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## The 100 greatest songwriters – number 28 – Woody Guthrie

At number 28 in Rolling Stone Magazine’s list of the 100 greatest songwriters is Woody Guthrie. I wonder how many of you reading this, particularly non-Americans, have heard of Woody Guthrie? I first heard of him when I became interested in Bob Dylan; he was a hero of the young Dylan and, in fact, Dylan wrote a song of tribute to him on his first album, “Song for Woody”.

Guthrie was born in Oklahoma in 1912, and so lived through the depression of the 1930s in a state which was particularly blighted by the depression and the ‘dust-bowl’. This led to thousands of farmers and their families from Oklahoma leaving for California (this story is the basis of John Steinbeck’s wonderful novel The Grapes of Wrath). Living through these dismal years had a long-lasting effect on Guthrie, and he spent a career as a folk-singer and activist championing the rights of downtrodden people.

At number 28 in Rolling Stone Magazine’s list of the 100 greatest songwriters of all time is Woody Guthrie.

Probably Guthrie’s best known song is “This Land is Our Land”, a song which has been translated into many languages, including into Welsh. Guthrie wrote this song in 1940, basing the lyrics to fit with an existing melody. He then altered the lyrics in 1944, which is when he first recorded it, and it was released in 1945. You can read more about the two different versions of the song here on its Wikipedia page.

This land is your land This land is my land
From California to the New York island;
From the red wood forest to the Gulf Stream waters
This land was made for you and Me.

As I was walking that ribbon of highway,
I saw above me that endless skyway:
I saw below me that golden valley:
This land was made for you and me.

I’ve roamed and rambled and I followed my footsteps
To the sparkling sands of her diamond deserts;
And all around me a voice was sounding:
This land was made for you and me.

When the sun came shining, and I was strolling,
And the wheat fields waving and the dust clouds rolling,
As the fog was lifting a voice was chanting:
This land was made for you and me.

As I went walking I saw a sign there
And on the sign it said “No Trespassing.”
But on the other side it didn’t say nothing,
That side was made for you and me.

In the shadow of the steeple I saw my people,
By the relief office I seen my people;
As they stood there hungry, I stood there asking
Is this land made for you and me?

Nobody living can ever stop me,
As I go walking that freedom highway;
Nobody living can ever make me turn back
This land was made for you and me.

Here is a video of Guthrie performing this song. Enjoy!

Which is your favourite Woody Guthrie song?

## Derivation of Planck’s radiation law – part 3

As I have outlined in parts 1 and 2 of this series (see here and here), in the 1890s, mainly through the work of the Physikalisch-Technische Reichsanstalt (PTR) in Germany, the exact shape of the blackbody spectrum began to be well determined. By mid-1900, with the last remaining observations in the infrared being completed, its shape from the UV through the visible and into the infrared was well determined for blackbodies with a wide range of temperatures.

I also described in part 2 that in 1896 Wilhelm Wien came up with a law, based on a thermodynamical argument, which almost explained the blackbody spectrum. The form of his equation (which we now know as Wien’s distribution law) is
$\boxed{ E_{ \lambda } d \lambda = \frac{ A }{ \lambda ^{5} } e^{ -a / \lambda T } d \lambda }$

Notice I said almost. Below I show two plots which I have done showing the Wien distribution law curve and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. As you can see, they are not an exact match, the Wien distribution law fails on the long-wavelength side of the peak of the blackbody curve.

Comparison of the Wien distribution law and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. Although they agree very well on the short wavelength side of the peak, the Wien law drops away too quickly on the long-wavelength side compared to the observed blackbody spectrum.

A zoomed-in view to highlight the difference between the Wien distribution law and the actual blackbody curve for a blackbody at a temperature of $T=4000 \text{Kelvin}$. Although they agree very well on the short wavelength side of the peak, the Wien law drops away too quickly on the long-wavelength side compared to the observed blackbody spectrum.

## Planck’s “act of desperation”

By October 1900 Max Planck had heard of the latest experimental results from the PTR which showed, beyond any doubt, that Wien’s distribution law did not fit the blackbody spectrum at longer wavelengths. Planck, along with Wien, was hoping that the results from earlier in the year were in error, but when new measurements by a different team at the PTR showed that Wien’s distribution law failed to match the observed curve in the infrared, Planck decided he would try and find a curve that would fit the data, irrespective of what physical explanation may lie behind the mathematics of the curve. In essence, he was prepared to try anything to get a fit.

Planck would later say of this work

Briefly summarised, what I did can be described as simply an act of desperation

What was this “act of desperation”, and why did Planck resort to it? Planck was 42 when he unwittingly started what would become the quantum revolution, and his act of desperation to fit the blackbody curve came after all other options seemed to be exhausted. Before I show the equation that he found to be a perfect fit to the data, let me say a little bit about Planck’s background.

