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The answer is, all relevant and useful ones. We can tell easily enough, without spending days searching through the surviving records, because of them being listed in the rates books of the time, i.e. what rate of duty had to be paid on imported goods.
The copy I have is a reprint of the 1586 rates book, in an old book which is the paper original of this google book:
http://books.google.co.uk/books?id=0uFRAQAAIAAJ&printsec=frontcover&dq=A+tudor+book+of+rates&hl=en&sa=X&ei=uPAQU67WNYre7Aay8oHgBg&ved=0CDoQ6AEwAA#v=onepage&q=A%20tudor%20book%20of%20rates&f=false

What I think is also clear is that a lot of these substances are imported not for alchemical use but for the use of physicians and painters. Both of their requirements, and in the case of physicians, understanding of the world, overlap.
In fact there are frequent mentions of plants, plant extracts and preparations all the way through, which at least shows that physicians were importing a great deal of their medicines, as should be clear from the recipes of the period. A herb garden wasn’t enough, people wanted treated with the best medicine you could get, which often meant foreign ones because of their mystique and expense.

Anyway, if we turn to the letter A, we find Argentum sublime, i.e. mercuric chloride, by the pound and hundredweight. A pound of course nowadays is 0.45kg, and a hundredweight about 50kg, although I think the pound in the 16th century was a little different, I can’t find my source book on weights and measures to check.
Antimonium is also imported by the hundredweight, although as usual it is unclear whether they mean the metal or the sulphide.

Also under A is argall, i.e. potassium tartrate, and ashes in barrels. And Armoniacum, which the modern editor thinks means Gum Ammoniac, I think means more ammonium chloride, since it is often called ‘sal armoniacum’. I think this is confirmed by a later mention of “Gum Armoniack”; although there are mistakes in the list, why call one armoniacum and the other gum armoniacum?
There’s arsenic, the hundredeight and by the pound.
And alome, of course, by the hundredweight.
And Azarum, by the pound, which the notes think is a midicament obtained from the asarum plant. In fact there’s quite a few products from plants all the way through, used in medicine or as herbs and spices in food.

Under B we find Brimstone, by the hundredweight.
Also Bedelum, which is apparently a gum-resin used in medicine.

In C, we find green and white copperas, and plain old copperas. These are sulphates, the green probably being the iron sulphate, often calcined and then treated to give a red liquid. The others would be blue copperas and white, the latter zinc based, the former copper.
Under L there is mention of Lapis Calaminaris, which is suggested to be calamine, a zinc ore. By the hundredweight you could certainly do something with it, and brass making has been known on and off by this time, although not on a large scale. Either way it would be useful for alchemists.
There;s also lead, but it helpfully says “Lead, look white leade or red”, which takes us to white or red lead, both of which are in demand for painters and the red is used on iron work.

Mercury sublime makes another appearance, by the pound.

On the other hand I might be wrong about the sal armoniac, given that it is mentioned under S, Sal armoniack, by the pound, and also sal gemma, white salt of various kinds, and most importantly for the alchemist, salpeter by the hundredweight.
There’s also Serusa by the pound, under S, which is most likley cerussa, another kind of white lead, the notes say used for medicine.
Most interestingly, we find mention of ‘spoons of alcumine, the groce’, which the notes suggest means Alcamyne or Alchemy, a metallic composition imitating gold” which is actually something I have noted from 14th and 15th century legal documents pertaining to alchemy. In some the term alcamyne means the actualy activity of alchemy, but in this case, it seems likely to be a gold like alloy.

Sulphur vivum is listed, by the pound. So what is the difference between brimstone and sulphur? None nowadays, but it is likely that back then the brimstone would be powder or adulterated or just not pure, wheras the sulphur vivum is pure yellow lumps straight from the volcano (A lot was gathered from Italian volcanoes).

Interestingly Tin Glass comes into it, by the hundredweight, the notes suggesting they mean bismuth, which is possible at this late date.
Tutia, meaning probably a zinc oxide also is mentioned, by the pound.
Vermillion by the hundredweight appears, as you would expect given its importance as a scarlet pigment, and there’s also verdegrese and Verditer, bother green pigments.
Vitolum might mean vitriol, which has already been covered under copperas, but the 1604 book apparently has ‘vitriolum Romanum’.

The obvious conclusion here is that customs officials use the common understanding of what things are, and if people think there are different varieties of copperas and sulphur and vitriol distinguished by colour and shape, then those are the names they’ll use. This is a continuance of names and perceived properties from the medieval period, and although alchemists and proto-chemists were busy identifying and labelling substances, it often took until the 17th and 18th centuries before they settled upon names linked to definite physical properties that was accurate in a modern sense. But the names and properties recognised then were pretty good and importantly, useful, and it is important to remember this.

I also think it clear that those items by the hundredweight were in widespread industrial level use, such as alum, brimstone, vermillion, ashes etc. Those by the pound were more specialised, often more pure. What sort of physician would use a hundredweight of arsenic? Not many, but a pound or two would be useful. Sulphur is of course for gunpowder, as is saltpetre. The various pigments are by the hundredweight, as you would expect with acres of canvas, wood and plaster to be painted.
The next question of course is who would handle and then subdivide it into parcels for selling to the people who needed it. Of course the Merchant venturers probably imported it, many of them were grocers, and it would be shifted by them to a network of middle men who would transport it to their preferred market towns and customers. Or if you were rich you just sent your servant to buy it in London directly from the importers. Now if I can only find a good book on the topic of internal trade.

At least it shows that by this time every substance required by alchemists would be available through importation.

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