on a machine with a different taper, e.g. R8 or vice versa, and simpler adaptors consisting of an externally and internally tapered sleeve to allow a small Morse tool to be used in a machine of larger bore. One of the first uses of tapers was to mount drill bits directly to machine tools, such as in the tailstock of a lathe, although later drill chucks were developed that held parallel shank drill bits. Brown and Sharpe Brown & Sharpe tapers, standardized by the company of the same name, are an alternative to the more-commonly seen Morse taper. Like the Morse, these have a series of sizes, from 1 to 18, with 7, 9 and 11 being the most common. Actual taper on these lies within a narrow range close to .500 inches per foot. Jacobs The Jacobs Taper (abbreviated JT) is commonly used to secure drill press chucks to an arbor. The taper angles are not consistent varying from 1.41° per side for No. 0 (and the obscure #) to 2.33° per side for No. 2 (and No. 2 short). There are also several sizes between No. 2 and No. 3: No. 2 short, No. 6 and No. 33. Jarno Jarno tapers use a greatly simplified scheme. The rate of taper is 1:20 on diameter, in other words 0.600" on diameter per foot, .050" on diameter per inch. Tapers range from a Number 2 to a Number 20. The diameter of the big end in inches is always the taper size divided by 8, the small end is always the taper size divided by 10 and the length is the taper size divided by 2. For example, a Jarno No. 7 measures 0.875" (7/8) across the big end. The small end measures 0.700" (7/10) and the length is 3.5" (7/2). The system was invented by Oscar J. Beale of Brown & Sharpe. Morse The Morse taper was developed by Stephen A. Morse, based in New Bedford, Massachusetts, in the mid-1860s. Since then, it has evolved to encompass smaller and larger sizes and has been adopted as a standard by numerous organizations, including the International Organization for Standardization (ISO) as ISO 296 and the German Institute for Standardization (DIN) as DIN 228-1. It is one of the most widely used types, and is particularly common on the shank of taper-shank twist drills and machine reamers, in the spindles of industrial