208 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 39 



In general, one may say that for major constituents, spectroscopic 

 methods of quantitative analysis are slightly inferior in precision to 

 chemical wet methods, for minor constituents they are equal in pre- 

 cision, and for traces they are superior, assuming sufficiently large 

 samples are available to make adequate chemical analyses. Spectro- 

 scopic methods have their greatest advantage when the samples 

 available are small, or concentrations are low, because the precision 

 of the spectroscopic method stays sensibly constant at all concentra- 

 tions. With it one can distinguish as readily between 0.0010 and 

 0.0011 percent concentration of material as between 10 and 11 percent, 

 for example. 



The concentration of a minor constituent is determined by observa- 

 tion of the intensisties of its spectrum lines relative to those of the 

 matrix material (which is composed of the major constituents), and 

 as these ratios vary with a number of factors, a null method must 

 be used. Standard comparison samples are made up which differ 

 from the sample to be measured only in regard to the contituents 

 being measured, and these samples and this unknown are burned 

 and photographed in identical manner. Then, if the intensities of the 

 line of the constituent in question are the same in any comparison 

 sample as in the unknown sample, the concentration of the constituent 

 will be the same in the two samples. 



Such rigid conditions might seem impossible to fulfill, but fortu- 

 nately any number of minor constituents and traces may differ in 

 the known and unknown samples without affecting the result. If 

 we are comparing the copper content of two bronzes, for example, 

 error may result if lead be present in one sample in amounts greater 

 than 1 percent, and not in the other, but in amounts less than about 

 1 percent a difference in lead content should not affect the results 

 appreciably. 



Returning to the crystal problem, having made up a series of sam- 

 ples of the material containing various known concentrations of 

 hafnium covering the range suggested by the qualitative analysis, 

 we now burn these in the arc in succession, sandwiched between alter- 

 nate exposures burning the unknown sample. When the plate has 

 been developed, fixed, and dried, we can measure the amount of 

 blackening of each of the hafnium lines on a microdensitometer, and 

 plot a "working curve" of density against concentration. Or, as is 

 more common, by calibrating the plates we can change densities into 

 the actual line intensities to which they correspond, and plot logio 

 intensity against log lo concentration. At low concentrations such a 

 plot is usually a straight line (as shown in fig. 1), which aids greatly 

 in interpolating between two standard intensities. By this means, 

 using care, precision to 3 percent can usually be obtained, which at 



