This is my own interpretation, and strictly follows Hibler and Kappen's book ("HK"), that was published in 1963. It does not involve the "monetary" so called dollars (HK777 through HK873), as they are all fairly well documented. I suppose to some readers this discussion may seem a bit long and perhaps overly analytical. Nevertheless, hopefully for some it will help to shed some light on this enjoyable but difficult to define area of numismatics. As a so called dollar collector I have never followed HKs guidelines to the letter, and I doubt the authors ever intended the book to be used that way anyway; but for the most part I think that the author's decisions, all things considered, were good ones. For me the book has always served as a good foundation for collecting these interesting and varied medals and tokens, and since it's publication in 1963 it has obviously been the major influence on everyone who has collected them.
A so called dollar is a medal or token that is commemorative in nature on at least one side. It should have a strong United States commemorative theme and measure 33 to 45 millimeters in diameter (size 21 to size 28 using the more traditional and somewhat less exacting method of measurement). Most collectors up to now stick with pieces made prior to 1960/1962 or so.
The vast majority of so called dollars commemorate a "public" or "special" EVENT (world's fairs, town or state anniversaries, statue dedications, famous battles, etc.), however using HK as a guide, they can also commemorate any of the following:
After both reading HK's introduction, and studying what is and is not in the book, the following assumptions can be made about what was excluded:
Note that if one side of a piece had any of the above exclusionary themes, the piece was not included in HK even if the opposite side commemorated a public or special event etc.
The following themes were generally allowed in HK on one side of a piece as long as the opposite side commemorated a public event that was different or somewhat unrelated. These themes can be referred to as being "neutral" in nature, neither causing a piece to be included or excluded from HK on it's own accord.
Another important note is that no holed or looped pieces were included, HK numbers 2 through 4 being the exceptions(HK states numbers 1 through 3 which is a misprint).
With regard to many of the categories of pieces not included in HK, a quote out of HK's introduction is important: "Some of these latter subjects, of course, have achieved an importance of their own and either have been treated by competent authorities or are worthy of such attention. In other cases, the material proved too abundant to permit proper consideration here."
Lastly, to make things interesting, the authors of HK occasionally appear to have stretched or even broken their own rules, but there were often good reasons. Below is a discussion of most of these pieces.
HK2-4: Although only found holed, it was included because of it's high historical and numismatic importance. It is the only Numismatic artifact from the 50 year anniversary of the signing of the Declaration of Independence.
HK8: This is a foreign piece that commemorates the Crystal Palace in London, not the Crystal Palace in New York, so perhaps the authors of HK should not have let this one in. It is obviously not of US origin or theme. Nevertheless, it is an attractive and desirable piece commemorating what some view as the the first Worlds Fair.
HK9-10: This event was held in Great Britain, but involved an American fighter with a large US following. Also, the medals were made in New York. There is also a companion piece to the one listed in HK that has Thomas Sayers for the obverse.
HK35-36: A school medal on the reverse even though Hibler and Kappen's introduction specifically states "no school medals"; but it is also a bit religious("Baptist") too.
HK114: This piece never seemed to me to quite fit HKs criteria due to it's totally political/patriotic theme, but I never really questioned it's inclusion because of it's association with the U.S. Centennial Exposition. Then I read one of Joe Levine's comments in one of his PCAC auction catalogs that made me think that maybe this piece should have not been included at all(read comment in Free Study regarding HK114). It was evidently minted sometime prior to the World's Fair, and thus not associated with the fair at all.
HK149: Sort of "advertising" in nature on the obverse, but a worthwhile inclusion nevertheless.
HK296: This is a "corporate" commemorative, and perhaps it could have been included with others of a similar nature, but it also commemorates an important part of American western history.
HK297-298: Advertising in nature on the reverse. I'm sure that the reason this piece was included was because it is such a nicely executed and substantial medal, unusual for an advertising/store card type piece. It is also perfectly sized for a so called dollar.
HK353-356: This is the smallest so called dollar listed in HK (excluding the gold dollar pieces). It measures 32.1mm which breaks the minimum size rule of 33mm. It was no doubt included because of it's significance as an official world's fair medal struck by the US mint.
HK434: Advertising in nature on the reverse again, but was included anyway, I guess because the other side commemorates a world's fair. As stated above, there are a lot of other pieces like this one that were not included in the book that are advertising in nature on one side, and commemorate a world's fair on the other.
HK465 and HK466: Once again advertising in nature on one side.
HK534-541: Like HK149 in nature.
HK733: Obvious advertising piece on one side, and partially so on the other side too. There are actually four or five other varieties of this piece, but the one listed in HK is the only one that goes beyond a strict advertisement by commemorating the "100th Anniversary Mechanics Fair Boston".
HK755: A trade association piece, but without a date. Sort of unique I guess.
HK832: Obvious silver dollar design, but no one knows for sure why it was made. HK states that this is the most controversial piece in the book.
Section C: This is HK's "miscellaneous" section. Some of these pieces are difficult to classify. There are a number of pieces regarding America's participation in World War One. These all seem legitimate under HK's guidlines. The Denver 1905 piece(HK876) also seems perfectly legitimate. The Loyal League piece and the KKK pieces are both completely political/fraternal in nature and thus are a bit dubious, especially in light of the fact that no completely Masonic or GAR pieces were included in the book. Perhaps they were included because of their patriotic slant, or perhaps simply because they had not been cataloged elsewhere. HK877-891 are all political in nature, but were possibly included because of their association with Thomas Elder. The Swift pieces(HK905-907) are somewhat unique. Their inclusion I guess is obvious from the standpoint of their "dollar" theme. There is also an unlisted Standard Oil Company piece that is very similar. The reverses of HK483 and HK484 are also sort of similar. The United Nations piece(HK914-915) is an undated souvenir token of a place. It is also the only "spinner" in the book. The very last piece (HK916-917) is totally patriotic/religious in nature, commemorating God, freedom and the grand old flag.