June 2012 page 2
Allan A. Mills

Gaocheng Calendrical Observatory, China

This article details the historical Gaocheng Calendrical Observatory in China, focusing on its construction in 1276 AD by Guo Shoujing, its role in calendrical observations for the Yuan Dynasty, and its design principles for measuring solstices and equinoxes using a monumental gnomon. It also describes the 'shadow-definer' device used for accuracy and the methods for orientation and timekeeping.
Dials: Noon Lines, Historical Dials, How Sundials Work, Mathematics of Dialling

June 2011 page 2
Allan A. Mills

The Rainbow as a Solar Timekeeper

This article explores the rainbow as an alternative solar timekeeping phenomenon, discussing its complex optical properties, formation of primary and secondary bows, and the dispersion of light into colours. It also describes a rainbow dial instrument for time determination.
Dials: Unusual, How Sundials Work, Mathematics of Dialling, Sundial Design & Layout

September 2011 page 16
Allan A. Mills

Ancient Egyptian Sundials

This article reviews ancient Egyptian timekeeping, debunking obelisks as gnomons and a Cairo Museum artifact as a sundial. It focuses on the ‘sloping’ or ‘inclined plane’ portable, seasonal-hour altitude dials, such as the Qantara dial, and earlier L-shaped 'shadow sticks' from the New Kingdom, discussing their construction, use, and the challenges in interpreting their time-telling functions.
Dials: Portable, Dials: Unusual, Historical Dials, How Sundials Work

June 2010 page 2
Allan A. Mills

The Sundial as an Aeolian Harp

This article explores the concept of integrating an aeolian harp into a sundial's support structure to complement the visual time-telling with ethereal wind-generated music. It details the history and theory of aeolian harps, including the physics of 'aeolian tones' and string resonance. The author describes the construction of a prototype venturi-type aeolian sundial using inexpensive materials, highlighting design considerations for soundboxes, strings, and the integration of a horizontal dial.
Construction Projects, DIY Sundial Projects, Dials: Unusual, Sundial Design & Layout

December 2010 page 7
Frans W. Maes
Allan A. Mills
Michael Lowne

Readers’ Letters

This section includes letters from readers. Frans Maes describes a multi-faceted obelisk sundial in Schwäbisch Gmünd, Germany, similar to one previously discussed. Allan Mills and Michael Lowne provide detailed explanations and practical advice on how to observe the optical phenomenon known as 'Haidinger’s brush,' which appears due to polarized light in the blue sky.
Dials: Multi Faced, How Sundials Work

March 2009 page 2
Allan A. Mills

A North-facing Polarization Sundial of Varying Hue

This article explores alternative methods for measuring the sun's position, specifically focusing on a north-facing polarization sundial. It delves into the principles of polarized light from the sky, its application in sundial design using materials like 'Sellotape', and the construction of an experimental translucent equatorial dial that produces varying interference colours throughout the day.
Construction Projects, DIY Sundial Projects, Dials: Polar, How Sundials Work

March 2009 page 14
Allan A. Mills

An Electronic Polarization Sundial and Photometer

This article describes an electronic polarization sundial and sky photometer designed to measure the intensity and polarization of skylight. It uses a rotatable polar and a selenium photovoltaic cell to detect the solar meridian to within ±8 minutes of time and quantitatively assess the percentage of linear polarization in light from a selected area of the sky.
Dials: Polar, How Sundials Work, Construction Projects

December 2009 page 10
Allan A. Mills

A tribute to Robert Hooke

This article celebrates the genius of Robert Hooke, highlighting his key scientific contributions. It covers Hooke's Law and its application to timekeeping, his work on a universal joint for delineating sundials, and his pioneering (though unpublished) insights into the catenary arch. It proposes a sculptural memorial to Hooke.
How Sundials Work, Sundial Design & Layout, Historical Dials

March 2007 page 9
Chris Lusby Taylor
Tony Ashmore
Allan A. Mills

Readers’ letters

This section contains correspondence from readers. Chris Lusby Taylor discusses the use of Hooke’s joint for delineating declining and reclining dials, while Allan Mills replies regarding an error in a previous paper. Tony Ashmore suggests an interpretation for the 'Egyptian Face' design on a sundial pillar at Lord Tennyson's home, attributing it to Ptolemy.
Dials: Unusual, How Sundials Work, Mathematics of Dialling

