174 PROCEEDINGS OF THE AMERICAN ACADEMY. 



by the use of the number 1.0075.* The German committee points out 

 in its last report that this difficulty may be avoided by giving the ele- 

 mentary student only the round numbers (which suffice amply for his 

 purpose), accompanied by the statement that these are rough approxima- 

 tions. There is obviously another way of avoiding the confusion, and 

 that is by doing away with hydrogen as a standard of specific gravity. 

 The difficulty of preparing this gas in a pure state and its great lightness 

 are arguments against it, in any case. Moreover, in my experience the 

 simplicity of the relationship between the specific gravity referred to 

 hydrogen and the molecular weight is quite as likely to be a stumbling- 

 block as an assistance. Many a beginner learns by heart the statement 

 that the specific gravity is twice the molecular weight ; for he does not 

 pause to think about it and see that he has inverted the ratio. If, on 

 the other hand, the specific gravity of oxygen is taken as the standard, 

 the adverse arguments disappear, and even a dull student can hardly 

 forget the reason why the specific gravity of the gas X referred to oxy- 

 gen must be multiplied by 32 to give the molecular weight. For several 

 years 1 have used this method with large classes, and find that it gives 

 no trouble. The only data needing recalculation are the specific gravi- 

 ties of the gases, and that is a simple matter. It seems to me, by the 

 way, that the use of 2 instead of R in physico-chemical formulae has the 

 same pedagogic fault of obscuring the source and nature of the symbol. 



The answers to the second international question, which seeks to de- 

 termine the number of decimal places to be given, support the German 

 committee in its position with a majority almost as overwhelming as in 

 the case of the first question. The minority of eight consists of three 

 Americans, three Germans, and two Japanese, all the others desiring to 

 omit all figures which are not certain to within half a unit. The com- 

 mittee, in summing up the opinions upon this subject, states that its 

 desire is to propose a table for common use, and that the minority, which 

 desires the retention of one uncertain decimal place, has rather had in 

 mind the requirements of work of the greatest precision. Undoubtedly 

 the curtailed table will answer for most purposes, but it seems to me that 

 the nature of the decimal notation causes an unfortunate incompleteness 

 in it. Although, in the face of so great a majority, this matter, like the 

 other, must be considered as settled, I am tempted to call attention to 

 this incompleteness in relation to numerical data of all kinds. 



* Much has been written upon both sides of this question. Besides the articles 

 already referred to, many references may be found in two papers by Kiister and 

 Brauner (Zeit. anorg. Chem. 14, 251 and 257 respectively (1897)). 



