I am confused as to exactly what you are trying to say. I merely posted a section of the article that gave further clues to the construction of the French curves. If you mean to say that the article volunteers these tidbits without reference, I certainly concur, but in absence of anything better, it is as close to an explanation as we have at present.

If you mean something else, can you elaborate?

I am confused as to exactly what you are trying to say. I merely posted a section of the article that gave further clues to the construction of the French curves. If you mean to say that the article volunteers these tidbits without reference, I certainly concur, but in absence of anything better, it is as close to an explanation as we have at present.

If you mean something else, can you elaborate?

It's there. Page 6, number 4. I found it by using the search box that is available in the pdf file. I searched the word French, and read the half dozen or so references until I found the phrase French Curve.

It's there. Page 6, number 4. I found it by using the search box that is available in the pdf file. I searched the word French, and read the half dozen or so references until I found the phrase French Curve.

Thanks for the replies. Acer, that link is interesting. I will read it more carefully in a short time, but I did do a quick search of that paper for "French Curve" to get to the salient point, and found the following:

Curves were employed by draftsmen for centuries; the majority of these curves were circles, but some were "free-form." Those are curves arising from applications such as ship hull design to architecture. When they had to be drawn exactly, the most common tool was a set of templates known as French curves. These are carefully designed wooden curves and consist of pieces of conics and spirals. A curve is drawn in a piecewise manner by tracing appropriate parts of a French curve. Another mechanical tool, called a spline was also used. This was a flexible strip of wood...

The words conics and spirals are more clues. Thinking about it further, it is almost inconcievable  that the Kinematician and Geometer Ludwig Burmester would have not used some kind of drawing apparatus or repeatable geometric construction to generate the various French curves. This is an important distinction from curves that might have been created "freeform." I would surmise that Burmester's curves are not simple splines, but I will nonetheless do some actual testing with splines this evening, to see if I can duplicate any of the French curves.

What the construction or apparatus was remains a fascinating mystery. The hunt continues...

Thanks for the replies. Acer, that link is interesting. I will read it more carefully in a short time, but I did do a quick search of that paper for "French Curve" to get to the salient point, and found the following:

Curves were employed by draftsmen for centuries; the majority of these curves were circles, but some were "free-form." Those are curves arising from applications such as ship hull design to architecture. When they had to be drawn exactly, the most common tool was a set of templates known as French curves. These are carefully designed wooden curves and consist of pieces of conics and spirals. A curve is drawn in a piecewise manner by tracing appropriate parts of a French curve. Another mechanical tool, called a spline was also used. This was a flexible strip of wood...

The words conics and spirals are more clues. Thinking about it further, it is almost inconcievable  that the Kinematician and Geometer Ludwig Burmester would have not used some kind of drawing apparatus or repeatable geometric construction to generate the various French curves. This is an important distinction from curves that might have been created "freeform." I would surmise that Burmester's curves are not simple splines, but I will nonetheless do some actual testing with splines this evening, to see if I can duplicate any of the French curves.

What the construction or apparatus was remains a fascinating mystery. The hunt continues...

Thank you for that tangible piece of information. It is an important clue, but it does not say how Ludwig Burmester actually designed it. Still, it provides for a fresh start.

The fact that the French Curve was designed by a German is a most fascinating point of trivia, and irony.

I will now work on searching for how Burmester actually designed it, but if anyone else has other information, kindly reply.

Thank you for that tangible piece of information. It is an important clue, but it does not say how Ludwig Burmester actually designed it. Still, it provides for a fresh start.

The fact that the French Curve was designed by a German is a most fascinating point of trivia, and irony.

I will now work on searching for how Burmester actually designed it, but if anyone else has other information, kindly reply.