72 BURTON EDWARD LIVINGSTON 



from water not strictly pure, to salts from the porcelain itself, 

 or to removal of the shellac coating, etc. To avoid the effects 

 of this possible alteration of standard cups it has long been 

 the practice to use a given cup as of known coefficient only once 

 (for not longer than three days) , or during the process of standard- 

 izing a single group of cups. The cup so used for the first group 

 became a cup to be standardized and a member of the next 

 group, the standard for the latter being a new cup, unused since 

 its standardization at some previous time. Some of the cups 

 whose coefficients from two periods of operation on the table 

 agreed (coefficients are actually calculated only to the second 

 place of decimals, for cups placed upon the market), were laid 

 aside for future standards and a large stock of these was always 

 on hand. 



To insure clearness in regard to the calculation of coefficients, 

 the operation may here be stated algebraically. If R is the 

 reading of the cup of known coefficient (the one used as stand- 

 ard) and this coefficient is C, while the corresponding reading 

 of any other instrument in the group is r, then the required 

 coefficient of the latter instrument (K), for this period of opera- 

 te 7? 

 tion upon the rotating table, is deduced as follows : K = — . 



Whenever this cup is used its readings are to be multiplied by 

 K, to make them comparable with the similar corrected readings 

 of any other standardized cup. 



As has been already emphasized, it is theoretically possible 

 to derive a coefficient of correction (for reducing the reading 

 of one cup to what would have been the reading of another 

 in the same time and place) only when the two cups compared 

 have very nearly the same form, size, etc. As in other similar 

 instances met with in physical science, the importance of this 

 whole matter depends upon the magnitude of the differences 

 involved. In the present instance it also depends upon the sort 

 of study to be carried out. It is quite readily possible to derive 

 a coefficient which will express the relation between the evapo- 

 rating powers of any two cups as shown by their operation on the 

 rotating table for, say, a single day. If the cups are not alike, 



