When you talk about the new machine arriving, are you talking about a machine that was already ordered, or a machine that will be ordered after all the original machines have been ordered and delivered?
Both. I've got to wait for a Jupiter to be delivered before I start earning anything or can join the company. It wouldn't be right for me to have a share in any proceeds until my machine is delivered and producing coin for the pool.
The emergency fund could simply be allocated some shares and receive payouts like everybody else. Alternatively, when calculating distributions, the values could be rounded down with the rounded part going into the fund. For example, if each share is supposed to get 0.033333333 BTC then it could be rounded down to 0.03333BTC and the extra 0.000003333 going into the emergency fund.
Lets say that 4 Saturns have been delivered and each one generates 1BTC every week. Every Sunday, at midnight, all the generated bitcoins are distributed to the shareholders.
Everybody with a share in the first 4 Saturn has 11 shares in the Company. This means that there are a total of 3432 (4x78x11) shares in the company.
On Sunday, at midnight, every Company share gets 4/3432 BTC = 0.0011655 BTC.
On Wednesday, Saturn #5 is delivered and powered on. Over the following 3.5 days (until midnight Sunday) it generates 0.5 BTC.
On Sunday, at midnight, every shareholder of Saturn #5 gets 0.0064103 BTC (0.5/78). Every share in the Company gets 4/3432 BTC. 858 (11x78) new shares are created in the Company and exchanged with the owners of Saturn #5.
The company now has 5 Saturns and there are now 4290 shares in the company.
The following Sunday 5 bitcoins have been generated over the previous 7 days and each share in the Company get 5/4290 BTC = 0.0011655 BTC.