8 PROCEEDINGS OF THE AMERICAN ACADEMY 



yet so long as it is there, and your analytical processes do not dis- 

 tinguish it from that portion of tiie same element which is chemically 

 combined, it is obvious that imj^urity of this kind will vitiate your 

 result to a far greater extent than an equal amount of wholly foreign 

 admixture ; and of what use can it be to refine processes or multiply 

 and discuss observations, if so large a door is left open to constant 

 errors ? Moreover, it must not be overlooked that such errors, from 

 their very nature, are apt to have a constant value, and are for that 

 very reason the more liable to deceive. In the investigation just 

 referred to, we showed that under constant conditions the composition 

 of the cr^'stals was definite and invariable, although they might con- 

 tain — as dirt or impurity, very possibly — an excess of one or the 

 other elementary substance when compared with the normal atomic 

 proportion. Assuming, then, such an excess to be present in the substance 

 selected for analysis, it is perfectly evident that a large error migiit 

 exist in the determination of an atomic weight, although there was a 

 close agreement in the analytical results. Sucli agreement therefore 

 is in itself no proof of accuracy; and far less sharp results may be 

 more trustworthy, if only it can be shown that the errors are properly 

 distributed. Errors of the last class can be to a great extent elimi- 

 nated by multiplying observations, while a constant error is oidy perpet- 

 uated thereb)\ 



The special cause of constant error we have been discussing is one 

 we have specially studied, and one therefore which we naturally select 

 to illustrate the principle we have aimed to enforce. It is not, how- 

 ever, the only cause of constant error which tends to change the 

 apparent ratio between the weights of the various elements of a com- 

 pound, or the one whose influence is most to be feared in the deter- 

 mination of an atomic weight. Our knowledge of the chemical and 

 physical relations of the materials analyzed, or of the circumstances 

 connected with the processes employed, is in many cases as yet so 

 far from perfect that to a certain extent we work as it were in the 

 dai'k, and are liable to fall into errors from which only more accurate 

 knowledge could protect our results. As will appear in the sequel, 

 this truth has been forced u2;)on us again and again during the course 

 of the present investigation, and it has led us to bestow upon the work 

 an amount of labor which is far greater than the importance of the 

 results would seem to justify. The experience, however, has left with 

 us a strong conviction on two important points ; and we shall describe 

 the several steps in our investigation more in detail than might other- 

 wise seem necessary, in order that the reasons of these convictions may 



