CH. 8 COMPARISONS OF PURCHASING POWER 113

that is to say, he means by this that it is likely to bearithmetically nearer to the truth than other formulae.This conclusion is the result of applying a numberof tests, as for example that the formula must besymmetrically placed in respect of the two extremesbetween which it is to lie. All these tests, however,are directed to showing, not that it is correct initself, but that it is open to fewer objections thanalternative a priori formulae. They do not provethat any one of the formulae has a leg to stand on,regarded as a probable approximation.

If, however, we regard formulae intermediate be-tween p and q, not as probable approximations, butmerely as conveniences for the purpose of rapid nar-ration, then we may legitimately be influenced byconsiderations of algebraical elegance, of arithmeticalsimplicity, of labour-saving, and of internal consistencybetween different occasions of using a particular systemof short-hand. If p and q are widely discrepant, anyform of short-hand may be seriously misleading ; butif p and q are nearly equal, it may be a nuisance to usethe expression “ between p and q ”, and much moreconvenient, without being seriously misleading, toname some intermediate figure, even if the choiceof this figure is quite arbitrary. Provided, therefore,it is understood that such formulae as Vpq are nomore than a convenient self-consistent short-handfor “ between p and q ”, I see no objection to them.

In practice, therefore, Professor Fisher’s formulamay often do no harm. The objection to the formulais that it leads just as easily to a comparison when nosuch comparison is legitimate, and that it does notbring home to the computer, as the previous methodsinevitably do, the nature and degree of the error whichis involved. Professor Fisher’s formula is condemnedby the fact that it appears on the face of it to permitwith equal facility a numerical comparison betweenany two price-levels whatever—regardless of whether

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