Predication in quid is distinguished from predication in quale quid and from predication in quale, as follows :
The basis of the distinction being the difference between three modes of signification, namely [1] essential and absolute, [2] essential and connotative, and [3] non-essential and connotative. See also HERE in Part III about the Predicables.
[3] comprises, according to scholastic metaphysics, the proprium and the accidens. For us, however, the proprium per se belongs to that what it is the proprium of, except when the causal path leading from the genotypic cause to the (phenotypic) proprium is very long, because then the proprium can be replaced or erased, while the Essence of the being remains the same. So apart from this exception, the term, standing for a proprium is essential and connotative. Or, said better : If a term signifies essentially, but connotatively (that is, signifying some essence by connoting a phenotypic effect of it) it can be predicated per se but still only in quale of a subject, that is, it belongs to the Predicable proprium. On the other hand, if a term signifies non-essentially and connotatively ( = [3] ) , it can also be predicated in quale, but now only per accidens, that is, it belongs to the Predicable accidens (to which not only terms such as ' white ' can belong, but also, for example, the term ' capable of laughing ' if we want to emphasize the long causal way leading from the genotypic cause to this property [which can, as a result of this long causal way, be erased or replaced while the Essence of the being carrying this property nevertheless remains the same, that is, is unaffected by this replacement or erasion] ).
Predication of such an accidens is in fact not a proper predication, because when we say ' man is white ' this can be denied (because man is only 'sometimes' white, in many cases he is black), and when we say ' Socrates is tanned ' we can affirm this, but we can also deny it, referring to the same person (because Socrates is not always tanned).