The attribution to Carolan is not proven, and was not asserted until the early 19th century; information at 'Contemplator' is always copied from elsewhere, usually without proper references, and so is not to be trusted unless independently verifiable.

Note that I'm not saying that Carolan didn't write the tune; just that we have no way of knowing whether he did, or whether it was merely attributed to him at a later date; as were a good many other pieces. See previous discussions here on 'Princess Royal'.