Leap Year Proportional Calculus

Leap Year Proportional Calculus

[UPDATE for this new text between square brackets

Today December the 19th 2015, I have been observing Sun’s rise from my window.

At 7:47 a.m. Spanish time (UTC + 1 -> 6:47 a.m. GMT), the first clarity in the sky (in total absence of the Moon’s light, which had set hours before and is now in half its reflected light influencing power, I think it is called third quarter in English, in Spanish its name is cuarto creciente, going towards full moon | luna llena,  the 25th, next week), could be seen looking South-East (there are some buildings preventing me from seeing the East clearly).

As we are [well… should be…] now close to Winter Solstice, here in northern hemisphere, dawn should take 18 clock minutes from the first clarity in the sky (whose time I wrote above) until it is clearly day to the average Joe. That happened at 08:05 a.m. (Spanish time: UTC + 1, which share the UTC time reference with cities much more on the East, adding inaccuracies all over, such as that I already explained for Iceland and London, though more on the East in this case).

Taking the Lemniscata curve for anticipation-delay from real (which I call here mezzogiorno, August the 31st, December the 24th, April the 15th, and June the 14th are the four dates in a year when both should occur simultaneously) to average mid-day, and depending on which point in the elliptical path of the Earth around the Sun we are, that is to say, depending on the date for the day to be measured, some minutes more must be added or subtracted, as I already talked about this and provided some links to find further information, I will only tell you the date in the distorted year I concluded we are today, December the 19th 2015:

We are in February the third (whose ‘Ort’ and ‘Ocas’ times [remember they are for Oviedo, Spain, Europe] you can read in the two rightmost elements in the row below) or the fourth:

3 856 1800  837 1837

This is so because of both 8:37 for sunrise and 18:37 (for which some (18 clock) minutes must be subtracted, being then 18:19 p.m. the time it should take place this afternoon).

In these two values it is easy to see there are 10 hours of sunlight for day, and days should go on decreasing until the 23rd, which is the date for Winter to start, so…

I also had on account an observation made by me many, many years ago in which I noticed, here in Asturias, there is an inertial climate drag among the dates for solstices and the temperatures increasing or decreasing accordingly. That is to say, here where I live, two months more or less after either of the solstices (those for day minimum and maximum durations) is when temperature reaches its lowest and highest peaks.

I concluded this being a little girl, I like snow, I think the city is beautiful all covered in white snow, the buildings, the streets, the trees, all with that white gravity and temperature arranged ice flaky halo upon or hanging below in icicles.

And here in Oviedo, when it snows, is usually in the first week of February.

END for the new text in this 19th December 2015 update]

In ‘Time Shift (VIII)’ post, I put some numbers quickly, which I said then, I would proofread later, I pasted the excerpt to make it more comfortable for you, I will correct in this separate post, and when I finish, I’ll update the ‘Time Shift (VIII) post with the calculus corrected.

‘I’ll add the leap year calculus here:
I’ll publish now, but beware I haven’t proofread yet 🙂 .
Given the fact that, at least in Spain 🙂 legal year has 360 days (which is so in order to calculate the amount of money in terms of severance pay for workers after being fired, thing I know because of a subject in the education system in Spain which was called FOL (I don’t know if it has been modified, or if it still exists, “Formación y Orientación Laboral”), this means each  legal month has 30 days (of the usual kind to everyone), so as the difference with the usual average year is 5 days and six hours, each four years, there is a difference with Spanish lapse of four legal years of 20 days and 6 x 4 = 24 hours, being then 21 days each four years (21 x 24 = 504 hours, in legal years), or to put it simpler, half an hour per each month all along the four years (the old known to everybody type of 365). This is 30 minutes per month (with a certain degree of error), so one minute per day in the average year (the usual one).
But, 504 hours of difference all along the four years lapse are, 504 x 60 = 30240 minutes all along the four years lapse. That’s the amount of minutes all along the 2103840 minutes (with that amount added) in the four years lapse. So 2103840 – 30240 = 2073600 minutes is what is considered throughout all that four years lapse, and the 30240 minutes varies from 0 (zero) displacement in March the First at 00:00 a.m. (pst, 😀 don’t move! [see note for this at the end of this post [before the 16th first update] and stop laughing!]) to February the 29th 23:59:59 p.m. each leap year.
As we are now in 2015, and next year there is a leap day to be added in February the 29th, let’s see:
18 days to December the 31st + 31 days to January the 31st + 28 days to February the 29th’

