First, you'd have to go back to the roman calendar to change that, and it'd still be from March first to February last.
Second, the 10 day drift of 1582 would put the solstice around December 15th in the 1200s, compounding the problem.
Third, I'd expect the rules to be written for the players, with the modern day expectations we have.
I therefore have no idea how your point could relate in any way with the concept of "next year" meaning "a year-long period starting on the solstice".
After three posts of hinting, I think I need to be more blunt. Ars Magica is a game of let's pretend - and in it we pretend, among other things, that the Ptolemaic model is true. So the earth resides at the center of the universe delimited by the fixed star sphere against the empyreum, and is circled by the sun along the ecliptic. So we also pretend - following the ancient and medieval scholars - that a year is the time the sun needs to perform that circle once, and that there is no distinction between the sidereal or solar/tropical year. Hence in-game the roughly 20 minutes of difference between the two do not exist. It is honorable to not be able to pretend a dated, falsified cosmology and in a game system fully follow through with it. But I will not make it my problem if a forum member just cannot do it, and will skip your further comments on the difference of solar and sidereal years.
I answered that already, but will do once more. The full phrase to interpret is "and the Aegis then lasts for the entire year" (underscore mine). If I tell somebody, that a battery will last for the entire year, I obviously do not promise him in that phrase that it will fail immediately after.
If you read the article in question even more closely, you will find, that it starts with the definition of the topic:
That's it, there you have the default definition of the term.
Some lines further into the article, we find:
So your alternatives are duely treated before the Wiki article begins to treat historical developments and cultural differences in definition, role and meaning.
Cheers
You are really confused. I don't want to say that 20-minute difference has nothing to do with what I was talking about, but it is essentially irrelevant. If you would prefer, I could write 365.2(4) instead. That 20-minute difference could drop to nothing and the problem would remain essentially unchanged. I'll continue to not worry about it, as you would like and as had done. The issue is that the earth's orbital period around the sun is not an integer multiple of its rotational period. Leaving out a ratio of 1 (tidal locking) or less for simplicity (and assuming an axial tilt under 90 degrees), this ratio describes the number of days in a planet's perspective per year in that planet's perspective. For the earth, since it's not an integer multiple, this means that a year isn't an integer number of days long. This is the reason for leap years working as they do. However, leap years do not need to have been invented as this simply exists (assuming you're playing Ars Magica in the last few millenia - go back long enough and you'll sometimes hit integer multiples when the earth was spinning faster).
When it comes down to it, your system has an Aegis last an entire year more often than mine does. But neither system always makes sure the Aegis lasts an entire year. So if not guaranteeing the Aegis lasting an entire year is the reason my system is faulty, then the same must be said of yours.
So, let me get this straight. You are really worried and fussy about this one line in Aegis of the Hearth's description. Yet you are totally willing to sweep away the sidereal/solar distinction? Even though the sidereal/solar distinction is not only explicitly part of canon, there are rules about durations in canon that depend upon it explicitly?
Now, if it helps we could make up a new term. (Maybe there is one, but I don't know it.) I was hoping to avoid this. Let's call it "rising/setting" and compare it to "solar" and "sidereal." Here "rising/setting" times are based on the celestial body being seen to pass the horizon. "Solar" can return to its proper use, and "sidereal" remains so. So, for instance, a rising/setting year is either 365 solar days or 366 solar days, depending on the year. Meanwhile both the solar year and the sidereal year are roughly 365.2(4) solar days. Note that rising/setting times depend highly on location and the others do not. Let's see which of the three are being used:
Diameter - rising/setting (depends on location)
Sun - rising/setting (depends on location)
Moon - triggers off rising/setting (depends on location); specific date could use any system
Year - triggers off rising/setting (depends on location); specific date could use any system
For those last two variable parts, which system would be most consistent with the other four things that are pretty specifically set?
So, if I say "Aegis of the Hearth lasts one entire day," you consider that a normal use of "last," right? My statement would not be misleading? If a hockey player asks how much longer the penalty will last while 45 seconds remain to it, would it be correct for the referee to reply "it will last 10 more seconds"? Or would that be misleading? What if your professor gives you a test and says "this test will last one hour" and tries to collect the test from you when an hour is up?
Your comment has an assumed "at least" in it. That's fine; it's colloquial. But if you're willing to accept that as colloquial (an assumed "at least"), then how can you not be willing to accept the colloquial "entire." Why is one assumption more valid than the other?
Yes, it starts that way. But what does it say about that start? The article explicitly says that it's own statement is only one of the common definitions. In fact, it mentions there are many ways and other ones are also common. I have no idea how many common ones there are, but apparently a few. The only other one I have specifically seen mentioned in this article is the one I'm using. If you want to find a source that actually says this is the default definition in non-scientific English, go for it.
