William lead Sherlock to the living room and gestured to the corner, a discreet bin there for convenience. Sherlock gave him a large smile as he walked over and dropped the burnt cancer stick into the trash and tuned back to William.
"So, what now Liam? I'm no longer dripping water everywhere, I've had a smoke and it's very much still raining." William hummed,
"I can see those things are indeed true. I had been planning on simply reading tonight, and of course dinner later with my family."

James Moriarty was going to meet and converse on his plans as the Lord of Crime. that would have to wait for another day.

He lead Sherlock to the library, a grand room beside his chambers. He spent much time in both rooms and them being adjacent had always proved helpful. He gestured to the walls full of books,
"Feel free to read anything that catches your interest." Then, with a charming smile he turned and made his way to an area he'd reserved for mathematics, textbooks, history books on the development and many books on the various theories of the mathematics world and physics lined these shelves. Many of the non-textbooks held much knowledge on science as well as mathematics, considering how intertwined the two are.

He picked up one of the newer books he'd had imported and settled in an armchair. Maths relaxed him, and with his fascination friend in his home he needed something to help him wind down a little. Sure, Sherlock didn't make him tense or uptight or anything. William loved being around him already don't get him wrong, but the predictability of math was grounding in a time when a variable he couldn't predict was currently roaming the room he occupied.

Opening the book to the beginning he began reading, letting his mind run analysis on each problem presented and compare his solutions to the ones given. Seeing where they went with the process and how it differed from where he did. Coming to understand where they came from and calculating how the two answers he now had gave new insight to the overall picture the problems painted. He was invested. This group of mathematicians were tackling problem types that many would call impossible, or ludicrous, but William loved math for it's unchanging nature and how one could study it infinitely and still find new relations from it to the world.

Being so engrossed in his book he failed to remember he sorta, kinda, really-fuckin-needed-to pay attention to his surroundings. He was startled from his book when he heard a deep, throaty grown from an armchair just in front of him and to his left.

"Sherlock?" He'd honestly forgotten the man was there at all. He felt a little guilty.

"Mhm. That's my name."

"Are you alright?" Said man turned to him with a deadpan stare and sleep deprived grin, his hands were shaking. He was gritting his teeth and fighting the urge to bounce his leg.

"No. You confuse me Liam. You truly do." The man had turned to face him more directly, head propped in his hand. "You've been sat there, nearly still as a bloody statue all day, just reading maths." The man sounded mildly manic, with undertones of awe, adoration, disbelief, fondness, affection... The raven haired man really gave away a lot in his voice. His eyes glinted in the soft candle light. William glanced to a window, the sun had long set.
"Well. It seems time has gotten away from me, do excuse how bad a host I have been won't you?" Sherlock just gave a hearty laugh and slapped his thigh.
"Good man Liam. I will need somewhere to sleep though. Unless you expect me to sleep here, though I doubt you're that sort of person." William gave him a soft smile and beckoned him to follow as he memorised which page he was on and returned the book to it's proper spot.

Walking to the door placed just by his math section of the library, he pushed it open and entered his bedroom. Gesturing for Sherlock to go ahead he followed the man in. Fetching some loose pajamas from his closet he handed them to Sherlock and pointed him towards his en-suite to change in. William himself changed into an oversized shirt made from soft material and black boxers. Climbing into his bed he arranged the pillows for two.

Once they were both settled on their respective sides of the bed, with no small amount of inappropriate jokes made (by Sherlock), William offered a quiet goodnight as he turned off the lights.