18 + 31 + 28 = 77 days, but I did the observation yesterday 12th December 2015 at 7:00 a.m. Spanish time, so it is not today, but yesterday’s date, and that’s one more day to add (I made the calculus in the 13th, but it was an update from the 12th, so, put it like this if you prefer: 19 + 31 + 28 =78):

77 + 1 = 78 days to February the 29th, and that’s 30 + 30 + 17 days and 17 hours to 00:00 a.m. February the 29th 2016 (or 30 + 30 +18 to whatever number of integer hours for February the 29th), and one additional day to the 1st of March (and subtract the subsequent amount of time to the time to calculate), which will be when the leap day for the leap year will be more close to a true time in the four years (of the usual kind to everyone) lapse, so one more day -> 78 + 1 = 79, giving a partial value of 30 + 30 + 18 days, and 17 hours to 00:00 a.m. (plus the amount to the hour to calculate from the date to) March the 1st 2016 (this is why then on, the day for the week takes one more step in the week), so taking  Saturday, December the 12th this year, next year will be Monday December the 12th because of the leap day taken in February the 29th.

Making this leap day count before February the 29th, does not make week take one step more, being February the 1st 2015 on Sunday, and the same date in 2016 on Monday.

504 hours of difference all along the four years lapse are, 504 x 60 = 30240 minutes all along the four years lapse. That’s the amount of minutes all along the 2103840 minutes (with that amount added) in the four years lapse. So 2103840 – 30240 = 2073600 minutes is what is considered throughout all that four years lapse, and the 30240 minutes varies from 0 (zero) displacement in March the First at 00:00 a.m. to February the 29th 23:59:59 p.m. each leap year.

This would be so calculating the (365 x 4) + 1 days as a whole, and that’s 1461 days.

[You know? it is strange… I made this calculus coping and pasting from to the calculator, unexpectedly, my calculator did a miscalculation of (356 x 4) + 1 = 1461… might be some virus or something…]



So, you take into those the date starting the First of March in a lapse year, and ending the 29th of February the lapse year inmediately following, so starting with zero, which as far as I know happens when the century starts (or ends), being 1900, a lapse year, as any other year counting in hundreds, so happens in 2000, 2100, 2200, 2300…, and adding by four to these 2000 + 4 = 2004, 2004 + 4 = 2008, 2008 +4 = 2012, 2012 + 4 = 2016, 2016 + 4 2020, and so on, but for each four years you add, one day must be added.

[ 1900, Nineteen hundred ‘La Leggenda del Pianista sull’Oceano‘ , Giuseppe Tornatore’s film storm scene link]

Being now 2015 and taking the 15th of December (take the 12th, and then is +2, or the 13th, and then is + 1), there are 16 + 31 + 29 to March the First 00:00 a.m. 2016, those are 76 days to subtract to the 1461 for the sequence, so

1461 – 76 = 1385

Or also 2103840 minutes / 1461 = 1440 minutes per day already corrected, multiplying by 76 days to March the First gives 109440 minutes, and that’s 1824 hours.

This with the day for the leap year already added, but without that difference added there are (in case you haven’t noticed 360 are the degrees for a circumference, that is why I calculated like this, but I am miscalculating five additional days in each of the four years, because the average year has 365, and not 360, despite legal years, and Gianicolo and Edinburgh cannons 🙂 ).

30240 minutes of difference if we take (5 x 4) + 1 = 21 days of displacement, and those in minutes divided by 1461 days every 4 years are 20,698151950718685831622176591376 minutes per day.

This is not correct already, because years have 365 days.

But, before I make that (easy to [almost] everybody calculus] I’ll add the context here for newcomers.

I told you I saw the stars positions very near to those I could observe with my eyes last year’s December and this year’s January. I told you also, I have wroted down some observations then because then I didn’t know what was happening. So, I concluded we are more or less in January the 15th, meaning that, a constant acceleration value for the Earth which has caused a mismatch between the should be(s) and what are the actual conditions.

Obviously, this acceleration has been steady, had it been otherwise, we would have noticed.