Chris
If I just ignore the 365.2(4), which looks very jumbled, that would resolve the issue. Unfortunately you are looking for a new problem below, partly with homegrown terminology, and never really find it, or spell it out.
This is the reason, why medieval scholars and astronomers (and in-game Hermetic magi) do define a year by the period of the full circle of the sun around the earth along the ecliptic. In modern terminology this is the solar year. This is also the year the Ars Magica rules consistently speak of. (No RPG I know of distinguishes in its rules between solar and sidereal years - but as we have seen, in particular Ars does not need to because that difference in its cosmology does not exist.) The counting issues of the calendars derived from the Julian are best left to the churchmen who need to determine Easter. But we can skip these here, I hope.
My reading makes sure that an Aegis cast at the right times – on or rather a little after the solstices and equinoxes – always lasts until the sunrise after the fourth following solstice or equinox, that is an entire year. I grant you, that a magus may be taxed to cast the Aegis at the right time, if a sunrise follows the astronomical event very closely (say, within a few seconds or minutes) – but that is another issue I already addressed in the thread.
We have seen that a distinction between solar and sidereal years does not exist in Ars Magica. What you now understand by the 'solar / sidereal distinction', and how it relates to our topic, I cannot find out by your post – but maybe is not critical anyway.
Luckily we will never use that “rising/setting year’ in the following, so I will just pass it over.
Well, Duration Diameter does not depend of time or location of casting, in particular not in the Ptolemaic model - where the sun always maintains the same distance to the earth, and moves along the eclipse with constant speed.
Apparently, your new term "rising/setting" has overridden your concern about the 'solar / sidereal distinction' a paragraph before. But I still don't see any problems with the spell duration definitions as are, and the role of Duration Year in them.
EDIT: You are not actually proposing here to use your homegrown "rising/setting" year as the reading of 'year' somewhere in Ars Magica ... or are you?
As our combined efforts at finding examples have shown (and a little sense would have shown as well), the meaning of phrases depends on their contexts, and the expectations of those uttering or hearing them. So, what is the context of "and the Aegis then lasts for the entire year", and what are the expectations of author and reader? The reader expects to understand the ramifications for his magus to cast an Aegis. And the author needs to explain that to him. So the author would mislead the reader when telling him that the Aegis "lasts for the entire year" if cast under certain conditions, but indeed the rules would stipulate that it could expire before: because of that information the organization of the reader's campaign depends. It would not concern the reader if it would last a few hours longer though - just like the buyer of the battery.
Very much. Wikipedia is an encyclopedia. And if an article in an encyclopedia defines a term immediately in the first phrase, that is the definition, as far as the encyclopedia is concerned. If it later states "The term solstice can also be used in a broader sense", it just lists other uses to later be able to put them into technical, historical and cultural perpective.
Cheers
That's a standard format for recording measured values.
I hope you see the contradiction above. You say the year is defined by the full circle. Then to get your Aegis to last an entire year you had to switch to a year as defined by sunrise/sunset. Had you remained consistent in your definition in the second case, your Aegis would not always last an entire year.
Also, as I explained, using the solar year versus the sidereal year does not get rid of the leap year issue.
Yes, it absolutely does.
I left it open as a question because it seems to work most consistently. And it's not my homegrown use of a year, it's actually the everyday western calendar use of a year - a very common use of year. You decided yourself to adopt it above for half your argument. Why were you so quick to use it yourself to try to make your case that it shouldn't be used?
Except the article explicitly says this is not the definition, but only one of many.
Chris
That would be your 'rising/setting year'? No.
Why would I? I would not touch that thing with a rabble when physical or magical durations are involved - and neither would medieval scholars or Hermetic magi, who know the mess of medieval calendars first hand. Medieval calendars are rather the domain of laws, contracts, work obligations and holidays.
So lets take it really slowly.
How much time expires between one winter solstice - the astronomical event - and the next? Exactly one (solar) year Y. So if I cast a Duration: Year Ritual on or a short time T after winter solstice, and if that T is smaller than the time T' between the next winter solstice and the sunrise on it, then the overall duration of my Duration: Year Ritual is: Y-T+T' > Y. OK?
Because I saw somebody dangerously veering towards it. 
It is the definition of Wikipedia for solstice.
Cheers
EDIT: It looks like we were driving a carousel all the way from Saturday December 15th ( catnip & garlic ) - when your 'rising/setting year' was still just a calendar year - through sidereal years and back here. I wouldn't like this to become the second round.
You say this, and yet you did:
It's not so surprising that someone would use this idea for a year. It is, after all, the colloquial (and generally assumed in non-scientific circles) standard in English (and I suspect in most European languages). Certainly, I don't celebrate my birthday on different dates from year to year depending on the time of day I was born and when the dates are in comparison to leap years. The only ones I know of who do this regularly in western culture are the ones born on February 29 because they don't have a choice.
