[Math] Tolkien's printed/published books as different scales

This is fun. I never was a fan of Tolkien, but that caught my eye.

This reminds Celsius to Fahrenheit conversion formula.

Shift, multiply and shift again.

Indeed, Tolkien's books can be seen as different scales!

Other popular books published at different times can be seen as scales too.

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                        NOTE ON REFERENCES 

      There is a certain amount of cross-referencing among the questions 
on both the FAQ and the LessFAQ lists.  Any questions so referred to are 
specified by the list, section, and question number.  Thus, the first 
question in the Hobbit section of the FAQ, "Were Hobbits a sub-group of 
Humans?" would be referenced as (FAQ, Hobbits, 1).  Note that the 
section "Tolkien And His Work" is referred to merely as "Tolkien" and 
the section "General History of Middle-earth" is referred to merely as 
"General".  E.g. the question "Who was J.R.R. Tolkien anyway?" is (FAQ, 
Tolkien, 1) and the question "What exactly happened at the end of the 
First Age?" is (LessFAQ, General, 1).

      Sources for quotations have been provided in the form of volume 
and page numbers; the specific editions utilized are listed in the next
paragraph.  For those occasions when the proper edition is not available 
(and the conversion table below is not applicable) the page numbers have 
been roughly located according to chapter, sub-section, or appendix, 
whichever is appropriate.  For example,  RK, 57-59 (V, 2) refers to 
pages 57-59 of Return of the King and further locates the pages in 
chapter 2 of Book V.  PLEASE NOTE the distinction in the case of _Lord 
of the Rings_ between *Volumes* and *Books*.  LotR is comprised of three 
Volumes (FR, TT, and RK) and of six Books (I - VI), which are the more
natural divisions of the story into six roughly equal parts.  There are
two Books in each of the Volumes.  Other sample references are below.

      References to _The Hobbit_ are from the Ballantine paperback (the 
pagination has been the same since the 60's.  All other references are 
to the HM hardcovers.  Sample references follow:

      Hobbit, 83 (Ch V)  ==   Hobbit, chapter V

      RK, 408 (App F, I, "Of Men", "Of Hobbits")  ==
                             p 408 in Part I of Appendix F, the sections 
                                      entitled "Of Men" and "Of Hobbits"

      Silm, 57 (Ch V)  ==  Silmarillion, chapter V  (BoLT and _The 
                              Annotated Hobbit_ treated similarly) 

      UT, 351 (Three, IV, iii)  ==  Unfinished Tales, Part Three, 
                                      Chapter IV, sub-section iii 
                                    (the Biography treated similarly)

      Letters, 230 (#178)  ==  letter number 178.  

      RtMe, 53-54 (3, "Creative anachronisms")  == 
                                 The Road to Middle-earth, in Chapter 3, 
                                     sub-section "Creative anachronisms"


CONVERSION TABLE 

      In _The Atlas of Middle-earth_, Karen Wynn Fonstad provided a 
Houghton-Mifflin-to-Ballantine conversion table, which is reproduced 
below.  The "table" is actually a set of formulae by which HM page 
numbers may be converted to Ballantine page numbers via arithmetic 
involving some empirically determined constants.  Since these are 
discrete rather than continuous functions the results may be off by 
a page or so.  

[NOTE: in the Fall of 1993, Ballantine issued a new edition of the mass 
market paperback of LotR in which the text has been re-set, thereby 
changing the page on which any given quote is located.  Thus, the 
following table will no longer work with the latest printings, which may 
be identified by the change in the color of the covers (the pictures are 
unaltered): in the previous set of printings all the covers were black; 
in the new set FR is green, TT is purple, and RK is red.]

      HM Page            Subtract            Divide By            Add
   -------------         --------            ---------          -------
   FR 10 to 423             9                  .818                18
   TT 15 to 352            14                  .778                16
   RK 19 to 311            18                  .797                18
   RK 313 to 416          312                  .781               386
    H 9 to 317              8                 1.140                14
   Silm 15 to 365          14                  .773                 2

Reference:  Atlas, p. 191 (first edtion), p. 192 (revised edtion)


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(the post first published at 20250227.)


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