Description is given of a transmission‐type, curved‐crystal focusing spectrometer for short wave‐length x‐rays, and gamma‐rays having a dispersion of 1.186 x.u. per mm at short wave‐lengths. The spectrometer utilizes the (310) planes of quartz in a crystalline plate of dimensions 80×70×1.0 mm curved cylindrically to a radius of two meters. High luminosity is obtained since the useful aperture in the crystal holder has an area of 10 cm2and subtends 0.00025 stereradians at the focus. It also affords high resolution since by photographic tests with x‐rays the curved plate has been shown to focus a specified x‐ray wave‐length to within 0.06 mm of the same position on the focal circle for all parts of its useful aperture and over the entire operating wave‐length range. The geometry of the mechanism permits absolute measurements with a precision screw of the sine of the Bragg angle on both sides of the reflecting planes, affording a wave‐length range which includes at longest wave‐lengths theK‐spectrum of silver and goes down to zero wave‐lengths. For short wave‐length gamma‐rays the source is placed at the focus. A multiple‐slit collimator of tapering die‐cast lead partitions spaced apart with tapering separators, is used at short wave‐lengths to transmit the monochromatic diffracted beam and absorb the directly transmitted and scattered heterogeneous beam. The present collimator limits the spectrum that can be studied to a shortest wave‐length of 7. x.u. corresponding to 1.75 Mev. The intensity of the diffracted beam is to be measured with a special multi‐cellular G. M. counting tube of high efficiency, provided with a number of thin lead partitions through which the beam passes successively. In photographic spectra made with this instrument the tungsten and also the silverK&bgr;1&bgr;3doublet is completely and clearly resolved. Reproductions of such photographic x‐ray spectra are shown in which the line breadths have substantially the natural breadth. Fluorescence spectra of silver have been made in 10‐minute exposures. A companion paper gives the all‐important precision technique of generating the curved cylindrical stainless steel clamping blocks for the crystal.