September 2007 page 102
Allan A. Mills

Hour Angle, Velocity and Acceleration of the Shadow Moving over a Sundial

This paper applies Hooke's joint equation of motion to sundials to calculate the hour angle, angular velocity, and acceleration of the shadow. It provides formulas and graphs for a direct south vertical dial at 52° N latitude, showing how these parameters vary throughout the day, with angular velocity minima at noon/midnight and maxima at 6 am/pm.
How Sundials Work, Mathematics of Dialling

December 2006 page 167
Allan A. Mills

Hooke’s Joint, Sundials and the Sundial-Clock

Allan Mills explores Robert Hooke's "Sundial Delineator," an instrument using a cross-shaped interior member (similar to a Hooke's joint) to simulate gnomon shadow motion for sundial delineation. The article details how Hooke's joint can be applied to delineate sundials and, when driven by a clock, create a "sundial-clock," explaining the underlying mathematical principles.
Sundial Design & Layout, Dialling Tools, Historical Dials

December 2005 page 175
Allan A. Mills

Sundials at the University of Leicester

This piece highlights four unusual sundials at the University of Leicester campus. It features a two-meter-high "Eye of Time" noon mark, a modern sculptural piece indicating both time of year and day via an analemma. Also mentioned are John Davis's "Newton" dial and two matching vertical declining dials in Westmoreland slate, one showing equal hours and the other seasonal hours.
Dials: Noon Lines, Dials: Unusual, Dials: Vertical

June 2003 page 58
Allan A. Mills
P. Stapleton
J. P. D. Hennessy

Sundials for the Blind

This article explores the concept of creating a sundial for the visually impaired. It reviews historical attempts, such as one by the 17th-century Jesuit priest Francis Hall, and discusses modern approaches that use the heat of the sun rather than visible light.
Construction Projects, DIY Sundial Projects, Dials: Unusual, Sundial Design & Layout

September 2003 page 96
Allan A. Mills

The Origin of Sine, Cosine and Tangent

Based on a talk at the BSS Annual Conference, this article traces the origins of trigonometry back to ancient Egypt and the 'rope stretchers' who used a 3,4,5 triangle to define right angles. It then moves on to the Greeks, specifically Pythagoras, and the Arabs, who are credited with preserving and developing trigonometry for astronomy.
Mathematics of Dialling

March 2002 page 39
Allan A. Mills

Calendar Dials

Explores dials intended to show the date rather than the time, by reading the shadow of an equinoctial ring on a scale on the stile.
Dials: Polar, Dials: Unusual, How Sundials Work

March 2001 page 32
Allan A. Mills

An Easily Made Horizontal Garden Sundial

Instructions for making a simple horizontal garden sundial using copying and laminating techniques. It offers a basic design computed for latitude 52.5°N, longitude zero, and explains how to adjust it for different locations by tilting.
DIY Sundial Projects, Dials: Horizontal

September 2001 page 113
Allan A. Mills

The Eye of Time

Describes a modern, three-dimensional noon mark sculpture in Portland stone, with analemma. It indicates both the instant of mean-time noon and the time of year by projecting a spot of sunlight onto an incised analemma. This design is believed to be the first of its kind that is 3-dimensional.
Dials: Noon Lines, Dials: Unusual, Equation of Time

February 2000 page 3
Allan A. Mills

Graeco-Roman Sundials, Part 1: Dials Based on the Sphere

Explores early Greek and Roman hemispherical and hemicyclium sundials, their geometry, historical usage, and accuracy.
Dials: Hemispherical, Historical Dials, How Sundials Work, Mathematics of Dialling

June 2000 page 64
Allan A. Mills

Graeco-Roman Sundials, Part II: Conical and Other Forms

Continues an exploration of ancient sundials, focusing on conical types and their mathematical construction and historical context.
Dials: Scaphe, Historical Dials, How Sundials Work, Mathematics of Dialling

October 2000 page 142
Allan A. Mills

Backwards Motion of the Shadow on a Sundial

Explains the rare conditions under which a sundial shadow can appear to move backward, at specific dates and latitudes, including astronomical and observational factors.
How Sundials Work, Mathematics of Dialling

