You know I love measuring tools of all sorts, and this I think is really a cool, and also a really beautiful one, another of which I can't find out there anywhere. (Plus I just love the word fathom, in all its connotations.)  Dated 1907, it was produced by Whyte Thomson Co, based on Sir William Thomson's patent--Thomson, aka Baron Kelvin of Largs, being the very important Scottish engineer, mathematician, and physicist. (More on him below.) A fathoms scale would have been used for sea depth sounding--in conjunction, I believe, with a lead line--a thin rope with a lead plummet on its end, and marked (using knots or tie marks) at certain intervals; for example: at 2, 3, 5, 7, 10, 13, 15, 17, and 20 fathoms. From what I've read Thomson himself, an avid seaman, argued that the use of hemp rope was outmoded, and himself used piano wire to sound to a depth of 2700 feet. He also invented a motor driven sounding machine that came into popular use in the early 20th c. I would guess this fathoms scale was designed to be used in conjunction with that machine. Quite a lovely and interesting thing. 

13 1/16" x 1 1/16" x 11/16" and in very good condition.

More:Sir William Thomson, Baron Kelvin, in full William Thomson, Baron Kelvin of Largs, also called (1866–92) Sir William Thomson, (born June 26, 1824, Belfast County Antrim, Ireland [now in Northern Ireland]—died December 17, 1907, Netherhall, near Largs, Ayrshire, Scotland), Scottish engineer, mathematician, and physicist who profoundly influenced the scientific thought of his generation.

Thomson, who was knighted and raised to the peerage in recognition of his work in  engineering and physics, was foremost among the small group of British scientists who helped lay the foundations of modern physics. His contributions included a major role in the development of the second law of  thermodynamics; the absolute temperature scale (measured in kelvins); the dynamical theory of heat; the mathematical analysis of electricity and magnetism including the basic ideas for the electromagnetic theory of light; the geophysical determination of the age of the Earth; and fundamental work in hydrodynamics.