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This illustration is from the Little Bright Eyes Storybook, pictured below. Published in 1901, it contained art by numerous artists of the day, including great-grandfather Chester Loomis.
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I think you can see from this photo that Chester's mother-in-law Arvilla Dana (Sara Dana's mother) is the inspiration for the grandmother in the illustration.
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The book is for sale on ebay at the moment --
click here to see the listing. Many thanks to Steve, the ebay seller, for sending a scan of the illustration.