The day that never happens

Some lunar days never collect a date, and the sheet steps straight over their number. In the first week of this January the fourth was one of them. The fast was two days off, and the sheet on the back of the kitchen door had been read down twice: Tuesday the 6th is the third, Wednesday the 7th is the fifth.

There is no fourth.

The first guess in most houses is that the printer has slipped. The second is that this year's sheet came from the wrong publisher and somebody should have ordered the old one. Neither is it. The number was taken out by a rule that is old and perfectly public, the fast still has a day, and the day is not the one most people would pick. The rest of this is about finding it.

The number is on the sheet after all

Start with the paper, because the paper has kept the record.

Get hold of a full sheet, the kind that prints every changeover rather than one name a morning, and read Tuesday again. The fourth is there. Tuesday's tithi column carries two entries: the third until 08:01 in the morning, and then the fourth, running on until 06:52 the following day. It was recorded to the minute. What it never managed to do was collect a date.

To see why, you need the one rule that hands the dates out. A day here runs from one sunrise to the next sunrise. Whichever tithi (तिथि), the lunar day, is running at the moment the sun comes up gives that whole day its name, and which day is your fast, actually works that rule through on real sheets. It asks its question once each morning, writes down the answer, and then stops asking.

Read it again and the hole in it appears. Suppose a tithi begins after one sunrise and finishes before the next. It is never on duty at a sunrise. No morning finds it running, and no date takes its name.

That is what the fourth did, and it missed at both ends. On Tuesday 6 January the sun rose in Delhi at 07:15, with 46 minutes of the third still to run, so Tuesday was the third. The fourth began at 08:01, the minute those 46 minutes ran out. It went on through the day and through the night, and it ended at 06:52 on Wednesday morning. Wednesday's sunrise was at 07:15. The fourth had been over for 23 minutes.

So Wednesday took its name from the fifth. Tuesday the third, Wednesday the fifth, and anybody reading down that column watches the count step over a number.

This is a kṣaya tithi (क्षय तिथि), a tithi that has suffered a loss. In English the almanac books call it expunged. It needs a tithi shorter than the stretch between two sunrises, which is common enough, since tithis run from about 20 hours at the shortest to nearly 27 at the longest. It also needs that short tithi to fall between two sunrises, touching neither one. The opposite case, where a tithi is long enough to be running at two sunrises in a row and its number is printed twice, is a separate piece of bookkeeping and a separate essay.

Where the fast went

Now the question that actually matters in a house. A monthly fast, a birth tithi, an annual rite for a parent: what do you do when the tithi it is pinned to has no day of its own?

The convention is settled, and it is easier than it sounds. The vanished tithi belongs to the day on which it began and ended. That is the earlier of the two dates, the one the sheet has named after the previous number. Robert Sewell and Sankara Balkrishna Dikshit put it plainly in their book The Indian Calendar of 1896: for an expunged tithi, the weekday is the day on which it begins and ends.

There is a reason it comes out that way. The day runs sunrise to sunrise. The vanished tithi begins after Tuesday's sunrise and ends before Wednesday's, so every minute of it falls inside the day that started on Tuesday morning. It is not homeless. It is a lodger in a day named after somebody else.

Watch that work in the kitchen we started in. The fourth of that dark fortnight carries Sakat Chauth (सकट चौथ), the fast a great many north Indian households keep for their children and break once the moon has been seen. The almanacs put it on Tuesday 6 January, the day their own tithi column calls the third. The moon rose that evening at 20:59 with the fourth still running, and the fast was broken as it always is. Nobody in that house had to do anything differently. They only had to stop hunting for the number.

Seven weeks later the same thing happened to a different fast. On Tuesday 24 February the eighth tithi of the bright fortnight began at 07:01, 10 minutes after sunrise, and ended at 04:51 the next morning, about two hours before the next sunrise. The monthly eighth-day observance stayed on that Tuesday, a day the sheet calls the seventh.

A shraddha, the annual rite for a parent, is decided from a different hour again. Its test is aparāhṇa (अपराह्ण), the fourth of five equal parts of the daylight, which lands in the middle of the afternoon. The question is which day has the tithi covering that stretch, and for a vanished tithi that is usually the earlier day once more. Where the tithi slips past even that window, households follow whichever book they have always followed, and those books do not all answer alike. If a date like that sits in your family, the person to ask is whoever keeps your family's sheet.

One more line, because you may see it marked on a sheet. A day on which two tithis end has long been kept clear of new undertakings. The reason is practical, not frightening: the tithi count changes twice inside that one day, and the tables used for choosing a good hour prefer a day where the count only changes once. It is a scheduling preference, and nothing in the arithmetic proposes harm to anybody. Meanwhile the fast that belongs to the vanished number goes ahead on that very day, because that is where the tithi actually was.

The same morning, four cities

One more fact about that Wednesday, because it explains why a cousin in another state may not know what you are talking about.

A tithi begins and ends at the same instant everywhere on earth. Sunrise does not.

The fourth ended at 06:52 on that Wednesday morning, and it ended at 06:52 for the whole country. In Kolkata the sun had come up at 06:18, more than half an hour before the tithi finished. So the Kolkata sheets found the fourth running at sunrise and printed Wednesday as the fourth. Chennai, where the sun rose at 06:33, did the same. Mumbai, where it rose at 07:14, lost the number exactly as Delhi did.

One morning, one sky, one clock across the whole country, and the fourth has a date in two of those cities and no date in the other two. If that sounds like an error somewhere, it is worth reading why two panchangs disagree, because it is the same honest arithmetic underneath.

None of this is new, and Sewell and Dikshit show how ordinary it already was in their own time. They printed an extract from a Poona almanac for 1894 and used it to point at a seventh tithi with no day: the sixth ran out about six minutes after Friday's sunrise, the seventh ran on until before Saturday's, and Saturday was named after the eighth. Six minutes of one morning decided it. The companion piece to this one, on the opposite case, does the yearly tally out of the same handbook, and of the two irregularities the missing numbers are much the commoner.

Where traditions differ about a vanished number, they differ in print rather than in secret, and Ekādaśī (एकादशी) is the case you can watch happen on one page.

On 30 December 2025 the eleventh tithi began at 07:50 in the morning, after sunrise, and ended at 05:00 the next day, before it. Expunged, by exactly the arithmetic above. The calendars printed the fast on Tuesday the 30th, the day named the tenth, which is where the rule we have been following puts it. They also printed a second date on Wednesday the 31st and marked it vaiṣṇava (वैष्णव), for households in the devotional tradition centred on Vishnu. Vaishnava practice says the eleventh lunar day must never share a day with the tenth. So when the eleventh has no sunrise of its own, its fast is moved to the next day instead of the earlier one.

There is a good deal more to how that particular fast is timed, and it belongs in a piece of its own. What I would keep from it is the shape of the printing. A sheet that has just dropped a number without a word turns round in the same column and hands one lunar day two dates, in the smallest type on the page, for two kinds of household.