The Moon is a Marble

Discourses Relating to Art and Science

Saturday, September 18, 2010


How to align a centrolinead

How to align a Centrolinead

James Gurney and Craig Elliot had posts about this tool from the by-gone days of board-drawing.  The centrolinead is a sort of adjustable T-square ruler that you can use to make tapered perspective lines to a vanishing point that may be dozens of feet off of the edge of the paper.

from, Mathematical Instruments: Drawing and measuring instruments, John Fry Heather, p. 10

How does it work?
The geometry of the Centrolinead is based on the Inscribed Angle Theorem.  A proof of the method can be found in the volume excerpted below, Geometry, plane, solid, and spherical, in six books, whose subtitle rambles to include, to which is added, in an appendix, the theory of projection, so far as it is auxiliary to geometry; with an account of the Plane sections of the cone and cylinder, in which certain general properties of the conic sections are demonstrated by help of the foregoing theory.

The proof.  (It is okay to skip this part)

This is fine and edifying reading material, to be sure, but the main idea is that four points remain on the line that describes a fixed circle:  the vanishing point, the two studs, and the intersection of the ruler's edges (the edges that slide on the studs).

How do you set the centrolinead to line up with your vanishing point?

I found several sources that simply say, "Adjust the centrolinead by trial and error."  If that answer is sufficient for you, good day to you and happy drawing!

If not, here is one explanation, including an example.  Note that they expect you to know the measurement of the distance between the studs and your vanishing point.  Start at "To set the centrolinead..."

A numerical method for setting your centrolinead
from, Mathematical Instruments: Drawing and measuring instruments, John Fry Heather, p. 10

Unless you are a master draftsman, you may not know precisely where your vanishing point is.  If you just have an existing line, and a pre-existing horizon, you can use this method:

Setting the ruler using a pre-existing line
from, Mathematical Instruments: Drawing and measuring instruments, John Fry Heather, p. 10-11

Finally, there is this method of setting the centrolinead first, and then varying where the second pin goes:

Setting the centrolinead first and then putting the lines in

A Descriptive Treatise on Mathematical Drawing Instruments, William Ford Stanley, p. 171

And if all these things don't work or don't make sense, you can always just work at a really long table, with a really long ruler.


thanks for this explanation of a weird old tool I just discovered today
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