228 Dr. Mac Culloch on the Herring. 



Man. If we take the nearest round numbers, and allow only two 

 herrings a day for an adult, this would be an annual supply of a 

 proportion of animal food for little more than 119,000 individuals. 

 But this quantity would scarcely be a sufficient supply of food for 

 40,000 persons, allowing six fish a day. It is hardly necessary to 

 remark how trifling a supply this is for the home consumption, in 

 an article of which the production seems to be illimitable. It is 

 plain that much may yet be done towards increasing the food of 

 the people, when the habit shall have been excited, and the cir- 

 culation of this article better understood. The price is not the 

 obstacle, because the price of 800 fish was only twenty shillings. 

 Animal food could not well be cheaper than when nearly two her- 

 rings could be procured for a halfpenny, or when an adult could 

 be completely fed for three halfpence a day. That, with such a 

 price and such possibilities, the poor of this country should have 

 wanted animal food in 1819, when the market was glutted to the 

 ruin of the proprietors, is not one of the least curious facts in a 

 science which has for some time abounded, even to weariness, in 

 theoretical writers. J. MAC CULLOCH. 



ART. IV. A new Demonstration of Taylor's Theorem. By 

 Edward Wilmot, Esq., T.C.D. 



[To the Editor of the QUARTERLY JOURNAL.] 



Sir, September 16, 1823. 



THOSE who are in the habit of lecturing in the elementary parts 

 of mathematics, must frequently feel the difficulty of making the 

 common proofs of Taylor's Theorem for the development of func- 

 tions intelligible to the junior students. This difficulty I have my- 

 self frequently felt, and I know it is complained of by the pro- 

 fessors in the French colleges. I am, therefore, induced to send 

 you a demonstration which appears to me at once simple and valid. 

 It is independent of those assumptions in functional principles which 

 are involved in the proofs, and which, though they are perfectly 

 clear to the expert and practised analyst, are always embarrassing, 

 and often absolutely unintelligible, to the beginner. The proof which 