February 1999 page 25
Allan A. Mills

Glass Sundials

This article introduces refractive sundials made from transparent solids like glass, specifically glass paperweight sundials for window sills. The nodus is an 'aperture' on the top of the paperweight, casting a spot on a dial card on the bottom, with a more compact pattern than in air.
Dials: Horizontal, Dials: Portable, Dials: Unusual, Sundial Design & Layout, DIY Sundial Projects

February 1999 page 48
Allan A. Mills

Hemicyclium: Ratae

This article describes a modern re-creation of a Roman hemicyclium dial, sculpted from Clipsham stone, now located in Leicester's Jewry Wall Museum. Funded by the Royal Society and British Association Awards Scheme, it will be part of the Leicester Time Trial, set to open in 1999.
Construction Projects, Dials: Scaphe

June 1999 page 62
Allan A. Mills

Noon Marks and the Projection of the Analemma, with some New Versions of these Old Instruments

This article explores noon marks and the analemma, detailing how the sun's daily and annual motion is used to determine local noon and time of year. It discusses simple horizontal and vertical noon marks, the use of aperture gnomons, and the historical and modern application of the analemma for time correction. New designs for polar and vertical analemmatic noon marks, including sculptural forms, are also presented.
Dialling Tools, Dials: Noon Lines, Equation of Time, Sundial Design & Layout

October 1999 page 120
Allan A. Mills

Book Review

This review critiques 'The Inequalities of Sundial Time' by Dr. Eilon Saroka, describing it as peculiar and unique. It covers the book's extensive detail on astronomical deviations from perfect constancy, but notes that all the factors examined are irrelevant for sundial accuracy, except for atmospheric refraction. The reviewer criticizes the lack of index and modern references, suggesting the work be split into two monographs on Earth's motion inequalities and the Equation of Time/analemma.
Book Reviews, Equation of Time, Mathematics of Dialling

October 1999 page 136
Allan A. Mills

A Nondial for Schools

This entry briefly describes a 7-inch diameter cast brass dial, with an elegant 51° gnomon, obtained by a Leicester primary school in 1969 from educational suppliers. The author notes that it is a 'nondial' due to its inaccurate hour-line calibration, implying it fails in its instructional purpose.
Sundial Design & Layout

February 1998 page 3
Allan A. Mills

The Sellotape Sundial: A Modern Version of Wheatstone’s Polarization Dial of 1848

Explains a shadow-free sundial using sky polarization: a fan of Sellotape (cellophane) sectors is viewed with an analyser at the Brewster angle. The brightest sector (or equal adjacent sectors) indicates hours and half-hours, and the dial can work with the Sun behind cloud or after sunset.
DIY Sundial Projects, Dials: Unusual

October 1998 page 27
Allan A. Mills

International Sundial Symposium

This article reports on the International Sundial Symposium in Genk, Belgium, which showcased designs from an international competition. It describes several winning sundials, including polyhedral, polar, catenary, and an innovative digital sundial by Hans Scharstein, highlighting the diversity and ingenuity in contemporary gnomonic design.
Construction Projects, Dials: Unusual

April 1997 page 29
Allan A. Mills

Sundials at the Royal Botanic Gardens, Kew

A survey of the varied sundials at Kew Gardens, describing their designs, historical backgrounds, and placement within the gardens’ landscape.
Historical Dials

October 1997 page 31
Allan A. Mills

Diptych Sundial Cards

This article describes how to make adjustable diptych sundials from card, acting as a modern, lightweight version of antique portable diptych dials. It explains the principle of two hinged plates with a taut string gnomon, a built-in compass, and the "theorem of the sundial" for adjusting to various latitudes (40-50° N and 50-60° N) by tilting the entire instrument.
DIY Sundial Projects, Dials: Portable, Sundial Design & Layout

February 1996 page 22
Allan A. Mills

Sunlight and Shadows

Scientific explanation of the principles behind shadow movement and sundial timekeeping, with educational value.
How Sundials Work

February 1996 page 34
Allan A. Mills

Refractive Sundials

A look at sundials that use lenses and refraction to tell time, particularly medieval concepts like the Dial of Ahaz.
Dials: Scaphe, Dials: Unusual

