A long established and very successful company, William Muir & Co. was based at the Britannia Works in Sherbourne Street, Salford, Manchester. A Scotsman, William Muir (1806-1888) earned a reputation as a prolific inventor and successful businessman, his early CV including what must have been an ordinary apprenticeship with Morton's of Kilmarnock before moving though various companies concerned with cotton spinning machinery including the Catrine Cotton Co., Messrs. Girdwood and Co. and Henry Houldworth - the latter two both based in Glasgow. Following evening studies at Glasgow University, he left Scotland in 1830 and went first to Liverpool, then Cornwall before, in 1831, moving to London, then a leading centre of precision engineering. He worked first for the remarkable Henry Maudslay where, at Maudslay, Sons and Field's, he acted as foreman with responsibility for constructing a road-going steam powered carriage ordered by Lord Cochrane - the successful completion of which earned him a considerable bonus. Working alongside him at Maudslay's were two young men later to become rather well known in engineering circles, James Nasmyth as a draughtsman and Joseph Whitworth (later Sir Joseph) as a fitter.
Muir's next moves were to two equally important concerns, the famous London-based Holtzapffel & Co., makers of ornamental turning lathes, and from there to became Foreman at Bramah and Robinson (where Maudslay had trained). By now his abilities must have been obvious, for he was next asked by Joseph Whitworth to manage his Manchester works - where he appears to have not only developed and designed machinery (including, incongruously, a road sweeper) but also taken a leading role in the Company's ground-breaking work that established the world's first standardised threading system - the Whitworth.
In 1842, having absorbed much from the leading engineering exponents of the time, he set up in business by himself at premises in Berwick Street, Manchester, where, with an obviously limited supply of capital, he had space to accommodate only a forge, lathe and workbench. By 1847 he had outgrown his cramped workshop and moved first to 50 Oxford Street and then to Miller's Lane where he shared premises with the inventor of railway tickets, Mr. Edmonson, whose printing enterprise on the upper floor was supplied with machines by Mr. Muir on the lower - who by now had also branched out into the manufacture of machine tools. By 1851 he was living at 13, Irwell Street, Cheetham, Manchester and listed in the census of that year as a "Machinist" who employed twenty-two men and twelve apprentices. At the time, of Muir's five sons, two were amongst his apprentices: Andrew aged 17 and William aged 14. Another son, Alfred, together with his sons, William, Harry and Leonard were in later years to continue the family tradition all being listed in the census for 1911 as: engineer, machinist,  toolmaker.
The middle years of the 19th century must have been a busy time for Mr. Muir, the Great Exhibition catalogue of 1851 listing his products as including: Amateur foot lathe, slide rest, eight gun-metal chucks.
Joiner's bench, tool-chest, and German cramp.
Large and small patent coffee-mill for grocers and private use.
Screw embossing press, for stamping envelopes, with dies, sets of alphabets, etc. Lever embossing presses, for embossing crests, etc. Copying presses.
Screw-stocks, taps, master-taps, and tap-wrenches. Machine taps and hand-screw tools.
Oil-testing machine (invented by Emanuel Thomas, of Manchester). Registered theodolite (designed by Henry Goss of Salford).
Specimens of embossing. Lithographs of copying and embossing presses.
Soap-cutting machine. Invented by Walter Storey, of Manchester. 
Muir's final move was to Strangeways, where a new factory,  the Britannia Works, was built and from where a number of important developments were to flow including such diverse inventions as equipment for the mass production of precision rifle sights and automatic machinery for winding cotton balls and bobbins.
Muir went on to build a variety of large machine tools including planers and giant lathes and, in 1937 changed their name to Muir Machine Tools - being taken over in 1944 and was incorporated into the machine tool division of the large David Brown and Sons Group; more can be read about the redoubtable Mr. Muir in a section of Graces Guide.
Typical of its time - and obviously intended for general workshop work - the 6" x 48" backgeared and screwcutting lathe shown below would have been manufactured circa 1880 to 1905 (another surviving example carried a plate stamped 1904). Supported on two large cast-iron box-like plinths and round 9 inches wide and 7 inches deep, the bed was of typically "English" style being flat on top and with V-edged ways - a detachable gap piece being an option as examples have been found with and without.
Machined without a bore, the 6 t.p.i headstock spindle ran in hardened steel cone bearings, these being adjustable for clearance by collars at the left-hand end with thrust taken out on a typically Victorian arrangement of an externally mounted plate that incorporated the changewheel tumble-reverse mechanism. Mounted on the usual eccentric shaft for engagement, the 8 d.p. backgears were usefully strong and gave a reduction in speed of a round 6 to 1.
Drive to the 4 t.p.i. leadscrew was by 10 d.p. changwheels, the usual very large set of around twenty being provided from 20t to 150t  that allowed threads to be generated from a spiral pitch of 71/4"  to 150 t.p.i.  The changewheels also powered the sliding and surfacing feeds, the drive being taken to the rear from where it connected to an exposed 3-speed gearbox -  this turning a keyed shaft that ran down the back of the bed. The shaft passed though and turned a wormwheel held in bearings built into the back face of the saddle, the feeds being selected and engaged by a full-circle handwheel at the tailstock, the pulling and pushing of which caused the shaft to be slid endways into three notched positions - plus one for neutral. A bronze plaque showed the feed rates: 32, 64 and 128 for sliding and 64, 128 and 256 for surfacing - these presumably being decimal fractions of an inch per one revolution of the headstock spindle. Rear-mounted power-feed drive was a common fitting on lathes of the 1800s, examples being made by another Manchester company, Spencer, whose larger lathes were so equipped as well as ones from the Liverpool maker Jones & Burton. Surprisingly the design lasted into the 1930s with Pool using the system on their larger lathe for amateurs, the Major. Probably the very last lathe to be so equipped was the English Mellor, a very heavily built small lathe current into the 1940s.
Instead of double clasp nuts to grip the leadscrew, the Muir economised by using just a half-nut, this being positioned above the leadscrew and moved downwards by a lever on the face of the apron. To prevent the leadscrew being bent, it was supported in a pair of half bearings cast into the bed, the distance between them appearing to provide just sufficient support to prevent other than a slight deflection.
One unusual feature of the Muir lathe - and possibly unique in its arrangement - was a quick-withdrawal mechanism for the screwcutting feed. Instead of the bearing for the cross-feed screw being direct in the casting of the saddle, it was carried in a short-handled screw of very coarse pitch threaded into the saddle casting. In operation the handle was held down to the right of the cross-slide handwheel by a spring-loaded catch, the job progressing until the end whereupon the catch was pushed in and the handle jerked upwards to pull back the cutting tool. To continue the job, the handle was pushed down and the cross-feed screw fed inwards a little. Some German Karger lathes used a similar but cam-operated system, possibly of the type fitted to this machine that incorporated an adjustable throw-out bar fitted just below the front edge of the bed.
Rather unusually for the era, the cross slide was equipped with a generously-large micrometer dial though what was on the top slide is unknown, parts being missing from the machine shown. However, it is likely that the form of toolpost used is original, a quickly-adjustable "Norman Patent" type as found on the later very popular Drummond M-Type lathe.
While almost all the larger Muir machine tools will have met the scrap man many decades ago, a number of their smaller lathes are known to have survived; if you have a Muir, the writer would be interested to hear from you.