Building on what's already been said by Tremyfro, and going full circle.
Surely the defining characteristic of a cast swarm in that passage is that a "cast is smaller" ?
MikeT has described what happens with one colony that might produce more than one swarm so ...
Start with one colony of bees that is preparing to swarm - there are queen cells. Once the first queen cells are sealed the colony is likely to swarm.
1) The first swarm to leave will contain the old, laying, mated, queen and about half the bees. This is the prime swarm. It is likely to contain enough bees and a laying queen, so the new colony should be immediately viable and will more than likely build up sufficient numbers for winter as well as giving some honey.
This is the 'load of hay' swarm.
2) Two or three days after the a new queen emerges from her cell, provided there are other maturing queen cells, the colony is likely to swarm again. This will be before the new queen has taken her mating flight(s).
This swarm will contain an unmated, virgin, queen and also about half the bees from the colony. This swarm may be about a quarter of the size of the first swarm because it will leave only 8-10 days after the prime swarm and will take half of the bees. (Half of half a colony is a quarter.) Okay, some bees laid by the old queen will have been emerging from their cells, but no new eggs will have been laid since that queen was taken away in the first swarm, and old foragers will have been dying off.
The queen in this cast swarm may take two or three weeks to start laying, depending on local conditions, so it could be as long as 9 weeks from swarming (3 weeks before the queen lays any eggs; 3 weeks eggs to bee; 3 weeks inside before foraging) before there are any new active foragers bees. That's over two months, and tests the viability of the colony.
This is the 'silver spoon' swarm. (Even now the price of a 'load' of hay would buy several silver spoons.)
Would that not mean that if the first swarm was headed by a virgin its a prime as long as its the biggest ?
No, because a prime swarm
always contains a mated queen. It is the best swarm to get because the queen will start laying immediately.
A swarm containing an unmated queen will take a long time to get going, it is a cast. Sometimes it is 'cast' (thrown) in with a colony that already contains a mated queen.
By the way, a swarm is not 'led' by the queen. The workers make the decisions. They reduce the current, and laying, queen's food supply so she slims down to a weight at which she can fly. They make her fly with the swarm, not the other way round.
And separately ...
Wally Shaw's booklet "There are queen cells in my hive", really is worth reading - and worth reading several times until the information sinks in.
http://www.wbka.com/wp-content/uploads/2015/02/a012queencells.pdf