WEIGHT AND VAN ORSTRANDI MINERAL ANALYSES 225 



molecular ratios or simple chemical formula numbers, and then pro- 

 ceed to determine how close the agreement is between the observed 

 values and those deduced from the inferred chemical formula. 

 This can be done by several different methods, which, however, are 

 not all equally rigorous. The best and most logical methods are 

 based on a comparison between the given analysis (weight per- 

 centages) and the weight percentage analysis computed from the 

 inferred chemical formula. Comparisons can also be made 

 between the mol numbers and the inferred molecular ratios, but 

 these are not strictly correct in principle. They have, however, 

 often been adopted, by chemists and mineralogists, and merit, 

 therefore, a brief word of description after the more rigorous 

 methods have been presented in detail. In all the methods the 

 assumption is made that after proper reduction of the weight 

 percentages of the given mineral analysis, the chemical formula 

 numbers (molecular ratios) can be inferred by simple inspection; 

 this signifies that in the case of solid solution we know, or are able 

 to determine, the particular molecules which should be consid- 

 ered together. 



First jnethod. In this method the chemical formula numbers 

 are first multiplied by the proper molecular (respectively atomic) 

 weights and the corresponding weight numbers {x) obtained. 

 These in turn are multiplied by a factor m which is determined by 

 the least square method and furnishes the most accurate values 

 {y') for the weight percentages. To find m we assume in accord 

 with usual practice that the theoretical weight numbers {x) 

 derived from the molecular ratios are free from error and that the 

 observed quantities {y, the weight percentages of the analysis) 

 contain errors of observation. Since the two series of numbers 

 stand in a constant ratio m to each other we have the observation 

 equations 



yi = mxi, y2 = mx-i, . . . yn = mx^. (1) 



The general equation, y = mx, is the equation of a straight 

 line passing thru the origin. The rigorous solution consists, 

 therefore, in adjusting the straight line thru the n given points. 

 A higher degree of precision would be obtained by considering the 



