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James Clerk Maxwell
   
 
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Lettera a LEWIS CAMPBELL   22 settembre 1848

 TO LEWIS CAMPBELL, Esq.

                                                                     Glenlair, 22d Sept. 1848.
 

When I waken I do so either at 5.45 or 9.15, but I now prefer the early hour, as I take the most of my violentexercise at that time, and thus am saddened down, so that I can do as much still work afterwards as is requisite, whereas if I was to sit still in the morning I would be yawning all day. So I get up and see what kind of  day it is, and what field works are to be done; then I catch the pony and bring up the water barrel. This barrel   used to be pulled by the men, but Pa caused the road to be gravelled, and so it became horse work to the men, so   I proposed the pony; but all the men except the pullers opposed the plan. So I and the children not working,  brought it up, and silenced vile insinuators. Then I take the dogs out, and then look round the garden for fruit and   seeds, and paddle about till breakfast time; after that take up Cicero and see if I can understand him. If so, I read   till I stick; if not, I set to Xen. or Herodt. Then I do props, chiefly on rolling curves, on which subject I have got a  great problem divided into Orders, Genera, Species, Varieties, etc.

One curve rolls on another, and with a particular point traces out a third curve on the plane of the first, then the   problem is:
Order I. Given any two of these curves, to find the third.

Order II. Given the equation of one and the identity of the other two, find their equation.

Order III. Given all three curves the same, find them. In this last Order I have proved that the equi-angular spiral possesses the property, and that no other curve does. This is the most reproductive curve of any. I think John  Bernoulli had it on his tombstone, with the motto Eadem mutata resurgo. There are a great many curious properties of curves connected with rolling. Thus, for example,—

If the curve A when rolled on a straight line produces a curve C, and if the curve A when rolled up on itself   produces the curve B. then the curve B when rolled upon the curve C will produce a straight line.

     Thus, let the involute of the circle be represented by A,

      the spiral of Archimedes by B,

      and the parabola by C,   then the proposition is true.

Thus the parabola rolled on a straight line traces a Catenary with its focus, an easy way to describe the   Catenary.
Professor Wallace just missed it in a paper in the Royal Society.
After props come optics, and principally polarised light.
Do you remember our visit to Mr. Nicol? I have got plenty of unannealed glass of different shapes, for I find  window glass will do very well made up in bundles. I cut out triangles, squares, etc., with a diamond, about 8 or 9  of a kind, and take them to the kitchen, and put them on a piece of iron in the fire one by one. When the bit is red  hot, I drop it into a plate of iron sparks to cool, and so on till all are done. I have got all figures up to nonagons,   triangles of all kinds, and irregular chips. I have made a pattern for a tesselated window of unannealed glass in the     proper colours, also a delineation of triangles at every principal inclination. We were at Castle-Douglas yesterday,     and got crystals of salt Peter, which I have been cutting up into plates to-day, in hopes to see rings. There are very   few crystals which are not hollow-hearted or filled up with irregular crystals. I have got a few cross cuts like   free of irregularities and long [wedge-shaped] cuts for polarising plates. One has to be very cautious in sawing,  and polishing them, for they are very brittle.

 
I have got a lucifer match box fitted up for polarising, thus. The rays suffer two reflections at the polarising angle   from glasses A and B. Without the lid it does for an analysing plate. In the lid there is set a plate of mica, and so  one observes the blue sky, and turns the box round till a particular colour appears, and then a line on the lid of the   box points to the sun wherever he is. Thus one can find out the time of day without the sun.  [Here follow  thirteen diagrams of patterns in triangles, squares, pentagons, and hexagons.] These are a few of the figures one sees in unannealed glass.

 Pray write soon and tell when, how, and where by, you intend to come, that you may neither on the other hand fall  upon us at unawares, nor on the one hand break and not come at all. I suppose when you come I will have to give  up all my things of my own devising, and take Poisson, for the time is short, and I am very nearly unprepared in  actual reading, though a great deal more able to read it.

I hope not to write any more letters till you come. I seal with an electrotype of the young of the ephemera. So, sir,   I was, etc.