Paul Delany, in (DHL’S NIGHTMARE, 1978), states that this painting, if exhibited in 1916,  would have stimulated the same disgust at aggressive sexuality that his “Creation of Eve” did (“Hunnish indecency,” and "buggery," were some of the stated impressions). Delany describes the men and women in the painting as sharing ambivalent sexual traits. "The heads and necks of the horses resemble giant phalluses"; the people in the painting "are all in pursuit of the horse's hindquarters on the left of the painting, which resemble the hindquarters of a man bending over rather than a real horse. The sexuality of the picture is utterly impersonal and sterile ...all in channelled into an endless round of mechanical futuility" (p.259).
He goes on to say the mechanical energy which DHL saw in the painting’s “soul-tearing obscenity” is partly due to “its atmosphere of bisexual violence.”

Lawrence had written to Gertler about the painting, “what a violent maelstrom of destruction and horror your inner soul must be . . .  it would take a Jew to paint this picture.” But he did not mention the sexuality Delany does, although he could have implied it.

There is some great web information on this fascinating artist and good friend of DHL:


 

Mark Gertler's Merry-Go-Round: Texts and  Images: great pictures and analysis of Gertler's career, the influence of WWI, and Gerlter as a moth circling round a flame, as DHL suggested.

Mark Gertler:  biography, links, large reproduction of "The Merry-Go-Round," quotes from DHL

from The Tate Gallery: view 14 Gertler paintings

the Dora Carrington Collection: "Carrington," the name she preferred, was Gertler's lover and fellow artist. Her correspondence is at the U. of Texas (Austin) Humanities Research Center. See also Gretchen Gerzina, Carrington (NY: Norton, 1989), and Noel Carrington [sic], Mark Gertler: Selected Letters (London: Hart-Davis, 1965).
 

Here is a perceptive analysis of the painting which I copied from the WWW last year. Unfortunately, I did not get the web location.  If anyone recognizes the source, please let me know.

 The viewer notes that virtually the entire canvas is filled. Sixteen men and
women are depicted on horseback within a carousel. All but one man are shown in groupings of three, and all but the single rider face the viewer frontally  or in profile. The elongated funnelshaped top of the carousel hides the tops of some riders’ heads. Near the bottom of the painting a crescentshaped frame continues around and in back of the horses
and riders, encircling them. Seven vertical poles appear to be attached to the top; they are visible behind the horses and riders and meet the bottom crescentshaped piece. The trios of figures are situated in such a manner that all are visible; they lean forwards or backwards alternately, allowing this visibility, while the horses are more nearly parallel. All of the
visible figures are openmouthed as are the horses. The costumes of the riders vary. Many wear hats, and some of the men are dressed in military uniform. At least one of the groups of riders is composed of clonelike figures. Riders in other groupings are not identical, but are similar. All of the figures look stiff or dummylike, and they appear to be gazing straight ahead. Strange banana shapes can be seen above and behind the top of the carousel; the poles previously mentioned do not appear to be connected to the horses.
Twodimensionally, the painting contains conflicting horizontal and vertical lines. The horses themselves project horizontal lines, and the horse grouping creates an oval shape; the vertical riders form another overlapping oval shape. The crescentshaped bottom and the top provide additional
horizontal lines which are met by the vertical poles. Threedimensionally the carousel forms a cylinder. All of the riders and horses are enclosed within this structure. Bright primary colors, blue and red, dominate in this painting. The texture of the canvas is smooth.

Deductions  This painting elicits an intense sensory reaction. One can imagine hearing the screams of the openmouthed riders, repetitive music, and the mechanical sound of the carousel at work. One can also imagine what it would feel like to be on this carousel. It would be like being pulled into a vortex. It seems to be only a matter of time before the
centripedal force of the mechanism will pull top and bottom together crushing the inhabitants of the merrygoround. Intellectual deductions focus on the experience of the riders. The patterned positions of the people
depict a total surrender of movement to the carousel’s mechanism, The expressions of the riders, the openmouthed smilelike grimaces, seem to indicate that the experience of riding on this carousel is one of agitation.

My emotional response to The MerryGoRound is quite unpleasant. When I imagine myself as a rider on the carousel, I feel dominated by the machine. I have little or no freedom of movement. My response to the experience is one of excitement, but not one of pleasure. I cannot leave the carousel
when I wish; essentially my experience is totally reactive (though I might not be aware even of this). As an observer of the scene I am troubled by the movement of the carousel. Watching the participants causes me to respond with a feeling of dizziness or a loss of equilibrium. One could
be mesmerized by this mechanized ride. The individuals on the carousel become a blur. The dominant colors of blue and red retain their conflicting values because they are intensely oppositional.

Speculation  The MerryGoRound seems to depict the horror of a society dominated by machinery or a mechanistic condition. The subjects of the painting are mindless people caught in and controlled by a mechanized environment. They retain little individuality. The varying clothing seems to underscore the power of the mechanistic experience by implying that these people were individuals before they were homogenized by this
experience. Their clonelike quality is more a matter of expression and  position than of dress or physical description. The entire mechanism of the carousel is sinister. The riders are caught between the heavy top
which appears to be moving downward in a crushing movement, while they experience a disorienting repetitive motion. The horses’ openmouthed expressions seem to reflect some evil intent. Even  the bananashaped clouds conform to the shape of the carousel, creating an aura of claustrophobia
and/or destruction.

The painting in its essence emphasizes sensational experience. The participants are not, however, engaged intellectually with this experience. The ride is a seemingly neverending climactic event—harsh in its denial of individual response. The very colors used in the creation of the
painting echo this harshness. They are not natural, but rather are garish, oppositional, and unnerving. The horizontal and vertical configuration underscores the harsh quality of the painting; one can almost
hear the sound of the grinding gears of the ultimate machine. The MerryGoRound thus depicts the conflict and pain of a mechanism given complete freedom. The human participants appear to have lost intellect, heart, and soul; they have become more extensions of the machinery itself, and all seems hopeless.

Does the artist intend to warn us of man’s ultimate surrender to machine? Are we fast becoming rats on a turning wheel? Does the world feel more manmade and less natural? People are in hot pursuit   of  marketable pleasures. Perhaps Gertler wished to warn twentieth century man of the “downside” of scientific progress. The MerryGoRound seems to portend the demise of individuality and humanity.