Radiometric Measurements of Constants of Indicators. 59 



than light of longer wave-lengths. The addition of 10 per cent of ethyl 

 alcohol rendered these solutions fairly stable to the action of light 

 and time. After standing for a day or two, solutions containing an 

 excess of acid often showed the presence of fine crystals. Large 

 amounts of these crystals could be obtained by strongly acidifying 

 a saturated solution of methyl orange. It is thought that the forma- 

 tion of these crystals, very probably helianthine itself, causes the 

 instability of the solutions in question. The obvious procedure to 

 follow was to use more dilute solutions, which were found to be quite 

 stable, and even the solution containing the excess of acid would remain 

 practically unchanged when exposed to the action of light for a short 

 time. However, when the concentration of methyl orange approxi- 

 mated 2X 10~ 4 gram-molecules per liter, as is the case for the solutions 

 given in table 32, the solution containing an excess of acid was pre- 

 pared last and its percentage transmission measured immediately. 

 The remaining solutions were kept in the dark until used. It is certain 

 that when such precautions are taken, no appreciable change in trans- 

 parency could occur before the radiometric measurements were com- 

 pleted. Table 32, the concentration of the methyl orange being 1.98 X 

 10~ 4 gram-molecules per liter, indicates that even the solutions con- 

 taining an excess of acid can be safely used in this way. 



The following shows how accurately small concentrations of hydro- 

 gen and hydroxyl ions can be estimated by radiometric measurements. 

 If the percentage transmission for the various solutions be plotted as 

 curves, the abscissae being wave-lengths and the ordinates percentage 

 transmissions, it will be noted that with increasing amounts of acid the 

 transmission curve for pure methyl orange is widely displaced towards 

 the red end of the spectrum. The solution curve corresponding to 

 the excess of acid is displaced about 400 A. u. from the curve corre- 

 sponding to a pure aqueous solution of methyl orange. From the 

 displacements produced by solutions containing known amounts of 

 acid, and the displacement given by a solution containing an unknown 

 amount, the concentration of the unknown amount of acid can be 

 quite accurately and quickly determined. In one case a solution was 

 prepared containing an amount of sulphuric acid unknown to us. The 

 concentration of the acid was determined by the above method, and 

 the value found was 0.00000216 gram per cubic centimeter. The 

 amount actually present was 0.00000210 gram per cubic centimeter. 

 Several similar attempts were made and they were quite as successful. 



RESULTS WITH METHYL ORANGE. 



The hydrolysis and ionization constants for methyl orange, recorded 

 in Tables 33 and 35, are to be regarded as part of the preliminary work. 

 Table 32 contains the percentage transmissions for nine solutions of 

 methyl orange prepared in accordance with the scheme given below. 

 The concentration of the mother solutions of methyl orange was 3.973 



