This wonderful book, Doctrina Copularum Linguæ Latinæ Sive De Vi Atque Usu Elegantiori Particularum AC, ATQUE, ET, -QUE Deque Earum Formulis, Commentarius by Henry Ellis Allen, A.B., published in 1830,* contains accents galore. What do they mean? Why are some vowels given an accent and others not? What's the difference in meaning between the accent grave and the circumflex? Is this system named or documented anywhere? I haven't been able to infer any simple rules other than that the diæresis indicates that two consecutive vowels should be pronounced as separate syllables rather than as a diphthong.
Here are some examples.
Nimirùm, ac est ipsum atque decurtatum.
The first two vowels in nimirùm are long and the ù is short, so there goes the theory that the accent grave marks a long vowel.
Copulativè ac et atque in iis ferè rebus adhibentur, quæ, naturâ quaddamodò conjunctæ, facilè ac lubenter inter se congruant consentiantque; cùm et et que, rerum delectu omni omisso, aurium arbitrium ponantur.
Could the circumflex mean only a long vowel that marks the ablative case?
“Quârè moneo vos, adolescentes, atque hoc meo jure præcipio.—” Cic. pro Sext. 23.
Apparently not.
“Hîc, ne quid mihi prorogetur, quod ne intercessor quidem sustinere possit, horreo; atque eò magis, quòd tu abes, qui consilio, gratiâ, multis rebus occurreres.” Cic. ad Att. v. 21.
Notice that one quod has an accent and the other doesn't.
*Thanks to Tom Cotton for bringing it to my attention.