## Who was Max Planck?

Max Karl Ernst Ludwig Planck was born in Kiel in 1858. At the time, Kiel was part of Danish Holstein. He was born into a religious family, both his paternal great-grandfather and grandfather had been distiguished theologians, and his father became professor of constitutional law at Munich University. So he came from a long line of men who venerated the laws of God and Man, and Planck himself very much followed in this tradition.

He attended the most renowned secondary school in Munich, the Maximilian Gymnasium, always finishing near the top of his class (but not quite top). He excelled through hard work and self discipline, although he may not have had quite the inherent natural ability of the few who finished above him. At 16 it was not the famous taverns of Munich which attracted him, but rather the opera houses and concert halls; he was always a serious person, even in his youth.

In 1874, aged 16, he enrolled at Munich University and decided to study physics. He spent three years studying at Munich, where he was told by one of his professors ‘it is hardly worth entering physics anymore’; at the time it was felt by many that there was nothing major left to discover in the subject.

In 1877 Planck moved from Munich to the top university in the German-speaking world – Berlin. The university enticed Germany’s best-known physicist, Herman von Helmholtz, from his position at Heidelberg to lead the creation of what would become the best physics department in the world. As part of creating this new utopia, Helmholtz demanded the building of a magnificient physics institute, and when Planck arrived in 1877 it was still being built. Gustav Kirchhoff, the first person to systematically study the nature of blackbody radiation in the 1850s, was also enticed from Heidelberg and made professor of theoretical physics.

Planck found both Helmholtz and Kirchhoff to be uninspring lecturers, and was on the verge of losing interest in physics when he came across the work of Rudolf Clausius, a professor of physics at Bonn University. Clausius’ main research was in thermodynamics, and it is he who first formulated the concept of entropy, the idea that things naturally go from order to disorder and which, possibly more than any other idea in physics, gives an arrow to the direction of time.

Planck spent only one year in Berlin, before he returned to Munich to work on his doctoral thesis, choosing to explore the concept of irreversibility, which was at the heart of Claussius’ idea of entropy. Planck found very little interest in his chosen topic from his professors in Berlin, and not even Claussius answered his letters. Planck would later say ‘The effect of my dissertation on the physicists of those days was nil.’

Undeterred, as he began his academic career, thermodynamics and, in particular, the second law (the law of entropy) became the focus of his research. In 1880 Planck became Privatdozent, an unpaid lecturer, at Munich University. He spent five years as a Privatdozent, and it looked like he was never going to get a paid academic position. But in 1885 Gottingen University announced that the subject of its prestigoius essay competition was ‘The Nature of Energy’, right up Planck’s alley. As he was working on his essay for this competition, he was offered an Extraordinary (assistant) professorship at the University of Kiel.

Gottingen took two years to come to a decision about their 1885 essay competition, even though they had only received three entries. They decided that no-one should receive first prize, but Planck was awarded second prize. It later transpired that he was denied first prize because he had supported Helmholtz in a scientific dispute with a member of the Gottingen faculty. This brought him to the attention of Helmholtz, and in November 1888 Planck was asked by Helmholtz to succeed Kirchhoff as professor of theoretical physics in Berlin (he was chosen after Ludwig Boltzmann turned the position down).

And so Planck returned to Berlin in the spring of 1889, eleven years after he had spent a year there, but this time not as a graduate student but as an Extraordinary Professor. In 1892 Planck was promoted to Ordinary (full) Professor. In 1894 both Helmholtz and August Kundt, the head of the department, died within months of each other; leaving Planck at just 36 as the most senior physicist in Germany’s foremost physics department.

Max Planck who, in 1900 at the age of 42, found a mathematical equation which fitted the entire blackbody spectrum correctly.

As part of his new position as the most senior physicist in the Berlin department, he took over the duties of being adviser for the foremost physics journal of the day – Annalen der Physik (the journal in which Einstein would publish in 1905). It was in this role of adviser that he became aware of the work being done at PTR on determining the true spectrum of a blackbody.

Planck regarded the search for a theoretical explanation of the blackbody spectrum as nothing less than the search for the absolute, and as he later stated

Since I had always regarded the search for the absolute as the loftiest goal of all scientific activity, I eagerly set to work

When Wien published his distribution law in 1896, Planck tried to put the law on a solid theoretical foundation by deriving it from first principles. By 1899 he thought he had succeeded, basing his argument on the second law of thermodynamics.

## Planck finds a curve which fits

But, all of this fell apart when it was shown conclusively on the 2nd of February 1900, by Lummer and Pringsheim of the PTR, that Wien’s distribribution law was wrong. Wien’s law failed at high temperatures and long wavelengths (the infrared); a replacement which would fit the experimental curve needed to be found. So, on Sunday the 7th of October, Planck set about trying to find a formula which would reproduce the observed blackbody curve.

