Chasing molecules ... and Vitamin C

During the course of this week I have finished both Chasing Molecules and an RSC monograph - Vitamin C - its Chemistry and Biochemistry (Davies, Austin and Partridge).

Whilst Chasing Molecules has prompted me to think more carefully about the leaching of pollutants from plastics, I found the book somewhat frustrating; as a scientist I didn't feel I was being presented with real evidence - just a sort of trust-me-I've-read-the-reports. However, the book is clearly written for the educated layman rather than a trained scientist this is probably an unfair criticism, and it is extensively referenced so I could look these studies up if I had time and appropriate library access. Overall, I thought that it was well-written and well-informed, if perhaps a little paranoid.

The book on vitamin C was a delight and I thoroughly recommend it to anyone wishing to know more about ascorbic acid. Undergraduate-level chemistry is probably needed to make the most of the text, particularly the latter sections on redox chemistry and complex formation, but the early chapters covering the discovery, isolation and structure determination of ascorbic acid, as well as scurvy as a medical condition, would be accessible to the general reader.

Reading update

The trouble with term-time is that I'm often so tired that reading is quite difficult to sustain. Not reading, like not listening to music, tends to make me unhappy. The last five weeks have been quite hectic, yet I have managed to make a little progress with a few books.

Thomas Hardy: A Laodicean was a gripping read, rather different from other Thomas Hardy novels that I've encountered. The notes in my copy suggest that the central character (George Somerset) was, in part, modelled on Hardy's own life. Unusually, this novel has a happy ending, although it is tempered with some sadness. I think it is perhaps the Hardy novel that Austen fans would most enjoy.

F. W. Taylor's Planetary Atmospheres started well, but I've found myself rather bogged down in the mathematics of the Physics. I'm persevering, though, because between the equations there is a great deal of interesting descriptive material. I do feel I've developed a better understanding of atmospheric temperature gradients and the section I've now come to is much more chemical than physical.

Elizabeth Grossman: Chasing Molecules was something that I picked up in Foyles in early January. It describes the dangerous chemicals used in modern materials as well as giving a view of the promise of Green Chemistry. The chemical industry comes in for some pretty hard criticism and she seems to assume that if a study is industry-funded it must  be biased. However, it has made me think a little more about the materials with which I'm in contact and reminded me that chemical exposure is not only found in laboratories. I will write more about this book when I've finished it (I'm currently about half-way through).

Music

It's been quite a good Christmas for getting new music: here are some thoughts on the CDs I've been given (or purchased - I strongly recommend visting Prelude Records if you are ever in Norwich!).

Words and Music is a 2007 release on the Chandos label with vocals and piano by Richard Rodney Bennett. There's a mixture of standards from the American songbook (I won't dance/ How long has this been going on?) and lesser known songs, as well as the title track, a Bennett composition.

Graduation features Richard Hills playing the Dickinson High School Kimball theatre organ with his usual style and flair. I particularly enjoyed his Songs from the British Isles and Viva Mexico - a Mexican fantasy. If you aren't familiar with Richard Hills or with theatre organ music, then watch this video of Hills playing Tiger Rag - I guarantee you'll like it!

I've also acquired a recording of the Bach tocattas (Angela Hewitt [Hyperion]) and Naxos recordings of Dvorak symphonies 3,4,6, and 8, which I'm getting to know for the first time and enjoying immensly. I've also bought a 2CD set of harpsicord suites by Jean-Henry D'Anglebert. I'd never heard of this composer (a friend of Lully) and have yet to listen to the CDs ... more to follow.

Resolution

Each year I make a resolution to write more on this blog. Maybe 1. i. 2012 will be the turning point?

Happy New Year to one and all!

Still no solution yet

I'm still thinking about the cone problem. I've now acquired a classic text on co-ordinate geometry that devotes substantial space to the conic sections. Brushing-up on this topic would probably be worthwhile in any case, but I'm hoping it will give me the apparatus to work on this problem.

More updates to follow in due course, I hope!

The mathematics problem from my previous post continues to occupy my thoughts. Whilst I have made some progress with a solution, I have come up against a seemingly insuperable barrier. One of the things I need to be able to determine is the ratio into which a section through a frustum of a cone divides the volume, as illustrated above.

I had approached the problem by imagining slicing the cone into discs. The section would then create cicrle segments whose areas could be integrated to obtain the volume. Unfortunately, the expression derived for the area in terms of the height is very hard to integrate. It seems such an obvious question to ask, I can't believe that a solution isn't out there somewhere!

Water in a glass

A scientist is someone who sees the world around them and wonders how it is like it is.

Even though I've been a scientist for most of my life, it still surprises me that so many interesting problems can arise from something as simple as a glass of carbonated water. Here are three that have occurred to me during the last week.

1. An economics problem: why is Sainsbury's own-brand carbonated water cheaper than their own-brand still water (by around 10%)? Surely, the carbonation process requires more input of energy and materials, so it should be more expensive.
2. A physics problem: when the bubbles rise they clearly accelerate, but is the acceleration constant, or is there a significant change of force with depth, resulting in non-negligible variable acceleration?
3. A mathematics problem: what is the relationship between the volume of water in the glass and the angle by which the glass can be tipped before the water spills? This would, of course, be the same regardless of the nature of the liquid in the glass, providing surface tension is ignored. I am assuming that the glass is a frustum of a right circular cone.
   

The economics question doesn't really interest me, although the answer might.

The physics problem could probably be answered with a bit of thought and some back-of-an envelope calculations and might make a useful diversion when stuck invigilating internal examinations next week.

It is the mathematics problem that has really gripped me. Despite appearing fairly straightforward initially, it turns out to be really quite complex, requiring a determination of volume of a conic section. There are 2 cases to consider:

a) a fairly full glass, where the liquid forms an eliptical section of the frustum;



b) a fairly empty glass, where the liquid forms a section of the frustrum in the form of a elipse segment (the base of the glass constituting the chord).



Finding the air/liquid contact area would be straight forward, but extending to the volume seems to be quite tricky. A volumes of revolution approach will not work as the volume section has no cylindrical symmetry. The internet doesn't seem to be very helpful, but then I might not be constructing a suitable search as the sections I'm interested in might have a "proper" name. My next stop will be my Euclid, although I don't hold out much hope.

Any suggestions would be most gratefully received.

Of course, being a scientist I could just be a bit empirical about this: I could go and get some data and then see if I can find a relationship. Maybe that should be my next stop ...