Today being Father’s Day, this week’s choice of picture is Thomas Gainsborough’s tender portrait of his daughters Mary, aged six, and Margaret, aged four or five: “Molly and the Captain”, as he nicknamed them.

The Painter’s Daughters Chasing a Butterfly is a loving depiction of carefree youth and innocence but a faintly troubling picture too, charged with feelings deeper than sentimentality alone. The two girls holding hands are radiant in their silk dresses of silver and yellow (Mary’s dress being one of the brightest passages of that unreliable colour, Naples yellow, in all of eighteenth-century painting, thanks to the unusual purity of Gainsborough’s pigments); but we find them in a dark wood, under a stormy sky, with dusk approaching.

The day is short and childhood quickly passes: a common enough feeling for any parent to have, but Gainsborough has caught it with absolute precision and authenticity, choosing as his subject one of those moments when childhood seems to be passing even as one looks. With an attentive father’s keenness of observation, the artist notes the difference made by even the small gap of age that separates the two girls. Mary, the elder of the two, has already developed a certain air of circumspection and self-consciousness, implicit in her careful gaze, her restrained posture and the nearly adult, upright carriage of her head. Looking across to her from the more impetuous, instinctive figure of her little sister, Margaret, whose arms and legs seem somehow less tense and organised, and whose face still has a certain toddlerish chubbiness about it, one might almost be looking at a single girl at different stages in her life. Between the two the artist has left his picture almost blank, a void of scribbled underpaint marking as it were not space alone but also the oblivious passage of time. It is as if Gainsborough has made visible the very process of growing up.

He has also preserved his own ambiguous attitudes towards it, paternal pride mingled with the sense that each new stage in a life, each new level of maturity attained, also marks a kind of small death, the loss of a littler person no less loved. The painter has perhaps put some of his own feelings into the expressions of Mary and Margaret. Mary has a faint air of foreboding. Margaret reaches out towards a butterfly, traditional symbol of life’s fragility and brief duration, with an expression of little-girl concentration which seems tinged with melancholy.

In 1756, when the picture was done, Gainsborough was living in his native town of Sudbury in Suffolk, where he earned a modest wage as portrait painter to the local gentry. He had already created the masterpieces of his early, highly finished and somewhat Dutch manner, including the National Gallery’s well-known picture of Mr and Mrs Andrews on their estate. But he was growing dissatisfied with such small-scale pictures, created in a style which was in danger of turning formulaic, and he was striking out towards something quite new: a freer and more lyrical art, informed as much by the rhythms and energy of nature as by appearances alone, and characterised by an improvisatory and sketchy handling of paint which blurred the distinction between the “finished” and the “unfinished” picture to an unprecedented extent. Gainsborough’s new approach was to bring him fame and considerable fortune when he moved to fashionable Bath and, later, London. It was also, quietly but profoundly, to transform the very texture of English (and French) painting. The Painter’s Daughters Chasing a Butterfly, an uncommissioned work painted almost to the scale of life, was one of Gainsborough’s earliest private experiments in this new, unconventional but instantly compelling style. So this memorial to the gradual maturing of his daughters marked a new phase in the artist’s life too.

No one has written more interestingly about the subtleties of Gainsborough’s later painting style than his contemporary Sir Joshua Reynolds, who seems to have been seduced by its beauty and troubled by its originality in almost equal measure. Reynolds noted Gainsborough’s habit of painting at night, by candle-light, which may explain the unusual luminosity of the girls’ faces and rich nocturnal colouring of their dresses. Reynolds also tells us that “from the fields Gainsborough brought into his painting room, stumps of trees, weeds, and animals of various kinds”, which accounts for the picture’s one small and unintentional departure from naturalism. As Judy Egerton notes in her impeccable catalogue to the National Gallery’s British School paintings, while Gainsborough wishes us to believe in its ability to fly away, it is clearly a dead specimen posed on a thistle. “Its wings, which in life would have been held vertically, have drooped and are unnaturally folded under the body.”

The most arresting feature of Gainsborough’s late style is perhaps its flirtation with a look of “unfinish”. Reynolds described it well, speaking of “all those odd scratches and marks, which, on a close examination, are so observable in Gainsborough’s pictures, and which even to experienced painters appear rather the effect of accident than design”. This effect – which, as he also pointed out, was an entirely conscious stratagem on Gainsborough’s part – is very noticeable in The Painter’s Daughters Chasing a Butterfly. Several areas remain barely indicated, yet without in any way impairing the illusion as a whole. Reynolds explained Gainsborough’s love of sketchy effects as a way of allowing free play to the imagination of the onlooker, but I wonder if it does not have a more precise significance in this particular picture. Having his two girls emerge, as they do, from an inchoate ground, the painter was perhaps proposing an equivalent, in his own, visual language, for the condition he sought to describe. He saw his daughters as “unfinished” creatures, changing and growing before his very eyes. He painted what they looked like but he also evoked their elusiveness and, fond father that he was, gently lamented it.