Here is Sargent's Carolus-Duran again, sitting patiently. Below is his right hand.
And below, I have superimposed some lines on that hand.
Theses are the major lines in the passage. Do you see how rhythmic they are? They all are concave, their obvious purpose is to enclose the forms within, but they also bear a relationship to one another. As each line swirls around the hand they echo and offset the movement of the other lines.
The longest and most important line runs along the thumb side of the hand, it is juxtaposed against a straight line, the cane. Notice how the squareness of the first finger also carries out this straight line.The contrast between the two gives variety and grace. These lines were installed by Sargent to give rhythmic grace to his painting. The appearance of the actual hand was distilled and refined by the artist into an abstract arabesque of lines that set one another off, not just delineate the form.