484 FRED, EUGENE WRIGHT 
attacking a problem, the different methods employed should be 
of about the same order of accuracy. It is useless to conclude 
that because precise methods are used on one part of a problem, 
the final result will be of the same order of accuracy, no matter 
what other methods are employed. The different methods should 
be co-ordinated and the observer should exercise proper judgment 
in applying his methods. Thus in rough traversing it would be 
a waste of time to use a theodolite and to read angles to seconds 
and then to measure the distances by pacing; or, vice versa, to 
attempt accurate triangulation with a pocket compass even though 
the base line be most carefully measured. There are cases, on the 
other hand, where certain mechanical operations, which are com- 
plete in themselves, can be readily and accurately performed, as, 
for example, the weighing of chemical precipitates; in this instance, 
it would be obviously improper to weigh the precipitate on a 
rough hand-balance, even though the probable error, resulting 
from such a procedure, might be within the probable error of the 
chemical methods employed. The order of accuracy of the final 
result would be unnecessarily decreased thereby, since its probable 
error is a direct function of the probable errors of the different 
steps involved in the process. To apply these principles success- 
fully to actual problems requires critical judgment on the part of 
the observer. 
All of this seems obvious, but it is not always realized in prac- 
tice. Instruments are used, but their adjustment is rarely tested. 
Extinction angles are measured to the minute, and so stated, but 
the observer may fail to test the adjustment of his microscope 
and the nicols may be out half a degree or more. 
The same holds true of the use of quantitative data. From 
a series of known facts a scientist evolves a theory and then 
searches for further data to substantiate or disprove his theory. 
This course of procedure is right, provided he examine critically 
into the data themselves—how they were obtained, their probable 
errors, and so forth. 
The use of mathematics in this connection is important. 
Mathematics is a system of highly perfected logic, expressed in 
the form of symbols, and can be applied to practically all problems 
