This Auto-registering Micrometer was used to register stars transits at the Sygros (Gautier) Meridain Circle of the Observatory.
The Photoelecric Photometer attached to the Micrometer (right on the photo) is a G. Rougier model (c. 1925).

Similar instruments:
Observatoire de Paris (Paris inv. 396, anc. 20-28)
Musée de l'Observatoire de Marseille (CM31 IM13000021)