Table of contents

Why are the `popular science' shelves of our bookshops groaning under the weight of the numerous books on cosmology, the quantum world, the fundamental particle zoo and similar topics both mysterious and esoteric? The answer is obvious, of course - because there's a market out there. A sizeable proportion of the avid readers are no doubt bright young people eager to read about the wonders of science, or in this case physics, and be awed (overawed?) by the strange behaviour of matter and energy on scales unimaginably larger or smaller than ourselves.

Good thing too, you might say. I agree - at least to the extent that this particular readership is excited and enthused by these popular tracts to study physics at A-level and perhaps beyond. Maybe not so good though, if the result is that some youngsters are turned off physics because it comes over as `OK for the bright ones but too difficult for me'. Cosmological and high energy physics is very difficult, and it's not just a matter of the mathematical skills that one needs to make any serious headway. The concepts involved are, to say the least, strange and counter-intuitive. This is great for triggering scientific curiosity and the excitement of physics, but how typical are they of the problems and challenges faced by the large majority of professional physicists, in industry, government research labs or, indeed, in academia? And how characteristic of the flavours of physics that the average A-level student or undergraduate will encounter?

Recent correspondence in Physics World indicates that our undergraduate physics programmes are on the whole disappointingly bland compared with the expectations of graduates seduced, perhaps, by glimpses of quarks, superstrings and black holes. My argument is not that we shouldn't sell physics in this way, but that we could try to provide a more balanced sample of what physics is really about. Above all, we need to sell the idea - to the public at large as well as the potential physics undergraduate - that it is fundamentally important in our everyday lives.

It is `person-sized physics' (give or take a factor of 10<sup>10</sup>!) which lies behind the numerous items that make up our world today, among them PCs, mobile phones, video CDs, `intelligent' materials and the multifarious means for medical imaging. Can't we promote an interest in physics through popular books and articles on wonders such as these? Yes, such books do exist, but on the bookshop shelves you will find scant representation of this type of physics among the well-written and superbly presented `pop' books like those of Hawking, Gribbin and Davies.

Until recently I was a Deputy Editor of this journal. During the past few years we have published numerous `special issues' focusing on a specific topic. Those I have edited have reflected my philosophy, and have included issues on Laser Applications, Energy Update, and the Physics of the Body. Other editors have produced equally `applied' special issues. Might youngsters (or even an oldster) be equally excited by the elucidation of the mysteries of the quantum world in the context of, say, the silicon chip as by the world of the fundamental particle? Surely the glamour of physics-based state-of-the-art recording technology or the latest PC or sleek new aircraft or medical imaging technique can compete with the `wonders of space and time' exhaustively recycled in the popular literature?

Come on popular science authors! Try your hand at dressing up the physics of everyday life so that the excitement and immediate relevance of physics is displayed before the people - not least, the young people - in the street.

Thanks to an award from the UK's Millennium Commission, science is being made accessible to bus passengers around Wales, and now the initiative is also being extended to those travelling around five cities in other parts of Britain.

Frank Burnet of Bristol first received funding of £10 170 in December 1997 from the Millennium Awards scheme to assist with his development of a series of posters combining strong visual images with careful copy to encourage passengers on bus routes throughout Wales to think about issues in contemporary science. This initial project was so successful that the UK Government's Office of Science and Technology decided at the start of 1999 to invest a further £133 746 to enable Frank to educate and entertain bus passengers in Bristol, London, Belfast, Edinburgh, Birmingham and Manchester with his ideas over the next 17 months.

Frank's initial proposal was typical of those which have received funding from the awards scheme, fulfilling a personal goal as well as benefiting the individual's community. On completion of the award each winner becomes a member of the Millennium Awards Fellowship - the single nationwide initiative which recognizes the personal achievement and contribution to the community that has been made in each case. By the new millennium there will be 40 000 Millennium Fellows; so far around 18 500 people have benefited from 57 existing schemes under the overall theme of `You and your community'.

Among the themes at this year's Edinburgh International Science Festival, taking place between Saturday 3 and Sunday 18 April, will be Ethics, Clean technology, Visions of the future, Life in space, Health and medicine and The car. Scientists, technologists and engineers from throughout Scotland, the UK and further afield will be assembling to communicate their work to an audience of over 150 000 adults and children, via a vast array of shows, workshops, talks, exhibitions, conferences, walks and tours within the city.

