26 Addilion to the Aiiali/ticai Investigation 



sorted to The simultat)eous action of the legs also, directing 

 the impelling power in the line of the body, will explain why 

 the velocity with which aquatic birds move in so dense a fluid 

 as water is greater than that with which they move on its sur- 

 face, where the legs are usually employed alternately, and the 

 moving force cannot be so advantageously applied ; and that 

 the velocity is frequently accelerated still further by the in- 

 strumentality of the wings, has been already noticed. 



Thus, in controverting the erroneous opinions of Montagu 

 relative to the diving of water-fowl, I have endeavoured to 

 substitute for them a satisfactory theory of this I'emarkable 

 phaenomenon. 



Crunipsall Hall, April 18th, 1832. 



VIII. Addition to the AyiaJytical hivestigation of a Formtdafor 

 the Belative Importance of the Boroughs ; [contained in the 

 March Number of the Phil. Mag. and Annals). And Reply 

 to Dr. M'Intyre's Remarks. By the Author of that Investi- 

 gation*. 



T> Y referring to the above-mentioned investigation, it will be 



-'-' found that putting 



H for the whole houses in all the boroughs; 



T the whole sum paid in assessed taxes ; 



B the numerical value of their united relative importance ; 



Also, putting h, t, b for the same of any one of the boroughs ; 



— the relative importance of a borough may be expressed by 



the formula 



= B [m'-^ +^''-f } (1 



in which B may be any number whatever, and ?«' and ?«' are 

 numbers which serve to adapt the formula; to some hypothesis 

 concerning the relation which House-importance bears to 

 Tax-importance. 



Such as have taken an interest in the question will recollect 

 that two rules for estimating the importance of a borough 

 were proposed: one was that ofLieulenantDrummond, which 

 was adopted by the Government in framing the Reform Bill; 

 and another, that proposed by Mr. Pollock in the House of 

 Commons, in opposition to Mr. Drummond's : this was, in 

 fact, the same in its operation as one proposed by Dr. M'ln- 

 tyre, in December of last year, to Lord Melbourne. The 

 propounders of these rules all asserted that they were founded 

 on just mathematical principles : it might therefore be a ques- 



* Coniniunicateii by tiie Aiitlior. 



