180 PROCEEDINGS OF THE AMERICAN ACADEMY. 



sodium hydroxide — or, expressed in mols, NaOH . 5.7G0 HoO. 

 The sodium present as carbonate — determined by successive titra- 

 tions using methyl orange and phenol phthalein as indicators, — was 

 ] .2 percent of the sodium present. The standardization of the acid 

 and alkaline solutions used for the titrations was based upon a series 

 of gravimetric analyses of silver chloride. 



The substances studied in dilute solution were hydrochloric, hydro- 

 bromic, hydriodic, nitric, and perchloric acids, and lithium, sodium, and 

 potassium hydroxides, as indicated by the title. The preparation of 

 these substances will be described in order in the pages immediately 

 following. 



Ili/dwchloric acid. 



The acid for this solution was obtained by fractional distillation and 

 condensing in quartz the constant boiling mixture of the purest obtain- 

 able acid. The middle third of the middle third was selected from 

 two successive distillations and this sample, one-ninth of the material 

 at first employed, was diluted with freshly distilled water to the de- 

 sired concentration. Two samples were prepared, the fii-st, sample A, 

 being standardized gravimetrically by the precipitation of silver 

 chloride, taking precautions such as one would use in determining 

 atomic weights, and the second, sample B, being estimated volumetri- 

 cally by titration with very exact standard alkali, standardized by 

 means of the first. The results of these analyses were as follows: 

 68.3590 and 69.4105 grams yielded respectively 5.3234 and 5.4048 

 grams of silver chloride. Using the usual atomic weight Ag = 107.88, 

 this acid is thus shown to contain 100.15 gram-molecules of water to 

 one of acid, the two experiments deviating from the mean by only 0.004 

 percent. The other acid B was found volumetrically to be slightly 

 more concentrated, having 99.97 gram molecules of water. These are 

 so nearly alike that careful determination of their specific heats 

 showed no essential difference between them. 



Hydrobromic acid. 



The very pure acid usetl for these experiments was prepared some 

 time ago for determinations of atomic weights. For the present 

 purpose it was redistilled, using a quartz condenser; the first and last 

 portions of the distillate were rejected. The middle fraction used was 

 perfectly colorless. The two portions (over 62 and 70 grams respec- 



