Mr Aiken refers to two documents issued by the Treasury on 20 October 2010 regarding annually managed expenditure (AME) funding and the Barnett formula that appear to be contradictory.

One of them applies directly to the funding of the Northern Ireland RHI scheme, and the other is a briefing given to MPs on AME and Barnett funding.

Image source, RHI Inquiry

He says that on the same day that the settlement letter is issued giving Northern Ireland an AME consequential Barnett budget for RHI, "the statement of funding policy that applies to Northern Ireland and the other devolved administrations says, according to the Treasury, this is not appropriate".

The GB RHI scheme could never truly be a demand-led scheme and in fact could only ever have a limited numbers of members, because it was given an annual budget limit, says Mr Aiken.

"Not everyone who might, in theory, be entitled to become a scheme member could become a scheme member," he explains. "There was only, in theory, room for a certain numbers of members."

Image source, RHI Inquiry

That reinforced the need for Stormont's Department for Enterprise, Trade and Investment (DETI), which set up the Northern Ireland scheme, to regulate the numbers of people who could claim from its initiative's budget.

That is a separate issue from the overcompensation of claimants because tariffs on offer were too high, he says, which was a critical flaw in the Northern Ireland scheme.

Looking at DECC's business case for the GB RHI scheme from October 2009, Mr Aiken points out that its officials had identified several risks posed by the initiative.

The unpredictability of fuel prices - a sharp rise in fossil fuels costs or a fall in biomass prices, for example - may cause a spike in uptake, DECC said back then, and that could be "critically damaging" to the ability to manage a budget for any scheme.

Mr Aiken says those are "strong words" for an official to use about the consequences of a scheme on a department's overall budget.

It was a major spike in applications to the Northern Ireland scheme in the autumn of 2015 that ultimately burst its budget and led to the colossal projected overspend of £700m, if permanent cost controls aren't introduced.

Why the Treasury did not tell Stormont more about the funding arrangements for the RHI scheme will be something the inquiry will have to consider, says Mr Aiken.

He says its knowledge of how the funding for the Great Britain RHI scheme operated would've been relevant for Stormont to have access to.

He adds: "It may be... that it was not an intentional: 'We're not going to tell them.'"

"But it may be something that just slipped through the net - nobody thought of communicating it."

Inquiry adviser Dr Keith MacLean says it could be seen that the Treasury had previously "its fingers burnt by trying to interfere in matters that were devolved" and it was simply "obeying an instruction" not to get involved.

Sir Patrick suggests that Stormont's attitude may have contributed to the situation, with its insistence from the outset that the RHI scheme for the region had to differ from the GB scheme.

Sir Patrick continues to appear less than impressed by the Treasury's answer to the inquiry on what it told Stormont about the funding for the RHI scheme.

He says that if the Treasury had answered "competently and straightforwardly", it would have simply have said it didn't tell Stormont's finance department about the RHI scheme arrangement with DECC, the 5% monetary penalty it would impose if the budget was exceeded, and its requirement for emergency reviews in the initiative.

Image source, PA

"That would be a straightforward, open, honest answer to that, would it not?" he asks.

He acknowledges that the inquiry cannot compel the Treasury to appear before it, but says that will not prevent an examination its direction regarding the scheme's funding.

Last evening, Mr Aiken was looking at the arrangements between the Treasury and Stormont's departments about how the RHI scheme would be funded.

Now turning to the Treasury's witness statement, he says it was asked by the inquiry if it had told Stormont about the process it had gone through with the Department for Energy and Climate Change (DECC), which ran the similar RHI scheme in Great Britain.

The Treasury says it "holds no records" that suggest detailed discussions were held with the Northern Ireland Executive about the design of the RHI scheme.

Image source, RHI Inquiry

But it says the design of the initiative "would be the sole responsibility" of the executive "within the funding policy and restrictions" set by the Treasury.

Mr Aiken interprets that as the Treasury saying that it didn't have to tell the executive about its arrangements with DECC because what happened with the money set aside for the RHI scheme in Northern Ireland was a matter for Stormont's finance department.

Inquiry chair Sir Patrick Coghlin takes issue with the latter part of the Treasury's statement, describing it as "fairly opaque" and saying it would have had "pretty big repercussions in Northern Ireland".

Proceedings are under way and inquiry counsel Joseph Aiken - sporting a snazzy new pair of clear-framed spectacles - picks up where he left off yesterday in his presentation on the funding of the RHI scheme.

Image source, RHI Inquiry

Mr Aiken used an interesting analogy involving a yeti yesterday, and he begins by saying that he'll not be returning to it until we find a better photo to accompany it for our live page coverage.

We'll take that as a 'must try harder', but it's good to know you're a fan, sir!

BBC News Northern Ireland

An independent inquiry into the RHI scandal was established in January by the then finance minister Máirtín Ó Muilleoir.

He ordered it in the wake of the huge public concern and what was then a developing political crisis surrounding the scheme.

Image source, Pacemaker

The RHI Inquiry began earlier this month and Sir Patrick Coghlin (above), a retired Court of Appeal judge, is its chair and has been given full control over how it will operate.

It is looking at:

• the design and introduction of the RHI scheme
• the scheme's initial operation, administration, promotion and supervision
• the introduction of revised subsidies and a usage cap for new scheme claimants in 2015
• the scheme's closure

For more information on the RHI Inquiry, you can read our handy Q&A.

When the scale of the overspend emerged, public and political concern rocketed.

As the minister in charge of the Stormont department that set up the RHI scheme, the Democratic Unionist Party (DUP) leader Arlene Foster faced calls to resign from her role as Northern Ireland's first minister in December last year.

Image source, PA

She resisted, and Sinn Féin's Martin McGuinness then quit as deputy first minister in protest at the DUP's handling of what had by then become a full-blown political crisis.

That move brought about the collapse of the Northern Ireland Executive, and as we near a year on from that Northern Ireland remains without a devolved administration.

You can find much more detail on the RHI scheme in our need-to-know guide.

Critical mistakes were made in the way the RHI scheme was set up that left it open to abuse and that later saw its budget spiral out of control.

Crucial cost curbs that existed in a similar scheme in Great Britain were not replicated and claimants could effectively earn more money the more fuel they burned.

That was because the subsidies on offer for renewable fuels were far greater than the cost of the fuels themselves.

As a result, the scheme racked up a huge projected overspend - £700m at the most recent estimate, if permanent cost controls aren't put it place - and the bill will have to be picked up by the Northern Ireland taxpayer.

Quick refresher before we start...

The Renewable Heat Incentive scheme - or RHI for short - came to the fore of the Northern Ireland public's knowledge in autumn last year.

Few people, if anyone, would have expected it to have the consequences it has done in the months that followed.

It was set up by the Northern Ireland Executive in 2012, as a way of encouraging businesses to switch from using fossil fuels to renewable sources for generating their heat.

Those who signed up were offered financial incentives to buy new heating systems and the fuel to run them.

Welcome along to the second session this week of the RHI Inquiry.

We're up at Stormont's Parliament Buildings and proceedings will begin shortly.