•j6 Proceedings. 



sole test of equality of weights is that one may be replaced 

 by the other without change in the position of rest. 

 If two weights are interchanged, and the balance vibrates 

 about the same point, the weights are equal. This suggests 

 the following method of procedure : — With the unknown 

 mass on one side, place weights P on the other until the 

 balance swings about some point not far removed from the 

 central position, or, better still, about that point at which 

 previous experience has shown the balance would come to 

 rest with equal loads of approximately the value of M. 

 Let 01 be the observed position. Interchange the two 

 masses without alteration of P. The position of equilibrium 

 will be slightly different, say 02. It follows that the position 

 of rest for equal weights is (0i + 02)/2, and if W is the weight 

 required to produce a change of one division the required 



a _ a 



mass of M differs from P by W. ^ ^ ^ - Whether P is 



larger or smaller than M is easily seen from the weighings. 

 This method has been followed in the Physical Laboratory 

 of the Owens College during the last two years with good 

 results. Its accuracy may of course be increased by repeating 

 the interchange of weights. Sufficient experience has not 

 yet been gained as to the most accurate way of obtaining 

 the value denoted by W, The method of interchanging 

 weights has, as far as I know, been first used in accurate 

 weighing by Miller in his researches on the standard pound, 

 and he gives Steinheil as his authority for ascribing the 

 method to Gauss. But I could find no reference to the 

 subject in any of Gauss' papers. On the other hand, I have 

 found a description of the method without its being 

 ascribed to any particular person in Fischer's PJiysikalisches 

 WorterbucJi, which was published in 1804. Gauss was then 

 27 years old, and had already published his famous 

 Disqmsitones arithmeticae, but as far as the record of his 

 published researches goes, he had devoted himself altogether 