He was not quite shooting in the dark, he had three pieces of information to help him. Firstly, Wien’s law worked for the intensity of radiation at short wavelengths. Secondly, it was in the infrared that Wien’s law broke down, at these longer wavelengths it was found that the intensity was directly propotional to the temperature. Thirdly, Wien’s displacement law, which gave the relationship between the wavelength of the peak of the curve and the blackbody’s temperature worked for all observed blackbodies.

After working all night of the 7th of October 1900, Planck found an equation which fitted the observed data. He presented this work to the German Physical Society a few weeks later on Friday the 19th of October, and this was the first time others saw the equation which has now become known as Planck’s law.

The equation he found for the energy in the wavelength interval $d \lambda$ had the form
$\boxed{ E_{\lambda} \; d \lambda = \frac{ A }{ \lambda^{5} } \frac{ 1 }{ (e^{a/\lambda T} - 1) } \; d\lambda }$

(compare this to the Wien distribution law above).

After presenting his equation he sat down; he had no explanation for why this equation worked, no physical understanding of what was going on. That understanding would dawn on him over the next few weeks, as he worked tirelessly to explain the equation on a physical basis. It took him six weeks, and in the process he had to abandon some of the ideas in physics which he held most dear. He found that he had to abandon accepted ideas in both thermodynamics and electromagnetism, two of the cornerstones of 19th Century physics. Next week, in the fourth and final part of this blog-series, I will explain what physical theory Planck used to explain his equation; the theory which would usher in the quantum age.

## Derivation of Planck’s radiation law – part 2

In the first part of this blog (here), I described how experimenters at the Physikalisch-Technische Reichsanstalt (PTR) determined the true spectrum of blackbody radiation during the 1890s, By the year 1900, primarily by the work of Heinrich Rubens, Ferdinand Kurlkbaum, Ernst Pringsheim and Otto Lummer, the complete spectrum, from the ultraviolet through the visible and into the infrared, was known for the very first time. As the true shape of the blackbody spectrum started to emerge from this experimental work, theoreticians tried to find a theory to explain it.

The first to meet with any success was Wilhem Wien. As I mentioned in the first part of this blog, in 1893 he came up with his displacement law, which gave a very simple relationship between the wavelength of the peak of the spectrum and its temperature.

$\lambda_{peak} = \frac{ 0.0029 }{ T }$

where $\lambda_{peak}$ is the wavelength of the peak in metres, and $T$ is expressed in Kelvin.

By 1896 Wien had come up with a theory to explain the shape of the spectrum (even though the shape in the infrared was not fully known at that time). In what we now call ‘Wien’s distribution law’ or ‘Wien’s approximation’, he tried to explain the blackbody spectrum using thermodynamic arguments, and assuming that the gas molecules obeyed the Maxwell-Boltzmann speed distribution for molecules (or atoms) in a gas. I will not derive that explanation here, but if any readers wish me to derive it I can do so at a later date.

Wilhelm Wiens, who in 1893 came up with Wiens displacement law, and in 1896 with the Wien distribution.

## Wien’s distribution law (1896)

What Wien suggested was that the energy of a black body in the wavelength interval $d \lambda$ was given by

$E_{ \lambda } d \lambda = \frac{ A }{ \lambda ^{5} } f( \lambda T) d \lambda$

Wien found, using the Maxwell-Boltzmann distribution law for the speed of atoms (or molecules) in a gas, that the form of the function $f( \lambda T)$ was

$f( \lambda T ) = e^{ -a / \lambda T }$

and so

$\boxed{ E_{ \lambda } d \lambda = \frac{ A }{ \lambda ^{5} } e^{ -a / \lambda T } d \lambda }$

where $A \text{ and } a$ were constants to be determined.

If we wish to express this in terms of frequency $\nu$ instead of wavelength $\lambda$ then we need to remember that, from the wave equation, $c = \nu \lambda$ and so $\lambda = c/\nu$. But, we also need to rewrite $d\lambda$ in terms of $d\nu$ and to do this we write

$\nu = \frac{ c }{ \lambda } \rightarrow d \lambda = \frac{ -c }{ \nu^{2} }\; d \nu$

We can ignore the minus sign as it is just telling us that as the frequency increases the wavelength decreases, and so substituting for $\lambda \text{ and } d\lambda$ we can write
that the energy in the frequency interval $d \nu$ is given by

$E_{\nu} d \nu = \frac { A \nu^{5} } { c^{5} } e^{ -a \nu / cT } \frac{ c }{ \nu^{2} } d \nu$

$\boxed{ E_{\nu} d \nu = A^{\prime} \nu^{3} e^{ -a^{\prime} \nu / T } d \nu }$

where $A^{\prime} \text{ and } a^{\prime}$ are also just constants to be determined.

