# Introduction

The tables inscribed on the seaman’s tobacco boxes sold by Pieter Holm in Amsterdam at his nautical school Regt door Zee were intended as an aide-de-mémoire for sailors and navigators. With the first table it was easy to work out the weekday and the lunar age for any calendar date. The second table enabled the seaman to obtain a rough estimate for the ship’s speed from which the daily progress of the ship could be calculated.

# The perpetual calendar

The following table summarizes the calendrical information commonly found on the lid:

 Jan (31) 1 Apr (30) 2 Sep (30) 6 – Nov (30) 10 – – – – – Jun (30) 4 Feb (28/29) 2 Aug (31) 6 May (31) 3 Oct (31) 8 Jul (31) 5 Dec (31) 10 – Mar (31) 1 – – 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 [year of fabri- cation]

Each month usually lists the number of days in the month (here enclosed between brackets) and the lunar age on the first day of the month.

The months are placed in such a way that the weekday of any day in the month can be found with little effort. Thus, if 1 January falls on a particular weekday (say Sunday), then 1 October, 2 April and 2 July, 3 September and 3 December, etc., will also fall on the same weekday. From then on, it is easy to determine the weekday of any other day in the month. To calibrate the table, one only needed to know the weekday of 1 January, or deduce the same from the current year’s Dominical Letter (or Sunday Letter). When this was A, Sunday fell on 1 January, for B on 2 January, for C on 3 January, etc. For a leap (or bissextile) year, two Dominical Letters are needed, the first for the months January and February and the second for the other months of the year.

The lunar age was determined from the numeral listed for each month that indicated the lunar age on the first day of the month. So, if the lunar age on 1 January happened to be 1 day, then the lunar age was 2 days on 1 February, 1 day on 1 March, 2 days on 1 April, etc. For a given year, the actual lunar age on 1 January was determined by a number known as the lunar epact.

From these two calendrical parameters, the Dominical Letter and the lunar epact, the seaman could swiftly work out the weekday and the lunar age for each day in that year. Especially for seamen sailing in coastal regions, the lunar age was a important parameter as it determined the times of high and low water.

See my Easter calculator for a convenient way to obtain the Dominical Letter and lunar epact for an arbitrary year.

# Example

As an example, let’s determine the weekday and the lunar age of 5 April 1722, the day when the fleet of the Dutch admiral Jacob Roggeveen discovered a small uncharted island in the middle of the Pacific Ocean that was so isolated that the local inhabitants had never bothered to give it a name. The Dominical Letter for 1722 (a common year) was D and the lunar epact was 12.

Dominical Letter D implies that the first Sunday of the year fell on 4 January, so 1 January was a Thursday and 2 April was also a Thursday from which it follows that 5 April was a Sunday. The lunar age on 1 January was 12 days, so the lunar age on 1 April was 13 days and the lunar age on 5 April was 17 days. As it was the first Sunday after the Paschal Full Moon (when the lunar age is 14 days), this day coincided with Easter Sunday.

In case you have not yet guessed the name of Roggeveen’s island, it was of course Easter Island (Isla de Pascua, or Paasch Eyland as Roggeveen named it – the local name Rapa Nui was first introduced in the late 19th century). Note that if the island had been discovered on the same day by an English vessel, its captain would have recorded the date as 25 March in his log book as he would still reckon time according to the Julian calendar that lagged 11 days behind the Gregorian calendar. This date also happened to be Easter Sunday in his calendar but it was also commonly known as Lady Day, so he could alternately have named it Lady Day Island.

# The speed table

The rightmost column in Holm’s table gives the vessel’s speed in German or geographical miles (assumed by Holm to be 22800 Rhineland feet in length) per 4-hour watch and their quartile parts as a function of the time needed to sail past a stationary object floating in the water.

The quartile parts of the speed are denoted either as dots or dashes in the table and the “0” is often denoted as “(”. So “( – –” should be interpreted as “0.5” and “6 – – –” as “6.75”. Some Holm tobacco boxes also tabulate the difference in speed between successive tabular entries in quartile parts.

Holm’s table is given below in modern notation.

 Time interval Speed [knots] Quartile intervals Time interval Speed [knots] Quartile intervals 4 11.25 8 16 3.00 1 5 9.25 7 17 2.75 1 6 7.50 3 19 2.50 1 7 6.75 3 21 2.25 1 8 6.00 3 23 2.00 1 9 5.25 2 26 1.75 1 10 4.75 2 31 1.50 1 11 4.25 1 37 1.25 1 12 4.00 1 45 1.00 1 13 3.75 1 65 0.75 1 14 3.50 1 100 0.50 1 15 3.25 1 200 0.25 –

The speed table was to be used as follows:

• First determine the time interval – to be counted in a special way, see below – that a small floating object cast into the water needed to drift past two marks set exactly 40 Rhineland feet (about 12.5 metres) apart above the vessel’s waterline.
• With this value enter the left column of the table and read off the vessel’s speed (expressed in German or geographical miles per 4-hour watch). Assuming a constant course, multiply by 6 to obtain the daily progress of the vessel.

The time was to be counted at such a rate that the sequence 21, 22, 23 up to 74 should take exactly thirty seconds. Alternatively, the time interval could be determined by counting the swings of a simple pendulum consisting of a small metal ball on a string that was exactly one Rhineland foot (31.39 centimetres) long. Holm adopted this method because a simple pendulum was easy to make (a ship’s carpenter would always have a Rhineland-foot measure somewhere) and chronometers displaying seconds would not become commonly available until the early 19th century.

As a German or geographical mile is equal to a 1/15th part of an equatorial degree or 4 nautical miles, Holm’s speeds are equivalent with the later measure of the same quantity in knots (i.e. nautical miles per hour).

# Literature on Pieter Holm and his tobacco boxes (chronological)

• Crone, Ernst, “Het Gissen van Vaart en Verheid, het Loggen en de Tabaksdoos van Pieter Holm”, De Zee: Zeevaartkundig Tijdschrift, 50 (1928), 552-559, 601-609, 668-674, 729-737 & 51 (1929), 81-89, 145-155, 217-228 – a partial English translation of this paper by the Dutch mathematician Dirk Brouwer with an introductory essay by Edwin Pugsley was published as: Pieter Holm and his Tobacco Box (Marine Historical Association, Mystic [Connecticut], 1953) [pdf copy].
• Blaauboer, Jan, “De Tabaksdoos van Pieter Holm”, De Zee: Zeevaartkundig Tijdschrift, 51 (1929), 657-658.
• Crone, Ernst, “Pieter Holm en zijn Zeevaartschool”, De Zee: Zeevaartkundig Tijdschrift, 52 (1930), 136-144, 185-195, 270-280, 352-362, 416-424, 489-497, 560-568, 642-651, 704-716.
• Crone, Ernst, “Pieter Holm en zijn Octant”, De Zee: Zeevaartkundig Tijdschrift, 63 (1941), 1-7, 35-41, 76-82, 111-115, 129-136, 161-165.
• Mörzer Bruyns, Willem F.J., Schip Recht door Zee: De octant in de Republiek in de achttiende eeuw (Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam, 2003 [= Werken uitgegeven door de Commissie voor Zeegeschiedenis, nr. XX]) [KNAW link].