The drawing appeared in the Christmas Supplement of the British magazine The World (1900). It would be Beerbohm's first  caricature of Sargent. By the turn of the century, John had a commanding reputation as the preeminent portraitist. Here, Max lampoons him -- very much against character type -- as the conceited king of all artists. 

To understand the joke would be to understand Sargent's real personality. In a letter from Gertrude Bell to her mother, in March of 1904, might give you a glimpse: 

 . . .I have been making friends, in a modest way, with Sargent whom I like particularly. He is incredibly unspoilt, simple and natural and outgoing. I spent a morning in his studio the other day - he wanted me to see a portrait he was painting. I liked the portrait very much and the painter still more. . .   The truth is that when he is at his best no one can touch him, and he generally is perfectly aware himself when he is not. . .

(The Gertrude Bell Archive, letter: Sunday, 20 March 1904 To Florence Spring-Rice nee Lascelles -- Rounton Grange, Northallerton, North Yorkshire, Emgland.) 

Notes 
Special thanks to Wonsug Jung, of Korea, a friend of the JSS Gallery, for originally getting this image onto the net. 

• See more on Max Beerbohm
• See the Tate Gallery, London
• See the year in review 1900