Similarly, do you, for Year+1, bother to figure out what time of day the spell was cast to figure out what date is a year later (and then add a day)? Or do you go to the same calendar date a year later (and then add a day)? I suspect most players would use the latter, not that it can't be done either way.
Good. So now you do see that casting the spell after the astronomical solstice and before sunrise is not sufficient to guarantee it lasting a year. You have to do so within certain extra constraints. So, as I said, using your method also does not guarantee the spell lasting a year if it cast at the time stated in the Aegis of the Hearth description. Since that was the point that was so bothersome about using my method and since neither one holds up to it consistently, either we must read the Aegis of the Hearth description a little more colloquially or throw out both interpretations and search for one that actually fits such a strict reading. I prefer allowing both your method and my method to having to throw both out.
Chris
PS: Forgot this:
Yes, it does; the distinction it is even stated. Ars Magica specifies working off sidereal years for some durations but goes on to, in essence, state that sidereal and solar years are so close that for game play we can estimate both of them similarly (the estimate being 1 month = 1/12 year, even though months vary).
That is quite irrelevant for the topic at hand - but certainly depends on the campaign, and the current SG's ideas to cause problems. I would at least give characters an easy Artes Liberales roll, if it is important for them to notice that scheduling their Aegis by their chaplain's calendar is a lousy idea.
Of course casting the spell after the astronomical solstice and before sunrise is not sufficient to guarantee it lasting a year. I don't recall to have ever said that, either. Casting it before sunrise is very important, though, because it is the condition to have the new Aegis come up while the current one is still in place - and thus to avoid the cumbersome pest hunt or worse.
So can we agree now, that the part of my reasoning which you quoted above is correct also from your point of view? In that case we can stop this exchange.
In the Aegis of the hearth description, we read "The Aegis is typically cast on the winter solstice, ... , and the Aegis then lasts for the entire next year." (Underscore mine as usual.) So there T = 0, while the case we just discussed - Aegis being cast sometime after the winter solstice - means T > 0.
That's interesting! Where is this stated?
Cheers
It's in TMRE. Look at the astrological stuff. There are several comments on the difference between the solar values and the sidereal values, and the sidereal ones are the ones used for the astrological stuff. I'm not sure the book ever says "sidereal." But They describe it. For example, the Sign duration is (for Hermetic magi) 1/12 of the time it takes the earth to complete a year with respect to the "fixed" (never really liked that term) stars. That is, Sign is a twelfth of a sidereal year. So the magi technically care about it. However, let's make it easy for the players, let's just estimate that as one month (which is not even consistently 1/12 of a solar year). But they do suggest making that estimate instead of dealing with what the magi actually deal with.
Chris
I walked through it again. In particular the chapters on Astrological Durations (p. 49f) and the Armillary Sphere (p.51ff), which both relate to this thread, were interesting to read once more. Weird is, how AstrologicaI Time (box on p. 49) is made location dependent with handwaving. I did not find any reference to sidereal years or values there, though.
Cheers
Look at how the measurements are made for Sign and the like. This is the easiest way to describe how someone can measure the difference between a sidereal year and a solar year or a sidereal day and a solar day. I don't believe the word "sidereal" is ever used there, but the sidereal periods are.
Interestingly, I considered the 20-minute difference and the lifetime of a magus. Assuming an average magus lives to be somewhere around 100, or roughly 75 years after gauntlet, things will have shifted about one calendar day during his lifetime. Magi who are interested actually live long enough to really notice this shift.
Chris
Of course the measurements described are 'sidereal' - by the very nature of astrological measurements.
So player character magi - if really interested - could by experience in their lifetime actually falsify the Ptolemaic model, if they found the 20 minutes difference per year. Of course, if they found the difference they would have also falsified the ArM5 rules: like those in ArM5 p.80 'The Limit of the Lunar Sphere' or A&A p. 16ff.
But it is anyway more likely that during their lifetime they have followed the general academic development and become observant Aristotelian magi, eschewing experience where it doesn't fit (A&A p. 10 upper box).
Cheers
I don't follow. How does this difference allow Hermetic magic to directly affect the moon, sun, or stars? Seeing their positions in the sky and having them affect Hermetic magic is a basic premise of the durations Diameter, Sun, Moon, and Year. But those don't break this limit.
Chris
It's simple. The paragraph summarizes the Ptolemaic model as base of Ars Magica's cosmology: "The lunar sphere is the innermost of the celestial spheres, which carry the stars and planets on their revolutions around the earth, ...".
Cheers
What is there to prevent him from creating the ritual with the small change that his access and control of access is only temporary? AFAIK, nothing what so ever. This is not a change in parameters. This is the kind of minimal modifications usually considered to be part of the design process.
