Intelligence and^Mhteltaneous Articles. 561 



maining terms ; but we vaeif'^WS^ k as great as we please, 

 aftt2zcr{3/i:-iWl.SlWfay(i)ip))a8il?lyf Bondferothisi fact6C > lifegbt^^ 

 without restricting the generality of the original equations, A 

 we may; always assume wlteu n,^ I, ,0 = sum of exclusiv«lyr 

 negative real quantities ; the absurdity of which proposition 

 shows that w cannot exceed unity. ac oiii e.is. 



Case 2. — Page 288, line 9, is derived from division, and bv 



KVi^T^-- r ;:, t- *"■ -'^/ ■^'■•"'•'^ ^''^ :u ciiuic.iyibdug IjinOli 



.*. the bracketed factor can evidently never become a square. . 



Line 21. — Tl^e introduction of v^ — 1 follows fromj^l^^r, 

 ch. xii. 



Line 26 to 28, deduced' from! tfee bindmial_^tl^^pfftjIqij{orn 



Page 289, line 2, add respectively. , 



Page 289, line 8 (after magnitude),; from tfee-^syjismetry of 

 the binomial expansion, setting out from either extreme. 



P.S. This case is immediately deducible from the first, by 

 considering x% i/- and z^ as raised to the odd wth power. 



Are Fermat's papers preserved ii^ no cMteau or biblio- 



N «/ X . S. M. D. 



November 21, i845.^^y_ Vs' '^^ + I'^'^- V ~ ^'^.^^ ■ ■ 



.< «|Tu _LXXX.u J^ii^ifg^nf^'atad Miscellaneous ArticM.-Y--'. 



udi bne J; ^n REsmRATioN. by prof. MAC^}gfy„j jool sriT 



IN a paper read before the Royal Academy at Berlm^" the "author 

 first enumerated the different views on the nature of respiration 

 which had been proposed, and especially urged against >^U those 

 theories which suppose that a chemical combination takes place in 

 the lungs between the oxygen and the blood, that they do not ex- 

 plain how it is that blood, after having been darkened by agitation 

 with carbonic acid, is again rendered of a bright red by oxygen or 

 atmospheric air, and is capable of again assuming its former arterial 

 colour, if its artdrlal tint depends upon oxidation ; foT carbonic 

 acid cannot deoxidize the blood, and how can it be conceived that 

 blood which has once been oxidized can be again oxidized a second 

 or third time, and so on, without having been deoxidized ? This 

 objection appears to the author so conclusive, that he considers it 

 sufficient to refute any theory which supposes chemical coinbidation 

 of oxygen with the blood to occur. ■ "-- ^^ nad // 



He*^ then alluded to the theory which he had proposed pi 837> 

 according to which the inspired oxygen does not contbiiife (iheiiii- 

 cally with the blood, but is only absorbed, and thus arrives in the 

 capillary vessels, where it is applied to the oxidation of certain sub- 