Notable speakers at the 1999 event will be: John D Barrow (Between inner space and outer space); Richard Wiseman (Investigating psychics); Heinz Wolff (Space travel - science or just a waste of money?); Melvyn Bragg (On Giants' Shoulders - milestones in the history of science, focusing on 12 individuals and their extraordinary breakthroughs); Adam Hart-Davis (Thunder, flush and Thomas Crapper - a history of the lavatory); Kevin Warwick (March of the machines); Ralph Lorenz (Habitable worlds - could the planets in our solar system support life?). Full information on the Science Festival can be obtained from the office at 149 Rose Street, Edinburgh EH2 4LS (tel: 0131 220 3977, fax: 0131 220 3987, e-mail: esf@scifest.demon.co.uk).

A total of £105m will be invested in the National Grid for Learning programme during 1999-2000, as part of the UK Government's drive to raise standards and open up learning to everyone. This was announced in December as part of the £700m for supporting investment on Information and Communications Technology (ICT) in UK schools and will enable up to half of schools in England to obtain the technical infrastructure needed to get wired up to the Grid. At least 15% of the £105m total has been reserved for software development, which should enable teachers to make use of good quality CD-ROM packages in which they have confidence. It also represents another step towards meeting the goals of modernizing the classroom, connecting all schools to the Internet by 2002 and providing all schools with access to the National Grid for Learning. Total investment during 1998-99 amounted to £102m.

The Grid is already providing curriculum support and teacher training materials through its Standards site and it is expected that there will be a substantial increase in the availability of learning resources on the Grid over the next year, including more resources aimed at young learners. Latest in the series of initiatives is the development of faster networks to expand the educational potential of ICT in schools, the creation and dissemination of interactive resources to support teachers and learners, including materials developed by schools themselves, and the use of public/private partnerships to secure value-for-money expenditure as well as the use of ICT as a means of revenue generation.

Early in January a new £2.5m programme aimed at developing the educational role of museums and art galleries over the next three years was also announced. Partnerships between schools, museums and galleries were invited to submit project proposals intended to forge closer links or spread existing good practice to other areas. Priority will be given to projects in areas such as: literacy, numeracy and science; using IT to develop museum/school links; developing museum and gallery work within schools through loan services or other means; employability and preparing young people for adult life. It is hoped that this new programme will give museums and galleries the opportunity to enlarge their inherent role in supporting learning both at school and now additionally in the home.

Key facts and figures about the labour market for new graduates in the UK were published recently in the IES Annual Graduate Review 1998-99, which indicates that the demand for graduates amongst the traditional recruiters has continued to grow steadily, along with reports of recruitment difficulties. It is noteworthy that last year one in three graduates went into fixed-term or temporary appointments, while many of those who took up permanent jobs went into lower level work that did not make use of their graduate skills. Many graduates are taking more than a year, and sometimes up to three years, to find their way into permanent jobs and careers.

Those graduating in computer science, engineering and mathematics, medicine and related subjects, or education have been the most likely to gain high level managerial, professional or technical jobs and have the lowest unemployment rates. In contrast, those with biological science, humanities, social sciences or creative arts degrees are most likely to be unemployed initially. Many new graduates commenced their jobs by earning salaries in the range £10 000-15 000, but they should of course continue to earn more than those lesser qualified, as well as having lower unemployment rates.

Of the 400 000 students who graduated in 1998 (more than double the total of a decade ago), over half had first degrees and the rest undergraduate or postgraduate qualifications. Despite the growth, entry to the physical sciences, engineering and technology has been falling, as has the proportion on sandwich courses. Women now comprise the majority of entrants to first degrees but remain under-represented in mathematics, physical science and engineering or technology courses.

Interestingly more than one in three students now has a paid job during their course; such work experience can be beneficial to their long-term job searches. In the longer term, numbers of graduates are expected to stay broadly constant over the next three years, followed by a slight growth in numbers. It is expected that the rising demand for graduates will be maintained but the number of openings for new graduates will not grow sufficiently quickly to absorb the higher numbers actually graduating. With the costs of a degree rising and the returns falling, students would be advised to be increasingly flexible in their investment in higher education and should view the long-term career options.

Employers, on the other hand, will have the challenge of recruiting graduates with the right skills and competencies. Those in the greatest demand will combine intellectual with personal attributes and skills in areas such as team-working, motivation and communication, as well as the ability to continue learning. Such attributes will also be important for those in technical areas where good specialist knowledge will rarely be enough. Working and communicating with nonspecialist customers and colleagues is required more and more. Employers should also be focusing on their actual needs in recruits and what they can offer by way of jobs and careers, so that a more realistic match between recruits and jobs, with better long-term performance and retention, ensues.