To that, I would add that i think a lot of covenants would be willing to also pay for the additional level of protection from a higher Aegis. Ie., the profit per Aegis would likely be more than just 2 Vis. So the pay would probably at minimum be based on the actual Aegis level. And it would be those covenants unable to cast a high level one themselves that would use the service(or those rich/lazy enough to not want to do it themself).
I expect the cost for a level 60 would somewhere in the 10 to 25 Vis range depending on overall supply and order situation in general.
And about Penetration, why the assumption that any use of WC would have to be with apprentices? I would expect the Mercurians to have some semblance of, if not cohesion, at least communication, which means this service could also be handled by a small group (2-5) of Mercurian magi, as long as one of them has the AC needed to get to the client covenants, it should be very workable.
Haven´t read the entire thread so hopefully not doubling up on something already said.
If nobody specializes in rego vim it is quite normal for you to have a not-that-great aegis. As DW points outwillingness to pay comes to the fore there 
If you expect trouble that is. We have had a level 25 aergis during whole sagas, even ones where supernatural enemies knocked on our door regularly, and it was OK. Big stuff you take out the artillery. Stuff at Might 25 or less (pests, according to ArM5 RAW) is unable to pester you. Enough for us. But if you want extra protection it would be nice, yup.
Sorry, my mistake. But vagrancy isn't that either. It's not having a House which is what I confused with not having a covenant. (It's in HoH:TL at page 49.) The article also adds that you can be charged with vagrancy for not residing in a Tribunal or not complying with a Tribunal's residency requirements. There may be tribubals who say you have to have a covenant. I'm almost sure there are but my memory is clearly not up to the task of retaining Hermetic Law clearly.
Still, I wouldn't trust the casting of my covenant's Aegis to any outsider. Pure paranoia on my part.
To me, this sounds like an appeal for a troupe decision.
When deciding, the troupe should also consider that such 'minimal modifications' on a spell requiring a major breakthrough to be invented with "different parameters" (ArM5 p. 161) could be manifold: if the caster's rights can be made to expire after some time that way, those of everybody else participating at the ritual can as well. Hence allowing such 'minimal modifications' will not increase the level of trust for an outside Aegis contractor, but rather reduce it considerably, as long as his customers are not able to check the features of the cast Aegis independently.
Cheers
Oh, I thought you were saying magic could now break the lunar limit. But I still don't follow. Why is it the Firmamento could not rotate at a slightly different angular rate than Sol? I thought this was part of the system. I get that the Ptolemaic model has problems, which is why it will be challenged and then replaced in a few hundred years. I'm just not sure why different rotation rate between the different spheres would do that. I thought the main thing with the shift to the Copernican model was dealing with epicycles and retrograde motion.
No such assumption. There were calculations showing how it might done with apprentices if a magus didn't want to share the profits. I could certainly imagine a group of Mercurians who cast WC for each other for a small share of the pay, which might only amount to 1 p.v.f. after a few castings.
Have to agree with One Shot here. Whoa! How'd that happen? 
Each troupe should agree what "different parameters" means? I have been tempted to start a thread with voting on that to get an idea where opinions lie. For example, with my pen-and-paper (can I really call it that if we all use laptops now?) troupe we felt the normal size of Boundary was too small for many covenants, so we figured a extra magnitudes for size were OK. So our decision was that Boundary could not be changed but that size could be just like strength. In the last saga that didn't last too long we were working on a huge boundary because the strong part of the Aura rotated seasonally and we didn't want to cast 4 Aegis rituals a year, both for Vis and time issues.
Chris
Chris
Problems with the geocentric and ptolemaic models were known since their definitions, and in consequence many variations have been proposed. For some early examples look up K. F. Johansen, H. Rosenmeier, A History of Ancient Philosophy: From the Beginnings to Augustine (1998) - or for something easier accessible en.wikipedia.org/wiki/Geocentric_model .
The standard ptolemaic model at the base of Ars Magica cosmology is presented in A&A p.16ff. It has an unmoving earth at the center of the fixed star sphere, which moves from east to west around the axis through the earth's poles, and in itself is unchangeable. It also provides the base rotation for the spheres in which moon, sun and the planets move - which we understand as the rotation of the earth. The sun performs a very simple movement with constant speed along the ecliptic, whose axis is inclined by 23.4 degrees against the axis through the earth poles.
This model does not leave room for a difference between the sidereal year and solar year. I try to give the explanation in utterly simple terms now: since the center of the earth is also the center of the fixed star sphere, both do not move against each other - so the movement of the sun observed/measured with respect to the fixed star sphere is the same as the movement of the sun observed/measured with respect to the center of the earth. To account for any difference in observation between sidereal and solar year in the context of the standard ptolemaic model, the stars on the fixed star sphere would have to move against each other on that sphere.
Cheers