Oe represents an original oi and remained a diphthong in those words in which it continued to be written. When the first element predominates over the second, oe passes into u, as in plura for ploera, punio from the root of poena, cura for coera. When the second element predominates, oe passes into ae (by a confusion) and ē, as in obscaonus and obscenus for obscaenus. But in words where oe is regularly written, it is to be pronounced as a true diphthong.
UI as a diphthong occurs only in a few interjections, as hui, fui, and in huic and cui. In both huic and cui it represents an earlier oi (hoic, quoi). In other words (e.g. exercitui, gradui, etc.) ui is not a diphthong, but each vowel is pronounced separately.
The Romans were the first people to call the letters of the alphabet by their sounds rather than by names, as was done in Greek and in the Semitic languages. Thus the Latin vowels were named by simply uttering their sounds; the mute consonants and h by uttering a vowel after them, and the so-called nasal and fricative consonants by uttering a vowel before them. This vowel was e except in the case of k, h, q, and x. Hence, a Roman boy saying over his alphabet, would have given it thus:
ah, bé, ké, dé, ê, ef, ghé, ha, î (ee), ka, el, em, en, ô, pé, qu (coo), er, es, té, oo, ix, (ü, zeta). (Prise, p. 540 P.)
In pronouncing Latin words, too much care can not be taken in distinguishing between long vowels and those that are short. Cicero says: Omnium longitudinum et brevitatum in sonis sicut acutarum graviumque vocum indicium, natura in auribus nostris collocavit; and student and teacher alike will find that if from the outset a correct and careful pronunciation of Latin be required, those bugbears of the learner--the rules of prosody--will almost teach themselves, because they will have a consistency and meaning that can never be obvious to the unfortunate victim of the "English system." Professor Richardson, who deserves honor as being one of the first American scholars to advocate and adopt the true method of pronouncing Latin, has well summed up the whole matter in a single paragraph:
"To teach the student, from his first entrance upon the study of Latin, the English system of pronunciation; to get him thoroughly habituated to this false method, and then by lodging in his brain some verbal rules of quantity and prosody, at war often with each other and commonly with his pronunciation, to attempt to make him appreciate and observe the rhythm of Latin poetry, is like keeping a child in a rude society where all the laws of a pure and finished language are habitually violated, and then expecting him, by virtue of committing to memory the common rules of grammar and rhetoric, to talk at once with grammatical and rhetorical correctness and elegance."
And this little treatise may be closed by citing the most obvious of the reasons for adopting the Roman System.
(1) Because it is approximately the system used by the Romans themselves.
(2) Because it is more musical and harmonious in sound, and makes the structure of Latin verse clear even to the beginner.