\ProvidesPackage{headers}

% Arguments. {1. Term} {2. Subject number and name} 
% {3. Full date (Day of the week, Day of the month, Month, Year} 
% {4. Starting time} {5. Ending Time}
% {6. Allowed time (Hours) {7. Mods or Prelims (PP)}}

\newcommand{\Prelim}[7]{%Prelims  -  CP1 papers
\centerline{}
\vskip5truemm
\centerline{\bf FIRST PUBLIC EXAMINATION}
\bigskip
\centerline{\bf #1}	% Trinity Term   or   Long Vacation
\bigskip
\centerline{\bf Preliminary Examination in Physics}
\bigskip
\centerline{\bf Paper #2}
\bigskip
\centerline{\bf also}
\bigskip
\centerline{\bf #7 in Physics and Philosophy} %#7 is mods or prelims for PP
\bigskip
\centerline{\bf #3, #4 -- #5} % date, start time, end time
\bigskip
\centerline{\bf Time allowed: #6 }
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf three} questions from Section B.}
\bigskip
\centerline{\it A list of physical constants, mathematical formulae}
\centerline{\it and conversion factors accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Moderators expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}

\newcommand{\PrelimM}[7]{%Prelims  -  CP3 papers
\centerline{}
\vskip5truemm
\centerline{\bf FIRST PUBLIC EXAMINATION}
\bigskip
\centerline{\bf #1}	% Trinity Term   or   Long Vacation
\bigskip
\centerline{\bf Preliminary Examination in Physics}
\bigskip
\centerline{\bf Paper #2}
\bigskip
\centerline{\bf also}
\bigskip
\centerline{\bf #7 in Physics and Philosophy} %#7 is mods or prelims for PP
\bigskip
\centerline{\bf #3, #4 -- #5} % date, start time, end time
\bigskip
\centerline{\bf Time allowed: #6 }
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf three} questions from Section B.}
\bigskip
\centerline{\it The use of calculators is {\bf not} permitted.}
\bigskip
\centerline{\it A list of physical constants, mathematical formulae}
\centerline{\it and conversion factors accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Moderators expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}

\newcommand{\PrelimP}[6] {%Prelims  -  CP2, CP4 Physics papers
\centerline{}
\vskip5truemm
\centerline{\bf FIRST PUBLIC EXAMINATION}
\bigskip
\centerline{\bf #1}	% Trinity Term   or   Long Vacation
\bigskip
\centerline{\bf Preliminary Examination in Physics}
\bigskip
\centerline{\bf Paper #2}
\bigskip
\centerline{\bf #3, #4 -- #5} % date, start time, end time
\bigskip
\centerline{\bf Time allowed: #6 }
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf three} questions from Section B.}
\bigskip
\centerline{\it A list of physical constants, mathematical formulae}
\centerline{\it and conversion factors accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Moderators expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}

\newcommand{\PrelimPP}[7] {%Prelims  -  CP4 Physics & Philosophy papers
\centerline{}
\vskip5truemm
\centerline{\bf FIRST PUBLIC EXAMINATION}
\bigskip
\centerline{\bf #1}	% Trinity Term   or   Long Vacation
\bigskip
\centerline{\bf #7 in Physics and Philosophy} %#7 is mods or prelms for PP
\bigskip
\centerline{\bf Paper #2}
\bigskip
\centerline{\bf #3, #4 -- #5} % date, start time, end time
\bigskip
\centerline{\bf Time allowed: #6}
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf two} questions from Section B.}
\bigskip
\centerline{\it A list of physical constants, mathematical formulae}
\centerline{\it and conversion factors accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Moderators expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartA}[4]{%Part A papers A1, A3
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part A: 3 and 4 Year Courses}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part A}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf three} questions from Section B.}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}



\newcommand{\PartAtwo}[4]{%Part A paper, A2
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part A: 3 and 4 Year Courses}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf three} questions from Section B.}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}



