Help the innumerate: map scales

Yoda

I thought about posting this to the Mathematics forum, but figured that the Weather forum would enjoy it more.

I have an 1842 map of Mayo with a scale legend of 1 inch = 10 Irish miles. What is its scale?

1 inch = 25.4 mm.
1 Irish mile = 2,240 yards = 2,048.256 m = 2,048,256 mm
10 Irish miles = 20,482,560 mm

20,482,560 mm ÷ 25.4 mm = 806,400.

Is the scale 1:806,400?
Or am I hopelessly innumerate?

Mothman

Yoda wrote:

I thought about posting this to the Mathematics forum, but figured that the Weather forum would enjoy it more.

I have an 1842 map of Mayo with a scale legend of 1 inch = 10 Irish miles. What is its scale?

1 inch = 25.4 mm.
1 Irish mile = 2,240 yards = 2,048.256 m = 2,048,256 mm
10 Irish miles = 20,482,560 mm

20,482,560 mm ÷ 25.4 mm = 806,400.

Is the scale 1:806,400?
Or am I hopelessly innumerate?

Is an Irish mile the same as a Mayo mile

FWIW, you are right, but you didn't have to go into mm to work it out

36 inches in a yard.
2,240yards = 80,640 inches * 10 miles = 806,400 (as above)

Yoda

Huh. Well, OK. Thanks. I've got some other maps here, an 1837 map of Wicklow which looks like it wants to be 1" = 4 Irish miles though the drawn scale rule is about a mm shy of a real inch. I'm calling the scale 1:322,560 anyway.

Then there's the 1761 map of Portugal, which has the lovely scale of 18mm = 70 English miles = 25 French leagues. I'll calculate and see what I get, after I find out how many mm in a French league....

Yoda

Well... there are several versions of French league, according to the French Wikipedia. There's a metric one (1 league = 4 km), a terrestrial one (1 league = 4.4448 km), and two others.

So ignoring those, and assuming that an English mile in 1761 is the same as one today, the scale is 1:1:6,258,560