## Wien’s ‘law’ breaks down

As I will show next week, Wien’s distribution law gave good (but not perfect) agreement with the blackbody curve on the short-wavelength side of the peak (what we now call the ‘Wien-side’ of the peak). But, as experimental results on the long-wavelength side started to emerge from the PTR, it became clear that his ‘law’ did not work on that side; it broke down on the long-wavelength side and showed very poor agreement with the actual observed curve.

Next week, in part 3 of this blogpost, I will also describe how and why Planck got involved in the problem, and what the solution he concocted was; the law which would correctly describe the blackbody spectrum and usher in the quantum age.

## The Penzias & Wilson CMB discovery paper

For the final part of my series to commemorate the 50th anniversary of the discovery of the Cosmic Microwave Background (CMB), today I’m going to show the original papers announcing this momentous discovery to the scientific community. I should point out that I have taken these photographs to portray the historical context, even though it is not easy to read what they say. The papers have been scanned and are available online for free in both gif and pdf format, follow this link to get them.

The announcement of the CMB’s discovery came in two back-to-back papers in the July 1st edition of The Astrophysical Journal (see the front page below). On pages 414 to 419 Robert Dicke and his team from Princeton (Dicke, Peebles, Roll and Wilkinson, 1965, ApJ, 142, pp414-419) described the theoretical work they had been doing which predicted a relic radiation from a hotter denser early Universe.

The front page of the July 1st 1965 volume of Astrophysical Journal, in which the Penzias and Wilson CMB paper is to be found.

Figure 1 from Dicke etal. in which they plot the “possible thermal history” of the Universe. It is due to the high temperatures in the early Universe that blackbody radiation would have been emitted when the Universe changed from being a plasma to being neutral (“re-combination” or “decoupling”) – shown in this figure as happening when the Universe had a radius of $10^{-3}$ (one thousandth of its current size)

The part of Dicke etal’s paper in which they refer to Penzias and Wilson’s observations.

Then, immediately following on from this paper, on pages 419 to 421 is the paper by Penzias and Wilson (Penzias and Wilson, 1965, 142, pp419-421). For the announcement of one of the most important discoveries in the history of science, both the title and content are very understated.
The title is A Measurement Of Excess Antenna Temperature at 4080 Mc/s, hardly a title to grab the attention.

The beginning of Penzias and Wilson’s paper. It possibly has the most understated title of any scientific paper of such importance.

The paper is nearly entirely technical, detailing their experiment and the steps they had taken to ensure that they accounted for the origin of every signal detected, apart from the “excess antenna temperature” of the title. At the end of the first paragraph of the paper is the following sentence – their only reference to its possible origin.

The only reference to the possible explanation for Penzias and Wilson’s “excess antenna temperature” (i.e.. signal) is the line “a possible explanation for the observed excess noise temperature is the one given by Dicke, Peebles, Roll and Wilkinson (1965) in a companion letter in this issue.”

The paper was submitted on the 13th of May 1965, as can be seen below.

The end of Penzias and Wilson’s paper, which was submitted on the 13th of May 1965.

Although the paper appeared in the July 1st volume of Astrophysical Journal, the New York Times had picked up on the story and ran its discovery as headlines in their issue on the 21st of May 1965. Although press releases of major discoveries are now often made when the paper is submitted, I would imagine it was rather unusual in the 1960s for scientific discoveries to be published in the popular press before the journal article had appeared. Does anyone now of other examples from this time and before?

A rather fuzzy screen capture of the front page of the New York Times from the 21st of May 1965

And this is the actual article, from the New York Times archives (one has to pay to get such articles, but it is not much).

The actual article as it appeared on the front page

The remainder of the article from the 21 May 1965 edition of the New York Times on the CMB’s discovery

That concludes my series to mark the 50th anniversary of this most important of discoveries. If you want to read far more about the history of the CMB’s discovery, as well as its 1948 prediction and what we can learn from it, then check out my book by following this link.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

## Derivation of Planck’s radiation law – part 1

One of my most popular blogposts is the series I did on the derivation of the Rayleigh-Jeans law, which I posted in three parts (part 1 here, part 2 here and part 3 here). I have had many thousands of hits on this series, but several people have asked me if I can do a similar derivation of the Planck radiation law, which after all is the correct formula/law for blackbody radiation. And so, never one to turn down a reasonable request, here is my go at doing that. I am going to split this up into 2 or 3 parts (we shall see how it goes!), but today in part 1 I am going to give a little bit of historical background to the whole question of deriving a formula/law to explain the shape of the blackbody radiation curve.

