potassium chloride in water may be expressed by a direct equation: _a_ = 29·2 + 0·275_t_, where _a_ represents the solubility at _t_°. For other salts, more complicated equations are required. For example, for nitre: _a_ = 13·3 + 0·574_t_ + 0·01717_t_^2 + 0·0000036_t_^3, which shows that when _t_ = 0° _a_ = 13·3, when _t_ = 10° _a_ = 20·8, and when _t_ = 100° _a_ = 246·0. [23] Beilby (1883) experimented on paraffin, and found that one litre of solid paraffin at 21° weighed 874 grams, and when liquid, at its melting-point 38°, 783 grams, at 49°, 775 grams, and at 60°, 767 grams, from which the weight of a litre of liquefied paraffin would be 795·4 grams at 21° if it could remain liquid at that temperature. By dissolving solid paraffin in lubricating oil at 21° Beilby found that 795·6 grams occupy one cubic decimetre, from which he concluded that the solution contained liquefied paraffin. [24] Gay-Lussac was the first to have recourse to such a graphic method of expressing solubility, and he considered, in accordance with the general opinion, that by joining up the summits of the ordinates in one harmonious curve it is possible to express the entire change of solubility with the temperature. Now, there are many reasons for doubting the accuracy of such an admission, for there are undoubtedly critical points in curves of solubility (for example, of sodium sulphate, as shown further on), and it may be that definite compounds of dissolved substances with water, in decomposing within known limits of temperature, give critical points more often than would be imagined; it may even be, indeed, that instead of a continuous curve, solubility should be expressed--if not always, then not unfrequently--by straight or broken lines. According to Ditte, the solubility of sodium nitrate, NaNO_{3}, is expressed by the following figures per 100 parts of water:-- 0° 4° 10° 15° 21° 29° 36° 51° 68° 66·7 71·0 76·3 80·6 85·7 92·9 99·4 113·6 125·1