Samples of the lunars clearing methods from one of the earliest American editions of Moore's "New Practical Navigator" which Nathaniel Bowditch and his publisher Edmund Blunt would soon rename the "New American Practical Navigator".
Method I (apparently more or less the same as the method of Jose
de Mendoza y Rios):
Method II (More or less Witchell's method):
Both of these methods are "series methods" of clearing the distance. Read about Easy Lunars for an example of clearing the distance using a handheld calculator that is very close to both of the above methods.