## ‘Blackbody’ does not mean black!

When I first came across the term blackbody I assumed that it meant the object had to be black. In fact, nothing could be further from the truth. As Kirchhoff’s radiation laws state

A hot opaque solid, liquid, or gas will produce a continuum spectrum

(which is the spectrum of a blackbody). The key word in this sentence is opaque. The opaqueness of an object is due to the interaction of the photons (particles of light) with the matter in the object, and it is only if they are interacting a great deal (actually in thermal equilibrium) that you will get blackbody radiation. So, examples of objects which radiate like blackbodies are stars, the Cosmic Microwave Background, (which is two reasons why astronomers are so interested in blackbody radiation), a heated canon ball, or even a canon ball at room temperature. Or you and me.

Kirchhoff’s 3 radiation laws, which he derived in the mid-1800s

Stars are hot, and so radiate in the visible part of the spectrum, as would a heated canon ball if it gets up to a few thousand degrees. But, a canon ball at room temperature or you and me (at body temperature) do not emit visible light. But, we are radiating like blackbodies, but in the infrared part of the spectrum. If you’ve ever seen what people look like through a thermal imaging camera you will know that we are aglow with infrared radiation, and it is this which is used by Police for example to find criminals in the dark as the run across fields thinking that they cannot be seen.

The thermal radiation (near infrared) from a person. The differences in temperature are due to the surface of the body having different temperatures in different parts (e.g. the nose is usually the coldest part).

Kirchhoff came up with his radiation laws in the mid-1800s, he began his investigations of continuum radiation in 1859, long before we fully knew the shape (spectrum) of a blackbody.

## Germans derive the complete blackbody spectrum

We actually did not know the complete shape of a blackbody spectrum until the 1890s. And the motivation for experimentally determining it is quite surprising. In the 1880s German industry decided they wanted to develop more efficient lighting than their British and American rivals. And so they set about deriving the complete spectrum of heated objects. In 1887 the German government established a research centre, the Physikalisch-Technische Reichsandstalt (PTR) – the Imperial Institute of Physics and Technology, one of whose aims was to fully determine the spectrum of a blackbody.

PTR was set up on the outskirts of Berlin, on land donated by Werner von Siemens, and it took over a decade to build the entire facility. Its research into the spectrum of blackbodies began in the 1890s, and in 1893 Wilhelm Wien found a simple relationship between the wavelength of the peak of a blackbody and its temperature – a relationship which we now call Wien’s displacement law.

Wien’s displacement law states that the wavelength of the peak, which we will call $\lambda_{peak}$ is simply given by

$\lambda_{peak} = \frac{ 0.0029 }{ T }$

if the temperature $T$ is expressed in Kelvin. This will give the wavelength in metres of the peak of the curve. That is why, in the diagram below, the peak of the blackbody shifts to shorter wavelengths as we go to higher temperatures. Wien’s displacement law explains why, for example, an iron poker changes colour as it gets hotter. When it first starts glowing it is a dull red, but as the temperature increases it becomes more yellow, then white. If we could make it hot enough it would look blue.

The blackbody spectra for three different temperatures, and the Rayleigh-Jeans law, which was behind the term “the UV catastrophe”

By 1898, after a decade of experimental development, the PTR had developed a blackbody which reached temperatures of 1500 Celsius, and two experimentalists working there Enrst Pringsheim and Otto Lummer (an appropriate name for someone working on luminosity!!) were able to show that the blackbody curve reached a peak and then dropped back down again in intensity, as shown in the curves above. However, this pair and others working at the PTR were pushing the limits of technology of the time, particularly in trying to measure the intensity of the radiation in the infrared part of the spectrum. By 1900 Lummer and Pringsheim had shown beyond reasonable doubt that Wien’s ad-hoc law for blackbody radiation did not work in the infrared. Heinrich Rubens and Ferdinand Kurlbaum built a blackbody that could range in temperature from 200 to 1500 Celsius, and were able to accurately measure for the first time the intensity of the radiation into the infrared. This showed that the spectrum was as shown above, so now Max Planck knew what shape curve he had to find a formula (and hopefully a theory) to fit.

In part 2 next week, I will explain how he went about doing that.

## Tân yn Llŷn (A Fire in Llŷn)

Last week, in this blog here, I shared a song “Dros Gymru’n Gwlad”, performed by Dafydd Iwan but written by the Reverend Lewis Valentine. I mentioned in that blog that Lewis Valentine held a special place in 20th century Welsh history, so today I am giving that history.

