Hi Coleman,
Finally!
I founded the Spencer Shooting Society (SSS) back in 2005, and have been the sole Moderator ever since. During these 15+ years I have only come across 9 exact Spencer serial #s. Your Spencer Carbine 18513 is #10. Your Spencer Carbine serial # 18513 WAS ISSUED to Company K, 11th Michigan Volunteer Cavalry on August 17, 1864, as noted in my SRS Research Books.
It would be great if you would post photos of your Spencer on the SSS Forum.
I will add your username/alias to our membership list.
Thank you for joining SSS and for contacting me.
Two Flints, Moderator
Spencer Shooting Society