\newcommand{\PartAtwoP}[5]{%Part A paper, A2P
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part A}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vskip7truemm
\centerline{\bf Time allowed: #5} % Time allowed
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf all} of Section A and {\bf one} question from Section B.}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartBtwo}[4]{%Part B paper B2
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf  Honour  School of Physics -- Part B: ~ 3 and 4 Year Courses}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part B}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer  {\bf five} questions with at least {\bf one} from each section:}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it Start the answer to each section in a fresh book.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartBone}[5]{%Part B papers - new B papers B1
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf  Honour  School of Physics -- Part B: ~ 3 and 4 Year Courses}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part B}
\vskip7truemm
\centerline{\bf #1}	%	subject first line
\centerline{\bf #2} %   subject second line
\vskip7truemm
\centerline{\bf #3, #4 -- #5}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer  {\bf five} questions with at least {\bf one} from each section:}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it Start the answer to each section in a fresh book.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartBthree}[4]{%Part B paper B3
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf  Honour  School of Physics -- Part B: ~ 3 and 4 Year Courses}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part B}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer  {\bf five} questions with at least {\bf two} from each section:}
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\bf Use different books for answers to questions in Sections A \&
B.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}

\newcommand{\PartBP}[5]{%Philosophers' math physics paper
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part B}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2}	%	subject
\vskip7truemm
\centerline{\bf #3, #4 -- #5}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer four questions.}
\medskip
\centerline%
{\it Questions in Section C may only be answered by candidates offering option B4}
\smallskip
\centerline{\it and these candidates may not answer questions in Section B.}

\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\bf Use different books for answers to questions in Sections A,
B and C.}
\vskip5truemm
\centerline{\it A list of physical constants and conversion factors accompanies this paper.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}




\newcommand{\PartC}[4]{%Part C papers - C1 C3 C6
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part C: 4 Year Course}%Natural Science
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part C}
\vskip7truemm
\centerline{\hbox to 40truemm{\hrulefill}}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf four} questions.}
\bigskip
\centerline{\it Start the answer to each question on a fresh page.}
\bigskip
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Examiners anticipate}
\centerline{\it assigning to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartCtwo}[5]{%Part C paper C2
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part C: 4 Year Course}%Natural Science
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part C}
\vskip7truemm
\centerline{\hbox to 40truemm{\hrulefill}}
\vskip7truemm
\centerline{\bf #1}	%	subject line one
\centerline{\bf #2}	%	subject line two
\vskip7truemm
\centerline{\bf #3, #4 -- #5}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf four} questions.}
\bigskip
\centerline{\it Start the answer to each question on a fresh page.}
\bigskip
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Examiners anticipate}
\centerline{\it assigning to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}


\newcommand{\PartCfour}[4]{%Part C paper - C4 Particle Physics
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part C: 4 Year Course}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part C}
\vskip7truemm
\centerline{\hbox to 40truemm{\hrulefill}}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer {\bf four} questions.}
\bigskip
\centerline{\it Start the answer to each question on a fresh page.}
\bigskip
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the 
Examiners anticipate}
\centerline{\it assigning to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\vfill
\centerline{\bf Pages 2 and 3 contain particle physics formulae and data for this paper.} 
\smallskip
\centerline{\bf The questions start on page 4.}
\vfill
\pagebreak\@titlepagefalse\input c4data
}

\newcommand{\PartCfive}[4]{%Part C papers - C5
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Physics Part C: 4 Year Course}
\vskip7truemm
\centerline{\bf Honour School of Physics and Philosophy Part C}
\vskip7truemm
\centerline{\hbox to 40truemm{\hrulefill}}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{.8cm}
\hrule
\vspace {.8cm}
\centerline{\it Answer {\bf four} questions.}
\bigskip
\centerline{\it Start the answer to each question on a fresh page.}
\bigskip
\centerline{\it A list of physical constants and conversion factors
accompanies this paper.}
\bigskip
\centerline{\it The numbers in the margin indicate the weight that the Examiners anticipate}
\centerline{\it assigning to each part of the question.}
\vskip.8cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\vskip.8cm
\noindent
 With wavenumber $\nu$ measured in cm$^{-1}$, the  radiance from the surface
 of a black body of temperature $T$ (in K) is given by  
	\[
B_{\nu}(T)\,\d\nu=\frac{c_1\nu^{3}\,\d\nu}{\e^{c_2\nu/T}-1}
\W\m^{-2}\sr^{-1},
\]
where $c_1=1.191043\times10^{-8}$ and $c_2=1.438775$.

The following equation of motion for a fluid relative to coordinates stationary with respect to a rotating body may %%@
be assumed:
\[
  \frac{\D \vV}{\D t}+2{\bf\Omega}\times \vV = -\frac{1}{\rho}\nabla p-g\vk \, ,
\]
 where $\vV$ is the velocity of the fluid, $\bf\Omega$ is the angular
velocity of the body, $p$ is the pressure, $\rho$ is the fluid density,
$g$ is the acceleration due to gravity and $\vk$ is a unit vertical vector. 