Well… seismicity, and temperature values, along with other climate features, such as droughts, or floods, or rain, or tides, have been increasing also steadily along the last two, or maybe three decades, it is sort of going on a train in the bar wagon with a set of glasses with drinks, which start vibrating stronger as the train varies its velocity. The Earth’s crust vibrates too as it moves, and magnetic increase means, accelerate to scape the force, or  get closer to the Sun, derailing a bit from the rails, making the journey a little more bumpy and perilous.

It might be that it is only rotation axis inclination, but that should be determined by astronomers, who are the people who know better when some astronomical phenomena such as November Leonids or October Orionids, December Geminids (should) occur, being them (and not me, who is not an astronomer) who have to measure all those values, and make them public to people, specially to technicians on these matters.

Because people take decisions and deploy things according to what they think is happening. And stating as secure a technology which is not, or burying pollutants under somebody else’s carpet, is not sensible nor adviceable, and in this global case can lead to global catastrophe.

Making people be aware of nothing about what they are working on, but some charts values, or obscuring (or simplifying too much) otherwise beautiful calculi, or giving the wrong figures for measurements, end up making a big difference.

Be calm, remember: I am not an astronomer, and even though, I think it can be solved.

And in this case, I told you the 12th, Winter and solstice had arrived with…

…This means a difference between the dates from 2014 to 2015 of almost eleven days: ten days and 22 hours (I haven’t had on account the day to be added next year in February the 29th, but stars have their own paces, and I am afraid they haven’t either…

According to my observations, there has been either an additional elliptical path shift from what I have been observing since March the 16th, more or less, of two days (remember lemniscata, and it does, or it doesn’t, being this, a variation respect the average mezzogiorno of |16 + 14| = |30| (so -6 taking the max min addition for the closed interval from -16 to +14) minutes depending on dates varing from November the 4th, to February the 13th, putting the zero in December the 24th, August the 31st, April the 15th, and June the 14th, which are the four dates in the year in which mezzogiorno and average mid-day coincide .



I had been observing five days in anticipation respect to those for spring, and summer this year.

[16th further explanation]

When I thought it was Ursa Minor, which eventually was not, who was swirling like that in the sky, I started thinking what could be happening, and wrote down, and calculated some things, which afterwards, I checked by observation.

I observed (and posted about most of it while happening), spring, summer, and autumn had come in anticipation with five days each (more or less) being then in March the 17th for spring, June the 17th (<- I’ll search for this one later) and September the 17th for autumn.

I then did an estimation for 2014 shifted winter solstice, which I did not observe then, because I noticed the 23rd something strange was happening, and had it been consistant with the rest of dates displacement, it should have took place in December the 16th (2014) last year. And that’s one year (a usual to the average Joe’s one) to today.

But, if it occurred the 12th, with… say 10 days and some hours of anticipation, that is 5 days more compared to last year’s estimation for its occurrence in difference with the 23rd of December that is the usual value for Winter solstice.

On the other hand (and don’t forget I am not an astronomer, nor a seismologist), there have been at least five IMPORTANT seismic crises taking place all along the past year and this, for one year and a half, in ICELAND, HAWAII, ALASKA, PAKISTAN, and NEW ZEALAND according to websites databases.

This is important because, seisms (earthquakes) and volcanoes eruptions occur where the crust has certain types of rocks, whose nature is highly ferromagnetic, and so, they are more sensitive to magnetic changes of any type.

Being aware of the differences in size, shape, density distribution, and rotation velocities among the Earth and the Earth’s core (this later I think some seismologists and geologists have not yet thought of. So, as far as I know, nobody else, but me perhaps in previous posts I wrote here, has written about it), being these:

The core (nucleus) more dense, much closer to a perfect sphere, approximately 3.5 to 6 in ratio difference for radius, and I am afraid 360 to 365.25 in respective years durations.

I explained to myself (and wrote here in order to communicate my findings to everybody, and that includes also the scientific world, who is who have to peer-revise all I have been writing about ‘Physics chemistry and mathematics

(also: https://learnwareenglish.com/category/science/physics-chemistry-and-mathematics/ in your address bars, a new category you’ll find in the dropdown tool for categories on the right column (click on ‘View full site | Ver toda la web | Vedere tutto il sito web’ in your mobile devices if you cannot see it)), and also my ‘Physical- Chemical Table of the Elements‘, which I had already developed and registered earlier.

