[Avodah] zman hadloko erev Shabbos and motzoei Shabbos

[Akiva Blum]

I wrote:
   >
   >> I don't understand this cheshbon.
   >> Accoring to RT, visable shkiah is irrelavant. It should follow that 
   >> calculating the length of a 'hour' would include the 72 minutes after 
   >> shkiah and 72 before haneitz. Total minutes in a day is 864 (instead of 
   >> 720 acc. To Gra).
   >> One hour is 864/12=72 minutes. One and a quater hours is 72*1.25=90 
   >> minutes. So plag is 90 minutes before 72 after shkiah which is... 18 
   >> minutes (zmanios, in the winter)  before shkiah.
   >
   >See Biur Halocho 261 d"h "lehakdim" who explains very clearly.
   >
 Let me try again.
My kashe is based on that biur halocho. He claims the difference between RT which is 1 1/5 hours after shkiah and plag which is 1 1/4 hours before tzeis is 1/20 of an hour. It would seem that you are mixing hours to reach 3 minutes.
RT can be calculated based on 40 mil from sunrise to sunset or 40 mil from dawn to tzais. To achieve a figure of 72 minutes, you must be working from sunrise to sunset: 40 mil in 12 hours is 72 minutes for 4 mil. The other cheshbon would arrive at 90 minutes or even 96.
The biur halocho works with plag 1 1/4 hours before tzais. This, I contend, must be 1 1/4 of 12 "hours" from dawn to tzais if we are to use it working back from tzais.Plag hamincha is a portion of the day. Thus 1 1/4 "hours" is  ((12 hours+8 mil)/12) * 1 1/4 which is 93.75 (if 4 mil is 90 min) or 95 minutes (if 4 mil is 96 min), or 90 (if 4 mil is 72 min)  leaving the difference between plag and shkiah at 3 3/4 minutes (90) before shkiah or one minute (96) after shkiah.
However, if RT is at 72 minutes, as you assume, then 1 1/4 "hours is ((720+72+72)/12) * 1.25 =90, and plag is18 minutes before shkiah.

If the biur halocho is also using 72 minutes, it appears that he is mixing "hours"; those from dawn to tzais for plag, and those from sunrise to sunset for 72 minutes.

Akiva