The passage is particularly difficult so we give two different translations below.
There is a discussion of Plato's description by D'Arcy Thompson in our archive. See Thompson Plato Planets
Translation by B Jowett of The Spindle of Necessity:
Now when the spirits which were in the meadow had tarried seven days, on the eighth they were obliged to proceed on their journey, and, on the fourth day after, he said that they came to a place where they could see from above a line of light, straight as a column, extending right through the whole heaven and through the earth, in colour resembling the rainbow, only brighter and purer; another day's journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above: for this light is the belt of heaven, and holds together the circle of the universe, like the under-girders of a trireme.
From these ends is extended the spindle of Necessity, on which all the revolutions turn. The shaft and hook of this spindle are made of steel, and the whorl is made partly of steel and also partly of other materials.
Now the whorl is in form like the whorl used on earth; and the description of it implied that there is one large hollow whorl which is quite scooped out, and into this is fitted another lesser one, and another, and another, and four others, making eight in all, like vessels which fit into one another; the whorls show their edges on the upper side, and on their lower side all together form one continuous whorl.
This is pierced by the spindle, which is driven home through the centre of the eighth. The first and outermost whorl has the rim broadest, and the seven inner whorls are narrower, in the following proportions - the sixth is next to the first in size, the fourth next to the sixth; then comes the eighth; the seventh is fifth, the fifth is sixth, the third is seventh, last and eighth comes the second.
The largest (of fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) coloured by the reflected light of the seventh; the second and fifth (Saturn and Mercury) are in colour like one another, and yellower than the preceding; the third (Venus) has the whitest light; the fourth (Mars) is reddish; the sixth (Jupiter) is in whiteness second.
Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth.
The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note.
The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens - Lachesis singing of the past, Clotho of the present, Atropos of the future; Clotho from time to time assisting with a touch of her right hand the revolution of the outer circle of the whorl or spindle, and Atropos with her left hand touching and guiding the inner ones, and Lachesis laying hold of either in turn, first with one hand and then with the other.
Translation by D Lee of The Spindle of Necessity:
After seven days spent in the meadow the souls had to set out again on the eighth and came in four days to a place from which they could see a shaft of light stretching from above straight through earth and heaven, like a pillar, closely resembling a rainbow, only brighter and clearer; this they reached after a further day's journey and saw there in the middle of the light stretching from the heaven the ends of the bonds of it; for this light is the bond of heaven and holds its whole circumference together, like the swifter of a trireme.
And from these ends hangs the spindle of Necessity, which causes all the orbits to revolve; its shaft and its hook are of adamant, and its whorl a mixture of adamant and other substances.
And the whorl is made in the following way. Its shape is like the ones we know; but from the description Er gave me we must suppose it to consist of a large whorl hollowed out, with a second, smaller one fitting exactly into it, the second being hollowed out to hold a third, the third a fourth, and so on up to a total of eight, like a nest of bowls. For there were in all eight whorls, fitting one inside the other, with their rims showing as circles from above and forming the continuous surface of a single whorl round the shaft, which was driven straight through the middle of the eighth.
The first and outermost whorl had the broadest rim; next broadest was the sixth, next the fourth, next the eighth, next the seventh, next the fifth, next the third, and last of all the second.
And the rim of the largest and outermost was many-coloured, that of the seventh was the brightest, the eighth was illuminated by the seventh, from which it takes its colour, the second and fifth were similar to each other and yellower than the others, the third was the whitest, the fourth reddish and the sixth second in whiteness.
The whole spindle revolved with a single motion, but within the movement of the whole the seven inner circles revolved slowly in the opposite direction to that of the whole, and of them the eighth moved fastest, and next fastest the seventh, sixth and fifth, which moved at the same speed; third in speed was the fourth, moving as it appeared to them with a counter-revolution; fourth was the third, and fifth the second.
And the whole spindle turns in the lap of Necessity. And on the top of each circle stands a siren, which is carried round with it and utters a note of constant pitch, and the eight notes together make up a single scale.
And round about at equal distances sit three other figures, each on a throne, the three Fates, daughters of Necessity, Lachesis, Clotho, and Atropos; their robes are white and their heads garlanded, and they sing to the sirens' music, Lachesis of things past, Clotho of things present, Atropos of things to come. And Clotho from time to time takes hold of the outermost rim of the spindle and helps to turn it, and in the same way Atropos turns the inner rims with her left hand, while Lachesis takes inner and outer rims with left and right hand alternately.