Here are a number of observations for you. I hope they help.
In generaly you can find the retail value of a typical William gold sovereign by adding about $100 US dollars to the base gold price. Find the base gold price by multiplying the current 'spot' price of gold (from web sites like Kitco.com) by 0.2354. The number 0.2354 is the number of troy ounces of gold in a sovereign.
If you can find a Gulielmus IIII sovereign in absolutely, fully uncirculated condition, wherein it was never touched by human hands, the $100 increment over base value goes way up, to $1000 or so. Such coins are rare, but they do exist in coin collections.
The coin in our picture is in great shape. It comes from Chard, a highly respected gold and bullion dealer in the UK. Chard's coin would probably fetch $500 over base gold value due to its excellent condition. CoinQuest thanks Chard for use of their coin photo. It is a nice one!
Wholesale values will, of course, be significantly lower than retail values. Wholesale values are what you can expect when you are selling a coin to a dealer. The difference between retail and wholesale is dealer mark-up, which the dealer uses to stay in business.
In 1834 a Gulielmus IIII half sovereign was issued with the same pattern as the sovereign. Here is a size comparison:
SOVEREIGN: 22 mm diameter, 0.2354 troy ounces gold
HALF SOVEREIGN: 17 mm diameter, 0.1177 troy ounces gold
Sue's particular coin is a rare and valuable one, but I would not call it *extremely* rare and valuable. There were only a handful of 1831 sovereigns minted (the catalog says 599,000 coins minted) compared to other sovereigns of the period (8,530,000 minted). This makes the 1831 date more desireable and increases its value over other William IV sovereigns by about 50 percent.
NEVER CLEAN A COIN. CLEANING RUINS VALUE.
With the 'cleaning warning' out of the way, the value of your coin will be determined by its state of preservation or numismatic condition. Don't clean it, and don't touch it with your fingers. Handle the coin only by the edges.
An 1831 sovereign catalogs for $200 US dollars in worn condition, $1200 in almost uncirculated condition, and well over $2000 in fully uncirculated condition. You indicated 'little or no wear' so we'll guess at a catalog value of $1000 for your coin.
Since you indicate that your coin is 'Raw' rather than in a numismatic holder, it is probably circulated. If you want to send us a picture, we can do a rough estimate of grade and therefore a better estimate of value. To start an e-mail exchange with CoinQuest, use the Contact Us link.
Also, be careful of the term 'catalog value.' See our Important Terminology link for an explanation.
Your WW and full stops analysis is a technical issue which we are not familiar with. (We Yankees call 'full stops' 'periods.') Our research spent preparing this appraisal did not turn up any information on this subject one way or another. Not only that, we do not use the Spinks Guide, so I can't compare what you say to that reference. The catalog values we quote come from the Krause Mishler catalog tempered with real, actual values quoted on reliable web sites. Please visit this site for more information.
Three more important points.
First, coin dealers and others who buy and sell rare coins are always looking for fresh material, and your coin qualifies. About 10% of dealers are crooks, and another 85% don't want to spend time developing a relationship with a potential seller. This accounts for the cold shoulder you have received so far on your quest. I hope CoinQuest is doing better ...
Second, Sue, you may consider having your coin authenticated, graded, and encapsulated by a third party service. This costs are usually less than $100, but is often well worth the investment. Not only do you find out what the grade (state of preservation) is, you get the coin guaranteed as genuine. Also, your coin is protected from the elements and becomes completely liquid in coin trading. For more info on third party services, look on the Internet for PCGS, NGC, ICG, and ANACS. Do not use other services.
Finally, beware that valuable coins are often counterfieted. If your coin has been in your family for years, this is not a problem. It you bought the coin on eBay, it could easily be a fake.