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Odd but interesting

I get quite a few letters and emails, many of them asking some very good questions.  I thought I would share some of these with you:

Q. I was intrigued when, in a recent broadcast of What the Ancients Did for Us (great programme!), you mentioned the Baghdad Jar, apparently an ancient way of generating electricity. You seemed to have some difficulty in deciding what they might have used the electricity for.

For some time I have had this crazy idea that the ancients might have used hydrogen balloons to help them lift the enormous stones that they used to build many monumental structures. Crazy, of course. Where on earth would they have got their hydrogen from? And anyway, some television presenter (it might have been you: I forget) has already demonstrated how the use of kites may have been beneficial in lifting stones. So, no need for balloons?

But, with electricity, and therefore electrolysis, hydrogen might have been produced. Is my balloon idea still so crazy? Probably! But you might consider, in a future programme, trying to make a balloon out of animal skins, filling it with hydrogen, and seeing what it could lift. Could be fun?

- J. Trevor Catlow

A. An ingenious idea, but highly improbable, for three reasons. First the Baghdad battery generates half a volt at best, and is highly susceptible to build-up of Back-EMF [reverse voltage]. To electrolyse water you need 1.23 volts. I doubt if you could ever get a sustained voltage as high as 1.23, since when you put a lot of batteries in series the Back-EMF is horrific.

Second, hydrogen is highly mobile, and leaks rapidly through most soft materials. I don't think it would be possible, even today with modern materials, to make a balloon from animal skins that would hold hydrogen.

Third, if you wanted to lift say a 1-ton stone you would need a hydrogen balloon perhaps 20 metres in diameter. That is an awful lot of animal skins to stick together. And a 10-ton stone would need a balloon 40 metres high. It's not on.

Nice try, though.

Q. Why do the people who regulate "Big Ben's clock use adding or subtracting old pennies to the weight on the bottom?
- John Gifford, London

A. Yes the period of pendulum is governed by its length and is independent of the mass at the end. But if you add an old penny to the bob of the pendulum of Big Ben, then you slightly alter its length; in fact you make it a bit shorter, because the centre of mass of the bob is slightly raised. Similarly if you take pennies off, you will in effect slightly lengthen the pendulum. This seems an odd way to do it, but it is obviously very convenient, and simpler than winding the bob up and down by a minute amount.

Q. Why can I tear a paper tissue one way only in a straight tear downwards, if I turn it round and tear then its a very ragged result?
- Mrs  J C Phipps, Kidderminster

A. The reason why a paper tissue will tear tidily in one direction and not the other is relatively simple. Paper is made by laying down fibres in one direction, like the warp on a piece of woven cloth. Fibres are then dumped in roughly the other direction from a suspension in water so it is like shaking a lot of parallel strings in a dish of spaghetti. Some of the spaghetti will lie across the strings and some all over the place.

When it is all dried out the paper looks even, but in practice it is highly directional, it will tear easily along the line of the original fibres, because there are weaknesses between them. However there is no particular direction across, so it will normally tear jaggedly. This is also very obvious with newspaper. If you take a broadsheet newspaper, it will normally tear very easily from top to bottom, but trying to do it from side to side is much more difficult.

Q. How does fresh air come into an open window, at the same time that stale air goes out?
- Mrs J C Phipps, Kidderminster

A. When you have a window open in a room you might think that no air would go in or out.  However there are two things going on that make fresh air come in. First there are random changes in air pressure. If you were to measure the air pressure just outside the window you would find it went up and down every minute or two. These changes in air pressure cause winds to blow, and they depend upon the heating of the earth's surface by the sun. So when there is a slight reduction in pressure outside, air from the room will flow out through the window. When the pressure outside gets a little higher, air will flow in again. Secondly, even when there are no changes in pressure the air is always moving slightly. Only very rarely is it absolutely still. If the air is moving both inside and outside the room inevitably some will flow out and some will flow in and it may go like waves, first out then in  or it may flow out at the top of the window and in at the bottom. Therefore even with quite a small window the air in the room will gradually get replaced with fresh air.

