Remarks upon the solar and the lunar years, the cycle of 19 years, commonly called the golden number, the epact, and a method of finding the time of Easter, as it is now observed in most parts of Europe

In Short

This technical treatise functions as a guide to the mechanics of timekeeping. It explains why the traditional Julian calendar, used in England in 1750, had fallen out of sync with the celestial reality of the sun and moon. The writing serves as a blueprint for correcting these discrepancies by aligning the "Golden Number" and the "Epact"—the tools used to track lunar cycles—with the Gregorian system. It remains a fascinating document of Enlightenment-era precision, demonstrating how a complex astronomical problem can be solved through methodical, century-spanning arithmetic.

The Story

The narrative begins with a clear, objective identification of a mounting problem: the mismatch between the Julian calendar and the actual movement of the sun. The author explains that the solar year is slightly shorter than the Julian calculation, causing equinoxes and solstices to "anticipate" or drift earlier over time. He details how the Gregorian reform of 1582 addressed this by omitting specific leap years to keep the calendar locked to the seasons. However, the author shifts his focus from the sun to the moon, identifying a more intricate issue: the lunar cycle, which governs the timing of Easter, is also drifting.

For centuries, the Church relied on the "Golden Number"—a cycle of nineteen years—to track the new moons. The author reveals that this method is flawed because nineteen solar years do not perfectly align with 235 synodical months. This mismatch causes the ecclesiastical moon to drift away from the real moon. He argues that this is not merely an abstract astronomical error but a practical one that affects the observance of Easter. He provides a rigorous set of rules for adjusting the Golden Numbers and the Epacts (the difference between solar and lunar years) to ensure that the ecclesiastical calendar stays true to the heavens.

The author does not stop at theory. He proposes a specific, actionable method for the Church of England to synchronize its Easter calculations with the Gregorian system used in much of Europe. He suggests that by systematically advancing or shifting the Golden Numbers at specific intervals—calculated to remain accurate until the year 4199—England could resolve its calendar confusion without abandoning the familiar tools of the Book of Common Prayer.

Toward the end, the scope of the argument expands into the nuances of long-term timekeeping. He introduces necessary exceptions to his general rules, explaining that certain pairs of numbers in the calendar must remain fixed during specific periods to account for the varying lengths of lunar months. He acknowledges the complexity of these adjustments but asserts that they are essential for long-term consistency. The book concludes by crediting a colleague, Peter Davall, for the initial inspiration behind these tables, framing the work as a collaborative triumph of applied mathematics. It ends not with a flourish, but with a firm commitment to the idea that a standard, reliable calendar is a matter of profound importance for the general public, and that such order is well within the reach of human calculation.

How It Unfolds

The astronomical baseline The author establishes the exact discrepancy between the mean solar year and the Julian year. He explains the logic of leap years and why the Gregorian reform was a necessary, if incomplete, intervention.

The lunar drift He turns to the cycle of nineteen years, detailing the mathematical gap between solar and lunar time. He demonstrates that the "Golden Numbers" currently in use have become detached from the actual phases of the moon.

The mechanism of correction The author provides a set of iterative rules for adjusting the Golden Numbers and Epacts. He explains how these shifts, performed at the turn of specific centuries, can maintain alignment for thousands of years.

The application to Easter He addresses the specific challenge of calculating Easter, explaining why current methods fail to align with the real lunar full moon. He offers a practical solution to harmonize the English practice with European standards.

The refinement of the rules The final section introduces necessary exceptions for specific numerical pairs within the calendar table. He explains that these adjustments ensure the system remains valid through the early fifth millennium.

The People

The text is driven by the perspective of George Parker, Earl of Macclesfield, an aristocrat and man of science. He acts as a mediator between the technical rigors of astronomy and the administrative needs of the Church and State. He is motivated by a desire for accuracy and public utility; he views the "erroneous" state of the calendar not just as a scientific curiosity, but as a failure of institutional precision that needs correction.

He is supported by the intellectual presence of Martin Folkes, the President of the Royal Society, to whom the letter is addressed. Folkes represents the scholarly community that valued such empirical inquiries. Finally, Peter Davall appears as a vital collaborator. Macclesfield credits Davall for the initial concept of using the Golden Numbers in a new way to solve the Gregorian problem. These figures are defined by their shared commitment to the Enlightenment ideal that the natural world should be measured and documented with absolute, verifiable clarity. They do not seek to change religious dogma but to ensure that the tools used to measure the passage of sacred time are as honest as the stars themselves.

In Its Own Voice

The mean Tropical Solar Year, or that mean Space of Time wherein the Sun, or Earth, after departing from any Point of the Ecliptic returns to the same again, consists, according to Dr. Halley's Tables, of 365d, 5h, 48´, 55´´: Which is less by 11´, 5´´, than the mean Julian Year, consisting of 365d, 6h, 0´, 0´´.

This opening provides the scientific foundation for why the calendar must be adjusted.

And the Sunday next after that Day is Easter Day in that Year, according to the Gregorian Account.

This sentence summarizes the ultimate objective of the complex calculations detailed throughout the book.

What It's Really About

The central theme is the triumph of human observation over the inherent chaos of orbital mechanics. The book posits that time is not merely a given, but a human construction that requires constant maintenance to stay aligned with the physical universe. It argues that scientific precision is a public duty, not a private hobby. The underlying question is how to balance tradition—represented by the established Church of England calendars—with the undeniable truth of celestial movement. Macclesfield makes a compelling case that simplicity and accuracy are not mutually exclusive; he seeks to provide a method that is both mathematically sound and accessible enough to be used by the "generality of mankind."

Why Read It Today

Readers with a fascination for the history of science or the evolution of the modern calendar will find this a deeply satisfying read. It offers a rare window into the mind of an eighteenth-century intellectual attempting to solve a problem that is both cosmic and mundane. The prose is dignified, patient, and remarkably clear, stripping away unnecessary jargon to focus on the essential logic of the calculation.

However, the modern reader should be prepared for the dense, technical nature of the subject. The book does not attempt to be a light narrative; it is an intensive, analytical argument filled with tables of dates and specific rules for leap-year adjustments. One encounters the period's language and its specific focus on the "Old Style" versus the "New Style," which may require some initial patience to decode. Yet, there is a profound sense of peace to be found in the author's meticulousness. In an era of instant, digital timekeeping, this book serves as a grounding reminder of the immense effort, centuries of observation, and careful arithmetic required to build the structured time that we now take for granted. It is a work of intellectual integrity that stays with you, leaving you with a heightened awareness of the celestial clockwork that ticks silently above our heads.