Hi Silvana:

Based on your numbers, the scale is (in inches or in centimeter) 1:142,560

The scale expresses the distance on the map in relation to the distance on the ground. The number that counts is what you measure on the map, although some maps reports the fraction or ratio of it. Independently from the unit measure (inches or centimeters) one number should be always 1 is the denominator of the fraction is reporting the 

Your scale either is given in English miles and inches (so, 1 inch = 2.25 miles or 142,560 inches since there are 63,360 inches in 1 mile) or in metric units (so, 1 cm = 142,560 cm)

You cannot give 1 inch in metric (you need to do a conversion like the one I did below).
The number 57217 is close --but clearly not the same -- as one divides 142,560 by 2,54 (equivalent to 1 inch, but in centimeter). However, it is wrong.

Here is the equation:
x_inches= 2.25 mi/in * 63360 in/1mi = 142,560
x_cm= 2.25 mi/cm * 160934.4 cm/mi / 1 in/cm * 2.54 cm/in = 142,560

This is my calculation -- on the back of an envelope -- with your numbers.

Good luck.

Lucia

On Tue, Jun 13, 2017 at 11:52 AM, <[log in to unmask]> wrote:
Hello all,
I am a rare materials cataloger who occasionally does maps, and I
struggle sometimes with determining scale. I am currently working on a
1868 map with a bar scale in English miles. I found a record that gives
an
approx. scale of 1:57,217, but I can't figure out how they came to that
number. The bar scale measures approx 2.3 in, with 1 inch approx 2.25
English miles. When I compare 1 mile against the NSI I get a scale
somewhere
between 140,000-145,000, so I have no idea where the number 57217 comes
from. I will try to attach some pics of the bar scale. Any help would be
appreciated.
Thank you
-Silvana