[Table link]).

I explained to myself and to anyone who reads my posts, I think a big part of what’s happening, can be a result of magnetism deviating rays of light coming from outside of the atmosphere, producing an angle perception variation, and also increased magnetism adding to the core, and thus accelerating the entire planet […hm… I think you already know wich one 🙂 ].

So, my calculus for the leap year day contribution to this 10 days + some hours between December the 22th 2014 to December the 12th 2015, or the 6 days + some hours between December the 22th 2014 to December the 16th (today) 2015 differences, finishes here, being now the scientific world who has the data they have, along with those I have explained, to peer-check, and do something about it (and don’t worry too much, it is not something new, it has been happening since time ago, the difference is now you are also aware, and it can still be solved).

Happy Christmas!

(This is the end of this post, although I’ll repeat it below).

Excuse me, but I am a bit tired today, so I will go on with this tomorrow [I’ll follow explaining above what I had not finished yesterday the 15th, now, the 16th], but meanwhile, do your observations, and measurements, because, today was very cloudy in the morning, but I think that everybody sees now there is a big difference.

I’ll go on updating tomorrow.


AN (Mil, Mus) marcha f; (fig) (=long walk) marcha f, caminata f
forced march marcha f forzada
an army on the march un ejército en marcha
we were on the march to the capital marchábamos hacia or sobre la capital
it’s a day’s march from here está a un día de marcha desde aquí; (fig) eso queda lejísimossee also quickA1see also stealA1


1[+ soldiers] hacer marchar, llevar
I was marched into an office me llevaron a un despacho, me hicieron entrar en un despacho
2[+ distance] recorrer (marchando)


1(Mil) marchar
forward march! de frente ¡ar!
quick march! al trote ¡ar!
to march past desfilar
to march past sb desfilar ante algn
2(=demonstrate) manifestarse, hacer una manifestación
to march into a room entrar resueltamente en un cuarto
to march up to sb abordar a algn
march past N (Mil) desfile m’
excerpt from wordreference multilingual dictionary (Collin’s tab).
non-ordinate pair

non-ordinate pair

(December the 16th 2015, some hours afterwards…).

These are yesterday’s photographs starting at 07:48 a.m. Spanish time convention, it was cloudy, today is even more cloudy, so I’ll make some photographs today, but they will look much more obscure because of clouds (it is raining right now, and the sky is totally covered),  and upload them after these of yesterday December the 15th.

(I’ll go on with the leap year proportional calculus after I have uploaded the photographs series of today, which I am not doing, when not writing… 🙂 , how much more easier my life would be having some extra arms to help me!… (sigh)… though less reliable in that case… 🙂 ).



IMG_20151215_075745 IMG_20151215_081522 IMG_20151215_081943 IMG_20151215_082230



IMG_20151215_083127 is the date and time (UTC + 1) Madrid, time convention.


16 853 1814  821 1855  735 1930  740 2107  659 2142  642 2206  657 2201  729 2126  803 2032  838 1939  817 1758  849 1748

TODAY’S photographs start here. I put the captions for the first and last (if you want to see all times, just right-click on the screen, and click on ‘View page source’ | “Ver código fuente”, and in the right top corner of your browsers click on the tools icon [the square with horizontal bars in Chrome] and put into the ‘find’ | “buscar” .jpg, it will find all .jpg into the source of the page. Click on the arrow on the right of the ‘find…’ bar, and browse the occurrences, and search for the IMG_20151216_hhmmss like title for the .jpg, into which you can see the date also).












Today’s values for ‘ort’ and ‘ocas’

8:49 17:48 (UTC + 1)

I have been working here for four hours or so, I’ll keep updating later, in the afternoon.

[You know? I kept updating… so now I spent seven hours writing here]

Go to: [16th further explanation] above.

Happy Christmas!


Acerca de María Cristina Alonso Cuervo

I am a teacher of English who started to write this blog in May 2014. In the column on the right I included some useful links and widgets Italian is another section of my blog which I called 'Cornice Italiana'. There are various tags and categories you can pick from. I also paint, compose, and play music, I always liked science, nature, arts, language... and other subjects which you can come across while reading my posts. Best regards.
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