Interesting question!
Without any further information, this could be one of two structures. It could either be:
1) E.H Bostock's Scottish Zoo and Hippodrome, opened in May 1897 and featuring a circus arena and cinema, or
2) Arthur Hubner's Hippodrome of the same year, housed in a conversion of a building which opened as a diorama in 1882, and was converted to ice-skating in 1885.
The former building soldiered on until 1918, with the cinema section having only been made permanent in 1911. This part of the building was known as the Zoo Electric Theatre, then the Joytown Grand Electric at various points in between! If only modern cinemas had such splendid names! The whole of Bostock's building still survives in the Cowcaddens area of the city, and currently hosts a Chinese supermarket and restaurant, a snooker club and an outdoorsy sport-type retailer. See:
http://www.chem.gla.ac.uk/~gbarr/cinema ... ooEPP.html
The latter building was taken over from Arthur Hubner by a Mr Hengler in 1904, Hengler having already run a famous circus in Wellington St until the lease expired in 1900. The building was very well appointed, and the main circular ring in front of the stage could be flooded with 100,000 gallons of water for spectacular water shows. It is also contentiously rumoured that this structure played host to Glasgow's first film screening, and films were presented reguarly, eventually becoming the main entertainment presented in the building under Hengler. The final circus season was in 1924. After as short period as a dance hall, the whole building was rebuilt in 1929 to become the Regal Cinema, later the ABC Sauchiehall St.
http://www.chem.gla.ac.uk/~gbarr/cinema ... regal.html
Interestingly, animal pens were still said to exist under the cinema at least until the conversion to bars and clubs recently, and the Scott St elevation of the building still has some ornate arched brickwork from the days as the Hippodrome:
http://www.chem.gla.ac.uk/~gbarr/cinema ... regal.html
I've a drawing of the interior of the auditorium as the Hippodrome/Hengler's Circus, and an etching of the exterior from that same time which I'll scan later.
Gary