192 Professor Whewell on the Mathematical Exposition 



gation, we may most easily discover what are difiicnlties of cal- 

 culation merely, and what, of principle. And in instances where 

 the calculations really are complex and confused, every mathe- 

 matician is aware how instantly the consideration of them in 

 the general case, points out the course or limits of the simpli- 

 fication which is attainable. 



2. It may perhaps appear to some unlikely, that any real 

 difficulty should aiise from such causes. But I think that none 

 who have read with attention books on the subject of Political 

 Economy, will be unaware that there is in them often a very 

 considerable complexity of numerical calculation, and no small 

 difficulty in determining how far this is necessary to the argu- 

 ment. I will venture to say also, that some books on these 

 subjects have not escaped fallacies arising mainly or entirely 

 from this complexity, and from the facility of .slipping in false 

 principles in the course of such reasonings. It may be allowable 

 to point out one such case. 



Mr. Ricardo (Polit. Econ. p. 301.) maintains that a tax on 

 wages must fall on labourers ; because if it did not so fall, wages 

 would rise, and in consequence of this rise of wages, the price 

 of manufactured goods would rise ; and in consequence of this 

 rise of goods, wages would again rise ; and so on, without any 

 assignable limits; which he considers to be an absurdity fatal 

 to the doctrine from which it is derived. Now if this argument 

 had been considered mathematically, the absurdity would have 

 disappeared altogether. Let wages rise to the whole amount of 



the tax ; say -- ; and let this rise in wages produce a rise of — 

 in the price of manufactured goods ,■ (not so much as — , because 

 only a part, say - , of the value of goods is wages ;) and let this 



