Full Chisel Blog

September 19, 2009

Of the Diagonal Scale

For your general use and amusement:

 

Of the DIAGONAL SCALE.

 

 

The chief use of such a scale as this, is to lay down any line from a given measure; or to measure any line, and thereby to compare it with others.  If the large division of oE be called units, the small divisions in Co will be 10ths, and the divisions in the altitude oB will be 100th parts of an unit.  If the large divisions be tens, the other will be units, and tenth parts.  If the large divisions be hundreds, then the other will be tens and units, &c. each set of divisions being tenth parts of the former ones.

For example, suppose it were required to take off 244 from the scale: fix one foot of the compasses at 2 of the larger divisions in oE, and extend the other to the number 4 in Co; then move both points of the compasses by a parallel motion, till you come at the fourth long line, taking care to keep the right hand point in the line marked 2; then open the compasses a small matter, till the left-hand foot reaches to the intersection of the two lines marked 4. 4, and you have the extent of the number required.  In a similar manner any other number may be taken off.

From Hawney’s Complete Measurer, 1801 Philadelphia

Stephen

2 Comments »

  1. I get it. It took me a minute, but I get it. You’d need to have a different scale for every, um, scale that you need to measure, though. Like, one for 1:12, one for 1:100, etc. Unless you just measure them all as-is and then do the math to adjust 1:1 to whatever scale you’re working in.
    Honestly, though, I think it would be a lot easier to start with the 4.4 and just set the second foot for the intersection of the same horizontal and 2. Starting at 2 on OE and then dragging it up and adjusting seems clumsy and unnecessary… but maybe I’m just missing something. Oh, when you’re measuring an existing setting on the dividers it might work better that way, but for setting the dividers to a particular size it would be easier the way I suggested.
    By the way… have you received your brass dividers yet? I bought a pair, myself. You can’t complain about the price… It would cost me more than that to buy the materials to make a pair.

    M.Mike

    Comment by Metalworker Mike — September 19, 2009 @ 11:54 am

  2. Thank you Stephen.
    This is a great tool in my arsenal for measuring furniture from pictures. Now if I know one dimension, I can calculate the rest by measuring with dividers and seeing where the measure on a properly scaled “diagonal scale”.
    Neat!
    Mike

    Comment by Mike Holden — September 19, 2009 @ 4:25 pm

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