xv.] ANALYSIS OF QUANTITATIVE PHENOMENA. 353 



pensating arrangement is conducive to accuracy. As a 

 general rule mechanical compensation is the last resource, 

 and in the more accurate observations it is likely to 

 introduce more uncertainty than it removes. A multitude 

 of instruments involving mechanical compensation have 

 been devised, but they are usually of an unscientific 

 character, 1 because the errors compensated can be more 

 accurately determined and allowed for. But there are 

 exceptions to this rule, and it seems to be proved that in 

 the delicate and tiresome operation of measuring a base 

 line, invariable bars, compensated for expansion by heat, 

 give the most accurate results. This arises from the fact 

 that it is very difficult to determine accurately the 

 temperature of the measuring bars under varying con- 

 ditions of weather and manipulation. 2 Again, the last 

 refinement in the measurement of time at Greenwich 

 Observatory depends upon mechanical compensation. Sir 

 George Airy, observing that the standard clock increased 

 its losing rate 0-30 second for an increase of one inch in 

 atmospheric pressure, placed a magnet moved by a baro- 

 meter in such a position below the pendulum, as almost 

 entirely to neutralise this cause of irregularity. The 

 thorough remedy, however, would be to remove the cause 

 of error altogether by placing the clock in a vacuous case. 

 We thus see that the choice of one or other mode of 

 eliminating an error depends entirely upon circumstances 

 and the object in view ; but we may safely lay down the 

 following conclusions. First of all, seek to avoid the 

 source of error altogether if it^cau be conveniently done ; 

 if not, make the experiment scTthat the error may be as 

 small, but more especially as constant, as possible. If the 

 means are at hand for determining its amount by calcula- 

 tion from other experiments and principles of science, allow 

 the error to exist and make a correction in the result. If 

 this cannot be accurately done or involves too much labour 

 for the purposes in view, then throw in a counteracting 

 error which shall as nearly as possible be of equal amount 

 in all circumstances with that to be eliminated. There yet 

 remains, however, one important method, that of Eeversal, 



1 See, for instance, the Compensated Sympiesometer, Philosophical 

 Magazine, 4th Series, vol. xxxix. p. 371. 



2 Grant, History of Physical Astronomy, pp. 146, 147. 



