The rhythm of the island is described as follows:
"the slow sing from dawn to quick dusk," which suggests perhaps that the mornings felt slow, but as night approached, they terrors began to come upon the boys. As the sun rises, the heat becomes something to be escaped it "became a blow that they ducked, running to the shade and lying there, perhaps even sleeping."
The description goes on to talk about the weird things that happened at noon, they saw things that didn't seem real, mirages and visions that came to the boys thanks to the incredible heat.
Then at night they "suffered unkonw terrors... and huddled together for comfort." They divided their days up according to the weather and the sun and the various things appropriate to each part of the day.
In Lord of the Flies, William Golding's description of the atmosphere of the island as a "rhythm" has two effects within the novel as a whole. First, it sets the mood of the group of stranded boys. Throughout the chapter, Golding mentions various quasi-musical sounds, including Jack's celebratory hunting chant and the boys screaming around the pig roast. The idea of the group having a rhythm creates an atmosphere that is somewhat tribal and intimates the notion of a tribe's social organization. This brings the reader's attention to the way the group structure is developing and changing as the boys spend more time on the island.
Secondly, Golding's use of the word "rhythm" shows that the routine of the boys is becoming more established. At this point in the book, the boys have been on the island for a while, and they are no longer in the disorganized panic mode of arrival. People have certain roles and activities that occur on a regular schedule in an organized way, like a rhythm.
In Chapter Four, what's interesting is that certain routines, or rhythms, are overtaking others. In this chapter, the signal fire goes out, and the boys miss an opportunity to signal a boat in the distance. The fire goes out because the boys are too occupied with making their first kill on a pig hunt. The signal fire going out represents the boys' shift of attention from civilization and rescue to savagery and killing. By naming the rhythm of the island, Golding brings the reader's attention to the boys' routines, thus underlining the social changes that are occurring within the group.
The "rhythm of the island" is the boys daily routine. They are used to idyllic mornings, roasting hot afternoons and nights filled with nightmares.
Hope this helps!