MATHEMATICS, ETC. 209 
I Ty 
Stone-Meteorites. Tron- Meteorites. 
MER ecta a sca vcnecirnceseracees) 2 Ds08 LI fey NN PAIR CHINE al (GEN 
“AT. ECE) YAR a 164] NICK OL es resect feces Senet 7.49 
MOG). <2--ce-- ens sonemn-ee--» 0-01 | Cobalt. ccs cescceasen WOsee 
Chromium ..eccccccceeee-e 0.44 $27.42) Chromium ..........css0000% 0.08 OS 62 
Manganese ..........00.c008 0.29 MAND ANESE Wh iestleees ss seo 0.08 
PA .cNeveeei seas Nes \0.03 BTU EE a SN Sasa Sa 0,08 
ROGPYEM css clewse .ccces scot -mes . 0.034 Wea de Pee WS leae en seee sve. et HOLOD 
PEED TIC. SS RETA G6) Copperwene Goin Leone 0.03 
Magnesia ........e...000... 18.53 
PAU TIEGUIAD, (fs, ices sks seceisvscec 2600 | 64.48 Magnesium.........c..ce00000 0.16 : 
SULIC AM Cee osacesseaeet seu ees tee 41.69 i VA Dna TID NRLITA Aes sisiaasioes weet ee oat 0.54 
LOM ARE SAS Meota side's dienes! (0880 Povassiunal Pec ssscpscchey sn WOOT 
Boies acess: (heed Odd 
Carbon....... abistbsieted. 3 v« 0:0%7)) Carbonic s. (sie 18. sesh 0.13) 
Phosphorus '..\.2.)..2.c0.c20- 0.0: | Phosphiorusi4.iiJvcicscast..s') 0106! 
UPENPAPLULPY Ni, sidetelida (240486 92546 2.35 | 245 Sulphur ilo... Gye sce elwletes 0.15 7 0-41 
MP HloIMe Lessee eh we ea es 0.02 | Chilorine cee ee 0.08 | 
Oxygen and loss...,....... 5.56 HORE Face acl samba etetaantnn yeh OGL 
100.00 100.00 
E. J.C. 
MATHEMATICS, NATURAL PHILOSOPHY, AND ASTRONOMY. 
UN THE RESOLUTION OF ALGEBRAIC EQUAIIONS. 
While the remarkable researches of Professor G. P. Young are passiug through 
the pages of this Journal, demonstrating the impossibility of solving algebraically 
the general equation of the fifth or higher order, a pamphlet has been published 
by the well-known analyst, Mr. Jerrard, in which he professes to demonstrate the 
possibility in the case of the general quintic. In reviewing this pamphlet, the 
editor of the Philosophical Magazine frankly confesses that he has not had 
courage to face the complicated analysis by which Mr. Jerrard attains his con- 
clusion, and asserts his contentment with Abel’s demonstration (as modified by 
Wantzel) of the contrary proposition. The validity of this demonstration has, 
however, been several times attacked, and, as we are not aware that it has ever 
been published in English, we here translate from Serret’s Cours d’ Algebre Supé- 
szieure the demonstration in Wantzel’s words, with an abstract of the preliminary 
propositions, from the same author, on which it is founded. 
By acireular permutation of any letters it is implied that if the letters be 
arranged round a circle, each one is to be replaced by the one that precedes it 
in going round the circle. Thus, a, 8, ¢, d, e, is circularly permuted into d, c,d, e, a. 
By a transposition is meant an interchange of two letters only. It is readily 
‘shown that every permutation among a given set of letters can be represented by 