IES Annual Graduate Review 1998-99: the Key Facts by R Pearson et al (IES Report 354, January 1999, ISBN 1 85184 283 7) costs £27.50 and is obtainable from Grantham Book Services, Isaac Newton Way, Alma Park Industrial Estate, Grantham NG31 9SD (fax: 01476 541061).

Students from around the UK are being offered the chance to work alongside some of the country's top scientists and engineers, thanks to an initiative from AEA Technology. The company is asking undergraduates, postgraduates and researchers to submit exciting project proposals related to work it carries out, and the successful applicants will be able to undertake these projects at one of AEA Technology's UK sites. Placements, which will be paid, will last for between six and eight weeks in the summer and up to ten are available.

The company, which is committed to supporting young scientists and engineers, operates in ten different business areas including Energy, Engineering software, Nuclear engineering and the Environment. Application forms and further information may be obtained from Anne Little, AEA Technology plc, 424.4, Harwell, Didcot, Oxon OX11 0RA (tel: 01235 432192, e-mail: anne.little@aeat.co.uk). The deadline for applicants is Friday 7 May 1999.

Physics in Mathematical Mood

Later this year, as part of the post-16 initiative of the Institute of Physics, a booklet with the above title will be published. In draft form, the booklet was discussed at the ASE conference in January. Some of the issues raised are briefly set out here. If you have any views to contribute, please write to Simon Carson at the Institute of Physics or e-mail simon.carson@physics.org.

A mathematical view of the world is intrinsically a part of physics and therefore physics should be studied in an appropriately mathematical way. However, we all know that, to some students at least, mathematics proves to be a stumbling block rather than a powerful aid to understanding. So how can we help?

Realizing that as physics teachers we need to deliver the mathematics necessary to an understanding of our subject is a start. Its corollary is that we need to find the space within the physics core. We may wish to use supplementary courses such as AS mathematics or QCA's new free-standing mathematics units, but requiring additional courses as a prerequisite to a study of A-level physics may deter students. Teaching the mathematics in context may aid understanding but we also must ensure that techniques are seen in a variety of contexts and that at some point the tool is abstracted from the background.

As teachers we need to be aware of the very basic mathematical difficulties that students bring with them: the use of calculators, standard form, simple algebraic manipulation, for example. Mathematical arguments need to be developed fully and carefully. Encouraging cooperation and discussion between students may help the less able to understand and the more able to appreciate and develop their own understanding through making explicit their reasoning by explaining it to others.

And what of new technology? Software tools allow students to develop their understanding about graphs, for example, enabling them to investigate the characteristics of particular functions. Modelling tools allow teachers or students to build models or more simply to create animations to demonstrate the properties of mathematical entities such as vectors. Graphical calculators mean that all students can have cheap access to such tools and it may be that some of the analytical mathematical tools we hold so dear are obsolete.

Other issues are discussed in the booklet and were aired at the ASE conference: the situation in HE, the approach to mathematics taken by the Salters Horners approach, ways to introduce special functions such as exponentials, ways of thinking about the relationships between variables as expressed in equations. Many practical suggestions are made in the booklet about how we can help and support students and, most importantly, how we can communicate to them some of the beauty and pleasure of Physics in Mathematical Mood.

Simon Carson

A perspective on apparatus

The effective deployment of apparatus is one technique available in physics that does not exist in some other areas of teaching. We should capitalize on this. Apparatus is a tool that can be used to enable thinking and learning. There are a number of purposes to be served by the effective use of apparatus. It is no more likely that apparatus will `teach' any more than nature `teaches' physics in the first place. Discussion and the creative interpretation of observation are both necessary to the sense-making process. Apparatus must be chosen with these opportunities in mind.

In a demonstration we are trying to persuade students that the world behaves in a particular way. An attempt is being made to persuade students that a particular conception of the world is worth considering and that this conception is a fruitful and truthful picture of the world. Apparatus chosen for this purpose must have clear links between what is to be measured and the representations of that measurement. The art of demonstration is very much like a magician's show, in that it must all be well rehearsed and produce surprising and convincing results with apparently little effort.