Lewis Valentine (1893-1986), together with Saunders Lewis (1893-1985) and D.J. (David John) Williams (1885-1970) were the three men who were involved in this particular event. Valentine was a Baptist minister in North Wales. Saunders Lewis was born and brought up in Liverpool in a Welsh-speaking family (his father was a minister in a Welsh-speaking chapel in Liverpool). He became a celebrated playwright and lecturer in English at Swansea University, and the founder in 1925 of Plaid Cymru, the ‘Party of Wales’. D.J. Williams (never known as David John!) was born in Rhydycymerau in rural Carmarthenshire, and in addition to writing short stories he was an English teacher at the Grammar School in Fishguard, West Wales (I went to that school in the 1970s but by that time it was a comprehensive school). In 1936, in protest to the

• ‘English’ preparations for war
• English imperialism in Wales (some 500,000 people had protested against the construction of the bombing school)
• the destroying of an historical Welsh landmark (Penyberth had been used for centuries as a stopping point for pilgrims going to Ynys Enlli (Bardsey Island), which is at the end of the Llŷn peninsula)

the three of them set fire to an RAF bombing school on the Llŷn Peninsula, at a place called Penyberth. At the time the men were in their early forties, and deliberately chosen by Plaid Cymru as the three were all middle-aged and respectable pillars of their communities.

DJ Williams (left), Lewis Valentine (centre) and Saunders Lewis (right); taken in 1936, the year they set fire to the bombing school in Penyberth on the Llŷn peninsula. In Welsh, they are often known as “y tri” (the three).

Penyberth is often seen as the first act of Welsh nationalism (patriotism) of the 20th Century. After setting fire to the bombing school, the three men made their way to the local police station where they gave themselves up and told the confused police officer what they had done and why. In the subsequent court case in Caernarfon a largely sympathetic jury of their peers failed to find them guilty, and so the trial was sent to the Old Bailey in London, where the three were found guilty and sent to jail. They each served 9 months in prison in Wormwood Scrubs. Saunders Lewis was, controversially, dismissed from his job at Swansea University before he had been found guilty of the crime. He was subsequently hired as a lecturer of English at Cardiff University (strictly speaking “University of Wales, Swansea” and “University of Wales, Cardiff”, as they were known at the time).

A plaque at the site of the arson of the bombing school in Penyberth.

An interesting historical quirk of their trial in Caernarfon is that, at that time (and up until the “Welsh Language Act” of 1967), a Welsh person had no right to give their testimony in Welsh in a court in Wales. Ever since the “Laws in Wales” acts of 1535-1542, English had been made the only language of legal proceedings in Wales. The only exception allowed to this rule was if one could prove that one’s English was inadequate. All three wished to give their testimonies in Welsh, but Lewis Valentine was the only one allowed to do so, as no evidence could be provided that he was anything like fluent enough in English.

As for the other two, Saunders Lewis had a degree in English from Liverpool University (the city where he was born and brought up); and D.J. Williams also had a degree in English from Aberystwyth (University of Wales, Aberystwyth), and had done post-graduate studies at Jesus College, Oxford! Additionally, at the time of the trial, Saunders Lewis was lecturing in English, and D.J. Williams teaching English at Fishguard Grammar School. Not surprisingly, their English was deemed to be good enough, and they were not allowed to testify in their own language.

If you want to read more about this episode of Welsh history, I can recommend the excellent book by Dafydd Jenkins, my copy is shown below.

My copy of the book “Tân yn Llŷn” by Dafydd Jenkins, which I bought in 1986.

Had you ever heard of Penyberth, or any of “y tri” before?

## Dros Gymru’n Gwlad – Dafydd Iwan (song)

Today I thought I would blog about this beautiful song (hymn), “Dros Gymru’n Gwlad” (For Wales, our country), written by the Reverend Lewis Valentine, and here performed by Dafydd Iwan. It is sometimes referred to as Wales’ second national anthem. This version of the song is, in fact, entitled “Gweddi Dros Gymru” (A Prayer for Wales) by Dafydd Iwan; but it is the same song, just with a different (and maybe more apt) title.

“Gweddi dros Gymru” (Prayer for Wales) appeared on Dafydd Iwan’s 1986 album “Gwinllan a Roddwyd” (A vineyard was given).

I will blog next week about who Lewis Valentine was, because he holds a particular place in Welsh history for an act of defiance he committed in 1936 along with DJ Williams and Saunders Lewis. But, today I will just concentrate on this song/hymn.
“Dros Gymru’n Gwlad” is usually set to the tune of Sibelius’ Finlandia, as it is in the video I include below.

Here are the words (in Welsh)

Y winllan wen a roed i’n gofal ni;
D’amddiffyn cryf a’i cadwo’n ffyddlon byth,
A boed i’r gwir a’r glân gae1 ynddi nyth;
Er mwyn dy Fab a’i prynodd iddo’i hun,
O! crea hi yn Gymru ar dy lun.

O! deued dydd pan fo awelon Duw
Yn chwythu eto dros ein herwau gwyw,
A’r crindir cras dan ras cawodydd nef
Yn erddi Crist, yn ffrwythlon iddo Ef;
A’n heniaith fwyn â gorfoleddus hoen
Yn seinio fry haeddiannau’r Addfwyn Oen.

