I have been reading the posts concerning swarming and when should you expect to see eggs/larvae in the old remaining hives. Also, I have been studying your Bee Math chart.
I have two 2nd year hives that were really cooking with bees. After splitting the strongest hive, I have had four swarms (suspect two swarms from each hive) beginning on April 6 thru April 14. I was able to capture all four swarms but lost one to the scout bees putting together a good story and convincing them to leave. I'll try your suggestion of the lemongrass oil next time!
Since a swarm generally happens a couple of days before the new queen emerges, should eggs/larvae be seen about 14 to 18 days after the swarm (difference between Laying in 28 days and Emerging in 16 days +- a few days per the Bee Math chart)?
This in no way is an insult to Michael Bush who has been a marvelous member for a very long time. But I'd like to point out two things (said very friendly of course) here goes:
1) By addressing it to MB directly, you start off by throwing "Collectively" thousands of years experience between the members on the forum - most people will just skip over it saying "If my knowledge, and ability to anwser you isn't good enough, then why as a commercial beekeeper for 40 years do you think I can't answer a question - it isn't the Michael Bush Show after all" (note, that character is ficticious and was not intended to represent any member here. But the point is the same, you have a resource of nearly 4000 members and I'm sure you can draw conclusions from repliies from our membership and it is a shame to waste that pool of knowledge and experience.
2) if you have a message for a particular member - then send them a private message - doesn't get much simpler and usually catches the member's eye a whole lot quicker.
I'm just passing this on, and not necessarilly to you, but as an example that you have here a great opertunity to collect data that would make you a better beekeeper (not saying you aren't already) by weighing the info and conclude feasible answers. It is the best way to do it.
Hope that was enlightening, it surely is not a bash toward you or Michael Bush: I just like members to understand the opertunities we have here and hate to see anyone miss the boat (especially date eccential questions) if Mike was on vacation or lecturing somewhere or God forbid tied up over something serious - you may have been out of luck. I won't even try to list the huge group of bee savvy people here who can also tackle that question, but you placed yourself in a box that really limited your responces. I can guarentee that a few tons of beekeepers saw your post, felt ditzed and even knowing the answer kept on walking by. This was written to be helpful, I surely hope you took it that way :) Best Days in Beemeeping!!!