Unless otherwise stated, $x$ and $y$ refer to the horizontal Eastward and
Northward directions and $z$ the upward direction with corresponding
velocities $u$, $v$ and $w$.

\vskip 5truemm

\centerline{$1000\mb=1000\hPa=10^5\Pa$.}

\pagebreak\@titlepagefalse
}



%argument is date
\newcommand{\ShortOptions}[1]{%Part B Short Options paper
\centerline{}
\vskip3truemm
\centerline{\bf FIRST PUBLIC EXAMINATION}
\vskip3truemm
\centerline{\bf Preliminary Examination in Physics}
\vskip3truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip3truemm
\centerline{\bf Honour School of Physics,}
\centerline{Parts A and B: 3 and 4 year Courses}
\vskip2truemm
\centerline{\hbox to 40truemm{\hrulefill}}
\vskip3truemm
\centerline{\bf SHORT OPTIONS}	%	subject
\vskip4truemm
\centerline{\bf #1}%	Date
\smallskip
\centerline{\bf 9:30 a.m.\ to 11:00 a.m.\ for candidates offering {\bf ONE} Short Option}
\centerline{\bf 9:30 a.m.\ to 12:30 p.m.\ for candidates offering {\bf TWO} Short Options}
\vspace{4truemm}
\hrule
\vspace{6truemm}
\centerline{\it Answer {\bf two} questions from each option for which you have entered.}
\vskip3truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip3truemm
\centerline{\bf If you have entered for two Short Options,}
\centerline{\bf keep your answers to the two options in different books}
\centerline{\bf and at the end hand in two bundles, one for each option.}
\vskip3truemm
\centerline{\it A list of physical constants and conversion factors accompanies this paper.}
\vskip3truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners anticipate}
\centerline{\it assigning to each part of the question.}
\vskip4truemm
\centerline{\bf Do NOT turn over until told that you may do so.}
\vskip6truemm

{\font\ab=cmbx9
\font\ac=cmr9
\parskip=1pt
\parindent=0pt
\centerline{\bf INDEX}
\begin{center}
{\ac\begin{tabular}{clr|clr}
\ab Section & \multicolumn{1}{c}{\ab Subject} & \ab Page & \ab Section & \multicolumn{1}{c}{\ab Subject} & \ab %%@
Page\\
\phantom{-}&&&&&\\
S1 & Functions of a Complex & & S10 & Medical and Environmental & \\
& \hfill Variable & \pageref{S1} & & \hfill Physics & \pageref{S10} \\
S2 & Astrophysics: from Planets & & S12 & Introduction to Biological \\
& \hfill to the Cosmos & \pageref{S2} & & \hfill Physics & \pageref{S12} \\
S3 & Quantum Ideas & \pageref{S3} & S15 & Chaos, Chance and & \\
S4 & Energy Studies & \pageref{S4} & & \hfill  Predictability & \pageref{S15} \\
S6 & History of Electromagnetism & \pageref{S6} & S16 & Plasma Physics & \pageref{S16} \\
S7 & Classical Mechanics & \pageref{S7} & S17 & Numerical Methods & \pageref{S17} \\
S8 & Covariant Electromagnetism & \pageref{S8} & S18 & Advanced Quantum Mechanics & \pageref{S18}\\
%S9 & Financial Physics & \pageref{S9} \\
\end{tabular}}
\end{center}
}
\centerline{\it Some sections start with a relevant rubric.}

\pagebreak\@titlepagefalse
}

\newcommand{\AdvQM}[4]{%Maths inst QM paper
\centerline{}
\vskip5truemm
\centerline{\bf SECOND PUBLIC EXAMINATION}
\vskip7truemm
\centerline{\bf Honour School of Mathematics}
\vskip7truemm
\centerline{\bf Honour School of Mathematics and Philosophy}
\vskip7truemm
\centerline{\bf #1}	%	subject
\vskip7truemm
\centerline{\bf #2, #3 -- #4}%	Dates, start time, end time
\vspace{1cm}
\hrule
\vspace {1cm}
\centerline{\it Answer two questions.}
\medskip
\vskip5truemm
\centerline{\it Start the answer to each question on a fresh page.}
\vskip5truemm
\centerline{\it The numbers in the margin indicate the weight that the Examiners expect to}
\centerline{\it assign to each part of the question.}
\vskip1cm
\centerline{\bf Do NOT turn over until told that you may do so.}
\pagebreak\@titlepagefalse
}