Thanks, ***** ***** are excellent and I can see all the detail now. This is a lovely object, is known as a gemel (sometimes spelled gimmel) bottle, two flasks blown separately and fused together and with necks and tops curving away from each other. Often used for oil and vinegar, or perfumes, and propped in a purpose made cradle or stand when not in use.
From the design and the style of the wheel engraved decoration and inscription it dates to the 1870s or 1880s. This type, with the ridge of raised decoration, called rigaree, was almost certainly produced at Nailsea Glassworks, an important centre for 19th century glass production near Bristol.
It was quite common at the time to give these as presentation items, with the recipient's name engraved on them and it's the artistic merit and interest of the engraving that gives them their value.
This example, for instance, with nicely done floral decoration sold on line for £33 and this one, with farm animals (a more popular subject) dated 1883, sold for £67.
I would give yours a value somewhere in between, say £35 - £50 at auction or on line, and at least £120 if you were to see it for sale in an antique shop. This is also the replacement value for insurance purposes.
If you were able to lay your hands on any family letters or other mentions of how this James McClure connects with Robbie Burns, the poet, then you would almost double the retail/replacement/insurance value. Even if you were to write down on a piece of paper what your grandfather told you about the connection, and keep it in an envelope with the bottle it would certainly do no harm to its value in years to come.
I do hope this helps!