Last week I’ve been reading Robertson’s “A Treatise of Mathematical Instruments”. It’s a reprint of an 18th century British work that includes some passages dealing with proportions. I ran across a few more nuggets that to me were interesting or at the least entertaining. Did you know that?
“It has been found, that one man in a minute, can raise a Hogshead (large barrel) of water 12 feet high upon a mean: For a stout man, well plied with strong liquor, will raise a hogshead of water 15 feet high in a minute.”
It also is filled with mathematical solutions to real problems encountered in the day. How many spars of white fir do you need to lash together to construct a raft to float 100 barrels of gunpowder and four men (a total weight of 12,600 pounds) three inches clear of the water? It defines a spar as 12 inches by 12 inches by twenty foot long. A bit hard to imagine going to the lumber yard and asking to look at their 48/4 stock and needing twenty footers, 56 of them total.
What really piqued my interest was this engraving above of a naval cannon barrel from the plates in the back of the book. It caught my eye because if you look closely it has numerous moldings circling the barrel. One thing that stood out is that it has bands with small fillets and beads or astragals that actually define the major sections of the barrel. I always thought the bands on these old cannons were to give it strength (which the accompanying text agrees with) but they also act to mark the borders between the parts of the gun such as the muzzle and the mid sections known as the first and second reinforce. This struck me as interesting because in the traditional uses of moldings small beads and fillets are often used as a separator.
You often see a bead near the top of a column to signal your eye that it’s about to terminate in the capital. Up on the entablature you may see a fillet to separate the frieze from the architrave. We often see a bead scratched into the edge of period drawer fronts or beading applied to the perimeter of drawers to work visually in the same way. What intrigued me most in the whole book is the way that Robertson describes the specifications for naval cannons. He describes them proportionally in much the same way as a designer would describe how to lay out the parts of a classic order. The author uses the cannon ball diameter as a “module” and describes every part in proportion to that. All the lengths and diameters are in multiples or fractions of that module. This practice is used frequently in describing the parts of a classic order, everything down to the smallest detail expressed in relation to the diameter of the column at the base. Then the author matter of factly states
“But a small variation in the lengths of these parts, will not materially affect the Gun, either in strength, use, or pleasing proportion.”
Wow! Here’s an 18th century scientist describing the design of big honking naval guns, referring to Vitruvius (a 1st century Roman architect and writer) who wrote that a good design should be functional (use), sturdy (strength), and beautiful (pleasing proportion).
Actually when I pull back and look at that engraving, it does have nice lines.