Students will be asked to engage in exploration and explanation using apparatus. Apparatus chosen for this purpose must not look as if it has been designed to give one specific answer. Students must feel confident that they can manipulate apparatus in such a way that the apparatus can serve to express their thoughts and be shaped to try out their hypotheses. Students will also be asked to engage in more traditional laboratory work that requires precision and a careful approach. Here the apparatus must be of sufficient quality and perceived modernity to allow the students to take the tasks seriously so that they will produce work of the expected quality.

A final use for apparatus is to allow students to engage in genuine open-ended investigation where their knowledge of physics both informs their plans before work is carried out and interprets the observations and measurements from that work. Here apparatus that measures well is at a premium. The connection between manipulating the system to be measured and the resultant measurement must involve short-term feedback loops: the students must see how the system is behaving. A necessary consequence of this requirement is that the measurements are presented in a form that makes physical sense. This may imply a good deal of processing of the raw data before the number is displayed. It is in this area of measurement that we see the greatest potential for the integration of IT into laboratory practice.

Apparatus worth developing. From this analysis and from the experience of trying to make its current practicals work it seems that we need to concentrate our development of apparatus in two areas. The first is to ensure that equipment which provides a range of a high quality, attractive and effective measurement tools is in place. In this area we can expect to see the exploitation of developments in information and sensor technology lead to new approaches which open up many possibilities. The second thrust must be to have a good supply of apparatus which can be can assembled and manipulated by students to suit their thoughts and purposes. This apparatus may well be rather simple and need not to be very expensive. This may compensate for some of the implied expense of the first thrust above. Alongside these two there will continue to be steady development of traditional apparatus, often used for a demonstration.

Affording apparatus. The key to developing the apparatus within a department must be to look towards fewer items, each of which can perform more tasks, deployed as measurement tools. In this the increasing computing power available, often at a small cost, can be deployed intelligently. Following a practice elsewhere we must expect most of this development to take place in software, not the hardware. This has clear implications for the apparatus manufacturers. Low costs in computing have followed from the adoption of the widespread standards that enable one device to be used for many purposes. A similar development seems likely in the provision of apparatus. Some elements are likely to prove expensive. Compensating for the use of these expensive elements will then prove to be the challenge which makes the whole package affordable.

Building up a department. Out of the post-16 initiative will come some thoughts developed from Advancing Physics that show how we can move from the current provision. New and effectively deployed apparatus can lead to an improvement in teaching and learning and in students' perceptions of physics.

Ian Lawrence

Naomi Moran, a student at the Arnewood School, New Milton, Hampshire was the first recipient of the `Achievement in Physics' prize awarded by the South Central Branch of The Institute of Physics. Naomi received an award certificate and cheque for £100 from Dr Ruth Fenn, Chairman of the Branch, at the annual Christmas lecture held at the University of Surrey in December. She is pictured with Dr Fenn and Steve Beith, physics teacher at the Arnewood School.

Figure 1. Naomi Moran receiving her award (photograph courtesy of Peter Milford).

The award is intended to celebrate personal achievement in physics at any level at age 16-17 and is not restricted to those who gain the highest academic results. Schools across the county were invited to nominate suitable candidates; Naomi's nomination by the school's deputy head of science impressed the judges because of her ability to grasp the most difficult parts of the subject quickly, in addition to the fact that she took her AS-level science in year 11 when she was only 16. She is currently studying A-level physics, chemistry and mathematics and hopes to continue her studies at university later this year.

The American Physical Society celebrates a Century of Physics (1899-1999) at its centennial meeting in Atlanta, Georgia, on 20-26 March 1999. There will be special centennial exhibitions, a community-wide physics festival, an International day on 20 March and a Teacher's day on 23 March. Among the invited speakers at this prestigious event will be Hans Bethe, Pierre de Gennes, Martin Klein, T D Lee, Burton Richter, Charles Townes, Klaus von Klitzing and Steven Weinberg. Full details of the meeting are available from the website at http://www.aps.org/meet/CENT99/.

A one-day workshop will take place on 23 April 1999 at the University of Edinburgh's Conference and Training Centre to consider the topic `The future of university teaching? Multimedia, web and new technologies'. The workshop is being organized by Edinburgh Parallel Computing Centre and will be attended by experts in distance learning from various institutions including the Clyde Virtual University and the Open University, plus a speaker from the USA. They will present case studies of the opportunities new technologies provide for higher education, covering all aspects from development of electronic courses through delivery mechanisms to user feedback.

