Classical (or transitional) bows are really only a further development of the long Sonata Bow championed by some later baroque masters such as Tartini. I find it strange to describe the continuous experimentation with bow design of the later 18th century as merely "transitional." After all, this is the era of Mozart, Haydn and early Beethoven. It is a fact that individuality and eccentricity were the norm, and just as in Literature and the visual arts, all previous formal conventions were expanded and broadened, though by no means rejected. What I prefer to call "Classical Bows" then are merely the more common tools of string players seeking this broader expression---less contained within the formal dance and song forms of the Baroque. From Sturm und Drang drama to Emfindsamkeit delicacy, performing musicians were not necessarily greater artists, only less content with common practice. It was, after all, the musicians themselves who demanded more from the bowmaker to suit an expanding expression within the steadily decreasing harmonic rhythm of the day. In short, long bows with much resilience were demanded. Both rapidity of response and available power were necessary. The creations of Dodd and especially a few French master craftsmen would be most successful, and eventually dominate the string world.
Some of the surviving bows of Meauchand, the Tourte family and Dodd are exquisite creations and have been my favourite models to reproduce.