Khemet isn't a scientist but he thinks the speed of light in a vacuum is one of those things that's the same across all the planes, which suggests it'd probably be the same in Velgarth? He doesn't have a guess why, though. 

(One of the staff members at the museum overhears them and pulls out a table of the elements and wants to know if Leareth thinks it matches Velgarth.)

Oh, that's brilliant! Velgarth alchemists have isolated some elements but never came up with that kind of categorization. Leareth peers at it for a while. He doesn't see any obvious mismatches, at least? 

After a couple of hours at the museum Leareth is pretty ready for lunch. 

If it matches then they've got pretty much the same speed of light, a significantly different one would mean different elements would be stable, the staff member says. 

They can get lunch at one of several dozen restaurants within a few blocks; Khemet picks one out that does palm-sized miniature pizzas and orders a dozen different ones for them to share.

It's a very good food concept, Leareth decides, even if it still seems very weird to him that you can teleport into the afterlife and get lunch at a restaurant there. He makes pleasant conversation with Khemet about goings-on in both their countries and some of Aroden's upcoming plans for Cheliax. 

Khemet seems more relaxed here; maybe it's the lack of guards and servants or the fact that no one knows or particularly cares who he is.

His relaxation level is sort of contagious, Leareth thinks, because he too feels lighter and looser than usual. It's nice. He appreciates it. 

"I think I would like to return to the apartment for a bit," he says when they're done. "And then perhaps do another thing if there is time afterward." 

"Sounds good." And they can head back on over to the big tall building and go up to the rooms he rented.

Leareth flops onto the couch. It's not a very characteristic-for-Leareth motion but he feels like it, right now, and it's not like he intrinsically cares about being dignified when there's no one around whose opinions it'll affect. 

He sits down next to Leareth's head on the couch and runs his hand through Leareth's hair and reveals from a pocket that he sneakily bought some souvenirs at the museum of measurement.

Leareth is also startled about Khemet touching his hair! And separately surprised that it's very pleasant. He oohs appreciatively at the souvenirs. He's visibly a lot happier than he was this morning. 

Well, good, that was most of the aim here.

Leareth can tell that this was Khemet's aim and that he's pleased about it working, which is really nice, actually. 

He unflops after a while. Maybe they can ride the trolleys and people-watch for a bit until it's a reasonable time to go back to the material plane and see Aroden? 

They can do that. Khemet is going to have his arm around Leareth possessively for it.

Aww. Leareth is, again, mildly surprised and quite pleased about this. 

"You're going to have to take us home once you're done here, I spent almost all my spells on the thing this morning and don't have another Plane Shift."

"Of course. I - do not want to leave until we definitely need to, because I am guessing you will not be able to go around hugging me in public in the palace." Leareth is...kind of confused, though very pleased, about today and what it means for his working relationship with Khemet going forward. He should probably just ask but it also feels confusing what question to start with. 

"I feel - less like this, in Sothis, I am somebody and cannot forget it and I'm bleeding Law just a little bit whenever I let you ignore all the rules because I like you, which is entirely on me and not on you at all but it's not great for a carefree mood...I don't strongly expect anyone would care if I hugged you, it's not as if I'm not permitted to hug people, everything just gets - weighted down by all the rules and all the guards and all the -" Shrug. "You seem to really need hugs, though."

"- Oh. I - had not even considered that, I am sorry, I - had mostly been distracted from the rules by tracking other strategic priorities, but if Law means the rules are strategically relevant for you then I will be much more careful." And he thinks he'll find it easier to remember, if it fits more naturally into that category of thing, which his mind tracks almost as effortlessly as breathing, as opposed to - he's not even sure how he was categorizing it before, actually. "It seems simplest if you do not hug me in public, then, it would - not feel the same anyway. Though...it does seem to help. Much more than I expected." 

He frowns at the passing city. "I...am just trying to wrap my head around what sort of relationship we have going forward, because - well, it was already confusing before, I think, and now even more so." 

"Well, one option is that we are professionally friendly heads of state who, when schedules permit them to depart the Material Plane, go on dates. Another is that we cut this out so as not to distract you from wife-finding - for me, at least, being in love with other people does distract a lot from wife-finding."

Leareth considers it, seriously, for a couple of minutes. 

"I think the former would make me very happy. I - am not sure if it would distract from wife-finding. Probably I should ask Aroden what he thinks, or ask Parmida, since I suspect I would be similar to Aroden on this axis." 

"That makes sense."

"Honestly, I do not think I would be less distracted if we we not doing this and I were wishing we could." 

"Fair enough."

Then Leareth will lean on Khemet while they ride the trolleys and stare at the passing buildings and tide of people, and Leareth basks in the sense of good and right and feels like home. 

When he Gates them back, he's instantly a little less relaxed, but he's no longer radiating misery the way he was before their outing. 

He invites Hemaka to dinner with Aroden and Leareth and Parmida.