There is certainly an increasing need for quality teaching materials and new ways of learning. The workshop will aim to discuss how those involved in university teaching can benefit from new developments such as multimedia, the Internet, as well as new computing and networking technologies. Participation is free, with lunch and refreshments provided. More information and registration details can be found at http://www.epcc.ed.ac.uk/epcc-tec/JTAP/workshop/ or by e-mail to epcc-tec@epcc.ed.ac.uk.

Figure 6 of the article `How I teach vectors' by Steve Bolter in the November 1998 issue of Physics Education ( 33 359-65) was not printed very well. Each of the five boxes labelled `Velocity diagram' should have been shaded grey as described in the text.

All the Letters to the Editor in this issue are in the same PostScript or PDF file.

Contents

Introducing magnetic flux density, BEd Le Quesne Victoria College Science Department, Mont Millais, St Helier, Jersey JE1 4HT, UK

Coping with random modular examinationsMike Ridley Strode's College, High Street, Egham, Surrey TW20 9DR, UK

Physics Education is pleased to publish the written version of the 1998/9 Institute of Physics Schools and Colleges lecture given by Professor Peter Kalmus. This lecture is currently touring around the UK. Professor Kalmus was featured in our `People in physics' columns in the July 1998 issue of the journal (page 266) and a list of the venues for the event appeared in the News section of the November issue (page 339).

This paper examines the issue of learning physics content through real-life contexts and focuses on the context of energy. It firstly examines a variety of meanings of context-based learning and then considers two projects, one from the UK and the other from Australia, which use a context-based learning approach.

Experiments in an accelerating frame are often difficult to perform, but simple computer software allows sufficiently rapid and accurate measurements to be made on an arrangement of weights and pulleys known as Atwood's machine.

A simple analysis of the impact with the ground of two or more elastic balls in contact yields some interesting results.

Quality assessment is becoming a common feature in universities (see the news item on page 338 of the November 1998 issue of this journal). The Quality Assurance Agency is currently working through all subjects in the UK universities and rating them - their reports are accessible on http://www.niss.ac.uk/ education/hefce/qar/. University physics departments seem to be behind chemistry departments in a proactive response to quality issues, but funding has been approved for further developments in the Physics Discipline Network based at Leeds University. This article describes what the chemistry educators have done and are doing.

In an unusual collaboration, a lecturer in mathematics education has been working with undergraduate students of physical science and engineering to study their problems with mathematics. This paper discusses some of the findings.

A popular new course in Sydney is based on the scientific approach to the search for extraterrestrial intelligence. Beginning with the famous Drake equation the course explores the biological and technological aspects of the search and the social implications of possible contact.

Artificial snow crystals can be produced by a fairly simple method in a small closed cylindrical chamber made by combining an aluminium tube and a plastic tube. The chamber is set horizontally at room temperature and the end of the aluminium tube is cooled by dry ice. Water vapour is supplied by a diffusion process from the end of the plastic tube for a suitable time after cooling. The snow crystals are formed on a black sheet inside the end of the aluminium tube. The artificial snow crystals were observed at room temperature using our partial cooling method.

Measuring the range of alpha particles is not as straightforward as it might seem: two techniques give a clearer picture than just one.

This is a further book in the CAMS Series and once again there is a tantalising title. If such an apparently varied title causes you to wonder what the book is about, and perhaps causes concern that it isn't really properly about anything, then those concerns are misplaced. The theme that runs through the book is coherent and the apparently diverse topics appear naturally. That said, as the book's cover implies, it is very suitable for both the NEAB Module PH4, Astronomy and Optics, and PH7, Medical Physics, and so the content does tend to fall into those two broad categories. I found in this book all the information I would want to support teaching of both of these topic areas. It would be a bonus if you happen to teach both topics at A-level but I suspect the book might be worth purchasing even if just half of the content is of curriculum interest.

The style of presentation in the book is particularly encouraging. When shown to a Year 12 student the layout was thought attractive and inviting. Indeed it even caused him to read a few more pages. There is good use made of pictures and diagrams which appear to illustrate a point. There are very few occasions when a picture is merely pretty; they are all doing some work. Sometimes this is to illustrate contemporary contexts, elsewhere to introduce the role of people in physics. The background information and exemplar contexts given are both interesting and appropriate. They broaden the scope of the study without diverting it. It is just as well that good use is made of such illustration because there is certainly a great deal of it, and if too much were peripheral it would certainly overwhelm the text.

