ANALYSIS OF QUANTITATIVE PHENOMENA. 409 



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 g, 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 a very accurate result, the observation of their vary- 

 ing temperature and the calculation of the corrections 

 being an uncertain and tedious work h . 



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

 eliminating a simple error depends entirely upon circum- 

 stances 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 can be conveniently 

 done ; if not, make the experiment so that the error may 

 be as small, but more especially as constant, as possible. 

 If the means are at hand for determining its amount 

 by calculation 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 in- 

 volves 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 Reversal, which will form an 

 appropriate transition to the succeeding chapters on the 

 Method of Mean Hesults and the Law of Error. 



8 See, for instance, the Compensated Sympiesometer, ' Philosophical 

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



h Grant, c History of Physical Astronomy,' pp. 146, 147. 