June 1995 page 39
Allan A. Mills

The Canterbury Pendant

A detailed study of a multi-faced pendant dial designed to tell time on multiple surfaces, including its design, layout, and astronomical considerations.
Dials: Portable, Dials: Unusual, Historical Dials

October 1995 page 18
Allan A. Mills

The Cooke Heliochronometer

A description of the Cooke Heliochronometer, an accurate sundial capable of giving clock time, including its principle of operation, advantages over traditional dials, and its place in the development of precision timekeeping instruments.
Dials: Heliochronometer

October 1995 page 19
Allan A. Mills

Chalice Dials

An overview of dials shaped like chalices, often used in ceremonial contexts or churches. The article discusses their optical characteristics, historical references, and functional design when filled with water for increased visibility.
Dials: Scaphe

February 1994 page 30
Allan A. Mills

More About the Equation of Time and the Analemma

Further elaboration on the Equation of Time and the analemma's form, including seasonal impacts on sundial accuracy and diagrammatic explanation.
Equation of Time

February 1994 page 32
Allan A. Mills

The 'Equation of Time for the Moon'

Discusses the lunar equivalent of the solar Equation of Time and its practical application for estimating time by moonlight.
Equation of Time

June 1994 page 20
Allan A. Mills

Ancient Sundial Re-created and Refined

Describes the reconstruction of a historically inspired sundial, elaborating on how its design was refined for accuracy and visual appeal. The piece combines historical research with practical insights, showing how ancient ideas can be adapted into educational tools and display dials for modern audiences.
Restoration projects

June 1994 page 30
Allan A. Mills

An Ancient Chinese Sundial with 100 Divisions to the Day

An account of a rare Chinese sundial that divides the day into 100 equal parts, reflecting non-Western conceptions of time. The author explains its structure, cultural context, and implications for timekeeping history, offering a comparative view with European traditions.
Dials: Unusual, Historical Dials

February 1992 page 22
Allan A. Mills

A Sundial Delineator

This article introduces a portable sundial delineator that simulates the sun's movement using a point-source lamp to project shadows. It allows for plotting hour lines on any surface, including irregular ones, by setting the gnomon at the correct latitude and revolving the lamp at 15-degree intervals. The device, suitable as a teaching aid, can also simulate declination for "dial furniture" like equinoxes and solstices by adjusting the lamp's height.
Dialling Tools, Sundial Design & Layout

June 1992 page 21
Allan A. Mills

Helical Sundials

This article introduces helical sundials as a variation of the equatorial dial, where the receiving surface extends axially along the gnomon in a helix. It describes a prototype by John Singleton, a monumental example in Lerida by J. Masuet, and Piet Hein's design at Egeskov Castle. There are two types: the first has a gnomon casting its shadow, the second uses the shadow cast by the other part of the helical strip. The article explains their operation, with the light/dark boundary marking time and hour markings set by the pitch.
Dials: Equatorial, Dials: Unusual, Sundial Design & Layout

October 1992 page 5
Allan A. Mills

The Scratch Dial and its Function

This article proposes that scratch dials, often found on old church walls, are effective "event markers" rather than precise timekeepers. It discusses their radial geometry, common south-facing position, and erosion due to acid rain. The article refutes theories about them being equal-hour sundials with bent gnomons, and explains their connection to seasonal hours and monastic prayer times.
Dials: Mass Dials, Historical Dials, How Sundials Work

February 1991 page 10
Allan A. Mills

Aligning the Gnomon.

Addresses the critical step of setting up an equal-hour sundial and suggests that aligning by observing Polaris, the pole star, can be a quicker and more accurate method. Simple tools like a peep-sight or telescope can be used for this purpose.
How Sundials Work, Dialling Tools

October 1990 page 15
Allan A. Mills

Seasonal-Hour Sundials for the British Isles

This article explains seasonal hours, a duodecimal system of dividing daylight used before mechanical clocks. It provides accurate patterns for horizontal and vertical seasonal-hour sundials suitable for latitudes 50-60° in the British Isles, noting that hour lines are shallow curves rather than straight.
Dials: Horizontal, Dials: Vertical, Sundial Design & Layout