The painting: HOLYHEAD AND KINGSTOWN MAIL PACKET "PRINCE ARTHUR"—400 TONS—PERIOD 1850-60. was the property of the City of Dublin Steam Packet Company, which was liquidated in 1924.
They used this ship on the DunLaoghaire-Hollyhead mail route from 1850, when they were awarded the contract to 1859 when the acquired replacement ships
So the painting has to be earlier than 1859
In 1891 a book was published "A Hundred Years by Post, by J. Wilson Hyde"
It incorporated this image of the painting.
The book was published by Project Gutenberg at
http://www.gutenberg.org/files/27688/27688-h/27688-h.htm#Page_115
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