And now for my translation. As always, I am not going to attempt to retain any rhyme or meter, just translate the words as best I can; so that you get the meaning of what Lewis Valentine was trying to say in his song/hymn.

For Wales our country, O Father I raise a wail,
This pure vineyard which was given to us to care for;
May You protect it vigorously and keep it forever faithful,
And let the true and the pure find in her a nest;
For your Son who bought it for himself,
Oh! create a Wales in Your image.

Oh! Let there come a day when the breezes of God
Are once again blowing over our wilted acres,
And the awful wasteland under the grace of showers from heaven
Gardens of Christ, fruitful to Him;
And her old sweet language with a cheerful vigour
Ringing out on high, the deserves of the Gentle Lamb.

Here is an alternative translation which I found. It is far more poetic and less clumsy than mine, but less true to what Lewis Valentine was actually saying in his lyrics.

For Wales our land O Father hear our prayer,
This blessed vineyard granted to our care;
May you protect her always faithfully,
And prosper here all truth and purity;
For your Son’s sake who bought us with His blood,
O make our Wales in your own image Lord.

O come the day when o’er our barren land
Reviving winds blow sent from God’s own hand,
As grace pours down on parched and arid sand
We will bear fruit for Christ by his command,
Come with one voice and gentle vigour sing
The virtues of our gentle Lamb and King

Here is a video I have created on YouTube of Dafydd Iwan’s version of this song/hymn.

Had you heard of this song before?

## Why do we have leap seconds?

At midnight on the night of Monday the 30th of June, an extra second was added to our clocks. A so-called leap second. Did you enjoy it? Me too 🙂 I got so much more done….. But, why do we have leap seconds?

In this blog here, I explained the difference between how long the Earth takes to rotate $360^{\circ}$ (the sidereal day) and how long it takes for the Sun to appear to go once around the Earth (the mean solar day). We set the length of our day, 24 hours, by the solar day. If there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, then there should be $24 \times 60 \times 60 = 86,400 \text{ seconds}$ in a solar day. But, there aren’t! The Earth’s rotation is not consistent, that is if we measure the length of a mean solar day, it is not consistently 86,400 seconds. This difference is why we need leap seconds.

A leap second was added at midnight on the 30th of June. It was the first leap second to be added since 2012.

But, how do we accurately measure the mean solar day (the average time the Sun appears to take to go once around the sky) , and what is causing the length of the mean solar day to change?

## How do we define a second?

When the second was first defined, it was defined so that there were 86,400 seconds in a mean solar day. But, since the 1950s, we have a very accurate method qof measuring time, atomic clocks. Using these incredibly accurate time pieces (the most accurate atomic clocks will be correct to 1 second over some tens of thousands of years) we have been able to see that the mean solar day varies. It varies in two ways, there is a gradual lengthening, but there are also random changes which can be either the Earth speeding up or slowing down its rotation.

## How do we measure the Earth’s rotation so accurately

In order to measure the Earth’s rotation accurately we use the sidereal day, which is roughly four minutes shorter than the mean solar day. By definition, the sidereal day is the time it takes for a star to cross through a local meridian a second time. But, actually, stars in our Galaxy are not good for this as they are moving relative to our Sun. So, in fact, we use quasars, which are active galactic nuclei in the very distant Universe; and use radio telescopes to pinpoint their position.

## The gradual slowing down of the Earth’s rotation

There is a gradual and unrelenting slowing down of the Earth’s rotation, which may or may not be greater than the random changes I am going to discuss below. This gradual slowing down is due to the Moon, or more specifically to the Moon’s tidal effects on the Earth. As you know, the Moon produces two high tides a day, and this bulge rotates as the Earth rotates. But, the Moon moves around the Earth much more slowly (a month), so the Moon pulls back on the bulge of the Earth, slowing it down. To conserve angular momentum, the Earth slowing down means the Moon moves further away from the Earth, about 3cm further away each year.

## The random fluctuations in the Earth’s rotation

In addition to the unrelenting slowing down of the Earth’s rotation due to the Moon, there are also random changes in the Earth’s rotation. These can be due to all manner of things, including volcanoes and atmospheric pressure. These random fluctuations can either speed up or slow down the Earth’s rotation.

We have been having leap seconds since the 1970s when atomic clocks became accurate enough to measure the tiny changes in our planet’s rotation. Since them we have added a leap second when it is decided that we need it, typically but not quite once a year. However, having that extra second at the end of June can cause glitches with computers, and so there are discussions to remove the leap second and replace it with something larger on a less frequent basis.