One aim of this series is to encourage self-study, and the short, compact sections are ideal for `nugget' revision and reading. The structure of the book is reassuringly but not restrictively rigid. Each chapter begins with clear and realistic learning objectives. Each section ends with a summary of key ideas. Throughout there are questions which, if tackled, confirm understanding and build confidence. The answers to these questions appear at the end of the book and often include some hint about working as well as a numerical result. The glossary allows a ready reference to the considerable vocabulary of astrophysics and medical physics.

This book weaves together with great skill what may appear two rather diverse subject areas. It is an attractive book but presentation has not triumphed over content, and it is also easy to use and non-trivial in its approach. I will not be purchasing a class set because we study neither subject area in detail at school, but I suspect I would if we studied either or both. However, there will certainly be a couple of copies in the library because I think the self-study style will lend itself to general and accessible background reading in two areas of considerable interest to students.

Boltzmann is one of the most interesting of the late nineteenth century physicists and is without doubt one of the most important. His work in kinetic theory and statistical thermodynamics laid the foundations for many of the major developments of twentieth century physics and it is a great pity that there are few English language biographies. Carlo Cercignani is Professor of Theoretical Mechanics at the Politecnico di Milano and is well equipped to describe and comment upon Boltzmann's theories - his own research includes applications of the Boltzmann equation.

This book is published by OUP and reminds me of Abraham Pais's excellent scientific biographies of Bohr and Einstein (also OUP). In fact I suspect the intention was to conform to the style and standards set by those books. To this end Boltzmann's physics is the centrepiece of the story and subtle technical details are discussed in the main body of the text (albeit with a minimum of mathematics). However, there are substantial appendices in which some of the main results (e.g. the H-theorem) are derived. I am not convinced that this division has been entirely successful since the author seems so eager to get to grips with fine detail that the broad sweep of Boltzmann's ideas is not always clearly explained, and a reader lacking a foundation in statistical thermodynamics will struggle to follow the points being made. However, there is a great deal of interest here and the book is one I am sure I shall return to many times in the future. In fact it is probably more suited for reference than for reading - the author's English style is often rather awkward and some passages are a struggle, but the content and organization are good and there is plenty of exciting physics.

The main part of the book begins with a short biography, but the next eight chapters deal with different aspects of his physics. The final chapters discuss his philosophy, his contemporaries and the influence of his ideas on twentieth century developments. There is an amusing postscript which is a translation of Boltzmann's own account of a trip to California: 'A German Professor's Journey into Eldorado'. I couldn't help feeling that the light-hearted self-aware character who wrote this funny little travel story seemed totally different from the character I had been reading about in the rest of the book. But then Boltzmann's suicide in Duino in 1906 also jars and it is obvious that we are dealing with a complex and multi-faceted man, a genius with just a touch of paranoia who was prone to bouts of deep depression.

For the reader who has studied statistical mechanics the arguments about irreversibilty and the status of the H-theorem and the second law are fascinating. The comparison of Boltzmann and Gibbs (who gave a more generalized version of some of Boltzmann's results and whose work seems to have been accepted much more rapidly than Boltzmann's) is also interesting. The arguments with Mach and the energeticists are well known but worth reviewing - it is hard to believe that scientists and philosophers can fight so passionately over the status of their ideas; it perhaps helps to explain why so many Austrian intellectuals of that era took their own lives. In fact it has been suggested that the conflict about atoms (whether they are real, as Boltzmann seems to have believed, or merely abstract mathematical models, as claimed by Oswald and Mach) was one of the pressures that drove Boltzmann over the edge in 1906. However, what I found most interesting was reading about the way Boltzmann dealt with continuous energy distributions by introducing a mathematical process of quantization in order to derive his main results. This technique was adopted and adapted by Planck in order to derive the famous formula for the spectrum of black-body radiation, and by Einstein for the photon theory of light. In fact the development of quantum theory seems to have relied on methods first used by Boltzmann some 20 years earlier. This link is explained very clearly. I was also surprised to learn that Boltmann's philosophy of science pre-empted the ideas of Thomas Kuhn, and the author quotes a number of passages that make some of Kuhn's work sound like plagiarism!

It is ironic that, as Boltzmann lost hope and hanged himself, Einstein had already published a paper on Brownian motion that established the reality of atoms - the energeticists were about to concede defeat. Boltzmann's discoveries and speculations are startlingly modern and he is without doubt one of the pioneers of the twentieth century revolution in physics. As we approach the twenty-first century this book will go some way toward cementing that reputation.