I cannot think of anything rather a letter that you receive on an even date. )
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MrPedanticI think it means "of the same date", in contracts, etc. So if his letter and your reply are both dated 23rd December, they are "of even date".It is more often used in deeds and contracts than correspondence. In a letter it would be more usual to say "dated today" or "of today's date".
MrP