## The Prediction of the Cosmic Microwave Background – the original paper

Last week I reposted my blog about the prediction of the cosmic microwave background (CMB), which I had originally written in April 2013. This month, July, marks the 50th anniversary of the first detection of the CMB, and I will blog about that historic discovery next week. But, in this blog, I wanted to show the original 1948 paper by Alpher and Hermann that predicted the CMB’s existence.

I learnt far more about the history of the CMB’s prediction whilst researching for my book on the CMB, which was published at the end of 2014 (follow this link to order a copy). In doing my research, I found out that many of the things I had been been told or had read about the prediction were wrong, so here I wanted to say a little bit more about what led up to the prediction.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

## Gamow did not predict the CMB

Many people either do not know of the 1940s prediction of the CMB, or they attribute its prediction to George Gamow. In fact, it was his research assistants Ralph Alpher and Robert Hermann who made the prediction, but as head of the group it is often Gamow who gets the credit.

Ralph Alpher had just finished his PhD on the origin of the elements, and after the publication of the famous Alpher, Bethe, Gamow paper (see my blog here about that), Gamow started writing a series of papers on the nature of the early Universe. One of these papers was entitled “The Evolution of the Universe”, and it appeared in Nature magazine on the 30th of October 1948 (Nature 1948, volume 162, pages 680-682) – here is a link to the paper.

Gamow’s October 1948 paper in Nature was entitled “The Evolution of the Elements”.

Although a man of huge intellect and inventiveness, Gamow was often sloppy on mathematical detail. Alpher and Hermann spotted an error in some of Gamow’s calculations on the matter-density, and so wrote a short letter to Nature magazine to correct these mistakes. The letter is entitled “Evolution of the Universe”, nearly the same title as Gamow’s paper, but with no “The” at the start. The letter is dated 25 October 1948. It appeared in Nature magazine on the 13th of November 1948 (Nature 1948, volume 162, pages 774-775) – here is a link to the paper.

Here is the paper in its entirety (it is short!), and I have highlighted the part which refers to a relic radiation from the early Universe, what would become known as the cosmic microwave background.

The original paper (letter) by Alpher and Hermann which makes the first prediction of the cosmic microwave background (CMB). It was published in Nature magazine on the 13th of November 1948.

As you can see, the prediction is not the main part of the paper, it just forms two sentences!

Next week, I will blog about the accidental discovery of the CMB by Penzias and Wilson, which was published 50 years ago to this month (July).

## How long is a day?

How long is a day? It seems like a stupid question. As everyone knows, there are 24 hours in a day. The Earth rotates on its axis once every 24 hours. Or does it?

## The difference between a ‘solar day’ and a ‘sidereal day’

In fact, there is a slight difference between how long the Earth actually takes to rotate $360^{\circ}$ (the ‘sidereal day’, the day as measured by the motion of stars in the sky) and how long it takes for the Sun to appear to go once around the Earth (the ‘solar day’). This is because, during the course of a day, the Earth has moved a little bit in its orbit about the Sun, and so the Earth has to rotate a little bit more than $360^{\circ}$ to bring the Sun back over the local meridian. We measure our day by the solar day, as otherwise the time of local noon would drift away from midday more and more, which we clearly do not want. (You may notice that this is related to the difference between a sidereal month and a synodic month, which I discussed here.)

The difference between a solar day and a sidereal day, which comes about because of the Earth’s motion about the Sun.

## Kepler’s 2nd law

This difference is easy to measure, with a sidereal day being, on average, 4 minutes shorter than a solar day. This means that stars rise about 4 minutes earlier from day to day, or over the course of a month about 2 hours earlier. But, this 4 minute difference is not constant. It changes because the Earth is orbiting the Sun in an ellipse, not a circle. This means that the Earth’s speed in orbit changes, it travels faster when it is closer to the Sun (in January), and slower when it is further from the Sun (in July). This fact, which was first noticed by Kepler, is now known as Kepler’s 2nd law of planetary motion. It is illustrated below.

Kepler’s 2nd law of planetary motion states that a planet will sweep out an equal area in equal time, so that in the same period of e.g. 1 month, the three areas A will be equal. This means that a planet travels quicker when it is near the Sun, and slower when it is further away.

When the Earth is travelling quicker it has to rotate a little bit more to complete a solar day, and when it is travelling slower it has to rotate a little bit less. So, the length of the actual solar day changes in the course of a year, but in a cyclical fashion (this is known as the equation of time, something I will explain more in a future blog). The equation of time is the reason for the East-West motion of the Sun as shown in the analemma, which I discuss here.

Because of these changes in the difference between a sidereal day and a solar day at any given time of the year, we define something called the mean solar day, and it is the mean solar day which should be 24 hours, or 86,400 seconds long. But, it isn’t! In a blog next week, I will explain how the Earth’s period of rotation is not consistent, and this is why we had a leap second at midnight on the 30th of June this year.