This lovely painting of the artist's daughter is also one that clearly shows that the artist knows what a piece of knitting looks like. Mary Isabella is holding fabulously long needles (not "parlour style"), with the ball of wool in a little basket on her arm. The knitting looks like a brioche stitch, very popular in the 1840s and 50s!
Maria Susan Chewett (1836-1918), née Ranney, knits in the English or "drawing-room style," with the right needle extending over the hand, much like holding a pen; this style was the "posh" way of knitting from some time during the Victorian period to the 1940s at least. Mrs. Chewett was born in England, spent much of her married life in Canada (where her six children were born), and returned to England to live out her widowhood with her artist son and a number of his siblings.
Note that this is not what is now generally called English-style knitting, in which the wool is held in the right hand and "thrown" or wrapped around the working needle (as opposed to continental-style knitting, in which the wool is held in the left hand and "picked" or scooped up by the working needle) -- here it has more to do with the way that the needle itself is held.
This style of holding the needles was almost certainly much earlier than this Edwardian-ish painting, but for the time being this post will have the "earliest known usage" label -- more on the "drawing-room style" to come ...
Larsson conveys the texture of knitted wool wonderfully even in a small watercolor -- though as knitters we'd perhaps like to see that interesting hem in more detail! This looks like a typical 1910s jumper, possibly with a finer one in cream underneath, or the grey has a cream collar in addition to the cream band around the wrists and possibly the hem as well. The cream color matches with the girl's hat, probably a felted knit much like this timeless one from Knit Picks.
A POLKA COAT, FOR A CHILD.
Cast on twenty-five [sic, 225] stitches, which will make seventy-five ribs, in the Brioche stitch, which is done by bringing the wool forward, slipping a stitch the purl way, and knit two together; bring the wool forward, knit twenty-four rows, or twelve turns of white; then commence the scarlet, by leaving eighteen stitches on each side, knit twenty-four rows, or twelve turns of scarlet; then begin to take in, which is done by knitting the first thirty on each side, without decreasing; then bring the wool forward, slip one stitch, and knit five together; repeat this till within thirty on the other side, which, knit without decreasing, until you have only forty ribs, or one hundred and twenty stitches; knit forty-eight rows, or twenty-four turns, in this manner, still leaving the white on each side; put thirty stitches on another needle for the front, knit those backwards and forwards for thirty-six rows, or eighteen turns; then knit all the stitches but one rib, turn back, and finish the row, and so on, leaving one rib more each time, till it is the proper length for the shoulder. Cast off, but be particular that the slanting side is not in front; finish the other side in the same way, then take up the stitches for the back; knit thirty-six rows, to correspond with the fronts for the arm-hole; then knit backwards and forwards, leaving one rib each way, until it is the same length as the slanting part in front, which are to be joined together; cast off; now take up the white stitches on each side, and knit till it is long enough to go up the sides; for the sleeves; cast on seventy-two stitches, knit thirty rows, then twelve more, leaving one rib on the one side to form the wide part; for the collar; cast on seventy-six stitches, and knit twelve rows, leaving one rib on each side; then sixteen rows of white; cast off; cast on eighteen stitches for the cuff, and knit till it is long enough to go round the bottom of the sleeve; twist a cord of the same coloured wool, and put in the waist behind, with a tassel at the ends; the same under the collar. These may be done in four-thread fleecy, but they look much better in double Berlin wool, No. 9 pins, by the Eagle gauge. For a lady's, you must cast on stitches in proportion, and larger pins.