This is a 12" surgical 'capital' saw (amputation saw) made by the firm William H. Armstrong & Co., of Indianapolis, probably some time around 1890-1910. The frame is nickel-plated and the removeable blade is high-carbon steel. I would assign this a condition of G+ : there is wear on the handle, with only about 60% of the plating remaining, but it is normal wear, not damage. The blade has suffered 100% surface rust (chemically removed), and some areas of mild corrosion or pitting. And the teeth are somewhat worn through use, with none missing or chipped.

All-metal surgical instruments like this generally belong to the era in which sterilization was practised, i.e. post-1880. It may be possible to narrow this down by dating the company. According to James Edmonson, American Surgical Instruments: An Illustrated History of Their Manufacture and a Directory of Instrument Makers to 1900 (Norman Publishing, 1997), Armstrong was in business between the years 1889-1900. [1889-90 at 92 S. Illinois St.; 1891-1897 at 77 S. Illinois St.; 1898-99 at 127 S. Illinois; and in 1900 at 224-226 S. Meridian, Indianapolis.] The location at 77 South Illinois is illustrated in the following 1898 engraving preserved in the University of Indiana photo archives ( http://purl.dlib.indiana.edu/iudl/archives/photos/P0024338 ).

... and the following is a contemporary advertisement, though it unfortunately does not seem to include the saw in question:

Unfortunately, Edmonson deals only with the period up to 1900. Tracing the company after that will require more work.

The fourth edition of its catalogue (see below) was issued in 1901.
The company was still advertising at 224-226 S. Meridian Indianapolis in July of 1902.
Wm H Armstrong secured a patent on Feb 1 1898 (pat. 598407)
and another on June 19 1906 (pat. 824057)

After 1906 I have so far found traces only of the man (Wm. H. Armstrong) but not yet of his company.

(The same?) "Captain" Wm. H. Armstrong of Indianapolis was president of the Trustees of the Indiana State Normal School in Tere Haute IN 1895-6 and 1902-1903.
(Terre Haute may have been his birthplace: a Wm H Armstrong (b. 1844) may have been mayor of Terre Haute 1883-1885)
A prominent Indianapolis citizen is described as "Col." Wm. H. Armstrong in a newspaper story 14 Sept 1900
Someone of the same name endorsed Jesse Overstreet for congress, Oct 27 1908
The same? Wm. H. Armstrong of Indianapolis is named to the National Council of Administration of the Grand Army of the Republic, October 1910

As for dating by comparables, a very similar but not identical saw appears in a surviving Armstrong surgical kit, dated to 1895,

I have not found another example of this precise design, nor identified its name (if any). But it belongs in general to the category of capital or amputations saws, not dissimilar to the popular "Satterlee's saw," which is still in production today, the first saw shown in the following late nineteenth-century catalogue:

Further information could doubtless be found in one of the Armstrong catalogues, to which I have not had access, e.g. Catalogue of surgical instruments : deformity apparatus, aseptic furniture and hospital supplies / Wm. H. Armstrong & Co. (4th ed. ; Indianapolis : Wm. B. Burford, c1901.) xxxi, 800 p. : ill. ; 27 cm. OCLC: ocm11296421. OCLC holdings by state: (AL) ABH (AR) AKM (FL) FUH (IL) ilwlm (IN) xhs (KS) KHM (KY) KLH (MN) bak UMM (NY) BUF (VA) VAM (WI) GZH