To determine optimum working conditions for spectrochemical analysis of the impurities in ammonium pa atungstate by the Carrier-Distillation Method,
(i) the author determined the degree of suppression of tungsten spectrum numerically by the equation,
E=S₃/S₁+S₂
where, S₁+S₂= intensity of tungsten spectrum lines.
S₃=intensity of impurity spectrum lines.
(ii) he then applied the statistical techniques in experiments, i. e., the orthogonal array method in the first experiment, and, randomized block method in the second experiment, taking E as the characteristics.
In spite of the existence of many unknown factors which might affect the results of analysis, the optimum conditions are thus obtained very efficiently.

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The resolution of infra-red spectrometer is discussed systematically on the basis of the papers of Strong, Walsh and others puplished recently.
First, it is proved for thermocouples and bolometers that the sensitivity-to-noise ratio is inversely proportional to the quare root of the sensitive area. Next, the Strong's formula for the amount of light which impinges on the detector through the exit slit is derived assuming that there are neither diffraction nor other factors which broaden the width of the spectral line. It the resolution of the spectrometer is kept constant, this amount of light I can be written as
I∞JλhTA/fdθ/dλδλ ²
where Jλ, is the spectral energy density at the entrance slit, h the height of the slit, T the transmission factor of the spectrometer, A the area of the collimating merror, f its focal length, dθ/dλ the angular dispersion of the prism (or the grating) and δλ the slit width measured in wave-len _th scale.
Provided that the signal-to-noise ratio is constant, the minimum difference of wave-length δλ which can be resolved is given by
δλ ∞(f/KJλhTAdθ/dλ)^½
where K is the sensitivity - to - noise- ratio of the detector.
For thermocouple or bolometer sensitive area of which is necessarily limited and very small, this formula becomes
δλ∞(f/hA)^¼(JλTdθ/dλ)^-½
as was derived by Walsh.
Although the results obtained in this paper are not new, the proof of the theorem concerning the sensitivity - to-noise ratio of the detector, the derivation of the Strong's formula and some part of the following deduction are due to the author's own idea.

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