Q. On Science Shack you heated a bath with cold water from a river ... how on earth did you do that?
- Luke Hutson, West Norwood

A. This is roughly how we heated the bath.

We took a fridge, and filled it with cold water from the river.  Then we switch it on, so that the water inside got a bit colder, and the coil on the back of the fridge got warm.  We used this warm coil to add a little heat to the water for my bath.  Then we returned the water to the river, a little bit colder than it was when we collected it.  Then we repeated the process, to  put a bit more water back in to the river a little colder than when it came out, and to warm the bath water a bit more. 

To make things simpler, we took the water from the river in a hosepipe, a pumped it continuously through the fridge, so that there was a stream of water coming out of the river, and going back in a little bit colder (about 2c colder, I think).  Meanwhile the bath water got warmer and warmer.  We stopped the process when the bath water reached 40c, because I did not want to be poached...

I hope this makes sense.  I did not believe it until I saw it with my own eyes.  In principle anyone could use this method to heat their house, taking heat either from a stream or from deep underground.

Q.  I understand how before the transit of Venus all the astronomers had were a lot of angles from which they could work out the relative distances but no actual distances. They only needed one distance to work out all the others.  I was able to follow how in Captain Cook's time, by observing the transit from different, widely spaced positions on the Earth, they were able to work out the distance of the Earth from the Sun.

However, I cannot work how Jeremiah Horrocks make his calculation of 59 million miles for the astronomical unit (the Earth-Sun distance)?  As Jeremiah was observing from only one position I cannot see how he had sufficient information to work anything out.  It has been suggested to me that the observation of the times of contact: the T1, T2, T3 and T4 times should help but I can't see how you can get from these times to give you a distance- I can only see a load of angles and no  distances.
- Keith Wells, Brighton

A. I went to my friend Prof David Hughes, The University of Sheffield who provided us with this most complete answer!

"You are absolutely correct about your conclusion, i.e. that Jeremiah 'calculated' a value of 59 million miles (14733 Earth Radii, 94 million km) for the astronomical unit (the Earth-Sun distance). 

(i) Horrocks knew that the distances between Mercury, Venus, Earth, Mars etc and the Sun where in the ratio 0.387:0.723:1.000:1.523 etc

(ii) He also knew that, at inferior conjunction, subtended an angle of 76 seconds of arc at the Earth.  This was (to him) the important result of his Much-Hoole transit observation.  The angular diameter of Venus had not been measured before, due to the problem of irradiance (i.e. the image of Venus was much too bright against the background) and the fact that the micrometer had not been invented.

(iii)  he also knew that planet Earth had a radius somewhere between 5800km and 6900km (I am not sure of whose value he used, there were a few about at the time, the two I give are about 10% each side of the correct value.)

(iv) Now for the naught bit. Horrocks assumed, just like Gottfried Wendelin 1635 (see a letter he wrote to Gassendi, dated May 1st; in Petri Gassendi Opera Omnia, Volume 6, Lyons, pp 427-429; 1658) that the radii of the planetary spheres were directly proportional to their distances from the Sun. Horrocks also followed Wendelin in the belie that all planetary spheres subtended the same angle at the Sun, this being 28 seconds of arc.  Under these circumstances the 'solar parallax' is 14 seconds of arc (i.e. 3.89x10to the -3 degrees). So for example, the radius of Earth divided by the Earth-Sun distance is the tangent of 3.89x10 to the -3 degrees.  This then means that the astronomical unit is 14733 times the radius of Earth. 

(v) Interestingly if we go back to the important measurement of 76 seconds of arc for the angular diameter of Venus as seen from Earth, by Horrocks, in 1639 we that things nearly fit:

Venus at transit was 0.277 au (i.e. 1.000 - 0.723 au) away from Earth and subtended 76 sec arc at Earth. Venus at transit was also 0.723 au away from the Sun and thus subtends an angle sec arc at the Sun , where a= 76x0.277/0.723= 29.  As 29 was very close to 28 you can see why Horrocks did not change his mind.  He died rather suddenly and so the story ends!"

Q. Could you explain why birds don't fall over when they stand on one leg? I have found my balance to be much better when I stand on both legs.

I was studying some ducks today and have spent several hours trying to work out why a duck would tuck one leg up, when it could put both on the ground - Becky Winn (a great fan)

A. Good question. Herons also spend quite a lot of time on one leg, but not, I think, pigeons, rooks, or little birds - robins, tits, or sparrows.

I don't know the answer, but could it possibly be that these water birds (a) have big webbed feet and can balance better, or (b) like to get one foot dry occasionally.

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