The phrase semper eadem, "always the same", is a fairly popular motto. It is easy enough to interpret semantically, but I could not convince myself about the exact grammatical interpretation of the phrase.
What is the word eadem in this phrase? It could be neuter plural nominative or accusative, meaning "always the same thing". It could be feminine singular nominative, but then some feminine noun should be understood. It could be feminine singular ablative functioning as ablativus viae, meaning "always along the same path". Semantically all these are more or less the same, but I wonder if there is a canonical grammatical reading of the phrase.
The ideas behind different uses of the motto may be different. Answers about individual uses are welcome.
Here are some auxiliary questions answering which might shed light on the phrase: Are there sources that indicate the length of the 'a' in eadem? For example, if it appears in hexameter, then the 'a' is long. Is the phrase considered part of a longer phrase? Are there official, authoritative or canonical sources that indicate how the phrase should be understood?