Edinburgh Northern Tramways
History
The Edinburgh Northern Tramways Company operated cable trams for just short of ten years, from the opening in 1888 to its take-over by the Edinburgh and District Tramways Company in 1897.
Uniforms
Several photographs exist depicting staff of the ENTCo, though seemingly all taken rather late in its life, namely, around the time of its take-over by the E&DTCo and possibly even all on the same day. Conductors and drivers wore smart but informal attire (probably self purchased), with soft-topped, railway-style caps, probably the sole officially issued item. These caps carried a round badge, which presumably bore the name of the company or a company device, though this is merely speculation, as to the best of my knowledge, no examples have survived. All jackets were thus devoid of insignia, and would therefore not have carried marked buttons.
Inspectors wore long, double-breasted overcoats with lapels, the upper part of which (the collars) bore Inspector in embroidered script lettering. Headgear took the form of a kepi-style cap which bore the grade - Inspector - again in embroidered script lettering.
Further reading
For a detailed history of the Edinburgh Northern Tramways Company, see: 'Edinburgh's Transport - Volume 1, The Early Years' by D L G Hunter; The Mercat Press (1992).
Images
Cable tram drivers and conductors
An unidentified ENTCo cable tram in Inverleith Row, around the time the company was taken over by the Edinburgh and District Tramways Company (1st July 1897). The driver (right) and conductor (left) are clearly wearing cap badges of some description. 
A blow-up of the above photo showing the driver, who is wearing workman-like attire, namely jacket and trousers, along with a soft-topped railway-style cap. Although the latter appears to bear two badges, it seems more than likely that it is in fact just a single round badge, with the bottom part actually being a reflection from the glossy chin strap.
Another blow-up of the first photo above showing the conductor, who appears to be wearing informal attire, along with the same style cap and badge as the driver. The figure on the right appears to be a senior official, though not an inspector, given that his cap bears no badge, unlike the individual shown below.
Another photo at the same location as above, once again an unidentified cable car, but with the driver clearly wearing a smart jacket and trousers.
A blow-up of the above photo showing the driver. Other than the cap, he is probably wearing self-purchased attire rather than an officially issued uniform.
Another blow-up of the above photo, this time showing the conductor, who also appears to be wearing smart but informal attire.
Yet another photo taken at Inverleith Row — photo undated, but probably taken shortly after the E&DTCo take-over.
A blow-up of the above photo showing the driver, who is clearly wearing a double-breasted uniform jacket with collar badges, as well as a kepi-style cap. The most likely explanation is that the photo was taken after the E&DTCo take-over, and the collar badges are 'E D T' initials. 
Another blow-up of the above photo, this time showing the conductor, who is once again in smart but informal attire, though this time without a cap.
Senior staff
A blow-up from the first photo above showing the inspector. His overcoat and kepi-style cap clearly bear his grade - Inspector - in embroidered script lettering.
A blow-up from the second photo above. The man depicted appears to be the same bearded individual seen in the first photograph above. He is clearly an official of some kind, though what grade he held and which company he worked for is unclear (the photo was possibly taken after the take-over by the Edinburgh and District Tramways Company).