reason; absurdly.

in an irrational manner

irrationally in The Century Dictionary, The Century Co., New York, 1911
irrationally in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913